Design Loads and Load Combinations

C H A P T E R

5 Design Loads and Load Combinations 5.1 DESIGN LOADS IN VIEW OF EXISTING CODES 5.1.1 Existing Load Codes and Their Relevancy In order to design a hydraulic structure that will satisfactorily and safely perform at a given location, two basic questions must first be answered: (a) What are the loads and other actions that the structure will be exposed to during its service life? (b) What are the performance parameters that can be considered satisfactory and safe? There was a time when answers to these questions depended on the wealth and goodwill of the project initiators. It still does in some regions of the world but these are, fortunately, exceptions. In most of today’s societies, national codes directly or indirectly answer these questions. Until about the end of 1970s, the existing codes defined the design loads in a so-called deterministic way, that is, by determining which value of a particular load should be taken into design, where exactly it should act, in which direction, and—if the load was variable—what its variation characteristics were. All this data was defined as single numerical values. In the simple static analysis, this resulted in the maximum applied stress of σ max. The material strength of the structure was determined in basically the same way, for steel commonly equaling the yield stress fy. The ratio of fy/σ max was supposed to be higher than the required safety factor (SF). If it was, the considered detail was strong enough. A common value of SF for components of hydraulic structures exposed to bending was 1.67. This value was based on acceptable performance without a measurable definition of that performance. This deterministic approach, also called the allowable stress design (ASD) or working stress design, was in the 1980s and 1990s gradually replaced by a semi-probabilistic approach, called the load and resistance factor design (LRFD) in the United States. It first happened in utility buildings, but later also in bridges and structures that traditionally follow the main lines of bridge codes, including hydraulic gates. As of today, there are generally no codes that comprehensively define loads of hydraulic gates, but there are codes that can help in defining such loads in view of the LRFD approach. These codes (Table 5.1) are often declared binding in construction contracts for hydraulic gates. The codes specified in Table 5.1 do not exhaust the list available, but they offer a good starting point for load definition. In addition, waterway authorities like USACE in the United States or Rijkswaterstaat in the Netherlands often modify the loads for hydraulic structures that are determined in these codes (see the USACE manual [1] as an example). Since a great majority of hydraulic gates are manufactured of steel, the codes for steel structures are included in Table 5.1. For gates of other materials, appropriate codes for structures of those materials should be consulted. As mentioned earlier, the design and engineering practice of hydraulic structures, certainly the large ones, traditionally follows the codes for bridges in several respects. That is why the principle codes for bridge loads are included in Table 5.1. Nevertheless, while both kinds of structures carry large and strongly varying service loads, the variation spectra of these loads for bridges are significantly different than that for hydraulic structures. The latter, especially in navigation locks, show more similarities with the loads of cranes (Fig. 5.1). Like in cranes, the loaded (closed) and unloaded (open) conditions of lock gates (Fig. 5.2) result in quite constant stress blocks. That is why the expertise and load codes for cranes can also be followed in gate design, particularly for the fatigue-related issues. The codes for bridges and cranes are, however, not the only ones that may be helpful when determining the design loads for hydraulic gates. In some specific issues, like the design of pressurized buoyancy tanks in lock gates, it may be advisable to follow the codes for pressure vessels, such as ASME Boiler and Pressure Vessel Code in the United States.

Lock Gates and Other Closures in Hydraulic Projects https://doi.org/10.1016/B978-0-12-809264-4.00005-7

325

© 2019 Elsevier Inc. All rights reserved.

326 TABLE 5.1

5. DESIGN LOADS AND LOAD COMBINATIONS

Basic Codes That Can Help Define Design Loads of Hydraulic Gates Europe (EU)

America (US)

Subject

Code no.

Title

Code no.

Title

Structural design basis

EN 1990

Eurocode EN 1990 (2002)/A1 Basis of structural design

AISC SCM (2011)

Steel Construction Manual, 14th Edition, Part 2: General Design Considerations

Loads and other actions

EN 1991

Eurocode 1 (2006): Actions on Structures, Parts 1–7: General actions—Accidental actions

SEI/ASCE 7-05

ASCE/SEI 7-05 Minimum Design Loads for Buildings and Other Structures

Steel structures, design general

EN 1993-1-1

Eurocode 3 (2005): Design of Steel Structures, Part 1-1: Gen. rules and rules for buildings

AISC 360-10, parts A-H

Specification for Structural Steel Buildings: A. General provisions—H. Design for combined forces and torsion

Loads on bridges, general

EN 1991-2

Eurocode 1 (2003): Actions on structures, Part 2: Traffic loads on bridges

AASHTO (2012)

AASHTO LRFD Bridge Design Specifications, LRFDUS-6

Loads on cranes, general

EN 13001-1 and -2

European Standard—Cranes, Part 1: General principles Part 2: Load actions

AISE T.R.13 (2003), ASME B30

AISE guide for the design and construction of mill buildings, ASME Crane Standards

FIG. 5.1 Typical stress spectra in details of three structures: bridge, lock gate, and crane.

FIG. 5.2 Lock gate closed (a) and open (b), Hilpolstein Lock on the Main-Danube Canal, Germany.

5.1 DESIGN LOADS IN VIEW OF EXISTING CODES

327

The design loads for mechanical equipment, including the gate drive systems, should be determined in accordance with appropriate mechanical norms. Still other norms or guidance documents are helpful when determining transport and installation loading cases, loads on walkways, loads from ice, ship collision, etc. These and other loads are discussed in the following sections.

5.1.2 Deterministic and Probabilistic Approach The deterministic load definition, or the ASD approach, had many advantages that will be summed up later. It had, however, one major disadvantage: the question how safe the structure actually was, could not be answered in measurable terms. It was not quite clear how “good” the SF of, for example, 1.67 really was and what kind of safety it stood for. Simple answers, like that it gave a safety margin of 67% above “nominal loads,” were no longer good enough because structures did not only carry nominal loads. And even if they did, then why just 67% and not, for example, 10%? The ASD methodology had no clear answers to such questions. The reason is that loads are by nature stochastic or probabilistic. These two terms have a similar but not quite the same meaning. They are often confused with each other, which is the reason to clarify them in this book. A simple distinction is that stochastic means perfectly random, while probabilistic means occurring with a certain probability that does not need to be perfectly random. This can be visualized by two dice as shown in Fig. 5.3. The “stochastic die” (a) is a cube and if its center of gravity (CoG) has not been manipulated, it will give equal probabilities of throwing the numbers of 1 through 6. The “probabilistic die” (b) is a cut rectangular pyramid and it gives unequal probabilities of throwing these numbers. The probability of getting 6 in a single throw is 1/6 for die (a), but less than that for die (b). After all, die (b) needs to land on its smallest face to produce this result. In probability theory, die (a) can be seen as a simple generator of a so-called normal distribution; and die (b) as a simple generator of a so-called extreme value distribution. Both types of distribution are interesting in view of probabilistic load definition, but the second one is especially useful to investigate the probability of occurrence of extreme loads. The readers interested in this subject can find more details and formulas in diverse publications on the probability theory. A very good and relatively simple guidance has also been provided in the report of the PIANC InCom Working Group 140 [2] that has recently finished investigating this matter for inland hydraulic structures. It is not only the loads that are by nature stochastic or probabilistic but the material strength, or in a broader sense the resistance of the structure, can also be considered in that way. As a result, both load effects Q (here called loads for simple) and resistance R can be modeled as independent probabilistic variables with mean values, respectively, Q and R and standard deviations, respectively, σ Q and σ R. The frequency distributions of loads Q and resistance R are then as drawn in Fig. 5.4a [2,3]. The graphs in this figure also illustrate the principal difference between ASD methodology and LRFD methodology [4]. The ASD method uses the so-called nominal values of loads Qn and resistance Rn, which lie close to the mean values Q and R with small offsets to the safe side. No account is taken of the probabilistic character, particularly the frequency distributions of Q and R. The ratio of nominal resistance to the superposed nominal load effects represents the SF: Rn SF ¼ X or : Qn,i i

(a) FIG. 5.3

“Stochastic die” (a) and “probabilistic die” (b).

(b)

(5.1)

328

Loads (Q)

Frequency

Frequency distributions of loads (Q) and resistance (R).

Resistance (R)

Rn – Qn fRn – g Qn

Q≥R

(a)

Q

Qn

gQn fRn

SF ¼

bs R–Q s R–Q s R–Q

R–Q ≤ 0 (exceedance)

FIG. 5.4

Frequency f (Q, R)

5. DESIGN LOADS AND LOAD COMBINATIONS

Rn R

Q, R

(R–Q) R–Q

(b)

R Xn α Qn, i

(5.1a)

i

where α is the “allowable stress modifier.” Eq. (5.1a) is introduced by USACE to increase the resilience of hydraulic structures above the average level. α ¼ 1.33 for emergency closures exposed to severe dynamic loads, 1.20 for gates that carry well-defined hydrostatic loads, and 0.90 for maintenance and temporary closures that do not carry emergency loads [1]. The LRFD method takes account of that frequency distribution. Instead of the SF, it defines the “reliability index” β, also called the “safety index”: RQ β ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ 2R + σ 2Q

(5.2)

This definition of β results from applying the so-called first-order second-moment method, the details of which can be found in the literature. Observe that the standard deviations σ Q and σ R make part of this formula, which indeed gives it a probabilistic character. The expression R  Q is a performance indicator, and the function R  Q is a performance function, of which the frequency distribution has been drawn in Fig. 5.4b. The structure is supposed to survive by positive values of this function and fail by its negative values, which leads to the definition of the probability of failure pf pf ¼ probðR  Q  0Þ

(5.3)

The considered structural detail can be accepted if pf is below an agreed threshold. In the United States, that threshold is commonly assumed as an annual probability of failure of 102 or 103, corresponding to, respectively, β ¼ 2.33 and 3.09. In Europe, the Eurocode EN 1990 (2002) recommends the maximal probabilities of failure in the range 105 to 107, corresponding to β ¼ 4.2 to 5.2, depending on the so-called reliability class, RC, of the structure [5]. These values apply to the ultimate limit state (ULS). For the serviceability limit state (SLS), the target reliability indices β are lower and lie in the same range as in the American LRFD practice. The relation between probabilities of failure and reliability indices can be different when distributions other than normal distributions are assumed. An example is the so-called lognormal distribution, frequently used in the United States. It usually gives slightly higher β values for the probabilities of failure, higher than about 102. Below that level (for pf ¼ 103 or less) the differences are insignificant. Both relations are presented in Table 5.2 in the common range of probabilities of failure. TABLE 5.2

Relation Between pf and β for Normal and Lognormal Distributions

Normal distributiona b

Lognormal distribution a b

pf

1021

1022

1023

1024

1025

1026

1027

β

1.28

2.32

3.09

3.72

4.27

4.75

5.20

β

1.96

2.50

3.03

3.57

4.10

4.64

5.17

According to Eurocode EN 1990 (2002) [5]. According to LRFD guidance in report [2].

5.1 DESIGN LOADS IN VIEW OF EXISTING CODES

329

The statistical meaning of β is graphically shown in Fig. 5.4b. The larger its value, the smaller the chance of (R  Q)  0, and hence the safer the structure. In the LRFD method, the safety condition is expressed as X ϕRn  γQn ¼ γ i Qn, i (5.4) i

where: ϕ¼the resistance reduction factor (usually 1); γ i ¼ load factors (usually 1). To express this condition in probabilistic terms, the nominal values of Rn and Qn should be replaced by mean values R and Q. This requires a so-called “bias correction,” even though the “bias” has deliberately been applied here. A simple way of bringing this correction is by introducing the factors λR and λQ that stand for the ratios λR ¼ R

 Rn

and λQ ¼ Q

 Qn

(5.5)

Eqs. (5.4) and (5.2) lead then to the following formula that brings the resistance factor ϕ in relation with load factors γ i, but then in probabilistic terms X λQ γ i Qn, i λQ Q n i qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ϕγ ¼ (5.6) λR Rn Q + β σ 2 + σ 2 R

Q

Eq. (5.6) is very important because it lays a relation between the LRFD method and its probabilistic basis. In fact, it enables a so-called calibration of this method. Such a calibration has been performed in the United States for bridges by a team led by Polish-American professor Andrzej (Andrew) Nowak [6]. The USACE also instrumented a number of miter gates in order to calibrate the LRFD load factors based on the work by Bruce Ellingwood [7]. Although no similar calibrations have been performed for other types of gates, yet the data gained from bridges and miter gates enabled acceptable estimations for some of these gates. When applying the LRFD method in practice, engineers only use the load factors and nominal load and resistance values; not the probabilistic data like mean values and standard deviations. These data are usually not available for a project. That is why the method is called semi-probabilistic and not (fully) probabilistic. Nevertheless, its probabilistic grounds are clear. It also sets the door open for defining loads in some special projects, for example, those of unique significance to the safety of large areas, in a fully probabilistic way. The latter has, in fact, already been practiced. The most convincing example is probably the design of the Eastern Scheldt Storm Surge Barrier in the Netherlands. If the numerous components of this project were designed separately, according to their different disciplinary codes and practices, the resulting inconsistencies would have made it impossible to guarantee the desired overall safety level, in this case against the 2.5  104 storm surge (once in 4000 years). However, it proved possible to build statistical databases of loads and resistances that allowed establishing a joint probability of exceedance function of storm surge loads and structure resistance [8]. Building these databases was an immense work that included the collection of historical data, scale model investigations, numerical simulations, material tests, diverse measurements, and other procedures. This work paid off. The approach that followed resulted in a high consistency between various designs, like concrete piers, steel gates, their drives, foundations, and the sill (Fig. 5.5). This approach was based on the advanced first-order second-moment method that has already been referred to by formula (5.2). After that, a detailed fault-tree analysis enabled assessing the system safety and, in consequence, ensured the compliance with the required 2.5  104 storm surge safety level. A good, practice-oriented guidance for a fully probabilistic approach to both loads and resistance of a structure is given by Baecher and Christian [9]. The focus of this book lies on soil and foundation technology but the presented methodology can to a large extent be used for the design of hydraulic gates. The discussion is rooted in engineering practice and includes references to the current norms.

330

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.5 Eastern Scheldt Storm Surge Barrier, Netherlands, with components of a pier and one of the 63 gated openings. Drawing by Rudolf Das, Rijkswaterstaat.

5.2 HYDRAULIC LOADS 5.2.1 Typical Hydraulic Load Components Not surprisingly, hydraulic loads are the main loads of hydraulic gates. Carrying these loads is the reason why hydraulic gates are being constructed; all other loads either result from the functions that facilitate this task (like gate drive loads) or are difficult to remove (like the gate self-weight). Hydraulic loads may have different characters depending on the considered operation conditions of the gate. In some projects, the character of these loads may also depend on the gate type and its structural system. This results from the interaction between loads and the structure. For example, an overtopping gate will be exposed to hydraulic loads of a different character (static and dynamic) than a gate that does not overtop (only static). Also the installation or maintenance conditions can generate hydraulic loads of a specific character. An example of this is the pressurizing and floating of the gates with air chambers to or from their maintenance locations. The hydraulic loads that usually need to be considered in the projects of movable hydraulic closures are summarized in Fig. 5.6. Below is a short introduction of these loads; the detailed discussion is provided in the following sections. These are not all possible hydraulic loads on gates. The loads that in most cases can be neglected, like waves from passing vessels or flows as result of saltwater and freshwater exchange are only briefly mentioned. Some loads, like

5.2 HYDRAULIC LOADS

331

FIG. 5.6 Hydraulic loads usually acting on gates.

tsunamis or waves, can have both hydrostatic and hydrodynamic character; and it is only for convenience they have been classified into one of these groups in Fig. 5.6. The criterion of this classification is of an engineering rather than scientific nature and can be summed up as follows: • Hydrostatic loads are in this book the fluid-induced loads that either are static or can be modeled using quasi-static pressure diagrams without giving further consideration to their dynamic effects. • Hydrodynamic loads are fluid-induced loads that either cannot be modeled by such diagrams or require additional analysis of typically dynamic phenomena, such as inertial forces or fatigue. A differential water head is the difference between water levels on the upstream and downstream side of the gate. This difference can be of a more permanent nature (e.g., on river weir or dry dock gates) or of temporary nature (e.g., on lock gates and flood or tide gates). The terms permanent and temporary are relative here, since the dry dock or river weir gates also need to be open or removed sometimes. The differential water head can have a regular and an accidental component. The first is, for example, the target water level difference on river weirs, navigation lock gates, or gates of hydroelectric plants. The latter results from extraordinary conditions of various kinds, like flood, drought, or a long lasting wind. This gives the differential water head a probabilistic character. That character is particularly strong in structures like flood barriers; and less so, for example, in canalized river locks and dams. This difference could already be observed in Figs. 2.4 and 2.9 that illustrated the operation profiles of lock gates and barrier gates. The hydraulic loads from these figures are put together and presented once again in Fig. 5.7 for a better comparison. Note that the loads of a flood barrier (in this case an overtopping storm surge barrier) in scheme (a) show much more variation than the loads of a navigation lock gate in scheme (b). Fluctuations of extreme high and low water levels at the lock gate (b) in this example are within the margin of 1.0 m. Similar fluctuations at the storm surge barrier gate (a) are within the margin of 6.7 m if referred to sea level during closing and 4.7 m if referred to sea level during opening. This can even result in a reverse differential water head, which the designers have indeed taken into account. Reverse flows, normally, do not happen in navigation locks with the exception of tidal and some complex lowland waterway systems. An example is the Chicago Harbor Lock, shown in Fig. 3.126, Section 3.9. Fig. 5.7 indicates that there are a number of hydraulic loads other than differential water head in both examples. The pictured loads also include wind-induced waves, current loads, and impact loads by water mass. Not represented here are the loads like tsunamis and local pressure variations due to flow separation or turbulence. All these loads are discussed in the following subsections. The two basic parameters when determining hydraulic loads are: • specific density ρw of water; and • acceleration due to gravity g. This looks trivial, but it is not. The specific density of water is a reference for specific densities of all other materials, but this applies only to water of strictly conditioned parameters. The water in hydraulic projects does not comply with these conditions. Salinity especially can result in substantial (up to about 3%) increase of ρw. Other factors like temperature or dissolved gasses may also require attention. The same may apply to the acceleration due to gravity g that,

332

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.7 Comparison of principle hydraulic loads in design of a flood barrier gate and lock gate: (a) gates of Hartel Canal Storm Surge Barrier near Rotterdam, the Netherlands [10] and (b) middle gate of Lock III in Wilhelmina Canal near Tilburg, the Netherlands [11].

as known, depends on the altitude and location on Earth. In most cases, however, g ¼ 9.806 m/s2 is a correct engineering assumption.

5.2.2 Modeling Hydrostatic Loads 5.2.2.1 Differential Water Head Observe that the differential water head load is in the cross-sections in Fig. 5.7 modeled as a trapezium, with the bottom side at right angles to the parallel vertical sides. In the case of an entirely dry downstream side of the gate, the trapezium becomes a triangle. The top point of the trapezium lies at the upper pool level; and the second parallel side runs down from the lower pool level. The line between these two points represents hydrostatic pressure pw, growing downwards on the gate skin plate. If z is the water depth then this pressure is simply p w ¼ ρw  g  z

(5.7)

In overtopping gates, a generally practiced, safe assumption is to assume that the top point of the trapezium is at the so-called “total energy line” of the upper pool, that is, ignoring the head loss above the gate. In simple terms, the total energy line here is the upper pool water level at some distance from the gate, provided that there are no changes in canal section at that distance. This method is slightly conservative as it does not discount for some energy losses over that distance, for example, due to friction or water viscosity. Conservative assumptions should, however, be welcome in hydraulic engineering.

5.2 HYDRAULIC LOADS

333

As shown in Fig. 5.6, the differential water head can have two components: an existing water level difference (e.g., the target lock lift) and its rise due to wind action. A drop due to wind action can, of course, happen too if the wind blows in reverse direction, but this case is now less interesting. These changes in the water level are only significant in water basins of large areas, like seas, large bays, or lakes and rarely in long canals stretching in the wind direction. The total difference between water levels at the windward and leeward bank of such a basin is also called the total wind setup S. It can be obtained from formula (5.8), with wind velocity Uw and geometrical data as indicated in Fig. 5.8. S¼C

Uw2  Lb  cos φ gd

(5.8)

The constant C in formula (5.8) depends on the factors like form, depth profile, and bottom condition of the basin in question [70]. In a general case, it needs to be empirically determined, which requires calibrating the formula by wind setup measurements at the location. This has been done for storm surge defenses along the North Sea coast of the Netherlands, resulting in a uniform C ¼ 3.4  106. Vrijling [12] recommends the range of C ¼ (3.5  4.0)  106. These values can also be used in estimations for other coastal locations if no calibration of formula (5.8) has been done. Note that the wind setup increases with the basin size (here Lb), but decreases with its depth d. At a particular gate location, the rise in the water level due to wind setup also depends on the shape of the coastline. This has been demonstrated in Fig. 5.8 by comparing the wind set-up effect in a rectangular or unrestrained basin in sketch (a) with that in a triangular basin in sketch (b). In the latter case, the water level rise by the gate will be much larger, if only to satisfy the constant volume condition. This and the rise due to depth reduction near the coast have painfully been experienced during the landfall of Hurricane Katrina on August 29, 2005 in New Orleans. Fig. 5.9 shows the global sequence of Katrina landfall and the locations of levee breaches. The first and most damaging was the storm surge entry from Lake Borgne in the east of the city. The levee breeches there were by far the largest. Observe the funnel-shaped defense line of the old levee system in that area. It certainly has contributed to the rise in water level by wind setup. This risk has now substantially been reduced by the construction of the Inner Harbor Navigation Canal (IHNC) Barrier, also called the Lake Borgne Barrier. Water level rise due to wind setup can occur in addition to the regular water level difference (like in lock gates or dry dock gates), or it can represent the main differential water head in the design (like in flood and storm surge gates). If the water depth d significantly varies over the distance Lb then it is advisable to divide this distance into sections of comparable water depth and to compute incremental wind setups in these sections from formula (5.8). The sum of these setups then gives the total S. If the considered distance Lb is large enough (like in storm surges), then some variation can also occur in the wind velocity Uw and in its approach angle φ over that distance. The way to deal with it is basically the same. One can also introduce integrals in the formula to cover such variations. If x is the distance as shown in Fig. 5.8, and d(x), Uw(x) and φ(x) are, respectively, the water depth, wind velocity, and wind angle at that distance, then the total wind setup can be expressed as Z x¼Lb 2 C Uw ðxÞ S¼   x  cos ðφðxÞÞ  dx (5.9) g x¼0 dðxÞ

FIG. 5.8 Wind setup on gates in two water basins: (a) rectangular and (b) triangular.

334

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.9 Hurricane Katrina landfall in New Orleans and the floodwater depths. Image by C&C Technologies.

For engineering applications, however, this formula has less use than Eq. (5.8) because d(x), Uw(x), and φ(x) can hardly be analytically determined. The incremental computing described above offers a more efficient approach. Measurements in the Netherlands proved that formula (5.8) gives correct results particularly for wind setups as result of storms at sea [12]. The depths d and distances Lb are then large. In the case of shallow waters and relatively small distances (in the range of 10–50 km), the measured wind setups showed some deviation. An example is the investigation performed for a large lake, the IJsselmeer, which proposed a modified formula for that area [13]. 5.2.2.2 Seiches and Translation Waves Hydrostatic loads other than the differential water head and its rise due to wind setup are long-period waves, including seiches, translation waves, and tsunamis. Long-period waves are also waves of large length, which entitles the gate designers to consider them as hydrostatic rise to the differential water head. This is in contrary to wind loads that are hydrodynamic by nature and their quasi-static models (see wind load graphs in Fig. 5.7b) are of different character than those of differential water heads. A seiche on a hydraulic gate is an oscillating variation of the water level, caused by an action at some distance along the canal or in open water. A common source of seiches is the oscillation of local but heavy rains that exercise pressure on the water surface. Other sources of seiches can be local pressure drops caused, for example, by tornados, distant seismic activities, human-caused large energy releases like explosions, implosions, and the like. An important feature of seiches is that they essentially do not cause flow, that is, the resulting water displacements are only vertical. Due to their large length and small slope, seiches are difficult to see as waves with the naked eye but pool level rise is visible. Photo (a) in Fig. 5.10 gives an impression of a small translation wave approaching a lock gate on one of the Dutch canals. In this case, the wave appeared on the side of the lower pool. Photo (b) in the same figure shows the effects of a

5.2 HYDRAULIC LOADS

335

FIG. 5.10 Effects of translation waves and seiches on navigation lock gates: (a) long wave approaching a lock gate in the Netherlands and (b) overtopping seiche on the Soo Locks, Great Lakes, United States. Photos (a) Rijkswaterstaat [14], (b) USACE.

seiche on a large lock gate in the Great Lakes area between the United States and Canada. This gate is not supposed to overtop under normal conditions. Most lock gates in large water basins in the world, like those in the Great Lakes area, are regularly exposed to seiches. Both the probability of, for example, heavy rain oscillations and their effects are relatively high. The gates of the Soo Locks between Lake Superior and the St. Mary’s River that are pictured in photo (b) suffer particularly from this phenomenon. Water that goes over the lock wall floods the culvert machinery and electrical components in galleries, which frequently causes malfunctions or failures. The predominately vertical motion of water is what distinguishes the seiches from translation waves. A translation wave is a wave in which water also moves in horizontal direction, which is in the direction of wave propagation. According to this definition, wind-induced waves are also translation waves when coming ashore (see sketch in Fig. 5.20). This case is, however, less interesting for a hydraulic gate designer. The translation waves that can deliver significant loads on hydraulic gates are long-period waves. Such waves are generated by different causes. On canalized waterways, a common cause is emptying or filling of lock chambers that engage large water volumes. If these operations proceed fast and if the canal flow profile is relatively small, it will produce a considerable translation wave moving toward the next lock. Translation waves may also have natural causes, like riverbank collapse, dam breach, temporary ice jam, or other obstacle in a river. Various translation waves occur, for example, on the Dutch canals and the St. Anthony Falls Locks in the United States. Although translation waves cause horizontal water displacements, these displacements cease in the vicinity of a closed gate. The translation wave then changes to a so-called “standing wave,” although the energy of the horizontal water displacements may cause a local wave height increase. Therefore, translation waves, like seiches, are considered to generate only hydrostatic pressure on gates. Their pressure diagrams are of the same character as those of differential water heads (see Fig. 5.11), which means that the wave heights can simply be summed up by the upper pool level (for locks) or wind setup level (for surge barriers). Note that only one of the two long-period waves, that is, either the translation wave or the seiche, is commonly taken into account when dimensioning a hydraulic gate. Both are very infrequent phenomena; and the probability of their coincidence can normally be ignored. Obviously, the wave type to be taken into account is the one that gives a less favorable effect in view of the considered limit state. This was the translation wave in the example lock gates in Fig. 5.11. Note also that in the case of seiches no consideration needs to be given to wave reflection. Due to the large length of these waves and the absence of horizontal water displacements, reflection against the gate does not occur or is negligible. This can be different for translation waves, which may show some local height increase as mentioned earlier. Such effects are comparable with reflection. They may, however, be ignored in very long and “flat” translation waves caused by filling and emptying of neighboring locks [12]. In the case of wind-induced waves, the reflection must be taken into account, which is indicated in Fig. 5.11. Loads by wind-induced waves are discussed in the following subsection. Hydrostatic design loads on gates in structures other than navigation locks and storm surge barriers can be determined in the same way as presented above. Nevertheless, their significance in the design of those gates can be different. This applies particularly to the gates carrying relatively high heads, and to deep located valves of, for example, culvert systems. In the design of those closures, wave loads of all kinds play a secondary role.

336

5. DESIGN LOADS AND LOAD COMBINATIONS

0.3

Translation wave

Upper crown

+32.90

Regular head

Wind wave

Translation wave 0.3

Wind wave

0.5

Regular head 0.5

Lower crown

Including reflection

Including reflection

+32.90

+24.75 +20.80

0.2

0.3

+20.80 +24.35

+16.80

0.2

0.3

+16.80

FIG. 5.11 Typical hydraulic design loads for river lock gates, from preliminary design of the new Maasbracht Lock gates in the Meuse, the Netherlands [15].

In some hydraulic gates, wave loads can even be considered insignificant. An example is the design of very low located intakes for penstocks or diversion conduits in the dams of hydroelectric plants. Fig. 5.12 presents an extreme situation of this kind. It refers to the study and preliminary design of the Shasta Dam enlargement in the Central Valley, California. The study was carried out by the Technical Service Center of the US Bureau of Reclamation [16] and resulted in a proposal to raise the height of the dam from the current 324.6 m (1065 ft) up to 390.1 m (1280 ft). The assumed intake gates were round vertical lift gates, 10200 in diameter, of the so-called ring-follower type, as shown

FIG. 5.12 Hydraulic loads on crest and intake gates in the Shasta Dam Enlargement study, CA, United States; based on data by US Bureau of Reclamation [16].

5.2 HYDRAULIC LOADS

337

in the inserted photo. One can see that these gates do not “feel” anything from wave loads on the Shasta Lake, although this lake is the largest freshwater reservoir in California. Yet, they do carry immense hydrostatic pressure. 5.2.2.3 Tsunamis The next type of hydrostatic loads shown in Fig. 5.6 is tsunamis. Tsunamis are waves generated at sea by extraordinary events, the most typical of which are earthquakes. Other events causing tsunamis can be underwater volcanic eruptions, explosions, sliding of large ice or land masses into the sea, and meteorite impacts. In this section, we will confine the considerations to large tsunamis caused by earthquakes, but the nature of other tsunamis is usually similar. Small tsunamis can be considered in the same way as translation waves or seiches. Hydraulic gates are, generally, not the best means to fight large tsunamis. Better means are to construct breakwaters at a distance to the defended coast, and floodwalls along that coast. Gates can, however, make part of these systems, for example to provide a passage for ships. In that case, their design follows the requirements of, respectively, breakwaters and floodwalls. In particular: • When part of a breakwater, the gate must withstand the quasi-static load generated by the tsunami wave but it should allow that wave to overtop. • When part of a floodwall, the gate must prevent flooding of the defended land, which means that it should not overtop or it should overtop at small rate only. The first mentioned application is not common, because breakwaters usually have openings for ship passages. Nevertheless, it can be favored under some conditions, for example, in long breakwaters at the entrances to the bays. In this case, the gates should preferably be designed to limit the incoming flow but open under the retreating flow, which seems technically feasible. Tsunamis may have different forms and different behavior depending on the bottom and shore profile, coastline geometry, and the presence of breakwaters. A great deal of knowledge in this field was collected from the tsunami that followed the Great East Japan Earthquake on March 11, 2011, known also as the T
ohoku Earthquake named after the affected region. The earthquake had a magnitude of 9.0 Mw, with the epicenter only 70 km from the Pacific coast, causing enormous devastation to coastal cities, infrastructure, and the industry. The profiles of the first tsunami crest measured by GPS buoys in that region are shown in Fig. 5.13 [17]. The data on the left-hand side of the dotted line were transmitted in real time to the Japan Meteorological Agency just before the line congestion and power failure. The data on the right-hand side were recovered from the base stations after the earthquake. One can see that the highest measured wave crests exceeded 6.0 m. This is in the same range as the 104 (once in 10,000 years) storm surge, which is the norm for the Dutch coast defense (see e.g., Fig. 5.7a). Since the water levels were

FIG. 5.13 Profiles of the first tsunami crest following the T
ohoku Earthquake in Japan in 2011, recorded on GPS buoys off the coast at six locations [17].

338

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.14 Water level variations in the Ofunato Bay and Ryori Bay during the tsunami of 2011 [17].

measured offshore at some distance from the coast, the levels of tsunami waters that approached and crossed the coastlines were much higher due to the run-up effect. This could especially be seen in bays. An example is the Ofunato Bay and Ryori Bay in the North Miyagi Prefecture, the coastlines of which are shown in Fig 5.14a. The existing breakwater in the first of these bays was struck and the tsunami in Ofunato Port reached the height of about 10.0 m [17]. After the event, numerical simulations were performed for the situation with and without the breakwater. Fig. 5.14b shows the resulting water level variation. Note that if there were no breakwater, the tsunami would have reached a height of nearly 15.0 m. This shows that before breaking and in broken condition the structure could still decrease the damage to the shore and in the harbor. The Ryori Bay had no breakwater. It was also more open to a direct hit of tsunami than the Ofunato Bay. This resulted in a totally different time profile for that hit, with more and higher peaks. Note that the numerical simulations, largely calibrated by the field data, showed for the second wave the water rise of nearly 25 m within only 2 s. Even if this graph contains some numerical dispersion, the fact is that a tsunami crest can reach very high horizontal velocity. This, in turn, results in a very fast vertical rise of water. The combination of both effects is devastating. The latter happens particularly when the earthquake occurs at large water depth. If d is this water depth and g is the gravity acceleration, then the velocity of a tsunami crest traveling horizontally vd follows from the formula: pffiffiffiffiffiffiffiffi (5.10) vd ¼ g  d As known, the affected region of Japan lies in the neighborhood of a very deep oceanic trench called the Japan Trench, which resulted in high values of vd. The tsunami wave crests can in extreme cases reach the velocities of 1000 km/h. When the water depth d decreases and the tsunami amplitude At is not a small fraction, then a growing part of the vertical motion of energy in a wave changes to a horizontal motion called the Stokes flow. The velocity of the Stokes flow in the neighborhood of the coast vc can be approximated by the formula: vc 

A2t  vd 2d2

(5.11)

Observe that when vd and At are high, like in the case of the Great East Japan Earthquake tsunami, then the velocity of the horizontal water of motion in a wave that approaches the coast is also very high. This and the angular shape of the Ryori Bay (“funnel effect”) explain why water at the bay rose high and fast as indicated in Fig. 5.14b. For the scope of this book, the velocity of tsunami crest travel vd (5.10) is less interesting because hydraulic gates are not constructed at open, deep sea. More interesting is the velocity vc (5.11) of the water in horizontal motion in the Stokes flow. The tsunami waves coming ashore in Japan had the velocity of 10–30 km/h. The Indian Ocean tsunami of December 26, 2004 moved at open sea with the velocity of up to 900 km/h, but the flows coming ashore had a velocity of 15–20 km/h. In both cases the maximal recorded rise in water level on land was about 30 m. Yet, the examples in Fig. 5.14 indicate that a lot depends on the form of the considered coastline, bottom profile, presence of breakwaters, and the shore profile. The PIANC reports [17,18] distinguish in this respect the types of tsunami waves coming ashore as shown in Fig. 5.15. The design load diagrams that are used for gate design under tsunami waves are commonly quasi-static. In fact, they resemble the diagrams that have already been presented for differential water head loads earlier. It deserves

5.2 HYDRAULIC LOADS

339

FIG. 5.15 Types of tsunami run-up and corresponding shore profiles. (a) Wave breaking type (sandy beach), (b) rapid run-up type, (c) water elevation type, and (d) overflow type (port and/or river).

recommendation to follow the Japanese expertise in this field that has also been recommended in the PIANC report [18] after Tanimoto et al. [19] and Asakura et al. [20]. It distinguishes between the tsunami pressure on deepwater gates (like dock caissons) and floodwall gates on land. Appropriate pressure diagrams are shown in Fig. 5.16a and b. Diagrams (a1) and (b1) are derived from, respectively, (a) and (b) and proposed by the authors of this book for overtopping situations. The following design recommendations are deterministic but based on thorough research. For very long period tsunamis with amplitude of a1, the design elevations of water at the gate locations η* should be assumed as follows: • For situations (a) and (a1) from Fig. 5.16 [19]: η* ¼ 2.2a1 • For situations (b) and (b1) from Fig. 5.16 [20]: η* ¼ 3.0a1 In accordance with Eq. (5.7), this results in the following formulas for the pressures p1 and pb from the diagrams in Fig. 5.16: p1 ¼ 2:2ρw  g  a1

(5.12)

pb ¼ 3:0ρw  g  a1

(5.13)

p

z

h*

a1

p

z

h*

a1

Another approach is that of the ASCE/SEI [21]. It allows for modeling dynamic tsunami flows as static loads if water velocities do not exceed 3.05 m/s (11 km/h), which is often the case when tsunami enters relatively shallow shores or when it comes on land. The design flood elevation (amplitude a1 in the notation as above) should then be increased by a surcharge depth dh:

pb

(b) p1

pb

(b1) p1

(a1)

z

p

h*

a1 z

p

h*

a1

(a)

FIG. 5.16 Tsunami pressure diagrams by PIANC [18], with extensions for overtopping situations: (a) and (a1) for gated closures in deep water and (b) and (b1) for gated closures in floodwalls on land.

340

5. DESIGN LOADS AND LOAD COMBINATIONS

dh ¼

CD  v2c 2g

(5.14)

where CD is the drag coefficient, which should, however, not be taken less than 1.25. The surcharge depth dh should be added to a1 to obtain the water pressure diagrams similar to those in Fig. 5.16. For more guidance on design load assumptions due to tsunami waves, readers are encouraged to consult the PIANC reports [17,18]. It is also recommended to collect and thoroughly study appropriate field data on tsunami characteristics at the concerned locations. 5.2.2.4 Buoyancy and Water Ballast Buoyancy, much like differential water head, is a result of hydrostatic pressure. The only difference is that the differential water head is usually associated with the horizontal water pressure on a submerged object, while buoyancy is the vertical resultant of that pressure. There is no difference between the two pressures in a physical sense, since pressure in motionless water is the same in all directions, according to the Pascal’s law. From the engineering point of view, buoyancy in hydraulic gates can be divided into two kinds: • unintentional buoyancy caused by physical laws; and • buoyancy intentionally applied by men. The buoyancy of the first kind is inevitable and must be taken into account in case it is significant. The buoyancy of the second kind is a means to obtain a desired gate behavior and it can be fine-tuned to this purpose by the gate designer. In many projects, the framing of a hydraulic gate is constructed of open steel profiles; the structure is fully deaerated and contains no intentional air chambers. The remaining buoyancy is then of the first kind and represents a minor load component in the design. In addition, it usually acts in a favorable direction, for example, decreasing the loads on bottom pintles or rail tracks of gates without causing stability concerns. In such cases, the designers tend to neglect the buoyancy in the global structural analysis. Additional reasons for this are that the water that causes buoyancy may drop to a lower level and the gate may eventually need to be set dry. Neglecting the buoyancy is then a correct, conservative approach. This approach is, however, less adequate in gates of other materials than steel, for example, timber or concrete, where the volumes involved are higher. Buoyancy load, like, for example self-weight, can be considered a “permanent action” in the sense of Eurocode [5], or “dead load” in the sense of ASCE/SEI [21]. In that case, both standards require that its design value B should be obtained by multiplying the characteristic value Bk by a load factor γ, when combined with live loads. The value of γ depends on whether the buoyancy effect is unfavorable or favorable. It should be chosen from Table 5.4. This completes the discussion if the buoyancy is of the first kind mentioned above (unintentionally applied). If it is of the second kind (intentionally applied), there are additional issues to be considered. The intentional buoyancy applications in hydraulic gates take place by means of fixed buoyancy tanks (also called air chambers) or a special open shape of the gate that allows air capture and outflow in order to raise and lower the gate. In both cases, the compartments containing air may stretch out over a limited part or main body of the gate crosssection. Examples of gates that incorporate fixed air tanks in their cross-sections are drum gates, roller gates, large rolling gates, and, occasionally, miter gates and vertically hinged sector gates. Examples of open-shape gates that capture air are horizontally hinged sector gates and bear-trap gates, also called roof gates. See Chapter 3 for the discussion on these gate types. In view of their operation, both buoyancy tanks and open buoyant spaces in gates can be (a) fixed and permanently submerged; (b) fixed but variably submerged; and (c) variable (allowing for filling and emptying). Fig. 5.17 shows these three arrangements for a cross-section of a hypothetical gate. Note that in cases (a) and (b) the vertical position of the gate is fixed. In case (c), this vertical position is variable. If the vertical position of the gate is fixed, the resultant of its self-weight and buoyancy usually points downward under all conditions and is transferred by a vertical support to rails or a pintle, or by suspension. If the vertical position of the gate is variable, this resultant can also change its direction and drive the gate up. Emptying the air chamber usually proceeds by air compression. The gate is then buoyant, which can be utilized for its closing and opening. It can also be utilized for removing the gate, floating it to a remote location for maintenance, and bringing it back again.

341

5.2 HYDRAULIC LOADS

FIG. 5.17 Types of intentional buoyancy applications in hydraulic gates: (a) fixed and permanently submerged, (b) fixed but variably submerged, and (c) variable.

Examples of fixed buoyancy applications have been provided in Chapter 3, when introducing various types of hydraulic gates. Note that several gates (particularly of large sizes) are constructed with refillable buoyancy tanks even if the gate opening and closing do not proceed by floating. The function of such tanks is then to provide optimum vertical support reactions by varying water level conditions. The tanks are in such cases refilled with ballast water or pressurized by air to remove the water, to limit the support reactions without jeopardizing the stability of the gate. In addition, these tanks are also used to lift the gate from its supports and to set it in the maintenance position either in the gate recess or at outside location. All large rolling gates presented in Section 3.10 employ such tanks (see, e.g., Figs. 3.163, 3.165, 3.167, and 3.177). Details of these systems are discussed in Chapter 8. Among the most spectacular buoyancy applications in hydraulic gates are those in storm surge barriers. Examples are two barriers in Gulf Intracoastal Waterway (GIWW) in New Orleans: one at the junction with IHNC, and the other at West Closure. Both gates of the first closure, the steel sector gate and the concrete swing gate, are buoyant when opening and closing. Their structural systems have been discussed in, respectively, Sections 3.9 and 3.12. Also the world’s largest sector gate in the Maeslant Storm Surge Barrier near Rotterdam makes extensive use of type (c) buoyancy tanks from Fig. 5.17. Its circular water retaining walls contain such tanks at two levels: in the gate float hull below and in the middle of its wall, as shown in Fig. 5.18. This figure also schematically indicates the other main hydraulic loads of the barrier. The tanks at both levels are divided into 15 compartments in either gate leaf. This division has here an additional reason. As discussed in Chapter 3, the gate leaves pass their loads to single spherical hinges (see Fig. 3.138), which allows for lateral trim movements during floating. These movements would have caused unacceptable displacements of water masses in the gate if the tanks ran open from one end of the wall to the other. The compartments are separated by diaphragm plates applied at the corners of the gate floodwall that, in fact, is polygonal and not circular. Fig. 5.19

Storm surge

Defended side

Upper buoyancy tank

Lower buoyancy tank

FIG. 5.18

Buoyancy and ballast tanks in the gate of Maeslant Storm Surge Barrier, the Netherlands.

342

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.19 Buoyant floodwall of the Maeslant Storm Surge Barrier near Rotterdam, the Netherlands: (a) truss arms to spherical hinge and (b) buoyancy tanks.

shows the buoyancy tanks in the docked, open position of the gate. Visible are also the air vents, piping of compressed air supply, and maintenance manholes atop the lower buoyancy tanks. An attentive reader may also notice the polygonal shape of the floodwall. The partitioning of the gate wall reduced the displacement of ballast water in the tanks, but it did not entirely remove the concern about it. After all, the water in tank compartments also reacts to the gate trim movements and the changes in closing and opening velocities. Due to the large number of variables and hydraulic load conditions, the design was supported by physical model investigations. Such an approach may also be advisable for other projects of large buoyant gates.

5.2.3 Modeling Hydrodynamic Loads 5.2.3.1 Wind-Induced Waves Wind-induced waves and flows of various nature are the main hydrodynamic loads acting on hydraulic gates. This section presents a brief discussion on loads by wind-induces waves. The loads by flows are discussed in the following section. Both types of loads and their effects on structures have been subject to extensive theoretical and experimental investigations in the past. There exists a wide expertise in this field, which cannot comprehensively be presented here for space reasons. This book confines itself to some general and most practical guidelines regarding the design approach of loads by wind waves and flows. In specific cases, the reader is encouraged to consult the literature on hydraulic mechanics. A good, practically orientated introduction to hydraulic mechanics is given in Ref. [22]. Practicing engineers will also find valuable guidance in the USACE Coastal Engineering Manual [23]. A number of wave-related issues and their solutions in hydraulic gate projects are presented in Ref. [24]. The character of loads from wind-induced waves (further called “wind waves” for short) depends on the type of these waves. The most common types of wind waves are the following: (a) nonbreaking waves; (b) breaking waves; and (c) broken waves. Fig. 5.20 presents schematically the development of these wave types for waves approaching the coast. An example plan and profile views on six existing coastal profiles can be found in Ref. [23]. For illustrative reasons, only two waves from each type are shown in Fig. 5.20; their actual numbers are higher. Note that as the water depth d measured from still water level (SWL) decreases, the wavelength L decreases too, but the wave height initially grows. As the wave period T essentially does not change, the phase velocity vc of the traveling wave must decrease, which follows from the basic relation λ ¼ T  vc

(5.15)

343

5.2 HYDRAULIC LOADS

(a) Non-breaking waves

(b) Breaking waves

(c) Broken waves

Crest SWL

a1 a1 L

Trough

L 2

Open sea Shore

FIG. 5.20

Most common types of wind waves (not to scale).

The other equations that define the relation between the variables mentioned above are as follows: • On deep water, commonly if d ½L: vd ¼

pffiffiffiffiffiffiffiffi gd

(5.16)

• On shallow water, commonly if d < ½L: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi gL 2π  d  tanh vc ¼ 2π L or

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gL  tanh ðkL  dÞ vc ¼ 2π

(5.17)

(5.17a)

where: kL ¼

2π L

(5.18)

is a so-called wave constant (m1). These equations describe the wave action with sufficient accuracy as long as the waves do not break or are in the early stage of breaking. An essential parameter to determine the loads on gates exposed to such waves is the design wave height Hd. At the time of writing this book, the rules for determining the design wave height are different in the United States and in Europe. In general: • US rules assume a deterministic approach, deriving the design wave height basically from the water depth data on the site. • European rules assume a semi-probabilistic approach, based on the so-called “significant wave height” definition which refers to actual wave measurements. The US ASCE/SEI standard (Ref. [21], chapter 5) specifies that the design wave height Hd should be the height of a breaking wave Hb determined as follows: Hd ¼ Hb ¼ 0:78  ds

(5.19)

where ds is the local still water depth. The procedure for vertical walls assumes a dynamic pressure and a static reflection component in the maximum combined wave pressure Pmax: Pmax ¼ Cp  γ w  ds + 1:2  γ w  ds where: Cp ¼ dynamic pressure coefficient (1.6 < Cp < 3.5); γ w ¼ refraction coefficient.

(5.20)

344

5. DESIGN LOADS AND LOAD COMBINATIONS

The ASCE/SEI standard specifies the dynamic coefficients Cp for different structure categories; and gives pressure distribution diagrams with SWL at one and both sides of the structure. Note that the term “breaking wave” here has a slightly different meaning than for the waves on open water (cf. Fig. 5.20). In Europe, there is no uniform, legally binding standard for wave load design assumptions, but the prevailing approach fundamentally differs from the ASCE/SEI rules. The water depth ds is a limiting but not the determining factor for the design wave height. The Hd follows from the so-called significant wave height Hs in front of the gate that, in turn, can be derived from the significant wave height Hs,0 on deep water at some distance from the gate. The term “significant wave height” has a complex statistic and an easy deterministic definition. The latter describes it as the mean trough-to-crest wave height of the highest one third of the waves in the design conditions under consideration. This means that Hs,0 should always be given in design specifications, in the same way as all the other hydraulic loads on the gate. Hs is then obtained by multiplying Hs,0 by coefficients K that represent different phenomena. The Dutch guidelines [25] specify it as follows: Hs ¼ Ks  Kr  Kd  Hs,0

(5.21)

where: Ks ¼ shoaling coefficient; Kr ¼ refraction coefficient; Kd ¼ diffraction coefficient. As the first approximation, or if the phenomena represented by the K coefficients do not occur, the designer may set the values of these coefficients equal to 1, which results in Hs ¼ Hs,0. As the design wave height Hd refers to a limit state situation, it should be higher than Hs. The common approach is to choose it so that its probability of exceedance during the considered design conditions is about 10%. If no other statistic data are available, then Ref. [25] recommends a safe assumption obtained for both coastal and inland structures in the Netherlands from the Raileigh distribution:  2:2  Hs Hd ¼ (5.22) max 0:9  dL=2 The reader may notice that the factor of 2.2 here is a factor similar to that for the design height of tsunami waves in accordance with the Japanese practice; compare discussion in Section 5.2.2.3. This is no coincidence. The nature of both factors is very similar. The lower condition in Eq. (5.19) applies if Hd from the upper condition is nearly equal to or larger than the water depth in front of the gate. This is physically impossible, because the wave will break sooner. Therefore, the design wave should never be higher than 0.9 of the water depth dL/2 at the distance of L/2 from the gate skin plate. The design wave can be subject to one more phenomenon: it can reflect. In the worst possible case, the reflected wave may be nearly as high as the incident wave. If both waves move in opposite directions, they will produce a so-called “standing wave” of nearly double height. This can be taken account by increasing the value of Hd by a reflection coefficient χ as follows: Hd,r ¼ ð1 + χ Þ  Hd

(5.23)

where: Hd,r ¼ design wave height increased by reflection; χ ¼ reflection coefficient (0 < χ < 1). The reflection coefficient strongly depends on the gate skin geometry in relation to the wave direction. The guidelines [25] recommend χ ¼ 0.7–0.9 for a vertical skin. A conservative assumption is χ ¼ 1. Note that reflection strongly decreases when the waves break or already are broken. Other phenomena, like flow and impact loads, then play a role, which will be discussed later. It is not, like in the United States, common to cover these phenomena by a dynamic pressure coefficient Cp. Using the reflection coefficient χ in combination with the earlier introduced factor of 2.2 is sometimes disputed in this approach. One point of discussion is that as Hd is a stochastic variable with a very low probability of exceedance, the chance that both the reflected and the next approaching wave have this height and produce a double-high standing wave at the gate is still a magnitude lower. Another point is that the crest of a standing wave does not, generally, appear simultaneously along the whole skin plate width, which is assumed in the analysis. Therefore, some engineers consider the factor 2.2 conservative enough to cover the reflection also. This is, however, not an official guideline.

5.2 HYDRAULIC LOADS

345

Having determined the height including reflection Hd,r of the design wave, its length, and period, one can compute the resulting design loads. There are diverse models and appropriate procedures for it in the literature, including the following: • Sainflou model: quasi-static, applicable to nonbreaking waves; • Goda model: quasi-static, applicable to nonbreaking and breaking waves [26]; • PROVERBS model: dynamic, applicable to breaking and broken waves [27]. Below, the first of these models is presented. The model of Goda is globally introduced in discussion of wave impact further in this chapter. It generally results in lower loads. The PROVERBS model is still less conservative but relatively complex and not frequently applied yet. If the application of this model is desirable, the readers are advised to consult the referenced literature. The Sainflou model [28] is simple, conservative, and recommended for engineering practice by many institutions, including USACE and Rijkswaterstaat. The method is often presented using trochoidal profiles of standing waves (Fig. 5.21), but it is also widely applied for cnoidal, sinusoidal, and other wave profiles. The choice between these and other wave profiles is usually based on observations, local records, and experimental research. Fig. 5.22 presents the Sainflou model for loads from a standing wave of trochoidal (a) and sine (b) shape. The trochoidal wave is not symmetric with respect to the still water level (SWL). With the notation as in Fig. 5.22a, the height difference η0 between SWL and the middle line of Hd,r is as follows:   π  Hd,2 r πd k  a2s  coth  coth ðk  dÞ (5.24) η0 ¼ ¼ L L 2 In this equation, known as the Sainflou formula, the amplitude as under full reflection (χ ¼ 1) is equal to the design height Hd of the nonreflected wave. If the crest of the standing wave coincides with the gate skin, then the quasi-static pressure from this wave acts in the same direction as the hydrostatic pressure from differential water head. The maximum value of this pressure p1 occurs at the SWL, and equals p1 ¼ ρw  g  ðas + η0 Þ

FIG. 5.21

Trochoidal waves in partial reflection, Amsterdam-Rhine Canal, the Netherlands. Photo Rijkswaterstaat.

(5.25)

346

5. DESIGN LOADS AND LOAD COMBINATIONS

p1

p0

p0

p0

Hd,r

as as ds

d

Hydrostatic pressure

Quasi-static wave loads

Hd,r

as as

SWL

Quasi-static wave loads

Hydrostatic pressure

ds

d

SWL

p1

L

h0

L

p0

(b)

(a)

FIG. 5.22 Wave pressure models according to Sainflou: (a) trochoidal wave and (b) sine wave.

According to Sainflou, the pressure p0 at the bottom edge level of the gate is p0 ¼

ρw  g  a s cosh ðk  ds Þ

(5.26)

Pressure distribution between these two levels is assumed to be linear. Note that in the case of a sine wave (Fig. 5.22b), η0 ¼ 0, p1 is the hydrostatic pressure over the amplitude as, and the Sainflou model needs to be used only for determining p0. In several design considerations, like the fatigue analysis, not only the load from wave crest on gate is interesting, but also the load from wave trough that appears afterwards. As shown in Fig. 5.22, wave troughs result in quasi-static pressures directed opposite to those from differential water head. Computation of these pressures proceeds in accordance with the same formulas as above. The only difference appears in formula (5.25), which then takes the form p1 ¼ ρw  g  ð a s  η 0 Þ

(5.25a)

Note, however, that a fatigue analysis will not necessarily be focused on the extreme wave loads. The loads that cause fatigue must also act frequently, which means that lower but more frequent waves will probably be more interesting in that view. 5.2.3.2 Loads Due to Flow Hydrodynamic loads generated by flows include a wide range of cases and phenomena. To begin with, “flow” is a collective term for all kinds of fluid motion and there are many of such kinds. The ASCE 7-05 code [21] gives some regulations concerning the loads induced by flow, but they do not cover crucial aspects of flow loads on hydraulic gates. See more comments on these regulations at the end of this section. In the most general view, as presented by Lewin [29], the flows that hydraulic gates are exposed to can be divided in two groups: • free surface flows • flows in closed conduits Following this division, hydraulic gates of various operation profiles can roughly be classified into the two groups mentioned above, as illustrated in Table 5.3. The flows sketched in Table 5.3 schematically show only a few of the many possible flow situations that may occur on hydraulic gates. The loads as result of two of these flow simulations are discussed as examples below: • Example 1: Overtopping in free surface flow. • Example 2: Underflow in a closed conduit.

347

5.2 HYDRAULIC LOADS

TABLE 5.3 Hydraulic Gates in Free Surface and Conduit Flows Gates in free surface flow

• • • • • • a

Gates in river weirs Gates in dam spillways Some lock gatesa (like sector gates) Gates in tide and flood barriers Gates in irrigation systems Gates in sewage processing plants

Gates in conduit flow

• • • • • •

Gates in conduits of hydroelectric plants Gates in dam diversion conduits Filling and emptying devices in locks Filling devices in shipyard docks Valves in industrial cooling systems Valves in drinking water processing plants

In this view, we consider most lock gate types (like miter gates) as operating under no-flow condition.

The discussion will in both examples focus on the dynamic effect that the flow has on hydraulic load distribution on the gate. One should not forget, however, that flow affects more than that. It introduces diverse phenomena, like vortex shedding, hydraulic downpull, vibration, deaeration, and cavitation. A brief discussion of these phenomena is presented in Chapter 6. Readers seeking more guidance on this field or more examples of load modeling in situations with flow are advised to consult specialist literature, like Refs. [12, 30–33]. The US Army Engineer Research and Development Center often conducts studies on flow-related issues available on Internet. An example is the study report on lock culvert gates [34]. Both the examples presented below demonstrate that consideration to the dynamic character of flow often allows for lower design load assumptions. This should not surprise. It follows from considering the loads on hydraulic gates in terms of energy rather than water heads only. A flow then represents the kinetic energy of water that the gate does not retain. It only retains the potential energy represented by a differential water head. Drawing a line between these two kinds of energy usually leads to smaller and smoother diagrams for quasi-static loads. Example 1: Overtopping gate in a free surface flow This example demonstrates that a quasi-static load definition on an overtopping gate in a way shown in Fig. 5.7a can be optimized to a less conservative model when the dynamic character of the flow is considered. The following solution is derived from the case presented by A. Richter in Ref. [31].

FIG. 5.23 Flow over a weir gate (extreme discharge), Lith Weir on the Meuse, the Netherlands.

348

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.24 Hydrodynamic pressure reduction on gate in overflow.

Let us consider an overtopping gate of a random type, in which the thickness is relatively small when compared to the height; and where the flow produces an aerated nape on the downstream side (see Fig. 5.23). If the flow has a permanent character (like in a river weir) then it is more convenient to refer to the so-called normal flow depth or piezometric head level H rather than to the energy line level. The difference between the two is shown in Fig. 5.24, with v being the mean velocity of the normal flow. The flow in a section of an open channel is called normal (or uniform) if its depth, cross-section, and velocity remain almost constant along that section. In the great majority of cases, the gate height hs is larger than the submersion h of its top edge. The effect of kinetic flow energy in the vicinity of the gate is then assumed to extend h below the gate top edge. The line between the predominately potential energy of motionless water and kinetic energy of flowing water can, in that case, be assumed as a parabola: z∗ ¼

1  x∗ 2 4h

(5.27)

The following discussion concerns the upstream side only. Hydrostatic pressure on a length unit of the gate with no account of the kinetic flow effect is obtained from the area of the hatched trapezium:   1 2 h + h  hs  ρw g (5.28) Pst ¼ 2 s The hydrodynamic pressure with account of kinetic flow effect is obtained by adding the area under the half-parabola in the upper part, and that of trapezium in the lower part of the graph:  2    4h ð3h + hs Þ  ðhs  hÞ 1 2 1 2 h + h  hs  h  ρw g + Pdyn ¼ (5.29)  ρw g ¼ 2 2 s 6 3 Note that the difference is Pst  Pdyn ¼

1 2 h  ρw g 6

(5.30)

In the extreme situation, when h ¼ hs, this makes 11.1% of load reduction. The benefit of dynamic load modeling is, therefore, not spectacular in this case but it can be significant for some considerations. Example 2: Gate underflow in a closed conduit The effect of dynamic load modeling is usually more significant in cases with underflow. A simple explanation of this is that underflow takes place at larger depths, that is, in the zones where in hydrostatic modeling the potential energy of differential water heads is larger. Therefore, the transitions of this energy into the kinetic energy of the flow are also relatively large. This applies to gates in both free surface flow (Fig. 5.25) and conduit flow, but it is particularly significant in the culverts of high head navigation locks and in deep conduits of hydroelectric plants.

349

5.2 HYDRAULIC LOADS

FIG. 5.25 Underflow at Emsworth Lock and Dam gates, Ohio River, United States. Photo Hydro Industry.

FIG. 5.26 Hydrodynamic pressure reduction on gate in underflow.

Pressure in vicinity of gate:

Gate hoist

Kinetic energy

y

H

Potential energy

Specific energy

ΔP y1

y0

Pdyn edyn

est

eΔ

Pst

x H·rwg

Let us again consider a gate of random type, in which the thickness is relatively small when compared to the height, but this time operating in a rectangular culvert or conduit intake not far from its opening (see Fig. 5.26). We also assume that the gate downstream side is aerated, the flow is a two-dimensional (2D), so-called potential flow, its height y1 is small when compared to the channel height y0, and there is no significant flow over the gate skin on its downstream side. It is common in hydraulic mechanics to analyze this case in an orthogonal x-y system, as shown in Fig. 5.23, rather than in the x-z system like in most other cases. In this case the y-axis runs up from the channel bed. The following solution is derived from the case presented by H. N€ olke in Ref. [31]. Hydrostatic pressure on a length unit of the gate with no account of the kinetic flow effect can also be obtained from the area of the hatched trapezium: Pst ¼

1 ð2H  y0  y1 Þ  ðy0  y1 Þ  ρw g 2

(5.31)

The hydrodynamic reduction of this pressure, resulting from partial transition of the potential energy of the water head to the kinetic energy of the flow, can be determined using the concept of a so-called specific energy. This concept

350

5. DESIGN LOADS AND LOAD COMBINATIONS

follows directly from the Bernoulli’s formula. The specific energy is defined as a sum of potential and kinetic energy per unit weight of water. In the discussed case, the first equals the water depth y (measured from the channel bed) and the latter equals the so-called velocity head, which can be expressed as follows: E¼y +

v2 2g

If the flow per unit width is q then the v in flow velocity head is v ¼ q/y, and  2 q 1 E¼y +  y 2g

(5.32)

(5.33)

In the considered case, the application of these relations allowed for deriving the dynamic reduction ΔP of hydrostatic pressure on the gate:  2  H y1   y1  ð y0  y1 Þ y0 ΔP ¼  ρw g (5.34) H + y1 Applying this reduction to the hydrostatic pressure from Eq. (5.31) gives 2  2 3 H y1   y1 7 6 y0 + y1 y0 6 7 Pdyn ¼ Pst  ΔP ¼ 6H   7  ð y0  y1 Þ  ρw g 4 5 2 H + y1

(5.35)

The heights of the resultants of loads Pst, ΔP, and Pdyn are, respectively, est ¼ y1 +

½ 3ð H  y0 Þ + y0  y1   ð y0  y1 Þ 6ðH  y0 Þ + 3ðy0  y1 Þ

  y0 y2  y21 H  ln  0 y1 2 eΔ   2  H  1  ð y0  y1 Þ y0  y1

(5.36)

2

edyn ¼

Pst  est  ΔP  eΔ Pdyn

(5.37)

(5.38)

The equations in this example represent an analytical solution. However, the reader might have noticed that this solution implies several assumptions, like a 2D potential flow, some dimensional proportions, no flow over the gate, and an approximation of the specific energy line by a logarithmic function. All these assumptions may be correct in engineering, but they are not entirely free of error. This applies also to the analytical solution in Example 1. Therefore, analytical solutions are not the only approach practiced in hydraulic mechanics, particularly not for complex flow cases or gate geometries. Other approaches include numerical simulations and physical modeling. They are discussed in more detail in Chapter 7. It is also good to remember that a number of the world’s leading research institutions developed handy software, diagrams, and other tools that help engineers to determine hydraulic loads on gates. Examples are the manuals [35–38] by the US Army Corps of Engineers, software packages like Delft3D-FLOW [39] by the Netherlands’ research institute Deltares, and many others. Some of these tools are free to download and other commercially available on the Internet. As mentioned earlier, the ASCE 7-05 code [21] also gives some guidance for the assumptions of design loads due to flow. It allows for taking account of the flow in the form of a surcharge water head dh on the upstream side, computed as shown in Eq. (5.14) earlier in this chapter. To compensate for the inaccuracy of this method, some limitations have been introduced, like the maximum flow velocity of 3.05 m/s (10 ft/s) and minimum drag coefficient of 1.25. This approach is generally too simple for determining flow loads on hydraulic gates, but it can be used in the early stages of projects or in the projects of small (e.g., irrigation) gates. Its limitations can in such cases be bypassed by using more specific guidance and data from Ref. [23] or [40].

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5.2 HYDRAULIC LOADS

5.2.3.3 Water Impact Loads The preceding two sections have shown that the analysis of wave and flow loads can finally lead to quasi-static diagrams of those loads. This is normally not the case for loads resulting from an impact of water masses. Impact is by its very nature a dynamic phenomenon that should be approached using dynamic models and formulas. There is some inconsistency in the literature about what should and should not be called impact load. The ASCE 7-05 code [21], as well as the FEMA CCM [40], names only the impact of “debris, ice, and any object” carried by water, not of the water itself. This implies that moving solids, not fluids, can only cause impact loads. This view seems to be shared by the authors who, like in Refs. [12,32], use the term “impulse” rather than “impact” when referring to water that strikes various objects on its way. Other sources, like Ref. [41], speak of fluid “shocks” in this context. In this book, we use the term “impact” also for loads by relatively compact, high velocity flows striking hydraulic gates or their components. The loads by moving solids, like vessels, debris, ice floes, and other objects, form another group of impact loads and are discussed separately later in this chapter. The term “impulse” is used in reference to the time integral of impact load, not to the load itself. Water impacts on hydraulic gates cover in this sense a range of cases, the most common of which are the following: • • • • • • •

high-velocity flows on gates in the underflow zone; high-velocity flows on gate components in the nappe and overtopping flow; wave slams against gates and their components; loads on flow breakers in culverts and filling and emptying devices in gates; waterfalls on rear structures of overtopping spillway or weir gates; loads by water jets on their guide blades, cutters, and breakers in hydroelectric plants; and impact loads by ship propeller jets hitting the gate structure.

A detailed load determination for all these and other cases goes beyond the scope of this book. Readers seeking guidance in this field are encouraged to consult specialist literature, like Refs. [12, 24, 27, 30–33]. Solutions to a number of relatively simple, practical cases have also been presented in the guidelines by USACE [23], Netherlands’ Rijkswaterstaat [25], FEMA [40], and other official institutions. As an example, the determination of design impact loads from waves slamming the gate is discussed below. Note that this discussion is different than for the loads from standing waves in Section 5.2.3.1. The expertise in this field originates, not surprisingly, from breakwater design. Breakwaters can have various forms, including a vertical wall that is exposed to slamming waves (Fig. 5.27) in basically the same way as a hydraulic gate. In order to assess whether and under which conditions wave impact loads on a gate should be analyzed, the flowchart in Fig. 5.28 can be followed. The chart in Fig. 5.28 has been developed in a joint European research program, called PROVERBS [25,27], as a tool for the classification of wave loads on breakwaters. Observe that the waves that should be considered for impact

FIG. 5.27 Wave hitting the Kalk Bay breakwater, Cape Town, South Africa. Photo Hewett Insite.

FIG. 5.28 Classification of wave loads on breakwaters including the impact loads [27]. Source: H. Oumeraci, et al., Probabilistic Design Tools for Vertical Breakwaters, A.A. Balkema Publishers, Amsterdam, 2001.

352 5. DESIGN LOADS AND LOAD COMBINATIONS

5.2 HYDRAULIC LOADS

353

(slamming) loads are basically only the breaking waves, that is, not the nonbreaking waves, or the already broken waves. An illustrative sketch of these types of waves is given in Fig. 5.20. In addition, the breaking waves must be “large,” which is assessed in the chart by a ratio of the significant wave height Hs to the water depth in front of the breakwater (in our case gate) hs. See Section 5.2.3.1 for a definition of the significant wave height. Finally, the ratio of an impact force to the following quasi-static load Fh,max/Fh,q must be higher than 2.5, otherwise the wave is not clearly a breaking wave and produces a pulsating rather than impact load. What in the flowchart is called “berm” can also make part of a gated closure, for example, in the form of a raised sill. Therefore, the chart in Fig. 5.28 can directly be utilized for wave load assessments on most types of hydraulic gates. Having determined whether, and if so then, which waves produce considerable impact loads, one can take the next step, which is the determination of impact pressures. There are a number of models for it, varying from very simple, like in the FEMA manual [40], to sophisticated and based on probabilistic research, like the PROVERBS approach [27]. The FEMA model considers lateral wave slam loads on elevated buildings. It gives a simple formula for the slam force Fs on a width unit of the slam-exposed elevated building. In our notation: 1 F s ¼ ρw g  C s ds h 2

(5.39)

This method is basically the same as for structures in flow (see Eq. 5.14), with the wave crest velocity set at its upper bound v ¼ (gds)½, and a slam coefficient Cs in place of the drag coefficient CD. Further, ds is here the still water depth in front of the structure, and h is the vertical distance between the breaking wave (breaker) crest and the bottom edge of the slam exposed floor. The FEMA recommends the value of 2.0 for the slam coefficient Cs in residential structures. This formula may be useful for some specific components of flood gates or in preliminary estimations of slam forces on gates, but it is generally too simplified for a detailed gate design. Therefore, a better-developed determination of slam loads is presented below. This method is based on the European (predominately German [42]) research within the PROVERBS program mentioned earlier. Although it also makes use of some simplifications, it takes account of more parameters involved than the water depth and breaking wave height, which makes it better suited for hydraulic gate design. For the understanding of this method, it is good to realize what the nature of a wave slam is. Wave slams comprise a number of phenomena. Graph (a) in Fig. 5.29 shows the course of a horizontal impact force Fh in time. The involved phenomena are schematically indicated. As shown, the first peak of Fh is caused by an impact of the breaker tongue. Then the force drops a little as result of damping by splashing water, to rise quickly again due to the compression of encased air pockets. At this point, the impact normally reaches its maximum. Then it drops as the height and energy of the breaker decrease. This happens with some oscillations caused by the oscillating pressure in encased air and by air escape. The last rise of Fh is caused by the breaker tail and has basically a quasi-static shape. This brief description does not account for the response of the structure. It has implicitly been assumed that the structure rigidly responds to the wave impact, which will usually be true in the case of massive breakwaters, but not necessarily in the case of elastic hydraulic gates of steel. The response character, for example, the natural frequency vibrations, can additionally affect the course of graph (a) in Fig. 5.29.

FIG. 5.29 Wave impact loading on a breakwater: (a) wave impulse as recorded in flow channel, (b) model of wave impulse, and (c) sketch for load definition. Drawn after H. Agerschou, et al., Chapter 7. Breakwaters, in: O.J. Jensen, H. Oumeraci (Eds.), Planning and Design of Ports and Marine Terminals, Thomas Telford Ltd., London, 2004.

354

5. DESIGN LOADS AND LOAD COMBINATIONS

It can be observed that the maximum impact force Fh,max occurs early in this graph, has a very short duration and a steep, approximately triangular time function. This leads to the modeling of load impulse as drawn in sketch (b) in Fig. 5.29, where Fh,max represents the highest Fh peak from graph (a). Some investigators go further and model the impact load distribution on a vertical wall as nonlinear [27,42]. Such an approach is usually supported by physical model investigations, which will globally be introduced in Chapter 7. However, for engineering purposes it is generally accepted to apply a simplified, linear distribution, as shown in Fig. 5.29c [27]. The notation in this drawing follows the notation that is commonly used in the model of Goda. The Goda’s formulas can directly be used to determine the loads by so-called “pulsating waves,” or the waves in the early stage of breaking (first two cases in Fig. 5.28). They need to be modified for loads by waves in an advanced stage of breaking. These formulas are quoted below, followed by the necessary modifications for wave impacts. Here is the basic set of the formulas of Goda [26]: η∗ ¼ 0:75  ð1 + cos βÞ  λ1  Hd

p1 ¼ 0:5  ð1 + cos βÞ  λ1 α1 + λ2 α∗  cos 2 β ρw g  Hd

(5.40)

p3 ¼ α 3  p1

(5.42)

p4 ¼ α 4  p1

(5.43)

pu ¼ 0:5  ð1 + cos βÞ  λ3 α1 α3  ρw g  Hd

(5.44)

(5.41)

Herein η* ¼ design wave crest height above SWL; β ¼ angle between wave crest and front of the structure (assumed β ¼ 0); p1, p3, p4 ¼ pressure per width unit at, respectively, SWL, caisson bottom level, and caisson top level; pu ¼ uplift pressure per width unit at front bottom edge of caisson (normally not in gates); λ1, λ2, λ3 ¼ factors of structure geometry (λ1 ¼ λ2 ¼ λ3 ¼ 1 for standing and not-provoked waves on gates with vertical, flat retaining walls); Hd ¼ design wave height (without reflection!), as discussed in Section 5.2.3.1. NOTE: Goda recommends Hd ¼ 1.8Hs for the design, which represents the exceedance of 0.1% in the Rayleigh distribution of wave heights. This corresponds to the mean of the 1/250 of the highest waves. As noted earlier, guidelines of the Netherlands [25] and some other countries recommend a higher design wave of Hd ¼ 2.2Hs (see formula 5.22). The designer should choose the Hd in line with the local standards of the project.  α1 ¼ 0:6 + 0:5 

4π  hs L  sinh ð4π  hs =LÞ

2

α∗ ¼ largest of α2 and α3   H  d Hd 2 2d  and α2 ¼ smallest of 3H Hd d   d + dc 1 α3 ¼ 1   1 cosh ð2π  hs =LÞ hs α4 ¼ 1 

smallest of Rc and η∗ η∗

(5.45) (5.46) (5.47) (5.48) (5.49)

where: L ¼ wavelength of the significant wave Hs; hs ¼ water depth in front of the structure; H ¼ water depth at a distance of 5Hd seaward of the structure; d ¼ water depth above the caisson berm (in our case the gate sill); dc ¼ height of the caisson effective berm (in our case the gate sill); Rc ¼ freeboard of caisson or gate wall above SWL. Note that the Goda formulas provide a direct link between the pressure parameters p1, p3, p4, and pu on the one hand and the input data like the significant wavelength L and design wave height Hd on the other hand. This is very convenient for the designer since these input data are normally determined in project specifications.

5.2 HYDRAULIC LOADS

355

As already mentioned, these formulas should be modified when the ratio of the wave slam force to its quasi-static load Fh,max/Fh,q is higher than 2.5. Only then the wave load assumes character of an impact, as described in Fig. 5.29. Based on the analysis of almost 1000 breakers of different types hitting a vertical wall, the following modifications have been introduced [27]: • Wave crest height η* should be replaced by the breaker elevation h* above SWL. It can tentatively be assumed as h∗ ¼ 0:8Hb

(5.50)

where Hb is the breaker height. • The Goda formula (5.41) for the maximum pressure p1 remains unchanged. • Impact pressure p3 at the bottom for breakers may be derived as p3 ¼ 0:45p1

(5.51)

• Impact pressure p4 at the top is obtained by the substitution of η* by h* in formulas (5.43) and (5.49): ( p4 ¼

0 if h∗  Rc h∗  Rc p1 if h∗ > Rc h∗

(5.52)

• Since Fh,max is modeled as an area of the pressure diagram, it can now be computed as Fh, max ¼ 0:5  Rc ðp1 + p4 Þ + 0:5  ðd + dc Þ  ðp1 + p3 Þ

(5.53)

The parameters h*, p1, p3, and p4 describe the impact load distribution by a simple modification of the Goda equation. This, in turn, allows for determination of the maximum value of this load Fh,max. There have also been other methods proposed, most of them based on statistic wave data and model investigations. Those methods may lead to more accurate results but they also require more input, which can be difficult to obtain. In specific cases, particularly those of large and complex projects, the readers are encouraged to consult specialist literature in this field, some of which have already been referred to in this chapter. These parameters do not, however, complete the solution. An important part of it is the determination of impulse data, notably the impulse risetime tr and total duration time td, as indicated in Fig. 5.29b. These times are crucial to assess the response character of the structure. When compared to the natural frequencies they allow, for example, to determine whether the gate will fully deform under computed impact loads, or whether its deformation will sufficiently be damped. There is a deterministic and probabilistic way to estimate the risetime tr and duration time td of a wave impact load. The deterministic way is simpler and faster. If we denote F*h, max as the relative maximum wave impact force F∗h, max ¼

Fh, max ρw g  Hb2

(5.54)

and ignore the effect of the breakwater berm (in gates raised sill), then the risetime of the impact load caused by this wave can be computed as [27] qffiffiffiffiffiffiffiffiffi hs =g (5.55) tr ¼ 8:94  km  ∗ Fh, max where km is the mass proportion of the water directly causing the impact on all the water in the wave profile. A recommended upper bound estimation is km ¼ 0.25. Field measurements have proven that the impact decay time is longer than the risetime. PROVERBS [27] documents estimate it as about 50% longer. The impact total duration time is then td ¼ 2:5  tr

(5.56)

The respective impact force impulses Ihr and Ihd, indicated in graph (b) in Fig. 5.29, emerge then as integrals of the function Fh(t) over, respectively, the times tr and td: Ihr ¼ 0:5  Fh, max  tr and Ihd ¼ 0:5  Fh, max  td

(5.57)

356

5. DESIGN LOADS AND LOAD COMBINATIONS

Short-lasting impulses are normally less dangerous than long-lasting impulses because the structure, due to its mass inertia, gets then no time to deform. Therefore, as Fh,max represents a dynamic force, it should be converted into the equivalent static force Feq,st that takes account of the structure response, particularly the period of its natural vibration involved TN. This takes place by means of a dynamic factor vD that binds the two forces: Feq,st ¼ vD  Fh, max

(5.58)

This dynamic factor has been determined in an extensive research program for breakwaters [42] but it is also used for other structures, including hydraulic gates:  0:55 td π  td + 0:5  c (5.59) vD ¼ 1:4  tanh TN TN with c ¼ 0:55  ðtd =tr Þ0:63

(5.60)

One should be aware that a hydraulic gate usually has more modes of natural vibration to be concerned about. This distinguishes it from a breakwater that commonly is a massive structure with one or only a few such modes. As a result, the equivalent static force may need to be determined several times for various modes of natural vibration and various components of a hydraulic gate. This is necessary to make sure that every component and vibration mode involved remains under control. In such cases, it may be helpful to use simple programs, calculation spreadsheets, or plot diagrams of Eq. (5.59). An example plot for a number of td/tr ratios is presented in Fig. 5.30 after Ref. [42]. Note also that despite the attention paid to the natural vibration periods TN, this checking is not about the risk of vibrations. It is in the first place about the static strength and stability of the structure. The question to be answered is, simply speaking, whether the inertial forces will dampen the short-lasting impact before allowing the structure to excessively deform or displace. Whether this impact can excite vibration is normally irrelevant because the frequency of wave slams is too low and too irregular to excite the natural frequencies of the structure.

5.2.4 Hydraulic Loads in Deterministic and Probabilistic View A general discussion on a deterministic and probabilistic load definition has been presented in Section 5.1.2. There is, however, a reason for some comments concerning the choice between these two approaches for hydraulic gates. The following comments reflect authors’ views, and do not necessarily have to be shared by all professionals.

FIG. 5.30 Diagram for the determination of dynamic load factor vD.

5.2 HYDRAULIC LOADS

357

There was a time when hydraulic loads were predominately determined in a deterministic way. Design loads for gates, for example, in a canalized river weir or hydroelectric plant reservoir resulted from the target water levels. The loads for gates in a flood or storm surge barrier followed the highest ever recorded differential water heads. Whether the flood of that size could happen tomorrow or over 100 years, was not a design issue. The allowable stresses were simply assumed with a safety factor (SF) of 1.5 under the yield stress; and no statistical analysis in terms of probability density functions was performed. Today, most engineers agree that this approach is outdated. Having said that, one should add, however, that the practice mentioned above was not groundless, as the most enthusiast followers of probabilistic methods claim today. It only represented a different vision. It did not say that a dam gate, for example, on the Mississippi River would sustain the 100 years flood, within the agreed probability of exceedance. Instead, it said that this gate would certainly hold it by the same river discharge as during the Great Mississippi Flood of 1927 (Fig. 5.31). It might even hold it for some time above that level, but that was uncertain because then the safety margin of the gate was not preserved any longer. This simple vision did not stand the test of time. It has been undermined from two sides: on the one side, the deterministic SF of 1.5 was often considered too conservative or not conservative enough. On the other side, it could not give an absolute certainty anyway, because absolute certainty did not exist in statistics. All quantifiable values were declared to have a mean value and standard deviation. This was a very different vision. It first prevailed in financial circles but it soon appealed to managers, investigators, scientists—and finally also to large groups of engineers. Adopting this vision was neither evident nor easy for engineers. The engineering culture is, after all, imbued with respect for physical laws, like the gravity law or the law of energy exchange, that give accurate answers to questions. In essence, engineering is just putting these laws at work in a controlled, systematic way. Therefore, correctly engineered structures are also supposed to be fully predictable and accurate. Agreeing on a probability of failure, certainly for structures like hydraulic gates, was at odds with professional ethics. Such gates should never fail. Let us give a moment’s thought to the US Army Corps of Engineers’ motto “Building strong” in this sense. It expresses exactly the ambition described above. Note that it does not plead for building as strong as agreed or strong enough—it pleads for building strong in an absolute sense. Most engineers in the world, perhaps even all, would still be happy to follow such an attitude. These remarks should make clear that switching to probabilistic design represented a big challenge for engineers; it asked a change of culture. Yet, this challenge has been taken up, and the culture is in the process of changing. It is important, however, that this culture should not change too much. After all, allowing a failure within the probability of exceedance that has been negotiated or specified in design codes justifies such a failure. Anyway, it removes the moral responsibility for it from both the designer and constructor of the gate. By doing this, it strips the engineer’s job of a part of its relevancy and pride, stimulating apathy or even cynicism. The latter must not happen. Avoiding it may become a challenge similar to adopting probabilistic design methods. What is really needed is alertness and constructive criticism toward the excess of statistical takeover in engineering. Below are a few typical situations that engineers are faced with and need to be alert in this matter, along with hints on how to handle them.

FIG. 5.31

Great Mississippi Flood of 1927: (a) railway near Helm (MS) and (b) Egremont station (MS); images from NMAAHC collections.

358

5. DESIGN LOADS AND LOAD COMBINATIONS

• Poor compliance of test or measurement arrangements with the design. Most sets of test results or measurements, either in the field or on physical models, are collected under slightly different arrangements than those of the designed structure. After all, the structure usually does not exist yet at the time of the design. Yet, the crucial characteristics of both should be similar. In cases of generic tests or measurements, not finetuned for a specific project, there is a chance that those crucial characteristics do not match. It is important to precisely check where, how, and under which conditions the statistical data have been collected; and evaluate the differences. Significant differences can also appear in poorly planned tests for a considered project. Be alert for statements in test reports saying, for example, that the tests took place under conditions simulating the design “as close as possible.” Such statements usually indicate that no thorough evaluation of the differences was performed. Demand such an evaluation and an insight to the test conditions. • Too few a number of representative trials or measurements. Statisticians often stress that only large numbers of trials and measurements produce reliable data, but when it comes so far, some deliver the data based on insufficient numbers of such trials. It is, therefore, advisable to check how many tests or field measurements were performed. A number of such tests less than about 30 should raise concern. Another indication of an insufficient number is a large standard deviation compared to the mean value, larger than about 10%. Some processes, however, show high dispersion, which may justify high standard deviations. Always ask for an explanation when there are high standard deviations. There are methods in statistics, like the Student’s t-test or the Bayes rule [9], that help assess the quality of such data. Ask to prove it by such tests. If it cannot be proven or if the test fails, it is to better to rely on a deterministic approach. • Semi-probabilistic criteria inadequate for the analysis of old steel structures. The introduction of LRFD method created a demand to apply it also for the analysis of old, existing steel structures. Yet, there are no statistical data sets for the steel grades from 1930s and earlier. Semi-probabilistic methods (LRFD in the United States) assume a skewed normal distribution of yield based on tests of current steel grades, while occasional tests of old steel samples often deliver different and differently distributed results. That is why testing a low number of samples from an old structure and applying the ASD analysis method will often represent a better approach than the LRFD method. • Controversies between different statistical data sets. As the status of probabilistic approach in engineering grows, more and more companies and research institutions see the collection and processing of data as a market to make money. The competition in this market proceeds not only on the ground of relevancy and accuracy of data, but it is also important which data will please the customer. As there are different customers, the statistical data sets of the same processes can also be different. Controversies between different data sets may also result from careless selection or lack of expertise by both the data provider and his client. If controversies are found, it is advisable to investigate their reasons and choose the data sets that are objective and better correspond with the nature and conditions of investigated processes. If the data providers do not cooperate or if no such data can be found, one can better turn back to deterministic methods. • Strange consensus on different data. Competition is not the only mechanism driving the data market. Another one is relation management. It is particularly noticeable in the circles of universities and research institutions, which also happen to be the most respected data providers. Such institutions actually value prestige higher than business; and one of the means to preserve prestige is a wide network of good relations. Therefore, these institutions do not openly question each other’s data or test results. One can see it in reports of working groups, especially in Europe, that admit the differences between each other’s data, but refrain from evaluating them. Engineers are then prompted to apply both data sets and take mean or more conservative results for further design. It is not advisable to follow such an approach. Demand a clear explanation of the differences. If no convincing explanation is given, one can better refuse using such data. • Falsified relation between loads and deformations. Application of load factors results in computed structure deformations that match the factored loads and not the nominal loads any longer. The relation between loads and deformations becomes, therefore, falsified. This applies to the size of deformations (when there is one uniform load factor) or to both the size and character of deformations (when the structure carries more loads with different factors). The designer must be aware of that. In cases when the actual

5.2 HYDRAULIC LOADS

359

shape of the loaded structure is a concern and should reliably be computed, the analysis must be performed using unfactored (nominal) load values. This includes, among other things, all tests of deflection criteria, all computations of vibration modes, all stress and deformation analyses for fatigue, and several tests of the serviceability limit state ( SLS). The choice between deterministic and probabilistic approach is also significant in a broader view. An effect of probabilistic methods is also that they discourage analytical investigation of natural processes. In consequence, even if there is an analytical explanation to deviant field measurements or test results, no effort is taken to find it. After all, statistics are meant to handle random dispersion, so if there is no such dispersion statistical tools can be missed. As statistics win ground in recent decades, there is a risk that analytical explanations to natural processes will gradually lose relevance. This would impoverish science and technology in the sense as expressed by Maslov in his phrase “If the only tool you have is a hammer, everything looks like a nail.” It would weaken the desire for understanding and adequately responding to natural phenomena at the cost of classifying these phenomena as random, which is not an attitude of an engineer. Deterministic methods do not introduce this risk; they are rooted in analytical solutions and they encourage them. If only for this reason, they should not be valued lower than probabilistic methods. In this sense, the correct, wellbalanced choice between deterministic and probabilistic definition of loads in hydraulic projects appears to be as presented in a flowchart in Fig. 5.32. Note that this flowchart confirms the importance of probabilistic approach in engineering, but it introduces a moral obligation to keep investigating the nature of physical phenomena, in this case the dispersion of hydraulic loads, whenever the collected data indicate any regularities. Such an approach, if supported by engineers and project owners, might result in putting the best of both methods at work. Obviously, the chart reflects only the general idea; the details (like what exactly a “good compliance” is or how “regularities in data dispersion” can be detected) still need to be specified, possibly not sooner than on the project level.

5.2.5 Loads in Anticipation of Climate Change At the time of writing this book, climate change is an intensively discussed subject, attracting attention of professionals all over the world. It is also one of the top subjects in discussions about technology and its mission in the coming decades, including hydraulic engineering. For designers and managers of hydraulic gates, climate change is particularly concerning as it brings higher water levels and heavier, more frequent storms. There are issues upon which specialists generally agree, and issues that remain controversial. What is not questioned any longer is, in essence, the following: • There is indeed a global climate change going on and its direct reason is the so-called “greenhouse effect” caused by the growing concentration of gases like CO2, CH4, and N2O in the atmosphere. DETERMINISTIC or PROBABILISTIC ?

DETERMINISTIC formulas? PROBABILISTIC methods

DETERMINISTIC methods

FIG. 5.32

PROBABILISTIC methods

Choice of deterministic and probabilistic definition of hydraulic loads, proposal.

360

5. DESIGN LOADS AND LOAD COMBINATIONS

• The “greenhouse gases” (GHGs) absorb heat, both solar and radiated by Earth. Particularly, the latter is largely absorbed and reradiated back to the Earth’s surface. This normally takes care of a livable climate on Earth, but with too high concentration of GHG it causes global warming. • The effects of global warming are visible in many fields. Most relevant for hydraulic gate design is the rising of sea level. It is caused by polar ice melting and thermal expansion of warmer seawater. Studies predict a global mean sea level rise of a few decimeters in 2100 [43]. • Other effects that hydraulic gate engineers should be aware of include more frequent and intensive extreme weather conditions like storms, hurricanes, floods, and droughts. The renewable freshwater resources are also at risk of partial extinction, especially in subtropical regions. The projections of global temperature rise are based on mean annual temperatures derived from actual measurements since about 1900 and extrapolated for 2100. These extrapolations have been computed for different scenarios. The higher bound or the so-called high-emission scenario RCP8.5 resulted in a global temperature rise of about 4°C, compared to the period 1986—2005. The lower bound or the so-called low-emission mitigation scenario RCP2.6 resulted in a global temperature rise of about 1°C, compared to the same period. See graph (a) in Fig. 5.33 for the projected courses of rising temperature in both scenarios and the bounds of those projections. The temperature rise has clearly a structural and global character, despite the regional differences that are indicated on maps (b) in Fig 5.33 [44]. As shown, there is a large margin of error in these projections. This is also one of the points why these projections evoke criticism in skeptical circles. Another such point is that GHG emissions are only about 4% anthropogenic (caused by humans). Major parts of these emissions result from natural processes, like volcano eruptions, and 40% comes from

FIG. 5.33 Global mean temperature rise as result of climate change according to [44]: (a) measured and projected in a low- and high-emission scenario and (b) indication per region in a low- and high-emission scenario.

5.2 HYDRAULIC LOADS

361

the seas, 27% from the vegetation, and 27% from the soil [43]. Therefore, it is questioned by the skeptics whether a change of the anthropogenic 4% of GHG emissions can have a substantial impact on the climate. The controversies surrounding these issues will probably last some time still, but the prevailing opinion is that particularly the anthropogenic emissions of GHG have spectacularly risen in recent decades and should, therefore, be seen as a significant cause of the climate change. Accepting this as a starting premise, hydraulic gate engineers should be concerned about two groups of issues: (1) How to limit the hydraulic project’s own contribution to GHG emissions. This group covers issues of climate-friendly material choice, service life planning, selection of manufacturing and construction methods, maintenance programs and technologies, and demolition techniques. The awareness that all these activities generate GHG emissions will not prevent the climate change yet, but it will contribute to the efforts of other technologies in this matter. These issues come near to sustainable gate design that is discussed further in Chapter 12. (2) How to make hydraulic gates resilient to the climate change and its consequences. That resilience should include continuation of service under the changed conditions, particularly the higher water levels. In several cases, it should also include the extension or modification of that service. For example, gates that currently operate as lock gates may need to be redesigned for combining it with floodgate operation. The issues of gate resilience to the effects of climate change, particularly the sea level rise, are discussed below. An obvious conclusion for managers of waterways and water resources is also that the rising of sea levels and growth of extreme weather conditions will lead to a growing global demand for hydraulic gates. It is, therefore, wise and welcome to invest in the technologies of such gates today and to stimulate the development of knowledge in this field. For hydraulic engineers, however, the most essential questions arise from the second group of issues mentioned above. These questions are as follows: • What exactly are the “climate-proof” design water levels for hydraulic gates? • Which other loads to gates than the differential water head does the climate change bring? • How exactly does climate change additionally affect the gate operation? However justified these questions may be, the answers can only be given by estimation. Regarding the sea level rise, the Intergovernmental Panel on Climate Change (IPCC) report [44] gives estimations based on global measurements recorded in a number of databases. These estimations are indicated by different colors on the left graph (a) in Fig. 5.34. The referred databases come from six different locations spread over the world: Stockholm (Sweden), Charlottetown (Canada), San Francisco (United States), Antofagasta (Chile), Manila (Philippines), and Pago Pago (American Samoa). The graphs representing different databases are aligned to have the same value in 1993, the first year of satellite altimetry data (red color). All lines show the course of mean annual values, with uncertainty margins (where assessed) in colored shading. The graph shows that the global mean sea level rose by 0.19 m at an average in the considered period of 110 years. A closer analysis indicates that while the mean rate of this rise was 1.7 mm/year over this period, past few years (1993— 2010) yielded the mean rate of 3.2 mm/year. However, this is not exceptional, since similar high rates seem to have occurred between 1920 and 1950. It is tempting to associate the latter with the World Wars I and II, but there is no evidence for that. In any case, the rate of 3.2 mm/year can by rough estimation be assumed as the lower bound of global mean sea level rise for the decades to come. Considering the inertia of processes involved, it is not likely that this rate will decrease in foreseeable future, even not by an immediate stabilizing or decrease of global GHG emissions. The projections performed by the IPCC lie in the same range (see the right graph in Fig. 5.34a). They foresee that the global mean see level will rise in this century of about 0.70 m in the high-emission scenario, and of about 0.40 m in the low-emission scenario. Also these projections have, however, large margins of uncertainty. In the absence of other data and when the losses by failure are moderate or low, one can consider choosing the values in the overlap of uncertainty margins for both scenarios. Global rates give a general tendency, but the regional rates may be substantially different. For example, the regional rates of sea level rise in Western Pacific are up to three times larger than the global mean rates, while those for some Eastern Pacific regions are near zero [44]. Another significant regional factor can be the soil subsidence or uplift as result of either natural or also anthropogenic processes. An example of the first is the oxidation of organic soil layers that have been set dry. An example of the latter is the extraction of natural gas. Both of these processes take place in the Netherlands, which increases the concern about sea level rising in that country. Similar concerns are in some regions of the United States, like on the coast of North Carolina where soil subsidence rates are up to 1.5 mm/year, or in New Orleans where soil subsidence is even twice as large [45]. An opposite process, known as “isostatic rebound,” takes

362

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.34 Global mean sea level rise, observed and projected according to Ref. [44]: (a) measured and projected in a low- and high-emission scenario and (b) indication per region in a low- and high-emission scenario.

place in Scandinavia in Europe and in some regions of North America, where the ground rises as result of stress release after the retreat of a glacier. This process can also occur when a glacial lake dries up, like in the Bonneville Salt Flats in Utah, United States. That area is a remnant of the Pleistocene Lake Bonneville and is the largest of many salt flats located west of the Great Salt Lake. It is, therefore, very important to combine the global projections with regional data when assessing the sea level rise for a particular project. When collecting this data, one should above all remain objective and keep an open mind. There are strong emotions surrounding the discussions about climate change, including the sea level rising, which does not help in obtaining reliable, well-founded data. These (partly understandable) emotions tend to reach the highest circles of politics and science. In the Netherlands, for example, this can be pictured by the following controversy: • The Delta Commission that directly reports to the Parliament recommends taking into account a sea level rise of 1.20 m in 2100. This does not include the soil subsidence of 0.10 m. • The country’s leading meteorological institute, KNMI, recommends a sea level rise of 0.85 m in the same year as the worst-case scenario for hydraulic projects. • Studies for the recently constructed large storm surge barriers, like the Maeslant and the Hartel Canal Barrier, resulted in a design sea level rise of 0.50 m in 100 years. Similar controversies around the issue of sea level rising can be observed in other countries, including the United States. As opposition to the voices pleading for action, the entire issue is questioned by other voices. Apart from this controversy, there is a growing conviction on all continents that sea level rising must be taken into account, but the size of it remains disputed.

5.2 HYDRAULIC LOADS

363

FIG. 5.35 Sea level rise projections for Pasquotank County, NC, United States, as for 2017: (a) measured sea level data from three relevant NOAA stations [45] and (b) sea level rise projections by University of North Carolina [46].

An example is the recent study on sea level rise for the Pasquotank County in North Carolina. Such studies make normally use of the sea level measurement data collected and processed by the National Oceanic and Atmospheric Administration (NOAA) at its stations along the US coastline. These data comprise physical and satellite measurements. In the case of Pasquotank County, the nearest stations were the ones named in the headlines of two first graphs in Fig. 5.35a. In addition, the data from other stations were considered, including Sewells Point, VA, due to its long history. The graphs in Fig. 5.35 present the most recent data collected at the time of writing this book; the data used for the discussed study were about 3 years older. Note that particularly the Sewells Point station, due to its long data history, offers a high confidence trend projection for the sea level rise. The analysis of this data, global trends, and other relevant processes resulted in the projections of relative sea level rise for Pasquotank County, as shown in graph (b) in Fig. 5.35. Note that the courses of the three scenarios considered [46], “high,” “medium,” and “low,” show the same or even higher dispersion than the global projections from Fig. 5.34a. This does not make things easy for engineers. The choice between the presented scenarios, including the historical trend, then becomes a political rather than engineering matter, which does not necessarily help solving the problem. Note also that the differences between the scenarios in graph (b) do not result from a random character of processes involved. There is nothing random at stake here. Science only does not know the nature of these processes well enough yet to issue better projections. The dispersion of such projections results, in fact, from human ignorance. The focus for the coming decades should, therefore, lie on narrowing the dispersion margins; not on inventing statistical tools for processing them. One of the means to serve the latter is a continuous collection, analysis, and exchange of data. Many countries utilize well-organized networks for this task. In the United States, the NOAA Tide Gauge Stations have produced systematically collected and processed data for many decades. Fig. 5.36 shows the locations and annual mean sea level rise rates from only those stations that in 2012 had records exceeding 50 years. Comparison of these data with those in Fig. 5.35 shows, for example, that the Sewells Point annual rate rose from 4.42 to 4.59 mm/year in the period of 5 years.

364

FIG. 5.36

5. DESIGN LOADS AND LOAD COMBINATIONS

Sea level rise rates at NOAA Tide Gauge Stations with records exceeding 50 years.

Information of this kind is very valuable for correct estimations of sea level rise rates, as it narrows the dispersion margins mentioned above. It is also important that this information is freely accessible on the Internet. The NOAA records can freely be accessed at the website given in Ref. [45]. This is, unfortunately, not the case in some other coastal regions in the world. Hopefully, the awareness of free data exchange will gradually grow because common problems (Fig. 5.37) require common action. As mentioned earlier, sea level rise is the main but not the only load on hydraulic gates that the climate change brings in. Other loads result from more frequent and more intensive extreme weather conditions like storms, hurricanes, floods, and droughts. However, while the sea level rise can be backed up with figures (approximate as they are), no scientifically clarified estimates for the other loads have so far been presented. Therefore, they cannot be handled in this book yet. Interested professionals and students are encouraged to follow prospective research in this matter. Finally, there is also good news regarding the predictability of loads from climate change: We certainly know that they will not occur next week or at any other time in the nearest future. This sounds trivial, but it is an essential difference that distinguishes these loads from nearly all other hydraulic loads on gates. After all, these loads act or can act

FIG. 5.37

Flooding by seawater in: (a) Norfolk City, VA, United States, 1962 and (b) Ho-Chi-Minh City, Vietnam, 2001. Photos (a) APWA, Norfolk, VA, (b) Trinh Cong Van.

5.3 SELF-WEIGHT LOADS

FIG. 5.38

365

Climate change and other hydraulic loads in time (service life figures exemplary).

on hydraulic structures at every moment. The probabilistic consequence of this difference has schematically been pictured in Fig. 5.38. Let us presume, for simplicity, that the gate resistance R and its mean value R do not change during the service life and that the loads from climate change grow linearly. Note that while the other hydraulic loads are then—in essence— time independent and result in the same safety level throughout the entire service life of the gate, the loads from climate change grow from zero to their maximal acceptable value that commonly coincides with the end of that service life. This means that they contribute to the gate probability of failure, defined in Eq. (5.3) as pf ¼ probðR  Q  0Þ

(5.61)

only in the last phase of the service life. This pf is, however, expressed by the reliability index β (see Table 5.2) under the assumption that time has no limiting effect on loads. Since in our case it has, we can allow a lower β to compensate for that. The gate will then comply with the required reliability index with respect to its whole service life, but the probability of failure will be lower at the beginning and higher at the end of it. In other words, the design codes allow taking lower loads from climate change (including the sea level rise) into account than the loads projected at the end of the service life. The question “How much lower?” should be answered after the analysis of local projections, but by engineering judgment the factor of ⅔ (67% of these projections) looks like a safe assumption. This is the “good news.” The “bad news” is that exchanging or additional reinforcing of the gate becomes a necessity at the end of its design service life, even when the gate condition still seems satisfactory. The loads caused by climate change will, after all, continue to grow. See the top graph with Q and R distributions on the climate change load line in Fig. 5.38.

5.3 SELF-WEIGHT LOADS 5.3.1 Self-Weight Load Components The term “self-weight loads” covers in this book all those loads that the ASCE 7 standard refers to as “dead loads” [21]; and the Eurocodes EN 1990 and EN 1991 refer to as “permanent fixed action” [5]. Both the ASCE 7 standard and the Eurocodes primarily refers to buildings. Nevertheless, the definition of “dead loads” by the ASCE 7 can serve as an example to define the self-weight loads for hydraulic gates in nearly the same way:

366

5. DESIGN LOADS AND LOAD COMBINATIONS

Self-weight loads consist of the weight of all materials of construction incorporated into the hydraulic gate including, but not limited to, its retaining wall, framing, possible drive arms, struts, rollers, wheels or other fixed guiding, fenders, air chambers, coating and other similarly incorporated architectural and structural items; and fixed service equipment including the weight of drive and control devices.

There are two reasons for choosing the term “self-weight” rather than “dead load” in this book: • Unlike a building, hydraulic gate is a movable structure. The position and direction of its self-weight is often (not always) fixed with respect to the gate itself, but not with respect to its supports and the surrounding. This gives less of a reason to call it “dead load.” • The term “dead load” is not as broadly used as “self-weight” and does not, for example, appear in the Eurocodes. This book aims at a broad international audience. For the same reasons (and to avoid confusion with other variables like depth and diameter), the self-weight loads are denoted by a symbol G in this book, and not D as in Ref. [21]. The above definition of self-weight loads also says which loads do not belong to this group. Apart from obvious cases, self-weight loads do not include buoyancy and ballast loads. Buoyancy and ballast by water, irrespective of whether or not applied intentionally, are in fact hydraulic loads, as discussed in Section 5.2.2.4. A convenient way to classify the ballast by other means than water is according to the fixity criterion. Fixed ballast makes them part of the self-weight load; adjustable ballast is a separate variable load. This should not restrain the designer from classifying ballast in a way that best suits the intended gate operation, as long as this is clearly documented. Other loads that normally are not considered as self-weight are the loads by glaze ice and sediment. These loads are discussed in more detail in Section 5.6. Also in this case, however, it can be convenient to quantify such loads as a percentage of self-weight loads, based on the data confirmed by field observations or other sources. The main item of the gate self-weight is normally the weight of its structure. In the case of structural steel gates, this weight is usually determined from global quantities (preliminary design) or bills of materials (final design). If the bills of materials are based on shop drawings, a 1.5%–2.0% allowance for welds and coating is often taken into account. In the design stage, however, that percentage is usually higher and includes some roundup for safety. For example, The Dalles Lock miter gates, discussed in Chapter 8, were computed with a 3.0%–5.0% weight allowance for welds and coating.

5.3.2 Favorable and Unfavorable Action The effect of self-weight loads can be both unfavorable and favorable. In the first case it decreases the gate safety (in the sense of reliability index β, see Section 5.1.2) and in the second case it increases it. For example, self-weight of a rolling gate has an unfavorable effect on its wheel and rail loads but a favorable effect on the gate stability during movement. Existing design codes cover this by introducing different load factors γ G for both situations. Among the most frequently used codes in this field are the Eurocode [5] and the American ASCE 7 standard [21]. As mentioned above, the first refers to self-weight loads as “permanent actions” and the second as “dead loads.” In addition, the European and American codes for bridge design can be consulted. When combined with live loads, the characteristic values Gk of self-weight loads should be multiplied by the γ G factors indicated in Table 5.4 to obtain the design values G. The factored self-weight values of G can directly be combined with live loads for further structural analysis of the gate. At the time of writing this book, the γ G factors are the same for favorable effects but not for unfavorable effects in Europe and in the United States. For the latter, the US codes prescribe a slightly higher γ G or further differentiate it.

TABLE 5.4

Load Factor γ for Permanent Actions (EU) or Dead Loads (US) in Load Combinations Load factor γ G

Region

Field

Code

Unfavorable effect

Favorable effect

Europe (EU)

General and buildings

EN 1990 (2002)

1.10

0.90

ASCE/SEI 7 (2005)

1.20

0.90

EN 1993-2 (2011)

min. 1.35a

0.90

AASHTO LRFD (2012)

1.25–1.50b

0.90

America (US) Europe (EU) America (US) a b

Bridges

Eurocode 3 leaves this to national annexes. Factors 1.35 and 1.00 come from the Dutch national annex. 1.25 for components and attachments; 1.50 for very high ( about 7.0) dead load to life load ratios.

367

5.3 SELF-WEIGHT LOADS

As all these codes are legally binding in, respectively, the European Union and the United States, the readers are advised to follow their regional legislation. Note that classifying the self-weight load as “unfavorable” or “favorable” does not have an absolute character. It depends on both the limit state and the load combination considered. The same self-weight load can act favorably in one case and unfavorably in the other. The designer must correctly assess it each time before continuing the analysis. On the other hand, common sense is also welcome in order not to drive this distinction to an absurd degree. It would, for example, be exaggerated to compute the ballast water in the caisson in Fig. 5.39 with low γ on the upstream side, and high γ on the downstream side when assessing the stability against overturning. A uniform γ ¼ 0.90 is here the best assumption, because the caisson ballast water has a favorable overall effect.

5.3.3 Weight Control As pointed out in the introduction to this book, hydraulic gates assume varying supporting conditions and are subject to many load combinations during their service life. Self-weight makes part of all these combinations and contributes either to the safety or to the failure of the gate. It is, therefore, important to have a correct and precise data of this self-weight. Such data should at least include: • global self-weight figure, and • location of center of gravity ( CoG). The importance of these data increases as construction projects become more and more international and globalized. An example is the rolling gates and culvert sluices of the new Panama Canal Locks that have been designed in the Netherlands with contributions from several other countries, constructed in Italy and Korea, and shipped to Panama over the Atlantic (gates) and Pacific (sluices). Fig. 5.40 shows one of the gate shipments on its departure from Italy and arrival in Panama. More details about these shipments can be found in Refs. [47, 48]. The gate structural system and the most essential details of its structure are discussed in, respectively, Chapters 3 and 8. It should not surprise that such an operation requires very reliable data about the gate self-weight and the location of its CoG. Therefore, it is recommended that these data are not only compiled from the design documents (like bills of materials) but also confirmed by physical weighing, sometimes at various stages of construction. Such an approach is called weight control. The procedures and techniques of physical weighing have for large structures been developed in the offshore industry. It became a standard approach in that field that structures like oil or gas platforms were entirely assembled on the mainland and then shipped to their locations at sea. Such shipments were usually carried out with the complete equipment installed, so that the shipped platform was a turnkey facility. After all, construction and installation activities at FIG. 5.39

Caisson gate in the old KielHoltenau Lock, Germany. Photo WSA KielHoltenau.

368

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.40 Departure (a) and arrival (b) of the new Panama Canal lock gates in 2014. Photos ACP.

remote offshore locations are expensive and less safe. Physical weighing offered reliable and accurate data to reduce risks when engineering such shipments. The weight control procedure of, for example, the 8500 tons heavy Oseberg 2 platform of Norsk Hydro (Fig. 5.41) included nine physical weighings aimed at verifying the calculated weight of all decks, devices, and materials installed at various stages of construction [49]. Hydraulic gates are normally not that heavy and stuffed with expensive equipment. The heaviest gates of the new Panama Canal locks weigh 4325 tons (see Table 3.22), which is about the half of the oil production platform shown in Fig. 5.41. Yet, the interests and risks in support of weight control are comparable. One should particularly keep in mind that hydraulic gates, like offshore platforms, require regular maintenance and repair, which is preferably performed in docks or construction yards on mainland, often at distant overseas locations. The handlings involved are then basically the same as during the first installation. They include various support and transport positions, hoisting, tilting, roll-in and roll-out movements. They can also include sea fastening and ballasting or setting afloat. Figs. 5.42 and 5.43 show some (not all) installation and deinstallation positions for two large hydraulic gates that are presented in detail in Chapter 8. Note that reliable data of the gate self-weight and CoG location are absolute conditions to correctly design and control the pictured procedures. This is the first reason why a correct weight database should make part of the gate documentation handed over to the owner upon the project completion. Another reason is to locate lifting lugs relative to the actual centroid, to ensure that the structure hangs plumb. Yet another reason is to enable keeping track of the gate self-weight and CoG location in the case of reinforcements or other modifications in the future.

FIG. 5.41 Norsk Hydro Oseberg oil production platform, North Sea/Norway. (Note: The described weighing included only the superstructure.) Photo Lars Grepstad.

FIG. 5.42 Some installation positions of The Dalles Lock gate in the Columbia River, WA/OR, United States: (a) roll-out of a constructed gate from manufacturer’s hall by Thompson Metal; (b) gate tilting before hoisting for installation; and (c) both gate leaves installed in the lock chamber. Photos by Travis Adams, USACE.

FIG. 5.43 Some installation positions of the Hartel Canal Barrier gates, the Netherlands: (a) Hartel Canal Barrier with gates lifted, Southern Gate on the foreground; (b) gate suspension to marine cranes for (de)installation and sidewalking; and (c) gate in position for a new coating at Hollandia BV in Krimpen a/d IJssel near Rotterdam.

370

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.44 Choice of gate suspension eccentricity in the project of Hartel Canal Barrier: (a) Southern Gate self-weight and CoG location; (b) relation between suspension eccentricities and wind velocities at which the gates come free from some of their lateral supports; and (c) Northern Gate self-weight and CoG location.

There are still other reasons for a thorough weight control, depending on the type of the gate. One of them is illustrated in Fig. 5.44 that shows how the suspension eccentricities of the vertical lift gates shown in Fig. 5.43a have been determined [50]. These gates are constructed without expanding devices, and slide between the guiding tracks in lifting towers with a certain nominal clearance, in this case 50 mm. In order to prevent lateral motions (“fluttering”) of the gates under windblasts, the following boundary conditions were considered: • The gate centres of gravity (CoG) should be at some distances eSG and eNG from the suspension plane. The resulting overturning moment should then produce lateral compressive reactions against the guiding tracks, which should prevent the fluttering. • Those lateral reactions had to be small enough not to produce local viscoelastic indentation in the UHMPE guiding tracks of the gates. Such indentations would have put the gate operation at risk. Large overturning moment was also undesired for other reasons. To choose the optimal eSG and eNG, a graph was computed showing the combinations of CoG eccentricities and wind velocities at which the fluttering actually began (see diagram (b) in Fig. 5.44). The wind pressure on gates was determined using the formulas from design codes of that time, similar to those in the Eurocode EN-1991 and the ASCE 7 of today. The CoG distances from the common centerline for both gates, as computed from the design weight databases, were 850 mm for the Southern Gate and 150 mm for the Northern Gate, both to the west. Under these conditions, the most convenient choice was to maintain the same suspension plane for both gates and to let it run in the middle between their CoG’s. The resulting eccentricities were eSG ¼ eNG ¼

1  ð850  150Þ ¼ 350mm 2

These eccentricities generate overturning moments acting in opposite directions, but in both cases care is taken that the gate does not flutter at wind velocities up to 22–24 m/s, which is Beaufort wind force 9. The physical weighing showed some deviations from the computed CoG locations. Taking these deviations into account, as well as the margin of error in the formula for wind pressure, allowed for saying that none of the gates would show any motion at Beaufort wind force lower than 8. This was considered acceptable.

5.4 LOADS FROM GATE DRIVE SYSTEMS 5.4.1 Gate Drive Linkages Loads from drive machinery are basically point loads such as a direct connected hydraulic cylinder on a miter gate or a strut arm connection to a miter gate. This section discusses the magnitude of these loads and also how the various types of mechanical drives transfer force into a hydraulic gate. A complete discussion of the different mechanical drive systems for hydraulic gates is provided in Chapter 11. An example discussion for a miter gate drive system is provided in this section since the miter gate is the most frequently used gate on navigation locks. A drive system for a rolling gate

371

5.4 LOADS FROM GATE DRIVE SYSTEMS

3 1

Pintle C L

3 1 180°

~L/4

L

Pintle C L 1

164°12′

Pintle C L

3L/Ö10

L

~L/3

L

Pintle C L

3

~L/4

~L/3

3

~0.25L

3L/Ö10

1

L 3

~L/2.5

~L/3 Pintle C L

~0.20L

3L/Ö10

0.3333L 0.1830L

(c) Pintle C L

~0.20L

Gear + Arm

Chamber C L

142°05′

0.3333L 0.1943L

(b) Pintle C L

(a)

L

Chamber C L

201°48′

Gear

L

0.4333L

Gear + Arm

163°55′

0.1803L

L

Pintle C L

Chamber C L

1

3L/Ö10 L/3

L

Pintle C L

3

180°

Pintle C L

L/3

L

0.1783L

3L/Ö10

0.255L

L/3 Pintle C L L/3

0.181L

3L/Ö10

0.260L

0.2535L

Pintle C L

or a vertical lift gate would have similar considerations. The determination of drive loads requires an analysis of the gate forces for the full range of gate travel. For example, on a rolling gate an analysis of drive forces should be done for the gate travel from the recess position to the closed position and then back again into recess. A miter gate drive would be similar. It is important to understand how drive machinery transfers force into a miter gate or any hydraulic gate for that matter. On a miter gate, a linkage including a strut provides the connection between the drive system and the gate itself. The strut force is what is of interest in determining the gate drive load. Mechanical linkages traditionally have been utilized to open and close miter gates. The majority of the lock sites in the United States built in the 1930s on the Mississippi and Ohio Rivers used mechanical linkages. So did the European locks with miter gates built in the first half of the 20th century. Recently, direct-connected hydraulic cylinders have become more prevalent and are used at both new locks and for the rehabilitation of existing locks both in the United States and in Europe. Three different types of miter gate mechanical operating linkages have traditionally been used. These systems are discussed in USACE engineering manual [51]. The linkages include the Panama Canal linkage, the Ohio River linkage, and the modified Ohio River linkage. In Europe, a direct rack-and-pinion linkage is still frequently used, usually with a straight rack. In small locks, however, circular racks can also be encountered (see example in Fig. 5.46d). A direct-connected hydraulic cylinder is also considered a linkage in the sense that it provides the connection between the drive system and the miter gate leaves. A direct-connected cylinder linkage consists of a hydraulic cylinder connected on or behind the lock wall, and a rod connected to a pin on the gate. The piston force is transmitted directly from the piston rod to the gate. An indirect linkage is, however, possible too. In that case, the piston rod is connected to a drive arm fixed to the gate leave. We will call this a “Naviduct linkage.” The Naviduct gates, discussed in more detail in Chapter 3, were not the first that utilized it but they specifically benefited from its advantages. The types of miter gate linkages discussed are schematically presented in Fig. 5.45. All the dimensions in this figure are related to the length L of a gate leaf. In the case of the Panama and Ohio River linkages, this relation has been

1

(d)

(e)

Chamber C L

Hydraulic cylinder

L

Chamber C L

Hydraulic cylinder

L

Chamber C L

Pinion

L

Rack

(f)

FIG. 5.45 Typical drive linkages to miter gates: (a) Panama Canal linkage; (b) Ohio River linkage; (c) modified Ohio River linkage; (d) rack-andpinion linkage with a spring buffer; (e) direct hydraulic cylinder linkage; and (f) indirect hydraulic cylinder linkage (Naviduct type).

372

5. DESIGN LOADS AND LOAD COMBINATIONS

derived from the USACE manual [51] and should be considered as relatively accurate for strut connections at L/3 from the leaf rotation axis. Other linkages offer more dimensional flexibility. The dimensional relations are in those cases only indicative, which is marked as “ .” Mechanical linkages include strut connection to the gate itself, often equipped with spring buffers to minimize shock loading to the gate. One can see that the US experience in this field is also followed in other countries (Fig 5.46). The principal difference between the three mechanical linkages mentioned above is the angularity of the connecting strut and sector arm at the extremities of gate travel. The modified Ohio River linkage has angularity between the strut and sector arms at the open (recessed) position only. The Panama linkage has no angularity at either the open or the closed (mitered) position, and the Ohio River linkage has angularity at both the open and closed positions. The Panama Canal linkage permits the gate to be uniformly accelerated from rest to the midpoint of its travel, than uniformly decelerated through the remainder of its travel, thus eliminating the need for motor speed control. This was an advantage before advances in motor speed control. This advantage is accomplished by locating the operating arm and strut on dead center when the gate leaf is in both the open and closed positions. The strut must be at a higher level than the sector arm to pass over the arm and become aligned for the dead center position when the gate is fully open. This eccentric connection is shown in Fig. 5.47 at Dresden Lock on the Illinois Waterway (a) and Kornwerderzand Lock in the Netherlands (b). The strut passes over the top of the sector gear. The kinematics of the operating cycle are such that the elimination of all angularity between the strut and sector arm reduces the velocity of gate movement near the limits of gate travel for uniform rate of movement (constant travel) of the operating machinery. This, in turn, reduces the peak loads on the operating machinery. The traditional Ohio River drive utilizes a hydraulic cylinder driving a rack gear, which subsequently drives a sector gear, the sector arm, and gate strut (Fig. 5.48a). With this configuration, load analysis for all components is possible. Overloads due to surges or obstructions are carried through the piston and converted to oil pressure, which is released

FIG. 5.46 Strut connections to miter gates: (a) lock 2 on the Mississippi River, United States; (b) Bonneville Lock on the Columbia River, United States; (c) Gezhouba Lock on the Yangtze River, China; and (d) small canal lock in Hekendorp, the Netherlands. Photos USACE, EP and RADAR Structural.

5.4 LOADS FROM GATE DRIVE SYSTEMS

373

FIG. 5.47 Panama Canal linkage to miter gates in the United States and the Netherlands: (a) Dresden Lock on the Illinois River and (b) Kornwerderzand Locks in the Afsluitdijk.

FIG. 5.48 Ohio River linkage to miter gates in United States: (a) Ohio River linkage with toothed rack gear, Ohio River Lock 52 and (b) modified Ohio River linkage with raised machinery, Mississippi River Lock 2.

through a relief valve. In this way, all machinery component loads can be determined based on the relief valve setting. The Ohio River linkage offers several advantages because of its unique geometric configuration relating to the acceleration and deceleration of the miter gates. Many Ohio River linkage designs today, however, utilize a motor and gear drive in lieu of the hydraulic cylinder and rack gear. The modified Ohio River linkage is similar to the Panama type except that the dead center alignment is obtained only when the gate is in the mitered (fully closed) position. Again, there is no angularity between the strut and the sector arm at the mitered position. With the modified Ohio River linkage, the strut and sector gear are at the same elevation, thus eliminating the eccentric strut connection and preventing the linkage from attaining the dead center position with the gate recessed. Special consideration needs to be given to the strut length, which becomes critical at the gate-closed position (mitered). Generally, some means of adjusting the strut length needs to be provided to ensure that the gate leaves are mitered when the sector arm and strut are fully extended. If the gate does not fully miter at this point, additional travel provided by the cylinder or motor will pull the leaves farther apart. As the gate leaf in this linkage approaches the mitered position, the sector arm, and strut move near the dead center. Should an obstruction be encountered at this time, the force in the strut becomes indeterminate. The modified Ohio River linkage does, however, provide restraint against conditions of reverse water head in the dead center position. The direct-connected linkage consists of a hydraulic cylinder supported in the miter gate machine room by a trunnion and cardanic ring (or so-called “gimbal”). The cylinder rod is connected directly to the miter gate, either with a spherical bearing-type clevis (Fig. 5.49a) or with two orthogonal pivots (Fig. 5.49b). The linkage kinematics is not mechanically determined; it requires that the acceleration of the gate be controlled using an oil pump of variable volumetric flow. The piston rod is dimensioned by the bending and buckling load criteria and needs to be designed as a strut. The maximum pressure of the system can be controlled with a pressure relief valve. To some degree, the hydraulic system also acts like a shock absorber to absorb any shock loads when moving the gate. This is possible thanks to a

374

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.49 Direct drive linkage by a hydraulic cylinder: (a) Mississippi River, Lock 1 at Minneapolis, MN and (b) Born Lock in Juliana Canal, the Netherlands. Photos (a) USACE, (b) Rijkswaterstaat.

certain compressibility of hydrocarbon-based hydraulic fluids (about 0.5%–0.7% of volume per 100 bar or 1450 psi) and the elasticity of the system.

5.4.2 Gate Drive Loads There will always be inertial forces to overcome in moving hydraulic gates. As such, a hydraulic gate should always be moved initially using the slowest speed possible. Once the gate moves, the drive speed can be increased. Shock loads such as obstacles and impact from debris or a vessel have to be considered. Spring-type miter gate struts commonly used with the Ohio River and modified Ohio River linkages help manage this issue. Springs built into the strut assembly act as a shock absorber to damp the loads transmitted to the operating machinery. In the case of electric motor operated machines, the compression in the springs permits the operation of a limit switch to cut off the current to the motor when the gate leaves are mitered or recessed. This switch also serves as a torque limit switch to protect the machinery against the extremely high loads that might occur if an obstruction is encountered when the strut approaches dead center in either direction. In addition, gate drive loads have to overcome the forces from friction (such as on pintles of miter gates, sector gates, or wheels of rolling gates), wind loads, surges, hydraulic drag forces, and head differential created by the gate moving through the water. This is common for all types of hydraulic gates on a navigation lock. For a miter gate drive, it is of interest to determine the required torque to move the gate about its rotation axis. The miter gate drive loads can be determined in several ways. The two most frequently practiced ways are as follows: • Analytically from the condition of gate movement against a small differential head. • Assisted by the results of physical model (and/or prototype) investigations. The first approach is more direct and issues the drive machinery that can certainly operate against a temporal head. It also often ends up being the governing case over the torques computed using physical model investigations. The advantage of the second approach is a better insight into the entire course of drive load variation during opening and closing of the gate. European designers commonly use the first way. It is also described in the USACE technical report [52]. A small differential head (depending on gate type and size, see Section 5.4.3) is, however, not the only load that determines the design drive forces. A number of load combinations are considered for this reason. The Dutch design manual [14] distinguishes 22 such combinations. The variable loads that should be included in these combinations are as follows: • • • • • •

maximum reverse head if physically possible; wind-induced wave; direct wind load on gate; translation wave or seiche; wave induced by passing ship; silt, ice, and debris loads;

375

5.4 LOADS FROM GATE DRIVE SYSTEMS

• • • • • • • •

gravity loads if vertically moved; residual water head (0.10–0.30 m); inertial load by attached water masses; load by current if expected; response of water in gate recess; inertial load by gate mass; friction in gate hinges, tracks, and guiding; and response of buffers, fenders etc.

In miter gate projects, American designers usually refer to the results of physical model investigations by the USACE WES [53]. The model tests conducted by the WES utilized a 1:20 scale model of a 33.5-m wide lock, typical of many US waterways. The testing method is discussed in detail in Chapter 7. The test results provide the torque required to move the miter gate about its pintle. Although the testing was done 50 years ago, the results compare favorably to multiple “real-world” examples in the United States. They also form the base of the current design practice, as recommended by the USACE engineering manuals [51]. The referred testing showed the peak hydraulic resistance to operation of the miter gate as the leaves entered the mitered position, which indicates that head differential on the two sides of a gate leaf is the primary cause of loads on the operating machinery. The same WES testing showed approximately equal peak resistances in terms of torques for the Panama and modified Ohio River linkages; and an about 40% higher peak resistance for the Ohio River linkage. Other conclusions from the testing (some partly intuitive) were as follows: • An increase in submergence of the gate leaves or increased speed of operation results in increased hydraulic resistance. • Closing forces (going into miter) are higher than opening forces (going into recess). • Hydraulic resistance increases as the bottom clearance of the gate leaves is decreased. • Hydraulic resistance decreases as the length of the lock chamber is increased. • Nonsynchronous operation of the gate leaves results in a slight reduction in peak torque. The relation between hydraulic resistance, expressed by the maximum torque recorded, and the gate submergence could further be estimated for the three types of mechanical linkages shown in Fig. 5.45. This relation is illustrated in Table 5.5 [53]: When using data from the model tests, it is necessary to adjust the data on the basis of the scalar ratios between the model and the proposed lock. The most essential of these scalar ratios is the length ratio LR of the prototype L1 to model L miter gate leaf. From this ratio, Froude’s law of similarity [52] gives the following relations between prototype or actual gate and the model: L1 LR ¼ L Volume, weight, and force: (LR)3: 1 Time and velocity: (LR)½ : 1 Torque: (LR)4: 1. Other parameters to be scaled include: gate submergence, time of operation, arc of gate travel, and the resulting torque about pintle. Table 5.6 presents the summary of all scalar ratios involved. This summary was used in the project of new machinery for the Upper Mississippi River Locks 2 through 10. The drive load calculation for this project is provided below as an example.

TABLE 5.5 Variation of Maximum Torque Required to Move a Miter Gate With the Gate Submergence Variation of maximum torque with gate submergence Torque peak position

Panama-type linkage

Ohio River linkage

Modified Ohio linkage

Closing (mitering)

1.5 power of submergence

1.5 power of submergence

1.9 power of submergence

Opening (recessing)

1.7 power of submergence

2.1 power of submergence

2.2 power of submergence

376 TABLE 5.6

5. DESIGN LOADS AND LOAD COMBINATIONS

Summary of Scalar Ratios Used in Mississippi River Lock Machinery Calculations

Parameter

WES model value according to [53]

Actual value of lock miter gate

Scalar ratio

Length of gate

L

L1

L1/L

Submergence

S & S2

S1

S1/S

Time of operation

T & T2

T1

T1/T

Arc of gate travel

K

K1

K1/K

Pintle torque

P

P1

P1/P

Here: P1, torque about pintle of proposed lock gate at selected position; P, torque about pintle shown on the curve of model study at selected position; L1, gate leaf length, pintle to miter end for proposed lock gates; L, gate leaf length, pintle to miter end for curves that have been plotted on model study; S1, submergence of proposed lock gate; S, actual submergence of model gate upon which curves are based; S2, adjusted submergence of model lock gate ¼ S(L1/L); T, actual time of operation of model gate upon which curves are based; T1, time of operation of proposed lock gate; T2, adjusted time of operation of model lock gate ¼ T(L1/L)½.

If the arc of travel of the proposed gate differs from that of the model gate, it will be necessary to adjust the operating time T1. In the case of the Upper Mississippi River gates and the physical model, the arc of travel was the same at 71.56 degrees so no adjustment was necessary. The adjusted operating time is noted by TA and equals TA ¼ adjusted operating time ¼ T1 (K1/K) The USACE manual [51] also notes that when using the Ohio Riven type linkages and torque data from Ref. [53], the pintle torque P1 should be adjusted for the under gate clearance in addition to submergence and time. To accomplish this, a bottom effects factor (BEF) was introduced. The required pintle torque is then calculated as follows by multiplying all the applicable correction factors together:  4  x  y L1 S1 T1 P1 ¼ P     BEF (5.62) L S2 T2 where: x ¼ power to which submergence must be raised for particular type linkage (see Table 5.5); y ¼ power to which time must be raised for particular type linkage, 1.0 for Ohio Linkage; BEF ¼ 1.35 for opening; BEF ¼ 1.38 for closing. The gate drive load calculations for the Upper Mississippi River Locks 2 through 10 included sector gear, sector arm, strut, and pintle torque forces. Of particular interest is now the strut force which is the drive load on the gate. Operating forces are extracted from actual data in a spreadsheet and presented in Table 5.7. These forces vary depending on whether the gate is opening (going into recess) or closing (going into miter). Gate drive loads are two to three times greater for the gate closing condition than for the gate opening condition. The loads are normally highest when the gate is approaching the miter. Note that 73 kips (325 kN) was the highest strut force in this case as the gate approached miter. At this moment, the machinery switched to slow speed and the force dropped. This is consistent with the physical model tests conducted by WES [53]. The measured model forces were adjusted using the scalar ratios in a way as described above. The linkage had a 164 degrees between the strut and the sector arm at the mitered position; hence the analysis was done assuming an Ohio River linkage (see Fig. 5.45b). The miter gates are designed to open or close in approximately 90 s. Each miter gate leaf weighs between 70 and 90 tons depending on the height. Gate heights range from 6 to 9 m and the gate lengths are all 18.4 m. The width of all the lock chambers is 33.5 m. To minimize the operating forces at start-up and when going into miter, the gate is then operated at slow speed. The machinery allows two operating speeds. Some different considerations apply when calculating miter gate drive loads from the direct connected strut or cylinder (see schemes (d) and (e) in Fig. 5.45). In order to minimize the piston length, the cylinder often needs to be connected closer to the gate leaf rotation axis compared to the strut linkage in schemes (a) through (c). This will require the gate pin connection to be located at distance of 20%–25% of the leaf length from the rotation axis; and the cylinder gimbal bracket to be positioned in such a way that it gives the best effective operating arm at each position throughout the entire stroke of the piston. As that arm is now lower, the forces into the gate need to be higher to compensate for the

377

5.4 LOADS FROM GATE DRIVE SYSTEMS

TABLE 5.7 Report [52])

Calculation of Operating Drive Loads for Mississippi River Lock Gate Machinery, Excerpt (According to USACE WES

Mississippi, Lock 5 – closing – normal pool Conditions:

Position (% mitered)

Reduction

2781

Gate bottom’s elevation

642.00

High speed slip

8.00%

Pool water elevation

660.00

Low speed slip

12.00%

Bottom effects factor

1.38

Time (s)

91.25

Effective submergence

18.00

W.E.S. torque about pintle (lb-ft)

Correction factor

Torque about pintle (lb-ft)

Effective arm about pintle (ft)

Force in strut (kips)

Effective arm about sector (ft)

0.0%

0

11484.3

0.0

20.00

0.00

4.45

1.2%

75

11484.3

861322.8

20.00

43.07

4.55

2.5%

35

11484.3

401950.6

20.00

20.10

4.70

5.0%

10

48025.3

480252.7

20.00

24.01

5.10

10.0%

7

48025.3

336176.9

20.00

16.81

5.80

20.0%

7

48025.3

336176.9

20.00

16.81

7.20

30.0%

7

48025.3

336176.9

20.00

16.81

8.50

35.0%

8

48025.3

384202.2

20.00

19.21

9.10

40.0%

8

48025.3

384202.2

20.00

19.21

9.75

45.0%

8

48025.3

384202.2

20.00

19.21

10.20

50.0%

9

48025.3

432227.4

20.00

21.61

10.40

55.0%

9

48025.3

432227.4

19.70

21.94

10.80

60.0%

10

48025.3

480252.7

19.50

24.63

10.83

65.0%

11

48025.3

528278.0

19.25

27.44

10.50

70.0%

12

48025.3

576303.2

18.70

30.82

10.25

75.0%

14

48025.3

672353.8

18.50

36.34

9.65

80.0%

16

48025.3

768404.3

17.60

43.66

8.75

85.0%

19.5

48025.3

936492.8

16.70

56.08

7.75

90.0%

24

48025.3

1152606.5

15.75

73.18

6.50

95.0%

29

11484.3

333044.8

14.70

22.66

4.75

97.5%

35

11484.3

401950.6

14.00

28.71

3.75

98.7%

37.5

11484.3

430661.4

13.60

31.67

3.25

100.0%

40

11484.3

459372.2

13.25

34.67

2.83

Recessed

Mitered

torque loss. If this linkage was used with a uniform traveling piston or rack, gate angular velocity would have been greatest at the extreme closed and open position. Therefore, speed reduction in these positions and additional shock absorption are of even higher importance than in schemes (a) through (c). For direct-connected hydraulic cylinders, USACE conducted prototype tests at Claiborne Locks on the Alabama River, giving ground to design guidance provided in Ref. [51]. A curve of drive torque plotted against percentage of gate closure was included so that torque at any submergence or time of operation can be computed by application of Froude’s law, adjusting the submergence and time to suit the new conditions. Operating oil pressures are typically 6.2–20.7 MPa (900–3000 psi). The time of gate operation automatically will be lengthened when the required gate torque exceeds the available gate torque from the machinery. This condition may occur during starting peaks or in

378

5. DESIGN LOADS AND LOAD COMBINATIONS

periods of higher submergence. It causes the pressure in the hydraulic cylinder to rise above the relief valve setting, which in turn reduces oil flow to the cylinder, slowing down the gate and limiting the pintle torque. At the time of writing this book, a new Chickamauga Lock that will utilize hydraulic cylinders directly connected to miter gates is being constructed on the Tennessee River, United States. The cylinder design was based on the Claiborne Lock model. The locations of the cylinder connection points were optimized based on the following three factors, in order of significance: • minimizing the maximum force on the piston rod; • minimizing the stroke length; and • minimizing the horizontal movement of the cylinder. The cylinder connection point to the gate leaf will be 3.6 m from the rotation axis. A total of 500 combinations of this connection point and cylinder trunnion coordinates were evaluated. The optimized solution results in a cylinder connection to the gate at 3.31 m from the pintle axis, maximum required force in the piston rod of 384 kN, maximum extended cylinder length of 7.4 m, and a total length of cylinder stroke of 4.3 m. The variation of cylinder forces during gate movement is shown in Fig. 5.50 in kips. Note that the graph for “closing” in this figure shows narrow similarities with the spreadsheet data for the gate drives of Mississippi Lock 5 presented in Table 5.7.

5.4.3 Residual Water Head For a hydraulic gate in a lock chamber, sometimes it takes a significant amount of time to bring water on both sides of the gate to the same level when filling and emptying the chamber. Bringing this water to exactly the same level can even be considered impossible, since there is nearly no differential water head to induce gravitational flow at the very end of filling or emptying. Therefore, hydraulic closures of navigation locks, shipyard docks, and the like are operated with a small residual water head to speed up the vessel transit time. Another process that can generate a small differential water head on a gate is the gate motion. This particularly occurs in gate types like miter gates or single-leaf (swing) gates, of which the movement brings large masses of water in motion. The inertia of these masses results in a slightly higher level of water on the side toward which the gate moves than on the opposite side. The difference between this phenomenon and the residual water head mentioned above is that it takes place over the whole distance of gate travel, and not only in the first stage of gate opening. Nevertheless, the resulting load is of a similar character, which is why we also refer to it as a “residual water head.” Some types of hydraulic closures can handle high, some low, and some nearly no residual water heads during motion. This property has been assessed in the summaries of advantages and disadvantages of diverse gate types in Chapter 3. A miter gate, for example, does not perform well in this view, while a vertically hinged sector gate can easily be opened under water head and closed under flow. In Table 5.8, diverse gate types discussed in 80 70 Force in (kips) (1 kip = 4.448 kN)

FIG. 5.50 Variation of cylinder force during gate movement in the New Chickamagua Lock [71]. Drawn after USACE: Chickamagua Lock Replacement Project, Lock Chamber Plans and Specifications, design documentation report, USACE Nashville District, May 2017.

60 50 40 Opening 30 20 Closing 10 0

0

10

20

30

40

50

60

% of opening

70

80

90

100

379

5.4 LOADS FROM GATE DRIVE SYSTEMS

TABLE 5.8

Classification of Gate Types in Regard to Fitness for Residual Water Heads Gate fitness for carrying residual water heads Δh while in motion

Very low

Fair

High

Operative: Δh  0.05 m Extreme: Δh  0.15 m

Operative: Δh  0.30 m Extreme: Δh  0.60 m

Operative: Δh  1.50 m Extreme: Δh  4.00 m

Miter gate, regular

Vertical lift gate, single-leaf

Hinged crest gate

Single-leaf (swing) gate

Vertical lift gate, multi-leaf

Horizontally hinged sector gate

Barge gate

Top hinged flap gate

Drum and roller gate

Dock caisson

Diverse irrigation gates

Rotary segment gate

Stack-up gate

Miter gate for reversible flow

Vertical lift culvert valve

Low

Moderate

Unlimited

Operative: Δh  0.15 m Extreme: Δh  0.30 m

Operative: Δh  0.60 m Extreme: Δh  1.50 m

Operative: Δh unlimited Extreme: Δh unlimited

Rolling gate

Inflatable gate

Radial gate, conventional

Sliding gate

Visor gate

Radial gate, reverse

Vane gate

Bear-trap (or roof ) gate

Vertically hinged sector gate

Bottom recessed vertical gate

Poiree and needle gate

Stoney and caterpillar gate

Stoplogs

Wicket gate

Cylinder gate

Chapter 3 are classified into six ranges of residual water heads that can be carried without additional provisions. The water head ranges are indicative and refer to moderate and large hydraulic closures. The classification in Table 5.8 does not mean that hydraulic gates cannot be designed for opening and closing beyond the indicated ranges of residual water heads. The designs of this kind are normally less economical, but there can be other reasons to justify such choices. Should there be no extraordinary reasons like that, then the residual water heads from this table can be used as an indication for setting up requirements in so-called “functional specifications” of hydraulic projects. The design loads from residual water heads can be computed as quasi-static in basically the same way as discussed for hydrostatic loads earlier (see Section 5.2.2). A special case of residual water head on a gate appears when the gate separates not only upper pool from lower pool but also salt water from freshwater. As already mentioned, specific gravity of salt water is up to 3% higher than that of freshwater. This means that under equalized hydrostatic pressure conditions the elevation of freshwater pool is slightly higher than that of saltwater pool. When the gate opens, the top layers of fresh water flow to the saltwater side and the bottom layers of saltwater penetrate the freshwater pool. This phenomenon can be observed in most sea locks of the world, including the large locks in the European North Sea harbors (Fig. 5.51b) and in Panama Canal. Also in the United States it affects the operation of some sea locks. An example is the Chittenden Lock in Seattle (WA) where, like in many European sea locks, a saltwater barrier system operates. One might expect that filling or emptying of a lock chamber equalizes in this case the pressure on both sides of a gate that needs to open, so that it does not affect the drive loads. Unfortunately, the life of an engineer is not that easy. Since the flows during filling and emptying take place through culverts or sluices in gates, flow directions are determined by the pressure differences at that level. The additional pressure from density difference on the saltwater side has, however, a triangular distribution while the equalizing pressure on the freshwater side is nearly equally distributed (see sketch (a) in Fig. 5.51). To equalize these pressures at the level of filling and emptying openings, freshwater must rise still further generating an unbalanced load on the gate. That load should be taken into account when determining the gate drive loads, especially in the case of miter gates.

5.4.4 Axial Load Buildup on Shafts It has been observed that heavily loaded hinges of hydraulic gates, like pintles and top hinges in miter gates or trunnions in radial gates, if long and frequently operated, can also generate loads in the hinge axial direction. This

380

5. DESIGN LOADS AND LOAD COMBINATIONS

Pso

Equalizing pressure

Gate

Fresh water

Actual pressure

do

Pressure from density difference

Salt water

Pfo=Pso

(a)

(b)

FIG. 5.51

Pressures on gate (a) and flows from salt and freshwater penetration during opening (b); photo of the Northern Lock IJmuiden, the Netherlands. Photo by Frans de Haan.

occurs in spite of the fact that the hinge in question does not carry any exterior loads in this direction. The phenomenon resembles the so-called “axial shaft floating” [54] and is particularly strong in not (or poorly) lubricated gate hinges. Since the lubrication of gate hinges brings potential risk of environmental pollution, axial load buildup on hinge shafts should be a concern of both designers and operators of hydraulic gates. Obviously, axial load buildup can particularly be observed on cylindrical shafts and pins. It is not an issue in gate hinges that employ spherical contact surfaces, like ball joints or pintles in American style miter gates. This does not mean that the processes causing axial load buildup do not appear on the segment level of a contact (see contact analysis levels in Ref. [50]). They do, but any initial displacement resulting from these processes is followed by a self-centering response of a spherical contact. Therefore, no actual load buildup can take place. One of the most prominent examples of axial load buildup is the top hinge of a miter gate. In Europe, such hinges commonly consist of a shaft, rigidly mounted to the gate heel post (gudgeon), and a ring bracket anchored in the lock crown. If the bracket vertical position on the shaft is not fixed, it has the tendency to creep up (or down in some arrangements) the shaft. In such cases, the empirical practice in the Netherlands is to account for an additional vertical load ΔV in the rotation axis of the gate leaf. This load strongly depends on the shaft and bracket contact materials; and also on the mounting stiffness and surface condition of both items, and the use of lubrication. A safe assumption recommended by the Dutch guidelines [55] is to estimate this load as a linear function of the hinge radial reaction H, in a way illustrated in Table 5.9. Note that the axial load buildup can be prevented by anchoring the top hinge in a flexible rather than rigid manner. Such solutions are recommended by the USACE engineering manual [51]. The focus of this manual lies, however, on the large locks of US inland waterways. For moderate and small locks, flexible anchoring is relatively complex, expensive, and requires intensive maintenance. Therefore, the designers usually favor a rigid anchoring, similar to the detail presented in Table 5.9. In such cases, it is advisable to take account of the axial load buildup as discussed earlier. TABLE 5.9

Determination of Loads From Axial Load Buildup in Lock Gate Hinges, According to [55]

Additional loads from axial load buildup in lock gate hinges [55]

kø metal-metal contacts

kø metal-thermoset contacts

kø metal-thermoplast contacts

0.30

0.20

0.10

5.5 VARIABLE WALK, VEHICLE, AND SERVICE LOADS

FIG. 5.52

381

Gate mitering device (a) and recess latch (b) at Mississippi River Upper St. Anthony Falls Lock in Minneapolis, United States.

5.4.5 Gate Locking and Other Loads Various types of hydraulic gates need to be locked in the open, closed, and (sometimes) intermediate position. For miter gates, for example, the locking can be required in both the mitered and recessed position. It is worthwhile to investigate what loads the locking devices, including lugs, pins, and other items on the gate, should be designed for. This issue appears particularly for miter and single-leaf gates under reversible loads and for temporal loads. However, gates under single-sided loads often need to have a locking function as well. A limited but perhaps the most exposed example of gate locking is a mitering device between two front posts of a miter gate (Fig. 5.52a). Its function is to guide the gate leaves into the mitered position before the hydrostatic pressure starts to build up. For miter gate drives with direct-connected hydraulic cylinders, US engineers nearly always provide latches for the mitered position and often also for holding the gates in the recess. If this is not done, the hydraulic cylinder pressure has to be both maintained and be adequate for holding the gate in recess. The latches (Fig. 5.52b) have to be designed to latch the gate automatically and then release the gate. In Europe, it is common to provide latches or other locking devices only for the gate recessed position. Also mitering devices are barely used. European engineers usually rely on the gate operating system and hydrostatic pressure to provide an accurate and stable mitering. Miter gate drives with mechanical linkages typically will not require a gate latch. Normally, a brake is provided in the drive system that prevents the linkage from moving. One consideration, however, is during flood conditions and when passing ice through the lock. In these cases, miter gates need to be tied back manually to prevent the gate from moving. Within USACE, a design requirement for miter gate locking is that either the latching system or machinery system should withstand the forces produced by a 0.38-m (1.25 ft) differential water head, and exceeding 30-s duration surge load or temporal load acting on the submerged portion of the gate. For this case, the machinery must be designed to maintain control over the gate when the gate is in the mitered position, or the latch must hold the gate. As mentioned earlier, the locking of miter gates and single-leaf (swing) gates is particularly required when the gate can be exposed to reversible loads. This issue has, however, extensively been discussed in Chapter 3. See examples in Figs. 3.5 and 3.38 and their discussion. The loads that the locking systems of this kind should be designed for are of similar nature as the drive loads on gates listed earlier (see the beginning of Section 5.4.2). The accurate determination of these loads depends much on the system choice and should be subject to individual investigation for a particular project.

5.5 VARIABLE WALK, VEHICLE, AND SERVICE LOADS Movable hydraulic closures often offer the possibility to provide a walkway or even a driveway across the closed section of water. This can be welcome for public use, but it is particularly appreciated by the gate operation and maintenance personnel as a service passage. After all, the alternatives are a bridge (high or movable in case of heavy navigation), tunnel, or an underground gallery. All of them can be significantly more expensive if the considered traffic is not heavy. The photos in Fig. 5.53 present two functionally equivalent solutions of a lock crown, both offering a

382

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.53

Lock rolling gates with and without a driveway on the top: (a) Northern Lock in IJmuiden and (b) Western Lock in Terneuzen; both in the Netherlands. Photo (b) GSB.

passage to light traffic when the gate is closed and blocking this traffic when the gate is open. Both gates operate in sea locks: (a) 50.0 m wide and (b) 40.0 m wide. Note that the traffic over the gate (a) does not make it that much heavier and more complex that a movable bridge like in photo (b) can be competitive. The weight data on both gates are illustrated in Table 3.19. This indicates that the option of a driveway or walkway over the gate can very often be favored. When a driveway or walkway over the gate is accessible for public traffic then all the parties involved, including the designer and project owner, should follow the official national codes for traffic loads on bridges. For Europe and the United States, these codes have been specified in Table 5.1. Professionals from other countries will easily find appropriate local codes on bridge loads. The recommendation to follow national codes for traffic loads on bridges is, unfortunately, not always shared by all project participants in this case. Since carrying traffic and pedestrian loads is not the primary function of hydraulic gates, some engineers tend to underestimate it and push for lower design loads that deviate from these codes. An example is the project of the new sea lock in IJmuiden, 70 m wide, in which an author of this book had intensive discussions to ensure the compliance with such codes [56]. One should realize that the traffic load codes for bridges do not only specify the minimum design values of such loads but also a number of related supplementary requirements that need to be met before pronouncing the traffic passage (in this case over the gate) safe. If a passage over the gate is not accessible for the public, there is no legal obligation to follow official traffic load codes. Also in this case, however, it is advisable to investigate whether the passage in question shows resemblance to a public passage. If it does, or if it there is a chance that it might do in the future, the designer should still consider applying the load codes for bridges. Otherwise, other load codes or guidance documents can be followed. There is not a uniform code for service loads only since such loads may include the use of heavy equipment, temporary support to disassembled or spare items, gate lift outs, transports, and the like. Many of these loads need to be individually determined, based on the projected service scenarios. There are, however, indications in various codes for the design loads on service walkways, platforms, handrailing, stairs, ladders, and the like. Table 5.10 presents a global comparison of such loads in design codes of Europe and the United States that are applicable at the time of writing this book. This comparison includes the codes for bridges and buildings. Other codes, like for mill structures or cranes, can also be helpful in specific cases. Moreover, since these loads are differently described in the referenced codes, the load descriptions in Table 5.10 form an effort to cluster similar kinds of loads under the same terms and often vary from the original descriptions or give incomplete classification criteria. Therefore, they are only meant as an indication here, not as legally binding design values. The last column of this table contains the variable walk and service loads that are suggested by the authors of this book for hydraulic gate design. These values are derived from the loads specified by the quoted codes. They should be seen as recommended for a midsize hydraulic gate project with common operation and maintenance requirements. The intention of these data is not to compete with local client specifications, and certainly not with national or other codes, but to give some guidance in the absence of better, more specific regulations. The reader is also encouraged to take further notice of different conditions regarding the load specifications in the codes quoted in Table 5.10. These conditions have partly been skipped over here for the sake of uniformity and space. In the cases when walkways over gates are also utilized for the passage of service vehicles, like in Fig. 5.54, or for permanent or temporary storage of equipment or materials, the design must obviously take account of this. Such situations are subject to additional, individual specifications for particular sites. If no such specifications have been issued

383

5.5 VARIABLE WALK, VEHICLE, AND SERVICE LOADS

TABLE 5.10

Loads Similar to Hydraulic Gate Walk and Service Loads in the European and USA Codes, Characteristic Values Bridge codes

Building codes

Load description

Units

EN 1991-3

AASHTO

EN 1991-1-1

ASCE 7

Hydr. gates (proposal)

Footpaths, walkways, fixed or elevated platforms, as whole

N/m2 (psf )

2500–5000a (52–104)

3590 (75)

3000 (63)

2870 (60)

3000 (63)

Footpaths, walkways, platforms, individual sections or members

N/m2 (psf )

5000a (104)

3590 (75)

3000 (63)

2870 (60)

3000 (63)

Miscellaneous service walks, catwalks, stairs and fire escapes

N/m2 (psf )

Not covered

Not covered

2000 (42)

1920 (40)

2000 (42)

Local load on footbridges, footpaths and walkways

N (Lb)

Service vehicle

Service vehicle

1500 (337)

1330 (300)

1500 (337)

Pedestrian railing load

N/m (plf )

1000b (69)

730c (50)

1000b (69)

730b (50)

730b (50)

Service railing load

N/m (plf )

800b (55)

Not covered

500b (34)

730b (50)

500b (34)

Concentrated load on railing parapets

N (Lb)

Not specified

890 (200)

To national annexes

890 (200)

890 (200)

Concentrated load on railing other longitudinal elements

N (Lb)

Not specified

890 (200)

To national annexes

220 (50)

220 (50)

Concentrated load on railing posts

N (Lb)

Not specified

45 + 0.16ad (200 + 0.05a)

To national annexes

220 (50)

890 (200)

Concentrated loads on fixed ladders

N (Lb)

To national annexes

Not covered

1000 (225)

1330e (300)

1330e (300)

a b c d e

Low for short (10 m) and high for long (200 m) bridge spans. Acting horizontally or vertically only on top (parapet) rail. Acting horizontally and vertically on all horizontal rails. Where a is the post spacing in m (ft). Acting at any point and for every 3.05 m (10 ft) of the ladder.

FIG. 5.54

Service vehicle on a walkway over miter gate of Mississippi Lock and Dam 2.

for the design, service vehicles should not have access to the walkways and the parties involved should not store there any materials, use the walkways as berthing structures, hookups for transport or in any other inappropriate way. This is very important, as it often happens that project owners fail to specify additional requirements; and later use their walkways in a way that was not covered in the design. Also the situation pictured in Fig. 5.54 raises concern about the safety of vehicle passage.

384

5. DESIGN LOADS AND LOAD COMBINATIONS

5.6 SEDIMENT, ICE, AND OTHER VERTICAL LOADS 5.6.1 Loads by Sediment, Sea Life, etc. Hydraulic gates are often exposed to additional variable loads by mineral, organic, or other sediment. Under mineral sediment we will basically understand silt and mud of diverse compositions. One of the most common forms of organic sediment is sea life. In practice, there is a large overlap between both sediments: silt often contains organic components also and a significant component of sea life is chalk of shellfish. Other sediments can, for example, be caused by mineral oil leaks and the chemicals to fight them, mine wastes, polluting harbor or shipyard activities, contaminating industrial processes, disasters like floods and levee breaches, etc. The discussion in this section concerns only the loads by sediment weight. It ought, however, to be mentioned that sediment causes more issues that gate engineers should be concerned about. Here is a shortlist of the most frequently occurring issues: • • • • • • •

global increase of gate weight, its support reactions, and drive forces required; local increase of component mass and volume; silting up of water inlets and outlets, as well as gaps and clearances required for correct operation; increase of abrasive wear in hinges, rollers, slide pads, running surfaces of wheels, and rails; attracting plant growth, mosses, bacteria, and other vegetation; and accelerated corrosion due to coating erosion, biochemical processes, etc.; general decrease in the gate esthetic value.

Deposits of sediment occur with different intensity at different locations. One of the locations where this phenomenon is very common is the harbor city of Bristol in the United Kingdom (Fig. 5.55). Tides bring many tons of sediment up and down the River Avon, which can be seen in photo (a) on the banks of the so-called “New Cut” of the river. This “New Cut” was constructed in the early 19th century. A section of the old river bed that run through the city was then closed by a number of lock gates, providing tide-free conditions for the city harbor, which since then is called “floating harbor.” As shown in photo (b), silting remains, however, an issue to take care about. Note that the timber fendering on lock gates is steeply inclined to minimize sediment collection. For the same reason, a number of new lock gates have partly or entirely been provided with double skin plates. Another way to keep the loads by sediment deposits under control is to actively remove it at certain intervals. This can be done by divers, which is not easy (poor sight conditions) and also can obstruct navigation. What also helps to some extent is a flow induced by a propeller that, in turn, can move on a guide rail over a certain distance. Fig. 5.56

FIG. 5.55 Sediment in the harbor city of Bristol, United Kingdom: (a) River Avon banks by low tide and (b) filling of a lock chamber in the “floating harbor.”

385

5.6 SEDIMENT, ICE, AND OTHER VERTICAL LOADS

FIG. 5.56 Simple device for sediment reduction in the Zandvliet Lock rolling gate, Belgium: (a) view of general arrangement; (b) rear view; and (c) front view. Photos Ivar Hermans, MOW.

shows a simple realization of this idea, popularly known as the “mixer,” in one of the Belgian rolling gates. Such gates, presented in detail in Chapter 3, comprise many components of large areas exposed to silt deposition. What Belgian engineers also do in some cases is monitoring the weight of these deposits and compensating for it by removing equivalent water ballast from the gate buoyancy tanks. Such a system operates, for example, in the Van Cauwelaert Lock gates in Antwerp. On the photo (a) in Fig. 5.56, some places with sea life sediment can also be observed. This is still a relatively mild example; the deposition of this kind of sediment can be a number of times thicker than that shown in this photo. The sea life sediment cannot be removed by inducing a flow. To the contrary, flow usually brings oxygen, plankton, and helps reproduction processes, which, in turn, stimulates the buildup of sea life. This buildup can result in a significant increase in the gate effective mass. These examples show that no uniform load figures can be given to cover sediment deposition for all hydraulic gate projects. Such figures strongly depend on the locations, structural arrangements, and the maintenance program of the gates in question. Also the changing conditions for local vegetation may have an impact. There are examples of sediment increase caused by seasonal or periodical buildup of algae, or by an introduction of new, invasive shellfish species. Such phenomena will likely occur with growing frequency in the future, following the climate change and global navigation growth. Table 5.11 illustrates some sediment figures that have been followed in a number of recent lock gate projects in and around the harbor of Antwerp, Belgium. This harbor is known for significant (although lower than in Bristol) silt TABLE 5.11

Characteristic Load Data by Sediment on Lock Gates for the Antwerp Harbor Area, Belgium

Data description

Units

Sea locks

Inland locks

Specific gravity ρ of sediment

kg/m

1300

1300

Silt layer thickness when no “mixers” are used

m

0.25

0.10

Silt layer thickness when “mixers” are used

m

0.15

0.05a

a

“Mixers” are not used on inland waterway locks in the Antwerp area.

3

386

5. DESIGN LOADS AND LOAD COMBINATIONS

deposition and sea life buildup. The data are not standard but they reflect local observations and concerns. They apply to all horizontal projections of submerged items and can be used as first estimation for other locations if no local data are available. Sea life deposits on vertical surfaces are also globally covered by these figures. They normally do not need to be added. They may, however, be relevant for local items or components of sea locks. In such cases, about 25% of the thickness data from Table 5.11 is usually a safe assumption. The USACE engineering manuals also state that silt loads should be based on site conditions [1]. They do, however, specify the minimum value of 25.4 mm (100 ) that should be taken into account in all the areas where silt can accumulate, regardless of drainage features. If no local data are available, the silt specific gravity shall be taken as 1400 kg/m3 (90 lb/ft3). This is 7% higher than the data for Antwerp, which can be considered almost equal. The USACE value is not location-bound. A special case of sediment loads occurs in hydropower plant intake bulkheads or intake gates that remain in place for over a year during the powerhouse rewind. According to the common USBR and USACE design practice, the lifting lugs and hoists of such bulkheads or gates must be designed for the structure weight increased by sediment that fully fills all the girders.

5.6.2 Ice, Glazed Ice, and Snow The loads by ice, glazed ice, and snow have an effect similar to those by sediment. The difference is that these loads will not cause an increase in gate weight as long as ice and glazed ice deposits are under water, because the specific gravity of ice is slightly lower than that of water. For the same reason, unfortunately, ice deposits and buildups have a tendency to move above water. This is additionally helped by the action of waves and—in case of lock gates—by varying water levels in lock chambers. Any rise of water gives the floating ice a chance to move to a higher position on the gate and to stay there. It also brings a fresh layer of water on the already present ice deposits, which quickly freezes in contact with them and with cold air. The latter proceeds earlier and faster in freshwater than in salt water, because the freezing temperature of water depends on its salinity as presented in Table 5.12. In practice, a saltwater basin needs to cool still further before icing can occur, because salt water has a higher specific gravity, which results in a different freezing process. The difference is as follows: • Freshwater has the highest specific gravity at 4°C. Above and below this temperature the specific gravity decreases. Stagnant water will, therefore, first entirely cool down to this temperature. Further temperature drop makes the surface water lighter. Therefore, it stays up and allows for ice formation, while the deeper water still has the temperature of 4°C. • Salt water (salinity 2.5% or higher) becomes heavier until it freezes. As the ambient temperature drops, the surface water cools down and sinks until all the water reaches the freezing point. Only then the ice begins to form. The whole process lasts, therefore, much longer than in freshwater. This difference has important consequences for ice deposits on lock gates. In freshwater, they will comprise both the ice floes driven toward the gate and ice formed by splash water, while in salt water only the latter will contribute. Ice floes do not form that easily in seawaters, with the exception of shallow lagoons and marshlands. Like in the case of sediment, ice for hydraulic gates is not only a matter of loads, but it also causes a range of issues to be concerned about. Fighting winter conditions and particularly ice (Fig. 5.57) is, in fact, one of the harshest tasks for operation and maintenance crews on locks, river dams, and hydroelectric plants. In general, both the loads and other issues caused by ice should be considered for three different stages. Depending on the local climate, these stages can occur once or a few times in the winter season. Some countries, like Canada or Russia, shut a large part of their waterways every year; other countries, like the most of the Western Europe, do it only during extreme cold periods. Below is a brief description of these stages, along with the forthcoming issues for navigation lock gates. The operators of other hydraulic closures experience similar issues.

TABLE 5.12

Freezing Temperature of Water by Various Salinity Values

Water salinity (%)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Freezing temperature (°C)

0

0.28

0.53

0.81

1.08

1.36

1.63

1.91

5.6 SEDIMENT, ICE, AND OTHER VERTICAL LOADS

387

FIG. 5.57

Fighting ice and winter conditions on lock gates: (a) tugs help operating gates in Welland Canal, Canada; (b) gates of Poe Locks steamcleaned from ice, USA-Canada; (c) gates of Lock Lauffen in the Neckar cleaned from ice, Germany and (d) fighting ice on Volkerak Lock gates, the Netherlands. Photos (a) Library of Toronto, (b) USACE & USCG, (c) BAW, (c) Rijkswaterstaat.

(1) Stage of ice formation: The priority is then often to keep the locks operating as long as possible. This often requires the assistance of tug boats and service barges, use of air bubblers and other equipment. The ice loads on gates then comprise the following: – vertical loads by deposits of floes on gate components that become submerged; – horizontal pressure by floes driven by ships; – deposits of glaze ice and ice formed by splash and leakage water (especially in lift gates). (2) Stage of navigation shut down: This stage begins as planned (e.g., in Canada) or when the operation of locks is not possible any longer (e.g., in West Europe). The lock gates do not operate, but they still experience loads by ice. These loads are mainly – horizontal loads by thermal expansion of ice; and – horizontal and vertical loads by ice brought by currents and storms. In extreme situations, it can be desirable to break solid ice slabs in order to reduce these loads. Such an operation can also generate loads on gates.

388

5. DESIGN LOADS AND LOAD COMBINATIONS

(3) Stage of resuming the operation: This stage precedes or takes place simultaneously with ice breaking, often helped by the action of icebreakers on the waterway. The ice loads on lock gates are then like in stage (2), with additionally the following: – loads due to ice breaking (in extreme cases by use of dynamite); – loads caused by mechanical or thermal cleaning (steamers) of the gates from ice. The photos in Fig. 5.57 have been taken in all the three stages mentioned earlier. Photos (a) and (d) refer to stage (1), photos (b) and (c) refer to stages (2) and (3). Note the various approaches being used in both keeping the gate recesses free from ice (tug operation, air bubblers) and cleaning the gates from ice (mechanically, steam cleaners). It is important that the gate designer keeps these handlings and their frequencies in mind when determining the design ice loads on gates. Analogically to the sediment loads, design loads by ice strongly depend on the local conditions, type of the gate, and operation and maintenance program of the gate. Therefore, no uniform figures can be given. Also the design load codes listed in Table 5.1 do not give guidance in this field; and neither do the manuals by USACE nor the European waterway authorities. As a rough indication, the characteristic loads by ice in one of the lock gate projects in the Netherlands are specified in Fig. 5.58. This project is presented in more detail in Chapter 3 (see Figs. 3.20 and 3.35a), and the related discussion. Ice can be driven by winds from both sides of the lock. Performed studies indicated, however, that the funnel-shaped guiding jetties retain rather than increase the ice driven toward lock gates. This resulted in moderate load figures. The ice loads indicated as 1 and 2 in Fig. 5.58 are normally applied only to the upstream gates (in Fig. 5.58, gates at both sides can alternately be upstream) and on their outer sides. Downstream gates in river locks are commonly exposed to lower ice loads because neither wind nor current but only ships can drive substantial masses of ice toward them [57]. However, these gates can be exposed to the same loads by glaze ice or ice from splash and leakage water as the upstream gates. American engineers also take account of the loads from ice, including its thermal expansion. Unlike in Europe, the ice loads are usually superposed with the loads by floating debris and considered as impact loads. The USACE manual [1] gives one common value for these loads, which is 73 kN/m (5000 plf ) horizontally, applied uniformly over a 0.61-m (2 ft) depth across the gate members exposed to ice. No values for vertical loads are specified. Instead, the manual recommends considering heaters on places where ice can accumulate and inhibit gate operation. In this view, the USACE requirements may seem milder than those in Europe, but the common practice is to follow the ASCE 7 design criteria that do specify both expansive and gravity loads by ice based on project location. This normally works out to a 25–50-mm (100 to 200 ) solid thickness of ice on the exposed perimeter of each structural shape. There is also much practical guidance issued by USACE regarding the engineering and design under ice conditions [58]. Vertical loads by ice are particularly significant for vertical lift gates. Nevertheless, also the gates of other types and in other structures than locks can be exposed to such loads. An example is the load deposits on the hinged crest gates of Coon Rapids Dam on the Mississippi River, United States, pictured in Fig. 5.59. These gates, like many other weir and spillway closures in the regions of average and cold climate, carry large loads from ice deposits every year. In addition, the gates in this photo can be an example of what has been mentioned earlier in this section: loads are not the only issue that ice brings about. In this case, ice seriously obstructs the operation of gate drives and by that the flow control.

Enkhuizen

Existing old lock 12 × 115 m

N

Ice loads on lock gates: “Naviduct” 2 × 12.5 × 125 m

IJsselmeer

Lelystad

Existing dam/road with a movable bridge

Underpass of the road

1. Thermal expansion of ice: lineload 50 kN/m in lock longitudinal direction, 0.2 m below SWL 2. Ice floes driven by winds and currents: lineload 50 kN/m perpendicular to gate skin, at SWL (not together with 1) 3. Ice and glaze ice deposits on gate girders: surface load 5 kN/m2, equally distributed on webs of all submersible girders

Markermeer

FIG. 5.58 Ice load assumptions on the lock gates of Naviduct Enkhuizen, the Netherlands.

389

5.7 LOADS FROM SHIPS AND FLOATING OBJECTS

FIG. 5.59 Hinged crest gates of Coon Rapids Dam, MN, on the Mississippi in winter. Photo USACE.

Hydraulic gates are not often subject to the loads by snow; and if they are then the size of these loads is usually marginal. Nevertheless, snow loads should be considered, especially in the areas where cold winters and heavy snowfalls are common. Obviously, these loads are more considerable for the types of gates that for long periods remain in air (like vertical lift gates, rotary segment gates, or visor gates) than for the types of gates that normally remain submerged or shielded from snow (like miter gates, sector gates, or hinged crest gates). Snow loads can, generally, be determined according to the following codes: • Europe: EN 1991-1-3, Eurocode 1: Actions on structures, Part 1–3 General actions—Snow loads; • United States: ASCE 7: Minimum design loads for buildings and other structures, Chapter 7—Snow loads.

5.7 LOADS FROM SHIPS AND FLOATING OBJECTS 5.7.1 Loads From Floating Objects, General Ships navigating through locks and other floating objects that incidentally pass through locks also introduce loads to the gates. In the sense of the USACE engineering and design manuals, like Ref. [1], these can be any of the following three: • usual loads, that is, loads that occur daily or frequently, including those that have a mean return period between 1 and 10 years; • unusual loads, that is, loads that occur infrequently but can be reasonably expected within the service life; and have a mean return period between 10 and 300 years; and • extreme loads, that is, loads that are possible but not likely to occur within the gate service life; and have a mean return period longer than 300 years. This classification reflects the USACE approach and is not common in other fields of engineering, or in hydraulic engineering outside the United States. Therefore, it is not followed further in this book. It can, however, be helpful when giving some loads proper place in the design process. This includes the loads from ships and other floating objects. Here are a few examples of such loads that represent the categories mentioned earlier.

390

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.60 Sunk barge in Southern Lock IJmuiden, the Netherlands. Photo Beeldbank Rijkswaterstaat.

• Usual loads: loads from ship propellers, waves from passing ships, loads by floating debris; • Unusual loads: ship collisions that cause damage but no operational loss of gate, sunk, or otherwise failed vessels obstructing the gate movement (Fig. 5.60); and • Extreme loads: ship collisions that cause damage and operational loss of gate, large uncontrollable floating objects carried by floodwaters. In the following subsections, three of the load cases mentioned above are discussed in more detail; one from each of the three groups in the USACE classification.

5.7.2 Loads From a Ship Propeller

Ship u0 D0 Dp

Jet dispersion ignored Propeller distance

FIG. 5.61 Idealized model of load on gate from a ship propeller.

Propeller depth

Gate

Ships that leave lock chambers do it by putting their rear propellers in motion that, in turn, generates a local flow. The energy of that flow must be balanced in some way, which happens by bringing the ship in motion. However, if the distance between the ship propeller and the closed lock gate behind it is not large then the same flow acts on the gate. Unlike the ship, the gate hopefully does not move, which means that it has to receive and fully dissipate the flow energy. The resulting horizontal load on the gate can normally be ignored if the water level on the other side of the gate is higher. However, it cannot be ignored if the water level in the chamber is higher (Fig. 5.61), because then the flow load

391

5.7 LOADS FROM SHIPS AND FLOATING OBJECTS

acts in the same direction as the differential water head, which increases its effect. According to the Dutch engineering practice, a safe assumption for medium and large locks is that the ship propeller can be at the distance of about 5.0 m from the gate. The local load Fs that this propeller induces on the gate can then conservatively be computed as π Fs ¼ ρ   D20  u20 (5.63) 4 where: ρ ¼ specific gravity of water (kg/m3); D0 ¼ effective diameter of the propeller (m); u0 ¼ flow velocity behind the propeller (m/s). The effective diameter of the propeller D0 is derived from its physical diameter Dp as follows: 8 for propellers without jet tubes; < 0:71  Dp for propellers inside jet tubes; D0 ¼ 1:00  Dp : 0:85  Dp for intermediate combinations: The flow velocity behind the propeller u0 is determined from the power output Pd (kW) of its engine: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi . u0 ¼ 1:15  3 Pd 2 D0

(5.64)

(5.65)

Formulas (5.64) and (5.65) reflect engineering practice in the Netherlands, presented in Ref. [14]. On many inland waterways in Europe, a normative ship for such calculations is the so-called RHK ship (Rhine-Herne Canal ship). It can be equipped with one or two stern propellers. If a single propeller is utilized, it has a physical diameter Dp ¼ 1.70 m and effective diameter D0 ¼ 1.45 m. The peak power output of its engine is 1200 kW, but then the ship is already at some distance from the gate. A safe estimation of the propeller jet load is, therefore, at the half of this power Pd ¼ 600 kW. Eq. (5.65) gives then the flow velocity behind the propeller u0 ¼ 7.6 m/s. This gives the load on gate Fs ¼ 95.4 kN from Eq. (5.63). This load can conservatively be considered as equally distributed on the same area of the gate as the effective circle of the ship propeller, with its center at the depth of 2.5 m or less. Similar calculations can be performed for the propellers of push tugboats that operate on US waterways, or any other propelled vessels. Fig. 5.62 leaves no doubt that the US tug boats have engines powerful enough to induce significant loads from propeller jets on lock gates. Currently, the USACE view is that these loads are covered by a requirement of minimum load applied to the top of the gate, which includes an additional 1.44 kN/m2 (30 psf ) hydrodynamic load. See the examples in Chapter 7 for more details on this matter. Note that the load model from Fig. 5.61 and the equations quoted above do not pretend to give an exact solution. Instead, they represent estimations that have proved to be safe in engineering practice. One should keep this in mind, FIG. 5.62 Tug boat pushing a convoy of 35 barges on American waterway. Photo USACE.

392

5. DESIGN LOADS AND LOAD COMBINATIONS

particularly when applying probabilistic design methods, or the American LRFD approach [4]. The main caution is that neither Eqs. (5.63)–(5.65) nor the input values assumed in the presented example can be regarded as leading to so-called “characteristic loads.” As discussed in Section 5.1.2, such loads are defined in terms of mean values and standard deviations. It will probably take some time before the databases on loads from ship propellers, as well as other loads from ships and floating objects, are sufficiently developed to support a reliable probabilistic design approach.

5.7.3 Ship Collision Ship collisions belong to the loads of potentially most damaging impact on hydraulic gates. They do not happen often, but if they do then the damage can vary from a local dent or torn off fendering to the total loss of the gate. The latter is particularly dramatic because it happens unexpectedly, which gives the owner of hydraulic structure no time to control or minimize the consequences. In terms of risk management, damage by ship collision represents, therefore, a more severe event than the same scale damage by extreme hydraulic loads, other extraordinary service, deteriorating technical condition, or other processes. This explains why there is all reason to take efforts that minimize the risk of such damage. A detailed discussion of appropriate measures in this field is presented in Chapter 6. In the current section, only the issue of design loads from ship collision is discussed. As mentioned in Section 5.7.1, ship collisions that do not result in a loss of gate can, according to the USACE manuals, be classified as “unusual loads”; while those that do result in a gate loss can be classified as “extreme loads.” Under a loss of gate we will understand a degree of gate damage in which (a) the gate cannot be operated anymore; and (b) regaining the operation requires gate exchange or major, time-consuming repair lasting longer than specified by project owner (order of magnitude: 1 month). This roughly corresponds with the distinction introduced by the USACE manual [1], which has been summed up in Table 5.13. The USACE manuals also determine the magnitude, location, and direction of the design loads from ship collision. This makes life easier for US engineers and evokes surprise in Europe, where no uniform figures on loads from ship collisions are used. There is, however, a reason for this different approach, apart from some local preferences for deterministic or probabilistic methods. This reason is that inland navigation on US waterways has a much more standardized character than in Europe. Its great majority consists of standard barge convoys, two or three barges wide, with the width of each barge 10.7 m (35 ft). Such convoys (like in Fig. 5.62 but narrower) are pushed by tugs that can also be classified in a number of standard capacity groups. Collisions with lock gates, rarely also with weir or other gates, take place nearly always at the front of a convoy. The most common are a downbound tow striking upstream gate and a downbound tow striking downstream gate when going into the chamber. These data allow for relatively accurate determination of possible place, magnitude, and direction of the load generated by collision. In Europe, most vessels are self-powered and there is less standardization in their sizes, which makes a similar, deterministic definition of ship collision loads nearly impossible. In addition, Europe is much less an administrative unity than the United States, so “nearly impossible” always means “impossible” there. TABLE 5.13

Distinction Between Unusual and Extreme Loads According to the USACE Manuals Load category

Feature

Unusual load

Extreme load

Governing Limit States

Strength and Fracture Limit States

Extreme Limit State

Main requirement

No significant damage or disruption of service allowed

Significant damage accepted as long as no catastrophic collapse occurs

Additional requirement

Damage may accumulate to require major rehabilitation after 50 years of service

Limited operational capability required to secure basic function (e.g., pool level)

Tolerated condition

Localized yielding (yield stress exceedance in localized areas) acceptable

Significant plastification, buckling, tearing, fracture and/or other damage acceptable

5.7 LOADS FROM SHIPS AND FLOATING OBJECTS

393

FIG. 5.63 Ship collision load schemas for waterways in the United States. Drawn after USACE, Design of hydraulic steel structures, Engineering and design manual ETL 1110-2-584, U.S. Army Corps of Engineers, Washington, DC, 30 June 2014.

Fig. 5.63 shows the load model for the ship collision on a miter gate, which is the most frequently used type of gate on US waterways. In accordance with Ref. [1], two loading cases should be considered to determine the maximum structural effect: (a) collision by a single barge train at a distance of one barge width or more from the lock wall, quasi-static collision force Fc ¼ 1112 kN (250 kips); and (b) collision by a wider barge convoy at the miter point of the gate, quasi-static collision force Fc ¼ 1779 kN (400 kips). The load should in both cases be applied in downstream direction to the girders above pool level. Similar approach is recommended for other types of lock gates used on US waterways, including vertical lift gates and vertically hinged sector gates. In all cases, the loads from ship collision apply only to gate framing, not to skin plate assemblies. This reflects the design philosophy for “extreme loads” that is indicated in Table 5.8. Below are the magnitudes of concentrated, horizontal loads from ship collision in view of the USACE manuals and the recent practice in New Orleans projects: • • • • •

vertical lift gates: 1112 kN (250 kips); old sector gates, vertically hinged: 556 kN (125 kips); new sector gates, vertically hinged: 890 kN (200 kips); radial (Tainter) gates in spillways: ship collision not specifically considered in design; closures in levees and floodwalls: negligible unless there is reason to believe that it may occur.

Note the lower load value from ship collision for vertically hinged sector gates. It has a reason. Such gates have a relatively high capacity to dissipate kinetic energy of the ship. As an example, see the sector gates that serve this purpose on the St. Lawrence Seaway in Canada, discussed in Chapter 3. Another way to dissipate the energy of ship collision is by utilizing ship arrestors. These devices are discussed in Chapter 9. Sketches in Fig. 5.64 show the character of global (elastic and plastic) deformation as result of ship collision for three types of lock gates most frequently used on American waterways: miter gate, vertical lift gate, and vertically hinged sector gate. Note that gate (c) undergoes a much larger deformation before it collapses than the first two, gates (a) and (b). Assuming that the kinetic energy Ec of colliding ship is the same for the three gates, the maximum collision force Fc is, therefore, less for gate (c) than for gates (a) and (b). This has been illustrated on the force-displacement graphs below the collision schemes. For the sake of simplicity, the entire Ec is assumed to be dissipated by gates; and the deformation effect of load is modeled as linear. This figure shows that loads from ship collision depend not only on the geometry and kinetic energy of the ship, but also on the type of gate. A sector gate is also not the only type capable of sustaining large deformation by a colliding vessel. A similar advantage is apparent for rolling gates, which can be seen on the photo in Fig. 5.65. The gate in this photo suffered severe damage by ship collision but did not collapse and could still provide minimum serviceability. The European engineering practice regarding ship collision loads on hydraulic gates differs from the practice described above. Apart from the already mentioned lack of uniformity, the Eurocodes do not give numerical values of ship collision loads specifically for gates. They do, however, give indicative values of such loads on dam piers, abutments and pillars of bridges, quay walls, and other massive structures [59]. These values have been estimated for the

394

5. DESIGN LOADS AND LOAD COMBINATIONS

Fc Dc

Fc

Fc

Dc

Dc

Fc

Fc

Fc,max Ec = ½mv2

Dc,max

Ec = ½mv2

Dc,max

Dc

(a)

Fc

Fc,max

(b)

Fc,max

Ec = ½mv2

Dc,max

Dc

Dc

(c)

FIG. 5.64 Dissipation of ship collision energy in three lock gates: (a) miter gate; (b) vertical lift gate; and (c) vertically hinged sector gate.

FIG. 5.65 Damage on rolling gate of Northern Lock IJmuiden after ship collision, the Netherlands. Photo Beeldbank Rijkswaterstaat.

so-called “hard collisions,” of which the energy is dissipated in elastic and plastic deformation of the ship. This assumption is opposite to the common engineering practice for hydraulic gates, in which the energy dissipation is assumed to take place in the gate (see, e.g., Fig. 5.64). Nonetheless, the Eurocode [59] can provide indicative upper bound values for ship collision loads on gates if no specific data is available for a particular project). Assuming that the ship velocities in the areas of inland locks and dams are of the same range as in harbor areas, the indicative maximum dynamic loads on these structures are as presented in Table 5.14. Note that ship collisions will commonly impose much higher loads on lock gates than on ship arrestors. The reason is that ship arrestors are more elastic or plastically deflectable, and offer longer deformation distances to dissipate the same amounts of energy. That is why the loads in Table 5.14 cannot be used in the design of ship arrestors. See Chapter 9 for specific guidance of ship arrestor design. Obviously, the loads in Table 5.14 can also substantially be decreased as soon as some elastic or plastic deformation of the gate is allowed. This is normally the case, because ship collision is an “unusual” or “extreme” load condition according to the USACE terminology (see Table 5.13). The design rules in other countries classify it in a similar way. As a result, the load factors applied in gate analysis allow for local yielding or even significant plastification of the gate

395

5.7 LOADS FROM SHIPS AND FLOATING OBJECTS

TABLE 5.14

Indicative Dynamic Loads by Ship Collision on Gates, Derived From Eurocode [59]

CEMT class

Reference type of ship

Ship length (m)

Ship massa (tons)

Force Fdxb (kN)

Force Fdyb (kN)

I

Peniche Barge

30–50

200–400

1000

500

II

Euro-Barge

50–60

400–650

1500

750

III

“Gustav K€ onigs”

60–80

650–1000

2000

1000

IV

“Johann Welker”

80–90

1000–1500

2500

1250

Va

Large Rhine ship

90 110

1500–3000

4000

1750

Vb

Push tug + 2 barges (long)

110–180

3000–6000

5000

2000

VIa

Push tug + 2 barges (wide)

90–110

3000– 6000

5000

2000

VIb

Push tug + 4 barges

110–190

6000–12,000

7000

2500

VIc

Push tug + 6 barges

190–280

10,000–18,000

8500

4000

VII

Push tug + 9 barges

290–300

14,000–27,000

10000

5000

a b

Total mass of a vessel including its structure, cargo fuel etc., equaling the so-called loaded displacement. Dynamic force by frontal (x) and lateral (y) collision, including the effect of added (hydrodynamic) mass.

areas affected by ship collision. The common practices followed in this matter in several countries are summarized below [58]: • In the United States, the design values and locations of ship collision loads are as discussed earlier in this section (see Fig. 5.63 and the related discussion). When following the LRFD method, the load from ship collision is combined with a factor of 1.0. When the ASD method is applied, the allowable stresses are increased by one-third above the specified working stress level. In addition, there are attempts to match the level of gate collision resilience with the acceptable risk level. Lock gates in “high use,” like in the Mississippi, Ohio, or Tennessee River, would require a higher resilience than those in “moderate use” or “low use,” like in the Cumberland River [7]. • In Germany, the approach recommended by the country’s DIN norm [60] is in the first instance to prevent ship collision by installing protective devices. These are mainly ship arrestors, as discussed in Chapter 9. Their required performance is defined in kinetic energy dissipation rather than loads, and varies from 1000 to 2000 kNm (MJ). Another way is to derive this energy from the type of vessel representative for the considered waterway. The vessel velocity v in the formula Ec ¼ ½mv2 should in this case be taken as • v ¼ 1.0 m/s for motor barges; • v ¼ 0.9 m/s for push tow units. In wide sea locks, where ship arrestors may not be economical, both the outer and inner gate are commonly designed for a ship collision load of 300 kN; and at least one standby gate is provided to replace the operating gate in the case of critical damage. This practice primarily applies to rolling gates but should be seen as indicator for other gate types as well. • In France, no legally binding norms for ship collision loads exist, but the technical division of the country’s Ministry of Infrastructure, CETMEF, issues recommendations on this matter. These recommendations specify neither collision loads nor kinetic energies directly, but they setup the calculation method. The basic equation for the energy to be dissipated by gate is [61]

where:

Eg ¼ Cm  Cc  Cs 

m  v20 2

(5.66)

Cm ¼ mass coefficient, to account for hydrodynamic effects, usually Cm ¼ 1.20; Cc ¼ confinement coefficient, to account for ship velocity reduction before collision as result of water confined between ship and lock, CETMEF recommends Cc ¼ 0.8; Cs ¼ ship coefficient, to account for collision energy dissipated by ship; Cs must be 1, but for rigid bows of ships Cs ¼ 1.0 is recommended; m ¼ total mass of colliding ship; v0 ¼ velocity of the ship in collision, typically in the range of 0.5–2.0 m/s.

396

5. DESIGN LOADS AND LOAD COMBINATIONS

The most significant component in formula (5.66) is the ship velocity v0. The CETMEF recommends determining the characteristic value of v0 from statistical data with the probability of exceedance in the range of 104–102 (see Ref. [61] for more details). • In Panama, the issue of ship collision against the Canal lock gates was for a century entirely under control of the site personnel. The old locks utilize locomotives to help transit the ships. This does not mean that collisions did not happen. After all locomotives have less power to control ship movements than the ship engines. In the new locks, it is primarily the ship captain’s responsibility to avoid collision. These locks contain simultaneously operated double rolling gates in each crown. Each gate has been designed to resist the impact of 160,000 metric tons displacement vessel moving at a velocity of 1 knot (0.5144 m/s). The gate may then suffer substantial damage, provided its watertightness and capability to be moved into the recess or floated out of the chamber are not compromised. The idea is that this gate will dissipate the full energy of collision and no subsequent damage will be transmitted to the gate behind it [62]. • In the Netherlands, the approach recommended by Rijkswaterstaat [55] is to begin with taking measures that minimize the risk of collision. These can be ship arrestors, but other options may prove even more adequate. Dutch waterways are very intensively navigated. Therefore, the space consumption, operation time, and probability of failure of ship arrestors are seen as disadvantages. The preferred measures usually include the following: • gate in closed position: applying fendering on gates and providing spare gates ready to replace operating gates in case of a severe collision damage; • gate in open position: substantial setback away from navigation channel. A minimum required setback of a gate (including fendering, cables, piping, etc.) is 50 mm. • minimizing the consequences of collision: in this view, the impacted gate may severely be compromised but its hinges or other supports must still hold it. Further, no specific loads from ship collision on hydraulic gates are given. Structures exposed to ship collisions are divided into rigidly responding (like bridge pillars or dam piers) and elastically responding (like guiding jetties and mooring piers). For collision loads on the first group, engineers are prompted to consult the Eurocode [59]. For collision energies to be dissipated by the second group, the EAU 2012 recommendations [63] are referenced. More details about ship collision against hydraulic gates, including both the means to prevent it and the estimation of design loads, can be found in the report of PIANC Working Group 151 [61] that has entirely been dedicated to this issue.

5.7.4 Debris and Uncontrolled Floating Objects Debris carried by water over or in the vicinity of hydraulic gates can be caused by several reasons and composed of various materials. The most forthcoming causes and kinds of debris that are relevant for hydraulic gates are collected in Table 5.15: TABLE 5.15

Six Common Groups of Debris Causing Loads on Hydraulic Gates Carried materials

No. Cause of debris

Generally

Examples

1.

Large river flooding

Predominately wood and other organic materials

Shrubs, trees, plants, dead animals, wooden structures

2.

Seasonal melting of snow and ice in highland areas

Basically bio-based mater

Dead wood, leaves, plants, shrubs, sometimes trees

3.

Hurricanes and heavy rainfalls

Mixed materials, depending on regions

Trees, wood, plastic, pallets, man-made structures and products

4.

Monsoon winds and rainfalls in (sub) tropics

Predominately wood and other organic materials

Dead wood, plants, crops, plastic, wrapping material, litter

5.

Tsunamis

Mixed materials, mainly related to local human activities

Man-made structures, boats, ship hulls, containers, harbor cargo

6.

Dam breaches, deforestation, other human failures

Mixed natural and man-made materials

Trees, pieces of houses, vehicles, other structures and products

5.7 LOADS FROM SHIPS AND FLOATING OBJECTS

397

Observe that both the causes and composition of debris carried by water can be very diverse. As a result, the character and sizes of loads on hydraulic closures are also diverse. Debris can, for example, induce an additional hydrostatic load by jamming the pool above the dam, but it can also cause an impact by hitting the gate. It is, therefore, important to correctly forecast the character and estimate the size of these loads. The USACE manual [1] not only considers debris as an impact load, but it also suggests that when debris is a concern from another point of view, it should apparently be considered that way or provisions should be made to prevent such an action. Also the ASCE-7 [21] and the FEMA manual [40] consider debris as an impact load. They give formulas to estimate its magnitude and location for buildings, and they also stress that locally adopted guidance may be more relevant. The photo in Fig. 5.66 helps to imagine various characters of loads that debris can induce. The shown situation is very unusual in the Panama Canal and refers to controlled cleaning outside the navigation channel, but it happens. This debris can be classified into the first group of Table 5.15. In Europe, there is little specific guidance concerning the design loads by debris. Like in the United States, an investigation of local conditions is generally recommended in order to determine the design loads by debris and uncontrolled floating objects. The issue is of particular concern in all scenarios of flooding, by rivers as well as by storm surges at sea. An example is the design of the Hartel Canal Storm Surge Barrier near Rotterdam, the Netherlands, the hydraulic loads of which have globally been presented in Fig. 5.7a. As shown in the figure, the barrier gates will operate under overtopping flow in the case of high storm surges. In that case there will be no ship movement in the area. However, as Rotterdam is the largest European harbor, there is a probability that storm surge water will carry uncontrolled floating objects, particularly containers. Therefore, a long floating ship arrestor was provided, as shown in Fig. 4.7, which, however, did not operate satisfactorily. In addition, the gates were designed to resist a direct impact of a container falling on any of the lateral trusses between the retaining wall and the read chord. This truss will be damaged in such a case but the gate will not collapse (Fig. 5.67). Similar cases were later investigated in Japan as part of the tsunami risks in harbors. The details and references to publications can be found in the PIANC report [18]. This report gives a simple equation for deriving the collision loads by floating containers on structures in harbors. The considered load is a horizontal impact force Fh, to be computed as Fh ¼ m 

vc Δt

(5.67)

where: m ¼ total mass of container including its cargo; vc ¼ estimated collision velocity; Δt ¼ deceleration time of container during collision. FIG. 5.66 Incidental debris in Gatun Lake area in the Panama Canal. Photo ACP.

398

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.67 Container overtopping the Southern Gate of Hartel Canal Barrier, design approach.

40 ft container: 12.19 × 2 .44 × 2.59 m

Storm surge side

Damaged truss out of service

Defended side

Remaining trusses still hold it

Although the report does not mention this, it is advisable to multiply the mass m by a factor Cm ¼ 1.20, to account for hydrodynamic effects, as in formula (5.66). The deceleration time is often difficult to determine. The report estimates it as 0.1–1.0 s depending on the stiffness of the container and the impacted structure. Hydraulic gates can usually be classified as relatively elastic, which means that Δt ¼ 0.5–1.0 s is probably a safe assumption (authors’ comment).

5.8 LOADS FROM SYSTEM MALFUNCTIONING 5.8.1 Obstacles During Gate Motion The last group of loads that can appear on hydraulic closures when in operation are loads from system malfunctioning. We will use this term as a collective name for various failures that might have been prevented if the gate system (and the systems that directly support it) operated as designed. This issue can be sensitive because it lies on the verge of human errors and people often don’t like to admit their errors. Here are two examples that should help clarifying it: (a) Obstacle in the way of gate travel obstructing the correct closing: Although the gate and its drives operate correctly in this case, it still should be classified as system malfunctioning. The obstacle should be prevented from finding its way to block the gate motion; and if it was dropped, it should have timely been detected and removed. This is a failure of systems that directly support the gate function. (b) Breach of levees in New Orleans during Hurricane Katrina in 2005: This levee breaching was, strictly speaking, not a result of system malfunctioning, because the New Orleans’ levee system was at that time not designed to resist loads of such a magnitude. As a result, the levees were too weak to withstand the magnitude of the storm surge, and as such it was not surprising that they would fail. The discussion in this section concerns the loads from obstacles during gate motion. This includes the cases of obstacles preventing gate closing, like in the above example (a), but it also covers the obstacles preventing gate opening. The obstacle must, obviously, be sufficiently strong and rigid to block the gate movement, otherwise it only slows down the gate motion or causes drive load to increase. For miter gates, for example, the Dutch design guidelines [55] distinguish the following load cases that can be induced by obstacles: • • • •

obstacle between gate leaf and sill; obstacle on the bottom between gate leaf and its recess; floating obstacle between gate leaf and recess; and floating obstacle between both leaves of a miter gate.

5.8 LOADS FROM SYSTEM MALFUNCTIONING

399

Obstacles can generate substantial loads, particularly on miter gate hinges, despite the common practice of limiting the drive loads when the gate approaches the mitered and the recessed position. A question that the designer needs to answer then is which position of the obstacle should be taken into account to estimate these loads. After all, positions close to the leaf rotation axis result in higher hinge reactions, so that small enough distance can, theoretically, break every pintle or hinge. An anecdote says that a young engineer asked this question once to Mr. E. Ypey, a highly respected head of Rijkswaterstaat Steel Structures Department in the 1970s and 1980s. The answer was “Take one meter.” For over 30 years since then, Dutch engineers always computed loads from obstacles at a distance of 1.0 m from the gate leaf rotation axis. Today, this one of the so-called “Ypey numbers” is slightly differentiated in Rijkswaterstaat guidelines [55]. For conventionally framed miter gates, the recommended distances are as follows: • in chamber widths up to 12.0 m: 1.00 m; • in chamber widths from 12.0 to 20.0 m: 1.25 m; • in chamber widths above 20.0 m: 1.50 m. An example of this practice is the determination of gate hinge loads from obstacle cases in the project of Naviduct Enkhuizen, which employs hydraulic cylinders linked indirectly, as shown in Fig. 5.45f. Two cases of the considered obstacle loads are presented in Fig. 5.68. The obstacle distance in this project has in both cases been set at 1.0 m, following the classical “Ypey number,” although the lock chamber is slightly wider than 12.0 m. The maximum cylinder drive forces and the resulting hinge reactions are illustrated in Table 5.16. The gates in this particular project are of the fixed-hinged type according to the European terminology (see sketch C1 in Fig. 3.17), meaning that all loads, including the hydraulic loads, are passed through gate hinges to the lock crown. The hydraulic loads proved to generate higher hinge reactions than the loads from obstacles in Table 5.16. However, if these gates were of the free-hinged type, the loads from this table would probably have been prevailing in the design. In load combinations, the Dutch practice is to investigate the cylinder force with a load factor of 1.20, and the resulting hinge reactions with additional load factor of 1.25. No yielding in gate hinges, their connections, or vicinities shall be allowed. These regulations are partly inspired by the same policy of controlling the damage mechanism as in the case of the ship collision (see Section 5.7.3). The US design practice is in this case similar. In the United States, no particular requirements to consider loads from obstacles are issued by USACE. The assumption is that these loads are prevented using air bubblers, raised sills and providing sufficient room in both gate recess and the gate itself in order not to allow debris get clammed between the gate and the wall. For example, the new gates in the Columbia River locks close against a 1.22 m (4 ft) deep sill. It permits debris to travel into the lock and then sink below the gate instead of getting trapped against the sill when closing the gate, or against the recess when opening it.

5.8.2 Drive Synchronization Failures Gates that consist of multiple leaves usually require well-synchronized opening and closing procedures of those leafs to operate correctly. This applies to the gates in which the leaves are supposed to move simultaneously, as well FIG. 5.68 Two cases of loads due to obstacles in the project of Naviduct Enkhuizen, the Netherlands. (a) Obstacle between gate and sill and (b) floating obstacle in recess.

400 TABLE 5.16

5. DESIGN LOADS AND LOAD COMBINATIONS

Cylinder Drive Forces Fc and Hinge Reactions Rx and Ry in Obstacle Cases From Fig. 5.68 Cylinder forces and obstacle assumptions

Angular gate leaf position

Maximum cylinder force

Distance obstacle—rotation axis

10 degrees from recessed position

175 kN (compression)

1.00 m

51.6 degrees of intermediate angle

305 kN (compression) +210 kN (tension)

Probability of obstacle negligible in this range

10 degrees from mitered position

+190 kN (tension)

1.00 m

Hinge reactions from obstacle between gate and sill (a) Gate hinge

Reaction Rx

Reaction Ry

Top hinge

175 kN

–

Bottom pintle

364 kN

151 kN

Hinge reactions from floating obstacle in recess (b) Gate hinge

Reaction Rx

Reaction Ry

Top hinge

+183 kN

+250 kN

Bottom pintle

+26 kN

+145 kN

as to the gates in which the leaves are supposed to move subsequently or in yet another synchronized manner. The most prominent example of the first group is a miter gate; examples of the second group are a multi-leaf vertical lift gate and vertical lift gate with a flap. Drive synchronization is also an issue in the gate systems that comprise single leaves, but in which the movement requires double or multiple drive actuators. Examples of this group are wide vertical lift gates, hinged crest gates, radial gates with double-sided drives, and steel-rubber gates driven by more bladders. In all these cases, the function of double or multiple drives is to symmetrically distribute the drive loads on a gate leaf, which usually results in identical actuators and their actions. Another reason for multiple drives can be to make them provide different motion components of the gate. In that case, the actuators usually differ from each other. Examples of this group are some rotary segment gates (like in the Thames Barrier), Poiree gates, barge gates, and hinged bridge gates. See the discussion of diverse gate types in Chapter 3 for global drive arrangements in all the types of gates mentioned earlier. This introduction should leave no doubt that there are many drive synchronization issues that require attention in hydraulic gates; and that can apparently generate loads in case of failure or malfunctioning. The designer’s way to manage these issues can be summed up in the following three objectives: • eliminate synchronization issues by providing single drives or hard couplings; • provide the best possible control of the remaining synchronization issues; and • minimize the hindrance and costs in case this control fails. Two simple solutions to the first objective are shown in Fig. 5.69, considering vertical lift gates as an example. It is obvious, however, that such solutions cannot be applied everywhere, certainly not to gates in wide, navigable openings. How serious the consequences of poorly synchronized gate drives can be is presented in Fig. 5.70. It shows the failure of the Melvin Price Lock gate on the Upper Mississippi River in October 2004. This accident is discussed in more detail in Chapter 16. For the purpose of the current discussion, it is relevant that the malfunctioning resulted in incorrectly mitered gate leaves, detected neither by the programmable logic controller (PLC) nor by the lock operating staff. While filling the lock, the growing water pressure forced the gate leaves downstream damaging the hinges and large parts of the structure. Another example that gives an impression of the range of loads which can result from system failures is given in Fig. 5.70. It shows the compromised low-tide gate of the Ems Canal Lock in Delfzijl, the Netherlands. In this case, the drives did not malfunction but the lock operator failed to close the gate in time before the low tide. After realizing his mistake, he still activated the closing, but with flow in the lock chamber. The result is visible in the photo. It raises questions not only about physical pressures on gates, but also mental pressures that the lock crews may experience.

5.8 LOADS FROM SYSTEM MALFUNCTIONING

401

FIG. 5.69 Avoiding synchronization issues in vertical lift gates: (a) single drive cylinders, tide control gates in Australia, AWMA Water Control Solutions, and (b) hard drive coupling to hoist drums, flood control structure in New Orleans, United States.

FIG. 5.70 Miter gate failure at Melvin Price Lock on the Upper Mississippi River: (a) gate leaves forced downstream and torn away from hinges; (b) broken top hinge anchors and strut arm of gate drive; and (c) damaged components of gate bottom pintle. Photos USACE.

In both examples (Figs. 5.70 and 5.71), the resulting loads on gates were so large and out of the ordinary that it would probably not have been economical to account for them in the design. This brings up the question, which loads from drive synchronization failures should be taken into account. The answer can be obtained by cost estimations of different options; and it strongly depends on the navigation intensity (lock gates) or economic significance of the defended areas (flood barriers). In the Netherlands, where these aspects are crucial for the country’s economy, official guidelines [55] require consideration to gate overloading as result of failing operating system. The top requirement is that a failure of this system may not result in a damage causing the loss of gate functionality. If the gate drive machinery does not explicitly eliminate that risk, the designer must assume that the gate can run against the sill or recess at full velocity. In a semiprobabilistic (LRFD) or probabilistic analysis, the frequency of such events should be estimated within the range of once in the 15,000 to once in 5000 closing or opening movements of an independently driven gate leaf. These values result from a failure probability analysis based on the data from Ref. [25]. If combined with the USACE design philosophy, these numbers would in most cases indicate a drive synchronization failure once a year or once in a few years. This classifies the loads from such failures as “usual,” with all the consequences of this in terms of load combination factors. The issue still needs to be researched, however, because statistical data in the United States may be different.

402

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.71 Damage to the gate of Delfzijl Lock in Ems Canal, the Netherlands. Photo Rijkswaterstaat.

5.8.3 Other Malfunctioning Loads As pointed out in Section 5.8.1, it is often difficult to unequivocally classify the loads from system malfunctioning as such and not as human errors. In fact, the cause of such loads can in many cases be found in the interface between the system and people, including site crews, maintenance crews, and the managers. The two failure examples from Figs. 5.70 and 5.71 had also, next to the system reasons, the contributions of human errors; the second probably to more extent than the first. The interface mentioned earlier becomes more and more significant as the systems grow more complex. Technological developments, particularly in information and control technology, take more and more control tasks over from humans. This makes work comfortable, but it also widens the distance between people and the physical conditions of both satisfactory operation and failures of hydraulic closures, reducing the understanding of these conditions and the commitment to control them. There is only about 20 years of difference between the manners of gate operation shown in photos (a) and (b) in Fig. 5.72. Moreover, the operator in photo (b) may count himself lucky that he can see the physical gates from a distance. The lock in photo (a) has no operator today, because all the 19 locks in the South Willem’s Canal have been refurbished,

FIG. 5.72 Direct and remote operation of hydraulic gates (a) gate operation in a lock of South Willem’s Canal, the Netherlands, in the 1970s and (b) control of navigation through the Thames Barrier in London in the 1990s. Photos Beeldbank Rijkswaterstaat.

5.9 TRANSPORT AND INSTALLATION LOADS

Control systems (C) Electrical (E) Mechanical (M)

Contact problems Drive problems Other reasons

223 (M)

434 (E)

39 610 (C)

Failures globally

FIG. 5.73

403

28 156

Herein mechanical (M)

Lock gate operation failures in the Rijkswaterstaat district of Limburg during the period 1999–2004, the Netherlands [50,64,65].

closed for the public; and are now remotely operated from a single place. It goes without saying that their operators, despite the cameras installed, will never see or sense the potential malfunctioning as well as the operator in photo (a). Since this development is irreversible, it is now more important than ever that gate designers correctly recognize all possible forms of system malfunctioning. This is not an easy task. It requires extensive expertise, anticipation skills, and independent, critical attitude that will not easily bow to the praising of diverse technologies by their suppliers. The designer’s colleagues and superiors may also not always appreciate this attitude. Yet, it is desirable. The number of potential loads from system malfunctioning including human errors is large—too large for a comprehensive discussion in this book. An indication of their nature has been provided in the investigation performed at request of one of the authors of this book in the Rijkswaterstaat district of Limburg. The waterways in this district comprise some of the Netherlands’ main navigation routes to Belgium, France, and Germany, which makes them very important for the economies of many regions in the Europe. The investigation was based on the failure data during the period from January 1999 till April 2004. Only the failures that caused significant (longer than about 1 h) operation break were considered. As shown in the left pie chart in Fig. 5.73, 82% of all the failures were caused by either control (PLC) or electrical system. Note that these two systems make the difference between the gate operation in photos (a) and (b) of Fig. 5.72. Only 18% of the failures had mechanical reasons, predominately contact issues (see the right pie chart). Again, the above does not mean that engineers should consider eliminating the PLC’s, let alone electric power. There is no going back. What it means comes down to the following two conclusions: • A more demanding, rigorous approach should be taken when selecting PLC-based control systems for hydraulic gates. This applies in the second place also to electric power systems. A proven low probability of failure under harsh operation conditions should each time be required. • Failures caused by operating and power systems should be considered in the design; and the loads generated by these failures should be made part of standard analysis of hydraulic gates. The load factors ought to be determined on the ground of risk analysis.

5.9 TRANSPORT AND INSTALLATION LOADS Hydraulic gates in most cases are entirely manufactured at contractor’s locations (fabrication shops), then shipped or otherwise transported to their project sites and installed there. Only very large gates or structures at hardly accessible locations are manufactured and transported in smaller subassemblies. Examples of the latter are the early large rolling gates in Germany and Belgium, large drum gates in US dams (like the Grand Coulee Dam), and the world’s largest sector gates of the Maeslant Storm Surge Barrier in the Netherlands. Some of these gates were not only bolted but also welded together (or riveted like Grand Coulee gates) on project sites due to their unique dimensions. This required longer planning periods and an extensive transfer of fabrication technology, including quality control, to the site. After all, the quality assurance procedures for field fabrication are identical to shop fabrication requirements [1]. One illustrative case of manufacturing, transport, and installation of hydraulic gates in subassemblies was the project of the Rhine River weirs in the Netherlands. The so-called visor gates of these weirs, presented in more detail in Section 3.11, were fabricated in sections as shown in photo (a) in Fig. 5.74.

404

5. DESIGN LOADS AND LOAD COMBINATIONS

FIG. 5.74 Construction of the Rhine River weir in Hagestein, the Netherlands (a) gate sections in fabrication shop ready for shipment and (b) visor gates assembled in the dry at the project site. Photos Beeldbank Rijkswaterstaat.

These sections were shipped to the site and assembled there in a new riverbed section that had deliberately been excavated and kept dry for construction purposes (see photo (b) in Fig. 5.74). Most assembly joints were riveted, which reflects the construction technology (late 1950s) of these gates. Today, the assembly joints of this kind would in most cases be bolted. Proper requirements for splices and assembly connections can, for example, be found in the AISC Steel Construction Manual [66]. The division of responsibilities between the owner, fabricator, and the erector of the steel hydraulic closure should be specified in the contract, based on standard practices in the country of the project. In the United States, such practices make part of the AISC-316 code that is entirely quoted in Ref. [66]. They are further worked out by USACE in Ref. [67]. In Europe, the bases of such practices are defined in Eurocodes 1 and 3; and the details make part of national appendices to these codes or recommendations issued by the national waterway authorities, like Rijkswaterstaat in the Netherlands [55]. These standard practices apply, obviously, also to the scenarios in which hydraulic gates are entirely manufactured and assembled in fabrication shops, then shipped to their project sites and installed there. Such scenarios have many advantages in terms of time, quality, and costs. They form a nearly standard choice in hydraulic projects of today. Transport and installation loads then make part of an erection plan that should mainly contain the following documents: • Description of gate transport and installation procedure in phases, including global drawings, lists of materials and conditions to be provided on the site, and the like. • Calculation of all loads and load combinations that may be of concern in this procedure. • Relevant data about both the gate and transport and erection equipment to be utilized, including legally required documents like certificates and test reports. • Documentation and approval reports of auxiliary transport and erection structures to be used, like temporary supports, so-called “rosters,” sea fastening, lifting lugs, spreader beams, and tilt supports. • Time schedule and the list of personnel involved, including their roles and qualifications. • Restrictions to navigation and/or traffic if required; and the plan to manage them. Transport and erection loads are in the first instance derived from the gate self-weight and the weight of auxiliary structures mentioned above. Yet, some wind loads and (if potentially possible) rain or snow loads should also be taken into account, although gate shipments and erections are normally carried out under good weather conditions. A common practice is to include about 50% of the characteristic values of these loads in the load combinations for transport and erection. The main component of these combinations—self-weight load—should in the LRFD approach be taken with a load factor as indicated in Table 5.4. However, this factor does not account for incidental inertial and impact loads that cannot entirely be eliminated during transport and erection. The existing codes also do not specify the magnitudes of these loads, leaving it to the gate erector. This is correct in the sense that safe gate installation is in the first instance his responsibility, but it weakens the position of external control and does not stimulate transparency.

5.10 DESIGN LOAD COMBINATIONS

405

Indirect indications for the choice of load factors to cover the effects mentioned above could be found per comparison with other normative regulations and practices. The following are a few examples: • The AASHTO bridge design code [4] states this about the jacking forces for bridges: “Unless otherwise specified by the Owner, the design forces for jacking in service shall not be less than 1.3 times the permanent load reaction at the bearing, adjacent to the point of jacking.” The loads due to bridge jacking and the risks involved [68] are comparable to those in hydraulic gate installations. • Manufacturers of heavy steel subassemblies and concrete prefabs use their own, practically proven dynamic factors for the handled weights. Below are approximate ranges of these factors, followed by many European companies in this branch [69]: • handlings in shop by stationary cranes: 1.10–1.30; • transport by a lift truck on flat surfaces: 1.30–1.60; • hoisting by a stationary crane on the site: 1.30–1.50; • hoisting by a mobile crane on the site: 1.50–1.60; • transport by a shovel on rough surfaces: 1.60–2.00; • transports under extreme conditions: >2.00. • In the offshore branch, heavy installations at sea are normally engineered with a dynamic factor of about 1.30 over the weight of installed subassemblies. This factor covers possible weather changes but no heavy storms, which normally lead to postponing such works. These data can help estimating the dynamic factors for transport and erection loads. The reader should not, however, confuse these factors with load factors in the sense of the LRFD method. Note that the factors mentioned here lead only to characteristic values of transport and erection loads including their dynamic effects, like inertial forces and small impacts. As such, they do not contain any safety margin. To provide the required safety in the LRFD method, one should additionally apply load factors γ G, for example from Table 5.4. In the ASD method, a proper safety factor SF should be applied to the stress that represents the nominal resistance Rn of the structure (see Section 5.1.2).

5.10 DESIGN LOAD COMBINATIONS The load cases as described in Sections 5.2–5.9 can be seen as basic for hydraulic closures, but they do not necessarily exhaust this category. Hydraulic structures can still be exposed to other, less common loads. Some of them are discussed Chapter 6; others like wind loads play usually a minor role (exceptions like vertical lift gates notwithstanding) and do not require apart discussion in this book. Having determined all the relevant single load cases, one can compile their combinations that have a reasonable probability of occurrence and should be investigated in further analysis. Such combinations are compiled for a number of so-called “limit states,” the theory of which can be found in the literature on structural mechanics. There are, normally, three to five limit states to be considered in the design of hydraulic gates, including the following: • Ultimate Limit State (ULS): normally associated with static strength of the structure and its components preventing the collapse. • Serviceability Limit State (SLS): normally associated with geometrical and physical properties enabling satisfactory operation. • Fatigue Limit State (FLS): normally associated with fatigue strength of the structure preventing both the collapse and loss of serviceability. The latest USACE manuals additionally distinguish the following two limit states: • Fracture Limit State: associated with the potential for fracture as opposite to the loss of shape by deformation; in fact a subcategory of ULS. • Extreme Limit State: associated with USACE category of “extreme loads” (see Table 5.13); in fact also a subcategory of ULS.

406 TABLE 5.17

5. DESIGN LOADS AND LOAD COMBINATIONS

Loads and Load Combinations for the Born and Maasbracht Lock Gates in the Meuse

The load combinations discussed in this book have focused on the first three limit states mentioned above, assuming that the ULS also covers the two additional limit states. Readers wishing to follow all the five limit states apart are advised to consult the USACE manual [1]. The discussion in this section is also limited to load combinations for actual gate structures. It does not cover the load combinations that are specific for drive machinery or the gate operating system. As pointed out in Section 5.4.2, the Rijkswaterstaat design guide [14] distinguishes 22 such combinations. Their discussion falls, however, beyond the scope of this book. Table 5.17 lists the design loads and shows their load factors in nine basic load combinations for a typical lock gate project in the Netherlands. This particular example refers to the new miter gates of the Meuse River locks in Born and Maasbracht that were refurbished in the early 2010s [15]. Typical hydraulic loads on these gates are shown in Fig. 5.11. Fig. 5.75 gives an impression of gate replacement in the downstream crown of one of the lock chambers in Born. This table reflects the views in the period when the Eurocodes were not entirely implemented yet and diverse load factors for semi-probabilistic design (term equivalent to US LRFD) were still under discussion for hydraulic gates. The quoted load factors may, therefore, slightly differ from those in the documents issued later. Nevertheless, Table 5.17 illustrates the general logic of load combinations in this design approach. The first two loads, “self-weight” and “service loads on walkways,” make part of most combinations; the second as a conservative assumption since there was not much place for loads on walkways anyway at those gates. The loads FIG. 5.75 Gate replacement in a chamber of the Born Lock in the Meuse (a) old gate leaf hoisted out and laid and tilted for barge shipment and (b) new gate installed and operating. Photos Rijkswaterstaat.

REFERENCES

407

below form a characteristic “staircase” in the table. Note that one of these loads (with a factor in shaded cell) is in each subsequent combination assumed to be the main concern. This “leading” load is given a high factor γ; in this case 1.50 if expected to occur frequently, or 1.25 if expected to occur very seldom. All the other loads make either no part of that particular combination, or (like permanent loads) are included with lower load factors than the “leading” load. Their inclusion or exclusion depends on the probability that they will coincide with the “leading” load, to be estimated by the designer. In most cases, it is quite evident. The load combinations in Table 5.17 have been compiled with respect to the three main limit states, as discussed earlier. In this project, the considerations that resulted in the choice of these combinations and the load factors can be summed up as follows: • Combinations A, B, D, and E are fundamental combinations for ULS. In A, the extreme hydraulic load has a lower γ factor due to its very low probability of occurrence. It reflects the Dutch guidelines [25]. This load can only occur when the next lock downstream the river fails causing dewatering of the lower pool. In the USACE approach, this would be classified as extreme limit state. • Combination B, but with lower γ factors as indicated in the table, also represents the combination for FLS. It was expected that it would govern the overall fatigue design of the gate. In the vicinity of drive connection, the fatigue design might be governed by combination C. • Combinations B and C are in this case also the combinations for SLS. The nominal residual water head in combination C has been set at 0.10 m. It is assumed that every opening and closing is exposed to this head, although it will happen sooner during opening. • Combinations F and G are alternative combinations for ULS. In correctly operated locks, the probability that the leading loads of these combinations occur is very low. Dutch practice allows, therefore, a limited local yielding in such cases, which explains the lower load factor. • Combination H can be significant for all the three limit states. It can affect the strength (ULS) or contribute to the wear (SLS) and fatigue (FLS) of hinge components. If the gate hinge system does not exclude it, its probability of occurrence is high. Therefore, high load factor is chosen. • Combination I is a fundamental combination for ULS in construction stage of the project. The high load factor is additionally justified by the fact that installations and removals will be carried out a number of times in the service life of the gate. This example does not cover all load cases that may be relevant for hydraulic gates, or all cases discussed in this chapter. Ship collision, for example, did not need to be considered because there were fixed ship arrestors across the lock chambers, one of which can be observed in photo (a) of Fig. 5.75. The same applies to diverse other loads like wind (insignificant) or leakage of air tanks (no tanks). Moreover, load combinations for hydraulic gats in other structures than navigation locks will differ still more from those in Table 5.17. Nevertheless, the discussed example should help setting up adequate load combinations also for other gates. Readers interested in load combinations that include different loads or cover gate types different than miter gates are encouraged to consult specialist guidance in this field. In Europe, it is usually provided by national waterway authorities, like Rijkswaterstaat in the Netherlands [55]. In the United States, proper guidance can be found in USACE engineering and design manuals, particularly in Ref. [1]. This manual contains separate tables with load combinations and load factors for the most frequently used type of hydraulic closures, like miter gates, Tainter gates, and vertically hinged sector gates. It does not handle all the load cases discussed in this book, but it gives more rules for associating diverse load cases with specific limit states. Finally, one should not forget that the load factors γ discussed in this chapter are not the only factors that should be applied in a semi-probabilistic analysis of hydraulic gates, or the LRFD method. As already mentioned, the factored loads must in this approach be compared with the—also factored—resistance of the structure. The factors to be used for that resistance are the resistance factors ϕ, as defined by Eq. (5.4). The Eurocodes use a symbol γ M for them, calling them “global partial factors for particular resistances.” This sounds long and confusing, which is why the term “material factors” can also be heard sometimes. It is recommended to consult the latest versions of appropriate codes for still more factors that the designer may be expected to apply.

References [1] USACE, Design of hydraulic steel structures, Engineering and design manual ETL 1110-2-584, U.S. Army Corps of Engineers, Washington, DC, 2014. [2] PIANC, Semi-probabilistic design, concept for inland hydraulic structures, Report of Working Group No. 140, PIANC Inland Navigation Commission (InCom), Brussels, 2015.

408

5. DESIGN LOADS AND LOAD COMBINATIONS

[3] CalTrans, Bridge design specifications, in: Bridge Design Practice, Chapter 1. California Department of Transportation, Sacramento, 2015. [4] AASHTO, AASHTO LRFD Bridge Design Specifications, American Association of State Highway and Transportation Officials, Washington, DC, 2012. [5] EN 1990 (2002), Eurocode—Basis of Structural Design, European Committee for Standardization (CEN), Brussels, 2002. [6] A.S. Nowak, Calibration of LRFD bridge design code, Department of Civil and Environmental Engineering Report UMCE 92-25, University of Michigan, Ann Arbor, 1993. [7] B.R. Ellingwood, Load and resistance factor design for steel miter gates, Johns Hopkins University and US Army Corps of Engineers, Washington, DC, 1993. Report ITL-93-4. [8] J.K. Vrijling, Design of concrete structures—probability design method, Proceedings “Eastern Scheldt Storm Surge Barrier” of the Delta Barrier Symposium, Rotterdam, 1982. [9] G.B. Baecher, J.T. Christian, Reliability and Statistics in Geotechnical Engineering, John Wiley & Sons Ltd., Chicester, 2003. [10] Daniel R.A. Schuiven van de Hartelkering – Ontwerpproces, presentation on the session of Steel Construction Society, Hollandia BV, Krimpen a/d IJssel, January 25, 1996. [11] R.A. Daniel, C. Pouw, A.L.J.M. Donkers, Wilhelminakanaal Vervanging Middendeuren Sluis III, Design report WIL-D-00100, Bouwdienst Rijkswaterstaat, Zoetermeer, 2000. [12] J.K. Vrijling, et al., Manual Hydraulic Structures, Revision of February 2011, Delft University of Technology, Delft, 2011. Course CT3330, . [13] C.C.L. Feij, Nauwkeurigheid van formules voor windopzet aan de hand van meetgegevens van het IJsselmeer, Delft University of Technology, Delft, 2015. [14] Bouwdienst Rijkswaterstaat, Design of Locks, Directorate-General of Public Works and Water Management, Civil Engineering Division, Utrecht, 2000 (part 1 in English, part 2 in Dutch), . [15] Rijkswaterstaat, Vraagspecificatie VS-1C Deel Sluiscomplex Maasbracht, Rijkswaterstaat Maaswerken, Maastricht, 2007 (not published), . [16] USBR, Shasta Dam and Reservoir enlargement, initial assessment study, Central Valley Project California, Technical Service Center of U.S. Bureau of Reclamation, Denver, CO, 1998. [17] PIANC, Tsunami disasters in ports due to the Great East Japan Earthquake, Report of Working Group No. 122, PIANC Maritime Navigation Commission (MarCom), Brussels, 2014. [18] PIANC, Mitigation of tsunami disasters in ports, Report of Working Group No. 112, PIANC Maritime Navigation Commission (MarCom), Brussels, 2010. [19] K. Tanimoto, et al., On the hydraulic aspects of tsunami breakwaters in Japan, in: Tsunamis—Their Science and Engineering, Terra Scientific Publishing Co., Tokyo, 1983, pp. 423–435. [20] R. Asakura, et al., Tsunami wave force acting on land structures, Proceedings of 28th International Conference on Coastal Engineering, Cardiff, Wales, 2002. 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Oumeraci, et al., Probabilistic Design Tools for Vertical Breakwaters, A.A. Balkema Publishers, Amsterdam, 2001. [28] G. Sainflou, Essai sur les digues maritimes verticals, Annales des Ponts et Chaussees, No. 98-11, 1928, pp. 5–48. Paris. [29] J. Lewin, Hydraulic Gates and Valves in Free Surface Flow and Submerged Outlets, second ed., Thomas Telford Publishing, London, 2001. [30] H. Chanson, The Hydraulics of Open Channel Flow, an Introduction, Butterworth-Heinemann (Elsevier), Oxford (UK)/Waltham (MA), 2004. [31] G. Schmaußer, H. N€ olke, E. Herz, Stahlwasserbauten – Kommentar zum DIN 19704, Ernst & Sohn, Berlin, 2000. [32] G. Wickert, G. Schmaußer, Stahlwasserbau: Theorie, Konstruktive L€ osungen, Spezielle Probleme, Springer-Verlag, Berlin, Heidelberg, New York, 1971. [33] USBR, Design of Small Dams, US Department of Interior, Bureau of Reclamation, third ed., US Government Printing Office, Washington, DC, 1987. [34] R.L.E. Stockstill, A. Hammack, J.E. Hite, Lock culvert valves: hydraulic design considerations, ERDC/CHL TR-11-4, U.S. Army Engineer Research and Development Center, Vicksburg, MS, 2011. http://acwc.sdp.sirsi.net/client/search/asset/1000842. [35] USACE, Hydraulic design of spillways, Engineering and Design Manual 1110-2-1603, U.S. Army Corps of Engineers, Washington, DC, 1990. [36] USACE, Hydraulic design of lock culvert valves, Engineering manual EM 1110-2-1610, U.S. Army Corps of Engineers, Washington, DC, 1989. [37] USACE, Hydraulic design of reservoir outlet works, Engineer manual 1110-2-1602, U.S. Army Corps of Engineers, Washington, DC, 1980. [38] USACE, Hydraulic design of navigation locks, Engineer manual 1110-2-1604, U.S. Army Corps of Engineers, Washington, DC, 2006. [39] Deltares: Delft3D-FLOW, simulation of multi-dimensional hydrodynamic flows, user manual, Version 3.15.34158, Deltares Systems, Deltares, Delft, 2014. [40] FEMA, Determining site-specific loads, Chapter 8. FEMA P-55, in: Coastal Construction Manual, fourth ed., 2011. https://www.fema.gov/ media-library/assets/documents/3293. [41] D. Pnueli, C. Gutfinger, Fluid Mechanics, Cambridge University Press, Cambridge, 1992. [42] O.J. Jensen, H. Oumeraci, Breakwaters, Chapter 7, in: H. Agerschou, et al., (Ed.), Planning and Design of Ports and Marine Terminals, Thomas Telford Ltd., London, 2004. [43] PIANC, Climate change and navigation, Report of Task Group 3 of PIANC, Environmental Commission (EnviCom), Brussels, 2008. [44] IPCC: Climate change 2014, findings of working group II, AR5, Intergovernmental Panel on Climate Change, www.ipcc.ch/report/ar5/wg2/ docs/WGIIAR5_SPM_Top_Level_Findings.pdf.

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[45] NOAA, Tides & Currents, Sea Level Rise Trends, NOAA National Ocean Service, Silver Spring, MD, 2017. https://tidesandcurrents.noaa.gov/ sltrends/sltrends_us.htm. [46] R. Harris, et al., Assessment of Vulnerability to Sea Level Rise and Recommended Mitigation Strategies for Pasquotank County, NC, University of North Carolina, Chapel Hill, 2015. [47] PIANC, Movable bridges and rolling gates – design, maintenance and control, Report of Working Group No. 173, PIANC Inland Navigation Commission (InCom), Brussels, 2017. [48] R.A. Daniel, Panama Canal opens its gates to more and larger vessels, Inzynieria Morska i Geotechnika, No. 4/2016, Gda nsk, (2016). [49] R.A. Daniel, Weight Control Reports of the Norsk Hydro Oseberg 2 Oil Production Platform (not published), Grootint BV and Iv Consult, Dordrecht-Zwijndrecht-Papendrecht, 1989–1990. [50] R.A. Daniel, Contact Behavior of Lock Gates and Other Hydraulic Closures – Research Results, Investigations and Field Experiences, LAP Lambert Academic Publishing, Saarbr€ ucken, 2011. [51] USACE, Mechanical and electrical design for lock and dam operating equipment, Engineering Manual EM 1110-2-2610, U.S. Army Corps of Engineers, Washington, DC, 2013. [52] USACE-WES, Study of the forces occurring during the movement of miter gates, U.S. Army Corps of Engineers Waterways Experimental Station, Technical report 74-11, Wicksburg, 1974. [53] USACE-WES, Operating forces on miter type lock gates, U.S. Army Corps of Engineers Waterways Experimental Station, Technical report 2-651, Wicksburg, 1964. [54] K.-H. Grote, E.K. Antonsson (Eds.), Springer Handbook of Mechanical Engineering, Vol. 10, Springer Science and Business Media, New York, 2009. [55] Rijkswaterstaat, Richtlijnen Ontwerpen Kunstwerken, ROK 1.4, Technisch Document RTD 1001:2017, Rijkswaterstaat Dienst GPO, Utrecht, 2017. [56] R.A. Daniel, Global ontwerp roldeuren Nieuwe Zeesluis, Plan van Aanpak (classified), Project Zeetoegang IJmond, Rijkswaterstaat, Utrecht, 2012. [57] L.J. Vankan, IJsbestrijding bij kunstwerken–Voorkomen en bestrijden van vorstproblemen, Bouwdienst Rijkswaterstaat, Uitgeverij Matrijs, Utrecht, 2000. [58] USACE, Engineering and design-ice engineering manual, EM 1110-2-1612, Change 2, U.S. Army Corps of Engineers, Washington, DC, 2006. [59] EN 1991-1-7 (2011): Eurocode 1—Actions on Structures, Part 1–7: General Actions-Accidental Actions, European Committee for Standardization (CEN), Brussels 2011. [60] DIN 19704-1 (2014), Hydraulic Steel structures—Part 1: Criteria for Design and Calculation, Deutsches Institut f€ ur Normung, Berlin, 2014. [61] PIANC, Design of lock gates for ship collision, Report of Working Group 151, PIANC Inland Navigation Commission (InCom), Brussels, 2014. [62] CICP: Panama Canal Third Set of Locks Project, Pacific Locks Complex Gate Type C, design analyses, CICP Consultores Internacionales, July 2010 (not published). [63] EAU 2012, Recommendations of the Committee for Waterfront Structures, Harbors and Waterways, ninth ed., Wiley–Ernst & Sohn, Berlin, 2015. [64] PIANC, Mechanical and electrical engineering—lessons learnt, Report of Working Group 138, PIANC Inland Navigation Commission (InCom), Brussels, 2013. [65] R.W.M. Boland, T.G. Van der Horst, Onderzoek storingen aan sluizen, not published, performed at request of R.A. Daniel, WED Rijkswaterstaat Directie Limburg, Roermond, 2004. [66] AISC, Steel Construction Manual, American Institute of Steel Construction, Chicago, IL, 2011. [67] USACE, Engineering and design-responsibility for hydraulic steel structures, ER 1110-2-8187, U.S. Army Corps of Engineers, Washington, DC, 2009. [68] R.A. Daniel, Expanding and raising of bridges to improve navigation conditions, IABSE conference “Assessment, Upgrading and Refurbishment of Infrastructures”, Rotterdam, 2013. [69] Hakron, Technische documentatie bevestigingsankers, doorkoppelsystemen, transportsystemen en stekkenbakken, Hakron Nunspeet BV, 2013. www.hakron.nl. [70] Rijkswaterstaat, Beschouwingen over stormvloeden en getijbeweging, Rapport Deltacommissie, Deel 4, Bijdragen 3, SDU, The Hague, 1961. [71] USACE, Chickamagua lock replacement project, lock chamber plans and specifications, Design documentation report, USACE, Nashville District, 2017.