Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 13, No. 3, 2024 

 

123 

Dynamic	Response	and	Stability	Analysis	of	Anti‐slide	
Pile	Reinforced	Slopes	under	Earthquake	Conditions	
Longqian Zhang 

Department of civil engineering Yunnan University, Yunnan, China 

 

Abstract: This paper examines the seismic stability of a slope located in Shimian County, Ya'an City, Sichuan Province. The 
earthquake activity level in the area is classified as VIII, with a designed peak acceleration of 0.3g. A three-dimensional finite 
element model was established using ABAQUS to analyze the effects of different amplitudes of Wenchuan earthquake waves 
(0.1g, 0.2g, 0.3g) on the skid pile slope. Research has found that as the intensity of seismic waves rises, the peak seismic 
acceleration and displacement at various monitoring locations on the slope surface also grow, and the amplification effect 
becomes more significant at higher altitudes. In addition, the peak horizontal displacement in the x-direction at different 
elevations of the slope surface also increases with the rise in seismic wave amplitude The first principal stress of the skid pile is 
mainly concentrated near the connection between the sliding surface and the skid pile, and the peak stress increases with the 
amplitude of seismic waves. Research has shown that the stability coefficient of skid piles under 0.3g earthquake conditions is 
lower than the standard requirements, indicating that using skid piles alone may not be sufficient to ensure slope stability. 
Recommendations to strengthen or resize the structural design. 

Keywords: Anti-slide pile; Stability; Seismic load; Numerical simulation. 
 

1. Introduction 
Skid pile is a commonly used method to enhance slope 

stability, [1] especially in improving its seismic performance. 
However, there is relatively little studies on the design of anti-
slip piles, especially in the exploration of stress changes 
inside the pile under earthquake conditions. [2] Since the 1995 
Hanshin earthquake in Japan, foreign researchers have begun 
to use dynamic centrifugal simulation tests to explore the 
effects of liquefaction and lateral displacement caused by 
earthquakes on the bending moment and deformation of piles. 
[3] Representative scholars include Brandenberg, Abdoun, and 
J Boulanger et al. [4] However, it should be noted that these 
studies mainly focus on pile foundations, which differ 
significantly from skid piles used as supporting structures. At 
present, research on the reaction to dynamic forces of skid 
piles in China is still limited. After the Wenchuan earthquake 
on May 12th, many skid pile support structures suffered 
varying degrees of damage. [2] Due to the lack of research data 
on the interaction mechanism between skid piles and 
deformed slopes under earthquake action in China. 
Considerable uncertainty exists in the design of anti-slip piles 
for disaster recovery and regions prone to earthquakes. 
Unable to accurately evaluate the rationality and effectiveness 
of design measures, as well as the degree of optimization of 
design schemes. Therefore, this study uses ABAQUS finite 
element calculation software to investigate the dynamic 
response of skid pile reinforced slopes under earthquake 
action, taking an actual case of skid pile reinforcement as the 
object, and using artificial seismic waves. The aim is to reveal 
the displacement and internal force changes of various parts 
of the pile body during the earthquake process, and provide 
theoretical support for the design of skid piles under 
earthquake action. 

2. Basic Theory 

2.1. Strength Reduction 
The strength reduction approach decreases the shear 

strength parameters c and ϕ of the slope's rock mass by a 
factor FS until the slope becomes unstable, with the 
corresponding FS being the slope stability coefficient. The 
slope stability coefficient is expressed as:[5] 

 
          tanc                    (1) 

 
After strength reduction, it can be obtained that: 
 

               'tanc''                    (2) 
 

             
sF

c
c'                       (3) 

In summary, we have: 
 

             
sF

 tan
'tan                    (4) 

 
Where: c and ϕ represent the initial parameters of the 

slope's rock and soil mass;c′and ϕ′represent the parameters 
when the slope's rock and soil mass reach the limit 
equilibrium state;FS represents the stability coefficient of the 
slope. 

2.2. Modal Analysis Theory 
Modal analysis examines the inherent characteristics of the 

structure, such as stiffness, natural frequency, and mode 
shape, before conducting dynamic analysis. Essentially, 
modal analysis involves solving the eigenvectors and 
eigenvalues of the structure.[6] 

The equation for undamped free vibration is: 



 

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            0KxM
..








 x               (5) 

 
Assuming the solution to the equation is: 
 

              )sin(   tux               (6) 

 
Substituting into the equation, we get: 
 

             0uMK 2  ）（                (7) 

 
For the above equation to have a solution, the condition 

must be met      ））（ 0MK 2  ,which constitutes the 

characteristic equation. Based on the characteristic equation, 
nnn characteristic roots (i.e., natural frequencies) can be 

obtained (i = 1, 2, ..., n). 2
i (i=1,2,……,n),Substituting the 

characteristic roots into equation (7),yields the corresponding 

non-zero vectors ）（iu (i.e., mode shapes). 

3. Engineering Overview 
A slope is situated in Shimian County, Ya'an City, Sichuan 

Province. Under the action of tectonic compression, the ridge 
is steep, with slope angles between 30° and 38°. The area 
belongs to an erosion-type canyon landscape with many V-
shaped gullies and river erosion-deposition topography. The 
area experiences a subtropical humid monsoon climate, with 
most rainfall occurring during the summer and autumn 
seasons. The area is also prone to earthquakes, with frequent 
fault activities of varying scales. This region falls within a 
high seismic risk zone, with a fundamental seismic intensity 
rated at VIII degree and a design peak ground acceleration set 
at 0.3g. 

4. Calculation Model 

4.1. Establishment of Numerical Model 
The ABAQUS finite element software is utilized to model 

the slope and anti-slide piles, as depicted in Figure 1. The 
overall dimensions of the slope model are 60m (length) × 10m 
(width) × 25m (height at slope bottom), with a top height of 
50m. The soil layers from top to bottom are fractured 
limestone, slightly to weakly weathered limestone, and intact 
limestone. The relevant rock mass parameters are provided in 
Table 1.The anti-slide piles are 28m long and have a diameter 
of 2×3m, with a spacing of 3m. Monitoring points A, B, and 
C are set on the slope surface (see Figure 1). 

 

 
Figure 1. Layout of Anti-slide Pile Support 

 
Table 1. Physical and Mechanical Properties of Slope Rocks and Skid Piles 

Name Density 
ρ/g·cm-

3 

Poisson's 
Ratio 

μ 

Elastic 
Modulus 
E/GPa 

Cohesion 
c/kPa 

Internal Friction 
Angle 
φ/()° 

Anti-slide Pile 2.5 0.25 35 — — 
Fractured Limestone 2.3 0.3 2.8 500 26 

Slightly to Weakly Weathered 
Limestone 

2.5 0.25 15 1200 32 

Intact Limestone 2.65 0.22 35.4 1900 41 
 

4.2. Parameter Selection and Boundary 
Conditions 

Considering the elastoplastic characteristics of the soil, the 
Mohr-Coulomb plastic constitutive model is adopted for the 
slope rock mass. Rayleigh damping is used to achieve kinetic 
energy decay, expressed as: 

 

                KMC                    (8) 

 
In this context, [C] represents the damping matrix, [M] the 

mass matrix, and [K] the stiffness matrix, while α and β are 
the mass-related and stiffness-related damping coefficients, 
respectively. 

To satisfy the orthogonality condition, the coefficients α 



 

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and β are determined as follows: 
 

    ),,2,1
22

k

k
k nk  （



           (9) 

 
Here, ξₖ represents the damping ratio, while ωₖ denotes the 

natural frequency. 
Using finite element software, two natural frequencies ωｉ 

and ωｊ can be calculated. Selecting ωｉ=ω１=2.5862 and 
ωｊ=ω３=3.6654,the damping ratios are typically taken as 
ξｉ＝ξｊ＝0.05. Substituting into equation(9),the coefficients 
are obtained as: α＝0.95225,β＝0.00255. 

Interface elements are used to simulate the interaction 
between the anti-slide pile and the rock mass. The normal 
stiffness Kn and tangential stiffness Kt for the interface 
between the anti-slide pile and fractured limestone are set to 
6.7×10¹⁰ MN/m² and 60 MN/m², respectively. The interaction 
between the anti-slide pile and intact limestone, Ｋｎand 
Ｋｔare set to 9.6×10¹⁰ MN/m² and 82 MN/m², respectively. A 
viscoelastic artificial boundary is used to eliminate or reduce 
the influence of reflected waves at the finite region boundary. 
The tangential and normal viscous forces of the dampers are 

given by: 
 

                 
ts

n

vpC

vCp





P0nt

              (10) 

 
Here, p0 represents the material density at the model 

boundary, CP is the P-wave velocity, CS the S-wave velocity, 
and vn and vt are the normal and tangential velocities of the 
propagating seismic wave, respectively. 

4.3. Selection of Seismic Waves 
This study selects the first 25s of the acceleration timeline 

of the 2008 Wenchuan earthquake recorded at the Chengdu 
CD2 station (see Fig. 2) to study the stability of the anti-slide 
pile-reinforced slope under different seismic wave amplitudes. 
The SeismoSignal software is used to filter and baseline 
correct the selected Wenchuan earthquake wave. The 
amplitude of the Wenchuan earthquake wave is adjusted to 
0.1g, 0.2g, and 0.3g. The effect of these three seismic levels 
on the anti-slide pile-reinforced slope is analyzed to reveal the 
relationship between earthquake magnitude and slope 
stability. 

 

 
Figure 2. Seismic Acceleration Time History Graph of the Wenchuan Earthquake Wave 

 

5. Results and Analysis 

5.1. Seismic Acceleration Study of Slope 
Reinforced with Anti-Slide Pile 

The seismic acceleration time history curves at various 
monitoring points on the slope surface, under different 
amplitudes of the Wenchuan earthquake waves, are presented 
below. 

As seen in Fig. 3, the seismic acceleration time history 
curves at different monitoring locations on the slope surface 
exhibit certain regularity under different amplitudes of the 
Wenchuan earthquake waves. Initially, the seismic 
acceleration at each point on the slope surface is relatively 
gentle due to the incomplete release of seismic energy. As the 
seismic energy gradually increases, the seismic acceleration 
begins to rise rapidly, especially when the seismic amplitude 

reaches its peak. The amplification effect is more pronounced 
at higher elevations, where the soil mass is more susceptible 
to significant vibration, resulting in increased acceleration. 

Further analysis shows that the seismic acceleration at 
different elevations on the slope surface is not uniformly 
distributed but amplifies with increasing elevation. This 
amplification effect is more evident at higher elevations due 
to the greater vibration response of the soil under seismic 
waves. For example, at monitoring point C, the peak seismic 
acceleration under a 0.1g seismic wave is 0.674g, increasing 
to 1.422g under a 0.3g seismic wave. This significant increase 
in acceleration indicates that the anti-slide pile's effectiveness 
in stabilizing the upper rock mass of the slope diminishes as 
the seismic wave amplitude increases, particularly under 
larger amplitudes, where the control over acceleration growth 
is limited. 

 



 

126 

   
(a) 0.1g                          (b) 0.2g 

 
(c) 0.3g 

Figure 3. Time History Curves of Seismic Acceleration at Various Monitoring Points under Different Seismic Wave Amplitudes 
 

 
Figure 4. Peak Seismic Acceleration at Various Monitoring Points under Different Seismic Waves 

 
The time history curves of relative horizontal displacement 

in the x-direction at multiple monitoring points on the slope 
surface under different amplitudes (0.1g, 0.2g, 0.3g) of the 
Wenchuan earthquake waves are shown below. The analysis 
of the relative horizontal displacement in the x-direction 
under different amplitudes of the Wenchuan earthquake 
waves reveals a trend in displacement variation over time. 
Initially, when the seismic wave amplitude is low, the 
horizontal displacement in the x-direction is minimal, 
demonstrating that the anti-slide pile effectively restrains the 
sliding of the slope soil mass during the early stages. However, 

as the seismic wave amplitude increases, the horizontal 
displacement in the x-direction begins to increase 
significantly, particularly when the seismic wave reaches its 
peak acceleration, resulting in the maximum displacement at 
every monitoring location on the slope surface. 

5.2. Seismic Displacement Analysis of Anti-
slide Pile Reinforced Slope 

Monitoring points A, B, and C are located on the slope 
surface, as illustrated in Figure 1. As seen in Figure 5, under 



 

127 

different amplitudes (0.1g, 0.2g, 0.3g) of the Wenchuan 
earthquake waves, The relative horizontal displacement in the 
x-direction along the slope surface varies with elevation, 
increasing as elevation rises rather than being uniformly 
distributed. Specifically, at higher elevations, the 
displacement peak is relatively larger, indicating that the soil 
mass at higher elevations is more prone to sliding under 
seismic wave action. For example, at monitoring point C, the 

peak displacement under a 0.3g seismic wave reaches 
530.516mm, while the peak displacements at monitoring 
points B and A are 304.22mm and 184.132mm, respectively. 
This indicates that the anti-slide pile's effectiveness in 
restraining the sliding of the upper soil mass of the slope is 
still insufficient, particularly under larger seismic amplitudes, 
where the slope's stability may be significantly challenged. 

 

   
(a)0.1g                                                (b)0.2g 

 
(c)0.3g 

Figure 5. Time History Curves of Seismic Displacement at Various Monitoring Points under Different Seismic Wave Amplitudes 
 

 
Figure 6. Peak Seismic Displacement at Various Monitoring Points under Different Seismic Waves 



 

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Analyzing peak horizontal displacements in the x-direction 

across multiple monitoring points on the slope surface under 
different anti-slide pile setups indicates that, at a 0.3g seismic 
wave amplitude, the peak displacement at monitoring point C 
(530.516mm) is greater than at point B (304.22mm) and point 
A (184.132mm). This indicates that the anti-slide pile 
effectively restrains the sliding of the upper soil mass of the 
slope, reducing the risk of slope instability under seismic 

action. 

5.3. Analysis of Seismic Principal Stresses in 
Slope Reinforced by Anti-Slide Pile 

The distribution of the first principal stress of the anti-slide 
pile under different seismic wave amplitudes is shown in Fig. 
7. 

 

        

(a) 0.1g                            (b) 0.2g                              (c) 0.3g 
Figure 7. First Principal Stress Distribution of Skid Pile under Different Seismic Wave Amplitudes 

 
The distribution pattern of the first principal stress on the 

anti-slide pile under various seismic wave amplitudes shows 
that the principal stress is focused around the connection 
between the sliding surface and the anti-slide pile. This stress 
concentration is mainly due to the slope's sliding tendency 
under seismic forces. During the earthquake, the anti-slide 
pile not only bears the active earth pressure from within the 
slope but also resists the passive earth pressure from outside. 
These complex force systems are transmitted through the anti-
slide pile to the vicinity of the sliding surface, leading to a 
sharp increase in stress in this region. 

As seen in Figure 7, the first principal stress of the anti-
slide pile is mainly concentrated near the connection between 
the sliding surface and the anti-slide pile. At varying seismic 
wave amplitudes, the first principal stress of the anti-slide pile 
is 1.221MPa (0.1g), 2.483MPa (0.2g), and 2.271MPa (0.3g). 
The anti-slide pile interacts with the sliding surface and the 
surrounding soil mass by embedding into the slope, forming 
a system that resists sliding. The change in stress indicates 
that under larger seismic amplitudes, the stress concentration 
in the middle region of the anti-slide pile is more pronounced, 
suggesting that the structure may bear significant deformation 
pressure. Therefore, the structural design of the anti-slide pile 
should particularly strengthen the middle region to address 
the stress concentration under seismic action. 

6. Conclusion 
Based on the background of an actual engineering project, 

this study established a three-dimensional finite element 
model of an anti-slide pile-reinforced slope under different 
seismic wave amplitudes. The slope's stability under seismic 
forces was examined, with an analysis of the movement 
patterns, seismic acceleration, and the first principal stress 
distribution in the anti-slide pile. The following conclusions 
were drawn: 

The dynamic displacement variation trends at different 
elevation points are essentially the same. The horizontal 
displacement in the x-direction at multiple monitoring points 

on the slope surface increases with the seismic acceleration 
amplitude, with the peak appearing around 7.56s, slightly 
later than the peak seismic acceleration time. The anti-slide 
pile effectively restrains the sliding of the upper soil mass of 
the slope, reducing the risk of slope instability under seismic 
action. 

The seismic acceleration at different locations on the slope 
surface increases with elevation, exhibiting a certain 
amplification effect. The effect of amplification becomes 
more significant with higher slope elevation. 

The first principal stress of the anti-slide pile primarily 
concentrated near the connection between the sliding surface 
and the anti-slide pile, requiring reinforcement of the 
structural design in the middle region of the anti-slide pile. 

Under 0.1g and 0.2g seismic conditions, the stability 
coefficient of the anti-slide pile meets the standard 
requirements. However, under 0.3g seismic conditions, the 
stability coefficient of 1.095 is less than the standard 
requirement of 1.10, indicating that the use of anti-slide piles 
alone as a slope reinforcement form is insufficient and 
requires improvements to the structure's design or dimensions. 

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