Long-term creep of frozen soils in multi-year tests

Tao Dachzhi Postgraduate student; Faculty of Geology; Lomonosov Moscow State University 119234, Russia, Moscow, Ramenki district, ter. Leninskie Gory, 1 taoolga@yeah.net Alekseev Andrei Grigor'evich Doctor of Technical Science Head of the Center for Geocryological and Geotechnical Research of the N.M. Gersevanov National Research Institute of Natural Sciences 109428, Russia, Moscow, Ryazan district, 2nd Institutskaya str., 6, building 12 adr-alekseev@yandex.ru

Brushkov Anatolii Viktorovich Doctor of Geology and Mineralogy Head of the Department of Geocryology, Faculty of Geology, Lomonosov Moscow State University 119234, Russia, Moscow, Ramenki district, ter. Leninskie Gory, 1 geocryology@mail.ru

Introduction

Climate change and an increase in average annual temperatures in the cold regions of the world have led to significant changes in the structure and properties of permafrost. Climatic changes are accompanied by the degradation of frozen soils, which endangers the stability of engineering structures such as highways and buildings located in permafrost areas ^{[1, 2, 3]}. One of the main problems is the creep of frozen soils — the process of prolonged deformation under constant load, which affects the stability of the foundations of buildings and structures ^{[4, 5]}.

The creep of frozen soils is caused by a number of factors: the type of soil, the ice content, humidity, temperature, and the magnitude of the load ^[6]. The presence of microcracks and ice slips in the structure of frozen soils, as well as the dependence of creep on temperature, make these materials a difficult object to predict ^[7]. Experimental data show that frozen soils exhibit attenuating creep, which consists of an initial unstable and stable stages, and non-attenuating creep, where a third stage appears - currents with progressive velocity ^{[8, 9, 10]}.

The study of long-term deformation processes in frozen soils is one of the key tasks of modern engineering geocryology. At one time, N.A.Tsytovich summarized the long-term research results, emphasizing the importance of long-term experiments for assessing soil behavior in permafrost conditions ^[11]. Important results were presented in ^[10], where long-term experiments were conducted that revealed nonlinear dependences of creep of frozen soils on temperature and cryogenic structure. These data are of key importance for predicting the stability of the foundations of structures in permafrost conditions.

One of the most important problems is the duration of the tests, since the expected attenuation of deformations during compression or uniaxial (triaxial) compression, characteristic of unfrozen soils, has not yet been experimentally substantiated for frozen soils. There is a possibility that with prolonged creep, deformation rates may change, including their increase, which is of fundamental importance for predicting the stability of foundations on frozen soils. Unfortunately, the maximum duration of experiments on the creep of frozen soils in various types of tests is no more than the first months ^[12], mainly due to the difficulties of maintaining a constant temperature. Therefore, the rare tests that were carried out were carried out mainly in Russia, in the underground laboratories of Igarka and Amderma ^{[13, 14]}. A field-scale experiment with a field press was also conducted relatively recently in Tibet ^[15]. In this experiment with step loads of 0.09 MPa, 0.19 MPa and 0.29 MPa, attenuating deformations under natural temperature conditions were observed for 8 years.

Existing approaches to modeling the creep of frozen soils can be divided into empirical models based on regression analysis ^[16] and rheological models describing soil behavior through mechanical elements such as Hooke springs and Newtonian cylinders ^[17]. We emphasize that most creep studies have been limited to short-term experiments (up to several months), which creates difficulties in predicting long-term deformation processes.

The present study analyzes long-term deformations of frozen soils (sand, sandy loam, and loam) using uniaxial compression in experiments conducted in the Amderma underground Laboratory ^{[13, 8]}. The purpose of the work was to study the dynamics of changes in the rate of deformation over time, assess the stability of soil deformations, and refine the parameters of creep models used, which is important for the design and operation of structures in permafrost conditions. As it is known ^[8], saline frozen soils have low strength and high deformation characteristics, therefore, in this work, frozen soils common on the Arctic coast were studied.

Experimental methods

Saline frozen samples of disturbed composition were used in the experiments. Samples of frozen soils were taken from modern marine and alluvial quaternary sediments in natural conditions on the Yamal Peninsula in accordance with the requirements of GOST 12071-2014. To obtain samples of disturbed composition, the dry soil was crushed and mixed with a solution of sea salt of a given concentration in order to achieve the set values of salinity and humidity. The preparation process included holding the samples to evenly distribute moisture in the soil under desiccator conditions at a positive temperature, as well as compacting the samples in clips, followed by freezing at -20 ° C to obtain a massive cryogenic texture. Freezing was carried out in heat-insulated containers with one-way cooling for 3-7 days. After completing the preparation process, the ends of the samples were cleaned, their dimensions and weight were recorded, and the ice content was determined. Cylindrical samples with a diameter of 45-50 mm and a height of 100 mm were used for uniaxial compression. Prior to testing, the samples were stored in underground laboratory chambers at test temperature, wrapped in double polyethylene shells, which prevented moisture loss.

Uniaxial compression tests were performed to determine the creep characteristics of frozen soils. For the tests, 18 soil samples (sand, sandy loam and loam) were used, of which 6 parallel samples were intended for each series of experiments. The samples were fixed in a uniaxial compression device. Constant loads were used to study long-term soil deformations. The equipment made it possible to record axial and transverse deformations. The duration of the experiments was up to 10 years. The tests were carried out in the underground laboratory of the Amderminsk permafrost station at a depth of 14 m, which ensured relative stability of temperature conditions with fluctuations of no more than ± 0.2 °C (in the final observation period up to ± 0.4 °C). The samples were placed in a thin rubber shell and additionally in a plastic cup partially filled with snow to prevent moisture loss. After the tests, control measurements were carried out, no changes in the ice content of the samples were recorded. The physical properties of the samples are given in the Table. The data obtained were compared with theoretical models of soil deformation.

Table 1. Physical properties of saline frozen soils in long-term tests

Research results

Based on the data obtained, curves of long-term deformation and deformation rate for frozen sea sand, sandy loam and loam are constructed.

Fig.1. Curves of long-term deformation of frozen sea sand at 0.1% salinity, soil density 1.91 g/cm3, particle density 2.4 g/cm3.humidity 0.26 and load 0.15 MPa. The temperature is -3 °C, the numbers indicate the sample numbers

Fig.2. Curves of the deformation rate of frozen sand. The temperature is -3 °C, the numbers indicate the sample numbers

Prolonged creep of saline frozen sand occurs at a decaying, constant and then increasing rate over time and ends with the destruction of samples, i.e. corresponds to the behavior of frozen unsalted samples and the results of short-term tests (Fig. 1). Unlike frozen saline sands and frozen unsalted rocks, saline clay frozen rocks deform mainly at a decreasing rate, just as in the previously conducted short-term tests ^[8].

3. Curves of long-term deformation of frozen sea sandy loam at a salinity of 0.2%, soil density of 1.75 g/cm3, soil particle density of 2.68 g/cm3, humidity of 0.38 and load of 0.31 MPa. The temperature is -3 °C, the numbers indicate the sample numbers

Fig.4. Curves of the deformation rate of frozen sandy loam, the numbers indicate the sample numbers.

Fig. 3 shows that during the experiment, there is a gradual accumulation of deformation of frozen sandy loam (salinity 0.2%, humidity 0.38, density 1.75 g /cm3) at a temperature of -3 °C and a load of 0.31 MPa. At the initial stage, the deformation increases rapidly, which is probably due to compaction of the soil structure and stress redistribution. Over time, the rate of deformation decreases, reflecting the transition to the creep rate stabilization stage. The rate of deformation varies non-linearly, which is probably due to complex processes in the structure of frozen sandy loam. For individual samples (for example, sample 3), there are sharp changes in the rate of deformation, probably indicating local structural changes.

Fig. 4. shows the change in the rate of deformation of frozen sandy loam over time. At the first stage, the velocity is high, but then it gradually decreases, which corresponds to the decaying phase of creep. In the interval of 1500-2000 days, the velocity of most samples stabilizes, which indicates the completion of active deformation processes. In some areas (Fig.4), fluctuations in the rate of deformation are observed, possibly related to local changes in the soil structure.

Let's consider the possible causes of fluctuations in the deformation rate.:

1. In some experiments, sharp deformation jumps are observed (Fig. 3). This is probably due to the heterogeneous distribution of pore ice and the presence of microcracks in the soil structure. When exposed to a load, local damage causes sudden jumps in deformation. The salinity of the soil can contribute to the local redistribution of pore ice, which temporarily reduces the strength of the material.

2. It is also possible to recrystallize and decompose ice (Fig. 4) in the pore space and migration of moisture under prolonged stress. Phase transitions (melting and subsequent freezing) of ice are also possible. The hardening of the frozen soil structure can also occur due to the formation of ice slips, which can lead to temporary stabilization of deformations.

3. There are some differences between the samples, which is probably due to the structural heterogeneity of the soil associated with the conditions of sample preparation. The uneven distribution of ice and salt inside the samples could lead to variations in the deformation behavior.

5. Curves of long-term deformation of frozen marine loam at a salinity of 0.5%, a soil density of 1.68 g/cm3, a particle density of 2.70 g/cm3, a humidity of 0.46 and a load of 0.1 MPa. The temperature is -3 °C, the numbers indicate the sample numbers

Fig.6. Curves of the rate of deformation of frozen loam. The temperature is -3 °C, the numbers indicate the sample numbers

Figure 5 shows the deformation graphs of frozen marine loam samples with a salinity of 0.5%, a density of 1.68 g/cm3 and a humidity of 0.46 at a load of 0.1 MPa and a temperature of -3°C. The curves show generally decaying deformation over time, characteristic of frozen soils. At the initial stage, there is an intense increase in deformation, followed by stabilization at later stages. However, samples No. 4 and No. 5 are distinguished by abnormal behavior: jumps or local deviations are recorded during the deformation process.

Figure 6 illustrates the variation of the deformation rate over time for the same samples. The general trend corresponds to two phases of creep: primary (decaying) and secondary (stable). In this case, the deformation rates change unevenly, which is expressed in the form of fluctuations. Special attention is drawn to sample No. 5, which demonstrates a significantly higher initial deformation rate, which may be due to a weakening of interparticle bonds due to the heterogeneous distribution of ice in the soil structure, or increased stresses in the soil matrix.

It is likely that sudden changes in the deformation curves can be caused by the local destruction of ice bonds or the redistribution of stresses within the soil structure. Such processes are typical for clay soils with high porosity and significant water content (Fig. 6). It is possible that changes in the rate of deformation over time are caused by several factors: the redistribution of ice in the pore space, as well as the formation and closure of microcracks under load, which causes local changes in the structure and leads to a temporary acceleration or attenuation of deformations. The salinity of the soil (0.5%) probably also affects the phase transitions of water and ice and their redistribution, which contributes to a change in deformation characteristics.

Long-term creep patterns

Common approaches include the so-called technical creep theories. The most well-known of them are the power and hyperbolic dependences based on the provisions of statistical mechanics (Eyring's formula), as well as the formula describing the theory of hardening. According to another theory (aging), the relationship is established not between the rate of deformation and stress, but between deformation, stress and time. This formula, known as S.S. Vyalov's equation, has been widely used due to his research. In addition, there are a number of alternative approaches used to describe the creep of frozen soils.

Three processing techniques based on the following formulas were applied to the data obtained ^[12].

First, the formula of the so-called technical theory of aging was used:

(1)

Where t is time; ε is deformation; 𝝈 is stress; 𝝃, α,m are parameters.

secondly, the theory of hardening:

(2)

Where t is time; ε is deformation; 𝝈 is stress; 𝔞, m, α are parameters.

and, thirdly, the theory of flow:

(3)

Where t is time; ε is deformation; 𝝈 is stress; b, n are parameters.

Experiments conducted over the course of 10 years have made it possible to investigate the patterns of soil deformation under prolonged exposure to constant stress. For each type of soil, the average strain value was calculated, which was used to describe the general trend of deformation change. Based on the data obtained, an approximation was performed aimed at determining the parameters of the models used. The final results are presented in table 2.

Table 2. Comparison of calculated deformation parameters in short-term and long-term tests for various soils

For sandy loams and loams in the three models, the parameters (α, m,b, n) differ significantly between the short and long-term periods. In the case of sand, changes in the parameters (𝝃, α) are minimal, so short-term models with trend extrapolation may be acceptable for a long-term forecast. Building structures require a certain margin of safety, since short-term testing does not allow reliable assessment of deformations over ten years.

7. Comparison of experimental data and calculated creep curves based on the theory of aging for different types of frozen soils

8. Comparison of experimental data and calculated creep curves based on the theory of hardening for different types of frozen soils

9. Comparison of experimental data and calculated creep curves based on flow theory for different types of frozen soils

To assess the accuracy of the predictions of each theory, an additional calculation of the average error (MSE, %) was performed for the discrepancy between experimental data and theoretical values. The standard deviation, as it is known, is a measure of accuracy that allows comparing the prediction errors of different models for a specific data set ^[18]. The standard deviation (MSE,%) for the theories of aging and hardening for sand is about 5%. For the theory of flow, the MSE for sand is much higher and reaches 37%. For frozen sea sandy loam, according to the theory of aging and hardening, the MSE is about 14%, and according to the theory of flow, 28%. For frozen marine loam, according to the theory of aging and hardening, the MSE is 8%, and according to the theory of flow, it is 18%.

Discussion of the results

The present study is aimed at studying the long-term creep of frozen soils (sand, sandy loam and loam) under constant temperatures and loads, with an emphasis on the change in the rate of deformation over time. The analysis of experimental data was carried out using the theories of aging, hardening and flow, which allowed not only to confirm existing theoretical positions, but also to identify new patterns important for engineering practice.

Sands exhibit minimal creep, while sandy loam and loam, which have greater porosity and ice content, are more susceptible to deformation. The low rate of deformation of sands has been confirmed (20-30% less than that of sandy loam and loam). Structural anomalies related to the heterogeneous distribution of ice were observed in the sandy loam, which was described earlier ^[19].

During experiments on all types of soils (sand, sandy loam and loam), it was found that at low loads, attenuating creep is observed, which stabilizes over 10 years of observations. These data are consistent with the results of ^[10], which also observed a stabilization of speeds under moderate loads.

For sandy loam and loam, the formation of ice slips was observed during the experiment, stabilizing the soil structure at low temperatures. This reduced the rate of deformation, especially in the initial period. These observations are consistent with the conclusions of ^[4], but complement them by describing long-term stabilization effects that were not considered in previous studies. In a certain range of salinity, saline soils, unlike unsalted ones, showed a lower tendency to destruction. For example, sandy loam with a 0.2% salinity had a lower deformation rate at the same temperature (-3°C) than sand with a lower salt content. This confirms earlier results that salinity strengthens ice structures in the ground and increases their stability ^[17].

The results of the study confirm the effectiveness of using the theories of aging and hardening to describe the creep of frozen soils. Both theories demonstrate high accuracy at the initial and intermediate stages of deformation for various types of soils such as sand, sandy loam and loam. This is consistent with the conclusions presented in the work of Vyalov S.S., which emphasizes the importance of taking into account time factors in modeling deformation processes in frozen soils ^[12]. However, in the later stages of deformation, there is a decrease in the accuracy of the aging and hardening models. This may be due to the complication of rheological processes, which confirms the opinion of N.A. Tsytovich, who noted the need to take into account the complex nonlinear properties of frozen soils ^[11].

Flow theory has shown significantly lower accuracy, especially in the later stages of deformation. The limitations of flow theory are discussed in the work of L.T. Roman, which emphasizes the need to introduce nonlinear corrections to improve the accuracy of models ^[20]. The applicability of each model in engineering practice depends on the required accuracy and complexity of calculations. The introduction of nonlinear corrections or the use of more complex mathematical models can improve the accuracy of flow theory, especially in the late stages of deformation.

The present study has been conducted for 10 years, which has allowed us to observe long-term changes, including stabilization of deformation rates. Most other studies were limited to short-term observations, which did not allow such effects to be recorded ^[21]

Conclusions

1. Long-term experimental studies have shown that the prolonged creep of frozen soils (sand, sandy loam and loam) has pronounced stages of deformation: initial damping, stabilizing and (in some cases) accelerating. Sands and sandy loams are characterized by stabilization of the deformation rate, while loams exhibit complex nonlinear behavior, possibly related to cracking and local structural restoration processes.

2. Sandy loams and loams are characterized by complex deformation dependences, probably due to the heterogeneous distribution of ice and the features of the porous structure. Saline soils show less deformability compared to unsalted samples in a certain range of salinity concentration.

3. The theories of aging and hardening satisfactorily describe the creep processes of frozen soils at the initial and intermediate stages of deformation, which is confirmed by low MSE values. The theory of flow has limited applicability. To improve the accuracy of the models, it is recommended to introduce nonlinear corrections or use more complex mathematical descriptions that take into account the rheological properties of frozen soils.

4. The data obtained are of key importance for the design and operation of engineering structures in permafrost conditions. The results make it possible to predict long-term deformation processes and improve the reliability of the foundations of buildings and engineering structures.