Experimental study on seismic response and progressive failure characteristics of bedding rock slopes

Mindon Zan,Guoxian Yan,*,Jinyu Don,Shenwen Qi,Jianxian He,Nin Lian

aSchool of Engineering and Technology,China University of Geosciences(Beijing),Beijing,100083,China

b Institute of Geosafety,China University of Geosciences(Beijing),Beijing,100083,China

c Research Institute of Geotechnical Engineering and Hydraulic Structure,North China University of Water Resources and Electric Power,Zhengzhou,450011,China

d Key Laboratory of Shale Gas and Geoengineering,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing,100029,China

e Innovation Academy for Earth Science,Chinese Academy of Sciences,Beijing,100029,China

f University of Chinese Academy of Sciences,Beijing,100049,China

g Department of Geotechnical Engineering,School of Civil Engineering,Southwest Jiaotong University,Chengdu,610031,China

Keywords:Bedding rock slope Large-scale shaking table test Seismic response Progressive failure characteristics

A B S T R A C T Bedding rock slopes are common geological features in nature that are prone to failure under strong earthquakes.Their failures induce catastrophic landslides and form barrier lakes,posing severe threats to people’s lives and property.Based on the similarity criteria,a bedding rock slope model with a length of 3 m,a width of 0.8 m,and a height of 1.6 m was constructed to facilitate large-scale shaking table tests.The results showed that with the increase of vibration time,the natural frequency of the model slope decreased,but the damping ratio increased.Damage to the rock mass structure altered the dynamic characteristics of the slope;therefore,amplification of the acceleration was found to be nonlinear and uneven.Furthermore,the acceleration was amplified nonlinearly with the increase of slope elevation along the slope surface and the vertical section,and the maximum acceleration amplification factor(AAF)occurred at the slope crest.Before visible deformation,the AAF increased with increasing shaking intensity;however,it decreased with increasing shaking intensity after obvious deformation.The slope was likely to slide along the bedding planes at a shallow depth below the slope surface.The upper part of the slope mainly experienced a tensile-shear effect,whereas the lower part suffered a compressive-shear force.The progressive failure process of the model slope can be divided into four stages,and the dislocated rock mass can be summarized into three zones.The testing data provide a good explanation of the dynamic behavior of the rock slope when subjected to an earthquake and may serve as a helpful reference in implementing antiseismic measures for earthquake-induced landslides.

1.Introduction

The stability of a slope subjected to an earthquake is a universal problem for researchers and geological engineers.Earthquakeinduced landslides worldwide have caused heavy casualties and tremendous economic losses in the last several decades.The geological structure of the rock slope is a crucial factor when accounting for the occurrence of earthquake-induced landslides(Qi et al.,2010,2015;Has and Nozaki,2014;Lan et al.,2019;Bao et al.,2020).For example,on May 12,2008,the Wenchuan earthquake(Ms=8)triggered more than 15,000 landslides(Yin et al.,2009),and a majority of them were induced by the sliding of bedding planes in rock slopes.The resulting debris blocked rivers and a great number of barrier lakes were formed,which put people living downstream at great risk.The largest barrier lake in the Wenchuan earthquake-stricken area was created by the Tangjiashan landslide.The volume of the main body of water was 3×107m3,with a height of 80-120 m,a length of 610 m,and a width of 800 m;and the backwater length was 20 km.The original slope had a dip of 30°-50°and a dip direction of 330°;and the bedding plane dipped at an angle of 40°out of the slope surface.The colossal Tangjiashan bedding landslide put more than 300,000 people’s lives in jeopardy.Given that bedding slopes are common,the study of the seismic response of such slopes is crucial for revealing the mechanism of earthquake-induced landslides and the formation of barrier lakes.

The shaking table test is an important method to examine seismic response and progressive failure characteristics of slopes directly.Shaking table tests were first employed to study dynamic problems of embankment dams(Clough and Pirtz,1956;Clough and Seed,1963).Wang(1977)and Wang and Zhang(1982)first used shaking table tests to study the dynamic stability of rock slopes.After that,numerous small-scale shaking table tests were conducted to study the failure mechanisms of slopes(Men et al.,2004;Hao et al.,2005;Wartman et al.,2005;Li et al.,2018).Lin and Wang(2006)and Wang and Lin(2011)conducted large-scale shaking table tests on soil slope models.They found that the acceleration amplification appeared to be nonlinear after the initiation of slope failure.The failure surface appeared to be fairly shallow and was confined to the slope surface.They also concluded that landslide initiation could be defined as surficial and local movement of the slope,and slope failure could be analyzed based on the massive movement of the slope.Xu et al.(2008)conducted large-scale shaking table tests on a soil slope model.They concluded that the natural frequency of the model slope gradually decreased and the damping ratio gradually increased with the increase of vibration time.They also found that the soil slope had an obvious amplification effect on the input seismic waves.The peak acceleration amplification factor(AAF)showed an increasing trend along the slope surface upward and increased sharply near the shoulder of the slope.Based on prototype slopes in the Wenchuan earthquake-stricken area,Xu et al.(2010)carried out large-scale tests on rock slopes with horizontally layered structures,including a rock slope featuring an upper hard rock overlying a lower soft rock and a rock slope with an upper soft rock overlying a lower hard rock.The results showed that the effect of lithological combinations on the acceleration response varied with the excitation direction.Under the horizontal seismic load,the hardnessupward slope demonstrated a larger amplification effect of acceleration than the softness-upward slope,whereas under the vertical load,the result was opposite.Dong et al.(2011)performed largescale shaking table tests on a bedding rock slope model.They found that the AAF increased with slope elevation,and its increment also increased with slope elevation.At the same slope elevation,the AAF of the slope surface was larger than that of the internal slope.They also found that the acceleration amplification effect was enhanced due to the reflection and refraction of discontinuity planes.Huang et al.(2013)carried out large-scale shaking table tests on hard bedding,hard antidip,soft bedding,and soft antidip rock slope models.They concluded that the response of slopes to horizontal seismic force exceeded that to vertical seismic force,and the seismic response of a hard rock slope under horizontal seismic force was stronger than that of a soft rock slope.They also summarized four rock slope failure patterns under strong earthquake shaking.Liu et al.(2013,2014)conducted largescale shaking table tests on homogeneous and layered rock slope models.They found that the horizontal AAF increased with the slope elevation,while the vertical AAF exhibited an S-shaped pattern with the slope elevation.They also found that the layered model slope produced a larger horizontal acceleration amplification than the homogeneous model slope.The upper half of the slope was influenced more seriously by the lithology,while the lower half was influenced more seriously by the slope structure.Che et al.(2016)performed large-scale shaking table tests on a scale model of a high and steep rock slope with bedding discontinuous joints to evaluate the influence of wave propagation on slope stability.They found that when the input acceleration amplitude reached a certain value,the top area of the slope completely collapsed along a sliding surface.Fan et al.(2016,2017,2019)conducted a series of large-scale shaking table tests to illustrate the application of the time-frequency analysis method to calculate the seismic safety factor of bedding and antidip rock slopes.The results showed that the surface displacement of the bedding rock slope was greater than that of the antidip rock slope,and the antidip rock slope was more stable than the bedding rock slope under the same excitation.They also found that the upper part of the bedding rock slope was more vulnerable to seismic damage,while the middle-upper part of the antidip rock slope was more vulnerable to seismic damage.Song et al.(2018a,b,2019,2021)performed a series of large-scale tests to clarify the seismic response characteristics of a rock slope with bedding and toppling structural surfaces.They found that bedding planes had a dominant effect on the slope failure.The P-waves caused settlement,while the S-waves induced horizontal sliding of the slope.They also found that the high-frequency components of seismic waves greatly affected the local slope deformation.In contrast,the low-frequency components have a controlling effect on the overall sliding of the slope.Li et al.(2019a)carried out a large-scale shaking table test to investigate the seismic response of bedding and antidip rock slopes and found that the sliding surface of the bedding rock slope was parallel to the slope surface,while the sliding surface of the antidip slopes skewed the layer under seismic force.He et al.(2021)conducted large-scale shaking table tests on a bedding rock slope model.They found that the AAF in the horizontal direction amplified at the middle and upper parts of the slope surface,while the AAF in the vertical direction showed stronger amplification at the lower part of the slope surface.The slope crest showed a nonlinear dynamic response when the excitation amplitude exceeded a certain value.They also characterized the deformation evolution of the rock slope in four stages.Furthermore,several research projects focused on the seismic response and deformation characteristics of antidip rock slopes through large-scale shaking table tests,and the results offered important insights into the failure mechanism of structural rock slopes under earthquakes(Yang et al.,2012,2018;Li et al.,2019b;Chen et al.,2020).

In summary,previous studies have proved that bedding planes significantly affect the seismic response and failure characteristics of rock slopes.However,some problems exposed by the earlier studies should be noted.First,the size of the slope models is not sufficient in length or height,as summarized in Table 1.More attention has been paid to steep rock slopes despite the originating slopes of earthquake-induced landslides being concentrated between 30°and 40°(Qi et al.,2015).Second,bedding planes of the model slopes are commonly treated as filled joints,as listed in Table 1,which has a negative impact on the analysis of slope deformation patterns(He et al.,2021).Finally,both bedding and antidip slope models have been constructed in the same model container in some previous studies(Dong et al.,2011;Huang et al.,2013;Liu et al.,2013,2014;Fan et al.,2016),which changes the boundary conditions of each slope model,causing complex seismic wave propagation paths(Li et al.,2014;Che et al.,2016),and the natural frequency of the slope model cannot be obtained accurately.To address these problems,this study conducts large-scale shaking table tests on a bedding slope model with an unfilled joint set that dips at an angle of 40°,the same as the slope of the model.The length,height,and width of the model are 3 m,1.6 m,and 0.8 m,respectively.The slope’s dynamic characteristics and acceleration responses are examined with a series of excitations in thehorizontal direction and in a combination of horizontal and vertical directions,covering wide ranges of frequencies and amplitudes.The deformation and failure processes observed are discussed critically.

Table 1Large-scale shaking table tests on bedding rock slopes from previous studies.

2.Shaking table tests

2.1.Similarity relation

According to similarity theory(Okamoto,1973;Kagawa,1978),the physical and mechanical parameters that participate in the dynamic problems involving the model slope and the prototype should be similar.To obtain the similarity relation,a dimensional analysis based on the Buckingham π theorem(Buckingham,1914)was performed to generate the similarity criterion(Brand,1957;Curtis et al.,1982;Meymand,1998).In the present study,15 parameters were considered,among which length,density,and elastic modulus were selected as the fundamental dimensions.These 15 parameters should satisfy the following physical function:

wherelis the length,ρ is the density,Eis the elastic modulus,μ is Poisson’s ratio,σ is the stress,ε is the strain,uis the displacement,v is the velocity,ais the acceleration,tis the time,cis the cohesion,φ is the internal friction angle,fis the frequency,λ is the damping ratio,andgis the acceleration due to the Earth’s gravity.

The parameters in Eq.(1)can be expressed using three fundamental dimensions,i.e.mass[M],length[L],and time[T],as listed in Table 2.On the basis of the three fundamental dimensions,the dimensionless similarity criterion function can be obtained as follows:

where π1,π2,…,π12are the dimensionless similarity criteria.

The general expression of the similarity criterion can be written as

where πidenotes theith dimensionless similarity criterion;anda1,a2,…,a15are the constants.

According to dimensional consistency,we can obtain the following equation by substituting the dimensions into Eq.(3):

Each term is merged,resulting in the following equation set:

The similarity criterion for each dimension can be calculated based on the matrix method,as listed in Table 3.According to the carrying capacity and technical parameters of the shaking table,similarity ratios for the fundamental dimensions,i.e.length,density,and elastic modulus,were set asCl=64,Cρ=1,andCE=64,respectively.Similarity ratios for the other parameters were derived,as listed in Table 4.

Table 2Dimensions of the considered parameters(the number is the dimension’s exponential term).

Table 3Similarity criteria based on the matrix method.

Table 4Similarity ratios for the parameters.

2.2.Test device

The test was carried out on a large-scale shaking table at the Institute of Engineering Mechanics,China Earthquake Administration,Harbin,China.The dimensions of the shaking table were5 m×5 m,with a capacity of 30 tonnes and a loading frequency ranging from 0.5 Hz to 40 Hz.The acceleration under full load ranged from-1gto 1gin the horizontal direction,and-0.7gto 0.7gin the vertical direction.Velocities under the full load ranged from-600 mm/s to 600 mm/s in the horizontal direction and-300 mm/s to 300 mm/s in the vertical direction;and displacements under the full load ranged from-80 mm to 80 mm in the horizontal direction and-50 mm to 50 mm in the vertical direction.The maximum overturning moment of the shaking table was 750 kN m.

2.3.Model preparation

To satisfy the similarity relation,the materials in the model slope were a mixture of iron powder,barite powder,quartz sand,gypsum,rosin,and alcohol at mass ratios of 8:53:26:6:1:6,according to the orthogonal experiment.The uniaxial compression test,the splitting test,and the direct shear test were conducted to obtain the physical and mechanical parameters(ASTM D7012-14,2014;ASTM D3967-16,2016;ASTM D5607-16,2016).The physical and mechanical parameters of the similarity model materials are listed in Table 5.

Table 5The physical and mechanical parameters of the similarity model materials.

The model slope had a length of 3 m,a width of 0.8 m,and a height of 1.6 m.The slope angle was 40°,and the dip angle of the bedding plane was 40°.The model slope was constructed inprefabricated,molded cubic blocks with dimensions of 20 cm×5 cm×4 cm(length×width×height).If the thickness of the block is too small,the block is difficult to form.Meanwhile,based on the similarity relation,if the block is toothick,the rock layer could not be simulated appropriately.Based on this analysis,the height of the block was designed to be 4 cm,and the volume of the prefabricated blocks was determined based on the dimensions of the model slope.The blocks were made of the similarity materials.During the construction,the physical and mechanical parameters were controlled by the density of the material.Each block was produced with the same weight of similarity material,and the height of the block was confirmed after the compaction.The blocks were then dried for one week before constructing the model slope.

The model slope was constructed in a rigid container,and a 10-cm thick polystyrene shock absorber was adopted to minimize the boundary effect of the rigid container(Fig.1a).Although the shock absorber cannot completely eliminate the wave reflection at the boundary,reliable testing data can be realized(Lin and Whitman,1986;Wartman,1999;Wartman et al.,2005).A smooth plastic film was pasted on the sidewall of the model container to reduce the frictional resistance between the model container and the slope model(Fig.1a).A layer of gravel was bonded on the bottom of the model container to increase the frictional resistance on the contact surface to avoid the relative displacement between the model and the model container during the excitation.The blocks at the bottom of the slope were cut into irregular shapes to satisfy the geometric requirement.Reference lines were drawn on the wall of the model container(Fig.1a).The model slope was constructed layer by layer based on those lines.When one layer was finished,the outline of the model was corrected using a spirit level.The blocks were staggered along the downhill direction and perpendicular to the slope surface(Fig.1a and b).Thus,the horizontal cracks and bedding cracks were continuous,while the longitudinal cracks were staggered,which minimizes the effect of the longitudinal cracks on the seismic response of the model.The blocks were cemented using a solution of rosin and alcohol(concentration of 15%w/w).The internal friction angle of the joint was 30.4°,and the cohesion was 0.28 MPa.The completed model slope is shown in Fig.1b and c.

2.4.Monitoring system

Monitoring the acceleration response is the primary purpose of setting up a monitoring system.The accelerometer(LC01 series)used in the test was made by Lance Technologies,Inc.,USA.Each accelerometer featured piezoelectric three-directional acceleration sensors with a sensitivity of 1975 mV/g in theXdirection,2055 mV/g in theYdirection,and 2033 mV/g in theZdirection;and the measuring range was 2.5g.In addition,an accelerometer(A0 in Fig.2)was placed on the table to record the input acceleration.There were 18 three-directional accelerometers set in the slope,as shown in Fig.2.

Fig.1.The construction of the model slope:(a)The top view of the model during construction;(b)The side view of the model after construction;and(c)The completed model slope.

Fig.2.Layout of accelerometers.Unit in m.

Photographs were taken before the excitation,and the vital friable parts were marked to analyze and compare the deformation and failure of the model slope during and after the test.Meanwhile,a high-resolution digital camera was used to record the overall test process.The positions of deformation and failure were measured,and detailed descriptions were recorded to facilitate the analysis of main characteristics of failure modes.

2.5.Input excitations

The seismic waves recorded in the field at the Wolong(WL)station during the 2008 Wenchuan earthquake were used as inputs to examine the dynamic behavior of the model slope with different directions and amplitudes.The WL waves were excited in the horizontal direction(Xdirection)and a combination of horizontal and vertical directions(XZdirection).The input amplitudes were set to 0.1g,0.2g,0.3g,0.4g,0.5g,0.6g,0.7g,and 0.8g,proportionally scaled from the peak ground acceleration of the WL wave.The eastwest(EW)and up-down(UD)components of the WL wave are shown in Fig.3.Before each excitation,the model slope was excited by white noise(WN),with a duration not less than 50 s and an amplitude of 0.03g-0.05g,to check the natural frequency of the model slope.The detailed excitation scheme is outlined in Table 6.

3.Results

3.1.Dynamic characteristics of the model slope

Fig.3.Acceleration histories of the WL wave:(a)EW component with a peak value of 9.76 m/s2;and(b)UD component with a peak value of 9.78 m/s2.

Natural frequency and damping ratio are the two main parameters that reflect the dynamic characteristics of a structure.The nonlinear dynamic characteristics of the model slope are of primary concern for a strong seismic shaking scenario.A shaking table test can examine the dynamic characteristics of the model slope,and the variations of those dynamic characteristics with changes of ground motion parameters can also be studied.

Before each excitation,accelerometers set at the slope surface were excited by WN to check the natural frequency and the damping ratio of the model slope.The transfer function of accelerationH(ω)was calculated according to the measured acceleration at the slope surfaceY(t)and the measured acceleration at the shaking table surfaceX(t):

whereSXX(ω)is the auto-power spectrum ofX(t),andSXY(ω)is the cross-power spectrum ofY(t)andX(t).

The vibration frequencies of the accelerometers A32,A43,and A51 are shown in Fig.4.The maximum frequency is 40 Hz.The frequency curves show that both the first-and second-order modals of the acceleration transfer function are well-defined under WN.The first-order vibration frequency obtained at each point on the slope surface is not entirely the same.Meanwhile,different slope parts have different amplifying effects on some frequency bands.The first-and second-order frequencies of A51 are lower than those of the other two,and their frequencies are closer to the natural frequency of the model slope.Therefore,accelerometer A51 was selected to characterize the dynamic performance of the model slope.The first-and second-order vibration frequencies and the corresponding damping ratios are presented in Table 7.It can be concluded that with the increase of vibration times,the natural frequency of the model slope tended to decrease,while the damping ratio tended to increase.This phenomenon is related to the reduction in dynamic shear strength and dynamic shearmodulus of the model slope under excitations.The reduction indicates some local damage to the structure of the model slope.

Table 6Excitation scheme.

Table 7The vibration frequency and corresponding damping ratio.

The dynamic characteristics of the model slope are related to the intensity of antecedent vibration-the stronger the antecedent vibration,the greater the reduction of the natural frequency.After the antecedent vibration,the natural frequency of the slope did not decrease significantly under the same amplitude of input excitation.When the input excitation was stronger than the antecedent vibration,the natural frequency decreased,and the damping ratio increased correspondingly.The testing results showed that the influence of antecedent vibration on the natural frequency and damping ratio is related to the strength of the model material and the peak amplitude of the input excitation.

Fig.4.Frequency curves of the acceleration transfer function at typical monitoring points.

The variation curves of the natural frequency and the damping ratio are shown in Figs.5 and 6,respectively.The first-and secondorder natural frequencies decreased,and the damping ratio increased after different amplitudes of input excitation.When the amplitude of the input excitation was small,the natural frequency decreased slightly.With the increase of excitation amplitude,the natural frequency decreased dramatically.These results indicate that the stronger the earthquake motion,the greater the range of structural damage.

3.2.Analysis of acceleration response

The seismic inertia force induced by seismic acceleration is an intrinsic factor that causes the deformation and failure of a slope.The amplification of acceleration is regarded as a critical parameter to reflect the dynamic response of the slope.According to Qi et al.(2003),the ratio of the peak acceleration recorded at any monitoring point to that at the slope toe is defined as the AAF.In this work,AAF-X refers to the AAF in the horizontal direction,and AAFZ indicates the AAF in the vertical direction.

Fig.5.Variation of natural frequency after different input excitations.

Fig.6.Variation of damping ratio after different input excitations.

The contour maps of AAF-X under WL(EW)wave excitations with amplitudes of 0.2g,0.4g,0.6g,and 0.7gare shown in Fig.7a-d,respectively.The isolines of AAF-X are nearly parallel to the bedding planes near the slope surface,which illustrates that the acceleration response is amplified significantly along the bedding planes within a certain depth below the slope surface.This phenomenon demonstrates the prominent effect of bedding planes on the acceleration response.Furthermore,the density of the isolines dramatically increases with the increase of excitation amplitudes in a particular range under the slope surface,and the greater the amplitude,the broader the range of the amplification area.In addition,the distribution of the AAF-Xs is nonlinear and uneven,with a dramatic increase near the slope crest and the upper part of the slope;however,AAF-Xs near the slope toe,in general,slightly decrease.The upper slope produces a stronger acceleration response,whereas the acceleration response diminishes near the slope toe due to the inhibitory effect of the topography.The distribution of the AAF-Zs under WL wave excitations in the vertical direction is similar to that of the AAF-Xs.

Although the absolute value of the AAF at a monitoring point makes little sense in terms of the analysis of the slope dynamic response,the trend in the relative variation of the AAFs at a series of monitoring points does make good sense.In Fig.8,the AAF-X and AAF-Z are amplified with the increase of slope elevation along the slope surface and reach their peaks at the slope crest.In addition,the AAFs show an approximately linear increase with the increase of slope elevation when the excitation amplitude is smaller than 0.6g.In comparison,the AAFs have a nonlinear increase with the increase of slope elevation when the excitation amplitude reaches 0.6g.There is a dramatic increase in the AAFs at the slope crest.Generally,both the AAF-X and AAF-Z increase nonlinearly with the increase of excitation amplitude at the same slope elevation.However,after the excitation amplitude reaches 0.6g,the AAFs decrease with further excitation amplitude.These results demonstrate that the model slope undergoes local deformation and damage when the excitation amplitude reaches 0.6g.

The variation of AAFs along the vertical section(accelerometers A13,A23,A33,and A43)is illustrated in Fig.9.In general,both the horizontal and vertical components of the acceleration are amplified nonlinearly with the increase of slope elevation.The AAFs increase with the increase of excitation amplitude,but the AAFs decrease when the excitation amplitude exceeds 0.6g,indicating that damage occurs within the slope after the WL wave excitation amplitude is larger than 0.6g.This phenomenon can also be observed from the AAFs along the slope surface(Fig.8).Besides,the maximum AAF appears near the slope surface,which indicates that the slope surface produces a stronger acceleration response than the interior of the slope.Furthermore,compared with the contour maps of AAF in Fig.7 and AAFs along the slope surface in Fig.8,it can be seen that the AAFs shows a dramatic increase when the slope elevation is greater than two thirds of the slope height,and the AAFs have a sharp increase at the slope crest.This is mainly caused by the free face effect on the acceleration response.In addition,the AAF-Z is a little larger than the AAF-X at the lower part of the slope;however,the AAF-X is larger than the AAF-Z at the upper part of the slope,especially when the excitation amplitude is greater than 0.6g.The result is consistent with the conclusions reached from shaking table tests by Yang et al.(2018)and He et al.(2021).

The variation of AAFs along the horizontal section(A41,A42,A43)is shown in Fig.10.The AAF-X decreases first and then increases with the decrease of horizontal distance to the slope surface(Fig.10a).Additionally,both the decrement and increment of AAF-X increase with excitation amplitude(Fig.10a).Similar patterns can be observed from the variation of AAF-Z,except when the excitation is 0.1g,as shown in Fig.10b.Nevertheless,the AAF-X is generally greater than the AAF-Z at the same accelerometer.As the horizontal section is set in the upper part of the slope,these results indicate that the upper part of the slope produces a stronger response to the horizontal component of acceleration.This result can also be concluded from the AAFs along the vertical section(Fig.9).

Fig.7.The contour maps of AAF-X under WL wave excitations with different amplitudes:(a)0.2g,(b)0.4g,(c)0.6g,and(d)0.7g.

3.3.Deformation and failure characteristics of the model slope

Fig.8.AAFs along the slope surface(A16,A25,A34,A43,A55,and A51)under WL wave excitations:(a)AAF-Xs,and(b)AAF-Zs.

Slope deformation and failure triggered by earthquakes reflect the dynamic response of the slope,and slope deformation usually occurs at the location where the strongest response is induced.According to the dynamic characteristics measured by accelerometers and the deformation features recorded by the camera,the progressive failure process of the bedding rock slope can be summarized into the following four stages:

(1)Stage I.When the excitation amplitude was less than 0.6g,no obvious deformation was observed.However,some local structural damage occurred in the interior of the model slope,as evidenced by the variations of natural frequency and damping ratio of the model slope(Figs.5 and 6).

Fig.9.AAFs along the vertical section(A13,A23,A33,and A43)under WL wave excitations:(a)AAF-Xs,and(b)AAF-Zs.

(2)Stage II.When the excitation amplitude was greater than 0.6g,a tensile crack first initiated at the slope crest with a length of approximately 25 cm(Fig.11a).The tensile crack developed along the joint between the blocks,and the aperture of the crack was approximately 1 mm,as shown in Fig.11a.

(3)Stage III.When the excitation amplitude increased to 0.7g,the cracks at the slope crest further widened and deepened to form penetrating cracks,and several new tensile cracks occurred around the slope crest with lengths of 20-30 cm and apertures of 2-5 cm.The shallow rock mass at the surface began to slide along the bedding plane(Fig.11b).Meanwhile,buckling of the rock mass was observed near the slope toe,and some blocks were uplifted at the slope toe with a dislocation of 2-4 cm(Fig.11c).In addition,a small number of rockfalls accumulated at the slope toe,as shown in Fig.11c.These failure phenomena were consistent with the field investigation on coseismic landslides induced by the Wenchuan earthquake(Yang,2011).

(4)Stage IV.When the excitation amplitude reached 0.8g,the existing cracks grew dramatically,and an overall sliding occurred along the first bedding plane(Fig.11d).After that,new sliding occurred along the second bedding plane followed by sequential sliding along the third and the fourth bedding planes,until the fifth bedding plane.Finally,cascaded failure formed at the slope surface.The failure was limited to a shallow depth beneath the surface,but some loose blocks were also observed deeper below the slope surface(Fig.11d).The dislocated rock mass can be divided into three zones:the first zone was the main scarp,with a length of 60 cm;the second 140-cm-long zone was covered by debris from the middle of the slope to the slope toe;and the last zone was an accumulation zone full of dislocated blocks,with a thickness of 30 cm.In the accumulation zone,the previously displaced blocks interrupted the movement of later arriving blocks,equivalent to a dam being formed in a river.The development of the Tangjiashan barrier dam during the Wenchuan earthquake followed a similar pattern.

4.Discussion

Fig.10.AAFs along the horizontal section(A41,A42,and A43)under WL wave excitations:(a)AAF-Xs,and(b)AAF-Zs.

Fig.11.Progressive failure process of the bedding rock slope:(a)The first crack appeared near the slope shoulder;(b)Tensile cracks occurred near the slope shoulder;(c)Buckling occurred near the slope toe;and(d)Overall failure of the model slope.

The model test results indicated that the seismic response of the bedding rock slope was significantly amplified at the slope surface and crest,confirming field observation data in earlier studies(Davis and West,1973;Meunier et al.,2008;Luo et al.,2014).This is because the constraint of the slope surface and crest is less than that at other parts of the slope(He et al.,2021).In addition,the progressive failure process of the bedding rock slope was also reproduced by large-scale shaking table tests.No obvious slope deformation was observed when the earthquake intensity was less than the 0.6gthreshold.However,local structural damage of the slope can be reflected through the variations of natural frequency and damping ratio(Figs.5 and 6),which revealed that block loosening and joint opening had occurred in the interior of the slope.When the earthquake intensity reached a specific threshold,visible deformation of the slope could be observed.With the growth of deformation,AAF decreased along the slope surface,horizontal section,and vertical section.When the earthquake intensity continued to increase,the deformation grew dramatically,and the positions of accelerometers changed.In this situation,the acceleration response does not accurately reflect the deformation state of the slope.In comparison,the progressive failure evolution can be characterized by observing the failure phenomena.After the excitations,the final morphology was steplike at the shallow surface of the model slope(Fig.11d),which demonstrated the prominent effect of bedding planes on the deformation of rock slopes under strong earthquakes.This phenomenon was consistent with the results from large-shaking table tests by Li et al.(2019a)and He et al.(2021).Additionally,largescale shallow sliding of the bedding slope that was observed in field investigations after the Wenchuan earthquake revealed that sustained and dramatic acceleration amplification occurred around the slope surface at shallow depth,as was the case in the present study(Fig.12).

We conducted a series of large-scale shaking table tests to study the effect of rock mass structure on rock slope seismic response(Dong et al.,2011;Yang et al.,2012,2018;He et al.,2021).Testing results and field investigations showed that the rock mass structure plays a dominant role in the deformation and failure of rock slopes.Model tests on homogeneous,antidip,and bedding slopes revealed that the closer the location to the surface,the larger the AAFs were,and significant amplification occurred at the slope surface and crest(Dong et al.,2011;Yang et al.,2012,2018;Zhan et al.,2019;He et al.,2021).However,some new phenomena were observed compared with the homogeneous model test(Zhan et al.,2019)and the antidip model test(Yang et al.,2018).The present model test indicated that with the increase of input excitation amplitude,the isoline of the AAF trended to be parallel to the bedding planes,and the large values of the AAFs extended deeper below the slope surface,which might result in the rock mass sliding along the bedding planes under strong earthquakes.This finding also concurred with the bedding model test results from He et al.(2021).Buckling of the rock mass was observed near the slope toe,and this was a deformation characteristic unique to bedding rock slopes.In addition,the bedding slope failure observed in the model test occurred due to sliding along the bedding planes,while the antidip slope failure occurred as toppling failure around the slope crest with an arc-shaped sliding plane(Yang et al.,2018).

Fig.12.Shallow sliding during the Wenchuan earthquake.

Fig.13.Buckling of bedding slope due to the Wenchuan earthquake(Yang,2011).

Lin and Wang(2006)found that the boundary of the rigid container would not affect the location of the sliding surface when the distance from the slope crest to the boundary was larger than twice the horizontal projected slope length.As shown in Fig.1,the present model slope did not have a long distance between the boundary and the slope crest.However,a polystyrene absorber was employed to minimize the boundary effect.Results showed that the AAFs were distributed in a reasonable range near the model boundary(Fig.7).Hence,the boundary effect had little impact on wave transmission at the rear of the model slope.Furthermore,the model slope in this study had a longer horizontal projected slope length(2 m)and a higher relative slope height(1.4 m)than previous bedding models(Dong et al.,2011;He et al.,2021);thus,the model provided a broader range to show the distributions of AAFs.He et al.(2021)found that the seismic response of a slope under sine waves was sometimes contrary to that under WL waves.The seismic response of the slope varied significantly depending on the characteristics of the input excitation.Therefore,different from the excitation schemes of Dong et al.(2011)and He et al.(2021),our model was excited by WL waves alone,and the deformation characteristics observed from the physical modeling were consistent with field investigations.However,large-scale shaking table tests on the seismic response of layered rock slopes under different types of input excitations should be conducted in the future.

The model tests indicated that tensile cracking and bedding sliding were first initiated at the slope surface and crest,revealing that the upper part of the slope mainly experienced a tensile-shear effect under seismic shaking.When the excitation amplitude increased to 0.7g,buckling of the rock mass was observed near the slope toe.Buckling of the rock mass near the slope toe was also found in field investigations after the Wenchuan earthquake,demonstrating that the lower part of the slope mainly experienced compressive-shear force under the effects of seismic wave and gravity(Fig.13).Therefore,different stress states and deformation characteristics should be considered for the aseismic design of slope engineering.Furthermore,much more attention should be paid to studying the effect of the rock mass structure on the seismic response and progressive failure characteristics of the rock slope,especially in areas of intense tectonic activity.

5.Conclusions

Based on the similarity relations,this study constructed a bedding rock slope model with a size of 3 m×0.8 m×1.6 m(length×width×height)to undertake shaking table tests.The main results are as follows:

(1)With increasing vibration time,the natural frequency of the model slope decreased and the damping ratio increased,demonstrating some local damage to the model slope structure.The dynamic characteristics of the model slope were related to the antecedent vibration intensity and the input excitation amplitude.When the excitation amplitude was stronger than the antecedent vibration,the natural frequency decreased.The larger the excitation amplitude,the greater the range of structural damage.

(2)The AAFs increased nonlinearly with the increase of slope elevation,whether at the slope surface or along the vertical section of the slope.A dramatic amplification of acceleration occurred primarily around the slope crest and the upper slope surface.In contrast,the acceleration response diminished near the slope toe due to the inhibitory effect of the topography.The rock mass was liable to slide along bedding planes at a shallow depth below the slope surface,which provided a reasonable explanation for the large-scale shallow sliding of rock slopes triggered by earthquakes.Bedding planes play a dominant role in the deformation and failure of bedding rock slopes.

(3)With increasing shaking intensity,the AAFs increased before obvious deformation occurred and then decreased after obvious deformation.The structural damage of rock mass dissipates more energy.

(4)The progressive failure process of the bedding rock slope can be divided into four stages:(i)Stage I-no obvious deformation was observed,and local structural damage occurred in the interior of the slope.(ii)Stage II-tensile cracks initiated at the slope crest.(iii)Stage III-tensile cracks grew gradually,and the rock mass began to slide along the shallow bedding plane.Simultaneously,buckling of the rock mass occurred around the slope toe.(iv)Stage IV-cracks grew dramatically,and progressive failure occurred along the bedding plane layer by layer.Finally,cascaded morphology formed at the slope surface.The dislocated rock mass can be summarized into three zones:the sliding zone below the main scarp,the coverage area from the middle of the slope to the slope toe,and the accumulation zone.These zones were identical to those observed for the Tangjiashan landslide that was triggered by the 2008 Wenchuan earthquake.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was funded by the National Natural Science Foundation of China(Grant No.41825018),the National Key Research and Development Plan of China(Grant No.2019YFC1509704),and the Second Tibetan Plateau Scientific Expedition and Research Program(STEP,Grant No.2019QZKK0904).