Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions

Tian, Rongyan; Huang, Xiaoming; Zhao, Runmin; Luo, Haoyuan

doi:10.3390/buildings14113612

Open AccessArticle

Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions

¹

College of Engineering, Tibet University, Lhasa 850000, China

²

School of Transportation, Southeast University, Nanjing 211189, China

³

School of Transportation, Kunming University of Science and Technology, Kunming 650031, China

^*

Author to whom correspondence should be addressed.

Buildings 2024, 14(11), 3612; https://doi.org/10.3390/buildings14113612

Submission received: 16 October 2024 / Revised: 6 November 2024 / Accepted: 12 November 2024 / Published: 13 November 2024

(This article belongs to the Section Building Structures)

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Abstract

:

In low-temperature stable permafrost regions, both active and passive cooling measures are commonly employed to ensure the long-term stability of highway structures. However, despite adopting these measures, various types of structural issues caused by permafrost degradation remain prevalent in high-grade highways. This indicates that in addition to preventing permafrost melting, structural reinforcement of the foundation is still necessary. Based on the analysis of the long-term foundation temperature field and settlement using the finite element method, which was validated through an indoor top-down freeze–thaw cycle test, this paper explores, for the first time, the feasibility of applying geosynthetic-encased gravel pile composite highway foundations—previously commonly used for permafrost destruction—in low-temperature stable permafrost areas where permafrost protection is the primary principle. By analyzing the long-term temperature field, settlement behavior, and pile–soil stress ratios of permafrost foundations influenced by both the highway structure and composite foundation, it was found that when the pile diameter is 0.5 m, pile spacing is 2 m, and pile length is 11 m, the mean monthly ground temperature of the permafrost foundation will not be significantly affected. Therefore, the properly designed geosynthetic-encased gravel pile composite highway foundation can be adopted in low-temperature stable permafrost regions where permafrost protection, rather than destruction, is required.

Keywords:

geosynthetic-encased gravel pile; finite element method; permafrost area; foundation temperature field; long-term settlement

1. Introduction

In the field of road structures in cold regions, it is commonly accepted that black asphalt pavement can lead to excessive heat accumulation in permafrost foundation, resulting in faster thawing of frozen soil and damage to road structures due to a lack of foundation bearing capacity [1,2,3]. To address this issue and ensure the stability of road structures in permafrost areas, there are two principles that have been widely accepted, the “protection principle” and the “damage principle” [4]. The “protection principle” aims to reduce the temperature of permafrost under road structures to protect the frozen soil from thawing. This principle is preferred in low-temperature stable permafrost regions [5]. However, in degraded warm permafrost or seasonal frozen ground areas, destructive measures, such as replacement filling, electricity or steam heating, and cement fly ash gravel (CFG) pile composite foundations, are needed to guarantee the stability of foundations [6,7] and are therefore called the “damage principle”.

For weak foundations, such as those consisting of soft or frozen soil, a common approach is to use a pile composite foundation. Previous research has demonstrated that incorporating piles into the foundation and utilizing geosynthetic materials in embankments can significantly enhance the stability of highway structures [8]. Furthermore, a well-arranged pile group can not only better support vertical loads but also effectively resist horizontal loads [9]. In Chinese degraded permafrost areas, there have been studies on pile composite foundations such as gravel pile composite foundations, CFG pile composite foundations, geosynthetic-encased gravel pile composite foundations, and cement concrete pile foundations [10,11,12]. These composite foundations were applied in degraded permafrost areas, and most of their structures were designed based on the function of thawing and eliminating frozen soil. For highway structures in low-temperature stable permafrost areas, such as the Qinghai–Tibet Plateau in China, there are also some researchers who have studied the application of pile composite foundations [13,14], but most of those studies focused on cement concrete piles and their bearing capacity. In terms of the effect of composite foundations on permafrost temperature, previous studies usually focus on short-term permafrost temperature change and refreezing speed during and after construction, and there is a lack of research on the long-term temperature field change. Therefore, active cooling measures are still preferred as the main measures to ensure structural stability in highway structures in low-temperature stable permafrost regions. However, the engineering practices in the Gonghe–Yushu Expressway show that it is still difficult to ensure structural stability with active cooling measures alone [15].

Although there have been studies on the use of pile composite foundations in permafrost regions, these studies have certain limitations. Firstly, rigid piles, commonly used in these studies, are not well-suited to permafrost conditions. The hydration-hardening process of rigid piles generates significant heat, leading to the thawing of permafrost, and the low ground temperatures impede the hydration-hardening and maintenance of these piles [16,17]. Additionally, ensuring the durability and structural integrity of rigid piles under freeze–thaw cycles in surrounding soil poses a challenge [18]. Consequently, the application of rigid piles is severely restricted in low-temperature stable permafrost regions, where safeguarding permafrost integrity is paramount.

In contrast, geosynthetic-encased gravel piles do not undergo exothermic hydration processes and have a lower thermal impact on permafrost ground temperatures. As discrete and flexible structures, they exhibit greater resistance to freeze–thaw cycles, provided the geosynthetic remains intact. Therefore, geosynthetic-encased gravel piles are more suitable for low-temperature stable permafrost regions compared to the rigid piles used in previous studies. However, research on the application of gravel pile composite foundations in permafrost regions is sparse and mostly focused on warmer degrading permafrost areas, where gravel piles aid in drainage and soil consolidation, crucial for structural stability [11]. In contrast, in low-temperature stable permafrost regions, where the soil remains frozen for most of the year, soil consolidation processes are less pronounced.

Considering these limitations, this study explored, for the first time, the feasibility of applying geosynthetic-encased gravel pile composite foundations for highways in areas where permafrost protection is the primary objective and assessed their long-term effectiveness in environments dominated by cryogenic freezing conditions. The effects of different pile parameters on the maximum foundation settlement, uneven foundation settlement, long-term temperature field, and pile–soil stress ratio were investigated. Finally, this study proposed several suggestions for the design of geosynthetic-encased gravel pile composite highway foundations applied in low-temperature stable permafrost areas in the future.

2. Materials and Methods

With commercial software Abaqus 2021, this study used the finite element method (FEM) to calculate the long-term deformation of pile composite permafrost foundation because experimental studies are usually complicated, extremely costly, and less repeatable. The constitutive model of frozen soil used in this study has been verified in previous studies [19,20,21], and the geosynthetic-encased gravel piles were verified with indoor experiments.

2.1. Thermal Properties and Mechanical Constitutive Model of Frozen Soil

Accurate calculation of the permafrost temperature field is essential for determining its mechanical properties and, consequently, for calculating long-term foundation deformation. The governing equations for the thermal parameters of permafrost used in this study were proposed and validated in previous studies by the authors [19,21], which are derived based on a two-dimensional partial differential equation of unsteady heat conduction that takes into account the ice–water phase transformation and water migration. A brief derivation process is listed in Appendix A.

There are obvious nonlinearity and elastic–plasticity properties in the mechanical characteristics of soil. Therefore, plenty of researchers have proposed a corresponding strength theory and elastic–plastic constitutive model for the nonlinear mechanical properties of soil. For example, Lu et al. [22,23] proposed a fractional elastoplastic constitutive model based on the 3D fractional plastic flow rule, which has been proved to be effective with a few material parameters. In the research scope of this study, the elastic–plastic properties of soil can be significantly affected by freeze–thaw conditions. Therefore, it is necessary to estimate the frost heave as well as the loss of elastoplastic strength due to thawing. The elastic–plastic constitutive model (E-P model) of frozen soil developed by Zhang et al. [20], which considers the influence of freeze–thaw cycles, was adopted in this study. A brief description of this constitutive model is given in Appendix B. This constitutive model fully considers the changes in mechanical properties and the corresponding elastic–plastic deformations of permafrost in different freezing states, and it has been proved to be effective in predicting the long-term freeze–thaw deformations of permafrost foundations by Fukuda et al. in 1997 [24]. Furthermore, given that the mechanical properties of gravel piles are strongly influenced by confining pressure, this study further validated the accuracy of confining pressure calculations using the constitutive model under freeze–thaw cycling conditions through indoor tests.

2.2. Material and Model Size

2.2.1. Equipment, Materials, and Sample Size of Indoor Test

To verify the accuracy of the thermal property controlling equations, as well as the constitutive model of permafrost adopted in this study, an indoor freeze–thaw cycle test was conducted on frozen soil specimens using a DX-40 freeze–thaw cycle test chamber in the laboratory facilities of the School of Engineering, Tibet University, as shown in Figure 1. The chamber was produced by Beijing Newlead Science & Technology Co., Ltd. (Beijing, China) in 2005, featuring a maximum power capacity of 3 kW and a temperature control range of ±40 °C. The frozen soil samples of the indoor freeze–thaw cycling validation tests in this study were obtained from the vicinity of the K3 + 016 section of the G109 highway, where the average annual ground temperature ranges from −4.0 °C to −1.0 °C. The soil sample was prepared according to the study of Qi et al. [25]. After the soil sample was collected, it was left to air dry for several days before being crushed. The sample was then sieved through a 2 mm mesh, and the resulting material was used as the experimental sample. The sample was then mixed with a measured amount of distilled water to achieve a target water content of approximately 30%.

Regarding the permafrost foundation as a cuboid, the impact of environmental thermal disturbances, such as solar radiation, air temperature, and heat absorption by the asphalt pavement, is primarily concentrated on its top surface, while the other 5 surfaces remain under relatively stable thermal conditions. Consequently, a top-down freeze–thaw cycle indoor test was developed to verify the accuracy of the thermal property controlling equations, as well as the constitutive model of frozen soil. In the indoor freeze–thaw cycle test, a high-strength Plexiglas cylindrical container was employed to house the soil specimens. The container had an internal diameter and height of 35 cm each, constructed with an open top. To facilitate a top-down freeze–thaw cycle for the soil sample within the container, the side walls and bottom of the container were tightly insulated with insulating material. In order to facilitate the installation of a soil pressure sensor on the surface of the pile, a cuboid model pile with flat surfaces rather than a cylindrical pile was adopted in the experiment. A wooden cuboid model pile with dimensions of 5 cm by 5 cm by 30 cm was embedded in the center of the soil specimen. Within the model, two temperature sensors and one soil pressure sensor were embedded. The temperature sensor (shown in Figure 2a) used in the study had a measuring range of −50 °C to 100 °C, with a measurement accuracy of 0.15 °C. The soil pressure sensor (shown in Figure 2b) was a resistance strain sensor with a measuring range of 0.5 MPa and a measurement accuracy of <0.3% full scale (F.S.). The specimen dimensions and sensor positions are presented in Figure 3, with the pressure sensor affixed to the side wall of the model pile; the horizontal compression force exerted by the soil on the pile’s side wall during freeze–thaw cycles can thus be measured. In order to accurately measure the horizontal pressure generated by soil frost heave on the pile and ensure that the change in the measured value of the soil pressure sensor during the freeze–thaw cycles was only caused by frost heave, the sample was first static until the soil pressure to the degree where it no longer changed significantly after the sample was generated and the sensor was buried and the soil settlement reached a stable state. In the non-freezing state, the pressure on the pile body does not change significantly. Therefore, during the freeze–thaw cycles, the pressure value after subtracting the initial value of the pressure sensor was then regarded as the soil pressure perpendicular to the pile surface caused by the frost heave.

Following the assembly of the specimen and sensors, the initial temperature was measured, indicating a relatively uniform temperature of approximately 15 °C throughout. Subsequently, the specimen underwent the freeze–thaw cycle test within the automatic low-temperature freeze–thaw tester, housed within the test chamber. The indoor test spanned 288 h, encompassing one-and-a-half freeze–thaw cycles, with data from each sensor recorded every 24 h. The 0–144 h was the freezing duration with a −27 °C freezing temperature; the 144–192 h was the thawing duration with a 10 °C thawing temperature; and the 192–288 h was another freezing duration with a −27 °C freezing temperature.

2.2.2. Model Size in FEM

To maintain consistency in the specimen size of the indoor test mentioned above, a 2D square FEM model measuring 35 cm by 35 cm was established according to Figure 3.

Since this study introduced the indoor tests conducted by Mo [26] to verify the mechanical property of the geosynthetic-encased gravel pile FEM model, the verification model for the geosynthetic-encased gravel pile in this study was a 2D rectangle in order to align with the indoor tests conducted in Mo’s study. Two types of composite foundations with geosynthetic-encased gravel piles (floating and end-bearing) were selected to verify the accuracy of the FEM, except for the soft soil foundation without piles. The 2D model sizes for all three models are shown in Figure 4.

In this study, the cross-section at K348 + 100 of the Gonghe–Yushu Expressway was used to calculate the long-term embankment deformation. The embankment top had a width of 14.2 m and the slope of the embankment side was 1:2. The crushed-rock interlayer in the embankment was 1.5 m thick and was located at the bottom of the embankment structure. Figure 5 shows the geometry and size of the numerical model used in this study. The modulus, arrangement, and size of the piles were categorized into 9 groups according to the L9_3_4 orthogonal table [27], as shown in Table 1. The values of these parameters at different levels in Table 1 were determined based on relevant studies [28,29,30] to ensure that their parameter ranges were reasonable.

2.2.3. Material Parameters in FEM

Both material mechanical parameters as well as the thermal parameters are detailed in Table 2, Table 3, Table 4 and Table 5, where the soil parameters for the E-P model were determined by the water content curve of the soil specimen in this study as well as the parameters in the literature [21], while some of them were also calibrated according to the FEM-calculated freezing force results to make sure that an accurate pile confining pressure can be calculated in the embankment and composite foundation models. The meanings of the abbreviations in Table 2 and Table 5 can be found in Appendix A and Appendix B.

2.3. Boundary and Initial Conditions of FEM

2.3.1. Boundary and Initial Conditions in Verification Models

According to the indoor freeze–thaw cycle testing described in Section 2.2.1, except for the top surface, all the other boundaries of the FEM were set to be completely adiabatic and completely fixed in all directions. Since the initial temperature at each point of the specimen measured at the beginning of the test was 15 °C, the initial temperature of the FEM model was also set at 15 °C.

For the gravel pile verification model, the two sides of the verification model in this study were fixed horizontally, while the bottom of the model was completely fixed in all directions. The loading plate was modeled as a rigid body to reduce computation costs.

2.3.2. Boundary and Initial Conditions in Formal Analysis Models

The embankment and composite foundation model maintained consistent heat convection and displacement boundary conditions, as detailed in the authors’ previous study [21]. Heat transfer was governed by second and third types of boundary conditions. Convection coefficients for asphalt pavement and natural ground varied with wind speed, while an average atmospheric temperature increase of 2.6 degrees over 50 years was assumed, accounting for global warming. Further specifics on both heat and displacement boundary conditions can be referenced in the literature [21].

The initial temperature field was established with uniform temperatures assigned to each layer, based on ground temperature measurements recorded in the summer of 2020 at the K3 + 016 section of the Qinghai–Tibet Highway, as listed in Table 6.

The initial stress field was determined through a geo-stress balance process, outlined as follows:

The permafrost was initially assumed to be in a completely frozen state. Applying gravity load on the embankment and composite foundation model, a static analysis yielded the first stress and displacement field, typically characterized by significant displacement values.
Utilizing the initial temperature field from Table 6, another model was established incorporating a frozen soil constitutive model. The stress field obtained from the previous step served as the predefined field. Employing a small time increment (1e−11 months in this study) for static analysis, a new stress and displacement field was derived. This process was iterated until the maximum displacement value in the final field was sufficiently small, indicating geo-stress equilibrium.
The stress field obtained in step 2 was then adopted as the initial stress field and used as the predefined field in subsequent calculation models.

Figure 6 illustrates one of the geo-stress balance processes in this study. It is noteworthy that in the initial model, the maximum vertical displacement reached 14.5 cm. After completing the geo-stress balance process, however, this maximum vertical displacement was reduced to 1.2 mm.

3. Results and Discussion

3.1. Verification of FEM

3.1.1. Verification of Finite Element Gravel Pile Model

In order to exclude the influence of soft soil in the validation model on the calculated results and validate the accuracy of the geosynthetic-encased gravel pile model, the study first validated the FEM model using the indoor test of soft soil foundation without piles in Mo’s study [26]. The results of both the indoor test and FEM calculation are shown in Figure 7.

As shown in Figure 7, both the soft soil deformation results from the indoor tests and finite element calculations exhibit significant nonlinearity, and the two curves show good agreement at both the lowest and highest levels of applied load. However, noticeable discrepancies arise at intermediate load levels, indicating that the numerical calculations introduce some errors during the initial yielding phase. This issue stems from the fact that in the validation model, the loading plate and soft soil are represented as a single entity with two different material properties, rather than as two separate components. Consequently, the soft soil under the loading plate is fully bonded to the plate without any relative sliding in the numerical model. In contrast, during the indoor tests, the soil beneath the loading plate can slide laterally. Once the elastic phase concludes, further loading causes the soil at the bottom of the plate to be extruded laterally due to shear yielding, resulting in greater settlement in the indoor tests compared to the finite element method (FEM)-calculated values during the early stages of yielding. As loading continues and more soil beneath the plate is extruded, the surrounding soil becomes further compacted. This makes lateral sliding of the soil under the loading plate less likely, so that in later stages of loading, vertical displacement in the indoor test is primarily due to the deformation of the soil during plastic yielding. Consequently, the experimental and calculated values align more closely at this stage. Despite the aforementioned discrepancies in the numerical model, the overall results depicted in Figure 7 remain in good agreement with the test results. Therefore, it was concluded that the soft soil FEM model, with the parameters listed in Table 2, accurately describes the mechanical properties of soft soil in the indoor test.

The results of the two different types of composite foundations with geosynthetic-encased gravel piles (floating geosynthetic-encased gravel piles and end-bearing geosynthetic-encased gravel piles) are shown in Figure 8, which includes the FEM calculation results and indoor test results.

Figure 8 shows that the settlement of the floating pile is significantly greater than that of the end-bearing pile under the same load, indicating that the bearing capacity of the end-bearing pile foundation is better. The load–settlement curve of the floating pile also exhibits more obvious nonlinearity compared to the end-bearing pile. In the indoor test load–settlement curve of the floating pile, there is an obvious turning point, while the FEM curve is much smoother. This may be because the pile modeled in the FEM calculations is slightly softer, causing the mechanical properties of soft soil to play a more important role in the FEM calculation. The same reason explains the slightly larger settlement of the end-bearing pile in the FEM calculation results compared to the indoor experimental results when the load is not large, as shown in Figure 8b. However, the overall trend in the two curves remains consistent and the values are in good agreement, proving the accuracy of the finite element pile model. The softer finite element pile model could also produce relatively conservative and safe calculation results.

3.1.2. Verification of Finite Element Frozen Soil Model

The measured temperatures as well as the corresponding temperatures calculated by the FEM are shown in Figure 9.

As illustrated in Figure 9, a notable disparity exists between the test results and the FEM calculations, particularly in terms of cooling and warming rates. This contrast is particularly pronounced during the initial freezing period, where the FEM-calculated rates are considerably slower than the measured results from the indoor tests. Moreover, the FEM-calculated lowest temperature value during the 288 h is higher than the measured data, while the calculated highest temperature value is lower than the measured data.

This outcome can be rationalized by examining the boundary conditions employed in the FEM calculations. The model’s boundaries, apart from the upper boundary, are set to be entirely adiabatic, meaning that heat flow only occurs through the upper boundary of the model. In contrast, in the actual tests, while heat-insulating materials cover the other boundaries (except the upper boundary), complete avoidance of heat exchange on those boundaries is not achievable. Consequently, the actual tests exhibit greater heat exchange between the model and its surroundings compared to the FEM calculation model. This discrepancy contributes to the observed differences in temperature trends and values between the FEM predictions and the experimental measurements.

During the freeze–thaw cycles, due to the change in the soil freezing state, the soil volume changes constantly, so the soil pressure perpendicular to the pile surface also changes with the change in freezing and thawing state. In the indoor test, as is explained in Section 2.2.1, this pressure can be measured by the soil pressure sensor. In the FEM calculation process, since the E-P constitutive model considered the volumetric freezing expansion and shrinkage of soils during the freezing process by the variation in porosity, as is explained in Appendix B, the pressure on the pile surface caused by the frost heave of soil during freeze–thaw cycles can also be determined by calculating the horizontal pressure on the pile surface. Figure 10 plots the lateral frost heave force results of both the FEM and indoor test-measured results.

While there is a more noticeable difference between the FEM calculations of the transverse frost heave force and the experimentally measured results compared to the temperature values in Figure 9, it is important to note that both sets of results are within the same order of magnitude. Additionally, their trends exhibit a basic similarity. These observations suggest that despite the pronounced discrepancy in the transverse freezing force, the adopted frozen soil heat transfer control equations, elastic–plastic constitutions, and the corresponding FEM models in this paper remain reliable.

3.1.3. Verification of Model Convergence

In this section, different mesh sizes were employed for structure 1, and the calculation results using these varying mesh sizes were analyzed to check the convergence of the numerical model. The calculation results with different mesh sizes are shown in Figure 11.

Figure 11 shows that the calculated maximum settlement increases as the mesh size decreases, indicating a slight influence of mesh size on the calculation results. However, these variations are no more than 0.05%, suggesting that the model is convergent. Additionally, when the mesh size is smaller than 0.5 m, the calculation results become more stable compared to those with a 0.1 m mesh size. Therefore, a mesh size of 0.5 m was adopted in this study.

3.2. Temperature Field of Pile Composite Permafrost Foundation

Compared to the traditional road permafrost foundation, the construction and existence of piles result in a significantly different temperature field in composite permafrost foundations. While cement fly ash gravel (CFG) piles have better integrity, higher modulus, and higher strength than gravel piles, the exothermic cement hydration reaction during its hardening poses a challenge. In seasonal permafrost areas, where the foundation treatment principle is to thaw the permafrost in advance, this exothermic process is helpful for the foundation treatment. However, in low-temperature stable permafrost regions, where the foundation treatment principle is to cool the permafrost and prevent it from thawing, known as the “protection principle”, the exothermic process of CFG piles could have a harmful effect on the temperature field within the permafrost [31,32,33]. As a result, the curing process and formation of the strength of CFG piles would be difficult due to the low temperature of the stable permafrost surrounding them [34]. Some researchers have also noted that it is not recommended to use the cast-in-place bored piles with the concrete hydration process in permafrost ground where the mean annual ground temperature (MAGT) is lower than −3.5 °C [35]. Hence, in this study, gravel piles were adopted rather than CFG or cement concrete piles.

Although gravel piles do not have an exothermic hydration process like CFG piles, they still affect the temperature field of the permafrost foundation due to the initial temperature of the pile material, the thermal disturbance during the construction process, and the differences in the thermal parameters of the pile material. Therefore, to account for this temperature influence, the FEM calculation considered setting the initial temperature of the embankment and the pile structure to 4 °C. According to previous research [36,37], the MAGT is defined to be the temperature at a depth of 15 m below the embankment surface. In this study, the mean monthly ground temperature (MMGT) was calculated at depths of 15 m below the embankment surface and 12 m below the natural surface (15 m minus the embankment height of 3 m). Figure 12 shows the MMGTs of different foundations.

Despite starting with the same MMGT, significant differences in MMGTs can still occur over time due to various highway structures. In comparison to natural permafrost ground, MMGTs under all types of highway structures are notably higher, and the use of geosynthetic-encased gravel piles further increases ground temperature. Figure 12 illustrates that while the discrepancies between MMGTs lessen over time, they will continue to persist.

For structure 3, which has the most significant thermal effect on the MMGT, the pile structure had the greatest impact on the ground temperature under the foundation during the first 18 months. The MMGT reached its peak during this time due to the warming effect of the piles on the ground temperature, which mainly occurred in the first 18 months. After the 19th month, the MMGT gradually decreased and eventually reached a new thermal equilibrium in the sixth year. It then began to increase again due to the influence of global warming. This finding is consistent with the study by Zhao [38], which showed that the melting of composite foundations caused by the thermal influence of piles is greatest at the end of the first year. However, the piles in Zhao’s study are concrete pipe piles, which had a greater impact on the foundation temperature due to the exothermic hydration of cement. As a result, the composite foundation in that study did not reach a new thermal equilibrium until the 10th year. In general, it can be concluded in Figure 11 that the impact of gravel piles on the permafrost temperature field is mostly focused on the early time period, while the long-term permafrost temperature field is not influenced significantly. This conclusion is consistent with previous research [11]. Figure 13 depicts the temperature fields at the end of the 1st, 35th, and 236th months for structure 3 compared to the structure without piles. It is observed that without piles, the permafrost beneath the embankment rapidly refroze after construction due to the cold atmosphere and surrounding frozen soil. Within one month, the melting core under the embankment had noticeably diminished.

In contrast, for structure 3, the initial heat from the piles significantly slows down the refreezing process. Even after one month, the melting core remained notably larger and concentrated around the pile areas, with the bottom of the melting core showing distinct undulations around the pile ends. By 35 months, when much of the initial pile heat had dissipated, there was little difference in size between the two melting cores. This suggests that the primary impact of gravel piles on the permafrost temperature field, especially in the early stages, stems from the initial heat generated by the piles rather than changes in the thermal properties of the permafrost foundation caused by the piles.

At the end of the 236th month, during the warm season of the 20th year following the construction of the highway, Figure 13 clearly illustrates that the melting lines beneath the two structures exhibit notably distinct shapes. By this time, the initial heat within the piles had dissipated, emphasizing that the differing thermal parameters of the piles in permafrost primarily account for the disparity in melting lines at this stage.

The embankment acts as a thermal isolation layer, typically causing the melting line beneath it to assume a convex shape during warm seasons. In contrast, when piles are used, Figure 13 shows that the melting line no longer exhibits a pronounced convex shape. This observation suggests that the thermal conductivity of the piles exceeds that of the permafrost. Consequently, the geosynthetic-encased gravel pile composite foundation possesses a higher overall thermal conductivity than a pure permafrost foundation, thereby reducing the embankment’s thermal insulation capacity.

Considering that the impact of gravel piles on the permafrost temperature field is mostly focused on the early time period, this study selected the maximum value of the MMGT during the first 18 months, which was referred to as the “initial ground temperature”, as the research object. The effect of different pile foundation parameters on the ground temperature was investigated using the orthogonal design method. The main effect plot for the initial ground temperature is shown in Figure 14.

According to Figure 14, the length of the pile has the greatest impact on the initial ground temperature. This can be easily understood, as the ground temperature monitoring point is located 12 m below the natural ground surface. The longer the pile, the closer the pile end is to the ground temperature monitoring point. Therefore, the higher the initial pile temperature, the more significant the influence on the ground temperature at the monitoring point.

The number of piles is the second most important factor that affects the initial ground temperature. This is because the variation in the number of piles has a greater impact on the foundation replacement rate compared to the variation in pile diameters (which range from 0.5 m to 0.7 m and are relatively small) in this paper. Increasing the number of piles can more significantly increase the foundation replacement rate, which leads to more initial heat and larger comprehensive foundation thermal conductivity.

Figure 14 shows that the increase in the modulus will lead to the decrease in the initial ground temperature. The reason for this phenomenon may be that the interaction among different factors could not be completely excluded in the analysis of orthogonal test results. After all, as a mechanical parameter, the pile modulus should not have any effect on the temperature field. Compared with the MMGT, whether the permafrost is frozen or not has a more pronounced effect on the mechanical property of the permafrost. According to the definition in previous research [39], the artificial permafrost table (APT) is defined as the depth of the maximum seasonal penetration of the 0 °C isotherm due to engineering activities. The APTs in this paper are calculated based on the natural ground surface depths, excluding the height of the embankment in the FEM model. Similarly, the permafrost table is defined as the depth of the maximum seasonal penetration of the 0 °C isotherm under the natural surface to be consistent with the APT. Thawing lines in the next 20 years are determined by the 0 °C isotherms under the natural ground and different foundations, as shown in Figure 15.

Similarly to the MMGT, the impact of the pile structure on the permafrost table is concentrated within the first two years. During this period, the thermal disturbance caused by the piles leads to a significant increase in the thaw depth of the frozen soil beneath the foundation during the summer months. Subsequently, the composite foundations, including the piles, gradually cool down due to the cold weather and the low temperature cooling of the surrounding frozen soil. As a result, the seasonal thaw depth of the permafrost gradually returns to normal levels, and the difference in the thaw depths of the permafrost tables under different foundations becomes less obvious.

The deepest annual artificial permafrost table under different foundations in 20 years can be obtained by interconnecting the deepest melting points of each year in Figure 15, as is shown in Figure 16.

After the first two years, the deepest annual artificial permafrost tables under all foundations, except for structure 3, returned to normal levels and gradually developed downward due to global warming. The degradation rate of the annual artificial permafrost table under each foundation was not significantly greater than that under the natural ground without embankment and foundation structures in the following 20 years. The difference in the permafrost table degradation rate among the different foundations, including the permafrost foundation without piles, was also not obvious. The influence of gravel piles on the thawing line of the permafrost foundation is concentrated in the first two years, and from the third year, the difference in the depth of the thawing line under each foundation would stabilize. This proves again that the heat brought by the construction process and the initial temperature of the piles are the key factors affecting the temperature field and melting line of the permafrost foundation, rather than the change in material properties caused by the replacement of frozen soil by piles.

The MAGT and MMGT represent temperatures at specific depths below the foundation, but they do not capture the spatial variability in the ground temperature across different depths influenced by the composite foundation. Figure 17 illustrates the changes in ground temperature along the depth at the centerline of the embankment, both at the beginning (13th and 20th month) and the end (229th and 236th month) of each of the four structures.

The impact of composite foundations on ground temperature follows a consistent pattern regardless of their type. Compared to a permafrost foundation without piles, the effect of piles on ground temperature is most pronounced in the initial stages, with colder weather showcasing a more noticeable influence than warmer conditions. Over time, the differences in ground temperature at various depths under different foundations become less apparent. This suggests minimal variance in thermal parameters between geosynthetic-encased gravel piles and permafrost and that changes in the comprehensive thermal characteristics due to the presence of these piles do not significantly alter the long-term temperature profile of the permafrost foundation.

Geosynthetic-encased gravel piles predominantly impact shallow ground temperatures more than deeper ones, especially within the range of pile length. However, their influence extends beyond the length of the piles; longer piles affect ground temperatures at greater depths. Figure 17 illustrates that structures 1, 5, and 9, all with identical pile lengths of 5 m but varying pile diameters and numbers, exhibit similar temperature influence ranges. This indicates that the extent of ground temperature influence under pile composite foundations primarily depends on the pile length.

3.3. Confining Pressure of Piles in Composite Foundation

Gravel pile, as a material composed of discrete particles without cohesion, has an axial strain determined by deviatoric stress. Therefore, for gravel piles, the axial bearing capacity is significantly affected by the confining pressure. According to Figure 15, when the depth does not exceed 4 m, the frozen soil in the foundation undergoes significant freeze–thaw cycles with the change in seasons, which causes the confining pressure around the gravel piles to alternate with the seasons. In winter, the permafrost freezes and the soil becomes stronger while expanding in volume, leading to an increase in the confining pressure of the gravel piles. In summer, the permafrost thaws and the strength of the soil decreases, while the volume shrinks, resulting in a decrease in the confining pressure. Taking the center pile in structure 1 as an example, according to the FEM calculation result in this paper, the fluctuation in the horizontal soil pressure at a depth of 1 m over a period of 20 years is shown in Figure 18.

Figure 18 shows that the horizontal soil pressure fluctuates significantly with the alternation of seasons, with a larger fluctuation amplitude over time. In winter, the confining pressure is significantly higher than in summer, which is consistent with the analysis presented above. However, this cyclic fluctuation in confining pressure can be detrimental to highway structures in permafrost areas. In summer, as the frozen soil in the foundation thaws and the bearing capacity weakens, gravel piles are needed to provide more bearing capacity. However, the confining pressure decreases at this time, which also weakens the bearing capacity of the gravel piles. To address this issue, the geosynthetic-encased gravel pile was adopted to prevent a decrease in the bearing capacity of the gravel piles in summer. It can be found in Figure 18 that the encasement of the geosynthetic eliminated the significant fluctuation in the confining pressure with the seasons, replacing it with a monotonically increasing trend. This trend is due to the growing thaw sinking deformation of permafrost foundations over time, which is caused by global warming and the heat-gathering effect of highway structures. As the foundation deformation increases, the radial expansion of the gravel piles under axial compression also increases, resulting in an increase in radial confining pressure. Therefore, geosynthetic encasement is an effective solution for designing and constructing highway structures in permafrost areas, as it helps to mitigate the negative effects of cyclic confining pressure fluctuations and improve the long-term stability of the structure.

3.4. Long-Term Settlement of Permafrost Foundation

Based on Table 1, the pile–soil stress ratio, the uneven foundation deformation, and the maximum foundation displacement were calculated for nine foundation structures. To demonstrate the impact of geosynthetic-encased gravel piles on permafrost foundation settlement, the deformation of the permafrost foundation without geosynthetic-encased gravel piles (structure 10) was also calculated in this study.

Figure 19 depicts the maximum MMGT for different foundations during the first two years, as well as the uneven foundation settlement and maximum foundation displacement for each foundation after 20 years. It is evident from Figure 19 that there is a strong correlation between the uneven foundation deformation value and maximum foundation displacement value. Additionally, the maximum MMGT shows a significant negative correlation with them.

Unlike the linear correlation between the uneven foundation settlement and the maximum foundation displacement, the correlation between the foundation settlement and the maximum MMGT is nonlinear. This indicates that in geosynthetic-encased gravel pile composite foundations for highway structures in permafrost areas, although smaller foundation deformations can be obtained at the cost of higher ground temperature, this optimization effect diminishes with the increase in ground temperature. As shown in Figure 19c, structure 3—with the largest pile diameter, pile number, and pile length in the study—has a maximum MMGT that is almost 40% higher than structure 4, which has the second-highest MMGT in the study. And structure 1—with the smallest pile diameter, pile number, and pile length—has the lowest maximum MMGT, except for the natural permafrost foundation. This is because the volume ratio of piles has an obvious influence on the MMGT. Since the initial temperature of the pile material is significantly higher than that of frozen soil, the larger the volume of piles in the frozen soil foundation, the higher the MMGT, and vice versa.

However, although the maximum MMGT of structure 3 is significantly higher than that of structure 4, the uneven foundation settlement of structure 3 is only 10.4% less than that of structure 4. Moreover, Figure 15 indicates that the artificial permafrost table under structure 3 is much deeper than that under other structures. Hence, when designing geosynthetic-encased gravel pile composite foundations for highway structures, it is not cost-effective to only consider long-term settlement while disregarding ground temperature.

As the analysis above demonstrates a strong linear correlation between the uneven foundation settlement and maximum foundation displacement, there is no need to analyze both of them in the orthogonal test results. In this study, only the uneven foundation settlement and pile–soil stress ratio were analyzed, as depicted in Figure 20.

Figure 20a shows that with the exception of the pile number, increases in all three other factors can reduce the uneven foundation settlement. Of these factors, pile length has the most significant effect on reducing uneven settlement, while increases in modulus and the area replacement ratio (i.e., pile diameter and number of piles) are not effective. Figure 20b indicates that the pile diameter is the most important factor affecting the pile–soil stress ratio. As pile diameter increases, the pile–soil stress ratio decreases significantly. In comparison, the other three factors have no significant effect on the pile–soil stress ratio.

Figure 21 shows that although the pile diameter has the most significant effect on the pile–soil stress ratio, there is no significant correlation between the uneven foundation settlement and the pile–soil stress ratio. Therefore, in composite foundation design, uneven settlement should still be adopted as the controlling index, as it has the greatest impact on highway structure stability. This means that determining the pile length is more important than determining the pile diameter.

To address uneven foundation settlement and the maximum foundation displacement in permafrost areas, the design of geosynthetic-encased gravel pile composite foundations for highway structures should guarantee enough pile length, as it has the most significant effect on both issues. Figure 14 and Figure 19a suggest using smaller pile diameters and larger pile spacing (fewer piles), as they have a weaker effect on the uneven foundation settlement and a relatively stronger effect on permafrost temperature.

3.5. Design of Geosynthetic-Encased Gravel Pile Composite Foundations

The analysis above led to the creation of a new composite foundation structure design scheme, combining the longest pile length, the smallest pile diameter, and the smallest column number, as shown in Table 7.

To compare this with the nine structures in the orthogonal test, the FEM was used to calculate the initial ground temperature, uneven foundation settlement, and the maximum foundation deformation at the end of the 20th year of the newly designed structure. The results were added to Figure 19c and are presented in Figure 22.

Figure 22 shows that the final designed structure is nearly at the turning point in the initial ground temperature–settlement curve. Further increases in ground temperature will diminish the mitigation effect of foundation settlement. Figure 23 also confirms that with the exception of the first two years, when the permafrost table under the highway structure is deeper due to the thermal influence of the composite foundation structure, the permafrost table under the highway structure is almost at the same depth or even shallower than that under the natural permafrost ground. These results validate the design principle of using the pile length as the primary index for composite foundations, as proposed in this paper.

4. Conclusions

This study explored the feasibility of applying geosynthetic-encased gravel pile composite highway foundations—previously commonly used for permafrost destruction—in low-temperature stable permafrost areas, where permafrost protection is the primary principle. Based on the results, the following conclusions were drawn:

(1): The geosynthetic-encased gravel pile composite foundation structure has a significant impact on the permafrost ground temperature. This effect is most pronounced in the first two years after construction and gradually diminishes over time, indicating that except for the geometrical characteristics of the piles, the initial temperature of pile materials and construction disturbance are also important factors that influence the permafrost temperature field. Among the geometrical factors that influence the temperature field in the composite foundation, pile length has the most significant effect, followed by the number of piles (pile spacing);
(2): The freeze–thaw cycles of the frozen soil around piles result in volume changes that cause the confining pressure provided by the frozen soil to fluctuate significantly with the changing seasons. Over time, the fluctuation amplitude becomes progressively larger. However, with the encasement with the use of geosynthetics, the seasonal fluctuation in the confining pressure is no longer significant. Thus, the use of a geosynthetic ensures the stability of the bearing capacity of the gravel piles;
(3): There is a strong correlation between the uneven foundation deformation value and the maximum foundation displacement value, while the maximum mean ground temperature (MMGT) shows a significant negative correlation with both of them. Therefore, in low-temperature stable permafrost areas, reducing uneven foundation settlement in geosynthetic-encased gravel pile composite highway foundations comes at the cost of increasing ground temperature and destroying permafrost. Since the correlation between foundation settlement and the maximum MMGT is nonlinear, the effect of reducing uneven settlement decreases with increasing ground temperature;
(4): Pile length has the greatest influence on uneven foundation settlement, while pile diameter has the greatest influence on the pile–soil stress ratio. However, there is no significant correlation between the pile–soil stress ratio and the uneven foundation settlement. Therefore, pile length should be the main consideration to guarantee the piles are long enough. Pile diameter and the number of piles (pile spacing) have little effect on the reduction in long-term uneven settlement but can impact the permafrost temperature field;
(5): When the geosynthetic-encased gravel pile composite foundation is properly designed, the MMGT of composite permafrost foundations will not be influenced significantly. It is suggested to adopt a 0.5 m pile diameter, 2 m pile spacing, and 11 m pile length.

There are also some limitations in this study that require further investigation in the future. Firstly, the study adopted a simplified 2D numerical model, making it challenging to account for pile layout along the driving direction. Therefore, it is hard to determine the optimal pile distributions along the path in the current study. Secondly, while global warming was considered, only one climate change scenario (an average atmospheric temperature increase of 2.6 degrees over 50 years) was included. Given the uncertainties surrounding future climate change, future research should encompass varying climate change scenarios.

Furthermore, the application and testing of the geosynthetic-encased gravel pile composite foundation proposed in this study in permafrost regions necessitate extensive engineering work and long-term observations, which are still ongoing. The validation of the model in this study was based on short-term indoor tests, which may not fully capture the complexities and long-term behavior of real-world conditions. Therefore, although the composite foundation structure proposed in this study demonstrates good performance in numerical calculations, field validation and long-term studies are essential to confirm its applicability and long-term behavior in geosynthetic-encased gravel pile composite highway foundations in low-temperature stable permafrost regions.

Author Contributions

Study conception and design: R.T. and X.H.; data collection: R.Z. and R.T.; analysis and interpretation of results: R.T., X.H. and H.L.; draft manuscript preparation: R.T., X.H. and H.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China, grant number U21A20152-1, and the National Key R&D Program of China, grant numbers 21YFB2600600 and 21YFB2600601.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A. Thermal Parameters of Frozen Soil

The thermal parameters of permafrost contain bulk specific heat capacity and thermal conductivity, which are not fixed values but vary with the freeze–thaw state of the permafrost as well as with the temperature. The derivation of the thermal parameters is based on a two-dimensional partial differential equation for unsteady heat conduction that takes into account the ice–water phase transition as well as moisture migration.

\frac{\partial}{\partial x} (k_{x} \frac{\partial T}{\partial x}) + \frac{\partial}{\partial y} (k_{y} \frac{\partial T}{\partial y}) = c ρ \frac{\partial T}{\partial t} - L ρ_{i} \frac{\partial w_{i}}{\partial t}

(A1)

k_{x}

and

k_{y}

are the thermal conductivity values of frozen soil (Wm⁻¹K⁻¹); T is the temperature; c is the specific heat of frozen soil (Jkg⁻¹K⁻¹);

ρ

is the density of frozen soil (kgm⁻³); L is the volumetric latent heat (Jkg⁻¹); t is time (s);

ρ_{i}

is the density of ice; and

w_{i}

is the ice content (%).

The two-dimensional partial differential equation of unsteady water migration is as follows:

\frac{\partial}{\partial x} (K_{x} \frac{\partial φ}{\partial x}) + \frac{\partial}{\partial y} (K_{y} \frac{\partial φ}{\partial y}) = \frac{\partial w_{w}}{\partial t} + \frac{ρ_{i}}{ρ_{w}} \cdot \frac{\partial w_{i}}{\partial t}

(A2)

K_{x}

and

K_{y}

are water transmissibility values (ms⁻¹);

φ

is the water head (m);

w_{w}

is the water content (%); and

ρ_{w}

is the density of water (kgm⁻³).

Then, the following can be derived from Equations (A1) and (A2):

\frac{\partial}{\partial x} (k_{x} \frac{\partial T}{\partial x}) + \frac{\partial}{\partial y} (k_{y} \frac{\partial T}{\partial y}) = c ρ \frac{\partial T}{\partial t} - L ρ_{w} \frac{\partial w_{w}}{\partial t} - L ρ_{w} [\frac{\partial}{\partial x} (K_{x} \frac{\partial φ}{\partial x}) + \frac{\partial}{\partial y} (K_{y} \frac{\partial φ}{\partial y})]

(A3)

The liquid water content

w_{w}

is a function of temperature

T

.

\frac{\partial w_{w}}{\partial t} = \frac{\partial w_{w}}{\partial T} \cdot \frac{\partial T}{\partial t}

(A4)

Then, Equation (A3) can be written as Equation (A5).

(c ρ + L ρ_{w} \frac{\partial w_{w}}{\partial T}) \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} (k_{x} + L ρ_{w} K_{x} \frac{\partial φ}{\partial T}) \frac{\partial T}{\partial x} + \frac{\partial}{\partial y} (k_{y} + L ρ_{w} K_{y} \frac{\partial φ}{\partial T}) \frac{\partial T}{\partial y}

(A5)

The partial derivative of the volumetric potential energy with respect to temperature can be written as Equation (A6).

\frac{\partial φ}{\partial T} = \frac{\partial φ}{\partial w_{w}} \cdot \frac{\partial w_{w}}{\partial T}

(A6)

The water diffusivity

D_{x}

D_{y}

(m²s⁻¹) and the differential water capacity

B_{w}

(m⁻¹) can be derived as Equations (A7) to (A9).

D_{x} = \frac{K_{x}}{B_{w}}

(A7)

D_{y} = \frac{K_{y}}{B_{w}}

(A8)

B_{w} = \frac{\partial w_{w}}{\partial φ}

(A9)

Substituting

K_{x}

and

K_{y}

from Equations (A7) to (A9) into Equation (A5), the following equation can be achieved:

(c ρ + L ρ_{w} \frac{\partial w_{w}}{\partial T}) \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} (k_{x} + L ρ_{w} D_{x} \frac{\partial w_{w}}{\partial T}) \frac{\partial T}{\partial x} + \frac{\partial}{\partial y} (k_{y} + L ρ_{w} D_{y} \frac{\partial w_{w}}{\partial T}) \frac{\partial T}{\partial y}

(A10)

Then, the volumetric specific heat C(T) (Jm⁻³K⁻¹) and heat conductivity coefficient of frozen soil

β_{x} (T)

β_{y} (T)

(Wm⁻¹K⁻¹) can be derived from Equation (A10).

C (T) = c ρ + L ρ_{w} \frac{\partial w_{w}}{\partial T}

(A11)

β_{x} (T) = k_{x} + L ρ_{w} D_{x} \frac{\partial w_{w}}{\partial T}

(A12)

{β_{y} (T) = k}_{y} + L ρ_{w} D_{y} \frac{\partial w_{w}}{\partial T}

(A13)

According to Xu. et al. [40], the specific heat capacities of unfrozen and frozen soil can be written in Equations (A14) and (A15).

c_{u} = (c_{s u} + w c_{w}) ρ_{d}

(A14)

c_{f} = (c_{s f} + (w - w_{w}) c_{i} + w_{w} c_{w}) ρ_{d}

(A15)

c_{u}

is the volumetric heat capacity of unfrozen soil (Jm⁻³K⁻¹);

c_{s u}

is the specific heat capacity of unfrozen soil (Jkg⁻¹K⁻¹);

w

is the water and ice content (%);

c_{w}

is the specific heat capacity of water (Jkg⁻¹K⁻¹);

ρ_{d}

is the dry density of frozen soil (kgm⁻³);

c_{f}

is the heat capacity of frozen soil (Jm⁻³K⁻¹);

c_{s f}

is the specific heat capacity of frozen soil (Jkg⁻¹K⁻¹); and

c_{i}

is the specific heat capacity of ice (Jkg⁻¹K⁻¹).

The liquid water content can be calculated with Equation (A16).

w_{w} = w_{0} {|T_{f}|}^{b} {|T|}^{- b}

(A16)

w_{0}

is the initial water content (%);

T_{f}

is the temperature at which the soil begins to freeze (

℃

); and b is the soil constant.

Substituting Equation (A16) into Equations (A14) and (A15), the following is obtained:

C = \{\begin{matrix} (c_{s u} + w_{0} c_{w}) ρ_{d} T \geq T_{f} \\ ρ_{d} c_{s f} + ρ_{d} c_{i} w_{0} + ρ_{d} (c_{w} - c_{i}) \cdot w_{0} {|T_{f}|}^{b} {(- T)}^{- b} T < T_{f} \end{matrix}

(A17)

Regarding the thermal conductivity coefficients of both frozen and unfrozen soil as constant values, and substituting Equations (A16) and (A17) into Equations (A11) to (A13), the following is obtained:

C (T) = \{\begin{matrix} (c_{s u} + w_{0} c_{w}) ρ_{d} T \geq T_{f} \\ ρ_{d} c_{s f} + ρ_{d} c_{i} w_{0} + ρ_{d} (c_{w} - c_{i}) \cdot w_{0} {|T_{f}|}^{b} {(- T)}^{- b} + ρ_{d} \cdot L \cdot w_{0} {|T_{f}|}^{b} \cdot b \cdot {(- T)}^{- (b + 1)} T < T_{f} \end{matrix}

(A18)

k_{x} (T) = k_{y} (T) = \{\begin{matrix} k_{u} T \geq T_{f} \\ k_{f} + ρ_{d} \cdot L \cdot D \cdot w_{0} {|T_{f}|}^{b} \cdot b {\cdot (- T)}^{- (b + 1)} T < T_{f} \end{matrix}

(A19)

With Equations (A18) and (A19), the temperature-dependent thermal conductivity and volumetric heat capacity of frozen or unfrozen soil can be derived according to the material parameters listed in Table 3. The calculation of those thermal parameters is completed with Abaqus subroutine UMATHT codes. In the Abaqus model, the subroutine UMATHT is required to provide specific heat DUDT, heat flux vector FLUX (I), and tensor DFDG (I, I), which represent the increment of the heat flux vector with respect to the temperature gradient. The specific heat DUDT can be derived by Equation (A20).

D U D T = C (T) / ρ_{d}

(A20)

The vector FLUX (I) can be calculated with Equation (A21).

F L U X (I) = - C O N D \times D T E M D X (I)

(A21)

where COND is the thermal conductivity calculated in Equation (A19). As is shown in Equation (A19), since the frozen soil is regarded as isotropic, COND can thus be regarded as a scalar. DTEMDX (I) is the temperature gradient vector at the end of the last increment.

The tensor DFDG (I, I), according to its definition, can be determined with Equation (A22).

D F D G (I, I) = - C O N D

(A22)

The 12 material parameters listed in Table 3 are firstly defined in the Abaqus CAE model and will be transferred into the subroutine UMATHT during the calculation.

Appendix B. Constitutive Model of Frozen Soil

The constitutive model, which considers the freeze–thaw conditions in this study, was developed by Zhang et al. in 2015 and is briefly described in this appendix. The detailed derivation can be found in the literature [20].

The normal compression line (NCL) and unloading–reloading line (URL) are firstly defined by Equations (A23) and (A24).

v = v_{0} - λ l n \frac{p^{'}}{p^{r}}

(A23)

d v^{e} = - κ \frac{{d p}^{'}}{p^{'}}

(A24)

v

is the specific volume,

v = 1 + e

;

e

is the void ratio;

v_{0}

is the specific volume at reference pressure

p^{r}

;

p^{'}

is the mean effective stress (1/3 of the first invariant of the effective stress); and

d v^{e}

is the elastic change in specific volume in the URL.

The

λ_{f}

and

κ_{f}

for frozen soil are determined as in Equations (A25) and (A26).

λ_{f} = λ e^{- α_{1} e_{i p}}

(A25)

κ_{f} = κ e^{- α_{2} e_{i p}}

(A26)

e_{i p}

is the pore ice ratio, which is a function of temperature, as shown in Equations (A27) and (A28);

α_{1}

and

α_{2}

are the soil parameters obtained by experiments.

e_{i p} = (w_{0} - w) \cdot 1.09 \frac{ρ_{s}}{ρ_{w}}

(A27)

w = w^{*} + (w_{0} - w^{*}) e^{a (T - T_{0})}

(A28)

w

is the unfrozen water content at the temperature T;

T_{0}

is the temperature at which the soil begins to freeze;

w^{*}

is the unfrozen water content at some low temperature;

w_{0}

is the water content in unfrozen soil;

a

is the soil parameter; and

ρ_{s}

and

ρ_{w}

are the densities of solid parts in soil and water.

The elliptical yield surface is adopted in the constitutive model.

f = q^{2} + M^{2} (p^{'} - p_{0 t}) (p^{'} - p_{0}) = 0

(A29)

p_{0 t}

is the isotropic tension yield stress of frozen soil;

p_{0}

is the isotropic compression yield stress of unfrozen soil.

When the soil is frozen, the soil will gain some tensile strength, which means

p_{0 t} \neq 0

, as shown in Figure A1.

p_{0 t}

can be determined as in Equation (A30).

p_{0 t} = p_{t} (1 - e^{- α_{3} e_{i p}})

(A30)

α_{3}

is the soil parameter;

p_{t}

is −1.0 MPa.

The evolution law of compressive yield strength during the soil freezing process is given in Equation (A31).

\frac{p_{0}^{f}}{p^{r}} = e^{(β e_{i p}) / (λ_{f} - κ_{f})} {(\frac{p_{0}}{p^{r}})}^{(λ - κ_{f}) / (λ_{f} - κ_{f})}

(A31)

p_{0}^{f}

is the isotropic compression yield stress of frozen soil;

β

is the soil parameter.

The volumetric freezing expansion of soils during the freezing process is defined by porosity increase, as is shown in Equation (A32).

d n = \frac{\partial n}{\partial t} = {\dot{n}}_{m} {(\frac{T - T_{0}}{T_{m}})}^{2} e^{1 - {[(T - T_{0}) / T_{m}]}^{2}} \frac{|\frac{\partial T}{\partial l}|}{g_{T}} e^{- (|{\bar{σ}}_{k k}^{'}| / ς)} e^{- (θ_{i} / θ_{w})}

(A32)

n

is the porosity;

{\dot{n}}_{m}

is the maximum porosity rate;

T_{m}

is the temperature at which the maximum porosity rate occurs;

|\frac{\partial T}{\partial l}|

is the temperature gradient in the heat flow direction;

{\bar{σ}}_{k k}^{'}

is the first invariant of the effective stress;

ς

is the material parameter; and

θ_{i}

and

θ_{w}

are the ice and unfrozen water fraction volumes.

With the porosity increment

d n

, the strain increment caused by frost heave

d ε^{f}

can be calculated according to Equation (A33).

d ε^{f} = \frac{d n}{1 - n}

(A33)

However, both the strain and porosity increment in Equation (A33) are scalars. Therefore, the scalar

d ε^{f}

should be transferred into a tensor during the FEM calculation. Since the soil is regarded as an isotropic material in this study, the strain increment tensor caused by frost heave

d ε_{i j}^{f}

can be determined according to Equation (A34).

d ε_{i j}^{f} = d ε^{f} [\begin{matrix} 1 / 3 & 0 & 0 \\ 0 & 1 / 3 & 0 \\ 0 & 0 & 1 / 3 \end{matrix}]

(A34)

Therefore, the total strain increment

d ε_{i j}

is composed of elastic strain

d ε_{i j}^{e}

, plastic strain

d ε_{i j}^{p}

, and frost heave strain

d ε_{i j}^{f}

in one FEM calculation increment.

d ε_{i j} = d ε_{i j}^{e} + d ε_{i j}^{p} + d ε_{i j}^{f}

(A35)

Figure A1. The NCL, URL, and yield condition of frozen soil.

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Figure 1. The freeze–thaw cycle test chamber.

Figure 2. The temperature sensor and soil pressure sensor: (a) temperature sensor; (b) soil pressure sensor.

Figure 3. The sample dimensions and sensor positions.

Figure 4. The sizes of verification models for the geosynthetic-encased gravel pile.

Figure 5. The geometry and size of the numerical model.

Figure 6. The geo-stress balance process.

Figure 7. The settlement of the soft soil sample.

Figure 8. The settlement of the composite foundation sample: (a) floating pile; (b) end-bearing pile.

Figure 9. The temperature results of both the indoor test and FEM: (a) temperature sensor #1; (b) temperature sensor #2.

Figure 10. The lateral frost heave force in both the indoor test and FEM.

Figure 11. The maximum vertical settlement with different mesh sizes.

Figure 12. The MMGTs of different permafrost foundations.

Figure 13. The temperature fields under structure 3 and the structure without piles.

Figure 14. The main effect plot for the initial ground temperature.

Figure 15. The thawing lines under different permafrost foundations.

Figure 16. The deepest annual permafrost table under different permafrost foundations.

Figure 17. The ground temperature along the structure centerline.

Figure 18. The horizontal soil pressure and pile confining pressure under structure 1.

Figure 19. The maximum MMGT, uneven settlement, and maximum settlement: (a) the results of 10 structures; (b) the relationship between the maximum settlement and uneven settlement; (c) the relationship between the maximum settlement and maximum MMGT.

Figure 20. The main effect plot for the uneven foundation settlement and pile–soil stress ratio: (a) uneven foundation settlement; (b) pile–soil stress ratio.

Figure 21. The relationship between the uneven settlement and pile–soil stress ratio.

Figure 22. The relationship between the maximum settlement and maximum MMGT.

Figure 23. The thawing lines under the newly designed structure and the natural ground.

Table 1. The pile parameters of 9 orthogonal experiments.

Number	Elastic Modulus (MPa)	Pile Diameter (m)	a (m)	b (m)	Pile Number	Pile Length (m)
1	40	0.5	2.72	1.78	9	5
2	40	0.6	1.6	1.1	13	8
3	40	0.7	0.95	0.65	17	11
4	50	0.5	1.57	1.21	13	11
5	50	0.6	0.92	0.76	17	5
6	50	0.7	2.75	1.55	9	8
7	60	0.5	0.89	0.87	17	8
8	60	0.6	2.73	1.67	9	11
9	60	0.7	1.62	0.99	13	5

Table 2. The mechanical parameters of the gravel pile and soft soil.

Material	Density (kg/m³)	Elastic Modulus (MPa)	Poisson’s Ratio	Friction Angle (°)	Dilation Angle (°)	Cohesion Stress (kPa)
Geosynthetic-encased gravel pile	1500	50	0.27	42.9	0	0
Soft soil	1900	0.7	0.3	0	0	3.5

Table 3. The thermal parameters of the frozen soil.

Layer	Embankment	Nature Ground Layer I	Nature Ground Layer II	Nature Ground Layer III
$c_{s f} (J \cdot {k g}^{- 1} \cdot K^{- 1})$	710	730	750	750
$c_{s u} (J \cdot {k g}^{- 1} \cdot K^{- 1})$	790	840	840	840
$c_{i} (J \cdot {k g}^{- 1} \cdot K^{- 1})$	2090	2090	2090	2090
$c_{w} (J \cdot {k g}^{- 1} \cdot K^{- 1})$	4182	4182	4182	4182
$ρ_{d} (k g \cdot m^{- 3})$	1800	1700	1300	1500
$w_{0} (%)$	25	30	30	30
$T_{f} (℃)$	−0.20	−0.10	−0.19	−0.05
b	0.610	0.733	0.574	0.474
$k_{f} (W \cdot m^{- 1} \cdot K^{- 1})$	1.98	2.69	1.22	1.82
$k_{u} (W \cdot m^{- 1} \cdot K^{- 1})$	1.92	1.95	0.87	1.47
$D (10^{- 6} \cdot m^{2} \cdot s^{- 1})$	9.35	46.6	373	3.44
$L (10^{3} \cdot {k g}^{- 1} \cdot J)$	334.56	334.56	334.56	334.56

Table 4. The thermal and mechanical parameters of other structure layers.

Thickness (cm)	Material	Density (kg·m⁻³)	Heat Conductivity Coefficient (J·h⁻¹·m⁻¹·K⁻¹)	Specific Heat Capacities (J·kg⁻¹·K⁻¹)	Elastic Modulus $(M P a)$	Poisson’s Ratio
4	Asphalt concrete-13	2300	4140	1670	1550	0.25
5	Asphalt concrete-20	2320	4320	1670	1500	0.25
12	ATP-25	2350	2916	1260	1200	0.25
24	Cement-treated macadam	2200	5616	960	1400	0.25
20	Graded gravel	2000	6048	1100	250	0.25
150	Crushed-rock interlayer	1490	1426	839	200	0.35

Table 5. The E-P model parameters of the frozen soil.

λ	κ	P₀ (kPa)	P^r (kPa)	M	α₁	α₂	β	w*	w₀	T₀ (°C)	a (°C⁻¹)	α₃	e₀
0.323	0.062	687	100	0.7	0.4	1.8	0.18	0. 083	0.306	0	0.131	0.6	0.43

Table 6. The initial temperature field.

Depth (m)	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0
Temperature (°C)	5.27	1.78	−0.29	−1.24	−2.19	−2.41	−2.7	−2.87	−2.87	−2.93
Depth (m)	5.5	6.0	6.5	7.0	7.5	8.0	8.5	9.0	9.5	10.0
Temperature (°C)	−2.96	−2.94	−2.99	−2.84	−3	−3	−3	−3	−3	−2.84

Table 7. The newly designed geosynthetic-encased gravel pile composite foundation.

Elastic Modulus (MPa)	Column Diameter (m)	Column Number	Column Length (m)
50	0.5	9	11

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Tian, R.; Huang, X.; Zhao, R.; Luo, H. Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions. Buildings 2024, 14, 3612. https://doi.org/10.3390/buildings14113612

AMA Style

Tian R, Huang X, Zhao R, Luo H. Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions. Buildings. 2024; 14(11):3612. https://doi.org/10.3390/buildings14113612

Chicago/Turabian Style

Tian, Rongyan, Xiaoming Huang, Runmin Zhao, and Haoyuan Luo. 2024. "Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions" Buildings 14, no. 11: 3612. https://doi.org/10.3390/buildings14113612

APA Style

Tian, R., Huang, X., Zhao, R., & Luo, H. (2024). Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions. Buildings, 14(11), 3612. https://doi.org/10.3390/buildings14113612

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Research on the Geosynthetic-Encased Gravel Pile Composite Highway Foundation in Low-Temperature Stable Permafrost Regions

Abstract

1. Introduction

2. Materials and Methods

2.1. Thermal Properties and Mechanical Constitutive Model of Frozen Soil

2.2. Material and Model Size

2.2.1. Equipment, Materials, and Sample Size of Indoor Test

2.2.2. Model Size in FEM

2.2.3. Material Parameters in FEM

2.3. Boundary and Initial Conditions of FEM

2.3.1. Boundary and Initial Conditions in Verification Models

2.3.2. Boundary and Initial Conditions in Formal Analysis Models

3. Results and Discussion

3.1. Verification of FEM

3.1.1. Verification of Finite Element Gravel Pile Model

3.1.2. Verification of Finite Element Frozen Soil Model

3.1.3. Verification of Model Convergence

3.2. Temperature Field of Pile Composite Permafrost Foundation

3.3. Confining Pressure of Piles in Composite Foundation

3.4. Long-Term Settlement of Permafrost Foundation

3.5. Design of Geosynthetic-Encased Gravel Pile Composite Foundations

4. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

Appendix A. Thermal Parameters of Frozen Soil

Appendix B. Constitutive Model of Frozen Soil

References

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