Experimental Study on Warm Permafrost Dynamic Characteristics under Cyclic Loading in the Cold Region

With the rapid development of infrastructure construction, some places have to face the problem of highway foundation disease, especially for the highway built on warm permafrost in cold region. In order to analyze the inuence of conning pressure and vehicle load to the warm permafrost, the dynamic triaxial tests were conducted on the frozen soil extracted from highway in Yakeshi City. While the load frequency is 6Hz and the test temperature is −1.5°C, we changed the conning pressure and axial stress amplitude, respectively, and then gained the deviator stress-strain curves. e test results show that the shape of deviator stress-strain curve is related to the deviator stress amplitude. When σ3 25 kPa and |σ1−σ3|max 75 kPa, the hysteretic loops approximately appear rectangular and the dynamic modulus increases with loading time increasing for the compression eect. e specimen did not fail when the test stopped, and its hysteretic loop is stable. When σ3 20 kPa and |σ1−σ3|max 100 kPa, the hysteretic loops become smoother and appear oval.e test stopped while the axial strain reached 5% after loading 1279 times, and the dynamic modulus decreases with loading time increasing. When σ3 30 kPa and |σ1−σ3|max 115 kPa, the test stopped just after the 154 loop, and the hysteretic loop area linearly decreased with increasing loading time. e research conclusions in this article have numerous reference values for the highway design, construction, and operation built on the warm permafrost.


Introduction
With large-scale construction of infrastructure in China, the highway mileage is largely increasing in the northeast region. For the cold climate, the subgrade works in a poor condition, and the problems of seasonal frozen soil and permafrost need to be solved. Permafrost', especially for the warm permafrost, accumulative plastic deformation is obvious under tra c loading that causes road settlement.
is study reveals the dynamic characteristics of warm permafrost under cyclic loading with di erent con ning pressure and dynamic stress amplitude, and it can provide technical reference for the highway design, construction, and operation in the future that built on the warm permafrost. It is also important to avoid highway foundation disease caused by excessive vehicle load. e warm permafrost is the frozen soil that the temperature is between −1.5°C and 0.0°C, so it is also called permafrost in phase change zone. e warm permafrost is sensitive to the temperature change, and its mechanical property is more complicated than other permafrost [1].
Xu et al. [2] studied the dynamic stress-strain relationship for frozen soil and presented the relation between the damping ratio and experimental temperature, con ning pressure, water content, and vibratory frequency. e main in uencing factors to the damping ratio are experimental temperature, con ning pressure, and frequency.
Zhao et al. [3] tested the frozen soil parameters including dynamic elastic modulus and dynamic damping ratio and found variation laws of dynamic mechanics parameters of frozen silty clay and ne sand are the same. e dynamic elastic modulus of frozen soil increases with increment of frequency.
Dynamic triaxial tests are carried out on frozen clay sampled from the Qinhai-Tibet railway under di erent temperature and con ning pressure [4]. e frozen soil dynamic strength linearly decreases with the increase in logarithmic cyclic number. Gao et al. [5] studied the dynamic characteristics of warm and ice-rich frozen soil. e dynamic modulus decreases as the dynamic strain increases when the confining pressure is larger than 0.5 MPa, while the dynamic modulus increases at first and then decreases as the dynamic strain increases when the confining pressure is below 0.5 MPa. e dynamic modulus of frozen soil is affected by confining pressure, frequency, temperature, and water content, and the damping ratio decreases as frequency increases and temperature decreases [6]. e dynamic properties of frozen clay are studied by hysteresis curves, and the result showed the soil stiffness increases, while the viscosity, degree of microscopic damage, residual strain, and energy dissipation decrease with the decreasing temperature and increasing vibration frequency when the temperature is −0.5°C to 4°C and the vibration frequency is 1-10 Hz [7]. e dynamic strength characteristics of frozen silty clay was studied using triaxial cycle tests when the confining pressures vary between 0.3 MPa and 16 MPa and the temperature between −4°C and −6°C.
e dynamic strength depended not only on the number of vibration and confining pressures but also on loss of energy resulted from cyclic loading [8].
e dynamic properties of the frozen soil were studied by experiments [9,10] in recent years.
Yakeshi City is located in west of the Greater Khingan Mountain's median ridge in the northeast of Inner Mongolia Autonomous Region, and the reference geological information reveals there is extensive warm permafrost in this area. In order to investigate the dynamic properties of frozen subgrade in this area, the frozen triaxial tests were conducted on the remoulded soil.

e Testing Instrument and Specimen.
All the tests were conducted on the STX-100 dynamic triaxial tester made by American GCTS Company, as shown in the Figure 1. e maximum axial pressure is 25 kN, the maximum frequency is 10 Hz, the maximum hydraulic cylinder stroke length is 50 mm, and the maximal confining pressure is 2 MPa. e tester connects to a homothermal liquid circulation system and maintains a constant temperature by cooling liquid circulator. e liquid temperature can be changed from −50°C to 200°C in this system. e specimens are remoduled by the soil extracted from highway subgrade in Yakeshi City, which is sifted by 2 mm geotechnical screen. e sifted soil dense is 1.74 g/cm ; then, the soil is remoduled to specimens with 16.5% water content. e radius of specimen is 38 mm, while its height is 76 mm. e specimen is installed in the freezing chamber in the tester and was kept at −1.5°C for 12 hours; then, uniformly start loading on the specimen.

Loading Process.
e cyclic loading is loaded on the top of frozen soil specimen, and the confining pressures are 25 kPa, 20 kPa, and 30 kPa, while the corresponding axial pressure is 25 kPa, 40 kPa, and 42.5 kPa respectively. First, linearly load axial pressure and confining pressure, then the both pressures remain stationary for consolidation, and then load the cyclic loading on the specimen. e loading process is shown in Figure 2.

Test Parameters.
e frozen triaxial test parameters such as temperature, frequency, confining pressure, and dynamic cyclic stress amplitude are listed in Table 1.
According to GB/T 50269-2015 [31], stop testing when the specimen axial strain reaches 5% or the cyclic number reaches 50000 whose axial strain still not reaches 5%.

e Test Result When σ 3 � 25 kPa, |σ 1 -σ 3 | max � 75 kPa.
e deviator stress-axial dynamic strain curves are shown in Figure 3 for the 100 th -110 th , 1000 th -1010 th , 10000 th -10010 th , 30000 th -30010 th , and 49990 th -50000 th hysteretic loop, respectively. e density degree of hysteretic loop increases with loading time increasing, and the hysteretic loop center moves to the right gradually, but the maximal axial strain is only 0.46% which does not reach 5% when the test stopped. e hysteretic loop is stable and the specimen did not fail in the test. e hysteretic loops of specimen appear rectangular, and the specimen has elastic and strain hysteretic properties during loading and unloading processes. In the primary phase, the dynamic load increased gradually and the pores were compressed, so the plastic deformation increased. With increasing cyclic loading time, the plastic deformation increment converged gradually, and the specimen maintains stability in the test. e area of hysteretic loops was gained from the 1000 th , 5000 th , 10000 th , 25000 th , and 5000 th curves, and it decreases linearly with increasing loading time, as shown in Figure 4. e hysteretic loop area can be calculated by the following equation: where N is the loading time, and S is the hysteretic loop area. e correlation coefficient is above 0.85 for equation (1). According to [12], the dynamic modulus E d is calculated according to the following equation and Figure 5. Advances in Civil Engineering where σ d is the dynamic axial stress, and ε d is the dynamic axial strain. e dynamic damping coefficient λ was calculated by the following equation.
where S shade is the shade area, and S ∆ABC is the area of ∆ABC in Figure 5. From the 1000 th , 5000 th , 10000 th , 25000 th , and 50000 th hysteretic loop curves, the dynamic modulus and damping ratio of warm permafrost were calculated, and the results are listed in Table 2.
e dynamic properties of warm permafrost are basically stable when the confining pressure is 25 kPa and the axial pressure is not more than 75 kPa. With the increasing loading time, the specimen is compressed to be stiffer, and its dynamic modulus slightly rises while the damping ratio drops slightly.

e Test Result When σ 3 � 20 kPa, |σ 1 -σ 3 | max � 100 kPa.
e deviator stress-axial dynamic strain curves are shown in Figure 6 for the 400 th -410 th , 800 th -810 th , and 1269 th -1279 th hysteretic loop, respectively. When the cyclic loading time is 1279, the axial strain reaches 5%, and then, the test stopped. e hysteretic loop curves are approximately oval. With increasing loading time, the hysteretic loop center moves to the right faster, which means the axial strain increases faster than the previous test.
e hysteretic loops are more intensive with increasing loading time.
After extracting the 400 th , 600 th , 800 th , 1000 th , and 1200 th hysteretic loop curves, the relationship of hysteretic loop area and loading times was gained, as shown in Figure 7. e hysteretic loop area S can be calculated by the following equation: where N is the loading time. e correlation coefficient is above 0.92 for equation (4). e dynamic modulus and damping ratio under different loading times are listed in Table 3. e hysteretic area linearly decreases with loading time basically. For the accumulation of damage in the specimen, the dynamic modulus decreased with increasing loading time basically in the test.

e Test Result When σ 3 � 30 kPa, |σ 1 -σ 3 | max � 115 kPa.
First, both the axial pressure and confining pressure linearly increased until the values reached 30 kPa and then gradually loaded the axial cyclic loading with a 42.5 kPa amplitude until the axial strain reached 5%.
Extracted the 40 th -50 th , 90 th -100 th , and 140 th -154 th hysteretic loops, as shown in Figure 8; the hysteretic loops presented to ovals in the loading and uploading processes.
e hysteretic loop appears with viscoelastic properties with high deviator stress for the warm permafrost. With increasing loading time, the hysteretic loop center moves to the bigger strain direction, and plastic deformation accumulated gradually until the axial strain reached 5%. e plastic deformation increment is smaller and smaller that is manifested by the hysteretic loop density in Figure 8.    When the cyclic loading time is 154, the axial strain reaches 5%, and then, the test was stopped. Extracting from the 50 th , 75 th , 100 th , 125 th , and 150 th hysteretic loops, the relationship between the loop area and loading time is shown in Figure 9.
e hysteretic loop area linearly decreases with loading time basically, and its value can be calculated by the following equation: where N is the loading time. e correlation coefficient is above 0.98 for equation (5). e dynamic modulus and damping ratio were gained from the 50 th , 75 th , 100 th , 125 th , and 150 th hysteretic loop curves and are listed in Table 4.
Both the dynamic modulus and damping ratio decrease with loading times basically, and the damage accumulation was always developing in this process until the sample failed.

Conclusion
Different deviator stress with 6 Hz is loaded on the specimens separately when the temperature is kept at −1.5°C, and the axial pressure is cyclic loading with different confining pressure and different amplitude. e results show that the mechanical properties of warm permafrost are related to the deviator stress. As the confining pressure and deviator stress amplitude are both 25 kPa, the hysteretic loops are approximately rectangular, and the specimen is always stable during the test process. When the confining pressure is 20 kPa and deviator stress amplitude is 40 kPa, the hysteretic loop curves become smother and appear oval. e specimen failed after 1279 loading times. With increasing deviator stress amplitude, the failed loading time declines rapidly. When the confining pressure is 30 kPa and deviator stress amplitude is 42.5 kPa, the specimen failed just after 154 loading times.
With the smallest deviator stress amplitude, the dynamic modulus increases slightly for the compression. When the deviator stress increases, the dynamic modulus decreases for the damage accumulation in other tests. e hysteretic loop area linearly decreases with loading time in all tests.

Data Availability
e data used to support the findings of this study are included within the article.

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