# Study on Shear Characteristics of Interface between Frozen Soil and Pile during Thawing Process in Permafrost Area

Authors: Ying Zhao; Xuesong Mao; Qian Wu; Wanjun Huang; Yueyue Wang
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

In permafrost areas, the degradation of permafrost greatly affects the stability of concrete pile composite foundations. Hence, direct shear tests were carried out to analyze the effect of the rising frozen temperature, moisture content, and normal stress on the mechanical properties of the frozen soil-pile interface during the thawing process of permafrost. A constitutive model was established to describe the shear stress-displacement variation law of interface, considering the hydrothermal coupling effect. The results show that the frozen strength of the interface was provided by the ice crystal structure formed at the interface, and its area increases with increasing water content. The whole shear process can be divided into three stages: the prepeak stage with growing shear stress, the postpeak stage with deep dropping shear stress, and the shear stress reconstruction stage. The peak frozen strength was positively correlated with water content and normal stress, however, it was negatively correlated with the rising frozen temperature. The residual frozen strength has a linear relationship with normal stress and water content, however, it shows different regularity with rising frozen temperature at different water content. Moreover, the Gompertz model prediction results are in good agreement with the experimental results. This model can describe well the stress-displacement variation law of interface with different rising frozen temperature and water content.


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## Body

## 1. Introduction

The concrete pile composite foundation is one of the effective treatment measures adopted for road projects in permafrost areas. Because of the stiffness difference, the pile and soil are subjected to different stresses, resulting in the relative slip between the soil and pile. In addition, with the degradation of permafrost, the ground temperature of the frozen soil around the pile is on a rising trend. Therefore, the shear characteristics of the frozen soil and pile interface during the thawing process are the key factors to study the bearing capacity of the composite foundation. Also, the study of mechanical properties of the permafrost-contact surface-structure system is of great engineering significance for the design and construction of foundation structures in permafrost areas.Frozen soil is frozen together with structures by the cementation of ice crystals to form a freezing interface. The shear strength of the interface between the frozen soil and foundation material is frozen strength [1,2]. Also, Qiu et al. defined the frozen strength as the maximum shear stress that the interface formed between the structure surface and the frozen soil can withstand [3]. The adhesion of ice to the surface of the structure can enhance the shear resistance at the interface [4], which is the difference between the frozen soil-structure interface and the unfrozen soil-structure interface. Chen [5] pointed out that the cementation of ice at the interface contributes to improving the stability of foundations embedded in permafrost. It is because of the strong cohesion provided by the ice crystal before failure occurs [6]. Tong and Guan [7] also present that the adfreeze bond was a key controlling factor of the tangential frost heave stress at the interface. Therefore, the adfreeze bond strength plays an indispensable role in the stability and bearing characteristics of the pile foundations in frozen areas.Several studies show that the adfreeze bond strength between piles and frozen ground is infected by temperature, moisture content, soil physical properties, loading types, and surface roughness [8–11]. In frozen areas, the moisture in the soil will be frozen to form a strong bond between soil particles [12]. It provides a strong cementation effect on the interface between the frozen soil and pile surface, which is closely related to frozen temperature. Du et al. [13] pointed out that the frozen temperature affects the development of shear stress between the frozen soil and structure surface by affecting the unfrozen water content. Correspondingly, the frozen temperature also controls the content and properties of ice crystal forms at the contact surface. Thus, temperature and moisture are the key problems of underground engineering in frozen soil areas.However, the ground temperature may change upon the environment [14], and the permafrost is on a trend of degradation year by year because of global warming and the laying of black pavement. The performance of the frozen soil-structure interface under the conditions of rising frozen temperatures needs to be paid due attention. Du et al. [13] found that the interfacial friction angle decreases first and then increases, while the interfacial cohesion increases first and then decreases relatively with rising frozen temperatures. Wang et al. [15] and Liu et al. [16] pointed out that with the increasing thawing temperature, shearing stress-displacement curves gradually transform from strain-hardening to strain-softening under high pressure, and they described the shear stress-strain relationship using the standard hyperbolic model and generalized hyperbolic model, considering the temperature effect.This paper investigated the shear properties of an artificially thawing soil-structure interface by direct shear tests. The effect of temperature, moisture content, and normal stress on the shearing mechanical performance was studied. The whole shear process was recorded by measuring the shear stress-shear displacement relationship, peak frozen strength, and residual frozen strength. This paper also proposes a mathematical model considering hydrothermal coupling to describe the stress-strain relationship of the thawing soil-structure interface.


## 2. Sample Preparation and Test Procedure

### 2.1. Testing Material

The testing soil was silty clay. Soil physical properties and particle size analysis are shown in Figure1. Particle size analysis showed that 2 mm to 0.075 mm sand accounted for 5.06%, 0.075 mm to 0.005 mm silt accounted for 69.01%, and clay <0.005 mm accounted for 25.93%. The plastic limit and the liquid limit are 17.69% and 30.5%, respectively. During the preparation of the sample, all of the soil was air-dried, sifted through a 2 mm sieve, dried in an oven for 12 h, and mixed with water to a specified water content.Figure 1
Grading composition and physical properties of silty clay.The concrete samples used in the direct shear tests were prepared into a cylindrical cutting ring, 61.8 mm in diameter and 20 mm in height. The concrete samples were cast with ordinary Portland cement, natural river sand, and gravel, with a particle size less than 5 mm. The mix ratio of cement, sand, gravel, and water is 1 : 1.5 : 2.4 : 0.4. After 28 days of curing, the concrete samples were removed from the cutting ring, as shown in Figure2.Figure 2
Concrete sample.


### 2.2. Testing Procedure

The frozen strength of the interface was determined with a strain-controlling direct shear apparatus. The shear apparatus consisted of two circular shear boxes, which accommodated concrete samples and soil samples (61.8 mm in diameter and 20 mm in height). The testing parameters involved different values for normal stress (100 kPa, 200 kPa, 300 kPa, and 400 kPa) and water content (14%, 20%, 26%, and 32%), determined by the engineering classification of frozen soil [17] and temperatures during the thawing process (-1°C, -2°C, and -3°C).Before the direct shear test, the concrete samples were placed in the lower part of the shear box, fixed the upper shear box, and compacted the soil of specific quality into the upper shear box to ensure that the soil achieved the required dry density. The interface model was completed, as shown in Figure3. Taking the shear test with 26% moisture content contact surface as an example, 5 models were made, and a PT100 temperature sensor was buried into one of the shear boxes, right on the interface, to monitor the temperature in real time. This interface model was prepared as a standard to ensure that the shear temperature reaches the set temperature. Figure 4 shows the schematic of the standard interface model. Secondly, all the interface models were placed in a high-low temperature test room, which was equipped with a temperature unit with an accuracy of ±0.5 °C. When the temperature of the interface reached -8°C, it is maintained and stabilized for 12 h. After that, all the interface models were removed and placed at room temperature (8–9 °C) for melting. The interface thawing process is shown in Figure 5. When the temperature of the interface achieved the predetermined temperature, all the models were put into the constant temperature room for shear tests. Finally, the shear stress and shear displacement are recorded. Figure 6 shows the schematic diagram of the whole process of the shear test.Figure 3
Schematic diagram of shear test and interface model: (a) interface model; (b) direct shear test.
(a)(b)Figure 4
Schematic of standard interface model.Figure 5
Schematic diagram of interface thawing process.Figure 6
Schematic diagram of the whole process of shear test.


## 2.1. Testing Material

The testing soil was silty clay. Soil physical properties and particle size analysis are shown in Figure1. Particle size analysis showed that 2 mm to 0.075 mm sand accounted for 5.06%, 0.075 mm to 0.005 mm silt accounted for 69.01%, and clay <0.005 mm accounted for 25.93%. The plastic limit and the liquid limit are 17.69% and 30.5%, respectively. During the preparation of the sample, all of the soil was air-dried, sifted through a 2 mm sieve, dried in an oven for 12 h, and mixed with water to a specified water content.Figure 1
Grading composition and physical properties of silty clay.The concrete samples used in the direct shear tests were prepared into a cylindrical cutting ring, 61.8 mm in diameter and 20 mm in height. The concrete samples were cast with ordinary Portland cement, natural river sand, and gravel, with a particle size less than 5 mm. The mix ratio of cement, sand, gravel, and water is 1 : 1.5 : 2.4 : 0.4. After 28 days of curing, the concrete samples were removed from the cutting ring, as shown in Figure2.Figure 2
Concrete sample.


## 2.2. Testing Procedure

The frozen strength of the interface was determined with a strain-controlling direct shear apparatus. The shear apparatus consisted of two circular shear boxes, which accommodated concrete samples and soil samples (61.8 mm in diameter and 20 mm in height). The testing parameters involved different values for normal stress (100 kPa, 200 kPa, 300 kPa, and 400 kPa) and water content (14%, 20%, 26%, and 32%), determined by the engineering classification of frozen soil [17] and temperatures during the thawing process (-1°C, -2°C, and -3°C).Before the direct shear test, the concrete samples were placed in the lower part of the shear box, fixed the upper shear box, and compacted the soil of specific quality into the upper shear box to ensure that the soil achieved the required dry density. The interface model was completed, as shown in Figure3. Taking the shear test with 26% moisture content contact surface as an example, 5 models were made, and a PT100 temperature sensor was buried into one of the shear boxes, right on the interface, to monitor the temperature in real time. This interface model was prepared as a standard to ensure that the shear temperature reaches the set temperature. Figure 4 shows the schematic of the standard interface model. Secondly, all the interface models were placed in a high-low temperature test room, which was equipped with a temperature unit with an accuracy of ±0.5 °C. When the temperature of the interface reached -8°C, it is maintained and stabilized for 12 h. After that, all the interface models were removed and placed at room temperature (8–9 °C) for melting. The interface thawing process is shown in Figure 5. When the temperature of the interface achieved the predetermined temperature, all the models were put into the constant temperature room for shear tests. Finally, the shear stress and shear displacement are recorded. Figure 6 shows the schematic diagram of the whole process of the shear test.Figure 3
Schematic diagram of shear test and interface model: (a) interface model; (b) direct shear test.
(a)(b)Figure 4
Schematic of standard interface model.Figure 5
Schematic diagram of interface thawing process.Figure 6
Schematic diagram of the whole process of shear test.


## 3. Characteristic of Frozen Soil-Concrete Interface

Figure7 shows the failure characteristics of the interfaces with different water content after the shear tests at -2°C. It can be seen that there were almost no ice crystals present on the shear interface with 14% water content. With the increasing water content, ice crystals were visible to the naked eye on the interface of 20% water content and were scattered. The ice crystals on the interface with 26% moisture content increased in a large area and distributed in a monolithic manner, covering the soil particles, while few soil particles were exposed. On the shear surface with 32% water content, the ice crystals combined into an entity, completely covering the interface as an ice layer, and no soil particles were exposed. It is because there is a difference in thermal conductivity between concrete and soil during the freezing process, where the cold energy reached the concrete surface first and formed the cold end. Therefore, a temperature gradient was formed between concrete and soil. Under the effect of the temperature gradient, the water kept gathering to the cold end to form a thin ice layer. Volokhov [18] and Wen et al. [8] also found the presence of ice film at the permafrost-structure interface in their experiments.Figure 7
Failure characteristics of thawing soil-concrete interface with different moisture content (-2°C).The strength of structure-concrete interface relies on the ice cementation strength (i.e., frozen strength) to resist external shear forces [2]. Thus, the mechanism of frozen strength formation is crucial to understand the bearing characteristics of the pile group foundation. According to the related research [16,19,20], the frozen strength of frozen soil-concrete interface in positive thawing state consists of three main components: (a) the cementation strength of ice crystals at the contact surface, (b) the cohesive force between soil particles and concrete surface, and (c) the frictional force between soil particles and concrete surface. The above components are closely related to the normal stress, temperature, and moisture content of the soil.


## 4. Characteristics of Shear Stress-Displacement Curves

Figure8 shows the shear stress-displacement curves of the frozen soil-concrete interface under different factors. The shear stress-displacement curves with different normal stress, water content, and shear temperature are shown in Figures 8(a)–8(c), respectively. It can be seen that normal stress, temperature, and water content have a severe impact on the peak frozen strength, residual frozen strength, and the failure process. From the shear stress response of the interface, it is found that the shear stress-displacement relationship presents brittle failure characteristics, i.e., strain-softening failure mode. The whole process of shear tests can be divided into 3 stages, i.e., the prepeak stage with growing shear stress, the postpeak stage with deep dropping shear stress, and the shear stress reconstruction stage.Figure 8
The shear stress-displacement curves under different factors: (a) shear stress-displacement curves vs. normal stress (26%, -1°C), (b) shear stress-displacement curves vs. water content (300 kPa, -3°C), and (c) peak frozen strength vs. temperature (200 kPa, 32%).
(a)(b)(c)In the prepeak stage, the shear stress-displacement curves present an approximate “S“ shape. At the initial stage of shear, the curve shows reverse bending and grows approximately exponentially. As the test proceeds, the curve is gradually steeper and grows in a nearly straight line. The shear stress increases proportionally with the shear displacement. Before the shear stress reaches the peak, the growth trend of curves gradually slows down, and the slope gradually decreases. The lower the shear temperature, the greater the moisture content, and the curve is close to linear change until the shear stress reaches the peak.After the shear stress reached its maximum value, the interface was rapidly sheared, and the ice crystals were destroyed, after which the interface evolved from maximum static friction to sliding friction [21]. It shows a rapid decline in the shear stress-displacement curves and a sudden decline of shear stress. It is because after the ice crystal was destroyed, the orientation of the reformed crystals changed in the direction of less resistance, resulting in a significant attenuation of shear stress.The curve of the shear stress reconstruction stage can be divided into two components, namely the shear stress growth stage and the shear stress stabilization stage. For the damaged interface, the residual frozen strength can be formed because of the ability of ice crystals to form secondary cementation in a lower temperature environment, which reprovides shear stress [22]. This stage is called the shear stress growth stage. In the shear stress stabilization phase, the residual frozen strength of the interface is formed, and the greater the water content and the lower the temperature, the smaller the residual frozen strength. Consistent with the interface frozen strength, the residual frozen strength also consists of three main components: (a) the secondary cementation strength of ice crystals, (b) the cohesive force between soil particles and concrete surface, and (c) the frictional force between soil particles and the concrete surface.


## 5. Mechanical Properties of the Frozen Soil-Concrete Interface during Thawing Process

### 5.1. Peak Frozen Strength

The maximum shear stress that the frozen soil-structure interface can withstand when frozen together is considered to be the frozen strength. When shear slip failure occurs at the interface, the peak shear stress in this critical state is the ultimate frozen strength, i.e., the peak frozen strength. The peak frozen strength under different conditions is presented in Figure9. The analysis reveals that the peak frozen strength of the interface increases linearly with increasing normal stress (Figure 9(a)). It is because of the fact that the normal stress drives the structure surface and the soil (permafrost) to squeeze each other, increasing the contact friction of the interface.Figure 9
Peak frozen strength under different conditions: (a) peak frozen strength vs. normal stress (-3°C), (b) peak frozen strength vs. water content (-3°C), and (c) peak frozen strength vs. temperature (26%).
(a)(b)(c)It is also found that the peak frozen strength increased logarithmically with the increase of water content, and the increase rate is first fast and then slow, as shown in Figure9(b). The reason is that the peak frozen strength is mainly contributed by the cementation force of the ice crystals, while the cementation force is closely related to its area. The analysis of Figure 7 indicates that the larger the water content, the larger the area of ice crystals. Also, the frozen strength of the frozen soil-structure interface is mainly composed of the cementation force of ice crystals and the cohesive force and friction between the soil particles and concrete surface. When the water content was 14%, less water in the soil migrated to the interface during the freezing process, resulting in fewer ice crystals and exhibiting a weaker cementation force. As the water content increased, the water film around the soil particles became thicker. The water converged to the interface and froze under the effect of the temperature gradient, leading to a dramatic increase in the cementation strength of ice crystals. The frozen strength of the interface is mainly contributed by the cementation force of ice crystals. Meanwhile, when the water content increases from 26% to 32%, the ice crystal area has almost completely covered the contact surface, leading to a slower increase in peak frozen strength.As illustrated in Figure9(c), the peak frozen strength decreases linearly with increasing thawing temperature. It is because the effect of temperature on shear stress is mainly attributed to the change of unfrozen water content at the interface [8,9]. When the soil temperature is between -3°C and -1°C, the unfrozen water is in a state of severe phase transition, and the higher the thawing temperature, the higher the unfrozen water content. When the interface is thawed to - 3 °C, most of the water exists in the form of ice crystals, and the shear stress is presented in the form of larger cementation strength. As the temperature rises but does not reach 0 °C, the content of unfrozen water increases and the lubricating effect of thin-film water leads to a decrease in the crystalline cementation strength.


### 5.2. Residual Frozen Strength

The residual frozen strength occurs after the interface shear slips. The shear stress is reshaped to the peak and stabilized, which is called the residual frozen strength. After the interface shear slips, the shear process is over from static friction to sliding friction, and the soil particles and the ice crystals start to slide completely. The ice crystal structure is regenerated at a low temperature until the shear stress reaches stability. Figure10 shows the variation curves of residual frozen strength with normal stress, moisture content, and temperature.Figure 10
Residual frozen strength under different conditions: (a) residual frozen strength vs. normal stress (-2°C), (b) residual frozen strength vs. water content (300 kPa°C), and (c) residual frozen strength vs. temperature (400 kPa).
(a)(b)(c)As shown in Figure10(a), it can be seen that the residual frozen strength increases with the increase of normal stress at the same shear temperature, i.e., the residual frozen strength is positively correlated with normal stress. The reason is that normal stress causes the concrete surface to extrude with the frozen soil, which increases the friction on the interface.Comparing the residual frozen strength of the interface at different water contents, as shown in Figure10(b), it can be found that the residual frozen strength shows an overall decreasing trend with the increase of water content, and the higher the shear temperature, the slower the decreasing rate. It is because the thermal equilibrium of the interface was disturbed by the frictional behavior in the shear process, resulting in an increase in unfrozen water content of the contact surface, which plays a lubricating role in the slipping process between soil and the concrete surface. Moreover, when the shear temperature is - 1 °C and - 2 °C, the relationship curves of the residual frozen strength vs. water content are relatively steep, i.e., the decline rate is faster. Even though the shear temperature is in a negative state, it is close to 0 °C. Thus, the thermal equilibrium state of the interface is easily disturbed, resulting in the increase of unfrozen water content, which makes the secondary cementation of ice crystals more difficult. However, the decay of residual frozen strength with increasing water content is not significant when the shear temperature is -3°C. It is because the lower negative temperature enhances the secondary cementation of ice crystals, although the increasing water content reduces the friction between soil particles and the concrete surface.As can be seen from Figure10(c), the residual frozen strength with rising frozen temperature is not consistent for different water content. At the water content of 14%, the residual frozen strength increased with the increase of shear temperature. Analyzing the reason, the ice crystal structure on the interface with 14% water content was not very developed. Meanwhile, the amount of unfrozen water content of interface was determined by the shear temperature, and the higher the thawing temperature, the greater the unfrozen water content. Coupling with the shear damage after the sliding friction effect leads to a further increase in unfrozen water content, which increases the viscosity and shear resistance of the interface. When the water content is 20% to 32%, the residual frozen strength tends to decrease overall with the increase of shear temperature. It is noted that the ice crystal structure of the interface with higher water content is more developed, especially when the water content is 32%, and the ice crystals almost completely cover the concrete surface. However, the increase of shear temperature leads to the melting of ice crystals and the increase of unfrozen water content, which mainly shows the lubrication effect on the interface. Thus, for the interface where ice crystals develop, the residual frozen strength can be weakened by the increasing thawing temperature.


## 5.1. Peak Frozen Strength

The maximum shear stress that the frozen soil-structure interface can withstand when frozen together is considered to be the frozen strength. When shear slip failure occurs at the interface, the peak shear stress in this critical state is the ultimate frozen strength, i.e., the peak frozen strength. The peak frozen strength under different conditions is presented in Figure9. The analysis reveals that the peak frozen strength of the interface increases linearly with increasing normal stress (Figure 9(a)). It is because of the fact that the normal stress drives the structure surface and the soil (permafrost) to squeeze each other, increasing the contact friction of the interface.Figure 9
Peak frozen strength under different conditions: (a) peak frozen strength vs. normal stress (-3°C), (b) peak frozen strength vs. water content (-3°C), and (c) peak frozen strength vs. temperature (26%).
(a)(b)(c)It is also found that the peak frozen strength increased logarithmically with the increase of water content, and the increase rate is first fast and then slow, as shown in Figure9(b). The reason is that the peak frozen strength is mainly contributed by the cementation force of the ice crystals, while the cementation force is closely related to its area. The analysis of Figure 7 indicates that the larger the water content, the larger the area of ice crystals. Also, the frozen strength of the frozen soil-structure interface is mainly composed of the cementation force of ice crystals and the cohesive force and friction between the soil particles and concrete surface. When the water content was 14%, less water in the soil migrated to the interface during the freezing process, resulting in fewer ice crystals and exhibiting a weaker cementation force. As the water content increased, the water film around the soil particles became thicker. The water converged to the interface and froze under the effect of the temperature gradient, leading to a dramatic increase in the cementation strength of ice crystals. The frozen strength of the interface is mainly contributed by the cementation force of ice crystals. Meanwhile, when the water content increases from 26% to 32%, the ice crystal area has almost completely covered the contact surface, leading to a slower increase in peak frozen strength.As illustrated in Figure9(c), the peak frozen strength decreases linearly with increasing thawing temperature. It is because the effect of temperature on shear stress is mainly attributed to the change of unfrozen water content at the interface [8,9]. When the soil temperature is between -3°C and -1°C, the unfrozen water is in a state of severe phase transition, and the higher the thawing temperature, the higher the unfrozen water content. When the interface is thawed to - 3 °C, most of the water exists in the form of ice crystals, and the shear stress is presented in the form of larger cementation strength. As the temperature rises but does not reach 0 °C, the content of unfrozen water increases and the lubricating effect of thin-film water leads to a decrease in the crystalline cementation strength.


## 5.2. Residual Frozen Strength

The residual frozen strength occurs after the interface shear slips. The shear stress is reshaped to the peak and stabilized, which is called the residual frozen strength. After the interface shear slips, the shear process is over from static friction to sliding friction, and the soil particles and the ice crystals start to slide completely. The ice crystal structure is regenerated at a low temperature until the shear stress reaches stability. Figure10 shows the variation curves of residual frozen strength with normal stress, moisture content, and temperature.Figure 10
Residual frozen strength under different conditions: (a) residual frozen strength vs. normal stress (-2°C), (b) residual frozen strength vs. water content (300 kPa°C), and (c) residual frozen strength vs. temperature (400 kPa).
(a)(b)(c)As shown in Figure10(a), it can be seen that the residual frozen strength increases with the increase of normal stress at the same shear temperature, i.e., the residual frozen strength is positively correlated with normal stress. The reason is that normal stress causes the concrete surface to extrude with the frozen soil, which increases the friction on the interface.Comparing the residual frozen strength of the interface at different water contents, as shown in Figure10(b), it can be found that the residual frozen strength shows an overall decreasing trend with the increase of water content, and the higher the shear temperature, the slower the decreasing rate. It is because the thermal equilibrium of the interface was disturbed by the frictional behavior in the shear process, resulting in an increase in unfrozen water content of the contact surface, which plays a lubricating role in the slipping process between soil and the concrete surface. Moreover, when the shear temperature is - 1 °C and - 2 °C, the relationship curves of the residual frozen strength vs. water content are relatively steep, i.e., the decline rate is faster. Even though the shear temperature is in a negative state, it is close to 0 °C. Thus, the thermal equilibrium state of the interface is easily disturbed, resulting in the increase of unfrozen water content, which makes the secondary cementation of ice crystals more difficult. However, the decay of residual frozen strength with increasing water content is not significant when the shear temperature is -3°C. It is because the lower negative temperature enhances the secondary cementation of ice crystals, although the increasing water content reduces the friction between soil particles and the concrete surface.As can be seen from Figure10(c), the residual frozen strength with rising frozen temperature is not consistent for different water content. At the water content of 14%, the residual frozen strength increased with the increase of shear temperature. Analyzing the reason, the ice crystal structure on the interface with 14% water content was not very developed. Meanwhile, the amount of unfrozen water content of interface was determined by the shear temperature, and the higher the thawing temperature, the greater the unfrozen water content. Coupling with the shear damage after the sliding friction effect leads to a further increase in unfrozen water content, which increases the viscosity and shear resistance of the interface. When the water content is 20% to 32%, the residual frozen strength tends to decrease overall with the increase of shear temperature. It is noted that the ice crystal structure of the interface with higher water content is more developed, especially when the water content is 32%, and the ice crystals almost completely cover the concrete surface. However, the increase of shear temperature leads to the melting of ice crystals and the increase of unfrozen water content, which mainly shows the lubrication effect on the interface. Thus, for the interface where ice crystals develop, the residual frozen strength can be weakened by the increasing thawing temperature.


## 6. Shear Stress-Displacement Relationship of Frozen Soil-Concrete Interface

### 6.1. Applicability of Gompertz Model

The group pile composite foundation in the permafrost areas is mainly loaded by the self-weight of embankment and the vehicle load, which is transferred downward through the pile-soil interaction. Therefore, determining the shear strength of the permafrost-pile interface is an indispensable link in the calculation of the foundation bearing capacity. In this study, only the part before which the shear stress-displacement curve reaches its peak is considered, and the part after which the brittle damage occurs is not considered. According to the above analysis, the shear stress-displacement curve before reaching the peak strength has a weak S-shaped trend. The existing theoretical models, such as the hyperbolic model, the elastic-plastic theory model, and the damage model, cannot respond well to the nonlinear deformation stage of displacement at low shear stress [22–24]. The Gompertz model curve is based on the growth process of things, i.e., from a slow growth at the beginning to a rapid growth in the middle and then to a basic steady state at the end. The growth process described by this curve is similar to the trend of the shear stress-displacement curve of the frozen soil-concrete interface in this study, and the Gompertz model equation [25] is shown in(1)τ=aexp−bexp−cδ,where τ is the shear stress, δ is the shear displacement, b,c is the model parameter, and a is the peak value of shear stress in the shear stress-displacement curve.To evaluate the quality of the fitting curve, the correlation factorβ [26] is introduced, which is defined as follows:(2)β=1−1n∑δi−δiδi,where δi is the shear stress of the predicted samples, δi is the shear stress of the observation samples, and n is the number of samples participating in the evaluation. Because of the difference of samples in the complete plastic stage of the shear stress-displacement curves, the values of the calculated correlation factor β vary accordingly. The evaluation criteria are established to evaluate the fitting effect, as shown in Table 1.Table 1
Evaluation standard of the correlation factor in the fitting model.
Evaluation factorEvaluation criterionExcellentGoodQualifiedUnqualifiedβ≥0.95≥0.90≥0.85<0.85The experimental data is brought into (1) to obtain several sets of δi and δi, and then the obtained sets are brought into (2) to obtain the correlation factor. The evaluation results are shown in Table 2. The analysis of the simulated data of the shear stress-displacement relationship shows that the values of the model fitting correlation factor β are greater than 0.90, and the results are good or excellent. It indicates that the Gompertz model is suitable for simulating the first half of the direct shear test curves of the interface between frozen soil and concrete.Table 2
Data simulation and evaluation of direct shear tests.
Temperature (℃)Water content (%)Normal stress (kPa)Model equationτ=aexp−bexp−cδEvaluation factorβEvaluate resultabc-114100150.8296.5854.7070.9741Excellent200180.5265.8163.3550.9717Excellent300245.9814.4252.3810.9849Excellent400271.3653.9071.9290.9672Excellent20100227.0823.9882.6290.9779Excellent200283.7595.2502.5860.9774Excellent300314.0424.4012.0350.9849Excellent400377.7094.6062.2840.9322Good26100258.7695.3492.5720.9702Excellent200331.1134.1801.8670.9133Good300396.6084.6141.9510.9551Excellent400441.8915.8042.1240.9534Excellent32100310.5174.3262.6870.9640Excellent200360.5784.5542.3570.9878Excellent300452.1744.3412.3260.9843Excellent400476.6393.6982.0400.9981Excellent-214100166.7186.114253.528560.9685Excellent200243.2744.633892.54360.9533Excellent300324.4365.241312.314060.9523Excellent400413.5775.234732.130340.9992Excellent20100268.9615.268452.680010.9541Excellent200412.9015.436172.137960.9726Excellent300430.1845.114932.283170.9868Excellent400457.3664.94621.811810.9578Excellent26100355.9215.774992.213450.9492Good200421.0935.49622.512830.9998Excellent300505.8516.215871.94110.9888Excellent400524.736.503022.053040.9843Excellent32100415.0735.866822.570550.9772Excellent200449.9225.147572.15990.9964Excellent300523.6395.033992.185070.9969Excellent400555.2156.048732.244820.9791Excellent-314100235.3856.369993.048770.9736Excellent200281.7666.841273.353520.9329Good300359.5175.377182.61250.9553Excellent400479.766.20762.271530.9573Excellent20100320.3867.024632.603070.9166Good200423.8918.15592.530910.9465Good300495.9425.132592.271110.9992Excellent400559.5185.791722.230520.9791Excellent26100446.3765.210851.848940.9579Excellent200490.2555.227572.080020.9365Good300559.5394.601161.893230.9982Excellent400611.7955.496322.04730.9460Good32100505.9427.509742.31930.9681Excellent200581.9125.868671.975480.9395Good300624.695.020871.859750.9226Good400657.7714.585641.761870.9463Good


### 6.2. Establishment of Shear Stress-Displacement Relationship Model considering Temperature and Water Content

The physical properties and stress state on the interface will change as the thawing temperature and moisture content change. In the process of freezing, moisture migrates to the contact surface under the effect of the temperature gradient, and the difference of water content significantly affects the formation area of ice crystal structure. Negative temperature is the controlling factor affecting the unfrozen water content and ice crystal content of the interface, which affects the cementation strength of the ice crystals and concrete surface by changing the ice and water equilibrium. Thus, the temperature and water content are key factors in the frozen strength of the soil-structure interface in permafrost regions. The engineering problems arising from foundations are the result of the disruption of the soil-structure hydrothermal equilibrium. Therefore, it is necessary to consider the coupling effects of temperature and moisture on the mechanical properties of the frozen soil interface based on the general shear stress-displacement constitutive model. According to the variation laws of parametersa, b, and c in Table 2, further fitting analysis of model parameters with thawing temperature and water content can lead to a unified refined expression as shown in Table 3, in which t denotes the thawing temperature, and w denotes the water content of the soil.Table 3
Empirical equations for model parameters considering hydrothermal coupling effect.
Normal stress (kPa)Empirical expressionCoefficient of determination100a=768.679e−0.234∗tw0.9480.9797lnb=1.985−0.059w−1−0.035tw−10.9006c−1=0.537−0.009tw−1−0.047w−10.9180200a=702.071e−0.206∗tw0.710.9124lnb=1.495−0.0146w−1−0.0212tw−10.9475c−1=0.608−0.002tw−1−0.036w−10.9293300a=769.071e−0.173∗tw0.6230.975lnb=1.557−0.018w−1−0.013tw−10.9591c−1=0.545−0.002tw−1−0.022w−10.9368400a=633.844e−0.186∗tw0.4340.9639lnb=1.568−0.025w−1−0.021tw−10.8730c−1=0.518−0.003tw−1−0.012w−10.9266Figure11 and Table 4 show the comparison between the curves fitted by Gompertz mathematical model and the experimental results under 100 kPa normal stress. It can be seen that the results of the direct shear tests are in better agreement with the Gompertz function curves considering the temperature-moisture coupling effect. In the initial stage of shear, the curves showed a nonlinear variation. It is because of the thin ice layer at the contact surface sliding in contact with the concrete surface when the shear stress is small under negative temperature conditions. With the increase of shear displacement, the thermal equilibrium state of the contact surface is broken, and some ice crystals absorb heat and undergo phase change when the contact surface is in a stable shear state. When the ice crystals are close to a completely destroyed state, the increase rate of shear stress decreases gradually with the increase of shear displacement. The constitutive model considering the coupling effect of temperature and moisture has good applicability to describe the shear stress-displacement curves for frozen soil-concrete interfaces.Figure 11
Fitting curves of shear stress-displacement under 100 kPa normal stress: (a) -1°C; (b) −2°C; (c) −3°C.
(a)(b)(c)Table 4
Evaluation of the model considering temperature and water content under 100 kPa normal stress.
Water content (%)Shear temperature (°C)−3−2-1Evaluation factor (%)βEvaluate resultEvaluation factor (%)βEvaluate resultEvaluation factor (%)βEvaluate result1487.18Qualified89.43Qualified84.44Unqualified2088.71Qualified88.17Qualified90.14Good2687.17Qualified85.93Qualified85.01Qualified3287.84Qualified82.29Unqualified90.96Good


## 6.1. Applicability of Gompertz Model

The group pile composite foundation in the permafrost areas is mainly loaded by the self-weight of embankment and the vehicle load, which is transferred downward through the pile-soil interaction. Therefore, determining the shear strength of the permafrost-pile interface is an indispensable link in the calculation of the foundation bearing capacity. In this study, only the part before which the shear stress-displacement curve reaches its peak is considered, and the part after which the brittle damage occurs is not considered. According to the above analysis, the shear stress-displacement curve before reaching the peak strength has a weak S-shaped trend. The existing theoretical models, such as the hyperbolic model, the elastic-plastic theory model, and the damage model, cannot respond well to the nonlinear deformation stage of displacement at low shear stress [22–24]. The Gompertz model curve is based on the growth process of things, i.e., from a slow growth at the beginning to a rapid growth in the middle and then to a basic steady state at the end. The growth process described by this curve is similar to the trend of the shear stress-displacement curve of the frozen soil-concrete interface in this study, and the Gompertz model equation [25] is shown in(1)τ=aexp−bexp−cδ,where τ is the shear stress, δ is the shear displacement, b,c is the model parameter, and a is the peak value of shear stress in the shear stress-displacement curve.To evaluate the quality of the fitting curve, the correlation factorβ [26] is introduced, which is defined as follows:(2)β=1−1n∑δi−δiδi,where δi is the shear stress of the predicted samples, δi is the shear stress of the observation samples, and n is the number of samples participating in the evaluation. Because of the difference of samples in the complete plastic stage of the shear stress-displacement curves, the values of the calculated correlation factor β vary accordingly. The evaluation criteria are established to evaluate the fitting effect, as shown in Table 1.Table 1
Evaluation standard of the correlation factor in the fitting model.
Evaluation factorEvaluation criterionExcellentGoodQualifiedUnqualifiedβ≥0.95≥0.90≥0.85<0.85The experimental data is brought into (1) to obtain several sets of δi and δi, and then the obtained sets are brought into (2) to obtain the correlation factor. The evaluation results are shown in Table 2. The analysis of the simulated data of the shear stress-displacement relationship shows that the values of the model fitting correlation factor β are greater than 0.90, and the results are good or excellent. It indicates that the Gompertz model is suitable for simulating the first half of the direct shear test curves of the interface between frozen soil and concrete.Table 2
Data simulation and evaluation of direct shear tests.
Temperature (℃)Water content (%)Normal stress (kPa)Model equationτ=aexp−bexp−cδEvaluation factorβEvaluate resultabc-114100150.8296.5854.7070.9741Excellent200180.5265.8163.3550.9717Excellent300245.9814.4252.3810.9849Excellent400271.3653.9071.9290.9672Excellent20100227.0823.9882.6290.9779Excellent200283.7595.2502.5860.9774Excellent300314.0424.4012.0350.9849Excellent400377.7094.6062.2840.9322Good26100258.7695.3492.5720.9702Excellent200331.1134.1801.8670.9133Good300396.6084.6141.9510.9551Excellent400441.8915.8042.1240.9534Excellent32100310.5174.3262.6870.9640Excellent200360.5784.5542.3570.9878Excellent300452.1744.3412.3260.9843Excellent400476.6393.6982.0400.9981Excellent-214100166.7186.114253.528560.9685Excellent200243.2744.633892.54360.9533Excellent300324.4365.241312.314060.9523Excellent400413.5775.234732.130340.9992Excellent20100268.9615.268452.680010.9541Excellent200412.9015.436172.137960.9726Excellent300430.1845.114932.283170.9868Excellent400457.3664.94621.811810.9578Excellent26100355.9215.774992.213450.9492Good200421.0935.49622.512830.9998Excellent300505.8516.215871.94110.9888Excellent400524.736.503022.053040.9843Excellent32100415.0735.866822.570550.9772Excellent200449.9225.147572.15990.9964Excellent300523.6395.033992.185070.9969Excellent400555.2156.048732.244820.9791Excellent-314100235.3856.369993.048770.9736Excellent200281.7666.841273.353520.9329Good300359.5175.377182.61250.9553Excellent400479.766.20762.271530.9573Excellent20100320.3867.024632.603070.9166Good200423.8918.15592.530910.9465Good300495.9425.132592.271110.9992Excellent400559.5185.791722.230520.9791Excellent26100446.3765.210851.848940.9579Excellent200490.2555.227572.080020.9365Good300559.5394.601161.893230.9982Excellent400611.7955.496322.04730.9460Good32100505.9427.509742.31930.9681Excellent200581.9125.868671.975480.9395Good300624.695.020871.859750.9226Good400657.7714.585641.761870.9463Good


## 6.2. Establishment of Shear Stress-Displacement Relationship Model considering Temperature and Water Content

The physical properties and stress state on the interface will change as the thawing temperature and moisture content change. In the process of freezing, moisture migrates to the contact surface under the effect of the temperature gradient, and the difference of water content significantly affects the formation area of ice crystal structure. Negative temperature is the controlling factor affecting the unfrozen water content and ice crystal content of the interface, which affects the cementation strength of the ice crystals and concrete surface by changing the ice and water equilibrium. Thus, the temperature and water content are key factors in the frozen strength of the soil-structure interface in permafrost regions. The engineering problems arising from foundations are the result of the disruption of the soil-structure hydrothermal equilibrium. Therefore, it is necessary to consider the coupling effects of temperature and moisture on the mechanical properties of the frozen soil interface based on the general shear stress-displacement constitutive model. According to the variation laws of parametersa, b, and c in Table 2, further fitting analysis of model parameters with thawing temperature and water content can lead to a unified refined expression as shown in Table 3, in which t denotes the thawing temperature, and w denotes the water content of the soil.Table 3
Empirical equations for model parameters considering hydrothermal coupling effect.
Normal stress (kPa)Empirical expressionCoefficient of determination100a=768.679e−0.234∗tw0.9480.9797lnb=1.985−0.059w−1−0.035tw−10.9006c−1=0.537−0.009tw−1−0.047w−10.9180200a=702.071e−0.206∗tw0.710.9124lnb=1.495−0.0146w−1−0.0212tw−10.9475c−1=0.608−0.002tw−1−0.036w−10.9293300a=769.071e−0.173∗tw0.6230.975lnb=1.557−0.018w−1−0.013tw−10.9591c−1=0.545−0.002tw−1−0.022w−10.9368400a=633.844e−0.186∗tw0.4340.9639lnb=1.568−0.025w−1−0.021tw−10.8730c−1=0.518−0.003tw−1−0.012w−10.9266Figure11 and Table 4 show the comparison between the curves fitted by Gompertz mathematical model and the experimental results under 100 kPa normal stress. It can be seen that the results of the direct shear tests are in better agreement with the Gompertz function curves considering the temperature-moisture coupling effect. In the initial stage of shear, the curves showed a nonlinear variation. It is because of the thin ice layer at the contact surface sliding in contact with the concrete surface when the shear stress is small under negative temperature conditions. With the increase of shear displacement, the thermal equilibrium state of the contact surface is broken, and some ice crystals absorb heat and undergo phase change when the contact surface is in a stable shear state. When the ice crystals are close to a completely destroyed state, the increase rate of shear stress decreases gradually with the increase of shear displacement. The constitutive model considering the coupling effect of temperature and moisture has good applicability to describe the shear stress-displacement curves for frozen soil-concrete interfaces.Figure 11
Fitting curves of shear stress-displacement under 100 kPa normal stress: (a) -1°C; (b) −2°C; (c) −3°C.
(a)(b)(c)Table 4
Evaluation of the model considering temperature and water content under 100 kPa normal stress.
Water content (%)Shear temperature (°C)−3−2-1Evaluation factor (%)βEvaluate resultEvaluation factor (%)βEvaluate resultEvaluation factor (%)βEvaluate result1487.18Qualified89.43Qualified84.44Unqualified2088.71Qualified88.17Qualified90.14Good2687.17Qualified85.93Qualified85.01Qualified3287.84Qualified82.29Unqualified90.96Good


## 7. Conclusions

The direct shear behaviors of the frozen soil-structure interface during the thawing process were investigated by manipulating silty clay at different rising frozen temperatures, various water content, and various normal stress conditions. The shear stress-displacement relationships were measured. The whole process of shear behaviors can be divided into 3 stages, i.e., the prepeak stage with growing shear stress, the postpeak stage with deep dropping shear stress, and the shear stress reconstruction stage. The following conclusions can be drawn:(1)
In the prepeak stage, the shear stress-displacement curves present an approximate “S“ shape. In the postpeak stage, there is a rapid decline in the shear stress-displacement curves. In the shear stress reconstruction stage, the residual frozen strength is formed, and it is controlled by the secondary cementation strength of ice crystals, the cohesive force, and the frictional force between soil particles and the concrete surface.(2)
Within the factor ranges in these tests, the peak frozen strength had a positive linear dependence on the normal pressure and rising frozen temperature, and it increases logarithmically with water content. It is because of the fact that the water content can affect the development of ice crystals. With the increase of water content, the ice crystal structure area of the contact surface is limited. The effect of temperature on shear stress is mainly attributed to the change of unfrozen water content at the interface.(3)
The residual frozen strength had a positive linear dependence on the normal pressure but had a negative linear dependence on the water content. It is because the thermal equilibrium of the interface was disturbed by the frictional behavior in the shear process, resulting in an increase in unfrozen water content of the contact surface. The residual frozen strength is positively correlated with the rising temperature with 14% water content, while it is negatively correlated with higher water content. It is closely related to the content of unfrozen water in the sliding process.(4)
The Gompertz model considering the coupling effect of temperature and moisture has good applicability to describe the shear stress-displacement curves for frozen soil-concrete interfaces during the thawing process.



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*Source: 1755538-2022-03-15.xml*