Long-qi Li I Neng-pan Ju I Shuai Zhang I Xiao-xue Deng I Daichao Sheng
Seismic wave propagation characteristic and itseffects on the failure of steep jointed anti-dip rockslope
Abstract Discontinuities, such as joints and beddings, usuallyplay a significant role in the seismic response and correspondingfailure process of slopes, especially for anti-dip rock slide accord-ing to field observations. Shaking table tests associated with nu-merical analyses are carried out in this paper to explore the effectof seismic wave on response of jointed anti-dip rock slopes. Shak-ing table tests involve anti-dip rock slope models with differentrock types and different excitation intensities. Ten accelerometersare installed inside each slope model to monitor the dynamicresponse and spectrum shifting characteristics. It is found thatthe area of failure zone in the soft rock anti-dip slope is approx-imate 1.5 times the size of that in the hard rock anti-dip slope.Meanwhile, the width and ridge number of the fast Fourier-transformation spectrum along the slope surface can reveal theinternal damage features within the anti-dip rock slopes, and themultiple failure planes can also be recognized according to thevariation of distance between the innermost and outermost ridgesin the fast Fourier-transformation spectrum. Moreover, the dis-tinct element method incorporating a damage model is used tointerpret the test results and to identify the main influencingfactors for seismic instability. It is found that the failure patternof a jointed anti-dip rock slope is more sensitive to beddinginclination than to joint inclination.
Keywords Jointed anti-dip rock slope . Seismic wave propagationcharacteristic . Model test . Discrete element method analysis
IntroductionAn anti-dip rock slope, also called toppling slope, is a kind ofstructural slope whose stratum dips inwards the slope surface(Goodman and Bray 1976; Cruden 1989; Cruden and Varnes 1996;Hungr et al. 2014). Previous research mainly focused on the top-pling classification and failure mechanism in gravitation-dominant environment (Schumm and Chorley 1964; Adhikaryet al. 1997; Nichol and Hungr 2002; Majdi and Amini 2011). How-ever, recent occurrence of massive regional earthquakes call forstudies of seismic wave propagation characteristics and their ef-fects on anti-dip rock slopes, which are widely distributed inmountainous areas (Aurelian et al. 2009; Huang and Fan 2013;Koukouvelas et al. 2015; Almaz and Havenith 2016). In particular,case studies show that the seismic wave transfer within slopes ishighly complicated when the rock layers are joint-spreading(Mineo et al. 2015). Much more complex refraction and reflectionphenomena emerge between discontinuities, which enhance localmotion enlargement effects, thus inducing various possible failurepatterns different from homogenous slope. Unfortunately, sucheffects have not been fully understood in the literature.
In the past decades, diverse means, including physical modeltesting, numerical simulation, theoretical analysis, were adopted
to investigate seismic wave propagation and rock slope failuremechanisms. Among them, physical modeling and numerical sim-ulation are two popular methods that are relatively easy to access(Goodman 1989; Mavrouli et al. 2009). With reference to physicalmodeling, shaking table tests were most commonly used to inter-pret tension and shear failure modes of uniform rock slopes(Wartman et al. 2005; Liu and Xu 2011). In addition, seismicexperiments on consequent bedding rock slopes with simple dis-continuities were undertaken to improve our understanding ofresponse characteristics and failure process (Dong et al. 2011; Cheet al. 2016). Seismic responses of rock slopes with silt intercalationwere investigated by Fan et al. (2016), who discussed the unevendistribution of amplification coefficient on slope surface.Employing shaking table tests to study the progressive failure ofslopes was reported by Shinoda et al. (2013) and Nakajima et al.(2016). Some researchers adopted small laboratory tests to studyflexural toppling failure of rock slopes, but the duration of appliedhorizontal loadings was too short and pulsating, while the verticalloading was relatively realistic (Nishimura et al. 2012; Li et al. 2015).Overall, large-scale shaking table testing is promising for investi-gating the response and failure mechanism of structural rockslopes, but still has challenges in interpreting more sophisticatedanti-dip rock slopes.
Numerical analyses for seismic effects on rock slopes based oncontinuum and discrete approaches have also been discussed(Eberhardt et al. 2004; Stead et al. 2006). In the realm ofcontinuum-based methods, numerical upper and lower boundtechniques were adopted to produce seismic stability charts forrock slopes by Li et al. (2009). Some scholars also discussed theapplicability of a three-dimensional numerical approach, in con-junction with genetic algorithm (GA), to investigate the effects ofearthquake force direction on minimum spatial slope safety factor(Asr et al. 2012; Zhang et al. 2012). Other researchers furtherexplored the effects of friction angle and cohesion on the dynamicdisplacements by means of the finite difference method (FDM) orthe pseudo-dynamic method (Latha and Arunakumari 2010; Ruanet al. 2013). At the same time, in the field of discrete methods, casestudies based on 2D distinct element method (DEM) or discontin-uous displacement analysis (DDA) were undertaken to clarifyamplification patterns affected by geomorphic conditions(Bhasin and Kaynia 2004; He et al. 2010; Pal et al. 2012; Zhanget al. 2013; Liu et al. 2014; Zheng et al. 2014; Lin et al. 2018). Inaddition, choosing appropriate kinetic damping values in discon-tinuous numerical analysis was also highlighted (Hatzor et al.2004; Gischig et al. 2015a, b; Zhang et al. 2015a, b).
Although the above methods have provided much meaningfulresults, they primarily focused on homogeneous rock slopes orslopes with simple joint features. There is little work on effects ofbeddings and discontinuous joints on seismic failure of anti-dip
Landslides 16 & (2019) 105
Original Paper
rock slopes. During the Wenchuan earthquake, diverse anti-diprock slope failures occurred at the adjacent region of the epicenter,largely due to existing condensed rock mass discontinuities. Forinstance, the Jianshan landslide and the Heifengkou landslide inthe Longmenshan region shared a similar stratum but differentdiscontinuity characteristics, while the failure surface of the for-mer was shallower than the latter, as shown in Fig. 1. Meanwhile,there also exist some typical unsolved problems in slope seismicengineering: (1) how to distinguish and extract meaningful indi-cators for damage of some special structural slopes, for example,slopes sliced by continuous beddings and discontinuous joints,before overall failure? and (2) what is the key impact factor fordamage in a jointed anti-dip rock slope? To answer these
questions, a systematic study using experimental and advancednumerical methods are needed.
In this paper, scaled shaking table tests as well as numericalanalysis using the commercial code UDEC integrated with a dam-age model (UDEC-DM) are combined to investigate seismic re-sponses of steep jointed anti-dip rock slopes. During theexperiment, a total of 20 acceleration sensors are placed at differ-ent levels to capture dynamic behavior of two generalized slopemodels. The characteristics of seismic response and the fastFourier-transformation (FFT) spectrum are analyzed by compar-ing the differences at the identical monitoring point inside twokinds of slopes. The failure patterns of model tests are thenverified by numerical analysis, and parametric analyses on
105°0'0"E
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104°0'0"E
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103°0'0"E
102°0'0"E
102°0'0"E
32
°0
'0"N
31
°0
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30
°0
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32
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31
°0
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30
°0
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0 40 8020
km
Russia
China
IndiaStudy area
Initial slope surfaceRock layer
Rock layerInitial slope surface
a b
Joint
Joint
0 30m 0 40mJoint Occurrence: 120° ∠ 53°
Joint Spacing: 2.2 m
Joint Occurrence: 155° ∠ 41°
Joint Spacing: 1.6 m
Chengdu
Wenchuan
Sichuan Basin
Qinghai-Tibet
Plateau
Fig. 1 Two kinds of anti-dip rock slope failure cases: a Jianshan landslide. b Heifengkou landslide
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Landslides 16 & (2019)106
influential factors are also undertaken. The studies presented inthis paper provide more insights into the failure mechanisms ofjointed anti-dip rock slopes under seismic loading.
Shaking table test on seismic wave propagation in jointed anti-dipslopes
Model test schemeTwo experimental slope models, with different lithologies ofhard or soft rocks, were generalized from several prototypeslocated in the Longmenshan region of Sichuan Province ofwestern China. Physical model tests should comply with simi-larity requirements, which apply to all model parameters in-cluding geometry, mechanic properties as well as boundaryconditions (Regmi et al. 2017). The geometric reduction factorCl was set to 100. Other model parameters were deduced basedon the prototype parameters, as shown in Table 1. The sub-scripts “p” and “m” denote the prototype and the model,respectively.
As per study of Meguid et al. (2008), artificial materials canapproximately simulate the macroscopic behavior of real slopemass if adequate component materials and appropriate massratios are adopted. In the present study, the slope model massconsists of mortar block and interlayer filling materials as wellas joints, which are made of a mixture of quartz sand, baritepowder, gypsum, glycerin, glycerin, and water. In order to guar-antee the quality of the slope model mass, prefabricated mortarblocks, with a length of 20 cm, a width of 20 cm, and a thicknessof 5 cm, were used to construct the rock layer, which wascemented by filling materials. During the manufacturing pro-cess, the surrounding temperature was set as 25 °C and thehumidity was kept to be 20%.
A great variety of laboratory tests were carried out, includingstatic triaxial tests which provide the shear strength parameterslike friction angel and cohesion, static elastic modulus, andPoisson’s ratio, as well as dynamic triaxial tests where thedynamic elastic modulus and dynamic Poisson’s ratio are ob-tained. The peak and residual shear strength parameters aredefined in Fig. 2. By adjusting the mass ratio of componentmaterials, appropriate values for the mechanical parameters ofthe simulated material were achieved and are shown in Table 2.The mixing mass ratios of hard mortar block are as follows:
and the filling material has the following mixing ratios:
quartz sand : barite powder : motor oil : water ¼ 18:2 : 13:8
: 9:2 : 7:4: ð3Þ
The simulation of joints in the slopes was carefully consid-ered. On one hand, the joint material should have a lowerstrength and a lower stiffness than the surrounding mortarblock. On the other hand, it should be inexpensive and easilyaccessible, due to the large amount of quantity required. Bycomparing among some common commercial materials, weselected a 12-cm-long Teflon strip, with an elastic modulus of23 MPa and a Poisson ratio of 0.45, to simulate discontinuousjoints in the slope mass. These Teflon strips were spaced 15-cmapart at an angle of 60° in the slopes.
The shaking table system adopted has an operating capacityof 80 tons, while the maximum loading frequency is 60 Hz. Twosteep anti-dip rock slope models, made of hard rock and softrock respectively, with 150 cm in length, 120 cm in width, and173 cm in height, were constructed in the test chute (see Fig. 3).Herein, the slope angle and the joint inclination were both setas 60°, and rock layer angles were 60° reverse to the slopesurface. Meanwhile, a piece of polystyrene sheet was set betweenthe slope model and the test chute to alleviate the adverseimpact of seismic boundary on the testing model. Ten acceler-ation sensors were installed in each slope model to monitor theseismic response under different earthquake excitations. Foreach slope model, five acceleration sensors, including A1 toA5, were installed near the slope surface to capture the surfacedynamic response, and another five acceleration sensors, in-cluding A6 to A10, were installed to monitor the response insideslope body, as shown in Fig. 4. During the test, the input seismicwaves were applied from both the horizontal and vertical direc-tions, adjusted based on the original ones (see Fig. 5) collectedfrom Wolong seismostation during the Wenchuan earthquake.According to Table 1, each input duration was squeezed from120 to 12 s by the time scale factor Ct. Meanwhile, the load-onsequence was set by changing excitation amplitude from 0.2 to0.8 g (level A to level D) in intervals of 0.2 g. Noting that inorder to accelerate the failure procedure, several white noisesand sine waves were applied alternatively as well (see Fig. 6).
Model construction and test procedureIn the present study, the test procedure was decomposed intothree major steps to ensure the reliability of the test results. Thefirst step was the model preparation. The slope body consistedof mortar block and interlayer filling, whose constituent ratiosand mechanic strength were achieved by several indoor tests inahead. Mortar blocks were prefabricated in some molds and
Table 1 Similarity coefficient used in the model experiments
Parameters Non-dimensional definition Scaled value
Length Cl = lp / lm 100
Displacement Cd = dp / dm = Cl 100
Unit weight Cγ = γp / γm 1
Elastic modulus CE = Ep / Em = CγCl 100
Poisson’s ratio Cμ = μp / μm 1
Cohesion Cc = cp / cm = CE 100
Friction angle Cφ = φp / φm 1
Time Ct = tp / tm = (Cl / Ca)1/2 10
Acceleration Ca = ap / am 1
Landslides 16 & (2019) 107
then stored under constant temperature and humidity conditionafter demolding to prevent formation of obvious shrink fissures.Meanwhile, the geometrical size of the slopes and the specificlocation of different sensors were labeled on the sidewall of thetest chute.
The second step was to cast the model slopes. The mortarblocks were stacked layer by layer from bottom to top slope atthe designated rock layer inclination, and interlayer fillingswere pasted between different layers, while the Teflon stripswere also installed simultaneously. In order to stop the mortarblock from sliding during the manufacture process, removablesupporting frames were set in front of the slope model to avoidinitial sliding. Meanwhile, different sensors were buried in thedesigned positions, where the surrounding materials were care-fully compacted and cemented to ensure proper stress transferto the sensors throughout the entire experiment.
The third step was to apply seismic load on slope models.When all the above work was finished, the slope model waskept for 24 h to attain the initial stable status. Afterwards, thescheduled seismic load was applied at the bottom of the slopemodel, and the corresponding responses at different locations
and time periods were monitored and analyzed. Meanwhile, aparallel model test was conducted to verify reliability of theresults monitored from the formal experiment.
Wave propagation analysis and ultimate failure patternAccording to previous studies by Che et al. (2016), the horizontalS-waves have primary impact on slope shear sliding and collapse.Hence, horizontal seismic responses are focused and analyzed inthe present study. The response under a white noise wave wasanalyzed by a function of tfestimate() in Matlab’s Signal Process-ing Toolbox. Figure 7 depicts the transfer functions of horizontalcomponent excitations, calculated for diverse monitoring points,A1, A2, A3, A4, and A5 in the soft rock slope model under the firstwhite noise. The resonance frequency is regarded as the average ofdominant frequency in the above five excitations. It can be seenthat the initial frequency of the soft rock slope model is 17.7 Hz.The initial frequency of the hard rock slope model is 26.3 Hz,achieved in the same way. Similarly, the average resonance fre-quencies under each white noise excitation are shown in Fig. 8.The resonance frequency shows a decrease tendency with loadingof white noise excitations, which reflects that the internal structure
0.0 0.5 1.0 1.5 2.0 2.5 3.00.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7 8 90.0
0.2
0.4
0.6
0.8
1.0
σ3=0.1 MPa σ3=0.3 MPa σ3=0.5 MPa
τ=(σ
1-σ3
)/2
(MPa
)
τ1ak
τ1ar
Strain (%)
σ (MPa)
ck
ϕk
τ=(σ
1-σ3
)/2
(MPa
)
σ3a σ1akσ3b σ3c σ1bk σ1ck
0.0 0.5 1.0 1.5 2.0 2.5 3.00.0
0.2
0.4
0.6
0.8
1.0
τ=(σ
1-σ3
)/2
(MP
a)
cr
ϕr
σ (MPa)σ3a σ1arσ3b σ3c σ1br σ1cr
0.15 39
ck (MPa) ϕk (° )
0.05 36
cr (MPa) ϕr (° )
Fig. 2 Typical triaxial test results for the simulated material. Subscript “k” represents values at the peak strength, while “r” represents the residual strength, σ3i (i = a,b,c)represents the static confining stress, σ1ik (i = a,b,c) represents the axial stress at the peak status, and τ1ak and τ1ar represent the peak and residual shear strength, respectively
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Landslides 16 & (2019)108
Table2Basic
mechanicalparam
etersoftheslope
geo-materials
Item
Unitweightγ
(kN/m3 )
Dynamicelastic
modulus
E d(MPa)
DynamicPoisson’sratioμ d
(−)
Elastic
modulus
E(MPa)
Poisson’sratioμ
(−)
Hard
rock
block
Prototype
26.9–27.3(27.2)
24,561.3–26,796.4(25,472.7)
0.23–0.26(0.25)
16,772.1–19,884.6(18,332.4)
0.22–0.25(0.24)
Model
26.2–27.9(27.1)
220.7–228.5(224.1)
0.21–0.28(0.25)
166.2–186.3(172.6)
0.18–0.23(0.21)
Softrock
Block
Prototype
24.4–26.9(26.2)
4416–5768(4932)
0.25–0.31(0.29)
1883–2398(2213)
0.19–0.24(0.22)
Model
25.9–26.6(26.3)
133.6–143.2(137.9)
0.27–0.29(0.29)
99.3–132.7(112.7)
0.19–0.21(0.20)
Interlayerfilling
Prototype
––
––
–
Model
17.3–18.6(18.4)
47.1–48.3(47.7)
0.29–0.33(0.32)
17.1–18.3(17.3)
0.29–0.34(0.32)
Item
Frictionangleatpeak
stateφk
(°)Cohesionatpeak
statec k
(MPa)
Frictionangleatresidualstateφr
(°)Cohesionatresidualstatec r
(MPa)
Hard
rock
block
42–49(45)
15.3–16.8(15.9)
38–44(42)
4.3–8.6(6.3)
39–44(43)
0.13–0.16(0.15)
36–45(40)
0.03–0.09(0.05)
Softrock
Block
33–36(34)
1.3–2.1(1.7)
23–34(30)
0.1–1.1(0.9)
37–41(38)
0.01–0.04(0.02)
24–33(28)
0.01–0.02(0.01)
Interlayerfilling
––
––
35–38(37)
0.01–0.03(0.02)
22–27(26)
0.008–0.013(0.009)
Notethatthenumbersinparenthesis
indicatethemeanvalues
Landslides 16 & (2019) 109
in a slope is becoming loose (Liu et al. 2014). Meanwhile, a sharpdecrease exists between the white noises 5 and 6, where a
Wenchuan wave with an acceleration (PGA) of 0.6 g is applied.This loading period has been identified to be a representativetarget, and responses under this seismic wave were only chosenas the analysis basis to avoid tedious description.
Figure 9a, c illustrates the x-direction acceleration variationand the corresponding FFT amplitude for two kinds of anti-diprock slopes along the slope surface when the PGA reaches 0.6 g,while Fig. 11a, c shows that variation at distance from the surface ofhalf slope height. The numbering of the plots in these figurescoincides with that in Fig. 4. The acceleration time history inFig. 9a, c shows an amplifying effect along the slope surface for
x(+)
y
z
Fig. 3 Anti-dip rock slope model layout
Fig. 4 Schematic model layout
a
b
0 20 40 60 80 100 120-1.0
-0.5
0.0
0.5
1.0
(noitarelecc
Ag)
Time (s)
-0.5
0.0
0.5
1.0
(noitarelecc
Ag)
Fig. 5 Time histories of original Wolong seismic wave: a at horizontal direction (E–W), b at vertical direction (U–D)
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Landslides 16 & (2019)110
both kinds of slopes, and the maximum acceleration is located atthe crest of the slope surface. Meanwhile, for the soft rock anti-dip(termed as SRA) slope, the PGA at A5 is 2.12 g, indicating theamplification coefficient is 2.65. For the hard rock anti-dip (termedas HRA) slope, the PGA at the A5 was 1.89 g, smaller than that ofthe SRA slope. The crest PGA of the SRA slope is 1.12 times largerthan that of the HRA slope. This characteristic can be ascribed totwo major facts: the smaller inherent material stiffness of the SRAslope than the HRA slope and the subsequent higher fracture levelof the SRA slope than the HRA slope during earthquake. Thesefacts lead to a more flexible SRA slope than the HRA slope, whichresults in a larger motion amplification in the SRA slope. It is alsoobserved that the acceleration time-history shows different varia-tion patterns along the slope height, depending on the slope rocks.For the HRA slope, the acceleration time-history amplificationmainly concentrated on two separate time intervals: 0–13 and30–40 s. While for the SRA slope, the acceleration in time intervalof 13–30 s also shows some amplification effect. These observationsmay require further studies on the effects of dynamic responsealternation during seismic crack evolution in rock mass. One
possible explanation is that the newly formed condensed cracksgenerate additional motion wave, which has the similar frequencywith the vibration in interval of 13–30 s.
Another interesting issue is the FFT spectrum variation at differentlocations for two kinds of slopes, which are shown in Fig. 9b, d. It canbe seen that the spectrum components become more complex withincreasing elevation. The FFT spectrum of the initial input wave isunimodal, while that of the response wave at higher location is mul-timodal. Meanwhile, there exists some elevation threshold where thenumber of ridges becomes constant. For the HRA slope, this elevationwas between 1/4 (at A2) and 1/2 (at A3) of the slope elevation, while forthe SRA slope it was below 1/4 of the slope elevation. This phenome-non can be closely related to the slide surface spreading conditions, asshown in Fig. 12. The elevation of the slide surface near the slopesurface actually coincides with the locationwhere the number of ridgesstarts to increase. This ismainly due to the fact that during earthquake,the slopemass becomes fragmentized near and above the slide surface,and transferred motion wave may generate complicated refractionand reflection, which alter the components of wave and induce chang-es to the ridge number. In addition, the distance between the inner-most and outermost ridges in the FFT spectrum (termed as DIOR) isalso shifting with increasing elevation. For the HRA slope, the DIORincreases monotonously with increasing elevation, while for the SRAslope, the DIOR first increases and then decreases with increasingelevation. Altogether, it can be inferred that the location of slide planenear the slope surface can be estimated by the change of the ridgenumber in the FFT spectrum, while the number of slide planes areassociated with the DIOR. If the DIOR experiences first an increaseand then a decrease, it is likely that several compound slide planesexist in the slope.
It can be also seen that the frequency at the largest ridge inthe FFT spectrum decreases with increasing elevation, while theFFT amplitude increases (see Fig. 9). We extracted the frequencyand the amplitude of the largest ridge in each FFT spectrumfrom Figs. 9 to 10. The frequency at the maximum amplitude inthe FFT spectrum decreases slightly with elevation increasingfrom A1 to A5 in the HRA slope, while it decreases sharply inthe SRA rock slope. In previous investigations, some researchershave suggested frequency shifting at the maximum amplitude asan internal damage indicator in slopes (Gischig et al. 2015a, b).According to our experiment results, not all kinds of slopedamage are sensitive to the frequency shifting at the maximumamplitude. It is only the damage of the highly flexible slope thatis closely associated with the frequency shifting at the maximumamplitude. Hence, the frequency shifting at the maximum am-plitude cannot be a universal indicator for identifying slopeinternal damage. In Fig. 10b, the difference in the FFT amplitudefor the two slope models are relatively small for positions belowA2, but increases sharply above A2. This observation suggeststhat there exists a certain elevation, where the response dispar-ity of different kinds of slopes becomes obvious under the sameseismic wave excitation. For our experiment, this location issuggested to be 1/4 of the slope height under the PGA of0.6 g. While for the experimental conditions of Liu and Xu(2011), it was suggested to be 1/2 of the slope height under thePGA of 0.6 g for homogenous hard rock slope and homoge-nous soft rock slope.
Figure 11 compares the variation of acceleration time-historyand the FFT spectrum from the superficial to the internal position
Load D
Load C
Load B
Load A
0 2 4 6 8 10 12 14 16 180.0
0.2
0.4
0.6
0.8
1.0
White Noise waveWenchuan waveSine wave
(ytisnetni
noitaticxE
g)
Loading sequence (-)
Fig. 6 Loading sequence during model test
0 10 20 30 40 50-8
-6
-4
-2
0
2
)-(noitcnuf
refsnartfotrap
yranigamI
Frequency (Hz)
A1A2A3A4A5
Fig. 7 Transfer functions of horizontal component excitations for diversemonitoring points, A1, A2, A3, A4, and A5 in SRA slope model under the firstwhite noise
Landslides 16 & (2019) 111
at half slope height. It can be seen that the number of ridgeschanges with increasing distance from the surface, for both kindsof anti-dip rock slopes. The location where the number of ridgeschanges a lot is located between A9 and A10 for the HRA slope andbetween A7 and A10 for the SRA slope, which corresponds to thefailure plane in Fig. 12a, b. According to Fig. 12, the size of thefragmentized zone in the SRA slope is approximately 1.5 timeslarger than that in the HRA slope, and the fragmentation degree ofthe SRA slope is also much more apparent than that of the HRAslope. Comparing with the HRA slope, notable settlement is ob-served on the top and local exfoliation in the lower front of theSRA slope surface.
Sensitivity analysis on effects of discontinuities
Numerical model configurationBased on the analysis in the previous section, an appropriatenumerical simulation should take into account two major issuesin investigating dynamic response of anti-dip rock slopes: toreveal the energy transition of seismic wave in refraction orreflection when passing through joints and beddings and tocapture the expansion of the original cracks as well as theformation of new cracks. The traditional finite element methodcannot capture the crack expansion in rocks due to its assump-tion of continuum and small deformation. While the classicaldiscrete element method provides some means to tackle thecrack issue, it only has advantages in dealing with crack devel-opment among rock blocks and layers. If we want to capturerandom fragmentation in rocks under seismic loading, theabove two methods fall short of a satisfactory solution. To solvethe problem, a revised damage model is introduced to thecommercial discrete element method code UDEC. In our newapproach, joints among rock blocks and layers were modeled bythe classical discrete element method, while a voronoi tessella-tion generator was employed to create randomly sized flawpolygons inside an intact rock block. This set-up of tessellationinside rocks is topologically consistent with natural defects ingeo-materials, which affect the failure pattern of an intact rock
mass (Griffith 1921). The tessellation can be obtained accordingto geometry features of natural defects in the material throughscanning electron microscope or CT images. Nevertheless, elec-tronic images are usually expensive and their quality relies onthe resolution and scale. To avoid the problem, Alzo’ubi et al.(2010) suggested a calibration method by assuming a basicvoronoi tessellation size distribution, i.e., a uniform distributionor a normal distribution, in a rock specimen. It should be notedthat if the stress exceeds the shear or tensile strength near someflaw, a new crack will initiate along a voronoi characteristic edgeinside the rock. The stress near the crack will then shift to theadjacent regions. If cracks are connected with each other, thewidth of them will expand continuously, leading to looser rockblocks and hence a less stable slope. For the convenience ofcomparison, the numerical model used the identical geometricsize and joint-spreading conditions with the experimental mod-el. In this way, crack behavior among layers and inside rockscan be modeled during earthquake. Afterwards, the normal andshear stiffness of a joint can be calculated by Eq. (4):
kn ¼ ks ¼ 10� maxK þ 4
3G
ΔZmin
0B@
1CA
264
375 ð4Þ
where ΔZmin stands for the minimum size of the adjacent meshesin the normal direction, Kand G are the bulk modulus and shearmodulus, respectively, which can be obtained by Eq. (5):
K ¼ E3 1−2μð Þ ;G ¼ E
2 1þ μð Þ ð5Þ
In the equation above, E and μ are the static elastic modulusand Poisson’s ratio, respectively. The stiffness and strengthparameters are assigned to the rock mass and joints to resistexternal loads. Lan et al. (2010) also recommended that the stiff-ness of the internal flaws should be two or three orders of
0 1 2 3 4 5 6 7 8
14
16
18
20
22
24
26
ycneuqerfecnanoser
egarevA
f )z
H(
White noise excitations
HRA slopeSRA slope
Fig. 8 Average resonance frequency under every white noise excitations
Original Paper
Landslides 16 & (2019)112
magnitude larger than the macroscopic overall stiffness. If theplastic deformation zone is spread through the whole domain, a
failure status is considered to be attained. The applicability oftessellation size can be testified based on the accordance of the
a0 20 40 60 80 100 120
-2-1012
-2-1012
-2-1012
-2-1012
-2-1012
-2-1012
(noitarelecc
Ag)
Time (s)
Input
A1
A2
A3
A4
A5
b
DIOR
0 2 4 6 8 10 12 14 16 18 20
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
(edutilp
mA
TFFg)
Frequency (Hz)
Input
A1
A2
A3
A4
A5
c0 20 40 60 80 100 120
-2-1012
-2-1012
-2-1012
-2-1012
-2-1012
-2-1012
(noitarelecc
Ag)
Time (s)
Input
A1
A2
A3
A4
A5
d
DIOR
0 2 4 6 8 10 12 14 16 18 20
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
(edutilp
mA
TFFg)
Frequency (Hz)
Input
A1
A2
A3
A4
A5
Fig. 9 Seismic response at diverse locations along slope surface. a and b represent the acceleration and the corresponding FFT spectrum of HRA slope, respectively. c andd represent the acceleration and corresponding FFT spectrum of SRA slope, respectively. The green line indicates location variation of the largest ridge in the FFT spectrum.The yellow zone is the separated ridge. DIOR denotes the distance between the innermost and outermost ridges in the FFT spectrum
Landslides 16 & (2019) 113
ultimate load when failure status is attained. Noting that theremay exist several different combinations of size parameters satis-fying the failure requirement, and we have tried these combina-tions of parameters in the seismic anti-dip rock slope failurecalculation. One optimal combination of parameters was finallychosen based on the calibration against the model test results andused in other numerical simulations. By trial and error, the lengthof the voronoi flaws was chosen between 10 and 13 mm, with auniform distribution in the present numerical model. The shearstrength and deformation parameters of slope mass are given inTable 3. The normal and shear stiffness of the internal flaws is setto 22.5 GPa, which is about 100 times larger than the macroscopicelastic modulus used in the model test.
Considering computational time limits and the maximum sizeof elements, which should be less than (1/10–1/8) of the wavelength in the UDEC dynamic module, the characteristic size oftriangular elements is set to 10 mm and the model consists of 8254discrete elements. The discrete elements containing voronoi tes-sellation is shown in Fig. 13. The model uses a viscous boundaryand a local damping ratio of 0.16, which can avoid the necessity ofestimating the intrinsic frequency of the numerical model. Note
that the acceleration excitation cannot be applied on the lowerboundary directly in UDEC. Instead, it should be integrated to avelocity time-history first (see Fig. 14) and then converted to adynamic stress record by the following equations:
σn ¼ 2 ρCp� �
Vn ð6Þ
σs ¼ 2 ρCsð ÞV s ð7Þ
where σn and σs stand for the normal and shear stress applied onthe lower boundary, respectively; Cp and Cs are the velocity of P-wave and S-wave and can be obtained by Eqs. (8) and (9); Vn andVs represent the normal and shear excitation velocity, respectively;and ρ is the mass density.
The reason that a factor of 2 is used in the front of the Eqs. (6)and (7) is to overcome the adverse effect of artificial viscousboundary (Itasca Consulting Group Inc 2014).
The ultimate failure patterns of the two kinds of anti-diprock slopes are shown in Fig. 15. The numerical sliding plane isbasically in agreement with that of the model test. Some appar-ent fragmentation is observed in the numerical model. Somesettlement at the top surface and some exfoliation along thelower surface are visible in the SRA slope.
To further testify the rationality of the model test results,acceleration responses extracted from the numerical analysis arecompared against the experimental data. Although we have con-ducted comparison for all the monitoring points in Fig. 4, wechoose point A3 here as a representative (see Fig. 16), while thecomparisons for other monitoring points lead to similar conclu-sions. It can be seen that the amplitudes in acceleration time-history between the model test and the numerical simulation arevery close, but the appearance time of ridge amplitudes did notconform exactly. The numerical appearance time is about 3 sahead that of the model test for the HRA slope, or 8 s behind forthe SRA slope. Some other minor differences also exist in theacceleration time-history between the model test and numericalsimulation results. All these differences in acceleration time-history lead to some disparities between the numerical and exper-imental FFT spectra, as shown in Fig. 16b. In the HRA slope, thedistance between the innermost and outermost ridges (DIOR) inthe numerical FFT spectrum is a bit of larger than that of themodel test. In the SRA slope, four ridges exist in the numericalFFT spectrum, whereas only three ridges were observed in themodel test. Despite that, the multiple ridges in the numericaland experimental FFT spectra all appeared above the failure plane(at monitoring point A3). As noted above, there exist some minordisparities between the numerical and experimental results. Onepossible reason for these disparities is that original micro-flawsexisted in rock blocks of the experimental slope models and createadditional reflection waves to the response data. These micro-flaws were not able to be fully considered in the numerical model,due to their scales and quantities. As mentioned above, a modelwith a large quantity of micro-flaws which exactly matches CTimages exceeds the current computational capacity. Despite such
a
A1
A5
Input
A1
A2
A3
A4
A5
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
Frequcency (Hz)
)-(noitaco
L
HRA slopeSRA slope
b
A1
A5
Input
A1
A2
A3
A4
A5
0.014 0.016 0.018 0.020 0.022 0.024
FFT amplitude(g)
)-(noitaco
L
HRA slopeSRA slope
Fig. 10 Spectrum characteristic at different elevation. a and b represent thefrequency and amplification value at the maximum amplification for the time-history response, respectively
Original Paper
Landslides 16 & (2019)114
minor disparities, the numerical simulation in the present studyhas reflectedmost major response characteristics of themodel test
and is meaningful for understanding the test results and particu-larly helpful for future studies.
a0 20 40 60 80 100 120
-2
-1
0
1
2-2
-1
0
1
2-2
-1
0
1
2-2
-1
0
1
2
Time (s)
A3
(noitarelecc
Ag)
A9
A10
A7
b
A3A7
0 2 4 6 8 10 12 14 16 18 20
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
Time (s)
A3(
edutilpm
ATFF
g)
A9
A10
A7
c0 20 40 60 80 100 120
-2
-1
0
1
2-2
-1
0
1
2-2
-1
0
1
2-2
-1
0
1
2
Time (s)
A3
A9
(noitarelecc
Ag)
A10
A7
d
A3A7
0 2 4 6 8 10 12 14 16 18 20
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
Frequency (Hz)
A3
(edutilp
mA
TFFg)
A9
A10
A7
Fig. 11 Seismic response along half slope height. a and b represent the acceleration and corresponding FFT spectrum of HRA slope, respectively. c and d represent theacceleration and corresponding FFT spectrum of SRA slope, respectively. The yellow zone is the separated ridge
Landslides 16 & (2019) 115
Effects of bedding inclinationTo investigate the effects of bedding inclination on the failurepattern of the anti-dip rock slopes, a model with a beddinginclination varying from 10° to 70° in interval of 20° has beenconsidered, with other parameters kept unchanged. Only theHRA slope is considered here. The SRA slope was also analyzedand showed similar tendency, but the results are not discussedhere to save space.
Figure 17 illustrates the failure pattern for four slope models.When the failure zone is located in a slope lower portion, aretrogressive failure pattern is observed, with the bedding inclina-tion angle smaller than 30°. When the main failure zone moves
upwards to an upper portion, an advancing type of failure patternis observed, with the bedding inclination angle larger than 30°. Thespecific failure pattern is mainly associated with the intersectionangle between the bedding and the joint. When the beddinginclination angle reaches 30°, the bedding plane is perpendicularto the joint. The intersection angle changes from an acute angle toan obtuse angle across this attitude, resulting in changed con-straint conditions between beddings and joints and subsequentlyleading to changes in the failure pattern. It suggests that theimpact of any single factor should not be overestimated, and thecombined effects of diverse factors are more crucial for controllingthe failure of the jointed anti-dip bedding slopes. The maximum
Crack
Crack
a
Settlement
Exfoliation
b
Fig. 12 Photos of the ultimate failure patterns: a HRA slope, b SRA slope. The red dashed line is the slope failure plane
Table 3 Mechanical parameters of geo-materials adopted in UDEC
Item Unitweightγ
(kN/m3)
Dynamicelasticmodulus Ed
(MPa)
DynamicPoisson’sratio μd
(−)
ElasticmodulusE (MPa)
Poisson’sratioμ
(−)
Frictionangle φ
(°)
Cohension c(kPa)
Tensilestrength
(kPa)
Hardrockblock
27.1 215.4 0.25 170.8 0.21 43 188 38
Soft rockblock
26.3 132.9 0.29 121.3 0.21 38 36 21
Joint andbed-ding
– – 0.32 21.8 0.45 32 22 19
Original Paper
Landslides 16 & (2019)116
displacement occurs in the slope with bedding inclination of 10°,which suggests that the HRA slope with a smaller bedding incli-nation may fail at the earlier time under same seismic excitations,despite the failure pattern is controlled by the intersection anglebetween beddings and joints.
Figures 18 and 19 respectively depict the PGA amplificationcoefficient and DIOR at the point A5 (see Fig. 4) with increasingbedding inclination angle. It can be seen that when the inputseismic wave PGA is relatively small (0.2 g herein), the differencein the PGA amplification coefficients between slopes with differentbedding inclination angles is not very apparent. With the inputseismic wave PGA increased to 0.6 g, a sharp increase in the PGAamplification coefficient is observed when the bedding inclinationangle reaches between 30° and 50°, according to Fig. 18. A similarpattern exists in the variation of DIOR with bedding angle, asshown in Fig. 19. When the input seismic wave PGA reaches
0.2 g, the DIOR for slopes with bedding angle of 70° and 10° are7.5 and 5.2 Hz, respectively, giving a ratio of 1.44 (or 7.5/5.2). Whenthe input seismic wave PGA reaches 0.6 g, the DIOR for slopes withbedding angle of 70° and 10° are 18.2 and 11.1 Hz, respectively,resulting in a ratio of 1.63 (or 18.2/11.1). The latter ratio was largerthan the former with increasing bedding angle, which reflects thatthe internal damage in the slope has altered greatly.
Effects of joint inclinationThe failure zone under different joint inclination angles is pre-sented in Fig. 20. Advancing type of failure pattern dominates andremains unchanged as the joint inclination increases. Combiningwith Fig. 17, we can conclude that the seismic failure pattern of thiskind of slope relies primarily on the bedding inclination and is lessaffected by the joint inclination. The failure zone becomes moreconcentrated as the joint inclination angle increases. It suggeststhat an anti-dip rock slope with a smaller joint inclination angle ismore prone to toppling failure under seismic loads.
Furthermore, it can be seen that the PGA amplification coeffi-cient and the DIOR are both decreasing accompanying the increas-ing joint inclination angle. The PGA amplification coefficient isless sensitive to the joint inclination angles (see Fig. 21) than to thebedding inclination angles (see Fig. 18). The DIOR shows a slightdecrease with increasing joint inclination angle (see Figs. 19 and22). The above results suggest that not only the failure pattern, butthe seismic responses are also more sensitive to the beddinginclination than to the joint inclination. It is reasonable to statethat the order of importance in assessing seismic instability ofanti-dip rock slopes is as follows: the combination of beddingsand joints, the bedding inclination, and then the joint inclination.
Effect of joint spacingThe failure zones of the HRA slope with different joint spacings(from 0.4 to 1.9 m in interval of 0.5 m) are depicted in Fig. 23. Itcan be seen that the size of the failure zone decreases with increas-ing joint spacing. When the joint spacing is 0.4 m, the failure planeapproximately expands from the top to the toe of the slope.However, the failure zone is located in the upper superficial areawhen the joint spacing is up to 1.9 m. This may attribute to threecauses. First, when the joint spacing was relatively small, a rockslope has a higher flexibility (or lower average stiffness), resultingin smaller self-stability. Second, a slope is more prone to slidesubjected to earthquakes when the main frequency is closer to theslope resonance frequency. A slope with a higher flexibility has asmaller resonance frequency, as shown in Fig. 24, which is closer tothe main frequency (2.4 Hz) of the horizontal excitation wave. Inaddition, some severe reflection and refraction among adjacentopen or half-open joints amplify the excitation wave and inducemore serious damage in the slope mass.
It can also be seen that the PGA amplification coefficient showsa two-phase variation with the joint spacing, as illustrated inFig. 25. A fast decrease in the PGA amplification coefficient ap-pears when the joint spacing is smaller than 0.9 m. The DIOR alsoshows a decreasing trend with increasing joint spacing, but thetendency is relatively mild, as shown in Fig. 26.
DiscussionIn the present study, seismic wave propagation characteristicsand the failure patterns in joint anti-dip rock slopes are
Beddings
Joints
Voronoitessellation
Base
Slope body
Fig. 13 Discrete element meshes containing voronoi tessellation
a
b
0 20 40 60 80 100 120-20
-10
0
10
20
)s/m(
ytiocoleV
)s/m(
ytiocoleV
Time (s)
-20
-10
0
10
20
Fig. 14 Velocity time-histories of the original seismic wave. a horizontal direction,b vertical direction
Landslides 16 & (2019) 117
analyzed by taking account of the effects of bedding inclination,joint inclination, as well as joint spacing, and the significantinfluential factors have been identified. The impact of geomor-phological and geometrical factors is however not discussedherein, which may also become significant in assessing seismicresponses and failure of anti-dip rock slopes. In real world,geomorphology may generate sophisticated effects on the slopeseismic failure, such as local amplifications at some concave-convex terrains, spatial non-uniformity in slide surface,
rhythmicity in stress or displacement field, and spatial sub-zone division in slide body. Meanwhile, if the slope surface ishighly rough, the influence of surface wave cannot by neglectedeither. However, if we considered the geomorphological factorsand the discontinuity factors simultaneously in one model, itwould be difficult to reach any realistic conclusions for engi-neering applications. The effects of various factors on anti-diprock slope stability can also refer to the previous investigationson uniform rock slopes (Monnereau and Yuen 2007; Hovius and
a
Experimental failure plane
Numericalfailure plane
Cracks
X-directionStrain /10-2
9.2
0.0
6.2
3.1
b
Experimental failure plane
Numericalfailure plane
Settlement
Exfoliation
28.6
0.0
19.1
9.5
X-directionStrain /10-2
Fig. 15 Comparison of ultimate failure patterns for two anti-dip rock slopes based on experimental and numerical results. a HRA slope, b SRA slope
a0 20 40 60 80 100 120
-2
-1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
(3
Afo
noitareleccA
g)
Time (s)
HRA+model test
HRA+numerical simulation
SRA+model test
SRA+numerical simulation
b0 2 4 6 8 10 12 14 16 18 20
-0.01
0.00
0.01
0.02-0.01
0.00
0.01
0.02-0.01
0.00
0.01
0.02-0.01
0.00
0.01
0.02
Frequency (Hz)
HRA+model test
)g(edutilp
maTFF
HRA+numerical simulation
SRA+model test
SRA+numerical simulation
Fig. 16 Experimental and numerical comparison of acceleration response as well as FFT spectrum at A3 for two kinds of anti-dip rock slope. The yellow zone indicates the separated ridge
Original Paper
Landslides 16 & (2019)118
Meunier 2012; Gordan et al. 2016). Nonetheless, the results fromour study are of applicable values in hazard assessment ofjointed anti-dip rock slopes, especially for slopes with simpleterrain.
Moreover, the voronoi method was adopted to tessellate thejointed anti-dip rock slope, and the distribution and size of theelements are also vital for the analyses. Generally speaking, themore elements we use, the more accurate results we will achieve.
a
10°
Failure zone0.0
22.2
14.4
7.1
X-directionStrain /10-2
b
30°
0.0
17.1
12.3
5.9 Failure zone
X-directionStrain /10-2
c
50°
10.3
0.0
6.8
3.4
Failure zone
X-directionStrain /10-2
d
70°
8.4
0.0
2.8
5.6
Failure zone
X-directionStrain /10-2
Fig. 17 Failure zones of HRA slopes with different bedding inclination angles. The inclination angle of joints was set as 60°, and inclination of the bedding was labeled inthe above sub-figures separately
10 30 50 701.0
1.2
1.4
1.6
1.8
2.0
2.2
)-(tneiciffeocnoitacifilp
maA
GP
Bedding inclination angle (°)
0.2 g 0.6 g
Fig. 18 PGA amplification coefficient at A5 under different bedding inclination angles
10 30 50 704
6
8
10
12
14
16
18
)zH(
ROI
D
Bedding inclination angle (°)
0.2 g 0.6 g
Fig. 19 DIOR at A5 under different bedding inclination angles
Landslides 16 & (2019) 119
However, too many elements will increase the calculation burdenand may exceed the capacity limit of the software. Therefore, atrial and error approach which balances the accuracy and time-consumption is a necessity. In our attempt, the ratio between the
average flaw size and the largest model edge is recommended to be5–10‰, which can attain a better balance of accuracy and compu-tational efficiency. In addition, although a normal distribution orWeibull distribution of flaw size is more common in real world,
a
Failure zone
Horizontal line
16.4
0.0
11.1
5.5
X-directionStrain /10-2
b
Failure zone
Horizontal line
12.5
0.0
8.3
4.2
X-directionStrain /10-2
c
Failure zone
Horizontal line
10.3
0.0
6.8
3.4
X-directionStrain /10-2
d
Failure zone
Horizontal line
9.1
0.0
6.1
3.0
X-directionStrain /10-2
Fig. 20 Failure zones of HRA slopes with different joint inclination angle. The inclination angle of beddings was set as 50° dip into the slope surface, and inclination of thejoint was labeled in the above sub-figures separately
20 30 40 50 60 70 801.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
)-(tneiciffeocnoitacilip
maA
GP
Joint inclination angle (° )
0.2 g 0.6 g
Fig. 21 PGA amplification coefficient at A5 under different joint inclination angles
20 30 40 50 60 70 80
6
8
10
12
14
16
18
20
22
24
)zH(
ROI
D
Joint inclination angle (° )
0.2 g 0.6 g
Fig. 22 DIOR at A5 under different joint inclination angles
Original Paper
Landslides 16 & (2019)120
ultimate failure patterns from the above two distribution modeshave little difference with that from a uniform distribution. On theother hand, the uniform distribution performs better in terms ofcomputational efficiency and was adopted in the present study.
Furthermore, in spite of several methods available in the liter-ature for seismic spectrum analysis, such as the Hilbert-Huangtransform, wavelet transform, and Z transform, results from thesetechniques are not easy interpret and have difficulties in
a
Failure zone
Joint spacing 0.4 m
23.4
0.0
15.6
7.8
X-directionStrain /10-2
b
Failure zone
Joint spacing 0.9 m
18.8
0.0
12.5
6.3
X-directionStrain /10-2
c
Failure zone
Joint spacing 1.37 m
10.3
0.0
6.8
3.4
X-directionStrain /10-2
d
Joint spacing 1.9 m
8.2
0.0
5.5
2.7
X-directionStrain /10-2
Fig. 23 Failure zone of HRA slopes with different joint spacing. The inclination angle of beddings were set as 50°dip into the slope surface, and joint spacing was labeledin the above sub-figures separately
0.0 0.5 1.0 1.5 2.0 2.518
20
22
24
26
28
30
)zH(
ycneuqerfecnanose
R
Joint spacing (m)
White noise 1
Fig. 24 Initial resonance frequency of slopes with different joint spacings
0.0 0.5 1.0 1.5 2.0 2.50.0
0.5
1.0
1.5
2.0
2.5
3.0
)-(tneiciffeocnoitacifilp
maA
GP
Joint spacing (m)
0.2 g 0.6 g
Fig. 25 PGA amplification coefficient at A5 under different joint spacings. The blueregion depicts the fast deceasing section
Landslides 16 & (2019) 121
identifying simple and practical indicators for anti-dip rock slopeseismic response. As a consequence, the FFT transform was cho-sen to analyze the spectrum features. Nevertheless, seeking furtherappropriate means to interpret and explore more useful informa-tion from spectrum for slope seismic hazard assessment is alsoattractive. Incorporating multiple methods in a seismic analysiscan be a promising approach for future investigation.
ConclusionsIn this study, shaking table test and DEM were integrated to inves-tigate the seismic wave propagation characteristics and its effects onthe failure of steep joint anti-dip rock slopes. The following conclu-sions can be drawn:
(1) The crest PGA of the jointed soft rock anti-dip slope is about1.12 times larger than that of the jointed hard rock anti-dipslope under identical seismic excitations. The area of failurezone in the soft rock slope is approximately 1.5 times the sizeof that in the hard rock slope.
(2) The location of slide plane is closely related to the change of theridge number in the FFT spectrum, while the number of slideplanes is associated with the distance between the innermostand outermost ridges (DIOR). If the DIOR experiences first anincrease and then a decrease, there is a good likelihood for theoccurrence of compound slide planes in the slope.
(3) When the joint inclination angle is given, the bedding incli-nation governs the anti-dip slope failure pattern under thesame seismic wave load.
(4) The seismic failure of a jointed anti-dip rock slope is primarilycontrolled by the combination of the bedding and joint, andthen by the bedding inclination, and less so by the joint incli-nation. The joint spacing can also affect the failure scope.>
AcknowledgementsThe authors appreciate the editors and reviewers for their com-ments on our manuscript.
Funding informationThe present study was financially supported by the National NaturalScience Foundation of China (Grant Nos. 41502299, 41372306) as well asResearch Planning of Sichuan Education Department, China (Grant No.16ZB0105), State Key Laboratory of Geohazard Prevention andGeoenvironment Protection Independent Research Project (Grant No.SKLGP2016Z007), ChengduUniversity of TechnologyYoung andMiddle-Aged Backbone Program (Grant No. KYGG201720), Sichuan provincialscience and technology department program (Grant No. 19YYJC2087),and China Scholarship Council Project (Grant No. 201708515101).
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L.<q. Li : N.<p. Ju ()) : S. Zhang : X.<x. DengState Key Laboratory of Geohazard Prevention and Geoenvironment Protection,Chengdu University of Technology,Chengdu, 610059, ChinaEmail: [email protected]
