Dynamic Behavior of Geosynthetic-Reinforced Expansive Soil under Freeze-Thaw Cycles

Expansive soil has a significant impact on the stability of many key construction projects in cold regions. To study the physical and mechanical properties of expanded soil under the condition of freeze-thaw cycle, cryogenic cyclic triaxial tests were conducted on the dynamic and the displacement characteristics of geosynthetic-reinforced expansive soil subjected to the freeze-thaw cycles. Compared with the unreinforced expansive soil samples, the effects of freeze-thaw cycles on the soil dynamics were discussed.-e dynamic shear modulus (Gd) and damping ratio (λ) of the expansive soil samples are improved by reinforcement. Reinforced soil can inhibit the axial compression of the sample and restrain the frost heave deformation of the sample during the freezing process. Meanwhile, it can delay the structural damage effect caused by frost heave and reduce the rate of change of the Gd and the λ with the freeze-thaw cycle. At the same time, reinforced soil can inhibit the axial expansion, reduce the rate of reduction of the Gd, stabilize it with a higher rate, and reduce the influence of the freeze-thaw cycles on the λ of the expansive soil sample. Finally, the change of mechanical properties of expansive soil under the condition of reinforcement is obtained. -e main conclusions of this paper can be used to reinforce the roadbed and foundation engineering of frozen soil in a cold region and provide support for the fiber reinforcement method of expansive soil.


Introduction
Expansive soil, identified as unsuitable construction materials for engineering, is low-graded because of its inferior mechanical properties, such as low strength and high potential for swelling and shrinkage [1,2]. Due to seasonal environments, the cyclic volume change of expansive soil causes severe damage to the lightly loaded structures founded on them [3,4]. e problems posed by expansive soil have been reported worldwide. erefore, it requires engineering solutions to alleviate the impacts on human activities [5]. As the third largest permafrost country in the world, China covers a vast area of permafrost [6]. Geological disasters and engineering practice reveal that, under the conditions of the freeze-thaw environment in seasonally frozen and abundant groundwater, the freeze-thaw cycles and traffic dynamic load have become essential factors that affect the stability of the slope and will induce landslides [7,8]. Meanwhile, frost damage and its prevention have been demonstrated [9,10]. Influenced by the annual freeze-thaw cycles, train transportation load will induce subgrade boiling, slope collapsing, settlement, destabilization, and strength reduction because of the destruction of soil structure [11,12]. At present, the main method to improve the mechanical properties of expansive soil under different working conditions is reinforcement [13,14], and good progress has been made. However, little is known about the mechanical damage of reinforced expansive soil under freeze-thaw cycles. e special variation based on different stress conditions is not clear enough.
Studies have shown that the dynamic behavior of soil is significantly influenced by the dynamic shear modulus and damping ratio [1], which indicates the importance to select the dynamic shear modulus and damping ratio of soil in the construction in the seasonally frozen soil area in the south of Heilongjiang Province, northeastern Inner Mongolia, and northwestern Jilin Province. At present, the characteristics of expansive soil under different environments and conditions have been reported. e freeze-thaw cycles test of expansive soil samples under different water content conditions was carried [10], revealing that during the freezethaw cycle, the volume will reduce when freezing meanwhile swell when thawing under the low moisture content situation; on the contrary, it will be a totally opposite position under the high moisture content. With the deformation measurement, unconfined compression tests, and microstructure tests [15] studied the permanent deformation and dynamic characteristics of expansive soil and modified expansive soil under repeated loading by dynamic triaxial tests, revealing the relationship between elastic strain, cumulative plastic strain, and dynamic strain of expansion soil under different confining pressures and repeated dynamic load. Mao and Qiu [16] reported the variation of dynamic shear modulus and damping ratio of unsaturated expansive soil, the trend of dynamic shear modulus, and damping ratio with the increase of shear strain. Soil freezing and thawing have been well-elucidated, including the physical characteristics [17,18] and stress-strain relationships of soil [19] after freezing and thawing. e strength reduction for unreinforced soil subjected to freeze-thaw cycles was also observed in previous studies [11,20,21]. However, there are few studies on the dynamic response of expansive soil under freeze-thaw cycles.
Especially, geosynthetic-reinforced soil structures including retaining walls, slopes, embankments, roadways, and load-bearing foundations, have gained increasing attention, in which several distinct advantages over their conventional counterparts have been demonstrated. As for expansive soil, the geosynthetic-reinforced method is an efficient mechanical way. Geosynthetics have great significance for the prevention and control of geologic hazards in constructions. e dynamic characteristics of reinforced soil are affected by many parameters, such as the properties of rebar, freeze-thaw cycle, loading times, confining pressure, frequency, and the amplitude of shear strain. Shahnazari et al. [22] studied the influence of geogrids on the dynamic characteristics of sand through the triaxial test, and the result shows that the shear modulus of reinforced sand decreases under low confining pressure (<100 kPa) and increases under high confining pressure. Konrad [23] carried out triaxial tests on geotextiles in reinforced silty sand, and the result shows that the dynamic modulus of silt content increases and the cyclic ductility of silty sand decreases with the increase of the pressure and the number of geotextile layers. Besides, with the addition of silt up to about 35%, the dynamic axial modulus decreases, and the cyclic ductility increases [3]. Some researchers have studied the strength and deformation characteristics of geogrid reinforced expansive soil [24] and the stability of reinforced expansive soil slope by triaxial tests.
Many studies have been conducted on the behavior of geosynthetic-reinforced soil structures; however, the dynamic behavior in the geosynthetic-reinforced expansive soil has not been fully elucidated, especially under freeze-thaw cycles. In this paper, the dynamic shear modulus and damping ratio of expansive soil (reinforced and nonreinforced) are tested under several freeze-thaw cycles by the temperature-controlled dynamic triaxial axis tests to provide theoretical reference for the construction of the expansive soil slope in the seasonal frozen soil areas.

Materials.
Laboratory physical and dynamic tests were carried out on a disturbing expansive soil, and the samples are yellowish-brown. e basic physical index and particle composition were analyzed after drying, crushing, and sieving (shown in Table 1). e particle size distribution curve of the sample is shown in Figure 1. e sample is expansive soil, the unloaded expansion rate of which is 28.8% and compactness is 0.88 [25]. e time-history curves of expansive soil under natural water content and natural compactness are shown in Figure 2. To prepare the triaxial axis specimen, the expansive soil, which was dried, crushed, and sifted, was made into a sample with a water content of 29.8% by adding distilled water and sealing for 42 hours. e height of the sample was 140 mm, the diameter was 70 mm, and the compactness was controlled to 88%.

Methodology.
e test was carried out on the positive and negative temperature static-dynamic triaxial axis instrument developed in the British GDS (shown in Figure 3).
In this test, three influencing factors for the expansive soil samples including confining pressure, freezing-thawing cycles, and reinforcement were considered. e confining pressure of soil is 50 kPa and 10 kPa, considering different soil stress conditions. e test took the expansive soil of a slope as the research object, so the consolidation method is nonisostatic consolidation because of the shear stress. e unidirectional grille, which is a reduced scale representation, was selected for the reinforcement in this test. e specific parameters are shown in Table 2, the layout is shown in Figure 4, and the detailed arrangement is shown in Table 3.
After the specimen was consolidated, the prescribed vibration load was applied. To ensure that the specimen would not be damaged due to excessive deformation during repeated dynamic loading, a cyclic loading mode of sinusoidal wave controlled by strain was considered. Under the condition of draining, dynamic load controlled by dynamic strain was applied step by step and the dynamic load cycle of each stage reached 20 times. To avoid the influence of the latter load made by the former one, after the former loading is completed, it should be restored to the initial setting value through advanced loading and stabilize for 1-2 minutes. e conventional test method for freezing and thawing cycle is in the sealed position: place it in high and lowtemperature test chamber, run the freeze-thaw cycle under the conditions of no confining pressure, and then conduct the dynamic triaxial tests [26]. e temperature was set at −15°C and 20°C. e time of freezing or melting of the soil sample is the standard way, demanding that the change of soil sample displacement is less than 0.01 mm within 2 hours. All the samples were subjected to the freeze-thaw cycles for 7 times, and the single freeze-thaw cycle is 24 hours. en, a dynamic load was applied while every freezecycle was completed. Finally, the different results were obtained under the various freeze-cycle situation.

Effect of Single Freeze-aw. Characteristics of soil will
show different changes under a single freeze-thaw condition [10]. e expansive soil samples under the unreinforced and reinforced states showed the change rule of frost heave and thaw settlement, as shown in Figure 5. When the temperature was reduced to −3°C, the samples were frozen and the volume increased rapidly, and the axial expansion appeared. When the temperature started to rise, the volume of the sample decreased. Meanwhile, the axial compressive deformation occurred, with the decreased back pressure-volume, and the moisture in the sample is discharged. Compared with unreinforced samples, it is obvious that due to the permeability of the geotextile layer, water can freely move and penetrate from the soil mass. During the freezing phase, ice crystals were formed, while these crystals melt and free water appeared in the sample during the thawing phase. e geotextile permeability facilitated water movement so that the change of the back pressure-volume of reinforced samples is more than that of the unreinforced samples after every freeze-thaw cycle.
When the confining pressure is 50 kPa, the axial frost heave deformation increases by 0.03 mm when the sample of the unreinforced expansive soil was frozen, while the deformation increases by 0.5 mm when the reinforced expansive soil was frozen, which is shown in Figure 5(a). e axial frost heave deformation of the reinforced sample is obviously higher than that of the unreinforced one, which is due to the radial constraint caused by reinforcement. is radical constraint was induced to have a larger expansion deformation in the axial direction of the samples. When the unreinforced sample was melted, the axial compression deformation was 1.03 mm, while the reinforced expansive soil sample was 1.35 mm. In the meantime, the axial Soil weight less than a particle size (%)  compression deformation of the reinforced sample is also higher than the unreinforced sample. It will be the reinforcement that weaken the radial frost heave why the sample was frozen and made the axial frost heave more significant. After a freeze-thaw cycle, the axial cumulative compressive deformation of the unreinforced sample is 1 mm, while the reinforced sample is 0.8 mm under this stress condition, which shows that reinforcement can reduce axial compression deformation caused by a freeze-thaw when the confining pressure is 50 kPa. Although the ultimate deformation of reinforced soil is less than that of unreinforced soil, according to Figure 5(a), the deformation value of reinforced soil during a freeze-thaw process is greater than that of unreinforced soil because the expansive soil will reduce in freezing and swell in thawing. e thermal conductivity of the added geogrid is greater than the thermal conductivity of the expansive soil, compared with the unreinforced soil.
When the environment temperature drops below 0°C, the soil moisture starts to freeze. As a result, ice crystals are formed in a freezing procedure and the sample is subjected to volumetric change. e volume of the crystal will increase up to 9 times and exert notable stress on soil aggregates, resulting in the change of soil characteristics in micro-and macroscales [23].
e influence rule of reinforcement on axial deformation of the sample under the stress state of 10 kPa is consistent with the influence rule under the stress state of 50 kPa, which is shown in Figure 5(b). e axial frost heave deformation of unreinforced expansive soil increases by 0.4 mm, while the reinforced one increases by 0.55 mm when the sample was frozen. e axial compression deformation of unreinforced expansive soil decreases by 0.23 mm while the reinforced one decreases by 0.5 mm when the sample is melted. After a single freeze-thaw, the axial cumulative expansion deformation of the unreinforced sample is 0.17 mm, while the reinforced sample is 0.03 mm under this stress condition, which shows that reinforcement can reduce axial expansion deformation caused by a single freeze-thaw when the confining pressure is 10 kPa. It indicates that the decrease and increase values are not the same and the specimens will not recover to their initial height.
Figures 5(a) and 5(b) indicate that the axial displacement of the expansive soil sample varies under different stress states during the freeze-thaw process. e maximum volume change rate of the expansive soil sample at confining pressure of 50 kPa occurs at the compactness stage of the soil after melting, while the sample at 10 kPa confining pressure occurs during the expansion phase of the soil after freezing.
is is because different stress states lead to different consolidation effects of the expansive soil sample. e axial deformation of the reinforced expansive soil samples under two stress states decreases after freezing and thawing. When the confining pressure is 50 kPa, freeze-thaw caused reconsolidation of expansive soil samples and axial compression deformation under high confining pressure, so reinforcement can restrain the axial compression deformation; when the confining pressure is 10 kPa, freeze-thaw caused expansion of expansive soil samples and axial expansion deformation under low confining pressure so that reinforcement can restrain the axial expansion deformation.

Effect of Freeze-aw Cycles on Axial Displacement.
e reinforced expansive soil shows different height changes, which indicated that the variety of axial displacement is smaller than the unreinforced soil under different freeze-thaw cycles. is change is the result of under the cycles shown in Figure 6. Geogrid can restrain the axial deformation of expansive soil samples under freeze-thaw conditions. When the confining pressure is 50 kPa, the axial compression displacement of the reinforced expansive soil sample is 9.32% lower than that of the unreinforced expansive soil sample after the seventh freeze-thaw cycles. As a comparison, under the confining pressure of 10 kPa, the axial expansion displacement of the reinforced expansive is 54.17% lower than the unreinforced one after the seventh freeze-thaw cycles. In addition, these results are consistent   with the findings of Wang and others [21] who reported the soil cohesion decreases with increasing the number of freeze-thaw cycles because voids between clay particles may increase due to forming ice lenses, and thus, the volume increases.
e confining pressure has a significant effect on the axial displacement [27], and similarly, due to the change of the freeze-thaw state of the soil layer, the moisture content will also have an impact on the stress change of the soil layer [28,29]. It can be found in Figure 7   axial displacement occurred when the sample went through the first freeze-thaw cycle under the stress of 50 kPa. With the increase of freeze-thaw cycles, the variation of the axial displacement decreases continuously, and the reinforced sample tends to be stable earlier than the unreinforced one, and the displacement changes tend to be consistent after the sixth freeze-thaw cycle. It can be found in Figure 7(b) that with the increase of freeze-thaw cycles, compared with the unreinforced sample, the absolute value of axial displacement of the reinforced sample decreases faster, and the axial displacement stopped after the fourth freeze-thaw cycle under the stress state of 10 kPa. By fitting the axial displacement of the expansive soil sample with the number of the freeze-thaw cycles, it indicates a significant exponential function change law between the two factors with R 2 large than 0.9, and it can be expressed as in the following equation, where the values of parameters are shown in Table 4: where Δh is a variation of axial displacement; FT is freezethaw cycles; A, B, C are coefficients related to confining pressure.

Effect of Freeze-aw Cycles on Dynamic Shear Modulus G d .
e dynamic shear modulus will be tuned by the freezethaw cycle in Figure 8. ere are two hypotheses to explain this effect: (a) consolidation or expansion effect caused by freeze-thaw cycle [30,31]; (b) structural damage effect caused by freeze-thaw cycle [32].
It can be found in Figures 8(a) and 8(b) that the dynamic shear moduli of the unreinforced and reinforced samples increase after the first freeze-thaw cycle under the same dynamic stress condition. e largest increase amplification of G d is 28% and 19%, respectively, in the dynamic strain of 1 × 10 −5 . e decrease extent of G d of the unreinforced samples after the second freeze-thaw cycle is 16%, while the decrease amplification of the reinforced samples after the third freeze-thaw cycle is 9%. is is because the freeze-thaw cycle not only induces new consolidation of soil under the high-stress state but also causes the pores and cracks in the soil because of Frost Heave and aw, which alters the soil skeleton and particle characteristics, transfers the soil structure, and changes the stress system. erefore, the dynamic shear modulus of soil decreases [33]. Ghazavi and Roustaie [11] reported the use of a geotextile layer could reduce the effect of freeze-thaw cycles on the mechanical characteristics of the soil by decreasing the triaxial strength reduction amount from 43% for unreinforced samples to 14% for geotextile reinforced samples. e time for the dynamic shear modulus begins to decrease when the reinforced sample is delayed. is is because the reinforcement restrains the frost heave deformation of samples during freezing and delays the structural damage effect caused by frost heave.
It is illustrated that the dynamic shear modulus both of the unreinforced and reinforced one also decreases with the increase of freeze-thaw cycles, under the strain condition of 10 kPa, from Figures 8(c) and 8(d). e decrease amplification of G d is 27% and 22%, respectively, after the seventh freeze-thaw cycle. is is because the freeze-thaw cycle can  Advances in Civil Engineering lead to the expansion of samples and the decrease of density under the condition of low confining pressure and low partial stress, which reduce the dynamic shear modulus of the samples as freeze-thaw cycles destroy the original soil skeleton structure. Compared with the unreinforced sample, the reduction rate of the dynamic shear modulus of the reinforced sample decreases after freeze-thaw cycles, and the trend of dynamic shear modulus is more stable under this stress condition. ese results are in good accordance with the findings [11], who conducted tests on friction angle during freeze-thaw cycles. e results indicated the unreinforced samples experience a negligible increase in the friction angle during freeze-thaw cycles, the friction angle of reinforced samples remained relatively constant.
From the relationship curve of dynamic shear modulus and dynamic strain in freeze-thaw cycles under the stress state of 50 kPa and 10 kPa, it can be found that the dynamic shear modulus of the reinforced expansive soil samples increases under these two stress states. When the confining pressure is 50 kPa, G d of the reinforced expansive soil samples without freeze-thaw cycles is increased by 4%; when the confining pressure is 10 kPa, G d is increased by 6%. is indicates that the effect of reinforcement on dynamic shear modulus is more significant under the two stress states. Reinforcement inhibits the trend that the dynamic shear modulus of expansive soil samples increases with the increase of freeze-thaw cycles. When the confining pressure is 10 kPa, the expansive soil sample with geogrid has a more

Effect of Freeze-aw Cycles on Damping Ratio λ.
It shows that the freeze-thaw cycle has an effect on the damping ratio of expansive soil in Figure 9. e damping ratio of the unreinforced and reinforced expansive soil under different stress states have a different variation pattern due to the influence of the freeze-thaw cycles. e maximum variation of damping ratio occurred in the first freeze-thaw cycle when the dynamic strain is 1 × 10 −3 . e damping ratios of the unreinforced and reinforced samples are increased by 36% and 19%, respectively. is is because a large number of cracks in the microstructure of the soil are produced due to Frost Heave and aw caused by freeze-thaw cycles, which leads to the increase of energy consumption during the propagation of the dynamic wave and greatly improves the damping ratio. Geogrid can constrain the frost heave deformation of samples during freezing and reduce the number of cracks and delay the structural damage effect caused by frost heave. e damping ratio of the unreinforced and reinforced samples decreases with the increase of freeze-thaw cycles starting from the third and fourth freeze-thaw cycles, respectively. is is because the consolidation effect caused by freeze-thaw cycles increases the soil compactness, while the effect of the freeze-thaw cycle on soil pore structure and soil particle skeleton is weaker than the previous two freeze-thaw cycles [10]. It can be found in Figures 9(c) and 9(d) that the damping ratio of the unreinforced and reinforced samples increases with the increase of freeze-thaw cycles under the same dynamic stress condition. is is because the freeze-thaw cycle can lead to the expansion of samples and the decrease of density under the stress state. Meanwhile, a large number of cracks are produced in the microstructure of soil due to Frost Heave and aw, which leads to the increase of the sample damping ratio. After the seventh freeze-thaw cycle, the damping ratio of unreinforced samples at the strain in 1 × 10 −3 is increased by 28% and the damping ratio of reinforced samples at the strain in 1 × 10 −3 is increased by 30%. e effect of freeze-thaw cycles on the damping ratio of expansive soil samples does not change noticeably due to reinforcement.
It can be found from the relationship curve of damping ratio and dynamic strain in freeze-thaw cycles under the stress state of 50 kPa and 10 kPa that the damping ratio of the reinforced expansive soil samples increases under these two stress states. When the confining stress is 50 kPa and the strain is 1 × 10 −3 , the damping ratio λ of the reinforced expansive soil samples without freeze-thaw cycles increased by 13%; when the confining stress is 10 kPa and the strain is 1 × 10 −3 , λ is increased by 11%. It shows that the variation of the confining pressure has a negligible effect on the damping of the reinforced soil. e results are in agreement with the previous results obtained by Naeini and Gholampoor [34]. e growth trend of dynamic strain and damping ratio of the reinforced expansive soil sample is faster than that of the unreinforced sample under the two stress states.
is is because the larger the dynamic strain, the more the energy dissipation of reinforcement.
In addition, both the dynamic shear modulus and the damping ratio change significantly after the first two freezethaw cycles, and the value gradually decreases as the number of freeze-thaw cycles increases because of the crack development effect on it [35]. e general feature of the development of cracks in the soil is that the new cracks develop rapidly, and the later cracks develop slowly. With the completion of the first freeze-thaw cycle, cracks in the soil developed rapidly. As the cracks developed, the damping ratio and dynamic shear modulus began to change rapidly. However, the crack development tends to stabilize after a certain number of times, and the influence that comes from confining pressure will make the damping ratio and dynamic shear modulus change relatively small [36].

Conclusion
Comparing the dynamic shear modulus and damping ratio of reinforced expansive soil and unreinforced expansive soil under different confining stress through freeze-thaw cycle experiments, the geosynthetic-reinforced grille influence on the expansive soil under the freeze-thaw cycle condition was discussed.
e change of the axial deformation, dynamic shear modulus, and damping ratio of the sample under different confining stress in one freeze-thaw cycle or multiple freeze-thaw cycles was also calculated. e main conclusions are as follows: (1) e axial displacement of the samples varies under different stress states. ere is a significant exponential increase of the axial displacement of the expansive soil sample with the number of freeze-thaw cycles. e characteristics of reinforced expansive soil under two stress states after a freeze-thaw cycle are as follows: at 50 kPa confining pressure, reinforcement can restrain the axial compression deformation; at 10 kPa confining pressure, reinforcement can restrain the axial expansion deformation.
(2) e reinforced expansive soil shows smaller strain changes than the unreinforced soil under different freeze-thaw cycles and reinforcement can restrain the axial deformation of expansive soil samples under freeze-thaw conditions. e axial compression or expansive displacement of the reinforced sample is lower than the unreinforced one, both in a confining pressure of 50 kPa and 10 kPa, after seven freeze-thaw cycles. It shows that reinforcement can alleviate the frost heave of expansive soil significantly. (3) Reinforcement can increase the dynamic shear modulus of the expansive soil sample and delay the structural damage effect caused by frost heave. e dynamic shear modulus of the unreinforced and reinforced samples increases after the first freezethaw cycle. It decreases after the second freeze-thaw cycle in the unreinforced one. e decrease of the dynamic shear modulus of the reinforced sample is delayed by a freeze-thaw cycle compared with the unreinforced one. e dynamic characteristics of expansive soil show complex changes under the coupling of structural damage caused by Frost Heave and aw and consolidation compactness, which needs to be further studied. (4) Reinforcement can increase the damping ratio of expansive soil under the two stress states. e λ of the reinforced expansive soil samples without freeze-thaw cycles is increased when the confining pressure is 50 kPa and the deformation is 1 × 10 −3 ; the λ is increased in 10 kPa confining pressure and 1 × 10 −3 deformation. It shows that the variation of confining pressure has a negligible effect on the damping of the reinforced soil. e energy dissipation effect of reinforced expansive soil is more significant with the increase of dynamic strain, which shows that the growth Advances in Civil Engineering trend of the damping ratio of reinforced expansive soil samples is higher than that of unreinforced samples.
rough triaxial tests of samples with or without reinforcement and under different pressure conditions under freeze-thaw cycle, the influence of reinforcement on soil layer under freeze-thaw damage is clarified, which can provide a solution for engineering construction in seasonal frozen soil area.
Data Availability e data were obtained from independent experiments and are not submitted.

Conflicts of Interest
e authors declare that they have no conflicts of interest.