1 Introduction

Frozen soil is commonly regarded as a solid material, because of cementation of soil particles by ice at subfreezing temperatures. When frozen soil is subjected to additional load, it responds with both instantaneous and time-dependent deformation [2, 18, 19, 32,33,34]. Distortional creep is considered to be the main source of time-dependent deformation, whereas consolidation is usually thought to be of secondary importance or not to take place [2, 3, 27]. In reality, a considerable amount of liquid water remains within frozen soil in bound form, especially at subzero temperatures close to the freezing point. This bound water can transfer positive as well as negative stress and has a significant influence on the strength and deformation behavior of frozen soils [5, 13, 15]. Several investigations have shown that the coefficient of permeability for water in frozen soils is not zero, and therefore Darcy’s law applies in these cases [7, 17, 28, 29, 31, 37]. Hence, for frozen soils at temperatures near the thawing point, consolidation related to pore-water pressure (PWP) dissipation may be substantial and should be taken into account in strength determination and deformation studies [6, 20, 23, 35]. Vyalov [24] noted, however, that the volume change exhibited by plastic frozen soils should not be considered as consolidation, but rather as volumetric creep because a very limited amount of unfrozen water is released in an extremely slow way. Confirming the exact mechanism that controls the deformation of warm frozen soils under applied load is of practical significance for researchers and geotechnical engineers. The objective is to obtain a deep understanding of the mechanical behavior of warm frozen soils and to perform accurate calculations of soil strength and deformation. The most direct and effective method to clarify this deformation mechanism is to measure the pore-water pressure.

Measuring PWP in freezing, thawing, and partially frozen soils has been of major concern to investigators [1, 4, 9,10,11, 14, 16, 21, 25, 30, 36]. However, in previous work, laboratory PWP measurements have mostly been focused on freezing or thawing soils where pressure variation is induced by the temperature gradient and pore-volume change is caused by alteration in ice-water phases. The mechanisms that underlie these changes are considerably different from those experienced by frozen soils subjected to external load. In addition, the amount of work carried out on the PWP of frozen soils has been limited because of the difficulties in measurement. Arenson and Springman [4] investigated PWP responses to strain rate in natural permafrost samples obtained from constant strain rate triaxial tests and analyzed the influence of these pressure changes on the mechanical behavior of samples. Hazirbaba et al. [12] measured negative, or minimal, excess PWPs at − 0.2 °C through strain-controlled, cyclic, triaxial tests. Subsequently, Kia [14] developed a new instrument to provide an accurate PWP measurement of partially frozen soils and measured variations under various loads and temperature conditions. Wang [25] discussed the effect of pore pressure on the shear strength of frozen soils using data from constant strain rate triaxial tests. These studies were significant because they emphasized the effect of pore pressure on frozen soil strength, but they could not provide any references to describe the long-term deformation mechanism of frozen soils under load. To remedy this, Zhang et al. [38] attempted to investigate PWP within warm frozen soil specimens in an undrained condition at various temperatures given a constant load, thus taking the first step toward understanding the load-induced deformation mechanism experienced in warm frozen soils. However, this work was inadequate to provide a clear picture of PWP behavior variations in frozen soils due to loading and could not provide a sufficient basis for discussing the role of PWP variation in deformation.

This paper reports on a series of long-term confined compression experiments aimed at measuring both PWP and displacement. Variation behaviors of PWP versus time are analyzed, and the mechanism that underlie the deformation of frozen soils are discussed.

2 Test apparatus and procedures

A series of load-controlled confined compression tests were carried out on warm saturated frozen soils to investigate PWP variation under constant load. Confined compression tests were used in this study because in these cases, stress within soil is uniform, and therefore specimen deformation will be entirely due to volumetric change. These attributes mean that clearer estimates of the role of PWP variation and induced displacement in the deformation mechanism of warm frozen soils can be obtained.

2.1 Test apparatus

To measure the PWP of a frozen soil, pressure transmission to a transducer is necessary. Hence, pressure measuring systems, such as transducers, tubes, porous plates, or tips, must be fully saturated with antifreeze, or measurement accuracy will be severely affected [14]. In practical applications, however, it is often difficult to reach absolute system saturation. Therefore, to minimize pressure measuring system error, a miniature pore-pressure transducer was used that could be inserted directly into frozen soils.

The miniature pore-pressure transducer used in this research consisted of a 6-mm diameter and 12-mm long stainless-steel cylinder with a ceramic filter tip (Fig. 1). The tip of this apparatus had a minimal volume of 0.019 cm3 and was filled with deaerated alcohol in a vacuum desiccator before installation. The transducer was then inserted about 10 mm into the soil specimen from the bottom of the sample. Alcohol was used as the pressure transmission liquid because it can eliminate the ice film that tends to form at the filter tip–soil sample interface [38]. Although alcohol has a drawback in that it thaws the frozen soil around the tip, this effect is extremely limited. The PWP within frozen soil is transferred through the liquid to an electrical sensing element behind the porous ceramic tip. The transducer used here was an HC-25 miniature pore-pressure sensor produced by Beijing Ruiheng Changtai Technology Co., Ltd.; this instrument has a measurement range between − 100 and + 200 kPa, an accuracy of 200 Pa, and a thermal sensitivity of ± 0.02% per °C.

Fig. 1
figure 1

Test system and miniature pore-pressure transducer

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Load-controlled compression tests were performed in a specially designed laterally confined cell (Fig. 1). This compression cell was similar to a common consolidometer, but was modified to include a plexiglass cylinder with a wall thickness of 10 mm, an inside diameter of 62 mm, and a stainless-steel base. This cylinder was screwed onto the base, and an O-ring was installed at the bottom of the cylinder wall to prevent leakage. A porous stone and a piece of filter paper were placed onto each soil specimen to enable unfrozen water to drain from the top surface during compression.

This cell was then placed into a loading frame inside a temperature-controlled insulation box modified from an ordinary refrigerator at the State Key Laboratory of Frozen Soil Engineering. This apparatus can control temperature accurately to within approximately ± 0.05 °C. Four thermistors were mounted inside the apparatus to monitor temperature variations during the experiment. The apparatus was placed in a constant-temperature room to minimize the influence of environmental temperature variations on the soil specimens, and displacement was measured with a high-precision displacement transducer.

2.2 Soil specimen preparation

Two types of soils, Qingzang silty clay and Lanzhou loess, were used in this experiment and were obtained from the Beilu River Basin on the Qinghai–Tibetan Plateau and from a site near Lanzhou City in Gansu Province respectively. Figure 2 and Table 1 show the physical parameters and grain size distributions of these soils. Soil specimens were prepared from a slurry made up of dry soil and deionized water at given mass ratios (e.g., 1:0.3, 1:0.4, and 1:0.5). This slurry was placed in a closed container for 24 h to soak the soil particles fully with water before the slurry was injected into the test cell with the miniature pore-pressure transducer already attached to minimize sample disturbance. The inside cell wall was greased with Vaseline® to eliminate friction between the soil specimen and the cylinder wall. The cell was then placed in a vacuum desiccator, causing air bubbles to be expelled from the slurry and ensuring soil sample saturation. All specimens were prepared before freezing with a diameter of 62 mm and a height of 50 mm.

Fig. 2
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Soil grain size distributions

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Table 1 Physical parameters of the soils used in this study
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2.3 Test procedures

After saturation, soil samples were placed in a freezer at − 20 °C for about 24 h to ensure that they were fully frozen. Once this state was achieved, 2.0 ml of 6% concentration saline water was poured onto the surface of each specimen before returning it to experimental target temperature (e.g., − 0.3 °C, − 0.5 °C, − 1.0 °C, and − 1.5 °C) for a further 24 h in the temperature-controlled box. This procedure was followed to thaw the specimen surfaces to ensure that unfrozen water could drain during the experiments. Finally, to evaluate the influence of drainage conditions on the evolution of excess PWP in frozen soils, a number of comparative tests were also performed under undrained conditions without the addition of saline water.

Once soil specimen reached a stable temperature, a constant 200 kPa load was applied using weights. The temperature in the insulation box was held constant during these tests, although it varied by ca. ± 0.03 °C around the target value (Fig. 3), in accordance with satisfactory experimental control procedures. Both PWP and displacement in specimen were recorded continuously using a data acquisition system (Table 2). The unfrozen water content of each specimen was also measured at various subfreezing temperatures using nuclear magnetic resonance (NMR).

Fig. 3
figure 3

Temperatures (T) recorded during the experiment

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Table 2 Overview of all PWP tests
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3 Results

3.1 PWP under different drainage conditions

Because of low liquid water content, aqueous migration within frozen soils under external load is invisible to the naked eye. Therefore, to verify that unfrozen water drainage is occurring due to loading, test results for drained and undrained conditions were compared. A layer of ice film formed during the freezing process on the top surfaces of the specimens and indicated the undrained boundary; the drained boundary was created by thawing the surface with saline water, enabling liquid water to discharge from the soil.

Figure 4 shows both PWP and deformation variation under different drainage conditions. Results show that either drained or undrained frozen loess showed a steep increase in PWP up to a similar peak value (mean ca. 130 kPa) at the beginning of the tests (Fig. 4a), before the pressure dissipated. Pressure dissipation occurred at a higher rate under drained conditions (mean ca. 28.6 kPa/day) than under undrained conditions (mean ca. 11.7 kPa/day). A great difference in PWP variation was seen in frozen silty clay under different drainage conditions (Fig. 4b); a peak value (mean ca. 87.5 kPa) was reached in 20.8 days when the soil was drained, but did not occur at all when the soil was undrained. These phenomena implied that the undrained condition created an environment for continuous increase in PWP until a steady-state was reached.

Fig. 4
figure 4

Results of PWP and deformation variation under different drainage conditions: a frozen loess; and b frozen silty clay (W0: total moisture content)

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When drained, specimens for either frozen loess or silty clay experienced larger compressive deformations and higher deformation rates than their undrained counterparts. Indeed, even though the specimen surface is not a strictly impermeable boundary in undrained cases, especially for frozen loess, the influence of drainage conditions on PWP and deformation is clearly shown. It could therefore be concluded that drainage of unfrozen water by loading does occur in warm frozen soils and likely exerts a significant impact on their deformation behavior.

3.2 PWP variation with soil temperature

The results obtained here show that the mechanical behavior of frozen soils is closely associated with soil temperature. This can be seen from the curves presented in Fig. 5, which presents a plot of test results at various temperatures for both soil types versus time. These tests were all performed under drained condition, hence similar relationships between PWP and temperature are seen for frozen loess and silty clay soils (Fig. 5a, b). Given a very high subfreezing temperature, a frozen specimen yields a rather high PWP. For example, a peak value of 134.8 kPa was generated by test LL-2 at − 0.3 °C, while a value of 136.9 kPa was generated by sample QC-1 at − 0.1 °C. As soil temperature decreased, lower PWP peaks were obtained, and more time was required to reach peak points. For example, in the case of frozen loess, 0.035 days were needed to reach peak PWP (134.8 kPa) at − 0.3 °C, but 11.7 days were needed to achieve a peak value (84.1 kPa) at − 1.5 °C. The time periods before peak points also greatly lengthened in frozen silty clay, although a peak was not seen at − 1.0 °C during the test period (sample QC-8). Furthermore, a decrease in soil temperature resulted in a dramatic reduction in post-peak dissipation rate.

Fig. 5
figure 5

Variation in PWP at various temperatures versus time: a frozen loess; and b frozen silty clay

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In all cases, specimens under constant load underwent steady deformation following instantaneous and primary deformations. The results of these tests show that, similar to ordinary confined compressive experiments, deformation rates increased with rising temperature.

3.3 PWP variation with moisture content

Figure 6 shows variations in PWP and deformation of samples with different moisture content. These tests were all carried out at − 0.3 °C on frozen silty clay. Results show that when the samples were subjected to the same load, similar PWP variation trends were seen for all specimens at different moisture contents. A slow increase in PWP occurred in the early stage of the tests until a peak value was achieved, followed by slow dissipation. As moisture content increased, however, the peaks were reduced in height, and the time spent to reach them increased. For the specimen with 50% moisture content by mass (sample QC-3), an abrupt drop in PWP was monitored following gradual development for 17 days, a phenomenon that might have been due to air bubbles that were not expelled from the slurry during specimen preparation.

Fig. 6
figure 6

Variations in PWP with various ice contents versus time

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In these cases, deformations at fairly constant rates were observed with time. Results show that the strain of the specimen with 30% moisture content was 0.19, which was similar to the specimen that had 40% content (0.16), but much larger than the specimen with 50% content (0.07).

3.4 PWP variation with soil type

Figure 7 shows the evolution of PWP in specimens for both soil types. These results show a large difference in PWP variation between frozen loess and silty clay. The PWP of frozen silty clay developed following a trend lagging behind that of frozen loess. After a load was applied, the PWP of frozen loess (sample LL-2) immediately reached its maximum value (134.8 kPa) before dissipating to the minimum (21 kPa) after 4 days. For frozen silty clay (sample QC-2), a much lower peak (97.9 kPa) was recorded after 7.78 days, which dissipated to 72.5 kPa after 26.7 days. Similar to the correlations between PWP and deformation at various temperatures or moisture contents, a faster development of pressure corresponded to a higher strain rate for different soil types.

Fig. 7
figure 7

Variations in PWP with different soil types

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4 Discussion

4.1 PWP test repeatability

A number of parallel tests were performed under same conditions to verify the repeatability of the PWP experiments. Figure 8 shows typical results from parallel tests on sample QC-7 under undrained conditions. The results show highly consistent variations in PWP and deformation. PWPs in both tests constantly increased while their rate decreased, such that the largest gap between them was approximately 15 kPa by the end of the test period. The results also reveal small difference in strain between the tests, although the strain rates during the steady deformation stage were almost the same in both cases, i.e., 0.00018 day−1 and 0.00019 day−1 respectively. These analyses present a satisfactory repeatability of the tests and the reliable measurement of the PWP.

Fig. 8
figure 8

Repeated tests for sample QC-7

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4.2 General characteristics of PWP and deformation

Results for drained loads show that the PWPs of various tests presented similar variation trends over time, including a slow increase in PWP up to a peak value followed by subsequent dissipation even over several months at an extremely low rate (Figs. 4, 5, 6, 7). Indeed, peak PWPs reached a considerable level, but remained much lower than the total stress, ranging between 43.8 kPa and 144 kPa for the samples investigated (Table 3). These results are distinct from those for thawed soils in which peak PWP was in close proximity to the additional load level. A further difference is that a considerable period of time was required for frozen soils to reach peak PWP, but little time was needed for thawed soils [8]. Hence, along with the PWP response, trends in volumetric compression of frozen soil samples did not level off at the end of the test, indicating that the samples had not reached a residual state and that compaction of pore spaces inside them was ongoing.

Table 3 Summary of test results
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The results of this study show that the PWP and deformation characteristics of frozen soil are dependent on soil temperature, moisture content, and soil type.

4.2.1 Temperature effects on PWP and deformation

The influence of soil temperature on PWP and deformation is shown in Fig. 9. A decrease in peak PWP was generally observed in association with decreasing temperature, revealing a pronounced nonlinear response. A similar trend was also seen in mean PWP dissipation rate following the peak and in mean strain rate during steady deformation stage. These properties are illustrated, for example, in the results for frozen silty clay under drained conditions (Fig. 9). Results show that as soil temperature decreased, characteristic values, including peak PWP, mean pressure dissipation rate, and mean steady strain rate, all decreased steeply before leveling off at much lower values. For example, peak PWP at − 1.0 °C was about one-third of the value at − 0.1 °C, implying a negligible peak value generated at a much lower temperature. It can be argued that unfrozen water content showed a similarly nonlinear variation with decreasing temperature (Fig. 10), and thus the behaviors of PWP and strain rate might be dominated by the unfrozen water content. Furthermore, the mean PWP dissipation rate at − 0.5 °C was just 1/26 of the value at − 0.1 °C while a dissipation did not even take place at − 1.0 °C. This dramatic change occurred because the decrease in temperature from − 0.1 to − 1.0 °C depressed the hydraulic conductivity of frozen soil by nearly two orders of magnitude [17, 37].

Fig. 9
figure 9

Effect of temperature on PWP and deformation of frozen silty clay

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Fig. 10
figure 10

Variation in unfrozen water content versus temperature in various samples (this graph show the fraction of total water content by mass)

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4.2.2 Moisture content effects on PWP and deformation

The results presented here show that the second important factor influencing PWP and deformation of frozen sample is moisture content. The results of this investigation confirmed a declining trend for peak PWP as well as for mean steady strain rate as moisture content increased at a given temperature (Fig. 11). In contrast, mean dissipation rate increased with increasing moisture content. All the trends presented a linear shape in general. These relationships are largely dependent on unfrozen water content. Higher moisture content, e.g., in clay, leads to considerably enhanced ice content, but lower unfrozen water content at a given temperature (Fig. 10). Increased ice content enhances cementation between soil particles, resulting in greater frozen soil stiffness [15]. These soils can bear more stress and therefore produce a lower peak PWP. The increasing PWP dissipation rate demonstrates higher hydraulic conductivity with increasing total moisture content, which is consistent with the result presented by Burt [7]. Note, however, that the anomalous variation in PWP for sample QC-3 may to some degree make this relationship debatable (Fig. 6).

Fig. 11
figure 11

Effect of moisture content on PWP and deformation of frozen silty clay

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4.2.3 Effect of soil type on PWP and deformation

The investigation has shown that soil type also exerts an important influence on PWP variation in frozen soils. Results illustrate that given 30% moisture content and a temperature of − 0.3 °C, frozen loess exhibited a faster volumetric deformation and has a higher peak PWP and a faster dissipation rate than frozen silty clay (Fig. 7). This result also implies that frozen loess is relatively less stiff and has better connectivity among its coarser-grained particles, as previously noted by Burt [7] and Su [22]. These relationships, however, cannot be explained by the unfrozen water content alone because frozen loess has less unfrozen water content than frozen silty clay because of its lower fine-grained particle content (Fig. 2). Addressing this issue requires testing of a large number of frozen samples for unfrozen water content, particle properties, PWP, pore-water connectivity, and ice-lens characteristics.

4.3 PWP variation processes

The present investigations of PWP have made it possible to consider the physical nature of the processes underlying variation in this characteristic within frozen soils at temperatures close to the thawing point when samples are subjected to a constant load. Then, some general laws of soil compression can therefore be stated.

It is well known that for saturated thawed soils, all stress is taken by pore water at zero time after loading and none is absorbed by soil skeleton. The water in void spaces is subsequently squeezed out, causing a degradation in excess pressure provided that water drainage is permitted, which in turn increases effective stress by an equal amount [8].

However, unlike the case of thawed soils, additional stress applied to frozen soils is primarily absorbed by the solid matrix (i.e., soil particles and ice crystals) at the instant of loading because the discrete particles are cemented into a combination by ice. The pore volume in frozen soil is pressurized by ongoing compression of the sample, resulting in a subsequent increase in measured PWP, which can be deduced from the curves in Figs. 4, 5, 6, 7. Simultaneously, the permeability of frozen soil allows PWP to dissipate gradually [7, 37] when unfrozen water drainage is permitted (i.e., unfrozen water migrates from the bottom to the top surface of a sample). This means that PWP fluctuates constantly as a result of the coupled actions of solid matrix compaction and unfrozen water drainage (Fig. 12). Hence, in general, a PWP curve can be divided into three stages. In the first, a specimen is compressed at a high strain rate, and therefore unfrozen pore water will respond with a rapid increase in PWP, which also translates to an enhanced hydraulic gradient and an increasing unfrozen water dissipation rate. A climbing PWP curve is presented when the increase rate of the pressure is higher than the dissipation rate. As strain rate decreases and PWP increases, an equilibrium between the two processes will be reached, and the peak PWP will be attained. In the third stage, the strain rate decreases further, and the PWP dissipation rate becomes higher than the rate of increase, causing a further dissipation trend on the curve.

Fig. 12
figure 12

Schematic illustration of the mechanisms leading to PWP variation in frozen soils

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Figure 13 shows the relationships between unfrozen water content, peak PWP, and strain rate in the steady stage. In this case, the mobilized strain rate increases with unfrozen water content in an approximately linear manner, although there is a pronounced difference in this effect depending on soil type (frozen loess or silty clay). This dependence of strain rate on unfrozen water content occurs largely because of the cementation interaction between ice and soil particles. The data also show a roughly linear relationship between peak PWP and strain rate in the steady stage, which confirms the assumption about progressive variation in water pressure. Hence, given the premise that PWP dissipates extremely slowly, a higher strain rate will give a higher peak water pressure.

Fig. 13
figure 13

Strain rate versus unfrozen water content and peak PWP

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In cases where an undrained sample was tested under load, a continued increase in PWP up to a steady-state value was expected with no dissipation, as in sample QC-4. For these cases, nevertheless, the undrained condition were serving as a comparison for validating pore-water expulsion from frozen soil samples. This condition was not sufficiently achieved and still resulted in PWP dissipation for frozen samples, such as in sample LL-1.

4.4 Consolidation

Frozen soils subjected to loading undergo a volumetric change that may be caused by three main types of deformation: instantaneous deformation, consolidation, and creep [23]. The results of our tests prove the occurrence of consolidation for the reason that frozen samples under drained load exhibited a much greater volumetric change because of pore-water expulsion than those under undrained load and that both PWP increase and PWP dissipation were observed over time. The latter process took place under the constant load and temperature conditions and implied the migration of unfrozen water along the pressure gradient as well as the stress transfer between pore water and solid matrix.

By comparing volumetric strains for drained and undrained samples, it is therefore possible to conclude that consolidation played a significant role in the total deformation of frozen soils at temperatures close to the thawing point (Fig. 14). For example, for sample QC-5, the consolidation deformation was so pronounced that it almost reached 73% of total deformation. This proportion is much higher than the corresponding value obtained in earlier work by Sayles [20]. The effect of consolidation on total response declines with decreasing soil temperature. However, considering the continuous PWP variation recorded in this study over the whole test period, it is impossible to distinguish deformation due to consolidation from that due to creep, for they underwent simultaneously. In addition, the shape of the time-deformation curve is also affected by the amount of consolidation. An increasing amount of consolidation generally promotes the nonlinearity of time-dependent deformation curves (Fig. 5).

Fig. 14
figure 14

Volumetric strain versus drainage conditions

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4.5 Effect of the structure of ice crystals

Because of the high total moisture content of frozen soils, a distinctive ice-crystal structure tended to form within them, especially in the case of frozen fine-grained material (Fig. 15). Specifically, a massive cryostructure was seen in frozen loess because of its high heat conductivity [26], whereas a reticulated cryostructure tended to develop in frozen silty clay. This structural difference might also be important in causing difference in PWP between frozen loess and frozen silty clay. As part of sample preparation, soil–water mixtures were frozen at a temperature of − 20 °C, leading to three-dimensional freezing. However, the water in the specimens was not instantly frozen in its original position and hence likely migrated along the thermal gradient, leading to formation of ice-crystal structures. It is not clear whether, or how, the structure of these ice crystals affected the test results. This issue will be investigated in future work by testing samples with various ice-crystal structures prepared by different sampling methods.

Fig. 15
figure 15

Soil sample profiles after tests: a frozen loess with 30% moisture content; and b frozen silty clay with 40% moisture content

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5 Conclusions

In this study, PWP variations in warm saturated frozen soils were investigated under various conditions, and the behaviors in this variation as well as the relation to deformation were discussed. From these investigations, a number of conclusions can be drawn:

  1. 1.

    If a frozen soil is subjected to load, excess PWP is characterized by initial increase up to a maximum and subsequent dissipation. In cases where drainage is not allowed, PWP does not dissipate, but levels off at a steady-state value. Comparison of test results between drained and undrained samples confirms that unfrozen water is expelled from frozen soils. Results show that changes in temperature, moisture content, and soil type all exert strong influences on PWP characteristics, which might be attributable to the unfrozen water content of frozen soils.

  2. 2.

    PWP variation is a result of complex interactions between the solid matrix and pore unfrozen water in soils. Compression of the solid matrix causes a continuous increase in PWP, whereas soil permeability allows this pressure to dissipate. It can therefore be concluded that both consolidation and creep are general mechanisms that control deformation in frozen soils.

  3. 3.

    Existing problems with the PWP measurement might have influenced the accuracy of the results obtained. Although the transducer filter tip was saturated with deaerated alcohol, it was impossible to entirely prevent air from entering the transducer during its installation. In addition, alcohol inevitably thaws frozen soil around the transducer tip and hence influences frozen soil structure. The authors intend to resolve these issues in future work by improving the measuring device and developing a more suitable hydraulic liquid.

  4. 4.

    These results were obtained the tests under the conditions of constant temperature and constant load, but how the pore-water pressure varies when subjected to a changing temperature, a cyclic or high level load, is still unknown. It is also a point of interest for us.