# Seismic Behavior of Qinghai-Tibetan Railway Embankment in Permafrost Regions: A Case Study

Authors: Tuo Chen; Jianzhou Wang; Bo Wang
Journal: Shock and Vibration
 (2023)

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## Abstract

The temperature is a critical factor that determines the unfrozen water content and ice content in the frozen soil. In view of mechanical properties of the frozen soil depend on the volume of components of the four-phase systems, thus the temperature has a significant impact on the mechanical behaviors and deformation properties. The thermal state of the embankment in permafrost regions has a significant seasonal difference, then the seismic performance of the embankment alters with the season. In addition, the seismic performance is highly influenced by the properties of the earthquake motion, especially the seismic intensity. Combining these factors, a numerical simulation was conducted in this study. In this study, taking a typical section of Qinghai-Tibet Railway as an example, a numerical case study on the seismic behavior of embankment was carried out using the dynamic explicit FEM code ABAQUS/Explicit. The El Centro excitation with different intensities was performed in numerical analysis and two distinct thermal states of the embankment in extreme cold and warm days were considered as well. The seismic behaviors of the embankment, including the acceleration responses, the strain response, and the displacement response, were studied effectively. This paper proposes approaches and methods to study the seismic failure mechanism of the infrastructures, and the results can serve as a scientific basis for resisting earthquakes and preventing disasters in cold regions.


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## Body

## 1. Introduction

The Qinghai-Tibet Plateau (QTP) is the largest high-altitude permafrost region at low- and mid-latitudes in the world [1]. The permafrost area on the Qinghai-Tibet Plateau is estimated to be about 1.04 × 106 km2 [2]. With the in-depth implementation of the western China development strategy and the construction of “Belt and Road,” there is an increasing demand for cold region engineering in China. It is imperative to construct major national strategic projects in high-altitude permafrost regions. The Qinghai-Tibet Expressway, the Golmud—Lhasa oil product pipeline, the high voltage power transmission and transformation line, and other major construction projects will be constructed on the QTP. Furthermore, it needs to be recognized that the tectonic movement and crustal deformation are very strong and active faults are widely distributed. The QTP is located in the region with the most intensive deformation and high-level seismic activities. Seismologists are now suggesting the QTP has entered the third active seismic period since 1995 [3]. A sequence of large earthquakes occurred, including the Mani earthquake (Ms 7.9) on November 8, 1997; the Kunlunshan earthquake (Ms 8.1) on November 14, 2001; the Wenchuan earthquake (Ms 8.0) on May 12, 2008; the Yushu earthquake (Ms 7.1) on April 14, 2010; the Yutian earthquake (Ms 7.3) on February 12, 2014, and the Menyuan earthquake (Ms 6.9) on January 8, 2022, has attracted attention from engineers and researchers. These earthquakes produced surface ruptures with complicated structures and a great length, which had brought enormous damages to the transport infrastructures in the QTP area. Figure 1 illustrates the surface rupture zone in the permafrost area caused by the Kunlunshan earthquake and the Menyuan earthquake, respectively. The potential earthquake risk has been a significant engineering challenge to the construction and maintenance of infrastructure in permafrost regions [4]. As a typical transport infrastructure, railway embankment damage, including rupture and deformation, may occur during an earthquake. Furthermore, the damage of the embankment was not observed in a typical earthquake. Thus the study of seismic response of linear engineering structures in permafrost regions, especially railway engineering, has become a key problem that needs to be solved as soon as possible.Figure 1
Surface rupture zone in permafrost area caused by earthquakes: (a) Kunlunshan earthquake; (b) Menyuan earthquake.
(a)(b)Frozen soil is a kind of composite material composed of soil, unfrozen water, and ice. Compared with ordinary soil, the most obvious physical quantities are freezing temperature and unfrozen water content [5, 6]. Due to mechanical instability and temperature sensitivity, frozen soil can be categorized as “special” soil and its physical and mechanical properties may broadly differ across seasons [7]. As for the embankment engineering in cold regions, the interaction between frozen soil and climatic system directly affects the seismic dynamic response and failure characteristics. The seismic performance varies significantly in different seasons and regions, directly influencing the strategies of earthquake prevention and disaster mitigation. Thus, it is essential to study the seismic response and dynamic stability of the embankment in permafrost regions. The most direct research approach to studying the seismic behavior of structures is the shaking table test. In recent years, this method has been used wildly in embankment engineering [8–11]. However, there still have some shortcomings to this method, such as the huge cost and time-consuming, reduced scale model testing. Furthermore, it is very difficult to consider the effects of environmental factors on the seismic behavior of the embankment, such as the freezing and thawing process. With the rapid development of computer technology, the numerical analysis method has become an important and practical tool and provides an economical way to study the seismic behavior of embankments in permafrost regions. Wang et al. [12, 13] studied the earthquake dynamic stress characteristic and seismic displacement characteristic of the roadbed on permafrost site, and then proposed the stress intensity criteria of earthquake breakage. Esmaeili and Noghabi [14] developed a finite-element model to investigate the dynamic behavior of ballasted railway tracks subjected to earthquake motion. Chen et al. [15] discussed the impact of permafrost change on the seismic site response and then studied the dynamic response of the traditional embankment in permafrost regions. Li et al. [16, 17] investigated seasonal differences in seismic responses of an embankment on a sloping ground in permafrost regions. In addition, a thermo-dynamic coupled model for the crushed-rock embankment was proposed and a series of numerical computations were conducted. However, despite the fact that seismic responses of embankments in permafrost regions have been studied by many authors, few papers have been published on the seasonal differences in seismic responses of embankments in permafrost regions induced by an earthquake with different intensities.In this work, based on a prototype of a typical traditional embankment at the Beiluhe section of the QTR, a full-scale simulation model is established to study the seismic behavior of the embankment under earthquake excitation. An actual seismic record (EI Centro earthquake, 1940) is selected as the input ground motion and different intensities were considered. Moreover, two distinct thermal states of the embankment on extreme cold and warm days are considered as well. The seismic behaviors of an embankment, including the acceleration responses, the strain response, and the displacement response, were studied effectively. The objective of this research is to obtain more details about the seismic behaviors of the embankment and to investigate the seismic damage evolution and failure process of embankment in permafrost regions.


## 2. Numerical Model and Basic Equations

### 2.1. Model of Railway Embankment

The Beiluhe segment, located in an arid climate region of QTP, belongs to the unfavorable and bad engineering geological section. The MAGT of this segment varies from −1.41 and −1.68°C. The freezing period of which is from September to the following April [18]. The active layer thaws in summer while freezes in winter, and the natural permafrost table of the segment is between −2 m and −3 m [19]. Moreover, the thick ice layer underground near the permafrost table is abundant, and the temporal and spatial variations in the thermal regime are observed in this segment. Whereas, different types of embankments have been constructed, such as traditional embankments, crushed-rock embankments, duct-ventilated embankments, and thermosiphon embankments.Figure2 illustrates the cross-section profile of a typical traditional embankment and the soil layer structure at the Beiluhe section K1137 + 700 of the QTR. The surface layer of the ground, defined as the active layer, is a gravelly sand layer. Beneath the active layer, there exists the frozen silty clay, also named as permafrost. The underlying permafrost contains the upper ice-poor permafrost with a thickness of 6 m and the lower ice-poor permafrost with a thickness of 22 m. According to the ground temperature measurement conducted by the State Key Laboratory of Frozen Soil Engineering, Chinese Academy of Science, the natural ground temperature variation and the distribution of mean annual ground temperature are defined; [20–22]. The natural permafrost table is approximately 2 m, and the temperature of the permafrost in this area is about −1.0°C.Figure 2
The cross-section profile and the soil layer structure of a typical traditional embankment.Based on the prototype of the typical traditional embankment at the Beiluhe section, a full-scale numerical model of the embankment is established, as shown in Figure3. The simulation is performed based on the plane strain assumption. In this study, the size of the mesh was controlled in order to guarantee the accuracy of dynamic analysis. The mesh size is limited by the shortest wavelength of the input seismic wave. To ensure the authenticity of wave propagation in the media, the maximum size of the element must be less than 1/10∼1/8 of the minimum wavelength. In our simulation, the maximum mesh size is only 1 m × 1 m, and the accuracy of calculation meets the requirements.Figure 3
The full-scale numerical model of a typical traditional embankment (unit: m).In the numerical model, two different boundary conditions are used, respectively. On the left and right sides of the numerical model, the free field method is taken to prevent wave reflection at the boundary of the embankment model. Moreover, the artificial boundary conditions are adopted at the bottom of the model where the horizontal direction is released and the artificial seismic waves are used as the input seismic motion for the numerical calculation.


### 2.2. Basic Equations

To study the dynamic behavior of the Qinghai-Tibet railway embankment under seismic loads, the nonlinear dynamic finite element analysis method is applied. The kinetic equation can be expressed as follows:(1)M∙xt¨+C∙xt˙+K∙xt=Pt,where M, C, and K are, respectively, the mass matrix, stiffness matrix, and damping matrix. Pt refers to the dynamic loading.When the dynamic loading is small, the soil is in an elastic stage which adopts the linear elastic model, its stress-strain relation meets Hook’s law. When the loading is getting greater, the elastoplastic properties of the soil need to be considered. As for any stress incrementdσ, the total strain increment dε includes elastic strain increment dεe and plastic strain increment dεp, which could be written as follows:(2)dε=dεe+dεp=DT−1dσ+dλ∂F∂σ,where DT is the elastic matrix related to temperature and unfrozen water, the dλ is the plastic coefficient, and F represents the plastic potential function.In this paper, the Mohr–Coulomb elastic-plastic yield criterion is utilized to express the plastic potential function. This criterion assumes that soil failure occurs when shear stress in the plane of the material exceeds the value, which is linearly dependent on the normal stress to that plane [23, 24]. The Mohr–Coulomb criterion can be written as follows:(3)F=J13sinφ+J2′cosθ−13sinθsinφ−Ccosφ=0,where J1 is the first stress tensor invariant; J2′ denotes the second deviatoric stress tensor invariant, and θ is the Lode angle. C denotes the cohesive strength and φ denotes the internal friction angle, C and φ are related to the temperature.


## 2.1. Model of Railway Embankment

The Beiluhe segment, located in an arid climate region of QTP, belongs to the unfavorable and bad engineering geological section. The MAGT of this segment varies from −1.41 and −1.68°C. The freezing period of which is from September to the following April [18]. The active layer thaws in summer while freezes in winter, and the natural permafrost table of the segment is between −2 m and −3 m [19]. Moreover, the thick ice layer underground near the permafrost table is abundant, and the temporal and spatial variations in the thermal regime are observed in this segment. Whereas, different types of embankments have been constructed, such as traditional embankments, crushed-rock embankments, duct-ventilated embankments, and thermosiphon embankments.Figure2 illustrates the cross-section profile of a typical traditional embankment and the soil layer structure at the Beiluhe section K1137 + 700 of the QTR. The surface layer of the ground, defined as the active layer, is a gravelly sand layer. Beneath the active layer, there exists the frozen silty clay, also named as permafrost. The underlying permafrost contains the upper ice-poor permafrost with a thickness of 6 m and the lower ice-poor permafrost with a thickness of 22 m. According to the ground temperature measurement conducted by the State Key Laboratory of Frozen Soil Engineering, Chinese Academy of Science, the natural ground temperature variation and the distribution of mean annual ground temperature are defined; [20–22]. The natural permafrost table is approximately 2 m, and the temperature of the permafrost in this area is about −1.0°C.Figure 2
The cross-section profile and the soil layer structure of a typical traditional embankment.Based on the prototype of the typical traditional embankment at the Beiluhe section, a full-scale numerical model of the embankment is established, as shown in Figure3. The simulation is performed based on the plane strain assumption. In this study, the size of the mesh was controlled in order to guarantee the accuracy of dynamic analysis. The mesh size is limited by the shortest wavelength of the input seismic wave. To ensure the authenticity of wave propagation in the media, the maximum size of the element must be less than 1/10∼1/8 of the minimum wavelength. In our simulation, the maximum mesh size is only 1 m × 1 m, and the accuracy of calculation meets the requirements.Figure 3
The full-scale numerical model of a typical traditional embankment (unit: m).In the numerical model, two different boundary conditions are used, respectively. On the left and right sides of the numerical model, the free field method is taken to prevent wave reflection at the boundary of the embankment model. Moreover, the artificial boundary conditions are adopted at the bottom of the model where the horizontal direction is released and the artificial seismic waves are used as the input seismic motion for the numerical calculation.


## 2.2. Basic Equations

To study the dynamic behavior of the Qinghai-Tibet railway embankment under seismic loads, the nonlinear dynamic finite element analysis method is applied. The kinetic equation can be expressed as follows:(1)M∙xt¨+C∙xt˙+K∙xt=Pt,where M, C, and K are, respectively, the mass matrix, stiffness matrix, and damping matrix. Pt refers to the dynamic loading.When the dynamic loading is small, the soil is in an elastic stage which adopts the linear elastic model, its stress-strain relation meets Hook’s law. When the loading is getting greater, the elastoplastic properties of the soil need to be considered. As for any stress incrementdσ, the total strain increment dε includes elastic strain increment dεe and plastic strain increment dεp, which could be written as follows:(2)dε=dεe+dεp=DT−1dσ+dλ∂F∂σ,where DT is the elastic matrix related to temperature and unfrozen water, the dλ is the plastic coefficient, and F represents the plastic potential function.In this paper, the Mohr–Coulomb elastic-plastic yield criterion is utilized to express the plastic potential function. This criterion assumes that soil failure occurs when shear stress in the plane of the material exceeds the value, which is linearly dependent on the normal stress to that plane [23, 24]. The Mohr–Coulomb criterion can be written as follows:(3)F=J13sinφ+J2′cosθ−13sinθsinφ−Ccosφ=0,where J1 is the first stress tensor invariant; J2′ denotes the second deviatoric stress tensor invariant, and θ is the Lode angle. C denotes the cohesive strength and φ denotes the internal friction angle, C and φ are related to the temperature.


## 3. Model Parameters and Input Seismic Motion

The freezing and thawing states are different at different times with the variation of the air temperature, which influences the soil water migrations in the embankment. The seismic behavior analysis of the embankment in the permafrost area is a very complicated problem when considering this impact. However, in order to simplify the study, two extreme situations including the warmest and coldest seasons are considered. In the warmest season, the roadbed filling and the active layer are supposed to be completely thawed. While in the coldest season, the roadbed filling and the active layer are fully frozen. The mudstone is always frozen all year round. The soil was regarded as an elastic-plastic material and the ballast was assumed to be a linear elastic material [25]. Then different soil mechanic parameters are endowed in different situations. The mechanical parameters of the numerical model are presented in Table 1, based on a series of triaxial tests [26–28]. The temperature in Table 1 is determined based on the ground temperature data at the Beiluhe section.Table 1
Soil mechanics parameters at the survey area.
LithologyWater content (%)Temperature (°C)Density (kN/m3)Elastic modulus (kPa)Poisson ratioCohesion force (kPa)Internal frictional angleBallast—520.02.00E50.30——Roadbed filling26.3219.06.10E40.313023°26.3−119.01.14E50.2912032°Silty clay200.518.02.80E40.3515022°20−118.05.40E40.3124030°Mudstone15.2−121.03.40E50.2534039°In this work, the El Centro earthquake wave (N-S direction) that occurred in 1940, is selected as seismic load in the numerical case study. Acceleration time history and fast Fourier transform (FFT) curves are presented in Figure4. The maximum acceleration is 0.348 g and the predominant frequency is 1.47 Hz.Figure 4
Acceleration time historie and FFT spectra of El Centro earthquake wave: (a) the acceleration time history; (b) the FFT spectra.
(a)(b)According to the seismic intensity zoning map in China, the QTP is located in areas with high seismic intensity above VII degrees. Thus in the numerical analysis, the acceleration amplitude of the input seismic motion is adjusted from 0.15 g to 0.4 g, which corresponds to different earthquake intensities (from intensity VII to intensity IX). The adjusted amplitudes and the amplification coefficients are shown in Table2.Table 2
Adjusted amplitudes and the amplification coefficients of the input seismic load.
Adjusted amplitude0.15 g0.2 g0.25 g0.3 g0.348 g0.4 gAmplification coefficients0.430.570.720.861.01.15Seismic intensityVIIVIIIVIIIVIIIVIIIIX


## 4. Numerical Simulation Results

In order to accurately capture the mechanical behavior of the embankment during the seismic loading, the acceleration response characteristics are investigated, as well as the dynamic strain and displacement response. Considering the dynamic stability of the embankment is largely concerned, then the characteristic pointS on the embankment’s shoulder and the characteristic point T at the toe of the embankment, are arranged in the model.


### 4.1. Acceleration Response Analysis

In this case study, the seismic input motion is in the horizontal direction and thus the horizontal acceleration response of the embankment in different seasons is investigated. The acceleration contour map of the embankment in warm and cold seasons, under the El Centro seismic motion, are depicted in Figures5(a) and 5(b), respectively.Figure 5
The Peak ground horizontal acceleration contour in different seasons: (a) horizontal acceleration contour map of the embankment in the warm season; (b) horizontal acceleration contour map of the embankment in the cold season.
(a)(b)It can be well demonstrated that the rail embankment has an obvious amplification effect on the seismic wave, comparing the natural surface. The acceleration response of the embankment is greater in the warm season than in the cold season. Furthermore, the maximum acceleration appears at the top of the embankment in the cold season, while the acceleration at both embankment slopes is more significant in the warm season. The main reason for this phenomenon is the stiffness improvement of the embankment in cold seasons. The elastic modulus and strength of soil inside the embankment are distinctly enhanced. Consequently, the seismic acceleration responses of the embankment are weakened, which is similar to the soil reinforcement effect.The acceleration time history curve of the characteristic pointS and point T is indicated in Figures 6(a) and 6(b), respectively. The maximum acceleration on the embankment’s shoulder is 8.45 m·s−2 and 7.86 m·s−2 in the warm and cold seasons, respectively. In contrast, the maximum acceleration at the toe of the embankment is 5.08 m·s−2 and 4.65 m·s−2 in the warm and cold seasons, respectively. The acceleration amplitude becomes larger in the warm season and the amplification effect of the embankment’s shoulder is more significant compared with the toe of the embankment.Figure 6
The acceleration time history curve of the characteristic point in different seasons: (a) characteristic pointS; (b) characteristic point T.
(a)(b)In order to quantify the seismic response of the rail embankment, the maximum acceleration is characterized using the amplification coefficient, which is defined as the ratio of peak ground acceleration to input seismic acceleration. The variation of amplification coefficients with the input ground motion acceleration amplitude, of characteristic pointsS and T, are illustrated in Figure 7.Figure 7
The variation of amplification coefficient with the input ground motion acceleration amplitude: (a) characteristic pointS; (b) characteristic point T.
(a)(b)The results indicate that the acceleration amplification coefficient of railway embankment is significantly larger in warm seasons compared with cold seasons, and the acceleration amplification effect on the embankment’s shoulder is more significant than the slope toe. Moreover, the acceleration amplification coefficient will decrease with the increase of input acceleration amplitude, exhibiting approximately linear characteristics. This tendency can be expressed using the following linear formula in slope-intercept form:(4)y=−kx+b.In the formula mentioned above (equation (4)), the slope parameter k indicates the attenuation degree of acceleration, and the intercept parameter b shows the maximum amplification coefficient, as shown in Table 3.Table 3
The value of slope and intercept parameter.
Characteristic pointThe locationCharacteristic timeSlope-intercept parameterskbSEmbankment’s shoulderWarm season0.142.89Embankment’s shoulderCold season0.042.41TEmbankment slope toeWarm season0.021.56Embankment slope toeCold season0.0071.36


### 4.2. Velocity Response Analysis

The velocity time history curve of the characteristic pointS and point T is indicated in Figures 8(a) and 8(b), respectively. The maximum velocity on the embankment’s shoulder is 0.84 m·s−1 and 0.67 m·s−1 in the warm and cold seasons, respectively. In contrast, the maximum acceleration at the toe of the embankment is 0.60 m·s−1 and 0.54 m·s−1 in the warm and cold seasons, respectively. The velocity response is greater in the warm season and the value is larger on the embankment’s shoulder compared with the toe of the embankment.Figure 8
The velocity time history curve of the characteristic point in different seasons: (a) characteristic pointS; (b) characteristic point T.
(a)(b)Figure9 illustrates the variation of the maximum velocity magnitude with the input ground motion acceleration amplitude. The maximum velocity magnitude increases with the increase of input acceleration amplitude. Moreover, the velocity difference ∆V between the point S and point T increases with the increasing input acceleration, and this value in the warm season ∆Vw is greater than in the cold season ∆Vc. It is indicated that the embankment is prone to cracking or deformation in the warm season.Figure 9
The variation of maximum velocity with the input ground motion acceleration amplitude.


### 4.3. Displacement Response Analysis

Figure10 illustrates the displacement time history on the embankment’s shoulder in a horizontal direction. This displacement is the relative value between point S and point T. The displacement changes nonlinearly with the duration time of the earthquake, presenting a maximum value at the peak acceleration time. The maximum displacement on the embankment’s shoulder is 7.44 cm and 6.74 cm in the warm and cold seasons, respectively.Figure 10
The displacement time history on the embankment’s shoulder.Figure11 illustrates the distribution of the maximum relative displacement with the input ground motion acceleration amplitude in different seasons. As observed in Figure 10, the horizontal displacement on the embankment’s shoulder is larger in the warm season than in the cold season. The displacement increases with the increase of input ground motion acceleration amplitude, and the variation tendency is approximately linear. The maximum displacement on the embankment’s shoulder can reach up to 9 cm under the action of 0.4 g seismic excitation in the warm season, while this value is only 2.6 cm under the action of 0.2 g seismic excitation in the cold season. It can be considered that cracks or even collapse will occur when the input peak acceleration reaches a certain value.Figure 11
The distribution of the maximum relative displacement.


### 4.4. Strain Response Analysis

Figure12 illustrates the maximum plastic strain of the embankment under the seismic motion with different peak accelerations, in different seasons. It is concluded from the results that the plastic zone gradually appears in the embankment when the seismic intensity reaches a certain value. The plastic zone starts to develop at the slope toe of the embankment, and there exists a continuous extension of the plastic zone with the increase of the seismic intensity. Moreover, on the left side of the embankment, where there is no pavement, the plastic strain exponent is larger and the plastic deformation was significantly higher.Figure 12
The maximum plastic strain of the embankment under the seismic motion: (a) in the cold season; (b) in the warm season.
(a)(b)Subsequently, the variation of the maximum plastic strain magnitude in the railway embankment with the input ground motion acceleration amplitude is illustrated in Figure13. With the increase of input acceleration amplitude, the maximum plastic strain magnitude increase, and this trend is more significant in warm seasons. In a warm season, there is no plastic zone generated in the embankment until the input acceleration amplitude reaches 2.0 m·s−2. The plastic strain magnitude ranges from 4.43 E − 3 to 2.92 E − 2, and the corresponding acceleration amplitude is within the range from 2.0 to 4.0 m·s−2. In a cold season, the plastic will appear when the input acceleration amplitude reaches 2.5 m·s−2, and the plastic strain magnitude varies from 2.19 E − 3 to 6.17 E − 3 when the input acceleration amplitude change from 2.5 to 4.0 m·s−2.Figure 13
The variation of maximum plastic strain with the input ground motion acceleration amplitude.


## 4.1. Acceleration Response Analysis

In this case study, the seismic input motion is in the horizontal direction and thus the horizontal acceleration response of the embankment in different seasons is investigated. The acceleration contour map of the embankment in warm and cold seasons, under the El Centro seismic motion, are depicted in Figures5(a) and 5(b), respectively.Figure 5
The Peak ground horizontal acceleration contour in different seasons: (a) horizontal acceleration contour map of the embankment in the warm season; (b) horizontal acceleration contour map of the embankment in the cold season.
(a)(b)It can be well demonstrated that the rail embankment has an obvious amplification effect on the seismic wave, comparing the natural surface. The acceleration response of the embankment is greater in the warm season than in the cold season. Furthermore, the maximum acceleration appears at the top of the embankment in the cold season, while the acceleration at both embankment slopes is more significant in the warm season. The main reason for this phenomenon is the stiffness improvement of the embankment in cold seasons. The elastic modulus and strength of soil inside the embankment are distinctly enhanced. Consequently, the seismic acceleration responses of the embankment are weakened, which is similar to the soil reinforcement effect.The acceleration time history curve of the characteristic pointS and point T is indicated in Figures 6(a) and 6(b), respectively. The maximum acceleration on the embankment’s shoulder is 8.45 m·s−2 and 7.86 m·s−2 in the warm and cold seasons, respectively. In contrast, the maximum acceleration at the toe of the embankment is 5.08 m·s−2 and 4.65 m·s−2 in the warm and cold seasons, respectively. The acceleration amplitude becomes larger in the warm season and the amplification effect of the embankment’s shoulder is more significant compared with the toe of the embankment.Figure 6
The acceleration time history curve of the characteristic point in different seasons: (a) characteristic pointS; (b) characteristic point T.
(a)(b)In order to quantify the seismic response of the rail embankment, the maximum acceleration is characterized using the amplification coefficient, which is defined as the ratio of peak ground acceleration to input seismic acceleration. The variation of amplification coefficients with the input ground motion acceleration amplitude, of characteristic pointsS and T, are illustrated in Figure 7.Figure 7
The variation of amplification coefficient with the input ground motion acceleration amplitude: (a) characteristic pointS; (b) characteristic point T.
(a)(b)The results indicate that the acceleration amplification coefficient of railway embankment is significantly larger in warm seasons compared with cold seasons, and the acceleration amplification effect on the embankment’s shoulder is more significant than the slope toe. Moreover, the acceleration amplification coefficient will decrease with the increase of input acceleration amplitude, exhibiting approximately linear characteristics. This tendency can be expressed using the following linear formula in slope-intercept form:(4)y=−kx+b.In the formula mentioned above (equation (4)), the slope parameter k indicates the attenuation degree of acceleration, and the intercept parameter b shows the maximum amplification coefficient, as shown in Table 3.Table 3
The value of slope and intercept parameter.
Characteristic pointThe locationCharacteristic timeSlope-intercept parameterskbSEmbankment’s shoulderWarm season0.142.89Embankment’s shoulderCold season0.042.41TEmbankment slope toeWarm season0.021.56Embankment slope toeCold season0.0071.36


## 4.2. Velocity Response Analysis

The velocity time history curve of the characteristic pointS and point T is indicated in Figures 8(a) and 8(b), respectively. The maximum velocity on the embankment’s shoulder is 0.84 m·s−1 and 0.67 m·s−1 in the warm and cold seasons, respectively. In contrast, the maximum acceleration at the toe of the embankment is 0.60 m·s−1 and 0.54 m·s−1 in the warm and cold seasons, respectively. The velocity response is greater in the warm season and the value is larger on the embankment’s shoulder compared with the toe of the embankment.Figure 8
The velocity time history curve of the characteristic point in different seasons: (a) characteristic pointS; (b) characteristic point T.
(a)(b)Figure9 illustrates the variation of the maximum velocity magnitude with the input ground motion acceleration amplitude. The maximum velocity magnitude increases with the increase of input acceleration amplitude. Moreover, the velocity difference ∆V between the point S and point T increases with the increasing input acceleration, and this value in the warm season ∆Vw is greater than in the cold season ∆Vc. It is indicated that the embankment is prone to cracking or deformation in the warm season.Figure 9
The variation of maximum velocity with the input ground motion acceleration amplitude.


## 4.3. Displacement Response Analysis

Figure10 illustrates the displacement time history on the embankment’s shoulder in a horizontal direction. This displacement is the relative value between point S and point T. The displacement changes nonlinearly with the duration time of the earthquake, presenting a maximum value at the peak acceleration time. The maximum displacement on the embankment’s shoulder is 7.44 cm and 6.74 cm in the warm and cold seasons, respectively.Figure 10
The displacement time history on the embankment’s shoulder.Figure11 illustrates the distribution of the maximum relative displacement with the input ground motion acceleration amplitude in different seasons. As observed in Figure 10, the horizontal displacement on the embankment’s shoulder is larger in the warm season than in the cold season. The displacement increases with the increase of input ground motion acceleration amplitude, and the variation tendency is approximately linear. The maximum displacement on the embankment’s shoulder can reach up to 9 cm under the action of 0.4 g seismic excitation in the warm season, while this value is only 2.6 cm under the action of 0.2 g seismic excitation in the cold season. It can be considered that cracks or even collapse will occur when the input peak acceleration reaches a certain value.Figure 11
The distribution of the maximum relative displacement.


## 4.4. Strain Response Analysis

Figure12 illustrates the maximum plastic strain of the embankment under the seismic motion with different peak accelerations, in different seasons. It is concluded from the results that the plastic zone gradually appears in the embankment when the seismic intensity reaches a certain value. The plastic zone starts to develop at the slope toe of the embankment, and there exists a continuous extension of the plastic zone with the increase of the seismic intensity. Moreover, on the left side of the embankment, where there is no pavement, the plastic strain exponent is larger and the plastic deformation was significantly higher.Figure 12
The maximum plastic strain of the embankment under the seismic motion: (a) in the cold season; (b) in the warm season.
(a)(b)Subsequently, the variation of the maximum plastic strain magnitude in the railway embankment with the input ground motion acceleration amplitude is illustrated in Figure13. With the increase of input acceleration amplitude, the maximum plastic strain magnitude increase, and this trend is more significant in warm seasons. In a warm season, there is no plastic zone generated in the embankment until the input acceleration amplitude reaches 2.0 m·s−2. The plastic strain magnitude ranges from 4.43 E − 3 to 2.92 E − 2, and the corresponding acceleration amplitude is within the range from 2.0 to 4.0 m·s−2. In a cold season, the plastic will appear when the input acceleration amplitude reaches 2.5 m·s−2, and the plastic strain magnitude varies from 2.19 E − 3 to 6.17 E − 3 when the input acceleration amplitude change from 2.5 to 4.0 m·s−2.Figure 13
The variation of maximum plastic strain with the input ground motion acceleration amplitude.


## 5. Discussion

It has now been confirmed that the seismic response of the embankment structure in permafrost regions is a very complicated water-heat-dynamic coupled problem. There is a real difficulty in the ability to simulate soil hydrothermal transport processes and the deformation-damage-failure process, especially under earthquake excitation. Because of this, very few theoretical and practical results available up to now. As a preliminary study, the numerical simulation in this paper still has some deficiencies. But despite this, the results of our study are consistent with the findings of previous research. Furthermore, our study has revealed some other interesting findings. It is observed that the location of the maximum plastic strain that occurred seems not to coincide with the peak acceleration locations. Because the plastic strain is a parameter to quantify the damage, which reflects the differences or the relationship between the stress and strength. While the acceleration response characteristic is mainly related to the soil layer stiffness.In this paper, starting from the variation of the dynamic response characteristics, we try to make a quantitative risk analysis of the embankment in permafrost regions. Through our research work, it is found that the vulnerability evaluation of the embankment becomes possible when associated with the variation of the plastic strain.


## 6. Conclusions

In this work, based on a prototype of a typical traditional embankment at the Beiluhe section of the QTR, a full-scale simulation model is established and a numerical case study on the seismic behavior of embankment is performed. Two different thermal states of the embankment in extreme cold and warm days are considered, and the influence of seismic intensity on the dynamic response is discussed. The following conclusions can be drawn from the results of this study:(1)
The dynamic response at different positions of the embankment varies greatly in different seasons. The maximum acceleration appears at the top of the embankment in the cold season, while the acceleration at both embankment slopes is more significant in the warm season.(2)
From the acceleration, velocity, and displacement analysis, it can be concluded that cracks or even collapses will occur when the input peak acceleration reaches a certain value. The embankment is prone to collapse or damage in the warm season.(3)
The acceleration amplification coefficient will decrease with the increase of input acceleration amplitude, exhibiting approximately linear characteristics. The displacement increases with the increase of input ground motion acceleration amplitude, and the variation tendency is approximately linear.(4)
With the increase of input acceleration amplitude, the maximum plastic strain magnitude increase, and this trend is more significant in warm seasons. In a warm season, there is no plastic zone generated in the embankment until the input acceleration amplitude reaches 2.0 m·s−2. In a cold season, the plastic will appear when the input acceleration amplitude reaches 2.5 m·s−2.



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*Source: 1737203-2023-02-20.xml*