Research needs for physical modelling in ice engineering: Reflections from a university ice tank

Cold Regions Science and Technology, 13 (1986) 57-65 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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RESEARCH NEEDS FOR PHYSICAL MODELLING IN ICE ENGINEERING: REFLECTIONS FROM A U N I V E R S I T Y ICE T A N K Robert Ettema Iowa Institute of Hydraulic Research, The University of Iowa, Iowa CiW, IA (U.S.A.) (Received July 17, 1985; accepted in revised form March 27, 1986)

ABSTRACT Given the complexities surrounding many ice engineering problems, engineers and scientists will continue to draw heavily on physical modelling techniques to obtain the required insights and data for designing structures and vessels in ice-covered waters. However, so that physical modelling might be well-founded scientifically, and not be yet another "black art," a programme o f rigorous research must still be undertaken to identify: (1) appropriate similitude criteria and scale effects in ice-force modelling; and, (2) improved model-ice material(s) together with improved methods for testing model-ice properties. Presented here are reflections on research activities needed to establish appropriate modelling criteria and model-ice materials. The reflections are not intended to be a complete statement o f all research needs. Rather, they somewhat wistfully mirror the author's concern for the slow development o f modelling practice.

INTRODUCTION Ice engineering is a relatively young subject that deals with complex phenomena. The analytically based tools which are available to the engineering profession for dealing with problems related to icestructure/vessel interaction are especially deficient. It is understandable, therefore, that in arriving at design decisions involving expensive constructed works, engineers have made extensive recourse to laboratory modelling as a predictive technique, 0165-232X/86/$03.50

despite the physical limitations of, and inadequate analytical basis for, many aspects of current modelling technology. The principal stumbling blocks encountered in ice modelling are the establishment of the formal requirements for dynamic similitude beiween model and prototype; and the development of a model-ice material, or materials, that meets these requirements. What follows is a brief review of the research needed to surmount these stumbling blocks. Requisite techniques for instrumenting model structures, or ship hulls, for experimentation in ice are not discussed here, and for a more detailed account of present modelling techniques, the reader is referred to Timco (1984a), or Schwarz (e.g., 1980). Ideally, geometric, kinematic and dynamic similarity should be maintained between model and prototype. This is rarely achieved, even in much simpler situations involving only single-phase, free-surface flows of water. In practically any modelling situation, it is necessary to determine what forces are dominant, and then to scale the model and model-material properties so as to maintain the same ratios between these forces in model and prototype. To the extent possible, one corrects, either experimentally or analytically, for the model's failure to faithfully reproduce the less important forces. In the case of ice modelling, the goal has been to correctly model the flexural strength and submerged weight of the model ice, probably because early activities in physical modelling in this field were concerned with icebreaker shiphull design. It is evident that extensive research activities still need to be pursued along the following two, related, lines:

© 1986 ElsevierScience Publishers B.V.

58 1. Similitude criteria and scale effects in ice-force modelling; 2. Model-ice material(s) and test methods. The thrust of research line 1 should be to examine critically the laws of motion related to ice-structure/ vessel interaction, and the ice constitutive relations (incomplete though they may be), and to derive a more complete, more rigorously founded, set of similitude parameters. The sensitivity of model-test results to the failure to fulfill one or another of the similitude criteria should be evaluated, using results from model-tests performed Using model-ice basins. Research line 2 should be a systematic effort, involving not only engineers but also physical chemists, to develop an improved model-ice material (or materials) for ice-force modelling - one whose properties satisfy the scaling requirements and which is reasonably easy to use. While the author was collecting his thoughts for this paper, Timco unveiled his latest model ice material, EG/AD/S ice, which holds promise of being a significant advance in ice modelling. EG/AD/S ice (ethylene glycol/aliphatic detergent/sugar as dopants) is still under scrutiny by the various ice tanks and has yet to be widely implemented. The call for improved similitude criteria, modelling techniques and model-ice material is long standing and has been issued by several national organizations involved with ice and arctic engineering, such as the NRC Panel on Sea Ice Mechanics (1981), the NAS Glaciology Panel (1982), and the NRC Committee on Glaciology (1983). For the moment, it seems, little research effort is being directed toward defining valid similitude criteria for physical modelling, and only a few research efforts, notably those by Timco (all references) have been undertaken to develop model ice materials. Before proceeding with the discussion on modelling monolithic ice, consider ice engineering problems centred around floating fragmented ice, in the form of ice rubble. One would think that these problems should be fairly amenable to physical modelling; especially since it would seem that the strength and material properties of ice sheets would not have to be simulated, and therefore only the usual similitude criteria for bodies in fluids need be applied. This, unfortunately, is not necessarily so. Picture the forces acting on an ice piece floating amidst fellow ice pieces (e.g., as in Fig. 1). Acting on

the ice piece are its bodily buoyancy force and the restraining reactions of neighboring ice pieces. Because ice pieces may freeze-bond or adhere to one another, and boundary or volume diffusion (see Kuroiwa (1961) and Hobbs (1974) for discussions on this) may occur, it is likely that the ice piece may become fused at its contact points with other ice pieces. Consequently, when the ice piece is externally loaded and disturbed (e.g., during the passage of a ship hull through the layer) its behaviour will be governed by the relative magnitudes of its buoyancy force and the total freeze-bond force restraining it. For a relatively large ice piece with a large volume to surface area ratio, buoyancy force may exceed the total freeze-bond force. Therefore, a layer of such ice pieces will behave largely as if it were comprised of discrete particles. On the other hand, for a relatively small ice piece, with a small value of volume to surface area ratio, the freeze-bond force may dominate. Consequently, a layer of such ice pieces would behave more as a skeletal framework of end-fused ice pieces. When buoyancy force dominates, we have fragmented ice that is commonly called ice rubble, while when freeze-bond force dominates we have socalled mushy ice. Brash ice is transitionally somewhere between the two ice-rubble types.

AIR

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~

FREEZE-BONDS AT CONTACTS

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Fig. 1. Forces on a submergedice piece. Rheological properties of ice aside, the problem for the ice modeller studying the behaviour of fragmented ice is to scale ice piece size yet still replicate the ratio of buoyancy and freeze-bond forces. Figure 2 illustrates the problem for the case of a scale-model simulation of ship-hull moving through an ice-clogged channel (Ettema et al., 1985). With decreasing value of the ice-piece diameter to hull beam ratio, the

59 resistance encountered by the hull decreases. But when the ice pieces become sufficiently small so that the freeze-bond force dominates ice behaviour, the layer undergoes a change in character, becoming a mushy continuum, and the resistance encountered by the model ship-hull rapidly increases. The increased resistance may in part be due to the change in character of the layer of fragmented ice, but it is also due to the non-scaling of the freeze-bond strength between ice pieces. MODEL ICE PIECES

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well as between ice and structure or vessel; the submerged weight of the ice; and the two-phase (liquidsolid) nature of ice motion. Therefore, the effects of gravity, inertia, ice-ice friction, ice-structure friction, ice-fluid friction, together with ice strength and deformation all have to be appropriately scaled in order to attain strict model-prototype similarity. However, this generally is not possible. As a matter of fact, the complete similitude requirements cannot be satisfied even for most single-phase flows. The problem is compounded by the absence of criteria for correctly scaling the mechanical properties of ice, which themselves are not well understood and less well formulated. Common practice (e.g., Michel, 1969; Schwarz, 1977; Timco, 1984) has been to assume that the criteria are satisfied if the global properties of ice sheets suitably scaled, on the basis of the following classical quantities, have the same value in model and prototype: inertial forces

Froude number,

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Reynolds number,

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=

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Fig. 2. Resistance to ship hull m o t i o n t h r o u g h a layer of ice

pieces: scale-modelsimulation (Ettema et al., 1985). SIMILITUDE CRITERIA AND SCALE EFFECTS IN ICE-FORMING MODELLING

inertial forces

VL

viscous forces

v

inertial forces

p V2

elastic forces

E

-

where V is a representative velocity, g the acceleration due to gravity, L a representative length, and =,,p, and E represent the kinematic viscosity and density of the fluid and the elastic modulus of the ice, respectively. Atkins (1975) proposed an additional similitude criterion, Ice number I n

inertial forces -

-

cracking forces

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Background

The ensuing condensed account of current modelling practice highlights areas of concern for scaling ice-structure interaction phenomena. In addition to the similitude criteria which must be satisfied for single-phase free-surface flows, physical modelling of ice dynamics must take into account the following: the strength and deformation properties of ice; friction between ice fragments, as

where K = fracture toughness of ice sheet. It can be shown (e.g., Timco, 1984) that I n is basically Ch modified to include the influence of resistance to crack propagation through ice. Fluids such as water do not allow the Reynolds number criterion to be satisfied, and therefore this criterion has been disregarded on the grounds that viscous or fluid-friction forces are small in comparison to forces attendant to displacing and frac-

60 turing ice. Consequently, Froude number controls the relationship between velocities and lengths, and in particular V ~ ~ . Because pressures scale as V 2 for Froude-number scaling (if the same fluid density is used in model and prototype), and fracture stresses have the same units as pressure, stresses must also scale as V2: Coincidentally, this is also the correct scaling relation for E versus velocity to satisfy Cauchy-number requirements. Therefore, it has been concluded (e.g., Michel, 1970; Schwarz, 1977, and others since) that the ratio ct/E (where a is usually taken to be the flexural strength of the ice) should take on the same values in model and prototype. It was argued further that the various other strengths of ice generally bear constant ratios to each other (e.g., flexural strength is proportional to compressive strength, and so on), and thus preservation of the ratio of, say, flexural strength to E in model and prototype ensured dynamic similitude of compressive strength and the entire ice-breaking process in the model. Several practioners of physical modelling (notably, Michel, 1970; Enkvist, 1972; Vance, 1975; Schwarz, 1977 and Timco, 1983) have treated ice as a linearelastic material, and have stressed the importance of keeping the ratio Ef/af (where Ef and af are elastic modulus and flexural strength determined from measurements by treating ice as a semi-infinite elastic beam or plate) approximately the same for model and prototype ice. Schwarz (1975) evaluated the El/of ratio for sea ice and found it usually to be in the range 2000 to 5000. Thus, according to current modelling practice, a scaling requirement for model ice is that El/of should not be less than about 2000. Present model-ice materials - urea-doped ice and synthetic ices - are barely able to satisfy this criterion as well as correctly scaling flexural strength at model scales less than about 1:30. However, the resuits of some studies (e.g., Tatinclaux, 1984) appear to correlate reasonably well with prototype data despite the failure to achieve the correct model value ofEt./of. The fact that inexact model representation of the ratio that the inexact model representation of the ratio Ef/af did not seem to significantly affect the modelling results is an indication that this ratio may not be the correct scaling parameter for the dynamics of ice fracture during ice impact with structures and vessels, and may impose overly stringent modelling

conditions. Another aspect of this is that Ef is not readily measurable with a high degree of accuracy. In current modelling practice, it is customary to scale the mechanical properties of the model ice according to the strength associated with the anticipated dominant failure mode of the prototype ice. Although this is suitable for many cases of structure or vessel impact with ice, it is a handicap for modelling more complex interactions of ice and structure when different ice-failure modes, such as flexure and crushing, may occur. The inaccurate scaling of one or more of the strengths may cause the true nature of a structure's interaction with ice to be obscured; or it may have little effect if the results are suitably normalized. Although they are useful for modelling the global behaviour of monolithic ice, the similitude criteria described above are, by themselves, incomplete for modelling the behaviour of a mass of ice comprised of fragments. The major shortcoming here being the introduction of an at times significant scale-effect associated with the mis-scaling of the ratio of freezebond force to buoyancy forces. For a floating mass of ice fragments, the ratio of Froude number to Cauchy number (i.e., the ratio of elastic (freezebond) to gravity forces) is an important similitude criterion. However, it is one that is difficult to satisfy for modelling the forces between locally fused ice fragments because the modeller has little direct control over the thermodynamics at play in a mixture of ice and water. Research needs

Clarification of the minimal similitude requirements for the faithful modelling of prototype behaviours would be a tremendous benefit to ice engineering. In particular, the following research activities should be pursued: (1) Derivation of the scaling laws for ice-structure/ vessel interaction in several ways, including dimensional analysis, normalization of the equations governing unsteady motion of nonlinear-elastic floating materials, and by normalization of the constitutive relations for ice, which are not known exactly. (2) Critical examination of the equations of motion governing ice impact with structures/vessels

61 and failure in different modes, in order to obtain estimates of the relative magnitudes of the individual terms in the governing equations for typical prototype situations, and thereby to identify the important scaling parameters. (3) Determination of the permissible variation of model Ef/af from the prototype values. It is likely that practical considerations will dictate that Ef/af will continue to be used as a primary scaling criterion. However, the sensitivity of results to its variation are not yet well established. Therefore, a series of laboratory tests would be conducted utilizing structures of simple geometry (e.g., circular cylinders, square cylinders) in which Ef/a.f is systematically varied while other quantities are held constant. The effects of the variations in Ef/af on the measured forces and observed icebreaking patterns would thereby be examined. Given the difficulties associated with independently fixing E f and at', this task would not be easy to achieve. (4) Experimental examination of the effects of surface roughness (of both model structure/ship and ice) on model ice forces and fracture patterns. These tests should be similar to those conducted under task (3), but the surface textures of the test body and the model ice should be systematically roughened to different degrees. (5) Conduction of a series of tests to determine the effects of basin width on model results. Refrigerated (and other) towing tanks generally are relatively narrow. Although Schwarz (1983) offers some rules-of-thumb on adequate ice-tank size for physical modelling, the effects of the lateral constraint of the ice on the results of tests on bluff bodies have not been examined rigorously. Therefore, tests should be conducted in which the ratio of the width of the test body to the width of the test basin is varied systematically with ice-sheet thickness, to delineate the acceptable basin widths in relation to test-body size and ice-sheet thickness. IMPROVED MODEL-ICE MATERIAL (S) AND TEST METHODS Background There is a pressing need to develop improved model-ice materials, and to establish techniques and

corresponding guidelines for testing the strength properties of model-ice materials. Development of improved model-ice materials has been repeatedly a high-priority research need listed by panels assembled to appraise the status of ice-mechanics (e.g., NRC Panel on Sea Ice Mechanics, 1981; NRC Committee on Glaciology, 1983). Before outlining necessary research steps in this area, it is perhaps useful to review very concisely existing model-ice materials and related modelling practice. Early physical modelling was mainly involved with scale-model tests of icebreaker ship hulls, and saline (NaC1) ice was generally used as the model-ice material. However, saline ice was considered to be unsuitable for models with scales less than about 1:15 to 1: 20, because the similarity criterion Ef/af >~ 2000 could not be satisfied at larger scales; the saline ice became less elastic and more plastic. The design of large marine structures and ice-breaking vessels has heightened the need for an improved model-ice material, which can be used with small-scale models. The past few years have seen the development of model ice materials which after some improvement over saline ice. One improvement has been the advent of urea-doped ice, which has enabled scale modelling to be conducted at scales down to about 1:40, although this limit is debated. Another claimed improvement over saline ice has been the development of several wax or synthetic (nonaqueous) ices such as the one originally developed by Michel (1969). The primary attractiveness of the wax ices lies in their use in non-refrigerated environments. Ad additional reported (e.g., by Schultz and Free, 1984) feature of wax ices is that the recipe of a mass batch can be varied in order to modify the rheological character of the wax. The major drawbacks of the synthetic ices are that they are proprietary, and therefore are not generally available; their use is expensive; and it is possible that, in some instances, their properties maybe somewhat exaggerated by the commercial companies marketing testing services utilizing them. Moreover, and perhaps most importantly, their friction coefficients (for ice-structure/ship and ice-ice contacts) are so far generally too large. Wartsila Arctic Research Center (WARC), of Finland, developed a fine-grained saline ice for use in its

62 model basin. The attractive properties of this ice, as reported by Enkvist and Makinen (1984a,b), are that it is nearly homogeneous and behaves in a brittle manner when loaded. Enkvist and Makinen describe their fine-grain ice as producing more realistic behaviour - i.e., better simulating sea ice -during iceship-hull interactions. Essentially, they claim that the crack pattern and ice-fragment sizes are more like those observed for icebreaker ships. An advantage of WARC's fine-grain ice is that it can be rapidly produced (according to Enkvist and Makinen, a 70 mm thick ice sheet can be formed overnight), although a special water-spray carriage and ancillary apparatus are needed to produce the model ice. However, as Timco (1984b) points out, the ratio of crushing strength to flexural strength (about 1:1) of the finegrain model ice is much lower than it is for ice sheets found in nature (typically 2 : 1 - 3 : 1). Consequently, for some instances of ice-structure/vessel interaction use of the fine-grain ice may lead to results which are insufficiently conservative for the purposes of designload estimation. Another fairly recent development to overcome scale limitations due to model-ice material, has been the construction of very large model-ice basins; the 70 plus metre long basins of Wartsila Arctic Research Center (WARC), Finland; and the Hamburgische Schiffbau Versuchsanstalt (HSVA) in Hamburg, W. Germany; and an 80 plus metre long tank recently constructed at St. Johns, Newfoundland, Canada. A problem with large ice basins, especially from the viewpoint of a university researcher, is that they are very expensive to operate and require processing of large volumes of ice. But, of course, the costs are orders of magnitude less than those for conducting full-scale tests in nature's own laboratory. At present, the brightest hope for an improved model ice is Timco's EG/AD/S ice. Timco (1985) gives a detailed description on the composition and properties of EG/AD/S ice, which appears to be superior to urea ice in its modelling performance, a key feature being that EG/AD/S ice does not have the occasionally problematical top layer that characterizes urea ice. The performance of EG/AD/S ice is reported only for moderately thick ice sheets; 4 cm thick. Its behaviour for lesser thicknesses has yet to be reported. It is likely that there may not be a single multi-

purpose model ice for use under all conditions. Indeed, for some cases of structure interaction with ice, certain types of model-ice material may be more suitable than others. For example, in situations not involving ice failure, and when the effects of freezebonding can be neglected, as can perhaps occur in some cases of ice-rubble movement through confined waterways (Tatinclaux et al., 1976; Sodhi et al., 1982), a rigid, nonfrozen model-ice material such as plastic may be used, at least for preliminary modelling. For tests involving ice forces on structures, ureadoped ice now is used in most of the world's refrigerated test basins. However, considerable uncertainty still surrounds its properties and the optimum means of its preparation. For example, it has been found in the course of testing at IIHR that minor factors, such as room humidity and rate of ice growth, can have seemingly disproportionate effects on the properties of urea-doped ice. Another factor contributing to this uncertainty is that the properties of the urea-doped ice are modified by even the design of the model ice basin and the cold room in which it is housed, as is discussed in a recent IIHR thesis (Cook, 1983) and by Ettema et al. (1984). Additionally, there is considerable lack of clarity concerning the relationship between urea concentration and the strength and elastic modulus characteristics of urea-doped ice. Also of concern to ice modellers is their inability to correctly simulate very thin ice sheets, and to simulate refreezing, or ice regrowth, between ice fragments. It has been found that sheets of model ice, both urea and saline, thinner than about 10-20 mm typically have values of E.f/o.f much less than 1500; in other words, the model ice has little elasticity and tends to deform plastically. Consequently, this inability to use relatively thin ice sheets may also limit the scale for a physical model, and is a nagging concern for the author who operates a smallish ice tank. Wet-seeding is the process used to produce small crystals in the upper layer of model saline and urea ices and, thereby to produce a weak ice for modelling. However, studies involving refreezing between ice fragments (e.g., studies related to rubble ice, brash ice, ice ridges, etc.) are limited presently insofar that the strength of refrozen ice cannot be reproduced; the refrozen ice, being unseeded, is too strong. A recipe for producing scale-model pressure

63 ridges is given by Schwarz (1983), who proposes the use of insulating blankets to cover and control the refreezing of preformed ice ridges. This technique only globally simulates the refreezing process that occurs in consolidated ice ridges. Research needs

A review of the literature reveals that only a few systematic quests have been made for an improved model-ice material (Michel, 1969; Timco, 1979, 1981; Enkvist and Makinen, 1984a,b). A well executed search would of necessity involve a physical chemist who is knowledgeable in the relationship between the mechanical properties of materials, their chemical composition, and their crystalline structure. This research activity should be directed toward finding a better model-ice material - one that accurately satisfies the similitude criteria; whose properties are not overly sensitive to the details of its preparation; and, ideally, which can be prepared without refrigeration. Failing that, further testing would be carried out with urea-doped ice, or with Timco's recently developed EGADS ice, to define the responses of model-ice properties to the method of preparation and to the ambient conditions during its preparation. Testing would also be conducted via standardized procedures so as to produce ice sheets of requisite characteristics. Specific activities that should be pursued along this line of research should be: (1) A review of existing model-ice materials, and the ice-ship/structure-interaction conditions for which they are suitable. (2) A review of available data on the physical properties of sea ice. (3) An investigation of the structural properties of urea-doped ice, in order to determine the factors controlling its strength and deformation properties; for example, this effort should extend the work of I-Iirayama (1983) and others. (4) A systematic search for a dopant which could be utilized to produce an improved model-ice material. (5) Tests at different scales to determine the effectiveness of selected chemicals in reducing the strength and the appropriate deformation properties of model ice. These tests should involve use of

appropriate materials testing equipment to assess the strength and deformation properties of the model ices. (6) Doped ice, prepared with the dopant(s) found to be superior, should be tested in a model ice basin. The tests should utilize simple geometrical bodies (circular and square cylinders) and, perhaps, a more complex model such as that of an offshore platform, or a section thereof, to evaluate the suitability of the new model-ice material for laboratory use. (7) An attempt also should be made to develop a model-ice material that does not require freezing. However, it is likely that such a material will not be generally suitable for instances in which ice-structure friction is important. During the process of strength-testing model-ice materials, improved test methods for measuring and controlling the mechanical properties of modelice materials should be developed. Recommended guidelines for testing ice, as stipulated by the IAHR Working Group on Ice Problems (1980), do not adequately take into account the nature of doped model-ice materials, and are not fully applicable for testing the mechanical properties of relatively "warm" thin sheets of doped ice. Timco (1981) described some techniques for measuring the mechanical properties of model ice; ihowever, experience at IIHR has shown that a considerable amount of further development is required for test methods. In designing the test methods, several important characteristics unique to doped model-ices must be considered. Briefly paraphrasing Timco (1981): first, the methods should involve minimal handling of ice samples; second, the tests should, whenever possible, be performed on the ice in-situ, because of the rapid brine drainage that occurs during sample handling; third, loading rates for strength testing should match the loading rates of the ice during its interaction with a model structure or vessel; finally, because only limited time usually is available for testing during the conduct of scale model tests, the ice-preparation methods must be simple, quick, easily conducted, and reliable. CONCLUDING REMARKS

Given the complex natures of many ice interactions with structures and ships, physical modelling

64 will often be the only method used to predict the behaviour of a particular prototype structure or ship in ice. However, in order that physical modelling be well founded in physics, there is a pressing need to formulate accurate similitude criteria for modelling practice, and to produce a model ice material, or materials, that simulates faithfully the behaviour of ice in nature. Some suggested guidelines for research are outlined in this paper. It is all very well to develop similitude criteria and a model ice material, or materials, but these must also be appropriate to the circumstances of experimentation. In other words, the desired modelling laws and model-ice properties must be such that they can be satisfied and evaluated relatively quickly and without much technical difficulty. The above discussion is the gist of lengthy ruminations on ice modelling between the author and Dr. John F. Kennedy, who practice ice modelling at the Iowa Institute of Hydraulic Research (IIHR).

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