# Seismic Response of Anchor + Hinged Block Ecological Slope by Shaking Table Tests

Authors: Hui Su; Yijun Hang; Yongsheng Song; Kunming Mao; Dongyue Wu; Xiao Qiu
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

Landslides caused by earthquakes and other natural disasters may cause serious economic and personal losses. Slope protections are usually applied in engineering practice to prevent significant slope slides and damages. Based on the mechanical and ecological requirements on slope protections, this paper put forward a new type of anchor + hinged block ecological slope and carried out shaking table tests on it and other three traditional slope protections for comparing. By shaking table tests, the acceleration amplification factors and Fourier amplitude spectrums of four different slope types are analyzed and compared to verify the suitability of this new slope protection under earthquakes. The results indicated that the natural frequency and the acceleration Fourier amplitude spectrum of the four tested slope protections change according to internal materials. The anchor + hinged block ecological slope has higher natural frequency comparing to traditional slopes, so the resonance cycle from earthquake excitation can effectively be avoided and as a result the anchor + hinged block ecological slope can achieve better seismic performance.


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## Body

## 1. Introduction

Slope protections usually utilize traditional materials such as vegetation and stone and modern reinforced concrete to prevent slope soil erosions and slides, including natural slope protection and artificial slope protection. With many years developing for slope protection types, the main slope protection types in China, of both traditional and newly developed, usually utilized riprap, concrete slab, sizing block stone, and flexible mesh fabric. Even they can prevent slope damage from external actions, such as earthquakes, rain, wind, and waves [1], and those slope protections also present some problems as following: (1) lacking of ecosystem on slope surfaces may destroy the original ecological integrity; (2) some slopes using stone materials have higher construction costs due to the mortaring and limitation stone resource; (3) most slopes only use brittle materials such as plain concrete and stone, leading poor performance in durability, adaptability, and structural instability; (4) in some slope destructions, rigid slopes constituted by brittle materials occurred large soil area overturn damaging and caused extreme difficult slope repairing and (5) flexible mesh fabric slope protection only provides reinforcement on plants, while due to lacking of protections for foundation soil erosion which usually happened after plants rooting, this flexible mesh fabric slope is not suitable for long-term water erosion [2]. Especially in recent years, with the awareness of environmental protection and sustainable development, the ecological requirements are more demanding. For slope protections, the engineering stabilities require higher strength and better drainage, which is unavoidable to change the groundwater height and generates contradiction with ecological requirements. So, it is very necessary to find out how to achieve balance between slope protection mechanical and ecological properties. Based on the abovementioned content, the new slope protection type of anchor + hinged block ecological slope was put forward. Figure 1 shows the anchor + hinged block ecological slope protections in application.Figure 1
The anchor + hinged block ecological slope protections in application.The anchor + hinged block ecological slope is a new flexible slope protection wall. By utilizing anchors to fix the concrete blocks onto the slope surface and hinges to connecting concrete blocks, the slope protection wall is connected with slope soil into one part to bear soil pressure and achieving good mechanical properties. To achieve ecological performance, there are holes set on the concrete blocks, by which plants can grow in the hole space. Furthermore, to simplify construction and reduce construction costs, grooves are set on block sides to generate tenon connections between blocks and save mortars. By the above methods and as a flexible slope protection, larger soil deformation is allowed and the following advantages are achieved: (1) holes on block reduce self-gravity load of slope protection wall, which improve the strength capacity; (2) the tenon connections will generate higher shear strength and improve slope protection mechanical performance; (3) the flexible slope protection utilizes the glass fiber rod to hinge blocks, and larger displacement and slips are allowed to exist between blocks, so the friction and interactions between blocks can help to consume earthquake vibration energy; (4) the holes on blocks and plants can help to generate better landscape engineering and achieve better ecological performance; and (5) the mortar-saving properties make constructions easier and reduce the weather influence.As the soil body at slopes will holistically slide under actions of self-gravity and external loads, slope protection plays the role of preventing soil slide. But once the sliding loads exceed antislide strength which is mainly generated by slope protection, slope protection will be damaged and more serious landslides may happen. Especially for the landslides caused by other natural disasters such as earthquake and concentrated heavy rainfall in short time, more serious economic and personal losses may be caused. Among those disasters causing landslides, earthquake is a more vital reason which may lead significant slope destructions. For example, in 2008, when the Richter 8.0 magnitude earthquake hit Wenchuan County in Sichuan Province, China, according to statistics, more than 20,000 cases [3] of landslides, collapses, and debris flows were caused by the earthquake. So, the seismic responses and properties of slope protections should be comprehensively understood and be properly designed. To prove the reliability and understand the seismic response of this anchor + hinged block ecological slope protection, this study carried out shaking table model test and finite element simulation on four different slope protection models, including the new developed anchor + hinged block ecological slope protection and three more contrastive common slope protection of the natural slope without vegetation, the hinged block slope, and the hinge block slope with ecological protection.


## 2. Slope Models and Test Process

### 2.1. Slope Model Similarity Ratio

This experiment was carried out on a 4 m × 6 m shaking table with maximum load of 2500 kN and maximum acceleration of 1.5 g. Limited by shaking table sizes, the experimental slope model applied the 1 : 5 reduced scale to reality slope. To ensure that the experimental model correctly reflects mechanical performance of real slope, the test model should satisfy similar theory requirements. According to the Buckinghamπ similarity theories [4–7], the parameters of the test model have been calculated and given in Table 1.Table 1
Similarity ratio of slope parameters.
Physical parameters
Similarity ratio
Remarks
Length,l
C
l
=
5
Control parameter
Acceleration,a
C
a
=
1
Control parameter
Density,ρ
C
ρ
=
1
Control parameter
Displacement,u
C
u
=
C
K
−
1
C
ρ
1
/
2
C
l
3
/
2
=
11.2
Speed,ν
C
ν
=
C
ρ
1
/
4
C
K
−
1
/
2
C
l
3
/
4
=
3.34
Cohesion,c
C
c
=
C
ρ
C
l
=
5
Need to be satisfied
Internal friction angle,φ
C
φ
=
1
Unchangeable
Stress,σ
C
σ
=
C
ρ
C
l
=
5
Strain,ε
C
ε
=
C
K
−
1
C
ρ
1
/
2
C
l
1
/
2
=
2.24
Time,t
C
t
=
C
l
3
/
4
C
K
−
1
/
2
C
ρ
1
/
4
=
3.34
Frequency,ω
C
ω
=
C
l
−
3
/
4
C
K
1
/
2
C
ρ
−
1
/
4
=
0.299
Note. Due to the limit of primary soil material, the similarity ratio of mass density and moisture content will be assumed to be 1.0.


### 2.2. Materials and Model Details

According to the similar ratio in Table1, the experimental model size, model in reality, and sensor configurations are shown in Figure 2.Figure 2
Model details (unit in mm). (a) Model sizes. (b) Model on shaking table in reality. (c) Acceleration sensor configuration. (d) Earth pressure sensor configuration.
(a)
(b)
(c)
(d)The sizes of the real hinged block of this experiment were 440 mm × 440 mm × 120 mm, and after scale reduction according to the size similarity ratio ofCl=5, the experimental model sizes were 88 mm × 88 mm × 24 mm. There were totally four experimental block models shown in Figure 3, including the natural slope without vegetation, the hinged block slope, the hinge block slope with ecological protection, and the anchor + hinged block ecological slope. The natural slope without vegetation is shown in Figure 3(a), which represented the bare slope without any protection. The hinged block slope shown in Figure 3(b) represented the bare slope with hinged block reinforcement. The hinge block slope with ecological protection shown in Figure 3(c) was the further reinforced hinged block slope by vegetation protection. The anchor + hinged block ecological slope shown in Figure 3(d) was the further reinforced hinge block slope with ecological protection by anchoring the hinged block onto the slope surface. Among the four experimental slope models, three models utilized the MU20 strength grade block, including the hinged block of the slope, the hinge block slope with ecological protection, and the anchor + hinged block ecological slope. The soil sample in this experiment was from the Qinhuai River renovation project site in Nanjing, China. The cohesive strength of the soil sample was 1.533 Kpa, with internal friction angle of 3.7°and moisture content of 32.21%. The vetiver vegetation was selected as ecological protection at slope top. The vegetation process included firstly vetiver growing and secondly vetiver transplantation after matures. The shaking table tests started after the vegetation completely rooted in slope soil. The four experimental slope models are shown in Figure 3.Figure 3
Test models. (a) Natural slope without vegetation. (b) Hinged block slope. (c) Hinge block slope with ecological protection. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)


### 2.3. Seismic Accelerations

This experiment adopted three earthquake acceleration waves according to the “Standard for test method of mechanical properties on ordinary concrete” [8]: the Taft wave, the Castaic wave, and one artificial seismic wave. The acceleration time history curves of each wave are shown in Figure 4. The acceleration loading process order was the Taft wave, the Castaic wave, and the artificial seismic wave. The loading of each acceleration wave was divided into several steps with different magnitudes. The loading acceleration magnitudes of the Taft wave and the Castaic wave were 0.1 g, 0.2 g, and 0.4 g, whereas the loading acceleration magnitudes of the artificial wave were 0.1 g, 0.2 g, 0.4 g, and 0.8 g.Figure 4
Acceleration time history curve of the three loading waves. (a) The Taft wave. (b) The Castaic wave. (c) The artificial seismic wave.
(a)
(b)
(c)


## 2.1. Slope Model Similarity Ratio

This experiment was carried out on a 4 m × 6 m shaking table with maximum load of 2500 kN and maximum acceleration of 1.5 g. Limited by shaking table sizes, the experimental slope model applied the 1 : 5 reduced scale to reality slope. To ensure that the experimental model correctly reflects mechanical performance of real slope, the test model should satisfy similar theory requirements. According to the Buckinghamπ similarity theories [4–7], the parameters of the test model have been calculated and given in Table 1.Table 1
Similarity ratio of slope parameters.
Physical parameters
Similarity ratio
Remarks
Length,l
C
l
=
5
Control parameter
Acceleration,a
C
a
=
1
Control parameter
Density,ρ
C
ρ
=
1
Control parameter
Displacement,u
C
u
=
C
K
−
1
C
ρ
1
/
2
C
l
3
/
2
=
11.2
Speed,ν
C
ν
=
C
ρ
1
/
4
C
K
−
1
/
2
C
l
3
/
4
=
3.34
Cohesion,c
C
c
=
C
ρ
C
l
=
5
Need to be satisfied
Internal friction angle,φ
C
φ
=
1
Unchangeable
Stress,σ
C
σ
=
C
ρ
C
l
=
5
Strain,ε
C
ε
=
C
K
−
1
C
ρ
1
/
2
C
l
1
/
2
=
2.24
Time,t
C
t
=
C
l
3
/
4
C
K
−
1
/
2
C
ρ
1
/
4
=
3.34
Frequency,ω
C
ω
=
C
l
−
3
/
4
C
K
1
/
2
C
ρ
−
1
/
4
=
0.299
Note. Due to the limit of primary soil material, the similarity ratio of mass density and moisture content will be assumed to be 1.0.


## 2.2. Materials and Model Details

According to the similar ratio in Table1, the experimental model size, model in reality, and sensor configurations are shown in Figure 2.Figure 2
Model details (unit in mm). (a) Model sizes. (b) Model on shaking table in reality. (c) Acceleration sensor configuration. (d) Earth pressure sensor configuration.
(a)
(b)
(c)
(d)The sizes of the real hinged block of this experiment were 440 mm × 440 mm × 120 mm, and after scale reduction according to the size similarity ratio ofCl=5, the experimental model sizes were 88 mm × 88 mm × 24 mm. There were totally four experimental block models shown in Figure 3, including the natural slope without vegetation, the hinged block slope, the hinge block slope with ecological protection, and the anchor + hinged block ecological slope. The natural slope without vegetation is shown in Figure 3(a), which represented the bare slope without any protection. The hinged block slope shown in Figure 3(b) represented the bare slope with hinged block reinforcement. The hinge block slope with ecological protection shown in Figure 3(c) was the further reinforced hinged block slope by vegetation protection. The anchor + hinged block ecological slope shown in Figure 3(d) was the further reinforced hinge block slope with ecological protection by anchoring the hinged block onto the slope surface. Among the four experimental slope models, three models utilized the MU20 strength grade block, including the hinged block of the slope, the hinge block slope with ecological protection, and the anchor + hinged block ecological slope. The soil sample in this experiment was from the Qinhuai River renovation project site in Nanjing, China. The cohesive strength of the soil sample was 1.533 Kpa, with internal friction angle of 3.7°and moisture content of 32.21%. The vetiver vegetation was selected as ecological protection at slope top. The vegetation process included firstly vetiver growing and secondly vetiver transplantation after matures. The shaking table tests started after the vegetation completely rooted in slope soil. The four experimental slope models are shown in Figure 3.Figure 3
Test models. (a) Natural slope without vegetation. (b) Hinged block slope. (c) Hinge block slope with ecological protection. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)


## 2.3. Seismic Accelerations

This experiment adopted three earthquake acceleration waves according to the “Standard for test method of mechanical properties on ordinary concrete” [8]: the Taft wave, the Castaic wave, and one artificial seismic wave. The acceleration time history curves of each wave are shown in Figure 4. The acceleration loading process order was the Taft wave, the Castaic wave, and the artificial seismic wave. The loading of each acceleration wave was divided into several steps with different magnitudes. The loading acceleration magnitudes of the Taft wave and the Castaic wave were 0.1 g, 0.2 g, and 0.4 g, whereas the loading acceleration magnitudes of the artificial wave were 0.1 g, 0.2 g, 0.4 g, and 0.8 g.Figure 4
Acceleration time history curve of the three loading waves. (a) The Taft wave. (b) The Castaic wave. (c) The artificial seismic wave.
(a)
(b)
(c)


## 3. Shaking Table Test Results

### 3.1. Acceleration Responses

By the experimental tests, acceleration responses were collected by sensors distributed shown in Figure2(c). After experimental, by comparing those data of different collecting sensors, it was found that data of A3, A4, and A7 exhibited less error and more stability, and the collected acceleration results under the three seismic waves exhibited the similar characteristics, so only the acceleration results of A3, A4, and A7 sensors under the artificial seismic wave were selected out as the analysis data. Afterward, by MATLAB programing and a bandpass filter, the selected test data were denoised. By drafting the data into acceleration time history curves, the PGA amplification factor-acceleration amplitude curves at the same sensor point and for same slope model were obtained as shown in Figures 5 and 6. Figures 5 and 6 also contain numerical analysis results, which will be presented in Section 4.Figure 5
PGA amplification factor-acceleration amplitude curves at the same sensor point. (a) PGA amplification factor-acceleration amplitude curves at sensor point A3. (b) PGA amplification factor-acceleration amplitude curves at sensor at point A4. (c) PGA amplification factor-acceleration amplitude curves at sensor at point A7.
(a)
(b)
(c)Figure 6
PGA amplification factor-acceleration amplitude curves for slope models. (a) Natural slope without vegetation. (b) Hinged block of slope. (c) Hinged block of ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)As shown in Figure5, the PGA amplification factors of the anchor + hinged block ecological slope at the A3, A4, and A7 sensor points are the lowest value comparing with that of other three slope models. The PGA amplification factors of the hinged block ecological slope are lower than that of the hinged block slope and the natural slope without vegetation. The natural slope without vegetation has the highest value of PGA amplification factors. With the acceleration magnitude of seismic waves increasing, the PGA amplification factor of all slopes firstly increase and then decrease after the acceleration magnitude of seismic waves exceed a certain value. This reducing effect of PGA amplification factor on acceleration magnitude is the lowest for the natural slope without vegetation while the highest for the anchor + hinged block ecological slope.From the curves shown in Figure6, the PGA amplification factor of same slope model varies with sensor point and slope altitude, as the altitudes of the A3, A4, and A7 points are different. It can be found from the curves in Figure 6 that the PGA amplification factor increases with the relative altitude. The acceleration amplification also effects on the PGA amplification factor, but the effects at the slope top are more obvious than that at the slope foot.Comparing the curves in Figures5 and 6, the following can be found:(1)
The natural slope without vegetation has relatively low rigidity and exhibits the most obvious acceleration magnified effect under seismic action.(2)
As the slope surface properties are improved by concrete block in the hinged block slope, the total stiffness is larger than that of the natural slope without vegetation, leading a less obvious acceleration amplification effect on hinged block slope comparing to that of the natural slope without vegetation.(3)
The hinged block ecological slope is further reinforced by vegetation based on the original hinge slope. When the plant roots grow into a certain depth, the plant roots can prevent soil deformation during earthquakes, which is similar to reinforced soil, whose soil structure is denser and the total stiffness is increased. Thusly, the earthquake acceleration amplification effect is lower than those two previously described slopes.(4)
For the anchor + hinged block ecological slope, the advances of all the above two reinforced slopes are combined. The application of anchor further improves the original soil layer. If the anchor length is sufficient, it is able to completely combine the slope body and soil surface into one part, to prevent the slope body splitting, so the anchor + hinged block ecological slope exhibits the lowest earthquake acceleration amplification effect and generates optimal seismic performance.


### 3.2. Fourier Amplitude Spectrum Analysis

Based on the acceleration data from sensor point A7 under the Castaic seismic wave. The acceleration Fourier amplitude spectrums [9] of the four tested slopes from both experimental test and numerical simulation are obtained and shown in Figures 7–9. The numerical analysis results will be presented in Section 4.Figure 7
Fourier acceleration amplitude spectrums at point A7 under the Castaic wave (0.1 g). (a) Natural slope without vegetation. (b) Hinged block of slope. (c) Hinged block ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)Figure 8
Fourier acceleration amplitude spectrum at point A7 under the Castaic wave (0.2 g). (a) Natural slope without vegetation. (b) Hinged block slope. (c) Hinged block ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)Figure 9
Fourier acceleration amplitude spectrum at point A7 under the Castaic wave (0.4 g). (a) Natural slope without vegetation. (b) Hinged block slope. (c) Hinged block ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)From the Fourier acceleration spectrum in Figures6–8, it can be found that under the same acceleration magnitude, all the four slope models exhibit the phenomenon of reducing high-frequency wave while enlarging relative low-frequency wave, which is mainly caused by the slope soil’s filtering effect on high-frequency component and amplification effect on low-frequency component in earthquake waves. The frequency value of the low-frequency amplification for different slope types changes regularly: the frequency value causing low-frequency amplification phenomenon concentrated in 0 Hz to 5 Hz for the natural slope without vegetation, 5 Hz to 10 Hz for the hinged block slope, 10 Hz to 15 Hz for the hinged block ecological slope, and 15 Hz to 20 Hz for the anchor + hinged block ecological slope. The reason for the frequency value changing phenomenon is related with the excellent frequency of slopes: from the sequence of the natural slope without vegetation, the hinged block slope, the hinged block ecological slope, and the anchor + hinged block ecological slope, the slope soil was reinforced gradually, so the soil stiffness in the slope and excellent frequency of the slope will be increased gradually


## 3.1. Acceleration Responses

By the experimental tests, acceleration responses were collected by sensors distributed shown in Figure2(c). After experimental, by comparing those data of different collecting sensors, it was found that data of A3, A4, and A7 exhibited less error and more stability, and the collected acceleration results under the three seismic waves exhibited the similar characteristics, so only the acceleration results of A3, A4, and A7 sensors under the artificial seismic wave were selected out as the analysis data. Afterward, by MATLAB programing and a bandpass filter, the selected test data were denoised. By drafting the data into acceleration time history curves, the PGA amplification factor-acceleration amplitude curves at the same sensor point and for same slope model were obtained as shown in Figures 5 and 6. Figures 5 and 6 also contain numerical analysis results, which will be presented in Section 4.Figure 5
PGA amplification factor-acceleration amplitude curves at the same sensor point. (a) PGA amplification factor-acceleration amplitude curves at sensor point A3. (b) PGA amplification factor-acceleration amplitude curves at sensor at point A4. (c) PGA amplification factor-acceleration amplitude curves at sensor at point A7.
(a)
(b)
(c)Figure 6
PGA amplification factor-acceleration amplitude curves for slope models. (a) Natural slope without vegetation. (b) Hinged block of slope. (c) Hinged block of ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)As shown in Figure5, the PGA amplification factors of the anchor + hinged block ecological slope at the A3, A4, and A7 sensor points are the lowest value comparing with that of other three slope models. The PGA amplification factors of the hinged block ecological slope are lower than that of the hinged block slope and the natural slope without vegetation. The natural slope without vegetation has the highest value of PGA amplification factors. With the acceleration magnitude of seismic waves increasing, the PGA amplification factor of all slopes firstly increase and then decrease after the acceleration magnitude of seismic waves exceed a certain value. This reducing effect of PGA amplification factor on acceleration magnitude is the lowest for the natural slope without vegetation while the highest for the anchor + hinged block ecological slope.From the curves shown in Figure6, the PGA amplification factor of same slope model varies with sensor point and slope altitude, as the altitudes of the A3, A4, and A7 points are different. It can be found from the curves in Figure 6 that the PGA amplification factor increases with the relative altitude. The acceleration amplification also effects on the PGA amplification factor, but the effects at the slope top are more obvious than that at the slope foot.Comparing the curves in Figures5 and 6, the following can be found:(1)
The natural slope without vegetation has relatively low rigidity and exhibits the most obvious acceleration magnified effect under seismic action.(2)
As the slope surface properties are improved by concrete block in the hinged block slope, the total stiffness is larger than that of the natural slope without vegetation, leading a less obvious acceleration amplification effect on hinged block slope comparing to that of the natural slope without vegetation.(3)
The hinged block ecological slope is further reinforced by vegetation based on the original hinge slope. When the plant roots grow into a certain depth, the plant roots can prevent soil deformation during earthquakes, which is similar to reinforced soil, whose soil structure is denser and the total stiffness is increased. Thusly, the earthquake acceleration amplification effect is lower than those two previously described slopes.(4)
For the anchor + hinged block ecological slope, the advances of all the above two reinforced slopes are combined. The application of anchor further improves the original soil layer. If the anchor length is sufficient, it is able to completely combine the slope body and soil surface into one part, to prevent the slope body splitting, so the anchor + hinged block ecological slope exhibits the lowest earthquake acceleration amplification effect and generates optimal seismic performance.


## 3.2. Fourier Amplitude Spectrum Analysis

Based on the acceleration data from sensor point A7 under the Castaic seismic wave. The acceleration Fourier amplitude spectrums [9] of the four tested slopes from both experimental test and numerical simulation are obtained and shown in Figures 7–9. The numerical analysis results will be presented in Section 4.Figure 7
Fourier acceleration amplitude spectrums at point A7 under the Castaic wave (0.1 g). (a) Natural slope without vegetation. (b) Hinged block of slope. (c) Hinged block ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)Figure 8
Fourier acceleration amplitude spectrum at point A7 under the Castaic wave (0.2 g). (a) Natural slope without vegetation. (b) Hinged block slope. (c) Hinged block ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)Figure 9
Fourier acceleration amplitude spectrum at point A7 under the Castaic wave (0.4 g). (a) Natural slope without vegetation. (b) Hinged block slope. (c) Hinged block ecological slope. (d) Anchor + hinged block ecological slope.
(a)
(b)
(c)
(d)From the Fourier acceleration spectrum in Figures6–8, it can be found that under the same acceleration magnitude, all the four slope models exhibit the phenomenon of reducing high-frequency wave while enlarging relative low-frequency wave, which is mainly caused by the slope soil’s filtering effect on high-frequency component and amplification effect on low-frequency component in earthquake waves. The frequency value of the low-frequency amplification for different slope types changes regularly: the frequency value causing low-frequency amplification phenomenon concentrated in 0 Hz to 5 Hz for the natural slope without vegetation, 5 Hz to 10 Hz for the hinged block slope, 10 Hz to 15 Hz for the hinged block ecological slope, and 15 Hz to 20 Hz for the anchor + hinged block ecological slope. The reason for the frequency value changing phenomenon is related with the excellent frequency of slopes: from the sequence of the natural slope without vegetation, the hinged block slope, the hinged block ecological slope, and the anchor + hinged block ecological slope, the slope soil was reinforced gradually, so the soil stiffness in the slope and excellent frequency of the slope will be increased gradually


## 4. Finite Element Simulation

The fundamental reason for earthquake soil liquefaction disasters is the increasing of pore water pressure caused by slope site earthquake vibrations. To supply supplementary calculation for this shaking table test, finite element simulation has been carried out.


### 4.1. Soil Dynamic Constitutive Model

Large number of experimental studies have proved that the three-parameter Davidenkov [10, 11] soil dynamic constitutive model can describe the nonlinear dynamic properties of all soils. However, as the actual ground motion in earthquake is usually nonequal amplitude, the stress-strain hysteresis curve of Davidenkov soil constitutive model should be further corrected according to certain rules. Byrne [12] used experimental data to establish empirical expressions between cumulative and incremental strain based on the Martin and Finn models [13, 14]. So, the Byrne pore water pressure increment model, which describes the liquefaction properties of soil, combined with the modified Davidenkov constitutive model will be utilized in the finite element simulation.


#### 4.1.1. Modified Davidenkov Soil Constitutive Model

The skeleton curve expression of the Davidenkov constitutive model proposed by Martin and Seed [15, 16] is(1)τ=G⋅γ=Gmax⋅γ⋅1−Hγ,among which(2)Hγ=γ/γ02B1+γ/γ02BA,where τ and γ are shear stress and shear strain, respectively, Gmax is the initial shear modulus, and A, B and γ0 are soil experimental test parameters.As shown in Figure10, the loading and unloading criteria of the modified Davidenkov constitutive model under irregular reciprocal stress action are as follows:(1)
In the initial loading process, the loading curve is in a linear skeleton, such as 0-1 curve segment shown in Figure10.(2)
If the loading curve or unloading curve intersects with the skeleton curve before the exchange of loading and unloading stages, such as the 1–3′ curve segment shown in Figure10, the “upper skeleton curve” rule in the extended Masing rule will be applied, in which the subsequent stress-strain curve will be exchanged into the skeleton curve, such as the 2-1-3′ curve segment been corrected to 2-1-3 curve shown in Figure 10.(3)
When the applied stress experiences loading and unloading stages exchange, the subsequent stress-strain curve will start at the current inflection point and develop to the largest (or smallest) strain point in history, such the 6-7′ curve segment will be corrected into the 6-7 curve segment shown in Figure10. According to the “n times law” proposed by Pyke [17], the stress-strain hysteresis curve at this time obeys the following:(3)τ−τc=Gmax⋅γ−γc⋅1−Hγ−γc2n,where τc and γc are the stress and strain at the point of loading and unloading.Figure 10
Stress-strain curves of modified Davidenkov model under irregular loading and unloading.


#### 4.1.2. Byrne Pore Water Pressure Increment Model

Based on the compatibility conditions of saturated soil volume changes during earthquake, Martin and Finn have established a basic formula for determining the incremental pressure of vibrating pore water in saturated soils:(4)Δεv,d+Δεv,r=Δεv,f,where Δεv,d is the soil volume reduction caused by cyclic shear, Δεv,r is the effective normal stress reduction caused by soil volume reduction, and Δεv,f is the volume reduction of pore water caused by each cycle shear.By assuming that no drainage occurred in saturated sand when the earthquake began, the value ofΔεv,f would be zero, and Equation (4) can be written as(5)Δεv,d=−Δεv,r.Assuming the values of effective normal stress reduction, effective normal strain, and volume reduction caused by pore water pressure are equal, the following can be obtained:(6)Δεv,r=ΔσEr=−ΔuEr.Substituting Equation (6) in (5), the following can be obtained:(7)Δu=ErΔεv,d.According to the experimental data from Martin and Finn, the relationship between cumulative body strainεv,d and body strain increment Δεv,d can be obtained(8)Δεv,dγa=C1exp−C2εv,dγa,Er=σc′−u1−mmkσc′n−m,where γa is the shear strain amplitude of the “n” times of stress cycle, σc′ is the initial effective normal stress, whose value will be the octahedral shear strain amplitude γoct and the initial octahedral σoct in the two-dimensional and three-dimensional conditions respectively, u is the ultrastatic pore water pressure, and C1, C2, m, n, k are the soil-related parameters.Byrne uses the experimental data from studies of Martin, Finn, Tokimatsu, and Seed to obtain the empirical expression of the coefficients which is expressed by the relative density of sand or the number of penetration hammers:(9)C1=0.076Dr−2.5orC1=8.7N1−1.25,C2=0.4C1.


#### 4.1.3. The Effective Stress Algorithm

To apply the Soil dynamic constitutive model into the finite element simulation, one custom material subroutine was applied in the finite element simulation software. The main tasks of the custom subroutine are: (1) give the corresponding strain incrementΔε according to the stress increment Δσ introduced by finite element simulation software; (2) update and solve the state variables that need to be passed during the calculation.The calculation of vibrating pore water pressure of soil required static and dynamic coupling calculation steps, which can be realized by multitask in software. In order to facilitate the usage of the custom subroutine, the constitutive model was divided into two stages: static and dynamic. In the static calculation stage, the original geostress balance calculation method supplied by the finite element simulation software was utilized. While in the dynamic calculation stage, the dynamic stress-strain relationship of the modified Davidenkov constitutive model combining with the Byrne pore pressure increment model was utilized.


### 4.2. Finite Element Simulation Model and Results

#### 4.2.1. Finite Element Simulation Model

Finite element simulation model was established according to the similarity ratio in Table1. The finite element simulation model is shown in Figure 11. The concrete damage constitutive model and solid element were adopted to simulate concrete block. The ideal elastic-plastic constitutive model and beam element were adopted to simulate steel rock bolts.Figure 11
Finite element simulation model.


#### 4.2.2. Amplification Factor and Fourier Amplitude Spectrum

The finite element simulation obtained the PGA amplification factor at related points of the four slope models shown in Figures5 and 6. And the finite simulation also obtained the acceleration Fourier amplitude spectrums at the same point with sensor point A7 and are also shown in Figures 6–8.By comparing results of the experiment and numerical simulation, it can be found that the general laws between experimental results and numerical simulation results are consistent but some differences exist. So, the finite elements simulation can partially provide supplementary results to the experiment while the simulation accuracy still needs to be improved especially for the contact effect simulation between plant roots and soil.


#### 4.2.3. Soil Liquefaction Area Distribution

Figure12 is the finite element simulated soil liquefaction area distribution for natural slope without vegetation and hinged block slope under 0.4 g magnitude Taft wave. In Figure 12, larger numerical value will be related with more serious liquefaction. It can be found that without hinged blocks, the slope is in serious liquefaction condition, and the most serious liquefaction area is in the middle part of the slope. For the slope with hinged blocks, the liquefaction area and value dropped rapidly comparing to the slope without hinged blocks, and only weak liquefaction exists at the slope top and bottom area, which coordinates with the experimental results. The simulation result also proved that the hinged blocks are able to effectively prevent soil liquefaction in earthquakes.Figure 12
Finite element liquefied area of slope. (a) Natural slope without vegetation. (b) Hinged block of slope.
(a)
(b)


## 4.1. Soil Dynamic Constitutive Model

Large number of experimental studies have proved that the three-parameter Davidenkov [10, 11] soil dynamic constitutive model can describe the nonlinear dynamic properties of all soils. However, as the actual ground motion in earthquake is usually nonequal amplitude, the stress-strain hysteresis curve of Davidenkov soil constitutive model should be further corrected according to certain rules. Byrne [12] used experimental data to establish empirical expressions between cumulative and incremental strain based on the Martin and Finn models [13, 14]. So, the Byrne pore water pressure increment model, which describes the liquefaction properties of soil, combined with the modified Davidenkov constitutive model will be utilized in the finite element simulation.


### 4.1.1. Modified Davidenkov Soil Constitutive Model

The skeleton curve expression of the Davidenkov constitutive model proposed by Martin and Seed [15, 16] is(1)τ=G⋅γ=Gmax⋅γ⋅1−Hγ,among which(2)Hγ=γ/γ02B1+γ/γ02BA,where τ and γ are shear stress and shear strain, respectively, Gmax is the initial shear modulus, and A, B and γ0 are soil experimental test parameters.As shown in Figure10, the loading and unloading criteria of the modified Davidenkov constitutive model under irregular reciprocal stress action are as follows:(1)
In the initial loading process, the loading curve is in a linear skeleton, such as 0-1 curve segment shown in Figure10.(2)
If the loading curve or unloading curve intersects with the skeleton curve before the exchange of loading and unloading stages, such as the 1–3′ curve segment shown in Figure10, the “upper skeleton curve” rule in the extended Masing rule will be applied, in which the subsequent stress-strain curve will be exchanged into the skeleton curve, such as the 2-1-3′ curve segment been corrected to 2-1-3 curve shown in Figure 10.(3)
When the applied stress experiences loading and unloading stages exchange, the subsequent stress-strain curve will start at the current inflection point and develop to the largest (or smallest) strain point in history, such the 6-7′ curve segment will be corrected into the 6-7 curve segment shown in Figure10. According to the “n times law” proposed by Pyke [17], the stress-strain hysteresis curve at this time obeys the following:(3)τ−τc=Gmax⋅γ−γc⋅1−Hγ−γc2n,where τc and γc are the stress and strain at the point of loading and unloading.Figure 10
Stress-strain curves of modified Davidenkov model under irregular loading and unloading.


### 4.1.2. Byrne Pore Water Pressure Increment Model

Based on the compatibility conditions of saturated soil volume changes during earthquake, Martin and Finn have established a basic formula for determining the incremental pressure of vibrating pore water in saturated soils:(4)Δεv,d+Δεv,r=Δεv,f,where Δεv,d is the soil volume reduction caused by cyclic shear, Δεv,r is the effective normal stress reduction caused by soil volume reduction, and Δεv,f is the volume reduction of pore water caused by each cycle shear.By assuming that no drainage occurred in saturated sand when the earthquake began, the value ofΔεv,f would be zero, and Equation (4) can be written as(5)Δεv,d=−Δεv,r.Assuming the values of effective normal stress reduction, effective normal strain, and volume reduction caused by pore water pressure are equal, the following can be obtained:(6)Δεv,r=ΔσEr=−ΔuEr.Substituting Equation (6) in (5), the following can be obtained:(7)Δu=ErΔεv,d.According to the experimental data from Martin and Finn, the relationship between cumulative body strainεv,d and body strain increment Δεv,d can be obtained(8)Δεv,dγa=C1exp−C2εv,dγa,Er=σc′−u1−mmkσc′n−m,where γa is the shear strain amplitude of the “n” times of stress cycle, σc′ is the initial effective normal stress, whose value will be the octahedral shear strain amplitude γoct and the initial octahedral σoct in the two-dimensional and three-dimensional conditions respectively, u is the ultrastatic pore water pressure, and C1, C2, m, n, k are the soil-related parameters.Byrne uses the experimental data from studies of Martin, Finn, Tokimatsu, and Seed to obtain the empirical expression of the coefficients which is expressed by the relative density of sand or the number of penetration hammers:(9)C1=0.076Dr−2.5orC1=8.7N1−1.25,C2=0.4C1.


### 4.1.3. The Effective Stress Algorithm

To apply the Soil dynamic constitutive model into the finite element simulation, one custom material subroutine was applied in the finite element simulation software. The main tasks of the custom subroutine are: (1) give the corresponding strain incrementΔε according to the stress increment Δσ introduced by finite element simulation software; (2) update and solve the state variables that need to be passed during the calculation.The calculation of vibrating pore water pressure of soil required static and dynamic coupling calculation steps, which can be realized by multitask in software. In order to facilitate the usage of the custom subroutine, the constitutive model was divided into two stages: static and dynamic. In the static calculation stage, the original geostress balance calculation method supplied by the finite element simulation software was utilized. While in the dynamic calculation stage, the dynamic stress-strain relationship of the modified Davidenkov constitutive model combining with the Byrne pore pressure increment model was utilized.


## 4.1.1. Modified Davidenkov Soil Constitutive Model

The skeleton curve expression of the Davidenkov constitutive model proposed by Martin and Seed [15, 16] is(1)τ=G⋅γ=Gmax⋅γ⋅1−Hγ,among which(2)Hγ=γ/γ02B1+γ/γ02BA,where τ and γ are shear stress and shear strain, respectively, Gmax is the initial shear modulus, and A, B and γ0 are soil experimental test parameters.As shown in Figure10, the loading and unloading criteria of the modified Davidenkov constitutive model under irregular reciprocal stress action are as follows:(1)
In the initial loading process, the loading curve is in a linear skeleton, such as 0-1 curve segment shown in Figure10.(2)
If the loading curve or unloading curve intersects with the skeleton curve before the exchange of loading and unloading stages, such as the 1–3′ curve segment shown in Figure10, the “upper skeleton curve” rule in the extended Masing rule will be applied, in which the subsequent stress-strain curve will be exchanged into the skeleton curve, such as the 2-1-3′ curve segment been corrected to 2-1-3 curve shown in Figure 10.(3)
When the applied stress experiences loading and unloading stages exchange, the subsequent stress-strain curve will start at the current inflection point and develop to the largest (or smallest) strain point in history, such the 6-7′ curve segment will be corrected into the 6-7 curve segment shown in Figure10. According to the “n times law” proposed by Pyke [17], the stress-strain hysteresis curve at this time obeys the following:(3)τ−τc=Gmax⋅γ−γc⋅1−Hγ−γc2n,where τc and γc are the stress and strain at the point of loading and unloading.Figure 10
Stress-strain curves of modified Davidenkov model under irregular loading and unloading.


## 4.1.2. Byrne Pore Water Pressure Increment Model

Based on the compatibility conditions of saturated soil volume changes during earthquake, Martin and Finn have established a basic formula for determining the incremental pressure of vibrating pore water in saturated soils:(4)Δεv,d+Δεv,r=Δεv,f,where Δεv,d is the soil volume reduction caused by cyclic shear, Δεv,r is the effective normal stress reduction caused by soil volume reduction, and Δεv,f is the volume reduction of pore water caused by each cycle shear.By assuming that no drainage occurred in saturated sand when the earthquake began, the value ofΔεv,f would be zero, and Equation (4) can be written as(5)Δεv,d=−Δεv,r.Assuming the values of effective normal stress reduction, effective normal strain, and volume reduction caused by pore water pressure are equal, the following can be obtained:(6)Δεv,r=ΔσEr=−ΔuEr.Substituting Equation (6) in (5), the following can be obtained:(7)Δu=ErΔεv,d.According to the experimental data from Martin and Finn, the relationship between cumulative body strainεv,d and body strain increment Δεv,d can be obtained(8)Δεv,dγa=C1exp−C2εv,dγa,Er=σc′−u1−mmkσc′n−m,where γa is the shear strain amplitude of the “n” times of stress cycle, σc′ is the initial effective normal stress, whose value will be the octahedral shear strain amplitude γoct and the initial octahedral σoct in the two-dimensional and three-dimensional conditions respectively, u is the ultrastatic pore water pressure, and C1, C2, m, n, k are the soil-related parameters.Byrne uses the experimental data from studies of Martin, Finn, Tokimatsu, and Seed to obtain the empirical expression of the coefficients which is expressed by the relative density of sand or the number of penetration hammers:(9)C1=0.076Dr−2.5orC1=8.7N1−1.25,C2=0.4C1.


## 4.1.3. The Effective Stress Algorithm

To apply the Soil dynamic constitutive model into the finite element simulation, one custom material subroutine was applied in the finite element simulation software. The main tasks of the custom subroutine are: (1) give the corresponding strain incrementΔε according to the stress increment Δσ introduced by finite element simulation software; (2) update and solve the state variables that need to be passed during the calculation.The calculation of vibrating pore water pressure of soil required static and dynamic coupling calculation steps, which can be realized by multitask in software. In order to facilitate the usage of the custom subroutine, the constitutive model was divided into two stages: static and dynamic. In the static calculation stage, the original geostress balance calculation method supplied by the finite element simulation software was utilized. While in the dynamic calculation stage, the dynamic stress-strain relationship of the modified Davidenkov constitutive model combining with the Byrne pore pressure increment model was utilized.


## 4.2. Finite Element Simulation Model and Results

### 4.2.1. Finite Element Simulation Model

Finite element simulation model was established according to the similarity ratio in Table1. The finite element simulation model is shown in Figure 11. The concrete damage constitutive model and solid element were adopted to simulate concrete block. The ideal elastic-plastic constitutive model and beam element were adopted to simulate steel rock bolts.Figure 11
Finite element simulation model.


### 4.2.2. Amplification Factor and Fourier Amplitude Spectrum

The finite element simulation obtained the PGA amplification factor at related points of the four slope models shown in Figures5 and 6. And the finite simulation also obtained the acceleration Fourier amplitude spectrums at the same point with sensor point A7 and are also shown in Figures 6–8.By comparing results of the experiment and numerical simulation, it can be found that the general laws between experimental results and numerical simulation results are consistent but some differences exist. So, the finite elements simulation can partially provide supplementary results to the experiment while the simulation accuracy still needs to be improved especially for the contact effect simulation between plant roots and soil.


### 4.2.3. Soil Liquefaction Area Distribution

Figure12 is the finite element simulated soil liquefaction area distribution for natural slope without vegetation and hinged block slope under 0.4 g magnitude Taft wave. In Figure 12, larger numerical value will be related with more serious liquefaction. It can be found that without hinged blocks, the slope is in serious liquefaction condition, and the most serious liquefaction area is in the middle part of the slope. For the slope with hinged blocks, the liquefaction area and value dropped rapidly comparing to the slope without hinged blocks, and only weak liquefaction exists at the slope top and bottom area, which coordinates with the experimental results. The simulation result also proved that the hinged blocks are able to effectively prevent soil liquefaction in earthquakes.Figure 12
Finite element liquefied area of slope. (a) Natural slope without vegetation. (b) Hinged block of slope.
(a)
(b)


## 4.2.1. Finite Element Simulation Model

Finite element simulation model was established according to the similarity ratio in Table1. The finite element simulation model is shown in Figure 11. The concrete damage constitutive model and solid element were adopted to simulate concrete block. The ideal elastic-plastic constitutive model and beam element were adopted to simulate steel rock bolts.Figure 11
Finite element simulation model.


## 4.2.2. Amplification Factor and Fourier Amplitude Spectrum

The finite element simulation obtained the PGA amplification factor at related points of the four slope models shown in Figures5 and 6. And the finite simulation also obtained the acceleration Fourier amplitude spectrums at the same point with sensor point A7 and are also shown in Figures 6–8.By comparing results of the experiment and numerical simulation, it can be found that the general laws between experimental results and numerical simulation results are consistent but some differences exist. So, the finite elements simulation can partially provide supplementary results to the experiment while the simulation accuracy still needs to be improved especially for the contact effect simulation between plant roots and soil.


## 4.2.3. Soil Liquefaction Area Distribution

Figure12 is the finite element simulated soil liquefaction area distribution for natural slope without vegetation and hinged block slope under 0.4 g magnitude Taft wave. In Figure 12, larger numerical value will be related with more serious liquefaction. It can be found that without hinged blocks, the slope is in serious liquefaction condition, and the most serious liquefaction area is in the middle part of the slope. For the slope with hinged blocks, the liquefaction area and value dropped rapidly comparing to the slope without hinged blocks, and only weak liquefaction exists at the slope top and bottom area, which coordinates with the experimental results. The simulation result also proved that the hinged blocks are able to effectively prevent soil liquefaction in earthquakes.Figure 12
Finite element liquefied area of slope. (a) Natural slope without vegetation. (b) Hinged block of slope.
(a)
(b)


## 5. Conclusions

(1)
The four slope types under earthquake action reveal an acceleration amplification phenomenon. However, the acceleration amplification for the anchor + hinged block ecological slope is the lowest, whereas it is the highest for the natural slope without vegetation.
(2)
The acceleration magnified effect of the four slope types differs with altitudes: higher acceleration magnified effect existed on higher slope altitude. It is suggested in practical engineering to reinforce the slope.
(3)
With increases in seismic load, the acceleration amplification decreases. The highest acceleration amplification reduction is in the anchor + hinged block ecological slope, while the natural slope without vegetation exhibits the lowest acceleration amplification reduction.
(4)
The natural frequencies of the four slope types changed depending on reinforcement. The anchor + hinged block ecological slope can effectively avoid resonance during earthquake because more sufficient reinforcement enlarged its natural frequency. And the finite element simulation proved that the hinged blocks can effectively prevent soil liquefaction on slope.



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*Source: 7684831-2018-11-08.xml*