The Rheology of Frozen Soils

Lukas U. Arenson*1, Sarah M. Springman2, Dave C. Sego1

1 Department of Civil & Environmental Engineering, UofA Geotechnical Centre, 3-065 Markin/CNRL Natural Resources Engineering Facility, University of Alberta, Edmonton, Alberta T6G 2W2, Canada

2 Institute for Geotechnical Engineering, ETH Zurich, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland

*E-mail: [email protected] Fax: x1.780.492.8198

Received: 2.6.2006, Final version: 2.8.2006

Abstract: The rheological behaviour of frozen soils depends on a number of factors and is complex. Stress and temperature histories as well as the actual composition of the frozen soil are only some aspects that have to be considered when analysing the mechanical response. Recent improvements in measuring methods for laboratory investigations as well as new theoretical models have assisted in developing an improved understanding of the thermo-mechanical processes at play within frozen soils and representation of their response to a range of perturbations. This review summarises earlier work and the current state of knowledge in the field of frozen soil research. Further, it presents basic concepts as well as current research gaps. Suggestions for future research in the field of frozen soil mechanics are also made. The goal of the review is to heighten awareness of the complexity of processes interacting within frozen soils and the need to understand this complexity when developing models for representing this behaviour.

Zusammenfassung: Das rheologische Verhalten von gefrorenen Böden hängt von einer grossen Anzahl verschiedener Faktoren ab und ist äusserst komplex. Druck- und Temperaturgeschichte, sowie die Zusammensetzung des gefrorenen Bodens sind nur einige Aspekte, welche betrachtet und berücksichtigt werden müssen, wenn man die mechanischen Eigenschaften analysiert. Neue Messtechniken bei Laborversuchen, sowie neue theoretische Modelle haben zu einem verbesserten Verständnis der mechanischen Prozesse gefrorener Böden beigetragen. Dieser Artikel fasst frühere Arbeiten sowie die gegenwärtige Forschung auf diesem Gebiet zusammen. Mit diesem Arti- kel soll das Bewusstsein der Komplexität gefrorener Böden geweckt werden. Es werden Konzepte der gegen- wärtigen Forschung vorgestellt sowie die Richtung zukünftiger Forschungsaktivitäten aufgezeigt. Dem Leser soll bewusst gemacht werden, dass bei der Formulierung von Modellen für gefrorene Böden jeder Situation spe- ziell Rechnung getragen werden muss.

Résumé: Le comportement rhéologique des sols congelés dépend d’un grand nombre de facteurs et est complexe. L’his- torique des tensions et des températures ainsi que la composition réelle du sol congelé sont seulement quelques aspects qui doivent être considérés en analysant la réponse mécanique. Les améliorations récentes des méthodes de mesure pour les essais en laboratoire ainsi que de nouveaux modèles théoriques ont aidé à développer une meilleure compréhension des processus thermomécaniques en jeu dans les sols congelés et la représentation de leur réponse à un certain nombre de perturbations. Cet article récapitule les précédents travaux et l’état actuel des connaissances dans le domaine de la recherche sur les sols congelés. De plus, il présente des concepts de base aussi bien que des lacunes présentes dans la recherche actuelle. Des suggestions pour la recherche future dans le domaine de la mécanique des sols congelés sont également faites. L’objectif de l’article est d’intensifier la prise de conscience de la complexité des procédés interactifs agissant dans les sols congelés et de la nécessi- té de comprendre cette complexité en développant des modèles pour représenter ce comportement thermo- mécanique.

Key words: frozen soil, permafrost, soil testing, shear strength, creep

Applied Rheology 12147-1 Volume 17 · Issue 1 1 INTRODUCTION the significant frost heave mechanisms. Howev- er, only since the beginning of the 20th Century, The term rheology was originally defined on April and in particular with the ground breaking pub- 29, 1929 by a committee that met in Columbus, lications of Taber in 1929 and 1930 [14, 15], as well Ohio after a proposal by E.C. Bingham and M. as those of Beskow in 1935 [16], were the funda- Reiner. By definition, the term refers to “the study mental processes presented to a wide academic of the deformation and flow of matter” [1 – 3] in audience. The basic concepts introduced at that terms of stress, strain, temperature and time, i.e. time are still generally accepted, as confirmed by it is concerned with the description of the flow Black and Hardenberg [17] in their report on the behaviour of all types of matter [4]. Frozen soil is historical perspective of frost heave research. matter whose thermo-mechanical properties In more recent years, new challenges have should be described in order to carry out stabili- arisen due to problems related to warming ty analysis of permafrost slopes or artificially frozen shafts. Research into the physical proper- ground temperatures associated with per- ties of frozen soils started in the 19th Century. Two mafrost degradation. Slope stability problems main developments were responsible for these have been recorded within mountainous envi- studies. The industrial revolution expanded into ronments [18 – 21] and new impacts on Arctic more remote areas of the Northern hemisphere infrastructure [22 – 25] or coastal zones [26] are that was underlain by permafrost, and artificial expected with the impacts of climate change ground freezing was introduced as a method for [27, 28]. constructing temporary support of structures The emerging demand for knowledge relat- and openings used in both mining and geotech- ed to the mechanical properties of frozen soils nical engineering. with respect to structures in permafrost, artifi- French [5] presents a detailed summary of cial ground freezing or frost action problems has the early works on periglacial geomorphology resulted in a significant number of laboratory and shows that the existence of perennially investigations on a variety of different soil types frozen ground was confirmed as early as during under extensive and varied boundary conditions. the mid 17th Century. Mikhail Vasilyevich Lomo- This vast quantity of research and publications nosov (1711 – 1765) probably offered the first has led to a number of summary papers and known scientific explanation on permafrost [6], reviews. The first section in this paper presents but the first publication on the existence of a selection of such papers to demonstrate the permafrost within the Shergin Well was pub- importance as well as the complexity of this topic lished by von Baer in 1838 [7]. Initial publications in science and engineering. Some related articles on problems related to engineering geocryology have also been published in Applied Rheo- were published in 1885 by a group of four logy [29]. scientists: The instructions for studying the The aim of this paper is to demonstrate the permafrost soils of Siberia. In 1927, Sumgin pub- diversity and variety of frozen soils and to follow lished an important summary of current knowl- up by presenting approaches on how to deal with edge at that time [8]. At about the same time as it. There is no such thing as the typical frozen soil. the engineering properties of permafrost were To understand the mechanical behaviour of a being studied, artificial ground freezing (AGF) frozen soil, factors such as its composition, stress was introduced in Wales (1862) and later in Ger- history, temperature, grain size, type and form, many (1883) by Pötsch [9, 10]. There are endless etc. have to be considered. This review sum- examples where AGF was used to improve soil marises some of the more recent research and properties with nearly no limits in dimension. puts it into context to help with understanding Shaft depths of 900m were achieved in the 1950s and assessing the influence of different variables in Canada, and to date AGF is used for a variety on the mechanical behaviour of various frozen of applications in geotechnical engineering soils. In addition, the review should provide a [e.g. 11, 12]. guide on how to deal with problems related to An important phenomenon observed with- frozen soils and where to find additional infor- in frozen and freezing soils is related to the mation on a particular challenge. It is not intend- dynamics during freezing and frost action. In ed to be a tool for the design of any particular 1854, Volger [13] presented the first evidence of engineered structure.

Applied Rheology Volume 17 · Issue 1 12147-2 Permafrost (T<0°C) Artificially Frozen Seasonal Frost

Dry (MC = 0%) Frozen Soil (MC > 0%)

Rock Soil Segregated Segregated Ice ice not visible ice visible frozen soil, soil freezing and frost action, however, are more focused on engineering, resulting in Individual Ice Poorly Bonded Ice with Soil Inclusions Inclusions substantially fewer manuscripts. Both trends

Well Bonded – No Ice Coatings on show a research boom in the seventies that was Excess Ice Particles Ice without Soil Classification Classification Standard Soil Soil Standard Standard Rock Rock Standard Inclusions related to the exploration of the Northern nat- Well Bonded - Random/Irregular Excess Ice Oriented Ice ural resources, predominantly in North America. Formations Representative Layer Thickness The culture of academic publishing has resulted Stratified/Distinctly th 10 Oriented Ice in a skyrocketing increase at the end of the 20 Formations 1.0 Century. 0.1 Ice Content Layer [m] Layer Based on the number of available publica- 0.01 0.1 1 10 100 1000 Maximum Grain Size [mm] tions, it comes as no surprise that various review and state-of-the-art papers have been published. In 1973, Anderson and Morgenstern [30] presented a review on the mechanics of frozen ground. Their publication summarises the important developments, mainly since 1963, with a special focus on the role of unfrozen water. Two additional thorough reviews were presented by Ladanyi in 1981 [31] and 1985 [32]. The for- Unfrozen mer presents a schematic representation of the Ice Intermediaten Ice Ice soil Poor Icec Content Rich failure envelope for frozen sand that is divided into various stages, and the latter focuses on the

Dirty Ice Dirty failure criterion that accounts for the hardening effects associated with dilatancy. In addition, a 0% 20% 40% 60% 80% 100% simple general creep equation is presented Volumetric Ice Content based on earlier work [33]. Ladanyi [32] and oth- ers [34 - 36] further emphasise that the temperature effect can not be described using the rate process theory because of the ongoing phase Figure 1: 2 THE HISTORY OF FROZEN SOIL change at the high homologous temperatures Soil classification for frozen usually encountered in engineering. Sayles [37] soils and permafrost sam- LITERATURE shows that with time, the quantity and quality ples (after [44] and [45]). The interest in research on frozen soils over the of the data increased, and that new empirical Figure 2: last century can be traced by the number of man- models as well as physics-based models became Frozen soil classification uscripts published in peer reviewed journals. The available to describe the mechanical behaviour according to the total volu- authors are completely aware that much signif- of frozen geomaterials. However, the paper also metric ice content. icant information and a vast number of primary reveals that there is still a need for further inves- papers have also been published in books and at tigations to assist practising engineers when conferences, such as the Ground Freezing Sym- dealing with complex boundary value problems posia, International Permafrost Conferences, in natural settings. Conferences on Cold Regions Engineering, and A comparison between creep of frozen and other additional conferences, meetings or work- unfrozen soils was presented by Ladanyi in 1999 shops. A compilation of the number of published [38]. The author shows that the study of frozen manuscripts that are available on the ISI Web of soil creep mainly followed development with ice Knowledge database shows that even though and high temperature metal approaches, where- not all of the publications from the early days as unfrozen soil creep descriptions are primarily may be recorded in the database, clear trends can based on the Cam Clay model [e.g. 39 - 41]. How- be distinguished. The available literature related ever, the Cam Clay model only provides a sound to permafrost is generally much higher since it basis for long-term extrapolation of experimen- includes many science as well as engineering tal data for non-dilating frozen soils at tempera- publications. Research related to the study of tures close to melting.

Applied Rheology 12147-3 Volume 17 · Issue 1 Description Bulk density Creep Mechanism [Mg/m3]

coarse grained Dirty Ice 0.9 – 1.0 Solid diffusion enhanced (steady state can exist) recrystallisation

Very Dirty Ice 1.0 – 1.5 Dislocation inhibited by (still unstructured) soil particles

Frictionless Frozen Soil 1.6 – 1.95 Creep is enhanced by presence of unfrozen water

fine grained Frictional Frozen Soil 1.95 – 2.30 Damped creep inhibited by soil structure

Vol. Ice 10% 30% 70% 90% Content Ice Poor Interm. Ice Cont. Ice Rich Dirty Ice

3 FROZEN SOILS AND PERMAFROST regated ice visible by eye (< 1 inch thick), and iii) Figure 3: ice (ice lenses thicker than 1 inch). Additional sub- Schematic representation of Generally, freezing is the process of cooling a liq- frozen soil samples at groups describe further characteristics such as uid to the temperature (freezing point) where it different volumetric ice the bonding of the ice, inclusions, and orienta- contents. undergoes phase change to a solid. In other tion. Such a classification system is of great words, a frozen soil is a soil that has been cooled importance when describing frozen soils. How- Table 1: to a point at which the pore water turns into ice. Frozen soil classification ever, since the classification is generally based on This definition implies that a liquid phase, nor- according to Weaver [47]. soil samples with limited dimensions (e.g. 150 by mally the pore liquid, must exist and that it changes phase. On the other hand, permafrost is 100 mm), it is possible that the more general defined exclusively by temperature and time. stratigraphy that may control the mechanical According to Muller [42], permafrost is defined behaviour will be lost in this detailed description. as “ground (soil or rock and included ice and To avoid this, we recommend that larger sections organic material) that remains at or below 0°C with thicknesses of up to several metres be clas- for at least two consecutive years”, which is a sified as a unit with respect to their ice content commonly accepted definition [43]. This defini- and stratigraphy depending on the grain size. tion does not include the physical state within The larger the grain size, the greater the thick- the ground, i.e. dry soils or rocks that meet the ness should be examined as a representative temperature requirements behave mechanical- layer (Figure 1). Weaver [47] proposed to classify ly similar to their unfrozen counterpart. Similar- the frozen soil based on the bulk density and the ly, freezing point depressions due to pore water recorded creep mechanism (Table 1). salinity or pressure melting may result in the soil A similar attempt is made by the authors. behaving like an unfrozen soil, even at tempera- Figure 2 shows a schematic that is based on its tures below 0ºC. It is therefore essential to mechanical response to aid the general classifi- describe clearly the actual state of the water in a cation of frozen soil at different volumetric ice particular soil within the current temperature contents, which will be discussed in the follow- regime. Frozen soils need not be permafrost. In ing sections. The authors want to emphasise that fact, seasonally (e.g. during winter) or temporal- there is no commonly accepted definition of the ly (e.g. artificial ground freezing) frozen soils are terms used in Figure 2. Ice-rich is often used for of significant engineering interest, but can not soils with a visible ice content between 20 and be defined as permafrost. 50%. The figures show that there is a gradual The original engineering classification for transition between the regions, which depends frozen soils was introduced by Linell and Kaplar on factors such as grain size, form of ice, unfrozen [44] and presented in a modified version by John- water content, temperature, or other possible ston [45]. Sayles et al. [46] published additional solutes in the pore water. Schematic represen- guidelines for this classification and index test- tations for each category are presented for coarse ing of frozen soils. The system divides the ice grained, non frost susceptible soils and fine within frozen soils into three main groups (Fig- grained, frost susceptible soils in Figure 3, respec- ure 1): i) segregated ice not visible by eye, ii) seg- tively.

Applied Rheology Volume 17 · Issue 1 12147-4 D C

ductile

B Stress A dilatant brittle Volumetric Ice Content

>0% Strain Strain Rate

Figure 4 (below): Coarse grained (a: coarse and the excess of pore water developing during sand) and frost susceptible thaw results in a loss of strength and substantial fine grained (b: Devon silt) deformations. Therefore, these soils are classi- soil in an unfrozen (top) and a frozen (bottom) state. No fied as frost susceptible and thaw weakening. change in the particle loca- The phenomena associated with frost sus- tion is noted for the sand, ceptible soils have been investigated for many whereas horizontal ice lens- years, not only in science, but particularly es (black) start to form in the silty sample (NB: The because of economic impact in terms of loss of sand freezes from the bot- serviceability and ongoing maintenance [14 – 16, tom upwards and the silt 48]. Depending on the freezing rate, i.e. the heat from the top down). extraction rate, the structure of the ice lenses Figure 5 (left above): changes [49], influencing the heave rate. Some Stress-strain behaviour for studies suggest that the heave rate is propor- ice subjected to a constant tional to the heat extraction rate [50 – 52]. How- strain rate (after [64]). A) ductile behaviour with ever, those studies suggest that water is always strain hardening; B) dilatant available, which might not be true in the field [53] behaviour with strain soft- because of changing water tables. Hermansson ening; C) brittle behaviour and Guthrie [54, 55] carried out laboratory tests with failure just after yield point; D: brittle failure. that demonstrate consistent reductions in the frost heave and water uptake rates with decreas- Figure 6 (right above): 4 FROST SUSCEPTIBILITY AND FROST ing height in water table. Stress response as a function In the early 1980s, Konrad and Morgenstern of the strain rate and the ice HEAVE content (after [65]). [56, 57] presented the concept of the segregation Before dealing with the strength and deforma- potential, which is defined as the ratio of water tion behaviour of a frozen soil, some characteris- intake rate and the temperature gradient in the tics that focus on the freezing process are zone between the warmest ice lens and the described, i.e. the transition from an unfrozen to unfrozen soil, called the frozen fringe [58]. The a frozen state. Generally, the particle structure of segregation potential is a soil parameter that coarse grained soils that are exposed to sub-zero best relates to the average size of the fines frac- temperatures changes marginally as the water tion, the specific surface area of the fines frac- in the pores freezes (Figure 3a). As the water tion, and the ratio of the material’s water con- changes phase, the volume increases by 9% and tent to its liquid limit [59]. The reduction of heave since the hydraulic conductivity of a coarse with increasing overburden pressure can be grained soil is high, excess water drains, and the accounted for by an empirical relationship soil structure remains unchanged. The lower between the segregation potential, the average hydraulic conductivity and surface activity of the size of the fines fraction, and the compressibility fine grained soils, on the other hand, affects the index of the soil [60 - 62]. To date, the concept of soil structure and lenses that are essentially pure the segregation potential is widely used in engi- ice form normal to the direction of heat flow (Fig- neering practice within the theory of frost heave ure 3b). The volume increase of the soil due to and has been adopted for the prediction of frost freezing generally results in uplift or frost heave, action.

Applied Rheology 12147-5 Volume 17 · Issue 1 Variable Effect on strength of frozen soil

Temperature Generally the strength increases as the temperature decreases. In addition, the stress-strain behaviour can change from ductile to brittle. The change in behaviour can be mainly attributed to the change in unfrozen water content, which is discussed later in the paper. Strain Rate An increase in strain rate results in an increase in strength, but 5 THE MECHANICAL RESPONSE OF also a change towards brittle behaviour, as shown in Figures 5 and 6. Under very low strain rates, creep dominates the FROZEN SOILS deformation and sample response, because complete relaxation takes place in parallel to the small increase in stress caused by Initially, rheological models were proposed to the added strain. Ice Content The strength increases as the ice content decreases because of describe the mechanical behaviour of frozen soils the structural hindrance that develops as solid particles first that are based on a combination of mechanical contact each other. Within a medium to dense frozen soil, the models consisting of springs, dashpots and brak- ice is the bonding (cohesive) agency. This apparent cohesion results in a higher resistance at zero (tensile strength) and low ing elements [e.g. 63], which are widely used for confining stress compared to unfrozen soils. The confining stress other materials [e.g. 64]. However, it was also represents the horizontal pressure applied on a soil sample during testing. Some researchers reported a slight decrease in indicated at that time that such models fail to strength for dirty ice [77, 78]. Numerical modelling on mixtures provide a quantitative description of the actual confirmed this observation and showed that the failure plane follows the boundaries between the ice matrix and the solids [79]. deformation process, as these models can not Air Content Only a few tests on the effect of air content on the strength incorporate all the peculiarities of the behaviour behaviour of frozen soils (or ice) are available [e.g. 67, 69, 80]. of a frozen soil, in particular the non-linearity of These tests suggest that the air within the samples suppresses any tendency for dilatancy to occur by providing significant the process associated with ever-changing soil opportunity for elimination of the air voids and associated properties (void ratio) during the deformation contraction. Confining Stress Confining stress has a minor effect on the strength of ice [81] at process [65]. Thus, most models are only valid for stresses below the melting pressure. Only when the ice content a narrow range of boundary conditions and soil decreases below approximately 60%, is the strength of a mixture increased by increased confinement. The more solid particles, the types. To understand the effect of different more pronounced the increase in resistance, because the boundary conditions on the mechanical behav- component of resistance due to frictional dissipation of work is a function of the confining stress. iour, the relative aspects will be discussed indi- Salinity The resistance of a frozen saline soil decreases as the salinity vidually in this section. increases [82 - 84]. This is explained by the freezing point depression resulting in higher unfrozen water contents at similar temperatures. In addition, Arenson and Sego [85] showed that 5.1 STRENGTH the ice crystal structure within a saline pore fluid environment is more fragile, which may be an additional cause for the lower The stress-strain behaviour for frozen soils is sim- resistance of saline soils compared to similar non-saline soils. ilar to the behaviour of ice, for which Gold [66] Dynamic Load Recent progress in the dynamic characteristics of frozen soils was summarised by Zhao et al. [86]. Various tests have shown presents four different responses (Figure 5) that that a critical strain rate exists at which the dynamic strength depend on the applied strain rates: is similar to the static strength. At higher strain rates, the dynamic strength is higher, with a slight decrease in peak strength a) ductile behaviour with strain hardening with an increasing frequency of oscillation. Contrary behaviour b) dilatant behaviour with strain softening was noted for lower strain rates. However, only a few data-sets c) brittle behaviour with brittle failure just after are available, and more research is needed. Refreezing Arenson and Springman [67] present some tests during which the yield point compression was stopped and broken bonds within the ice matrix d) brittle failure were allowed to refreeze. Immediately after reloading, the resistance exceeded the values expected under comparable More recent tests on ice-rich permafrost soil conditions with ongoing continuous loading. The resistance samples [67] and artificially manufactured converged towards the continuous values following additional shearing with no obvious volume change. It is thought that the frozen samples [68, 69] confirmed this behav- extra resistance is mobilised to break the refrozen ice bonds. iour. However, solid soil particles influence the stress-strain response of a frozen soil that is not only a function of the applied strain rate, but also depends on the volumetric ice content (Figure 6). addition, the particle sizes, as well as their grad- Table 2: Even though brittle behaviour may occur for ing, influence the shape of the stress-strain rela- Effects of different variables on the strength of frozen heavily compacted unfrozen soils, the difference tionship. Table 2 summarises the effect of differ- soils. between dilatant and ductile behaviour is gen- ent variables on the resistance (strength) and the erally presented as a function of the soil density, stress-strain behaviour of frozen soils. However i.e. the void ratio [70, 71]. Additional investiga- various trends, such as small strain effects, volu- tions of the stress-strain behaviour of frozen soils metric responses and the effect of refreezing are show an initial plateau in the diagram present- still poorly understood and additional research is ing a first resistance peak for small strains [72 - needed to confirm these initial conclusions. 75]. Andersen et al. [76] investigated the small Based on these observations, it can be con- strain behaviour and showed that the ice matrix, cluded further that the resistance of a frozen soil the strain rate and the temperature control the at large strain is similar to the resistance of the form and intensity of this first yield region. In unfrozen soil, as all contributing ice bonds are

Applied Rheology Volume 17 · Issue 1 12147-6 1200

1000 ice poor unfrozen soil

[kPa] 800

h Vol. Ice Content (decreasing)

0% 600 intermediate

ice rich Shear Strengt 400

dirty ice

Ultimate Shear Stress ice 200 1600 1200 0 800 100% 400 100 80 Normal Stress 60 40 Volumetric Ice Content [%] 20 0 0 Confining Stress [kPa]

Figure 7: broken and the measured cementation is lost at the there is a lack of dependency of the friction Post-peak shear strength as this strain. Direct shear tests on frozen sands con- on temperature, strain rate and time [33, 95]. a function of the volumetric ice content and confine- firm these conclusions where an expansion of Based on this postulation, Arenson and ment for a sandy gravel at a the shear zone was noted due to crack propaga- Springman [96] present an angle of friction f temperature of about - 2ºC tion along the shear zone as well as mobilisation for a well graded coarse frozen sandy gravel and an axial strain rate of of ice granules and particles acting and dilating about 1·10-7.s-1 (after [94]). (funfrozen = 32.5º) as a function of the volumetric together [87]. This effect can also be described as The data are valid for these ice content wi. The cohesion c, however, was tem- particular conditions only. rubblisation [87, 88]. However, very large strains perature, strain rate and ice content dependent. are necessary for this behaviour, which might not The ultimate shear strength (i.e. strength at large Figure 8: be attained during a particular laboratory inves- Schematic representation of strain) t can be calculated as: the failure envelope for tigation using either triaxial or direct shear test- frozen soils at a distinct ing. t = c + s tanf temperature. (1) 5.1.1 Unfrozen water f = 32.5 32.5 w2.6 i (2) The unfrozen water plays a very important role

on the measured resistance of a frozen soil and where s is the normal stress and wi the unfrozen will be discussed later in detail in this paper. The water content between 0 and 1. amount of unfrozen water can be significant, Figure 7 shows the dependency of the post- even at temperatures below 0ºC. Water can be peak shear strength on the volumetric ice con- present as an adsorbed water film around fine tent and the confining stress. The data in Figure particle surfaces or as free water in the pores. The 7 are only valid for a sandy gravel at a tempera- smaller the particles, the higher the unfrozen ture of about - 2ºC and an axial strain rate of water content [89 - 92] at a certain temperature about 1 · 10-7s-1. The shape of the surface, as well accompanied by suction that increases as the as the strength parameter presented change for water film becomes thinner around the particles. different materials and conditions. However, Freezing point depression due to pore water general trends are described that are typical for chemistry will further increase the amount of most frozen materials: unfrozen water. Generally, an increased un- At low confinement stress, the strength is frozen water content, i.e. reduced ice content, ice higher than the strength of the unfrozen bonding and extra-particle suction, reduces the material. This behaviour is a result of the cohe- apparent cohesion and therefore the shear resis- sion contribution from the ice matrix. tance is lower, and the sample behaviour is less The strength of ice (wi = 1.0) is independent of stiff for similar soil skeletons. However, as suc- the confining stress at the stresses tested. tion develops, the effective stress counteracting Ultimate shear strength increases with a this effect will be increased. decrease in volumetric ice content is noted at higher confining stresses. This is different 5.1.2 Strength formulations from the peak strength that increases with Fish and Zaretsky [93, 94] present a model to decreasing ice content for unconfined com- calculate the shear strength as a function of tem- pression [e.g. 97]. perature based on the Mohr-Coulomb failure The maximum value of the large strain shear criterion, while considering the ice melting pres- strength is reached for low volumetric ice con- sure. All three parameters required (angle of fric- tents, where the structural hindrance and tion, cohesion and melting pressure) are tem- hence the dilatancy is well developed, and perature dependent. Some authors postulated cohesion due to the ice matrix is available. In

Applied Rheology 12147-7 Volume 17 · Issue 1 Figure 9: Creep-curve definitions (a) and variations (b) [e.g. 32].

addition, the ice provokes an increase in the to occur. A series of compression tests and sim- thickness of the shear zone, which was ple shear creep tests on dirty ice suggest that observed during direct shear tests [87]. This loosely arranged particles weaken the frozen soil effect has been described as rubblisation [87, (dirty ice) [e.g. 67, 77, 99, 100], however, the 88]. mechanisms involved are not fully understood. As the number of particles increase beyond a crit- 5.1.3 Time ical value so that they are in contact with each Details about the effect of time on the behaviour other, structural hindrance is possible at large of frozen soils will be discussed in the section on strain and this strengthens the sample. In case of creep behaviour. However, it needs to be briefly pressure melting, the soil skeleton takes over the stresses, providing strength at high normal addressed related to the strength of a frozen soil. stresses. In ice poor samples, the ice matrix pro- Similar to the large strain strength, the long term vides cementation between the particles. If these strength of a frozen soil approaches the unfrozen contacts are present, the peak strength of the ice- large strain strength. Vyalov [65] presents a for- soil mixture can be significantly higher than the mulation for the unconfined compression strength of the unfrozen soil alone (see sections strength s as a function of time t using two soil above). As pressure melting affects the ice, only parameters b and B. The parameters b and B are the unfrozen strength can be reached, which is temperature and strain rate dependent [e.g. 98]. similar to the large strain behaviour, where all ice The unfrozen large strain strength is the cut-off cementation is destroyed during shear. When for the relationship. the ice content is zero, no cementation, i.e. cohesion, is available that would influence the peak b s(t) = strength of the soil at low normal stresses. This ln()tB (3) results in a dramatic drop in resistance. It has to be noted that Figure 8 is a schematic; the transi- tions between the different forms of behaviour 5.1.4 Failure envelope and the actual increase in resistance are a func- The behaviour that has been observed for vari- tion of all the parameters discussed above and ous boundary conditions can be summarised have to be determined for each situation. schematically by a series of failure envelopes representing peak strength (Figure 8). This figure is 5.2 CREEP similar to the representation by Ladanyi [31] Creep defines the time dependent deformation except for the extension into a third dimension, of matter under constant stress conditions. using the volumetric ice content. At low normal Based on various laboratory studies, three stages stress, strain softening controls the behaviour, can be distinguished during creep: primary, sec- which changes into strain hardening as the nor- ondary (or steady state) and tertiary creep (Fig- mal stress increases and hence in an increased ure 9). In 1955, Glen [101] proposed using a power strength. At higher normal stresses, pressure law to calculate the steady state creep rate of melting of the ice occurs, initially only due to glacier ice: localised stress concentrations in the shear plane(s) and later throughout the whole sample. = n The soil particles within the sample affect these e A s (4) stages differently depending on their percentage by volume. Pure ice samples have the ability to The steady state creep rate is therefore a power mobilise shear stress as pressure melting starts function of the compressive stress s and two soil

Applied Rheology Volume 17 · Issue 1 12147-8 Figure 10: Estimation of creep curves based on a series of constant strain rate (CSR) tests (after [94]).

parameters Aand n. It is commonly accepted that is equal to the ratio of the strain ef and time tf at n is equal to 3 for pure ice [e.g. 102 - 104] and that failure: the factor is temperature independent. The parameter A, on the other hand, changes with tem- e f perature. Voytkovskiy [105] proposed an empiri- e = min t cal relationship for the creep strain rate with f (7) temperature that various authors have used subs uently [e.g. 102, 106]: More recent data confirm the validity of this assumption and it is therefore possible to esti- 1 mate the creep of a frozen soil based on a series e of constant strain rate tests (Figure 10a) [96]. 1+T (5) Data for a creep test is found by taking the strain rate at a certain stress and a particular magni- Arenson and Springman [96] show for alpine per- tude of strain from the constant strain rate test mafrost that this proportionality can be used and and transforming it to the creep test at this stress a relationship for A can be found that is separat- level (Figure 10b). ed into a temperature term that is independent

of the ice content wi, and a term that depends on 6 THE ROLE OF UNFROZEN WATER the ice content: The unfrozen water within the frozen soil has a significant influence on the strength and creep a log A= +bw() behaviour of frozen soils, as discussed. Depend- + i 1 T (6) ing on salinity, temperature, grain size and pressure, the amount of unfrozen water can be sig- In addition, they show that n decreases linearly nificant [89, 90, 92, 112]. As an incompressible with increasing solid content. Analysis with data substance, water can transfer positive as well as from Arenson et al. [68] confirmed the validity of negative stresses, or suction, between soil parti- the above relationships. cles and ice crystals. However, if drainage is allowed, excess pore water pressures will dissi- pate and the original stress state will be re-estab- 5.3 STRESS VERSUS CREEP lished. This results in a change in volume and is Constant strain rate tests as well as constant complex for unsaturated soils due to the water stress (creep) tests are generally used to repre- flow into gas filled voids [e.g. 67, 69]. Research sent the mechanical behaviour of a frozen soil. by Hivon and Sego [82] shows that the structure A two-way dependency can be found for of the frozen soil and the location of the unfrozen unfrozen soils [e.g. 107, 108], which was further water also has an important influence on the enhanced by Ladanyi [33] and later in conjunc- mechanical behaviour. However, expressing the tion with Johnston [109 - 111] for frozen soils. The strength as a function of the total unfrozen water assumption is based on laboratory test results, content, which was a combination of tempera- · showing that the minimum creep strain rate e min ture and salinity, was not successful. Recent

Applied Rheology 12147-9 Volume 17 · Issue 1 investigations into the microscopic structure of soil being evaluated. This requires a range of lab- the ice within saline and non-saline frozen soils oratory investigations, which will then allow site [113] show that the ice structure is more fragile and project specific soil parameters to be deter- for saline soils and the location of the unfrozen mined. Due to the great variety of mechanical water is different depending on how the sample responses of different soils, extrapolations from initially freezes [114 - 117]. other sites are not recommended. Boundary conditions, such as temperatures and strain rates 7 RESEARCH NEEDS have to be carefully chosen to represent the prob- lem under investigation. To understand the mechanical behaviour of Time has a significant influence on frozen frozen soils, future research at the microscopic soil strength and deformation because the com- scale is required. Currently, the interactions position may alter with stress changes resulting between and the actual stresses of the various in consolidation due to water migration, or pre- constituents are ignored and only macro stress- viously broken ice bonds may refreeze and es and deformations are evaluated. The charac- strengthen the soil. In addition, solute rejection teristics of a particular soil are summarised in a during freezing is highly dependent on cooling series of soil parameters that have to be deter- rates. It is therefore important to know the freez- mined for a specific application. This approach ing history of a soil. A permafrost soil, for exam- requires intensive laboratory testing that is gen- ple, could have existed for thousands of years and erally interpreted as being conservative. In the may behave quite differently to an artificially future, research should therefore focus on mea- frozen soil that was recently frozen using freez- suring the stresses between the particles and ing pipes with a coolant temperature of -30ºC. within the unfrozen water. In addition, it is These frozen soils again might behave different- important to understand the difference in the ly to a soil that froze through the cold winter frozen soil structure with changing boundary months. Even though all those soils have the conditions, such as cooling rates and pressure same unfrozen characteristics, the different versus time. This review has demonstrated that freezing processes potentially affect their frozen a large number of publications have presented soil behaviour. the properties of frozen soils, each of which was When estimating the strength and defor- determined during a different laboratory inves- mation behaviour of a frozen soil, three main tigation. However, this situation is evidence of characteristics have to be considered: i) ice con- the variety of different sample responses rather tent, ii) unfrozen water content, and iii) frost sus- than a clear evaluation of the actual behaviour ceptibility. Frozen soil samples that are super- of frozen soils. Changing boundary conditions saturated with ice, i.e. the ice content is larger make it difficult to use this published data to cre- than the pore space volume, show significant ate unified models and to identify factors that creep deformation and the strength is mainly control the strength and deformation behaviour controlled by the characteristics of the ice and its of frozen soils. Research efforts are therefore interaction with the soil particles. A distinct required to revisit available testing standards for increase in strength is noted for volumetric ice frozen soils with regard to sample preparation, contents lower than about 40%, where particle strain rates, stress levels, temperature varia- interactions and dilation effects create more tions, etc. Work to this end should be coordinat- decisive mechanisms in contrast with ice rich ed with the organisations representing artificial samples. The strength characteristic of the freezing organisations and seasonal freezing embedded particles is of secondary importance associated predominantly with ground infra- compared to these interactions. structure evaluation. Frozen soil samples with low volumetric ice contents show an increase in strength compared 8 SUMMARY AND CONCLUSIONS to the unfrozen state due to the cementing effect The mechanical behaviour of a frozen soil is of the ice matrix. In addition, rubblisation effects dynamic and complex. When formulating a rela- can occur that enlarge the failure zone. Stiffness, tionship for the strength and deformation, it is peak strength and creep deformations depend essential to understand the characteristics of the on a number of factors and have to be deter-

Applied Rheology Volume 17 · Issue 1 12147-10 mined for a particular situation by carrying out REFERENCES laboratory tests under the corresponding bound- [1] Bingham EC: The History of the Society of Rhe- ary conditions and sample characteristics. How- ology from 1924 - 1944 (1944). ever, lower limits can be postulated for the long [2] Scott Blair GW: Survey of general and applied term and large strain strength behaviour, which rheology. Sir Isaac Pitman & Sons, London (1949). is the unfrozen behaviour of a particular soil, [3] Reiner M: The Deborah Number. Physics Today where the cementing effect due to the ice no 17 (1964) 62-62. [4] Doraiswamy D: The origins of rheology: A short longer is an influence. historical excursion. Rheological Bulletin 71 Unfrozen water weakens a partially frozen (2002) 1-9. soil resulting in a strength decrease and larger [5] French H: The development of periglacial geo- deformations, because the presence of water morphology: 1-up to 1965. Permafrost and reduces the cementation and changes how the Periglacial Processes 14 (2003) 29-60. ice structure forms. However, if drainage is slow, [6] Yershov ED: General geocryology. Cambridge suction can develop, temporarily increasing University Press, Cambridge (1998). [7] von Baer KE: The ground ice or frozen soil of effective stresses and hence strengthen the par- Siberia. Journal of the Royal Geographical Soci- tially frozen soil. Migration of free water during ety London 8 (1838) 210-213. freezing may further change the mechanical [8] Sumgin MI: Permafrost of Soil in the limit of properties of a soil with time. Frost susceptible USSR. Moscow (1927). soils tend to have a substantial amount of [9] Hoffmann D: Acht Jahrzehnte Gefrierverfahren unfrozen water at temperatures below zero nach Pötsch – Ein Beitrag zur Geschichte des Schachtabteufens in schwierigen Fällen. Verlag centigrade and therefore the frost susceptibility Glückauf, Essen (1962). of a soil has to be understood in addition to the [10] Pötsch FH: Das Gefrierverfahren - Methode für volumetric ice content and unfrozen water char- Abteufen von Schächten im wasserreichen Ge- acteristics. Coarse grained soils that are non frost birge. Craz & Gerlach, Freiberg i.S. (1885). susceptible do not change their inter-particle [11] Harris JS: Ground freezing in practice. Thomas structure when frozen. Frost susceptible soils, Telford; Distributed by American Society of Civil e.g. clays and silts, on the other hand, change this Engineers, New York (1995). [12] Huder J, Herzog P and Ramholt T: Gefrierver- structure during the freezing process and the ice fahren, Institut für Grundbau und Bodenmecha- lenses formed as the soil freezes can control the nik der ETH Zurich (1979). overall mechanical behaviour. Consolidation of [13] Volger GHO: Über die Volumenänderungen, the partially frozen frost susceptible soil due to welche durch Krystallisation hervorgerufen wer- the suction can, however, have a beneficial effect den. Annalen der Physik und Chemie, Vierte on the measured strength. It is therefore recom- Reihe Band XCIII (1854) 232-237. [14] Taber S: Frost heaving. Journal of Geology 37 mended to determine the strength of frost sus- (1929) 428-461. ceptible soils carefully by first understanding [15] Taber S: The mechanics of frost heaving. Journal their freezing history in detail. of Geology 38 (1930) 303-317. [16] Beskow G: Soil freezing and frost heaving with ACKNOWLEDGMENTS special applications to roads and railroads. Swedish Geological Society, C, No. 375, Year Book The authors would like to thank the editors of No. 3 (translated by J.O. Osterberg) in Historical Applied Rheology for their invitation to publish Perspectives in Frost Heave Research, USA Cold this manuscript, which is based on some publi- Region Research and Engineering Laboratory, cations that were presented in 2003 at the 8th Special Report 91-23 (1935) 41-157. [17] Black PB and Hardenberg MJ: Historical perspec- International Conference on Permafrost in tives in frost heave research, U.S. Army Corps of Zurich. We also thank Dr. Kevin Biggar for his Engineers. Cold Regions Research and Engineer- valuable comments on an earlier version of the ing Laboratory (1991). manuscript. The first author appreciated the [18] Haeberli W, Wegmann M and Vonder Mühll DS: financial support from the Swiss National Sci- Slope stability problems related to glacier ence Foundation (grant No PA002-108947) and shrinkage and permafrost degradation in the Alps. Eclogae Geologicae Helvetiae 90 (1997) the Izaak Walton Killam Memorial Postdoctoral 407-414. Fellowships. [19] Haeberli W and Beniston M: Climate change and its impacts on glaciers and permafrost in the Alps. Ambio 27 (1998) 258-265.

Applied Rheology 12147-11 Volume 17 · Issue 1 [20] Gruber S, Hoelzle M and Haeberli W: Permafrost [34] Murayama S and Shibata T: Rheological proper- thaw and destabilization of Alpine rock walls in ties of clays. in 5th International Congress on Soil the hot summer of 2003. Geophysical Research Mechanics and Foundation Engineering, Paris, Letters 31 (2004) Art. No. L13504 12004. France (1961) 269-273. [21] Harris C, Davies MCR and Etzelmüller B: The [35] Andersland OB and Douglas AG: Soil deforma- assessment of potential geotechnical hazards tion rates and activation energies. Géotech- associated with mountain permafrost in a nique 20 (1970) 1-16. warming global climate. Permafrost and [36] Mitchell JK: Shearing Resistance of Soils as a Rate Periglacial Processes 12 (2001) 145-156. Process. Journal of the Soil Mechanics and Foun- [22] Instanes A: Climate change and possible impact dation Division 90 (1964) 29-62. on Arctic infrastructure. in Eighth International [37] Sayles FH: State of the art: Mechanical proper- Conference on Permafrost, M Phillips, SM ties of frozen soil. in 5th International Sympo- Springman and LU Arenson, A.A. Balkema, sium on Ground Freezing 88, RH Jones and JT Zurich, Switzerland (2003) 461-466. Holden, Balkema, Rotterdam, (1988) 143-165. [23] Nelson FE, Anisimov OA and Shiklomanov NI: Cli- [38] Ladanyi B: Creep behavior of frozen and mate change and hazard zonation in the circum- unfrozen soils - A comparison. in 10th Interna- arctic permafrost region. Natural Hazards 26 tional Conference on Cold Regions Engineering (2002) 203-225. - Putting Research into Practice, JE Zufelt, Amer- [24] Anisimov OA, Shiklomanov NI and Nelson FE: ican Society of Civil Engineers (ASCE) Lincoln, N. Global warming and active-layer thickness; H. , USA (1999) 173-186. results from transient general circulation mod- [39] Akai K, Adachi T and Ando N: Existence of a els. Global and Planetary Change 15 (1997) 61-77. unique stress-strain-time relation in clays. Soils and Foundations 15 (1975) 1-16. [25] Williams PJ: Permafrost and Climate Change: [40] Prevost J-H: Undrained stress-strain-time Geotechnical Implications. Philosophical Trans- behaviour of clays. Journal of the Geotechnical actions: Physical Sciences and Engineering 352 Engineering Division - ASCE 102 (1976) 1245-1259. (1995) 347-358. [41] Sheahan TC: Interpretation of Undrained Creep [26] Forbes DL: Climate-change impacts in the Tests in Terms of Effective Stresses. Canadian coastal zone: Implications for engineering prac- Geotechnical Journal 32 (1995) 373-379. tice. in Géo Québec 2004: 57th Canadian Geot- [42] Muller SW: Permafrost or permanently frozen echnical Conference, D Demers, D Leahy et al., ground and related engineering problems. J.W. Québec City, QC, Canada (2004) 7A, 10 - 17. Edwards, Ann Arbor, MI. (1947). [27] Nelson FE: (Un)frozen in time. Science 299 (2003) [43] van Everdingen RO: Multi-language glossary of 1673-1675. permafrost and related ground-ice terms, [28] Lunardini VJ: Climatic warming and permafrost. National Snow and Ice Data Center/World Data in NATO advanced research workshop on Per- Center for Glaciology, Boulder, CO (1998 revised mafrost response on economic development, May 2005) environmental security and natural resources, R [44] Linell KA and Kaplar CW: Description and classi- Paepe, VP Melnikov et al., Kluwer Academic Pub- fication of frozen soils, Corps of Engineers, U.S. lishers. Dordrecht, Netherlands, Novosibirsk, Army, Cold Regions Research and Engineering Russian Federation (2001) 341-366. Laboratory (1966). [29] Cua EC and Shaw MT: Creeping Sphere-plane [45] Johnston GH: Permafrost : engineering design squeeze flow to determine the zero-shear-rate and construction. Wiley, New York (1981). viscosity of HDPE melts. Applied Rheology 14 [46] Sayles FH et al.: Classification and laboratory (2004) 33-39. testing of artificially frozen ground. Journal of [30] Anderson DM and Morgenstern NR: Physics, Cold Regions Engineering 1 (1987) 22-48. chemistry, and mechanics of frozen ground : A [47] Weaver JS: Thesis. University of Alberta (1979). review. in Second International Conference on [48] Penner E: The mechanism of frost heaving in Permafrost, National Academy of Science, soils, U.S. Highway Research Board (1959). Washington D.C., Yakutsk, USSR (1973) 257-288. [49] Xia D et al.: Freezing process in Devon silt - using [31] Ladanyi B: Mechanical behaviour of frozen soils. time-lapse photography. in 58th Canadian Geot- in Mechanics of Structured Media, Internation- echnical Conference, Saskatoon, Saskatchewan al Symposium on the Mechanical Behaviour of (2005) CD-ROM. Structured Media, APS Selvadurai, Elsevier, [50] Penner E: Influence of freezing rate on frost Ottawa, Canada (1981) 205-245. heaving, U.S. Highway Research Board (1972). [32] Ladanyi B: Stress Transfer Mechanism in Frozen [51] Kaplar CW: Phenomenon and mechanism of frost Soils. in Proceedings of the tenth Canadian Con- heaving, U.S. Highway Research Board (1970). gress of Applied Mechanics, (1985) 11-23. [52] Horiguchi K: Effects of the rate of heat removal [33] Ladanyi B: An engineering theory of creep of on the rate of frost heaving. in International frozen soils. Canadian Geotechnical Journal 9 Symposium on Ground Freezing, Ruhr-Univer- (1972) 63-80. sität Bochum, Germany (1978) 25-30.

Applied Rheology Volume 17 · Issue 1 12147-12 [53] Hermansson A: Laboratory and field testing on LU Arenson, A.A. Balkema, Zurich, Switzerland rate of frost heave versus heat extraction. Cold (2003) 39-44. Regions Science and Technology 38 (2004) [70] Taylor DW: Fundamentals of soil mechanics. 137-151. Wiley, New York (1948). [54] Hermansson A and Guthrie WS: Frost heave and [71] Bolton MD: The strength and dilatancy of sands. water uptake rates in silty soil subject to variable Géotechnique 36 (1986) 65-78. water table height during freezing. Cold Regions [72] Da Re G, Germaine JT and Ladd CC: Triaxial test- Science and Technology 43 (2005) 128-139. ing of frozen sand: Equipment and example [55] Guthrie WS and Hermansson A: Frost heave and results. Journal of Cold Regions Engineering, water uptake relations in variably saturated ASCE 17 (2003) 90-118. aggregate base materials. Geology and Proper- [73] Sayles FH: Triaxial constant strain rate tests and ties of Earth Materials (2003) 13-19. triaxial creep tests on frozen Ottawa sand, Unit- [56] Konrad JM and Morgenstern NR: A mechanistic ed States Army Corps of Engineers CRREL (1974). theory of ice lens formation in fine-grained soils. [74] Mellor M and Cole DM: Deformation and failure Canadian Geotechnical Journal 17 (1980) of ice under constant stress or constant strain- 473-486. rate. Cold Regions Science and Technology 5 [57] Konrad JM and Morgenstern NR: The segrega- (1982) 201-219. tion potential of a freezing soil. Canadian Geot- [75] Jones SJ and Parameswaran VR: Deformation echnical Journal 18 (1981) 482-491. behaviour of frozen sand-ice materials under tri- [58] Miller RD: Freezing and heaving of saturated and axial compression. in Fourth International Con- unsaturated soils, U.S. Highway Research Board ference on Permafrost, Fairbanks, Alaska (1983) (1972). 560-565. [59] Konrad JM: Frost susceptibility related to soil [76] Andersen GR et al.: Small-strain behavior of index properties. Canadian Geotechnical Journal frozen sand in triaxial compression. Canadian 36 (1999) 403-417. Geotechnical Journal 32 (1995) 428-451. [60] Konrad JM: Estimation of the segregation poten- [77] Hooke RL, Dahlin BB and Kauper MT: Creep of ice tial of fine-grained soils using the frost heave containing dispersed fine sand. Journal of response of two reference soils. Canadian Geot- Glaciology 11 (1972) 327-336. echnical Journal 42 (2005) 38-50. [78] Ting JM, Martin RT and Ladd CC: Mechanisms of [61] Konrad JM and Morgenstern NR: Effects of strength for frozen sand. Journal of the Geot- applied pressure on freezing soils. Canadian echnical Engineering Division, ASCE 109 (1983) Geotechnical Journal 19 (1982) 494-505. 1286-1302. [62] Konrad JM: Segregation potential - pressure - [79] Arenson LU and Sego DC: Modelling the strength salinity relationships near thermal steady-state of composite materials using discrete elements. for a clayey silt. Canadian Geotechnical Journal in 58th Canadian Geotechnical Conference, 27 (1990) 203-215. Saskatoon, Saskatchewan (2005) CD-ROM. [63] Vyalov SS: Rheological properties and bearing [80] Gagnon RE and Gammon PH: Triaxial experi- capacity of frozen ground. CRREL Translation ments on iceberg and glacier ice. Journal of (1965). Glaciology 41 (1995) 528-540. [64] Zupancic A: Influence of additives on the rheo- [81] Jones SJ: The confined compressive strength of

logical properties of TiO2 suspensions. Applied polycrystalline ice. Journal of Glaciology 28 Rheology 7 (1997) 219-226. (1982) 171-177. [65] Vyalov SS: Rheology of frozen soil. in Proceedings [82] Hivon EG and Sego DC: Strength of frozen soils. of the International Conference on Permafrost, Canadian Geotechnical Journal 32 (1995) 336-354. National Academy of Sciences: National [83] Sego DC, Schultz T and Banasch R: Strength and Research Council, Publication 1287, Lafayette, deformation behaviour of frozen saline sand. in Indiana, USA (1963) 332-339. Third International Symposium on Ground [66] Gold LW: Process of failure in ice. Canadian Geot- Freezing, U.S. Army Corps of Engineers, Hanover, echnical Journal 7 (1970) 405-413. New Hampshire, USA (1982) 11-17. [67] Arenson LU and Springman SM: Triaxial con- [84] Nixon JF and Lem G: Creep and strength of frozen stant stress and constant strain rate tests on ice- saline fine-grained soils. Canadian Geotechnical rich permafrost samples. Canadian Geotechni- Journal 21 (1984) 518-529. cal Journal 42 (2005) 412-430. [85] Arenson LU and Sego DC: The effect of salinity [68] Arenson LU, Johansen MM and Springman SM: on the freezing of coarse grained sands. Canadi- Effects of volumetric ice content and strain rate an Geotechnical Journal 43 (2006) 325-337. on shear strength under triaxial conditions for [86] Zhao SP, Zhu YL and He P: Recent progress in frozen soil samples. Permafrost and Periglacial research on the dynamic response of frozen soil. Processes 15 (2004) 261-271. in Eighth International Conference on Per- [69] Arenson LU, Almasi N and Springman SM: Shear- mafrost, M Phillips, SM Springman and LU Aren- ing response of ice-rich rock glacier material. in son, A.A. Balkema, Zurich, Switzerland (2003) Eight International Conference on Permafrost, 1301-1306.

Applied Rheology 12147-13 Volume 17 · Issue 1 [87] Yasufuku N et al.: Stress-dilatancy behaviour of edge and priorities for research - report prepared frozen sand in direct shear. in Eighth Interna- for the International-Commission-on-Snow- tional Conference on Permafrost, M Phillips, SM and-Ice, with support from the United-States- Springman and LU Arenson, A.A. Balkema, National-Science-Foundation. Cold Regions Sci- Zurich, Switzerland (2003) 1253-1258. ence and Technology 3 (1980) 263-275. [88] Take WA and Bolton MD: The use of centrifuge [103] Sinha NK: Constant strain-rate and stress-rate modelling to investigate progressive failure of compressive strength of columnar-grained ice. overconsolidated clay embankments. in Consti- Journal of Materials Science 17 (1982) 785-802. tutive and Centrifuge Modelling: Two Extremes, [104] Cole DM: Strain-rate and grain-size effects in ice. SM Springman, Lisse, A.A. Balkema, (2002) 191- Journal of Glaciology 33 (1987) 274-280. 197. [105] Voytkovskiy KF: Mekjanicheskiye svoystva lda [89] Anderson DM and Tice AR: Predicting unfrozen (The mechanical properties of ice), Izvestiya water content in frozen soils from surface area Akademii Nauk (1960). measurements, Highway Research Record [106] Sego DC and Morgenstern NR: Deformation of (1972). ice under low stresses. Canadian Geotechnical [90] Williams PJ: Unfrozen water content of frozen soils and soil moisture suction. Publications of Journal 20 (1983) 587-602. the Norwegian Geotechnical Institute 72 (1967) [107] Singh A and Mitchell JK: Creep potential and 11-26. creep rupture of soil. in Seventh International [91] Williams PJ: Suction and its effects in unfrozen Conference on Soil Mechanics and Foundation water of frozen soils. Publications of the Norwe- Engineering, (1969) 379-384. gian Geotechnical Institute 72 (1967) 27-35. [108] Vaid YP and Campanella RG: Time-dependent [92] Williams PJ: Unfrozen water in frozen soils. Pub- behavior of undisturbed clay. Journal of the lications of the Norwegian Geotechnical Insti- Geotechnical Engineering Division, ASCE 103 tute 72 (1967) 37-48. (1977) 693-709. [93] Fish AM and Zaretsky YK: Temperature effect on [109] Ladanyi B and Johnston GH: Evaluation of in situ strength of ice under triaxial compression. in creep properties of frozen soils with the pres- Seventh International Offshore and Polar Engi- suremeter. Proceedings of the second Interna- neering Conference, International Society of tional Conference on Permafrost (1973) 310-318. Offshore and Polar Engineers, Honolulu, Hawaii, [110] Ladanyi B and Johnston GH: Behavior of Circular USA (1997) 415-422. Footings and Plate Anchors Embedded in Per- [94] Fish AM and Zaretsky YK: Ice Strength as a Func- mafrost. Canadian Geotechnical Journal 11 (1974) tion of Hydrostatic Pressure and Temperature. 531. CRREL Report (1997). [111] Johnston GH and Ladanyi B: Field Tests of Grout- [95] Andersland OB and AlNouri I: Time-dependent ed Rod Anchors in Permafrost. Canadian Geot- strength behavior of frozen soils. Journal of the echnical Journal 9 (1972) 176-194. Soil Mechanics and Foundation Division, ASCE [112] Watanabe K and Mizoguchi M: Amount of 96 (1970) 1249-1265. unfrozen water in frozen porous media saturat- [96] Arenson LU and Springman SM: Mathematical ed with solution. Cold Regions Science and Tech- description for the behaviour of ice-rich frozen nology 34 (2002) 103-110. soils at temperatures close to zero centigrade. [113] Arenson LU and Sego DC: The effect of salinity Canadian Geotechnical Journal 42 (2005) 431- on the freezing of coarse grained sands. Canadi- 442. [97] Goughnour RR and Andersland OB: Mechanical an Geotechnical Journal 43 (2006) 325-337. properties of a sand-ice system. Journal of the [114] Stähli M and Stadler D: Measurement of water Soil Mechanics and Foundations Division, ASCE and solute dynamics in freezing soil columns 94 (1968) 923-950. with time domain reflectometry. Journal of [98] Sayles FH: Creep of frozen sands, United States Hydrology 195 (1997) 352-369. Army Corps of Engineers CRREL (1968). [115] Panday S and Corapcioglu MY: Solute rejection [99] Nickling G and Bennett L: The shear strength in freezing soils. Water Resources Research 27 characteristics of frozen coarse granular debris. (1991) 99-108. Journal of Glaciology 30 (1984) 348-357. [116] Konrad JM and McCammon AW: Solute parti- [100] Weaver JS and Morgenstern NR: Simple shear tioning in freezing soils. Canadian Geotechnical creep tests on frozen soils. Canadian Geotechni- Journal 27 (1990) 726-736. cal Journal 18 (1981) 217-229. [117] Arenson LU et al.: Brine and unfrozen water [101] Glen JW: The creep of polycrystalline ice. Pro- migration during the freezing of Devon silt. in ceedings of the Royal Society of London. Series ARCSACC, K Biggar, G Cotta et al., Edmonton, AB, A, Mathematical and Physical Sciences 228 (1955) Canada (2005) 35-44. 519-538. [102] Hooke RL et al.: Mechanical-properties of polycrystalline ice - an assessment of current knowl-

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