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Review of ridge failure against the confederation bridge
Cold Regions Science and Technology 42 (2005) 1 – 15 www.elsevier.com/locate/coldregions
Review of ridge failure against the confederation bridge Eric LemeeT, Thomas Brown Department of Civil Engineering, University of Calgary, 2500 University Dr NW, Canada T2N 1N4 Received 1 March 2004; accepted 26 October 2004
Abstract This paper discusses previous ridge keel failure models and uses data from Confederation Bridge to support the need for a new model that incorporates pier profile into the formula. Three independent data sources from Confederation Bridge show that there is a lack of sustained rubble pressure below the waterline cone and this is not predicted by existing keel failure models. The data sources are: regression analysis showing no correlation between load and keel depth, pressure panel data allowing an analysis of pressure distributions, and visual observations showing that sea life on the pier shaft was not scoured off by keels. D 2004 Elsevier B.V. All rights reserved. Keywords: Ice ridges; Ice rubble; Ice–structure interaction; Ice forces
1. Introduction
2. Confederation bridge
Theories have been developed since the 1970s to describe the failure of ice ridges and rubble fields interacting with offshore structures. All these models were created assuming a very simple geometry for the structure, such as a simple vertical cylinder or a wide structure for which plane-strain behaviour of the ice feature could be assumed. Structures such as the Confederation Bridge Piers, the Kemi-1 lightpier, and Tunoe Knob and Middelgrunden wind farms in Denmark all have geometries that vary with depth. The variation in geometry changes many of the assumptions that formed the basis for the currently used local and global (plug) keel failure theories.
The Confederation Bridge is located in Northumberland Strait, connecting New Brunswick and Prince Edward Island, in Eastern Canada. Ice conditions in the strait can be described as very active under the influences of significant tidal currents and wind forces. Consequently, there is considerable motion and deformation in the ice cover causing ridging and rubble fields. An estimated 6000 ridges and rubble fields will interact with any of the midStrait piers every year (Lemee et al., 2001). To limit the forces due to level ice interactions with the piers, an ice-breaking cone, as shown in Fig. 1, was designed into the pier to cause flexural failure of the ice sheet. In the case of keel interactions, the cone acts as a protruding section that will contact the keel before the keel has reached the pier shaft.
T Corresponding author. Fax: +1 403 282 7026. E-mail address: [email protected] (E. Lemee). 0165-232X/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2004.10.007
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E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
Fig. 1. Configuration of instrumented Confederation Bridge pier.
To measure the response of the bridge to the large number of ice features encountered, two piers near the center of the strait have been instrumented with equipment including: tiltmeters, from which the total load can be derived; pressure panels, both on the cone and pier shaft to record local pressure; sonars and an Acoustic Doppler Current Profiler (ADCP) to record underwater ice profiles; and video cameras to view ice interactions. The tiltmeters were calibrated by a full scale pull test of the pier. The test was conducted by pulling on a nylon cable connected to an ice breaking vessel. The test measured both the static and dynamic responses of the pier. The slower loading rates of ridge interaction events are similar to the static loading which was accurately modeled by the pull test. The pull test permitted the comparison between two direct measurements of load applied to the pier, and the response of the pier, as measured by tilt. The tiltmeters had previously been calibrated and, at static load, were accurate to within 1%. The discrepancy between
the two load measurements was never more than 3%. Accordingly, it is concluded that the relation between measured tilt and applied static ice load is accurate to within 5%, and probably less. For the ridge interactions discussed in this paper, the applied load is essentially static. A more detailed description of the instrumentation can be obtained from Bruce et al. (2001) and Brown (2001).
3. Review of existing rubble failure theories It has long been recognised that many offshore interactions involve rubble ice and that there is a corresponding need to develop models for the resulting loads. Because of the physical similarities with geotechnical materials, much of the failure modelling has been based on soil failure theories, and the material modelling has used the Mohr–Coulomb failure envelope for shear strength, with a cohesion c, and an internal friction angle, u. For first-year
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ridges, it was recognised that failure of the keel could take place as a local failure (Dolgopolov et al., 1975), pffiffiffiffiffiffiffiffi hk c e K p þ 2 Kp c Fk ¼ hk De q ð1Þ 2 or as a global failure, also known as plug failure (Croasdale et al., 1993), 0:26hk þ 0:39De þ 0:2WR tanx Fk ¼ WR De hk Kp cosx ce tan/
ð2Þ
In Eqs. (1) and (2), h k is the keel depth, Wr the width of the ridge, D e the structure diameter, c e is the buoyant density of the rubble, and K p is the passive pressure coefficient. q is a factor to account for the increased keel depth caused by the interaction, and x is the angle of the global failure planes with respect to the direction of motion of the ridge or rubble field. Local failure load is dominated by the depth of the keel; a deeper keel will cause a higher load. Local failure is progressive and will continue forward through the ridge as it is indented. Rubble will be cleared past the pier during indentation. Global failure load, resulting in a complete failure through the ridge, is based on the area of the keel
3
failure planes; a smaller keel area will result in a lower load. The two theories will dominate at different penetrations of the keel as they are limited by different parameters. The minimum of the two loads is selected as the failure load for that penetration increment. More recent work has been based on a single model for all failure types that uses an algorithm that searches for the failure plane corresponding to the minimum load for a given penetration (Cammaert et al., 1993; Croasdale et al., 1995; Ka¨rna¨ et al., 2001). Fig. 2 shows the crossover model by Cammaert et al. (1993). The model calculates the minimum failure load comparing local and global failure theories at convenient penetration increments of the keel. Fig. 2 suggests that, in many cases, the maximum value of neither failure mode will be the ultimate load during a keel interaction. The local failure load will increase with the keel depth to a maximum near the center of the keel. The global load will be a maximum at the beginning of the interaction and will decrease as the remaining keel area decreases throughout the interaction. The maximum keel load will occur some way through the keel when a plug failure will require less load than a local failure. The exact indentation location of maximum failure load will depend on the geometry of the keel.
16.00 14.00
Dolg. Load (MN) Total Plug (MN) Failure Load (MN)
Load (MN)
12.00 10.00 8.00 6.00 4.00 2.00 0.00 0.00
10.00
20.00
30.00
40.00
Penetration (m)
Fig. 2. Cross-over model showing progression of failure load.
50.00
4
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4. Analysis of recorded load The results of two models, the crossover model using Eqs. (1) and (2), and the General Passive Failure Model (Croasdale et al., 1995), with possible ice rubble strength parameters, are compared against the recorded loads in Table 1. The two ridges compared are typical ridges for Northumberland Strait where the two side slopes are not equal and there is a flat base to the keel. Fig. 3 gives the keel profile as measured by a sonar approximately 30 m upstream of the instrumented pier. The models significantly over-predict the loads recorded by the bridge piers by as much as 500%. Neither of the models compared in Table 1 include the failure of the consolidated layer, for which the load must be added to obtain the complete failure load, causing a further increase in the calculated load. It is evident that the models over-predict the keel failure load for a structure such as Confederation Bridge. Keel strength, which clearly has a significant effect on load prediction using Eq. (1) and (2), depends on many factors, information on most of which is unavailable in Northumberland Strait. The amount of sintering that has taken place, dependent on the age and thermal history of the keel; the amount of consolidation, dependent on whether, and to what extent, grounding has taken place; and the conditions prevalent at the formation of the ridge, all affect the keel strength. However, all of the work that has taken place in Northumberland Strait, including the work
Depth (m)
-2 -4 -6 -8 -10 -12 -14 15:06
15:07
15:07
15:08
15:09
15:10
15:10
Time Fig. 3. Keel profile.
reported here, has been related to all ridge interactions, regardless of the size of the ridge and the time of year of the interaction. In fact, the highest loads are measured in the late winter period, from mid-March to April, when the consolidated layers are at their maximum, and interactions with previously grounded ridges embedded in previously fast-ice formations occur. It is therefore likely that the results reported in Table 1 are for ridges the keels of which may have been strong.
5. Statistical results A statistical analysis based on 71 keel interactions with the instrumented bridge pier was performed where the interactions were selected on the basis of the presence of a keel recorded by the sonar and ADCP, and a large load recorded by the tiltmeters. Five
Table 1 Comparison of observed load with predicted load during ridge interaction
1 2
Keel geometry
Keel+consolidated layer recorded load
Keel load cross-over model u=30, c=5
u=35, c=5
u=0, c=15
u=20, c=10
depth=12.7 m width=2.8 m depth=7.9 m width=67.2 m
2.5 MN
7.5 MN
8.2 MN
12.8 MN
10.8 MN
2.26 Mn
5.3 MN
4.66 MN
6.8 MN
7.2 MN
General passive failure model (keel load only)
1 2
depth=12.7 m width=28.8 m depth=7.9 m width=67.2 m
u=30, c=5
u=40, c=0
u=40, c=5
u=0, c=15
2.5 MN
8.0 MN
10.1 MN
7.5 MN
9.6 MN
2.26 MN
5.3 MN
6.8 MN
4.7 MN
6.4 Mn
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4.50 4.00 3.50
Load (MN)
3.00 2.50
y = -0.0042x + 1.9385 R2 = 0.0002
2.00 1.50 1.00 0.50 0.00 2.00
4.00
6.00
8.00 10.00 12.00 Keel Depth (m)
14.00
16.00
18.00
Fig. 4. Effect of keel depth on load.
parameters were selected to describe each interaction: keel depth, keel width, keel interaction speed, tide height and the consolidated layer thickness. Tide height, not an obvious parameter, was included because a change in tide will change the crosssectional area of the cone interacting with the keel.
The tide height will also cause a change in waterline diameter for the consolidated layer interaction. In all existing keel failure models, especially models for local failure, the parameter affecting load the most is the dimensions of the keel, primarily the depth. Fig. 4 shows that the keel depth has very little
4.50 4.00 3.50
Load (MN)
3.00 2.50 2.00
y = 2.1347x + 0.5815 R2 = 0.2631
1.50 1.00 0.50 0.00 0.25
0.50
0.75
1.00
Consolidated Layer Thickness (m) Fig. 5. Effect of consolidated layer on load.
1.25
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effect on the load. There is no apparent increasing trend of load with keel depth although such a trend could possibly be concealed in the very high scatter. A possible explanation as to why there was very little effect on load will be presented in the following section. None of the other parameters had any effect on the total load, except for the consolidated layer thickness. In Fig. 5, it can be seen that load is correlated to consolidated layer thickness showing an increase in load for thicker consolidated layers. Since this is the only parameter that shows any form of trend it can be interpreted that a large portion of the load is derived from the consolidated layer. Consolidated layer thickness was determined from the video monitoring system by observing block thickness in the rubble pile during events.
6. Pressure panel results Previous models assume that pressure will be exerted on a cylindrical pier shaft over the whole depth of the keel, which generates the load necessary to cause the shear failure planes in a global failure. The complex shape of the Confederation Bridge pier changes the failure mechanics, therefore the assumed pressure distribution needs to be confirmed. One pier was instrumented with pressure panels on both the cone, and on the pier shaft, in two parallel sets extending down to 15 m below mean sea level as shown in Fig. 1. The panels on the cone, measuring pressures from the upper portion of the keel, have recorded significant and sustained pressures during all keel interactions. The pier shaft panels showed significantly lower pressure and for shorter durations. A representative sample of events to test for pressure during keel interaction was taken during 3 days; March 23, 1998, February 26, 1999 and March 17, 1999. The 3 days were selected because of high recorded loads and deep keels profiled by the seabed upward looking sonar. During the 3 day period, 399 keels greater than 6 m deep were observed. Only keels greater than 6 m were selected for analysis because smaller keels would not interact with the pressure panels below the cone. The keel depth distribution is shown in Fig. 6.
250
Number of Keels
6
200 150 100 50 0 6-7
7-8
8-9 9-10 10-11 11-12 12-13 Keel Depth (m)
Fig. 6. Keel depth distribution from test periods.
During the 3 days, only 29 min of pressure were recorded on the shaft in 48 separate trigger files. Although each of the 3 days had similar amounts of ridge interaction, the amount of recorded pressure on each day was very different. March 23, 1998, saw the majority of the pressure during three main interaction events where some pressure was recorded on panels extending down to 9.5 m below sea level. The upper panels closest to sea level showed much more activity than the lower panels, both in duration of peak load and the number of pressures recorded. When activity was recorded, pressure was often of longer duration but lower intensity as shown in Fig. 7. The high frequency response of the three signals is electronic noise from the instrumentation system, not pressure fluctuations. This type of response could indicate a number of blocks pushing on the pressure panels with constant force over relatively long durations (tens of seconds). It is believed that this could be because the underside of the cone provides an upper surface for the blocks to rest against and cause sustained pressure on the panels just below this surface. The response of the panels lower down on the pier shaft is shown in Fig. 8. In comparison to the upper panels, the lower panels showed some of the highest pressures but only sustained for a short duration. This indicates that blocks were striking the pier shaft with a higher velocity causing impact loads instead of a constant force from sustained or slow moving blocks. The very small number of sustained pressures below the cone and the smaller number recorded below the uppermost set of pressure panels leads to the conclusion that pressure is not sustained below the cone and is less than is predicted by models. This
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
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35 Pressure panels 30
41
42
45
Pressure (kPa)
25 20 15 10 5 0 58:17.4
58:20.9
58:24.3 Time (min:sec)
58:27.8
58:31.2
Fig. 7. Sustained response on upper panels.
strengthens the statistical results presented above that concluded that keel depth had no apparent affect on the overall load. If pressure is only recorded on the cone and not on the shaft, the only action of the keel will be in the top 4 m of the keel, corresponding to the depth of the cone.
7. Underwater video At the end of the 2001–2002 season a diver was sent to visually assess the status of the pressure panels. What was filmed proved very valuable because it showed sea life that could be used to
800 700 46 55
Pressure (KPa)
600
48 56
500 400 300 200 100 0 51:11.5
51:28.8
51:46.1 52:03.4 Time (min:sec)
52:20.6
Fig. 8. Example event showing large pressure response on multiple channels.
52:37.9
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interpret the frequency and intensity of ice rubble impacts on the pier shaft. There was no visible active sea life on the waterline cone. Ice action has removed all sea life including barnacles (Semibalanus balanoides). Barnacles are a crustacean that attaches itself to almost any hard surface in contact with seawater. The barnacle is protected from predators and abrasion by a series of shells around its perimeter that form a cone with an opening at the top. On the waterline cone all that remained were white rings, the base of the exterior protective shells. The sea life on the pier shaft below the cone was much more abundant and diverse than on the cone. There were three different species; barnacles, sea anemones (Metridium senile) and micro-algae. Fig. 9 shows that the anemone growth was extensive on the side of the pier shaft that face the direction of current flow. Current in Northumberland Strait is almost all tidal resulting in predominant flow directions, SE and NW. The difference in physical strength of anemones and barnacles allow a very rudimentary estimation of a maximum pressure caused by ice against the pier. Fig. 9 shows a scour/impact on the leading face of the pier shaft. The upper left side of the picture shows that all the anemones were cleared off the pier while some barnacles remain; the lower right portion shows live anenomes. It should be noted that the size of barnacles on the shaft are of varying sizes. Barnacles only spawn in the late spring and early summer (Minchinton and
Fig. 9. Anemone growth and undamaged barnacles on pier shaft.
Fig. 10. Scour of algae growth on side of pier shaft.
Scheibling, 1991). The varying sizes present would therefore indicate that there exists multiple years of growth. Barnacles on the cone are all the same size, and therefore age, because they are all scoured off in the winter. Impacts against the sides of pier, the faces that are parallel with the current direction, show long linear scours as shown in Fig. 10. The rapidly regrowing algae clearly show scours that occurred late in the season. Again, there are barnacles that have not been destroyed by the ice scour indicating that the pressure exerted by the ice is marginal, but enough to remove any soft vegetation.
8. Visible failure conditions A video system monitors and records the ice failure mechanics and ice conditions at the two instrumented piers. The video is time stamped therefore it can be synchronized with the logger system that records load and pressure measurements. Fig. 11 shows an annotated load trace from one pier describing the failure mechanics throughout the interaction. From the figure, it is clear that the load variances and visually observed failures coincide very closely. At every failure, even smaller consolidated layer buckling, the load decreased. The clear relationship between the visible failure mechanics and the total load on the pier shows that the rubble pile size and consolidated layer failure mechanisms are just as important as the keel failure.
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
4 3.5 3
Rubble pile Failure in collapse Consolidated Layer
Load (MN)
Rubble pile Increase
Failure in Consolidated Layer then bow forms
Buckle in Consolidated Layer
Split/plug then rubble pile collapse
Failure of bow and failure in consolidated layer
Plug then bow forms
Plug
2.5
9
Rubble pile growth
2 Floe rotates off pier
1.5 1 0.5
Rapid rubble pile growth
0 19:12.0
22:04.8
24:57.6
27:50.4
30:43.2
33:36.0
36:28.8
39:21.6
Time (min:sec) Fig. 11. Correlation between visual observations and load.
8.1. Rubble pile characteristics The rubble pile volume, as defined by height and horizontal extent, has a definite effect on the load as shown in Fig. 11. Theoretically, rubble pile height is a key parameter in determining the flexural failure load as it will require more force to push the consolidated layer through a larger rubble pile and lift the rubble
pile as the sheet slides up the cone. For these reasons, the change in rubble pile geometry during keel interactions must be quantified. When the keel and consolidated layer contact the cone the rubble pile volume increases. This is the result of additional volume, compared with level ice failure, of the keel pushing up and the additional thickness of the consolidated layer. There is some increase as the
14 Maximum height above water level of level ice interaction, from Mayne and Brown ( 2000)
Rubble Pile Height (m)
12
0.64
H = 7.59h
10 8 6 4 Pile-up
2
Ride-up
0 0.00
0.50
1.00
1.50
2.00
Consolidated Layer Thickness (m)
Fig. 12. Rubble pile height of ridge interaction compared to level ice failure.
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E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
sail is incorporated into the rubble pile, but this increase is generally small. The specific distribution of this additional rubble volume is important to understanding the effect on the failure mechanics. Fig. 12 plots the rubble pile height for the ridge interactions where all heights are measured relative to the water level. The pile heights are not substantially larger than pile heights that can be produced from level ice failure (Mayne and Brown, 2000). The upper bound height for level ice is only exceeded by a few ridge interaction events. Although not included in Fig. 12, similar height observations were reported at Kemi-1 for ungrounded rubble pile (Brown and Ma¨a¨tta¨nen, 2002). Ride-up heights were significantly higher than the associated event’s rubble pile. The increased consolidated layer block size and thickness allows very large blocks to be ejected from the top of the pile climbing up to the top of the 788 cone, +7 m above mean sea level. Ride up height cannot be significantly higher than 7 m because of the instability of ice pieces climbing up an almost 908 surface. As the rubble pile height does not get significantly larger during a ridge interaction the additional rubble must cause horizontal growth of the rubble piles. Fig. 13 shows the progression of the rubble pile footprint in the horizontal plane.
12
10
Distance (m) 6 4
8
1
Pier
2 1 2 3 4 5 6
2 3
0
Pier 14:08:46 14:09:07 14:09:34 14:10:00 14:10:35 14:10:46
Pier
5
0 2 4 6 8
4 6
Side Distance (m)
10
10 12
Direction of Flow
14 Fig. 13. Rubble pile footprint change during ridge interaction.
For the interaction shown in Fig. 13, the front of the pile grows by approximately 2.5 m when the sail interacts with the cone. Continued interaction with the ridge does not produce any additional increase in the forward length of the pile. The keel produces the largest gain in volume on the sides of the pile where the width of the pile has increased by up to 4 m on each side of the cone.
9. New model The video monitoring system has shown that the consolidated layer failure changes with the presence of a ridge keel. The keel and consolidated layer failures must be considered to act together. The approach of calculating a keel failure load and a consolidated layer failure load separately then adding the two does not correctly consider all of the failure mechanics. The following equation illustrates the logic of the possible failure combinations in the new model: 2
3 flexural failure ðconsolidated layerÞ þ local failure 6 flexural failure þ plug ðupper planeÞ 7 Ridge Load ¼ min4 5 plug failure ðside planesÞ þ plug of consolidated layer
ð3Þ
The different failure components are discussed in the following paragraphs. 9.1. Keel local failure The local failure of the keel is greatly complicated by the geometry of the cone. The leading edge (base) of the cone will contact and disturb the rubble before it reaches the pier shaft. The resulting strain state is not plane strain because of the variable geometry of the water line cone. Therefore, any theory such as Prodanovic (1979)
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
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that uses Prandtl theory does not accurately describe the mechanics and should not be used for structures with variable geometry such as Confederation Bridge. Three different sources have shown that there is very little or no sustained pressure on the pier shaft below the cone. This data would support the theory that the leading edge of the cone is disturbing all the cohesive bonds in the rubble and the rubble is then flowing around the pier in a fluid motion (Fig. 14). The new model only uses sustained pressure on the cone with the shaft having a negligible contribution. The local rubble failure is better described by the theories of Dolgopolov et al. (1975) and Nevel (2001), which are based on a Mohr–Coulomb failure pressure over the cross-sectional area of the structure. Using these theories, the stress at failure is: 1 1 þ sin/ 1 þ sin/ 2 rx ¼ ð4Þ rz þ 2c 1 sin/ 1 sin/ rz ¼ ce ðhk zÞ
ð5Þ
where r x is the horizontal stress, r z is the vertical stress, c e is the effective buoyancy, c is the ice rubble cohesion, / is the ice rubble internal friction angle and h k is the keel depth. The total force against the pier is the integral of stress over the depth of the cone as described in Eq. (6). The effective structural diameter, D e, is a variable that depends on the depth, ranging between 14 m at the waterline and 20 m at the base. Z Dtop Fk ¼ rx De dz ð6Þ Dbottom
The above equation assumes all of the rubble acting on the cross section of the cone to be at failure. It is improbable that the stress in the rubble would be able to redistribute without significant motion. When this significant motion occurs, the full cohesive strength has already been exceeded and therefore cannot act concurrently with the full friction stress. Therefore, only a portion of each contribution should be used, such as that proposed by Ka¨rna¨ et al. (2001), where the stress is: ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " u 12 #2 u 1 þ sin/ 2 1 þ sin/ rx ¼ t ð7Þ rz þ 2c 1 sin/ 1 sin/ Clearing around the cone is done by local water current. The pier is a narrow structure therefore clearing is rapid and will not contribute significantly to the forces.
Fig. 14. Failure mechanics of ridge failure against confederation bridge.
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Since keels deeper than the cone are assumed not to contribute significant load to the shaft the only effect of deeper keels will be an increase of the rubble strength near the waterline. This will be from increased vertical stress, due to buoyancy, and increased sintering from the increased vertical stress. Tests have been conducted on ridges in Northumberland Strait (Croasdale, 1997) to determine the rubble properties but exact Mohr–Coulomb values could not be derived from the tests. For this paper it was assumed that a reasonable value to apply to floating ridges that would interact with the instrumented pier is a friction angle of 308 and a cohesive strength of 5 kPa. Using Eq. (7) in Eq. (6), results in a load of 1.44 MN for a ridge 10 m deep. Even the largest ridge, 18 m deep, which is the bathymetric limit, with a friction angle of 358 and a stronger cohesive strength of 15 kPa will result in a local failure load of 3.52 MN, significantly less than the results of Table 1. 9.2. Consolidated layer failure From the video monitoring system it has been observed that there is a significant upward thrust by the rubble in the keel on the underside of the consolidated layer. This effect, caused by rubble jamming between the cone and the consolidated layer, will reduce the force required to cause flexural failure. This has not yet been addressed by the research but work is ongoing. The effect of the upward thrust is visible when the support conditions provided by the keel are removed. At the end of a ridge interaction there is often a dramatic downward failure of the rubble pile and the consolidated layer because, once the support of the keel is reduced, the consolidated layer cannot support the weight of the increased rubble pile. The flexural failure equation of Croasdale et al. (1994) was used to account for the flexural failure of the consolidated layer. The theory separates the horizontal force into terms (H B, H P. . .) that describe the different force components required to cause flexural failure. The non-homogeneity of the consolidated layer, compared with level ice, combined with the upward thrust provided by the keel would change the formula in the following ways: ! The force required to break the consolidated layer (H B) is reduced because of the decreased distance from the pier of the circumferential crack. ! The force to push the layer through the rubble pile (H P) is reduced because the consolidated layer is not at the base of the rubble pile, but can ride halfway through or even on the top of the rubble pile. ! Force to lift the rubble (H L) will be reduced by the vertical pressure of the keel. Also the consolidated layer is not at the base of the rubble therefore the lifting force would again be less. The behaviour discussed here has been observed for ridge interactions in the monitoring programme. The winters of observation have been below average in severity thus far, and therefore consolidated layer thickness and strength have been lower than expected. Larger and stronger consolidated layers may not exhibit these failure characteristics and may behave differently by pushing through the pile and producing higher loads. 9.3. Plug failure The plug theories of Ka¨rna¨ et al. (2001) and Croasdale and Cammaert (1993) include the deviation angle x for the plug. In theory, an increase in the angle x will cause an increase in load. A failure mode will always seek the path of least resistance. Therefore, without modification; a deviation angle of 08 would yield the lowest load that would correspond to failure. When the deviation angle is 08 the horizontal stress state is most likely neutral, therefore the normal pressure on the vertical face will be half the buoyant pressure at that location. As the deviation angle is increased the pressure state moves closer to the active state (0.3–0.5 buoyant pressure). The sudden drop in load during plug failures can
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
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be explained by the change from neutral pressure to active pressure on the failure surface. The deviation angle will cause the failure planes to move apart, greatly reducing the normal pressure on the faces. Load is also a function of the area of the failure plane. An increase in the deviation angle will cause an increase in the failure plane surface area causing an increase in load. The minimum load will be achieved at the angle that not only produces the reduction in normal pressure but also minimizes the failure plane area. Observations of plug failures have suggested that the deviation angles are about 158, indicating that this corresponds to the minimum load. There are three possible failure planes: two vertical failure planes and one failure plane under the consolidated layer. Eq. (8) gives the load from the side failure planes. The friction and cohesion terms are added in the same way as in the local failure because, again, they cannot act together. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 Fk ¼ 2 ce hk Ktan/Ak cosx þ ctop Ak cosx 3 3
ð8Þ
where A k is the area of the side walls and K is the pressure coefficient (either at rest or active) and c top is the cohesion at the top of the keel. The load on the failure plane below the consolidated layer is calculated by Eq. (9). The cohesion on this failure plane is the upper cohesion and is not averaged for the variation with depth. 2 Fk ¼ ce hk tan/ þ ctop Ac coshslip ð9Þ 3 Ac ¼ De ðW xÞ þ ðW xÞ2 tanx where h slip is the angle of the failure plane measured from horizontal and x is the penetration into the ridge. The upper failure plane load is much higher than the side failure planes because of the high normal force on the failure plane and the high cohesion just below the consolidated layer.
Fig. 15. New crossover model showing effect of lower local failure load.
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E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15 5
Calculated Load (MN)
4
y = 0.9898x R2 = 0.6824 3
2
1
0 0
1
2 3 Recorded Load (MN)
4
5
Fig. 16. Comparison of new model to recorded events.
9.4. Comparison of the model with measurements The loads resulting from the two failure modes were calculated at penetration intervals, similar to the Cross-over model (Cammaert et al., 1993), based on Eqs. (3), (6), (7) and (8). Fig. 15 shows the load from the different failure components at each indentation step into a representative ridge with a 10 m deep keel and side slope angles of 218. The failure load of the consolidated layer is based on Croasdale et al. (1994) and is not shown in the diagram for simplicity as it would have to be added to both local and global failure modes. From Fig. 15 it can be seen that the maximum load from the keel will be from the local failure. Fig. 16 compares 10 actual ridge interactions with the revised failure theory and consolidated layer loads calculated from Croasdale et al. (1994). The new keel failure model calculates loads that are much closer to the recorded values, with excellent agreement between measurements and theory.
10. Conclusion and recommendations Failure of the consolidated layer thickness is the dominant term in determining the keel load in ridge interaction. Pressure panel observations indicating no sustained pressures on the pier shaft below the cone, lack of correlation between maximum ridge loads and keel depth, and the presence of fragile marine growth on the tidal faces of the pier shaft, suggest that the keel does not contribute significantly to the total ridge load. The reasons for this are not fully understood, but the pier geometry, particularly the sharp edge at 4 m, clearly contributes to the disintegration of the keel.
One other factor, which is not often considered, is the effect of current in clearing entrained ice pieces from around the pier. The observations from the Confederation Bridge Pier monitoring programme suggest that the disintegration of the keel takes place well away from the pier, and that current then clears the ice pieces from the pier. This effect would not be seen on wider structures where high keel forces have been seen. Ridge interactions have limited effects on the rubble pile, resulting in a slight elevation of the rubble pile, but a significant extension of the rubble pile circumference. A modified model using observations from the bridge, no pressure below the cone and consolidated
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
layer failure changes, correlates well with the observed load.
Acknowledgement The authors would like to acknowledge the support of Strait Crossing Bridge, Public Works and Government Services Canada, the Program for Energy Research and Development (PERD), and the Natural Sciences and Engineering Research Council (NSERC) through grant CRD 193623.
References Brown, T.G., 2001. Four years of ice force observations on the confederation bridge. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 285 – 298. Brown, T.G., Ma¨a¨tta¨nen, M., 2002. Comparison of Kemi-I and confederation bridge cone ice load measurement results. Proceedings of the 16th IAHR Symposium on Ice, Dunedin, New Zealand, vol. 1, pp. 503 – 512. Bruce, J.R., Brown, T.G., 2001. Operating an ice force monitoring system on the confederation bridge. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 299 – 308. Cammaert, A.B., Jordan, I.J., Bruneau, S.E., Crocker, G.B., Mckenna, R.F., Williams, S.A., 1993. Analysis of Ice Loads on Main Span Piers for the Northumberland Strait Crossing. Contract Report for J.Muller International–Stanley Joint Ventures, CODA contract # 5022.01, 108 pp. Croasdale, K.R., 1997. In-Situ Ridge Strength Measurements. Report submitted to the National Energy Board, Canada, Calgary.
15
Croasdale, K.R., Cammaert, A.B., 1993. An improved method for the calculation of ice loads on sloping structures in first-year ice. Proceedings of the First International Conference on Exploration of Russian Arctic Offshore, St. Petersburg, Russia, pp. 161 – 168. Croasdale, K.R., Cammaert, A.B., Metge, M., 1994. A method for the calculation of sheet ice loads on sloping structures. Proceedings of the IAHR ’94 Symposium on Ice, Trondheim, Norway, vol. 2, pp. 874 – 875. Croasdale, K.R., Associates, 1995. Ice Load Models for FirstYear Pressure Ridges and Rubble Fields – Phase 1. Joint Industry Project Report for National Energy Board and PERD. 192 pp. Dolgopolov, Y.V., Afanasev, V.A., Korenkov, V.A., Panfilov, D.F., 1975. Effect of hummocked ice on piers of marine hydraulic structures. Proceedings IAHR Symposium on Ice, Hanover, NH, USA, pp. 469 – 478. Ka¨rna¨, T., Rim, C.W., Shkinek, K.N., 2001. Global loads to firstyear ice ridges. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 2, pp. 627 – 638. Lemee, E., Bruce, J.R., Brown, T.G., 2001. Ice ridge encounter rates for the confederation bridge. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 359 – 366. Mayne, D.C., Brown, T.G., 2000. Rubble pile observations. Proceedings of the 10th International Offshore and Polar Engineering Conference, Seattle, USA, vol. 1, pp. 596 – 599. Minchinton, T.E., Scheibling, R.E., 1991. The influence of larval supply and settlement on the population structure of barnacles. Ecology 72 (5), 1867 – 1879. Nevel, D., 2001. First year ridges acting on conical structures. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 369 – 374. Prodanovic, A., 1979. Model tests of ice rubble strength. Proceedings of Symposium on Port and Ocean Engineering Under Arctic Conditions, Trondheim, Norway, pp. 89 – 105.
Review of ridge failure against the confederation bridge Eric LemeeT, Thomas Brown Department of Civil Engineering, University of Calgary, 2500 University Dr NW, Canada T2N 1N4 Received 1 March 2004; accepted 26 October 2004
Abstract This paper discusses previous ridge keel failure models and uses data from Confederation Bridge to support the need for a new model that incorporates pier profile into the formula. Three independent data sources from Confederation Bridge show that there is a lack of sustained rubble pressure below the waterline cone and this is not predicted by existing keel failure models. The data sources are: regression analysis showing no correlation between load and keel depth, pressure panel data allowing an analysis of pressure distributions, and visual observations showing that sea life on the pier shaft was not scoured off by keels. D 2004 Elsevier B.V. All rights reserved. Keywords: Ice ridges; Ice rubble; Ice–structure interaction; Ice forces
1. Introduction
2. Confederation bridge
Theories have been developed since the 1970s to describe the failure of ice ridges and rubble fields interacting with offshore structures. All these models were created assuming a very simple geometry for the structure, such as a simple vertical cylinder or a wide structure for which plane-strain behaviour of the ice feature could be assumed. Structures such as the Confederation Bridge Piers, the Kemi-1 lightpier, and Tunoe Knob and Middelgrunden wind farms in Denmark all have geometries that vary with depth. The variation in geometry changes many of the assumptions that formed the basis for the currently used local and global (plug) keel failure theories.
The Confederation Bridge is located in Northumberland Strait, connecting New Brunswick and Prince Edward Island, in Eastern Canada. Ice conditions in the strait can be described as very active under the influences of significant tidal currents and wind forces. Consequently, there is considerable motion and deformation in the ice cover causing ridging and rubble fields. An estimated 6000 ridges and rubble fields will interact with any of the midStrait piers every year (Lemee et al., 2001). To limit the forces due to level ice interactions with the piers, an ice-breaking cone, as shown in Fig. 1, was designed into the pier to cause flexural failure of the ice sheet. In the case of keel interactions, the cone acts as a protruding section that will contact the keel before the keel has reached the pier shaft.
T Corresponding author. Fax: +1 403 282 7026. E-mail address: [email protected] (E. Lemee). 0165-232X/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2004.10.007
2
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
Fig. 1. Configuration of instrumented Confederation Bridge pier.
To measure the response of the bridge to the large number of ice features encountered, two piers near the center of the strait have been instrumented with equipment including: tiltmeters, from which the total load can be derived; pressure panels, both on the cone and pier shaft to record local pressure; sonars and an Acoustic Doppler Current Profiler (ADCP) to record underwater ice profiles; and video cameras to view ice interactions. The tiltmeters were calibrated by a full scale pull test of the pier. The test was conducted by pulling on a nylon cable connected to an ice breaking vessel. The test measured both the static and dynamic responses of the pier. The slower loading rates of ridge interaction events are similar to the static loading which was accurately modeled by the pull test. The pull test permitted the comparison between two direct measurements of load applied to the pier, and the response of the pier, as measured by tilt. The tiltmeters had previously been calibrated and, at static load, were accurate to within 1%. The discrepancy between
the two load measurements was never more than 3%. Accordingly, it is concluded that the relation between measured tilt and applied static ice load is accurate to within 5%, and probably less. For the ridge interactions discussed in this paper, the applied load is essentially static. A more detailed description of the instrumentation can be obtained from Bruce et al. (2001) and Brown (2001).
3. Review of existing rubble failure theories It has long been recognised that many offshore interactions involve rubble ice and that there is a corresponding need to develop models for the resulting loads. Because of the physical similarities with geotechnical materials, much of the failure modelling has been based on soil failure theories, and the material modelling has used the Mohr–Coulomb failure envelope for shear strength, with a cohesion c, and an internal friction angle, u. For first-year
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
ridges, it was recognised that failure of the keel could take place as a local failure (Dolgopolov et al., 1975), pffiffiffiffiffiffiffiffi hk c e K p þ 2 Kp c Fk ¼ hk De q ð1Þ 2 or as a global failure, also known as plug failure (Croasdale et al., 1993), 0:26hk þ 0:39De þ 0:2WR tanx Fk ¼ WR De hk Kp cosx ce tan/
ð2Þ
In Eqs. (1) and (2), h k is the keel depth, Wr the width of the ridge, D e the structure diameter, c e is the buoyant density of the rubble, and K p is the passive pressure coefficient. q is a factor to account for the increased keel depth caused by the interaction, and x is the angle of the global failure planes with respect to the direction of motion of the ridge or rubble field. Local failure load is dominated by the depth of the keel; a deeper keel will cause a higher load. Local failure is progressive and will continue forward through the ridge as it is indented. Rubble will be cleared past the pier during indentation. Global failure load, resulting in a complete failure through the ridge, is based on the area of the keel
3
failure planes; a smaller keel area will result in a lower load. The two theories will dominate at different penetrations of the keel as they are limited by different parameters. The minimum of the two loads is selected as the failure load for that penetration increment. More recent work has been based on a single model for all failure types that uses an algorithm that searches for the failure plane corresponding to the minimum load for a given penetration (Cammaert et al., 1993; Croasdale et al., 1995; Ka¨rna¨ et al., 2001). Fig. 2 shows the crossover model by Cammaert et al. (1993). The model calculates the minimum failure load comparing local and global failure theories at convenient penetration increments of the keel. Fig. 2 suggests that, in many cases, the maximum value of neither failure mode will be the ultimate load during a keel interaction. The local failure load will increase with the keel depth to a maximum near the center of the keel. The global load will be a maximum at the beginning of the interaction and will decrease as the remaining keel area decreases throughout the interaction. The maximum keel load will occur some way through the keel when a plug failure will require less load than a local failure. The exact indentation location of maximum failure load will depend on the geometry of the keel.
16.00 14.00
Dolg. Load (MN) Total Plug (MN) Failure Load (MN)
Load (MN)
12.00 10.00 8.00 6.00 4.00 2.00 0.00 0.00
10.00
20.00
30.00
40.00
Penetration (m)
Fig. 2. Cross-over model showing progression of failure load.
50.00
4
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15 0
4. Analysis of recorded load The results of two models, the crossover model using Eqs. (1) and (2), and the General Passive Failure Model (Croasdale et al., 1995), with possible ice rubble strength parameters, are compared against the recorded loads in Table 1. The two ridges compared are typical ridges for Northumberland Strait where the two side slopes are not equal and there is a flat base to the keel. Fig. 3 gives the keel profile as measured by a sonar approximately 30 m upstream of the instrumented pier. The models significantly over-predict the loads recorded by the bridge piers by as much as 500%. Neither of the models compared in Table 1 include the failure of the consolidated layer, for which the load must be added to obtain the complete failure load, causing a further increase in the calculated load. It is evident that the models over-predict the keel failure load for a structure such as Confederation Bridge. Keel strength, which clearly has a significant effect on load prediction using Eq. (1) and (2), depends on many factors, information on most of which is unavailable in Northumberland Strait. The amount of sintering that has taken place, dependent on the age and thermal history of the keel; the amount of consolidation, dependent on whether, and to what extent, grounding has taken place; and the conditions prevalent at the formation of the ridge, all affect the keel strength. However, all of the work that has taken place in Northumberland Strait, including the work
Depth (m)
-2 -4 -6 -8 -10 -12 -14 15:06
15:07
15:07
15:08
15:09
15:10
15:10
Time Fig. 3. Keel profile.
reported here, has been related to all ridge interactions, regardless of the size of the ridge and the time of year of the interaction. In fact, the highest loads are measured in the late winter period, from mid-March to April, when the consolidated layers are at their maximum, and interactions with previously grounded ridges embedded in previously fast-ice formations occur. It is therefore likely that the results reported in Table 1 are for ridges the keels of which may have been strong.
5. Statistical results A statistical analysis based on 71 keel interactions with the instrumented bridge pier was performed where the interactions were selected on the basis of the presence of a keel recorded by the sonar and ADCP, and a large load recorded by the tiltmeters. Five
Table 1 Comparison of observed load with predicted load during ridge interaction
1 2
Keel geometry
Keel+consolidated layer recorded load
Keel load cross-over model u=30, c=5
u=35, c=5
u=0, c=15
u=20, c=10
depth=12.7 m width=2.8 m depth=7.9 m width=67.2 m
2.5 MN
7.5 MN
8.2 MN
12.8 MN
10.8 MN
2.26 Mn
5.3 MN
4.66 MN
6.8 MN
7.2 MN
General passive failure model (keel load only)
1 2
depth=12.7 m width=28.8 m depth=7.9 m width=67.2 m
u=30, c=5
u=40, c=0
u=40, c=5
u=0, c=15
2.5 MN
8.0 MN
10.1 MN
7.5 MN
9.6 MN
2.26 MN
5.3 MN
6.8 MN
4.7 MN
6.4 Mn
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
5
4.50 4.00 3.50
Load (MN)
3.00 2.50
y = -0.0042x + 1.9385 R2 = 0.0002
2.00 1.50 1.00 0.50 0.00 2.00
4.00
6.00
8.00 10.00 12.00 Keel Depth (m)
14.00
16.00
18.00
Fig. 4. Effect of keel depth on load.
parameters were selected to describe each interaction: keel depth, keel width, keel interaction speed, tide height and the consolidated layer thickness. Tide height, not an obvious parameter, was included because a change in tide will change the crosssectional area of the cone interacting with the keel.
The tide height will also cause a change in waterline diameter for the consolidated layer interaction. In all existing keel failure models, especially models for local failure, the parameter affecting load the most is the dimensions of the keel, primarily the depth. Fig. 4 shows that the keel depth has very little
4.50 4.00 3.50
Load (MN)
3.00 2.50 2.00
y = 2.1347x + 0.5815 R2 = 0.2631
1.50 1.00 0.50 0.00 0.25
0.50
0.75
1.00
Consolidated Layer Thickness (m) Fig. 5. Effect of consolidated layer on load.
1.25
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
effect on the load. There is no apparent increasing trend of load with keel depth although such a trend could possibly be concealed in the very high scatter. A possible explanation as to why there was very little effect on load will be presented in the following section. None of the other parameters had any effect on the total load, except for the consolidated layer thickness. In Fig. 5, it can be seen that load is correlated to consolidated layer thickness showing an increase in load for thicker consolidated layers. Since this is the only parameter that shows any form of trend it can be interpreted that a large portion of the load is derived from the consolidated layer. Consolidated layer thickness was determined from the video monitoring system by observing block thickness in the rubble pile during events.
6. Pressure panel results Previous models assume that pressure will be exerted on a cylindrical pier shaft over the whole depth of the keel, which generates the load necessary to cause the shear failure planes in a global failure. The complex shape of the Confederation Bridge pier changes the failure mechanics, therefore the assumed pressure distribution needs to be confirmed. One pier was instrumented with pressure panels on both the cone, and on the pier shaft, in two parallel sets extending down to 15 m below mean sea level as shown in Fig. 1. The panels on the cone, measuring pressures from the upper portion of the keel, have recorded significant and sustained pressures during all keel interactions. The pier shaft panels showed significantly lower pressure and for shorter durations. A representative sample of events to test for pressure during keel interaction was taken during 3 days; March 23, 1998, February 26, 1999 and March 17, 1999. The 3 days were selected because of high recorded loads and deep keels profiled by the seabed upward looking sonar. During the 3 day period, 399 keels greater than 6 m deep were observed. Only keels greater than 6 m were selected for analysis because smaller keels would not interact with the pressure panels below the cone. The keel depth distribution is shown in Fig. 6.
250
Number of Keels
6
200 150 100 50 0 6-7
7-8
8-9 9-10 10-11 11-12 12-13 Keel Depth (m)
Fig. 6. Keel depth distribution from test periods.
During the 3 days, only 29 min of pressure were recorded on the shaft in 48 separate trigger files. Although each of the 3 days had similar amounts of ridge interaction, the amount of recorded pressure on each day was very different. March 23, 1998, saw the majority of the pressure during three main interaction events where some pressure was recorded on panels extending down to 9.5 m below sea level. The upper panels closest to sea level showed much more activity than the lower panels, both in duration of peak load and the number of pressures recorded. When activity was recorded, pressure was often of longer duration but lower intensity as shown in Fig. 7. The high frequency response of the three signals is electronic noise from the instrumentation system, not pressure fluctuations. This type of response could indicate a number of blocks pushing on the pressure panels with constant force over relatively long durations (tens of seconds). It is believed that this could be because the underside of the cone provides an upper surface for the blocks to rest against and cause sustained pressure on the panels just below this surface. The response of the panels lower down on the pier shaft is shown in Fig. 8. In comparison to the upper panels, the lower panels showed some of the highest pressures but only sustained for a short duration. This indicates that blocks were striking the pier shaft with a higher velocity causing impact loads instead of a constant force from sustained or slow moving blocks. The very small number of sustained pressures below the cone and the smaller number recorded below the uppermost set of pressure panels leads to the conclusion that pressure is not sustained below the cone and is less than is predicted by models. This
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
7
35 Pressure panels 30
41
42
45
Pressure (kPa)
25 20 15 10 5 0 58:17.4
58:20.9
58:24.3 Time (min:sec)
58:27.8
58:31.2
Fig. 7. Sustained response on upper panels.
strengthens the statistical results presented above that concluded that keel depth had no apparent affect on the overall load. If pressure is only recorded on the cone and not on the shaft, the only action of the keel will be in the top 4 m of the keel, corresponding to the depth of the cone.
7. Underwater video At the end of the 2001–2002 season a diver was sent to visually assess the status of the pressure panels. What was filmed proved very valuable because it showed sea life that could be used to
800 700 46 55
Pressure (KPa)
600
48 56
500 400 300 200 100 0 51:11.5
51:28.8
51:46.1 52:03.4 Time (min:sec)
52:20.6
Fig. 8. Example event showing large pressure response on multiple channels.
52:37.9
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E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
interpret the frequency and intensity of ice rubble impacts on the pier shaft. There was no visible active sea life on the waterline cone. Ice action has removed all sea life including barnacles (Semibalanus balanoides). Barnacles are a crustacean that attaches itself to almost any hard surface in contact with seawater. The barnacle is protected from predators and abrasion by a series of shells around its perimeter that form a cone with an opening at the top. On the waterline cone all that remained were white rings, the base of the exterior protective shells. The sea life on the pier shaft below the cone was much more abundant and diverse than on the cone. There were three different species; barnacles, sea anemones (Metridium senile) and micro-algae. Fig. 9 shows that the anemone growth was extensive on the side of the pier shaft that face the direction of current flow. Current in Northumberland Strait is almost all tidal resulting in predominant flow directions, SE and NW. The difference in physical strength of anemones and barnacles allow a very rudimentary estimation of a maximum pressure caused by ice against the pier. Fig. 9 shows a scour/impact on the leading face of the pier shaft. The upper left side of the picture shows that all the anemones were cleared off the pier while some barnacles remain; the lower right portion shows live anenomes. It should be noted that the size of barnacles on the shaft are of varying sizes. Barnacles only spawn in the late spring and early summer (Minchinton and
Fig. 9. Anemone growth and undamaged barnacles on pier shaft.
Fig. 10. Scour of algae growth on side of pier shaft.
Scheibling, 1991). The varying sizes present would therefore indicate that there exists multiple years of growth. Barnacles on the cone are all the same size, and therefore age, because they are all scoured off in the winter. Impacts against the sides of pier, the faces that are parallel with the current direction, show long linear scours as shown in Fig. 10. The rapidly regrowing algae clearly show scours that occurred late in the season. Again, there are barnacles that have not been destroyed by the ice scour indicating that the pressure exerted by the ice is marginal, but enough to remove any soft vegetation.
8. Visible failure conditions A video system monitors and records the ice failure mechanics and ice conditions at the two instrumented piers. The video is time stamped therefore it can be synchronized with the logger system that records load and pressure measurements. Fig. 11 shows an annotated load trace from one pier describing the failure mechanics throughout the interaction. From the figure, it is clear that the load variances and visually observed failures coincide very closely. At every failure, even smaller consolidated layer buckling, the load decreased. The clear relationship between the visible failure mechanics and the total load on the pier shows that the rubble pile size and consolidated layer failure mechanisms are just as important as the keel failure.
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
4 3.5 3
Rubble pile Failure in collapse Consolidated Layer
Load (MN)
Rubble pile Increase
Failure in Consolidated Layer then bow forms
Buckle in Consolidated Layer
Split/plug then rubble pile collapse
Failure of bow and failure in consolidated layer
Plug then bow forms
Plug
2.5
9
Rubble pile growth
2 Floe rotates off pier
1.5 1 0.5
Rapid rubble pile growth
0 19:12.0
22:04.8
24:57.6
27:50.4
30:43.2
33:36.0
36:28.8
39:21.6
Time (min:sec) Fig. 11. Correlation between visual observations and load.
8.1. Rubble pile characteristics The rubble pile volume, as defined by height and horizontal extent, has a definite effect on the load as shown in Fig. 11. Theoretically, rubble pile height is a key parameter in determining the flexural failure load as it will require more force to push the consolidated layer through a larger rubble pile and lift the rubble
pile as the sheet slides up the cone. For these reasons, the change in rubble pile geometry during keel interactions must be quantified. When the keel and consolidated layer contact the cone the rubble pile volume increases. This is the result of additional volume, compared with level ice failure, of the keel pushing up and the additional thickness of the consolidated layer. There is some increase as the
14 Maximum height above water level of level ice interaction, from Mayne and Brown ( 2000)
Rubble Pile Height (m)
12
0.64
H = 7.59h
10 8 6 4 Pile-up
2
Ride-up
0 0.00
0.50
1.00
1.50
2.00
Consolidated Layer Thickness (m)
Fig. 12. Rubble pile height of ridge interaction compared to level ice failure.
2.50
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
sail is incorporated into the rubble pile, but this increase is generally small. The specific distribution of this additional rubble volume is important to understanding the effect on the failure mechanics. Fig. 12 plots the rubble pile height for the ridge interactions where all heights are measured relative to the water level. The pile heights are not substantially larger than pile heights that can be produced from level ice failure (Mayne and Brown, 2000). The upper bound height for level ice is only exceeded by a few ridge interaction events. Although not included in Fig. 12, similar height observations were reported at Kemi-1 for ungrounded rubble pile (Brown and Ma¨a¨tta¨nen, 2002). Ride-up heights were significantly higher than the associated event’s rubble pile. The increased consolidated layer block size and thickness allows very large blocks to be ejected from the top of the pile climbing up to the top of the 788 cone, +7 m above mean sea level. Ride up height cannot be significantly higher than 7 m because of the instability of ice pieces climbing up an almost 908 surface. As the rubble pile height does not get significantly larger during a ridge interaction the additional rubble must cause horizontal growth of the rubble piles. Fig. 13 shows the progression of the rubble pile footprint in the horizontal plane.
12
10
Distance (m) 6 4
8
1
Pier
2 1 2 3 4 5 6
2 3
0
Pier 14:08:46 14:09:07 14:09:34 14:10:00 14:10:35 14:10:46
Pier
5
0 2 4 6 8
4 6
Side Distance (m)
10
10 12
Direction of Flow
14 Fig. 13. Rubble pile footprint change during ridge interaction.
For the interaction shown in Fig. 13, the front of the pile grows by approximately 2.5 m when the sail interacts with the cone. Continued interaction with the ridge does not produce any additional increase in the forward length of the pile. The keel produces the largest gain in volume on the sides of the pile where the width of the pile has increased by up to 4 m on each side of the cone.
9. New model The video monitoring system has shown that the consolidated layer failure changes with the presence of a ridge keel. The keel and consolidated layer failures must be considered to act together. The approach of calculating a keel failure load and a consolidated layer failure load separately then adding the two does not correctly consider all of the failure mechanics. The following equation illustrates the logic of the possible failure combinations in the new model: 2
3 flexural failure ðconsolidated layerÞ þ local failure 6 flexural failure þ plug ðupper planeÞ 7 Ridge Load ¼ min4 5 plug failure ðside planesÞ þ plug of consolidated layer
ð3Þ
The different failure components are discussed in the following paragraphs. 9.1. Keel local failure The local failure of the keel is greatly complicated by the geometry of the cone. The leading edge (base) of the cone will contact and disturb the rubble before it reaches the pier shaft. The resulting strain state is not plane strain because of the variable geometry of the water line cone. Therefore, any theory such as Prodanovic (1979)
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
11
that uses Prandtl theory does not accurately describe the mechanics and should not be used for structures with variable geometry such as Confederation Bridge. Three different sources have shown that there is very little or no sustained pressure on the pier shaft below the cone. This data would support the theory that the leading edge of the cone is disturbing all the cohesive bonds in the rubble and the rubble is then flowing around the pier in a fluid motion (Fig. 14). The new model only uses sustained pressure on the cone with the shaft having a negligible contribution. The local rubble failure is better described by the theories of Dolgopolov et al. (1975) and Nevel (2001), which are based on a Mohr–Coulomb failure pressure over the cross-sectional area of the structure. Using these theories, the stress at failure is: 1 1 þ sin/ 1 þ sin/ 2 rx ¼ ð4Þ rz þ 2c 1 sin/ 1 sin/ rz ¼ ce ðhk zÞ
ð5Þ
where r x is the horizontal stress, r z is the vertical stress, c e is the effective buoyancy, c is the ice rubble cohesion, / is the ice rubble internal friction angle and h k is the keel depth. The total force against the pier is the integral of stress over the depth of the cone as described in Eq. (6). The effective structural diameter, D e, is a variable that depends on the depth, ranging between 14 m at the waterline and 20 m at the base. Z Dtop Fk ¼ rx De dz ð6Þ Dbottom
The above equation assumes all of the rubble acting on the cross section of the cone to be at failure. It is improbable that the stress in the rubble would be able to redistribute without significant motion. When this significant motion occurs, the full cohesive strength has already been exceeded and therefore cannot act concurrently with the full friction stress. Therefore, only a portion of each contribution should be used, such as that proposed by Ka¨rna¨ et al. (2001), where the stress is: ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " u 12 #2 u 1 þ sin/ 2 1 þ sin/ rx ¼ t ð7Þ rz þ 2c 1 sin/ 1 sin/ Clearing around the cone is done by local water current. The pier is a narrow structure therefore clearing is rapid and will not contribute significantly to the forces.
Fig. 14. Failure mechanics of ridge failure against confederation bridge.
12
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Since keels deeper than the cone are assumed not to contribute significant load to the shaft the only effect of deeper keels will be an increase of the rubble strength near the waterline. This will be from increased vertical stress, due to buoyancy, and increased sintering from the increased vertical stress. Tests have been conducted on ridges in Northumberland Strait (Croasdale, 1997) to determine the rubble properties but exact Mohr–Coulomb values could not be derived from the tests. For this paper it was assumed that a reasonable value to apply to floating ridges that would interact with the instrumented pier is a friction angle of 308 and a cohesive strength of 5 kPa. Using Eq. (7) in Eq. (6), results in a load of 1.44 MN for a ridge 10 m deep. Even the largest ridge, 18 m deep, which is the bathymetric limit, with a friction angle of 358 and a stronger cohesive strength of 15 kPa will result in a local failure load of 3.52 MN, significantly less than the results of Table 1. 9.2. Consolidated layer failure From the video monitoring system it has been observed that there is a significant upward thrust by the rubble in the keel on the underside of the consolidated layer. This effect, caused by rubble jamming between the cone and the consolidated layer, will reduce the force required to cause flexural failure. This has not yet been addressed by the research but work is ongoing. The effect of the upward thrust is visible when the support conditions provided by the keel are removed. At the end of a ridge interaction there is often a dramatic downward failure of the rubble pile and the consolidated layer because, once the support of the keel is reduced, the consolidated layer cannot support the weight of the increased rubble pile. The flexural failure equation of Croasdale et al. (1994) was used to account for the flexural failure of the consolidated layer. The theory separates the horizontal force into terms (H B, H P. . .) that describe the different force components required to cause flexural failure. The non-homogeneity of the consolidated layer, compared with level ice, combined with the upward thrust provided by the keel would change the formula in the following ways: ! The force required to break the consolidated layer (H B) is reduced because of the decreased distance from the pier of the circumferential crack. ! The force to push the layer through the rubble pile (H P) is reduced because the consolidated layer is not at the base of the rubble pile, but can ride halfway through or even on the top of the rubble pile. ! Force to lift the rubble (H L) will be reduced by the vertical pressure of the keel. Also the consolidated layer is not at the base of the rubble therefore the lifting force would again be less. The behaviour discussed here has been observed for ridge interactions in the monitoring programme. The winters of observation have been below average in severity thus far, and therefore consolidated layer thickness and strength have been lower than expected. Larger and stronger consolidated layers may not exhibit these failure characteristics and may behave differently by pushing through the pile and producing higher loads. 9.3. Plug failure The plug theories of Ka¨rna¨ et al. (2001) and Croasdale and Cammaert (1993) include the deviation angle x for the plug. In theory, an increase in the angle x will cause an increase in load. A failure mode will always seek the path of least resistance. Therefore, without modification; a deviation angle of 08 would yield the lowest load that would correspond to failure. When the deviation angle is 08 the horizontal stress state is most likely neutral, therefore the normal pressure on the vertical face will be half the buoyant pressure at that location. As the deviation angle is increased the pressure state moves closer to the active state (0.3–0.5 buoyant pressure). The sudden drop in load during plug failures can
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
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be explained by the change from neutral pressure to active pressure on the failure surface. The deviation angle will cause the failure planes to move apart, greatly reducing the normal pressure on the faces. Load is also a function of the area of the failure plane. An increase in the deviation angle will cause an increase in the failure plane surface area causing an increase in load. The minimum load will be achieved at the angle that not only produces the reduction in normal pressure but also minimizes the failure plane area. Observations of plug failures have suggested that the deviation angles are about 158, indicating that this corresponds to the minimum load. There are three possible failure planes: two vertical failure planes and one failure plane under the consolidated layer. Eq. (8) gives the load from the side failure planes. The friction and cohesion terms are added in the same way as in the local failure because, again, they cannot act together. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 Fk ¼ 2 ce hk Ktan/Ak cosx þ ctop Ak cosx 3 3
ð8Þ
where A k is the area of the side walls and K is the pressure coefficient (either at rest or active) and c top is the cohesion at the top of the keel. The load on the failure plane below the consolidated layer is calculated by Eq. (9). The cohesion on this failure plane is the upper cohesion and is not averaged for the variation with depth. 2 Fk ¼ ce hk tan/ þ ctop Ac coshslip ð9Þ 3 Ac ¼ De ðW xÞ þ ðW xÞ2 tanx where h slip is the angle of the failure plane measured from horizontal and x is the penetration into the ridge. The upper failure plane load is much higher than the side failure planes because of the high normal force on the failure plane and the high cohesion just below the consolidated layer.
Fig. 15. New crossover model showing effect of lower local failure load.
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E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15 5
Calculated Load (MN)
4
y = 0.9898x R2 = 0.6824 3
2
1
0 0
1
2 3 Recorded Load (MN)
4
5
Fig. 16. Comparison of new model to recorded events.
9.4. Comparison of the model with measurements The loads resulting from the two failure modes were calculated at penetration intervals, similar to the Cross-over model (Cammaert et al., 1993), based on Eqs. (3), (6), (7) and (8). Fig. 15 shows the load from the different failure components at each indentation step into a representative ridge with a 10 m deep keel and side slope angles of 218. The failure load of the consolidated layer is based on Croasdale et al. (1994) and is not shown in the diagram for simplicity as it would have to be added to both local and global failure modes. From Fig. 15 it can be seen that the maximum load from the keel will be from the local failure. Fig. 16 compares 10 actual ridge interactions with the revised failure theory and consolidated layer loads calculated from Croasdale et al. (1994). The new keel failure model calculates loads that are much closer to the recorded values, with excellent agreement between measurements and theory.
10. Conclusion and recommendations Failure of the consolidated layer thickness is the dominant term in determining the keel load in ridge interaction. Pressure panel observations indicating no sustained pressures on the pier shaft below the cone, lack of correlation between maximum ridge loads and keel depth, and the presence of fragile marine growth on the tidal faces of the pier shaft, suggest that the keel does not contribute significantly to the total ridge load. The reasons for this are not fully understood, but the pier geometry, particularly the sharp edge at 4 m, clearly contributes to the disintegration of the keel.
One other factor, which is not often considered, is the effect of current in clearing entrained ice pieces from around the pier. The observations from the Confederation Bridge Pier monitoring programme suggest that the disintegration of the keel takes place well away from the pier, and that current then clears the ice pieces from the pier. This effect would not be seen on wider structures where high keel forces have been seen. Ridge interactions have limited effects on the rubble pile, resulting in a slight elevation of the rubble pile, but a significant extension of the rubble pile circumference. A modified model using observations from the bridge, no pressure below the cone and consolidated
E. Lemee, T. Brown / Cold Regions Science and Technology 42 (2005) 1–15
layer failure changes, correlates well with the observed load.
Acknowledgement The authors would like to acknowledge the support of Strait Crossing Bridge, Public Works and Government Services Canada, the Program for Energy Research and Development (PERD), and the Natural Sciences and Engineering Research Council (NSERC) through grant CRD 193623.
References Brown, T.G., 2001. Four years of ice force observations on the confederation bridge. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 285 – 298. Brown, T.G., Ma¨a¨tta¨nen, M., 2002. Comparison of Kemi-I and confederation bridge cone ice load measurement results. Proceedings of the 16th IAHR Symposium on Ice, Dunedin, New Zealand, vol. 1, pp. 503 – 512. Bruce, J.R., Brown, T.G., 2001. Operating an ice force monitoring system on the confederation bridge. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 299 – 308. Cammaert, A.B., Jordan, I.J., Bruneau, S.E., Crocker, G.B., Mckenna, R.F., Williams, S.A., 1993. Analysis of Ice Loads on Main Span Piers for the Northumberland Strait Crossing. Contract Report for J.Muller International–Stanley Joint Ventures, CODA contract # 5022.01, 108 pp. Croasdale, K.R., 1997. In-Situ Ridge Strength Measurements. Report submitted to the National Energy Board, Canada, Calgary.
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Croasdale, K.R., Cammaert, A.B., 1993. An improved method for the calculation of ice loads on sloping structures in first-year ice. Proceedings of the First International Conference on Exploration of Russian Arctic Offshore, St. Petersburg, Russia, pp. 161 – 168. Croasdale, K.R., Cammaert, A.B., Metge, M., 1994. A method for the calculation of sheet ice loads on sloping structures. Proceedings of the IAHR ’94 Symposium on Ice, Trondheim, Norway, vol. 2, pp. 874 – 875. Croasdale, K.R., Associates, 1995. Ice Load Models for FirstYear Pressure Ridges and Rubble Fields – Phase 1. Joint Industry Project Report for National Energy Board and PERD. 192 pp. Dolgopolov, Y.V., Afanasev, V.A., Korenkov, V.A., Panfilov, D.F., 1975. Effect of hummocked ice on piers of marine hydraulic structures. Proceedings IAHR Symposium on Ice, Hanover, NH, USA, pp. 469 – 478. Ka¨rna¨, T., Rim, C.W., Shkinek, K.N., 2001. Global loads to firstyear ice ridges. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 2, pp. 627 – 638. Lemee, E., Bruce, J.R., Brown, T.G., 2001. Ice ridge encounter rates for the confederation bridge. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 359 – 366. Mayne, D.C., Brown, T.G., 2000. Rubble pile observations. Proceedings of the 10th International Offshore and Polar Engineering Conference, Seattle, USA, vol. 1, pp. 596 – 599. Minchinton, T.E., Scheibling, R.E., 1991. The influence of larval supply and settlement on the population structure of barnacles. Ecology 72 (5), 1867 – 1879. Nevel, D., 2001. First year ridges acting on conical structures. Proceedings of 16th Conference on Port and Ocean Engineering Under Arctic Conditions, POAC, Ottawa, Canada, vol. 1, pp. 369 – 374. Prodanovic, A., 1979. Model tests of ice rubble strength. Proceedings of Symposium on Port and Ocean Engineering Under Arctic Conditions, Trondheim, Norway, pp. 89 – 105.