Engineering Geology, 13 (1979) 7--18 © ElsevierScientific Publishing Company, Amsterdam -- Printed in The Netherlands
GENERAL REPORT SESSION II: MECHANICAL PROPERTIES
B. LADANYIand F.H. SAYLES INTRODUCTION In reviewing the papers on the mechanical properties of artificially frozen soil for construction purposes, it became clear that the understanding of the mechanical properties, strength and constitutive relationships that have been developed for permafrost can be used in the design of an engineering structure of artificially frozen ground. However, there are important differences between permafrost and artificially frozen ground that must be considered. In permafrost the temperature below the active zone is nearly constant at values above --15°C and except in polygonal soil where ice wedges exist the ice structure in the soil is dominated by horizontal ice lenses formed by the natural freezing front advancing downward. In contrast, the temperature of artificially frozen ground usually is characterized by steep temperature gradients with temperatures as low as liquid nitrogen temperatures near the freezing elements and varying up to 0°C at the freezing front. Since the orientation of the ice inclusions in frozen soil is usually controlled by the direction of freezing, the orientation of the ice lenses can be artificially orientated to the best advantage for the purpose of the retaining structure. In the case of horizontal freezing by vertical freezing pipes the ice content is dominated by vertically oriented ice lenses, as reported by Radd and Wolfe at this symposium. The ice pattern reported in that paper also shows horizontal ice lenses. The vertical ice lenses are to be expected since they are perpendicular to the direction of he.at extraction. The horizontal inclusions may be the result of the soil bedding as explained by Radd and Wolfe or perhaps by horizontal cracks that developed by desiccation during the freezing process as suggested by Chamberlain and Blouin (1977), or some other phenomenon. Further study of ice patterns in horizontally deposited soils that have been frozen from the vertical direction is needed since the orientation of ice crystals clearly influences the mechanical properties of frozen soil (Vialov, 1962). In artificially frozen soil the freezing temperature and the rate of freezing can be controlled (within limits dictated by economics) but in permafrost we must accept the temperature that nature has provided. There are distinct differences between natural permafrost and artificially frozen ground, however, if these differences are taken into account, much of
the information acquired from permafrost studies can be applied in the design of artificially frozen structures. The exchange of information between the two fields has been generally good up to now, and there are several specialists at present w h o have been active in both fields. Nevertheless, there have been as y e t very few opportunities for the specialists in the two fields to meet at a symposium, to discuss their mutual problems and to compare their experiences in permafrost and artificially frozen ground. The organizers of this symposium should be c o m m e n d e d for initiating and organizing such a meeting. Altogether, eleven papers have been submitted to this session. For the purpose of this review, these papers have been grouped into the following three headings. (1) Papers dealing with frozen soil as a homogeneous and isotropic material. (2) Papers dealing with the effects o f macroscopic structure on frozen soil behavior. (3) Papers dealing with thawing. It is admitted that, in some cases, it was not easy to place a particular paper in one group only. Moreover, it was found that some papers in Sessions I and III contain also very valuable information concerning the determination and analytical representation o f some aspects o f frozen soil behavior. In addition, it is clear that such a relatively small number of papers cannot be expected to cover all the most important aspects o f the frozen ground behavior and its determination. The reporters have, therefore, decided to give the subject a little wider coverage, in order to establish a general framework for the discussion and to define some promising areas of future research. Within the framework, the presented papers have filled several important gaps, and pointed to a number o f little known areas to which future research should be oriented. DESIGN REQUIREMENTS
To design a retaining structure o f artificially frozen soil it is necessary to establish the allowable design stress and deformations to be permitted in the structure. The strength of the structure must be such that catastrophic failure will not occur; therefore design stresses must be below the ultimate creep strength of the frozen soil by an adequate factor of safety. It is now a well established fact that the creep strength of a given frozen soil is a strong function of temperature o f the soil, and of the duration and intensity of the applied stress. As mentioned in the introduction, while a permafrost engineer and a ground freezing specialist both deal with a frozen ground, the former has to adapt his design to a given natural temperature environment, while the latter creates its own artificial environment so that it satisfies best his design requirements. This basic difference affects both the type of information
TABLE I Differences between permafrost and artificially frozen ground Aspect
Any soil or rock, ice-poor to ice-rich.
Usually ice-rich, low mineral cohesion, loose silts, sands, weak clays.
Rarely below --15°C; naturally controlled; small variations in time and space.
Usually lower than --20°C, even down to --160°C; if liquid nitrogen used; design parameter to be selected ; large variations.
Mostly horizontal ; thickness and frequency decreasing with depth.
Mostly close to vertical, or nearly parallel to freeze pipes.
Mostly long-term (permanent structures).
Mostly short and medium-term (temporary structures).
Determination of mechanical properties for design
In naturally frozen state; undisturbed samples; lab. and field tests.
Relevant samples can only be obtained after freezing; difficult to estimate in advance because of unknown ground ice structure when frozen.
on frozen soil needed for the design, and the methods to be used for its determination. Table I summarizes some most important differences between the t w o fields. One difference is in the t y p e of ground under study. In permafrost engineering any t y p e o f soil or rock, ice-rich or ice-poor, may be encountered. In ground freezing practice, one is mainly concerned with freezing low-mineral-cohesionless soils, such as loose sands, silts and weak clays under the water table, which, when frozen, become fine-grained ice-rich soils.. Such softs are also very prone to ice-segregation during freezing, which gives them an oriented ice-lens structure, as reported by Radd and Wolfe at this symposium. In permafrost, ice lenses are not present in all soils and tend to fade o u t below a certain depth. When they are present, their main orientation is parallel to the ground surface. In an artificially frozen ground, in usual freezing installations for open excavations or vertical shafts, one can expect to find ice lenses that are mainly parallel to the freezing pipes, giving the ground a complex anisotropic structure. As far as the temperature is concerned, natural permafrost soils at the foundation depth are rarely colder than a b o u t --15°C, and their temperature variation with time and depth below the foundation is relatively small. In ground freezing, depending on the m e t h o d used, the lowest soft temperatures around the freezing pipes m a y vary from a b o u t --20°C down to --160°C. Once the frozen wall has stabilized, the temperature distribution
remains reasonably constant with time. However, the temperature varies strongly across the wall with the minimum temperature at the pipes and a temperature close to zero at the t w o surfaces of the wall. As far as the t y p e o f loading is concerned, in permafrost engineering one is most often concerned with permanent structures, which means, with load duration of 20 to 100 years. The situation is clearly quite different in ground freezing, where the frozen wall is used only as a temporary support to be replaced as soon as possible by a permanent lining or abandoned. The time under load of such a wall will rarely be more than a year and will most often n o t exceed one or two months. Finally, as far as sampling and testing is concerned, in permafrost, because the soil is already frozen, the main problem is h o w to get representative undisturbed frozen samples of natural ground for testing in the laboratory, or h o w to test the soil in the field to get necessary design information. In ground freezing, in turn, the design of a frozen wall is most often based on information obtained by freezing the soil in the laboratory and submitting it to appropriate tests. However, when reading some of the papers presented to this symposium, it is doubtful that laboratory freezing of samples could properly reproduce the ice-lens structure similar to that obtained in large scale ground freezing installations. D E T E R M I N A T I O N OF MECHANICAL PROPERTIES
As mentioned in the foregoing, the earth material to define in-ground freezing is usually an in-situ frozen, ice-rich, fine-grained soil, with distinctly oriented ice-lens structure. Its temperature varies across the wall from zero inside, over a minimum in the middle of the wall and back to zero at the outside. In other words, the frozen wall we have to design has a distinct anisotropy, because of the ice lenses, and a distinct non-homogeneity of strength and rigidity, because of the temperature variation. In general rheological terms, we are then confronted with the problem of determing the time and temperature dependent deformation and strength properties of an anisotropic and non-homogeneous material under a general triaxial state of stress. The problem is still more complicated by the fact that the material, due to the wide temperature range, may have at different points of the wall, quite different types of behavior. Its behavior may be brittle around the freezing pipes, where the temperature is below --20°C, and it may be plastic close to the wall surface where the temperature is close to zero. When one is faced with such a complex situation, one can use t w o different approaches to arrive at a solution • the first consists in attempting to find explicit solutions based on some idealized and simplifying assumptions on frozen ground behavior, using, e.g., an average temperature across the wall and assuming a homogeneous and isotropic material. Another approach, in turn, m a y consist in trying to define as closely as possible the true behavior of the frozen soil in the wall, and in using a numerical m e t h o d for finding a solution, which takes into account the
11 anisotropy and the non-homogeneity of the wall. The first m e t h o d has done up to n o w excellent service to the engineers w h o had to design many frozen ground structures, and can u n d o u b t e d l y continue to be used with success b y experienced designers in future. However, the reporters consider that for the future, the second m e t h o d seems more promising, and proper efforts should be made to supply all necessary design parameters for its more extensive use. P A P E R S D E A L I N G W I T H F R O Z E N SOIL AS A H O M O G E N E O U S ISOTROPIC M A T E R I A L
There are three papers in this group, dealing directly or indirectly with the problem of testing and interpretation of results in the brittle to plastic transition area. This aspect is important in connection with ground freezing because of high temperature gradients involved. In addition, there is one paper discussing the best loading sequence in creep testing, and one dealing with the behavior of frozen soil under cyclic loading. In the paper "Strain rate effect on the compressive strength of frozen sand", Baker reports on a series of uniaxial compression tests performed on cylindrical specimens of a fine Ottawa sand compressed between four different types of end platens. The sand was compacted to e = 0.577, and was nearly completely ice-saturated. It was tested at --5.5°C at constant strain rates, varying from 6 . 1 0 .6 to 6.10-1 min-l. The tests showed that neither the unconfined compressive strength nor the axial strain to failure were significantly affected by the t y p e of platen, b u t the modes of failure at low strain rates were different for each platen type. Of the four types of platens used in the tests, only the Maraset compliant platens did n o t produce any noticeable bulging at low strain rates. At high strain rates, all of the platens produced conjugate shear failure planes. In the tests, no change in creep regime was found at higher strain rates, contrary to what was reported by some earlier investigators (Rein et ai., 1975) and by Takegawa et al. at this symposium. One reason for it, mentioned by the author, m a y be the use of compliant platens which give a better stress transfer at specimen ends, w i t h o u t stress concentration and tensile splitting stresses. A practical conclusion that can be drawn from that paper is that one has to be very careful with the testing conditions especially when trying to cover large intervals of temperature and strain rate, because various combinations of the two parameters may produce very different failure modes. An important addition to this kind o f study would be the determination of plastic to brittle transition rate at a given temperature. For that, several different criteria might be used, one o f which is described in the paper b y Zaretsky et al. at this symposium. Two others are: the peak to residual strength ratio, and the uniaxial compressive to tensile strength ratio, respectively. Similar findings are reported in the paper " E f f e c t of specimen shape on
12 creep response of a frozen sand" by Ladanyi and Arteau. They also report on uniaxial compression tests with a nearly ice-saturated fine quartz sand at a temperature of --5°C and at strain rates varying from about 5 . 1 0 -6 to 5" 10-1 min-1. However, their sand density was considerably lower than that in Baker's paper (e = 0.770). They are particularly concerned with the effect of testing conditions, such as the stress transfer at specimen ends and the slenderness of the specimen, on its observed behavior in the brittle and the ductile range, respectively. Similarly as Baker, they find that a strict control of density or a density correction, is necessary in any such study with frozen sand. As far as the peak strength is concerned, they find that, with smooth platens, it increases at any strain rate when the height to diameter ratio increases from 0.5 to 2, while the opposite is true with rough platens. While the differences in strength are not more than 14%, this may, nevertheless, have an important effect on the design, if extrapolations to much lower or higher rates are made. The authors discuss also the post-peak behavior of frozen sand and the problems of its proper determination in laboratory compression tests. The reporters consider the latter aspect to be very important in compression testing of frozen earth materials, in connection with the ground freezing, because the frozen soil in the wall m a y undergo large strains reaching far into the post-peak region. In other words, if the design of a frozen wall is made by assuming the formation of a "plastic" zone, the knowledge of the post-peak behavior of the frozen soil becomes a basic requirement for the design. In the paper entitled "Ice behavior under load", Zaretsky, Chumichev and Solomatin find that in creep testing of columnar-grained ice at temperatures ranging from --4°C to --13°C, there is a critical stress level, independent of temperature, which defines the brittle to plastic transition in such an ice under uniaxial compression. Here, plastic creep is defined as that resulting from processes at a molecular energy level, such as slip, recrystallization, twinning and crystal face distortion. Brittle creep, in turn, is associated with crack formation, cavity formation, and crushing phenomena, all of which produce acoustic emission that can be recorded instrumentally. This cracking activity effect was used earlier by Gold (Ref. 10 in the paper) for finding the brittle to ductile transition stress in ice. Once the critical stress or the creep limit is exceeded, the microcracks multiply and result in a progressive creep, eventually leading to failure. The authors find that, for stresses beyond the creep limit, linear strain under uniaxial compression is directly proportiooal to the total surface area of microcracks that can be deduced from the recorded intensity o f acoustic emission, and propose an equation for calculating that strain. The paper is clearly very relevant to the problem at hand of creep behavior in brittle range of very ice-rich soils, in which there is no direct contact between the grains. In such a frozen soil, even if one cannot count on any long term strength based on intergranular friction or cohesion, one can at least define a critical stress level below which the creep is of an attenuating type. In fact, it seems that the behavior of such materials is
13 more rock-like than soil-like. In addition, the acoustic emission recording may become a useful tool for monitoring the performance of frozen earth structures in situ. While in the previous papers only either stress- or strain-rate-controlled tests were used for studying.the frozen soil or ice behavior, in which only one creep curve or one stress--strain curve was obtained from each specimen, Eckardt, in his paper on "Creep behavior o f frozen soil in uniaxial compression tests", uses a stage-loading method for determining creep parameters for frozen soil from a single test. The stage-loading m e t h o d of creep testing has been used extensively in creep testing of metals and plastics, and is also quite c o m m o n in the field testing of frozen soils. In laboratory creep testing its principal advantage is that it greatly reduces the scatter of test results due to the variability of properties o f different samples. The method is probably quite justified in connection with relatively short term creep phenomena such as occurring in artificial soil freezing. Extrapolation to long term creep from such short term tests is, however, usually very difficult and necessitates a number of additional assumptions, one of the most important ones being the existence of the constitutive creep equation for the material, implying that its behavior is independent of the loading history. Li, Baladi and Andersland in their paper entitled "Cyclic triaxial tests on frozen sands", report a b o u t a series of strain-controlled cyclic triaxial tests which they performed on a frozen uniform fine (Ottawa) sand with three different ice contents: 35%, 55% and 80% by volume, respectively. The tests were carried o u t on cylindrical samples, at temperatures of --I°C, - 4 ° C and --10°C under confining pressures of zero, 0.345 MPa and 1.378 MPa, using frequencies of 0.05 to 5.0 cps. From the tests, they determined the dynamic Young's modulus and the damping ratio, both o f which are the basic soil properties used in analytic techniques for prediction of ground surface motions which occur during an earthquake. Their results show that, under the conditions of their tests, the dynamic Young's modulus increases with increasing loading frequency, confining pressure, and sand content, b u t decreases with increasing axial strain and temperature. On the other hand, the damping ratio was found to decrease with increasing loading frequency, sand content and lower temperature, b u t was less influenced b y the confining pressure and axial strain. It should be n o t e d that, in dynamic work on frozen soils, the Poisson's ratio has n o t y e t been measured directly. Poisson's ratio by Stevens (1975) and others is determined b y computing it from measured values of shear and Young's modulus. The reporters consider the paper as an important parametric s t u d y of frozen sand behavior under cyclic loading, which is relevant to many ground freezing problems related to the construction and maintenance of tunnels under active railway or road traffic. One such case is presented b y Jones and Brown in Session III of this symposium. A particular interest of the paper is
14 also that it deals with saturated and over-saturated sand--ice mixtures, showing clearly the effect of ice (or sand) content on their behavior. PAPERS DEALING WITH THE EFFECTS OF MACROSCOPIC STRUCTURE ON FROZEN-SOIL BEHAVIOR There are three papers in this Session that can be classified into this group, one of them dealing with large-scale mineral elements and two others evaluating the effects of ice lenses on frozen-ground behavior. When a frozen soil is composed of a large granular aggregate embedded in a fine-grained matrix, such as it is often the case with glacial tills, direct experimental determination of its thermal and mechanical properties is sometimes difficult because it requires manipulation and testing of very large samples for which the testing equipment is usually rather scarce. However, as shown b y Tsytovich and Kronik, some of these properties can also be evaluated indirectly by using certain laws of mixtures. In their paper, they distinguish between "skeleton-type" and "non-skeleton-type" coarse-grained soils, the b o u n d a r y between the two being at a b o u t 50% porosity of the coarse-grained aggregate. The parameters they determine by this m e t h o d for the mixtures are the specific heat, the thermal conductivity, the coefficient of relative volume change and the modulus of deformation. Their equations may be adequate for estimating the soil properties where only approximate values are required. It should be pointed out that these equations do not take into account the ice texture of the soil and, where more precise values are required, testing of the in-situ material is necessary to confirm these estimated values. The reporters consider that similar principles could probably also be used for evaluating some mechanical properties of sand--ice mixtures, for which some attempts have already been made in the past (Ruedrich and Perkins, 1974). In the paper "Creep characteristics of frozen soils" by Takegawa et al., the authors show the results of a series of unconfined compression creep tests carried out on two kinds of frozen silt samples, both with and w i t h o u t ice lenses. For the tests, undisturbed block samples were taken from unfrozen silt deposit. The samples were then frozen by two different methods, one resulting in ice lens formation and another producing uniform soil w i t h o u t lenses. The test temperatures were --10°C, --25°C and --40°C, respectively. In the tests with samples containing ice lenses, the load was applied at an angle of 45 ° to the direction of the lenses. The results of tests performed on these samples show that, for samples with lenses, compression strength is about 10% smaller, and elastic modulus about 20% smaller than for comparable samples without ice lenses. Another interesting finding made by the authors is the presence of a stress level which they call "upper yield value". This stress level corresponds by definition to the "creep limit", determined for ice by Zaretsky et al. in their paper at this symposium.
15 The existence of such a creep limit has been observed in uniaxial creep testing in brittle domain of material such as rocks and concrete, and is considered to be connected with the cracking activity leading to brittle failure. One should, however, be careful n o t to consider this limit to be identical with the true long-term s~rength of frozen soil in plastic range, which is known to be related to the intergranular friction and mineral cohesion that can only be fully mobilized either after large strains or after consolidation, both of which take long periods of time. A particular aspect o f this paper is that it describes a procedure that one would usually adopt for obtaining information on the soil to be frozen, necessary for the design of a future frozen wall. The paper by Radd and Wolfe, "Ice lens structures, compression strengths and creep behavior o f some synthetic frozen silty soils", is a very significant contribution, in that it is the only one containing a comparison between the behavior of small-scale samples and that of large samples containing largescale lens structure, that were taken directly from a frozen wall. The soil was mostly an in-situ frozen, varved silty clay with a complex ice lens network. Most lenses were oriented 10°--45 ° from the vertical, and their orientation remained constant to within 90 cm of the freeze pipes. Approximately 75% of the ice was in the heat-flow-produced vertical lenses, while the rest was within the cracks and the contacts between bedding planes. Laboratory unconfined compression tests were conducted on small (1.27 X 1.27 X 2.54 cm) samples, both cut from cores and taken from the wall, at temperatures o f --10°C, --40°C and --80°C, respectively, using a rather high compression strain rate of 0.02 min- 1. The samples taken from the wall, which contained a n e t w o r k of 3 mm thick ice lenses were weaker than those from the cores which contained only some thin randomly oriented lenses. Still more difference in strength was found when compressing on the site much larger specimens (5--7.5 cm wide and 10--15 cm high) with a portable manual testing machine. The strength was, however, higher than that obtained on small samples from the same area, which is clearly due to the much higher strain rate (25 times faster) used in compressing the large samples. Normally, at the same rate of strain one would expect to get smaller strengths for larger samples because of the size effect and the presence o f large-scale ice lenses in larger samples. The authors carried o u t some laboratory creep tests on the same soil and found a substantial difference between the clay creep strengths parallel and perpendicular to the bedding planes, showing clear anisotropy effects. The authors conclude with good reason that for obtaining reliable design parameters for such a highly anisotropic and heterogeneous material with large-scale lens structure, one would have to test large specimens that properly reproduce all the representative soil elements. In addition, the laboratory test results should always be checked later by appropriate field tests made on the frozen wall. The reporters completely agree with this conclusion.
16 PAPERS DEALING WITH THAWING There are three papers that can be classified in this group. The methods for computing the energy and time required to thaw frozen soil suggested by Jumikis in his paper on artificial thawing of frozen soil, may have application to freezing ground. However, the problem of transferring heat from the pipe surface to the surrounding soil is somewhat different. On the double-wall closed system the heat transfer can be hampered by the lack o f soil contact against the outside wall of the thawing pipe and, further, if the temperature of the thawing pipe is too high, the moisture may be driven from the contiguous soil, and an insulating layer of dry soil will be formed around the pipe, thus reducing the energy transfer and lengthening the thaw time. In freezing, the moisture migrates to the freezing front and adheres to the freezing pipe insuring intimate contact with the soil for heat transfer. It would be of interest to validate the thawing computation b y laboratory and field tests. Where a heated shaft in frozen soil is to be lined with a permeable material such as concrete, Novikov in his paper on "Pressure of thawing soils on the concrete lining of vertical mine shafts", points out that high vertical as well as lateral stresses can occur in the lining from the thawing annulus of soil around the shaft. When there is nonuniform thawing around the shaft, the eccentric loads on the lining can cause rupture. The theoretically developed expressions for vertical stresses around the shaft lining were reported to be confined by data from tests on a laboratory model of a shaft in a frozen clay. In the theoretical development of the equations for loads in the shaft lining, the cohesion and angle of friction were assumed to be the same for both the shaft lining and the interface between the frozen and thawing soil. Although these expressions for vertical stresses were confirmed by experiment, the question still arises as to the values of cohesion and friction angle at a thawing interface. Since this problem arises in slope stability, in buried heated pipe line and many other engineering structures, research is required to develop techniques for evaluating these parameters at the thawing and freezing fronts. The artificially freezing method of construction involves usually only one freeze--thaw cycle. Nevertheless, even this one cycle can have important effects on the mechanical behavior of the ground when thawed, especially if a high a m o u n t of ice segregation has occurred during freezing. Such effects were studied b y Johnson et al. in their paper " E f f e c t of freeze--thaw cycles on resilient properties of fine-grained soils". Their in-situ and laboratory tests made on silt and clay subgrade soils in connection with the design of pavements, show great differences in resilient moduli obtained for the same soil when frozen, during the thawing period and when fully recovered. The knowledge a b o u t changes in mechanical properties of soils after they have been artificially frozen is clearly very important in connection with the design of permanent tunnel or shaft linings, intended to replace the temporary support supplied by a frozen wall. Another little known parameter
needed in the design of permanent linings is the state of stress in the ground that follows the thawing, discussed in the previously reviewed paper by Novikov. RESEARCH NEEDS
Areas in which the review has shown that further research and development are needed for improvement in the design and construction of artificially frozen soil structures are summarized below. (1) Theoretical and experimental studies are needed on the strength and rheology of soils artificially frozen in different directions at low temperatures, with a goal o f developing a practical creep and strength theory that can be used in the design of frozen soil structures. (2) Methods are needed for determining the in-situ physical and mechanical properties of frozen ground and for estimating how an unfrozen ground will behave after it is frozen and subsequently thawed. (3) Further experimental studies are required to evaluate the strength parameters, cohesion and friction angle, at the freezing and thawing fronts. (4) Further analytical and experimental studies are required to evaluate the settlement due to thaw consolidation and the interaction of this process with the structure. (5) Additional studies are required on the ice texture and orientation of ice inclusions in frozen soil with respect to their influence on the strength and rheology of frozen soft. (6) Field validation tests are required for the strength, rheology and thermal performance of artificially frozen ground structures. P R O P O S A L S F O R DISCUSSION
(1) Effects of ice-lens structure of a frozen soil on its strength and creep properties. (2) Methods for reproducing in laboratory-frozen samples ice-lens structures similar to those observed in large-scale ground freezing. (3) Creep and strength of ice-rich frozen soils in plastic and brittle range. (4) Problems of "creep limit" and "long term strength" determination. (5) Monitoring, by mechanical, acoustic, and other methods, the extent, the properties and the performance of artificially frozen structures. REFERENCES Chamberlain, E.J. and Blouin, S.E., 1977. Frost action as a factor in enhancement of drainage and consolidation of fine-grained dredged material. U.S. Army Eng. Waterw. Exp. Stn., Teeh. Rept., D-77-16. Rein, R.G., Hathi, V.V. and Sliepcevich, C.M., 1975. Creep of sand--ice systems. Proc. ASCE, 101(GT2): 115--128. Ruedrich, R.A. and Perkins, T.K., 1974. A study of factors influencing the mechanical properties of deep permafrost. J. Petrol. Tech., 1974, pp.1167--1177.
18 Stevens, H., 1975. Response of frozen soils to vibratory loads. U.S. Army C.R.R.E.L., Tech. Rept., 265. Vialov, S.S. (Editor), 1962. The Strength and Creep of Frozen Soils and Calculations for Ice Soil Retaining Structures. USSR Acad. Sci. (USA CRREL Transl., 76, 1965)