response of high-strength rock slope to seismic waves in a...

Response of High-Strength Rock Slope to Seismic Waves

in a Shaking Table Test

by Hanxiang Liu, Qiang Xu, Yanrong Li, and Xuanmei Fan*

Abstract Studies on landslides by the 2008 Wenchuan earthquake showed that thetopography is of great importance in amplifying the seismic shaking. The present studycarried out experiments on rock slopes by means of a shaking table. The recordedWenchuan earthquakewaves are scaled to excite the model slopes.Measurements fromaccelerometers installed on free surface of the model slope simulating high-strengthrocks are analyzed, with much effort on acceleration responses to both horizontaland vertical components of seismic shaking. It is found that the amplification factorof peak horizontal acceleration (PHA) is increasing with elevation of the model slope,though the upper and lower halves of the slope exhibit different increasing patterns. Theamplification factor of peak vertical acceleration (PVA) exhibits a lying S-shapedchanging trend with the elevation, indicating attenuations of PVAs at the toe andtop of a slope. In addition, the XZ-direction shaking produces a horizontal and verticalresponse stronger than X-direction and Z-direction shaking alone. Both PHA and PVAincreasewith the excitation intensity. However, the corresponding amplification factorsgenerally decrease, indicating the acceleration response of a slope weakens with theexcitation intensity of shaking. Finally the statistic of ratio of PVA to PHA indicatesthat 85% of the slope height, especially the upper middle part, is likely subject to PVAsgreater than or equal to 2=3 of PHA and 32% of the slope height to PVAs greater than orequal to PHA. This indicates the nonignorable role of PVA in responses of a slope to anearthquake and necessity of considering during design work.

Introduction

The 2008Ms 8.0 Wenchuan earthquake triggered a greatnumber of landslides in Sichuan Province, SouthwesternChina. The earthquake-induced landslide failures demon-strate obvious topographic and geological effects, as theyaccumulate at the slope crests, the transition section of slopegradients and thin mountain ridges (Huang and Li, 2008). Inaddition, landslide types (e.g., rock fall and toppling) havebeen found to greatly depend upon the lithology and geologi-cal structures (Gorum et al., 2011). Based on interpretationof remote sensing images, Qi et al. (2010) revealed the land-slide occurrence varied with elevation, lithology, and slopestructure, and the spatial distribution of landslides even hadstrong positive correlation with slope gradients. Similarstatistic results can also be found in other researches (Yinet al., 2009; Dai et al., 2010). Based on the ground-motionrecordings from several monitoring stations, peak ground ac-celeration (PGA) in vertical component seems to be greaterthan that in horizontal component (Li et al., 2008).

Since 1970s, various analysis methods (e.g., numericalmodeling and experimental testing) have been widely usedfor achieving topography response, quantitative and/orqualitative, to seismic waves. According to study on the SanFernando earthquake (9 February 1971), Boore (1972) foundhigh elevation in hilly terrains may cause the PGA to be in-creased by 100%, and a ratio (about 3) of SH wavelength tothe width of a hill may cause great response of the hill bodyto the earthquake. Bouchon (1973) observed amplification(100% amplification in horizontal displacement) of incidentSH, P, and SV waves at the crest of a mountain ridge andattenuation (30% reduction in horizontal displacement) nearthe bottom of a depression using a single frequency methoddeveloped by Aki and Larner (1970). Similar results wereobtained by Rogers et al. (1974) based on two-dimensionalscale models for incident P waves. A systematic review ontopography effects was made by Geli et al. (1988), who com-pared theoretical and experimental results and found quali-tative agreement about the amplification at mountaintops.However, the time-domain crest/base amplification ratiosremained below 2 in theoretical results, while the corre-sponding values reached around 8 in experimental results.

*Also at International Institute for Geo-information Science and EarthObservation, University of Twente, Enschede, P.O. Box 217, 7500 AE En-schede, The Netherlands

1

Bulletin of the Seismological Society of America, Vol. 103, No. 6, pp. –, December 2013, doi: 10.1785/0120130055

Moreover, the theoretical crest/base spectral amplificationranges between 2 and 7 for other complex models, whilethe experimental spectral amplification can reach 30. Theresearches afterward showed that diverse parameters (lithol-ogy, slope gradient, earthquake intensity etc.) and configu-ration of topographic units were responsible for acomplex seismic motion (Bouchon et al., 1996; Razmkhahet al., 2008).

Responses of rock slope to earthquake are alwaysaffected simultaneously by topography, lithology, and struc-tures of the slope itself. Harp and Jibson (2002) found, it wasthe anomalously strong shaking in Pacoima Canyon resultingfrom topographic amplification that explained the spatial dis-tribution of rock falls. Bozzano et al. (2011) pointed out,joint conditions of the involved rock mass were responsiblefor the seismic amplification of the landslide-prone volumebased on a finite difference stress–strain numerical modelingof the Scilla landslide. Numerical models by Sepúlveda et al.(2005), Sepúlveda, Murphy, and Petley (2005), and Martinoet al. (2006) also clearly indicated the dynamic response ofrock slope to seismic waves.

Shaking table tests have been widely adopted in studieson slope responses to seismic waves (Yang et al., 2002; Linget al., 2005; Lin and Wang, 2006; Wang and Lin, 2011). Shi-mizu et al. (1986) conducted three kinds of two-dimensionalmodel tests to investigate the dynamic failure modes of rockslopes. The maximum amplification of about 300% was ob-served in accelerometers embedded at the top of a shakingtable model of 600 mm long and 400 mm high. Kumsar et al.,(2000) used shaking table tests to validate application of limitequilibrium methods on wedge failure of jointed rock slopestaking into account dynamic effects. Nowadays, studies inthis particular field are carried out by using advanced shakingtables, which allow large models and diverse waves to beinvestigated (Liang et al., 2005; Dong et al., 2011; Ye et al.,2012).

In the present study, a shaking table with six degrees offreedom (three translational motions and three rotational mo-tions) is used to excite two model slopes with horizontal rocklayers. Each model slope is instrumented by nine accelerom-eters at different elevations on the free surface. The modelslopes are subjected to a broad range of shaking levels, inhorizontal and vertical directions, scaled from the 2008 Wen-chuan earthquake waves. Characteristics of slope responsesto seismic waves, especially the topographic effects, are dis-cussed in detail based on recordings from the installed accel-erometers. The present paper focuses on the model slopewith materials of high strength, the observations from theother model slope will be reported later in another paper.

Test Program and Procedure

Prototype Landslides

Two large-scale landslides triggered by the 2008Wenchuan earthquake in the Beichuan County are taken as

prototypes, the New Beichuan Middle School (NBMS) land-slide and the Wangjiayan landslide. The NBMS landslideburied a number of buildings, including the NBMS, andcaused 700 deaths. The Wangjiayan landslide, with a volumeof 1.4 million m3, buried most of the old Beichuan area andcaused 1700 deaths. The post-earthquake research confirmsthat the occurrence of these two landslides is closely relatedto the strong ground motion, steep topography, and fracturedlithology in Beichuan area (Xu et al., 2009).

As shown in Figure 1a, the Beichuan County is north-east of the epicenter, Yingxiu Town, with a distance of about125 km. Figure 1b shows the Yingxiu–Beichuan fault (themain causative fault) passing through the Beichuan County.The NBSM landslide is on the footing wall while the Wang-jiayan landslide is on the hanging wall. The perpendiculardistance from the central point of the two landslides tothe fault is only 300 and 400 m, respectively.

Figure 2 gives the typical cross section of the landslides.Before the earthquake, both landslides had a convex shape.The latitude is 950–980 m above sea level at the rear edgeand 650–660 m at the slope toe, making a great relief ofabout 300 m and a slope angle of about 60°. The bedrockdeveloped in the NBMS landslide is mainly composed of hardlimestone with a dip angle of 17°. The bedrock in the Wang-jiayan landslide is composed of soft siltstone and slate with adip angle of 35°.

Model Materials

Based on the topography of the NBMS and Wangjiayanlandslides, two model slopes are prepared in the model con-tainer forming a U-shaped valley, and the slope angle of eachmodel is specified as 60° (Figs. 3 and 4). The left model slopein Figure 3 is composed of material of high strength. This isused to simulate rock slopes with layered hard rocks, lime-stone. The right model slope is composed of material of lowstrength and is used to simulate rock slopes with layered softrocks, slate. For simplification purpose, the two model slopesare structured only by horizontal layers with even thicknessin the present study.

Buckingham’s π theorem is based on dimensional analy-sis and gives the transformation from a function of dimen-sional parameters, f�q1; q2; q3…qn� � 0, to a related fun-ction of dimensionless parameters, F�π1; π2; π3…π4� � 0

(Louis, 1957; Curtis et al., 1982). In the present study, di-mensional parameters (length L, density ρ, and elasticitymodulus E) are choosen as the fundamental quantities withscaling factors of CL � 100, Cρ � 1, and CE � 100, respec-tively. The dimensions of key parameters used in this studyare listed in Table 1. And the π terms for the F function andthe corresponding scale factors of all key parameters arelisted in Table 2.

Barite powder, quartz sands, gypsum, glycerol, andwater are mixed in weight proportions of 32:53:5:1:9 toproduce the high-strength material of model slopes whichsimulates hard rock, while a mixture of the same components

2 H. Liu, Q. Xu, Y. Li, and X. Fan

in proportions of 33.5:55.5:2.5:2:6.5 are to make the low-strength materials, which simulates the soft rock. Note thatthe above proportions are determined through trial and error.The barite powder (maximum particle size of 0.074 mm) andquartz sands (0.074–0.85 mm) work as fines and coarseaggregates in the mixture, and the gypsum and water worktogether as cement. Glycerol was used to slow down thecurling of the mixture, in order to achieve the desiredstrength. Direct shear tests in accordance with Chinese Stan-

dard for Soil Test Method (GB/T 50123-1999) were con-ducted to obtain the cohesions and internal friction angles ofthe mixture, and uniaxial compression strength tests in accor-dance with Standard for Soil Test Method (GB/T 50123-1999) were conducted to obtain the elasticity modulus.The mechanical properties of the interfaces between layerswere obtained through direct shear tests (GB/T 50123-1999).The properties of materials for model slopes are listed inTable 3.

Figure 1. The study area: (a) surface rupture map of the 2008 Wenchuan earthquake and (b) location of the prototype landslides for theshaking table test. The color version of this figure is available only in the electronic edition.

Response of High-Strength Rock Slope to Seismic Waves in a Shaking Table Test 3

Model Preparation

The model slopes are prepared in a rigid steel modelcontainer with a length of 3.1 m, width of 2.78 m, and heightof 2.45 m. To minimize the influences of boundary of the

model container on the input seismic waves, an absorbermade of polystyrene wrapped with polyethylene film isplaced on the four sides of the container. A 20 cm thick foun-dation, with the same material to the model slope is laid at thebottom of the model container. The model slope is preparedby wet pouring and compacting, layer by layer, a certainvolume of mixed material into a 15 cm thick layer. Sucha method ensures the desired unit weights as listed in Table 3.Black fine sands of 3 mm thick were spread on the contactsurface between layers. During build-up of the model slopes,a modeler is used to keep the slope angle at the designated60°. The final products are two model slopes standing face toface in a model container, forming a U-shaped valley asshown in Figure 3.

Test Setup

The shaking table used in this study has a capacity of35t, and the maximum working frequency is 48 Hz. The sizeof the table is 6.0 m by 3.0 m. The ranges of displacement,velocity, and acceleration are −150 to �150 mm, −800 to�800 mm=s, and −1 to �1g in two orthogonally horizontaldirections, and are −100 to�100 mm, −600 to�600 mm=s,and −1 to �1g in the vertical direction, respectively.

As shown in Figure 3, a total of 9 three-component ac-celerometers with a measuring capacity of up to 6:0g are in-stalled at different elevations on the surface of each modelslope. In order to minimize the boundary effects, sensorsare placed along the middle line from toe to top of the model.An accelerometer (A1 in Fig. 3) is fixed on the bottom plateof the shaking table to check the excitation waves. The finalinstrumented physical model is shown in Figure 4.

Input Motions

The horizontal and vertical components of the acceler-ations recorded at the Wolong seismic station during the2008 Wenchuan earthquake are scaled for the model loadinginputs, and the seismograms are obtained from the China

Figure 2. Typical cross section of the prototype landslides:(a) New Beichuan Middle School (NBMS) landslide and (b) Wang-jiayan landslide.

Figure 3. Setup of the shaking table model.

Figure 4. Orthogonal view of the model slope. The colorversion of this figure is available only in the electronic edition.


Earthquake Networks Center (see Data and Resources). TheWolong station is located in Wolong town of WenchuanCounty. The altitude on the station ground is 919 m abovesea level and altitude on the top of the mountain nearby is3187 m. The overlying soils at the station are mainly com-posed of Quaternary alluvial and diluvial gravels andpebbles. As shown in Figure 1a, the monitoring station wasabout 23 km southwest of the epicenter. The distance fromthe station to the Beichuan County is about 145 km. Itrecorded the maximum PGAs, of which the horizontal andvertical components were 957.7 gal and 948.1 gal, respec-tively (Wen et al., 2010). Both components had the dominantfrequencies of 2.4 Hz and 8.1 Hz, respectively. Taking themeasured horizontal component as reference, horizontal(X direction) waves of 23.4 Hz (about 10 times that of thedominant frequency of the Wenchuan horizontal compo-nent), with different amplitudes (from 0.1 to 0:95g at an in-terval of 0:05g) are employed in the test, according to thesimilitude relations in the Model Materials section. The ver-tical waves, inputted in the test, have the dominant frequencyof about 38.7 Hz (about 5 times that of the Wenchuan verticalcomponent). This is due to the capacity of the shaking table,

which does not allow a frequency greater than 48 Hz. Themodel slope is excited, respectively, by the above horizontal(X direction), vertical (Z direction) waves, and their combi-nations (XZ direction). The input waves of horizontal andvertical components collected on the table A1 are shownin Figure 5, together with their Fourier amplitude spectrums.

Test Procedure

The test started with exciting the model slope by a whitenoise with a flat Fourier spectrum in all frequencies(<50 Hz) so as to obtain the initial dynamic characteristicsof the model slope. Based on the responding signals in themodel under white noise excitation, transfer function of themodel is obtained using MATLAB’s function tfestimate inSignal Processing Toolbox (see Data and Resources).Figure 6 gives the transfer functions, under horizontal andvertical excitations, calculated for different monitoringpoints in the model. The dominant frequency identified fromFigure 6 is regarded as the resonance frequency of the modelslope. The resonance frequencies for horizontal and verticalshakings are 16.2 Hz and 27.3 Hz, respectively. Thus, no

Table 1Dimensions of the Key Parameters Considered in Dynamic Similitude

Parameters Dimensions Parameters Dimensions Parameters Dimensions

Length �L� � �L� Friction angle �φ� � �1� Acceleration �a� � �L��T�−2Density �ρ� � �M��L�−3 Stress �σ� � �M��L�−1�T�−2 Velocity �v� � �L��T�−1Elasticity modulus �E� � �M��L�−1�T�−2 Strain �ε� � �1� Displacement �u� � �L�Poisson ratio �μ� � �1� Time �T� � �T�Cohesion �c� � �M��L�−1�T�−2 Frequency �f� � �T�−1

Table 2The π Terms and Scale Factors of Key Parameters

Dimensionless π Terms Scale Factor Dimensionless π Terms Scale Factor

Fundamental quantity CL � 100 1 Cε � 1

Fundamental quantity Cρ � 1 πt � t=Lρ0:5E−0:5 Ct � CLC0:5ρ C−0:5

E � 10

Fundamental quantity CE � 100 πf � f=Lρ−0:5E0:5 Cf � C−1t � 0:1

1 Cμ � 1 πa � a=L−1ρ−1E Ca � C−1L C−1

ρ CE � 1

πc � c=E Cc � 100 πv � v=ρ−0:5E0:5 Cv � C−0:5ρ C0:5

E � 10

1 Cφ � 1 πu � u=L Cu � CL � 100

πσ � σ=E Cσ � 100

Table 3Physical and Mechanical Parameters of the Prototype Slopes and the Model Slopes

Lithology ModelDensity ρ(103kg=m3)

Cohesion c(MPa)

FrictionalAngle φ (°)

ElasticModulus E (MPa)

Poisson’sRatio μ

Hard rock Prototype model 2.65 18 42 55:8 × 103 0.262.56 0.12 40 56.3 0.23

Soft rock Prototype model 2.53 4 25 2:0 × 103 0.342.45 0.05 23.8 15.2 0.31

Interface 0.018 19.2


Administrator

Highlight

resonance would occur as the dominant frequencies of inputwaves (23.4 Hz in horizontal and 38.7 Hz in vertical) duringthe present tests are totally different from the natural frequen-cies of the model slope.

Each step lasted for about 10.8 s which is scaled at a1:10 rate according as the mainshock duration of the Wen-chuan earthquake at the Wolong seismic station. Betweentwo steps, there is a break to examine if the models have anydeformation or failure. In order to obtain as clearly as pos-sible the seismic response to increasing shaking intensity,waves with intensity from 0.1 to 0:95g are applied on themodel slopes in a loading sequence listed in Table. 4.

Results and Discussion

In the left model of Figure 3, a column of three-component accelerometers, A2, A3, A4, A5, A6, A7, andA8, are arranged along the middle line from the toe to thetop of the slope surface. Baseline correction and Butterworthlow-pass filtering were conducted on the raw dataset tocorrect it in the MATLAB 8.0, before any further analysis.Two dimensionless ratios are used in the following discus-sion to study the seismic responses of the model slope, intime domain and frequency domain: the amplification factorand the Fourier spectral ratio.

Amplification Factor

The amplification factor (R) is defined here by the ratioof the PGA measured in any monitoring point to that mea-sured on the bottom plate of the table. Such a definitionmakes a R > 1:0 indicate real amplification, R � 1:0 non-amplification, and R < 1:0 attenuation. The considered mo-tion directions in each monitoring point are horizontal (X),vertical (Z), and their resultant (XZ) direction, as shown inFigure 3. It is found that even being excited in single direc-tion, the model slope would respond slightly in the other two

orthotropic directions. Only responses in the original excita-tion directions are analyzed to prevent the ratio (R) frombeing calculated from two accelerations in the same direc-tion. PGA is obtained by taking the maximum absolute valueof the measured acceleration in time domain for each mon-itoring point. The relative elevation (h=H) is defined as theratio of height (h, measured from the toe of the model slope)of any monitoring point to the total height (H) of the slope.

Fourier Spectral Ratio

Fourier spectral ratios of accelerations are always used toobtain the nonlinearity characteristics of soils based on in situground-motion recordings (Beresnev et al., 1995; Lee et al.,2006). According to these researches, Fourier spectral ratiocan be utilized to estimate the site resonance frequency, espe-cially the fundamental one. Referencing Borcherdt (1970),who took recordings of nearby bedrock as the reference fora soil site, and Lee et al. (2006), who took recordings ofdownhole bottom as reference, the bottom plate of the tableis used in the present study as the reference site to determinethe standard spectral ratio (SSR). The SSR is, therefore, calcu-lated as the record in the model slope divided by that on thetable bottom plate. Procedures for this are as follows: (1) pre-pare the Fourier spectrum of corrected accelerogram;(2) smooth the spectrum using the moving average in theMATLAB 8.0 program; and (3) calculate the SSR.

Figure 7 shows the smoothed spectra of A7 (in the slope)and A1 (on the bottom plate) and their spectral ratios for theX-direction and Z-direction shakings under an excitation in-tensity of 0:1g at the early stage of the test. It can be seen thatthe first maximum ratio occurs in frequency of 16.6 Hz forthe horizontal component and in 27.0 Hz for the verticalcomponent. These dominant frequencies coincide with theinitial resonance frequencies calculated based on the whitenoise excitation in Figure 6. Hence, in the data analysis

Figure 5. Excitation accelerations for the horizontal (X direction) and vertical (Z direction) shakings: (a) time history and (b) Fourierspectrum.


of this paper, the spectral ratios obtained with the methodillustrated in Figure 7 are used to estimate the resonancefrequency of the model slope at different stages of the test.

Horizontal Component of Acceleration

Figure 8 gives the amplification factors of peak horizon-tal accelerations (RPHA) at different elevations, A2, A3, A4,A5, A6, A7, and A8, on slope surface of the model subjected

to X- and XZ-direction shakings. In general, along the slopeelevation, the RPHA tendency by the two kinds of shakings israther the same, for the RPHA is increasing with relativeelevation h=H. In addition, XZ-direction shaking seems toproduce horizontal responses a little bit stronger than X-direction shaking, but has no influence on the overall chang-ing tendency of RPHA with elevation. Another observation isRPHA demonstrates different change patterns between theupper and lower halves of the model slope. In the upper half(h=H > 0:6), RPHA exceeds 2.0 and increases fast to itsmaximum at the slope top, indicating an obvious topographicamplification effect. In the lower half (h=H ≤ 0:6), most ofRPHA ranges between 1.0 and 2.0. Despite the overall in-creasing tendency of RPHA in the lower half, its dependencyon relative elevation is not as strong as in the upper part.

The change of horizontal response with excitationintensity of XZ-direction shaking is shown in Figure 9 interms of PHA, RPHA, and fundamental resonance frequency.The PHAs in all monitoring points on the slope surfacegenerally increase as the excitation intensity strengthens.The corresponding amplification factor RPHA decreases withexcitation intensity but remains above 1.0 during the test,though its changing tendency in the lower slope part is differ-ent from that in the upper part. For monitoring points in the

Figure 6. Model slope transfer functions based on the white noise excitation at the first stage of test for (a) X-direction shaking and(b) Z-direction shaking.

Table 4Loading Sequence of the Shaking Table Test

Number Features of Input Waves at the Base of the Model Slope

1 White noise. Intensity is 0:01g.2–3 Z-direction excitation. Intensity is 0.1 and 0:15g,

respectively.4–8 X-direction excitation. Intensity ranges from 0.1

to 0:3g at an interval of 0:05g.9–19 XZ-direction excitation. Intensity ranges from 0.1

to 0:6g at an interval of 0:05g.20–35 Z-direction excitation. Intensity ranges from 0.2

to 0:95g at an interval of 0:05g.36–42 XZ-direction excitation. Intensity ranges from 0.65

to 0:95g at an interval of 0:05g.


lower slope part, A2 and A3 for example, the RPHA fluctuatesbelow the level of 1.5with aminor decrease. In the upper slopepart, RPHA of each monitoring point presents a gradual de-creasewith excitation intensity and finally approaches a stablevalue, about 1.0 for A4, A5, A6, andA7, and about 2.0 for A8.The RPHA for A8 located at the crest of the model slope, forinstance, decreases from 4.6 at the excitation intensity of0:15g to about 1.8 at the excitation intensity of 0:95g. Thisresult indicates an attenuation in horizontal accelerationresponse in the upper slope part with the excitation intensity,regardless of the increasing PHAs. In other words, with theexcitation intensity, the horizontal acceleration response ofthe slope weakens, especially in the upper part. This alsocoincides with the PHAversus h=H curves in Figure 8, whoseupper part (from A5 to A8) slopes more gently with theexcitation intensity increased from 0.1 to 0:3g. The decreaseof RPHA with excitation intensity in the upper slope is mainlyattributed, as will be shown later, to the large decay of its innerstructure. The decay of slope structure causes increase ofdamping and reduction of amplification. In addition, highpeak acceleration tends to result in large strain and modulusreduction, which restrains the high frequency response due tothe wave focusing at the crest of slope.

The fundament resonance frequency (f0) of the modelslope at different excitation intensity is shown as circle pointsin Figure 9, based on the Fourier spectrum ratio technique.Generally speaking, the fundamental frequency of all mon-

itoring points decreases from about 17 to 10.0 Hz with theexcitation intensity. This decreasing trend indicates a gradualdeterioration of the inner structure of the slope, which causesthe attenuation of horizontal acceleration response. In thecase where the excitation intensity is less than 0:3g, the PHAlinearly increases, a little bit faster than the later ones. This isdue to the minor disturbance of slope structure by lowexcitation intensity. During this stage, only micro-cracks de-velop locally in the model. Chen et al. (1998) conducted anumerical modeling on damage evolution of rock slope andconfirmed that local micro-cracks would not influence thesystem’s linear response.

Another observation is that the decreasing trend, as wellas the magnitude of the fundamental frequency, are slightlydifferent between the upper and lower parts of the slope. Asshown in Figure 10, the average fundamental frequency ofthe upper slope part (by averaging A5, A6, A7, and A8) ex-periences a sharp drop at the excitation intensity of about0:65g, while that of the lower slope part (A2, A3, and A4)keeps decreasing, at a seemingly constant rate, with the ex-citation intensity. The sharp drop on the curve of upper partin Figure 10 indicates a sudden decay of the slope structurein this part. This can be evidenced by visible cracks devel-oped in the top layer of the slope when the excitation inten-sity of XZ-direction shaking reaches 0:65g (Fig. 11). Before0:65g, only microscopic disturbance accumulates/developsin the model slope, which finally causes the sudden change

Figure 7. Fourier spectrum of response accelerogram and spectral ratio at early stage of the test for (a) X-direction shaking and(b) Z-direction shaking.


of the slope structure. The process is in good agreement withTang et al. (2009). In their work of numerical simulation, aspalling failure occurred suddenly on the surface of a rockslope, though the disturbance of the incident wave and thereflected wave on the surface was continuously observedfrom the beginning of excitation.

On the other hand, considering the upper and lower partsof the model slope as two geological layers, the fundamentalfrequency of each layer equals to V=4H (i.e., f0 � V=4H),where H is the layer thickness in the direction of seismicshaking (Beresnev et al., 1995). As Figure 3 shows, the hori-zontal thickness of upper and lower parts of the slope is50.3 cm, and 93.4 cm, respectively. Therefore, the greaterhorizontal thickness of the lower part makes a lower funda-mental frequency of it than that of the upper part (Fig. 10).

Vertical Component of Acceleration

Figure 12 gives the amplification factors of peak verticalaccelerations (RPVA) at different elevations, A2, A3, A4, A5,A6, A7, and A8, on slope surface of the model subjected toZ- and XZ-direction shakings. Along the slope surface (A2through A8), the RPVA tendency by the two kinds of shakingis rather the same. When the excitation intensity is less than0:3g, RPVA gradually increases to its maximum until therelative elevation h=H reaches 0.8, followed by a drop. ForZ-direction excitation, attenuation of PVA occurs in the lowerslope with RPVA below 1.0. The similar responses in lowerslope were also found in linear elastic region by other re-searchers. Bouchon (1973) found an attenuation of verticaldisplacement in the zone near the bottom of a depression

Figure 8. PHA amplification factor, RPHA, by X- and XZ-direction shaking and their ratios versus relative elevation h=H. Figure 9. Response of the model slope to horizontal component

of XZ-direction shaking: PHA, RPHA, and fundamental frequencyversus excitation intensity.


topography and extended in the lower part of the slope.When the excitation intensity is stronger than 0:3g, RPVA ex-hibits a lying S-shaped pattern with the relative elevationh=H. The turning of this pattern occurs at the relative eleva-tions of h=H � 0:2 to 0.4 and h=H � 0:8, respectively. Be-fore the first turning point, RPVA decreases to values below1.0, indicating an attenuation of PVA. After that, RPVA in-creases up to its maximum (the second turning point), fol-lowed by a drop. The variation of vertical-componentresponses in the lower slope before and after the excitationintensity of 0:3g may be caused by the nonlinear change ofthe slope structure.

Another observation from Figure 12 is that the RPVA byXZ-direction excitation is somehow 20% greater than that byZ-direction excitation alone, suggesting the contribution ofthe X component of the XZ-direction excitation to provokingthe model slope. However, this contribution of X componentweakens with elevation, as the ratio of RPVA by XZ-directionexcitation to that by Z direction is decreasing with therelative elevation though it is always greater than 1.0.

The change of vertical response with excitation intensityof XZ-direction shaking is shown in Figure 13 in terms ofPVA, RPVA, and the resonance frequency (fr). It is found thatPVA of all monitoring points on the slope surface increaseslinearly, but RPVA decreases as the excitation intensitystrengthens. This indicates a gradual weakening in vertical

acceleration response with the excitation intensity regardlessof the increase in PVA. In other words, with the excitationintensity of shaking, the vertical acceleration response of theslope attenuates.

The resonance frequency calculated from the measure-ments of each monitoring point shows similar pattern withthe excitation intensity (Fig. 13). Their average is taken asthe resonance frequency (fr) of the model slope and plottedin Figure 14 with the excitation intensity; fr experiences asudden drop at the excitation intensity of about 0:35g andlevels off at both ends. As shown in Figure 11, the relativeelevation h=H of the dislocation belt of the model slope is0.8, just corresponding to the maximum vertical-componentresponse in Figure 12. This indicates that it is the vertical-component force that makes the top two layers detach fromthe underlying part, while the horizontal-component force isresponsible for the dislocation along the interface. At the end

Figure 11. Crack development indicating the change of slopestructure.

Figure 12. PVA amplification factor, RPVA, by Z- and XZ-direction shakings and their ratios versus relative elevation h=H.

Figure 10. Average fundamental frequency, f0, of the modelslope under horizontal component of XZ-direction shaking.


of the test, the top two layers slide outward along the brokeninterface, as shown in Figure 15. The failure mode is similarto what is observed in the NBMS landslide.

Comparison between the Horizontaland Vertical Components

The ratio of PVA to PHA (RV–H � PVA=PHA) is calcu-lated for each monitoring point on the slope surface whensubjected to levels of shaking intensity in XZ direction andplotted along relative elevation h=H in Figure 16. The figureshows that the ratio RV–H changes with relatively high valuesin the middle height and low values at both ends (toe and top)of the model slope. For each monitoring point, the number ofrecords with RV–H greater than or equal to 2=3 is counted,and the percentage of this number out of total number of re-

cords for this monitoring point is calculated and plotted inFigure 17a. The records with RV–H equal to 1.0 has also beendone the same and plotted in Figure 17b. Such a statisticalresult shows that, in relative elevation ranges from 0 to 0.36,0.41 to 0.5, and 0.8 to 0.9, 50% of PVAs are greater than orequal to 2=3 of the PHA. Furthermore, PVA in elevationranges from 0.5 to 0.8 is all greater than 2=3 of PHA. Theseranges together count for 85% of the slope height. As shown

Figure 13. Response of the model slope to the vertical compo-nent of XZ-direction shaking: PVA, RPVA, and resonance frequency.

Figure 14. Average resonance frequency of the model slopeunder the vertical component of XZ-direction shaking.

Figure 15. Failure of the model slope in the shaking table test.

Figure 16. Distribution of ratio of PVA to PHA, RV–H, alongelevation of the model slope.


in Figure 17b, 50% of PVAs in the elevation range from 0.5 to0.82 are greater than or equal to PHA, counting for 32% ofthe slope height.

One of the commonly observed phenomena involvingstrong vertical ground motion is the parabola ejection of thetop slope. Yin (2009) regarded the ejection as kinetic processfor majorities of landslides triggered by the 2008 Wenchuanearthquake, as there is no obvious evidence of friction at theinterface. Tang et al. (2009) conducted numerical modelingon a simple slope and found that the abrupt ejection wascaused by tension waves reflected from upward compressionwaves (P wave). When a slope is filled with structure planes,reflection can occur at any interface, which causes a morecomplicated effect of vertical earthquake. Aoi et al.(2008) presented a trampoline model and explained theasymmetric surface acceleration observed in the 2008Iwate–Miyagi earthquake of Japan. In their opinion, theupper slope part can be directly uplifted by the strong verticalforce and the upward force may speed up failure process byreducing the shear resistance of the slope.

The analysis presented is based on a model with two-dimensional topography in the X–Z plane of Figure 3.Though the shaking table model is excited directly at the bot-tom, lack of propagation effect in real geological body, to-gether with the incomplete simulation for high-frequencyexcitation waves (>48 Hz), the above statistic suggests thatvertical component does play an important role in responsesof a slope to an earthquake. The design codes currently usedin some parts of China, where the vertical component ofearthquake wave is either out of consideration or is assumedto have a value of 2=3 of the horizontal component, mayneed to be reevaluated for the efficiency of such a scheme.

Conclusions

An experimental study has been conducted on the seis-mic responses of a high-strength rock slope by means of ashaking table. The recorded Wenchuan earthquake waves arescaled to excite the model slope. The acceleration responses,

especially the topographic effect, to both horizontal and ver-tical components are analyzed. The following conclusionscan be drawn.

1. The amplification factor of RPHA is increasing with rel-ative elevation h=H of the model slope. The upper andlower halves of the model slope exhibit different changepatterns of RPHA, as RPHA exceeds 2.0 and increases fastin the upper half (h=H > 0:6) but ranges between 1.0 and2.0 in the lower half, indicating an obvious topographicamplification effect.

2. The amplification factors of RPVA exhibit a lying S-shaped changing pattern with the relative elevation, indi-cating attenuations of PVA at the toe and top of a slope.

3. The XZ-direction shaking produces a horizontal and ver-tical response stronger than X-direction and Z-directionshaking alone.

4. Both PHA and PVA on the surface of the model slope in-crease with the excitation intensity. However, the corre-sponding amplification factor RPHA and RPVA generallydecreases, indicating the acceleration response of a slopeweakens with the excitation intensity.

5. The local fundament frequency decreases with the exci-tation intensity, indicating a gradual deterioration of theinner structure of the slope. The upper slope part tends toexperience a sharp drop of fundamental frequency, sug-gesting a sudden decay of the slope structure in this part.

6. The statistic of ratio of PVA to PHA indicates that, 85% ofthe slope height, especially the upper middle part, islikely subject to PVAs greater than or equal to 2=3 ofPHA, and 32% of the slope height to PVAs greater thanor equal to PHA. This indicates the nonignorable role ofPVA in responses of a slope to an earthquake and neces-sity of considering during design work.

Data and Resources

The China Earthquake Networks Center database wassearched using www.csndmc.ac.cn/newweb/data.htm (last

Figure 17. Percent of RV–H greater than a threshold: (a) 2=3 and (b) 1.0.


www.csndmc.ac.cn/newweb/data.htm





accessed February 2013). The database can be visited by reg-istered users. The definition and application of MATLAB’sfunction tfestimate() can be searched using http://www.mathworks.cn/cn/help/signal/ref/tfestimate.html (last ac-cessed February 2013).

Acknowledgments

This research is financially supported by the National Basic ResearchProgram “973” Project of the Ministry of Science and Technology of thePeople’s Republic of China (2013CB733200), the National Science Foundfor Distinguished Young Scholars of China (Grant Number 41225011), theChang Jiang Scholars Program of China and the open fund on “Research onlarge-scale landslides triggered by the Wenchuan earthquake” provided bythe State Key Laboratory of Geo-environment Protection and Geo-hazardPrevention. Jianjun Chen and Wei Zou who assisted in the tests are thankedsincerely. The authors are grateful to Niek Rengers and Janusz Wasowskiand unnamed reviewers for their valuable comments on the early versionof the manuscript.

References

Aki, K., and K. Larner (1970). Surface motion of a layered medium havingan irregular interface due to incident plane SH waves, J. Geophys. Res.75, 933–954.

Aoi, S., T. Kunugi, and H. Fujiwara (2008). Trampoline effect in extremeground motion, Science 322, 727–730.

Beresnev, I. A., K. L. Wen, and Y. T. Yeh (1995). Seismological evidence fornonlinear elastic ground behaviour during large earthquakes, Soil Dy-nam. Earthq. Eng. 14, 103–114.

Boore, D. M. (1972). A note on the effect of simple topographic on seismicSH waves, Bull. Seismol. Soc. Am. 62, 275–284.

Borcherdt, R. D. (1970). Effects of local geology on ground motion near SanFrancisco Bay, Bull. Seismol. Soc. Am. 60, 29–61.

Bouchon, M. (1973). Effect of topography on surface motion, Bull. Seismol.Soc. Am. 63, 615–632.

Bouchon, M., C. A. Schultz, and M. N. Toksöz (1996). Effect of three-dimensional topography on seismic motion, J. Geophys. Res. 10,5835–5846.

Bozzano, F., L. Lenti, S. Martino, A. Montagna, and A. Paciello (2011).Earthquake triggering of landslides in highly jointed rock masses:Reconstruction of the 1783 Scilla rock avalanche (Italy), Geomorphol-ogy 129, 294–308.

Chen, Z. H., C. A. Tang, and Y. F. Fu (1998). Infinite element simulation ofcatastrophe induced by evolution of rock microfracturing damage,Chin. J. Geotech Eng. 20, 9–15 (in Chinese).

Curtis, W. D., J. D. Logan, and W. A. Parker (1982). Dimensional analysisand the pi theorem, Lin. Algebra. Appl. 47, 117–126.

Dai, F. C., C. Xu, X. Yao, L. Xu, X. B. Tu, and Q. M. Gong (2010). Spatialdistribution of landslides triggered by the 2008 MS 80 Wenchuanearthquake, China, J. Asian. Earth. Sci. 40, 883–895.

Dong, J. Y., G. X. Yang, F. Q. Wu, and S. W. Qi (2011). The large-scaleshaking table test study of dynamic response and failure mode ofbedding rock slope under earthquake, Rock Soil Mech. 32, 2977–2983 (in Chinese).

Geli, L., P. Y. Bard, and B. Jullien (1988). The effect of topography on earth-quake ground motion: A review and new results, Bull. Seismol. Soc.Am. 78, 42–63.

Gorum, T., X. M. Fan, C. J. Westen, R. Q. Huang, Q. Xu, C. Tang, and G. H.Wang (2011). Distribution pattern of earthquake-induced landslidestriggered by the 12 May 2008 Wenchuan earthquake, Geomorphology133, 152–167.

Harp, E. L., and R. W. Jibson (2002). Anomalous concerntrations of seis-mically triggered rock falls in Pacoima Canyon: Are they caused by

highly susceptible slopes or local amplification of seismic shaking?Bull. Seismol. Soc. Am. 92, 3180–3189.

Huang, R. Q., and W. L. Li (2008). Research on development anddistribution rules of geohazards induced by Wenchuan earthquakeon 12th May 2008, Chin. J. Rock Mech. Eng. 27, 2585–2592(in Chinese).

Kumsar, H., ö. Aydan, and R. Ulusay (2000). Dynamic and static stabilityassessment of rock slopes against wedge failures, Rock Mech. RockEng. 33, 31–51.

Lee, C., Y. Tsai, and K. Wen (2006). Analysis of nonlinear site responsesusing the LSST downhole accelerometer array data, Soil Dynam.Earthq. Eng. 26, 435–460.

Li, X. J., Z. H. Zhou, H. Y. Yu, R. Z. Wen, D. W. Lu, M. Huang, Y. N. Zhou,and J. W. Cu (2008). Strong motion observation and recordings fromthe great Wenchuan earthquake, Earthq. Eng. Eng. Vib. 7, 235–246.

Liang, Q., W. Han, R. Ma, and W. Chen (2005). Physical simulation studyon dynamic failures of layered rock masses under strong groundmotion, Rock Soil Mech. 26, 1307–1311 (in Chinese).

Lin, M. L., and K. L. Wang (2006). Seismic slope bahavior in a large-scaleshaking table model test, Eng. Geol. 86, 118–133.

Ling, H. I., Y. Mohri, D. Leshchinsky, C. Burke, K. Matsushima, andA. H. Liu (2005). Large-scale shaking table tests on modular-block reinforced soil retaining walls, J. Geotech. Geoenviron. 131,465–476.

Louis, B. (1957). The Pi theorem of dimensional analysis, Arch. Ration.Mech. Anal. 1, 35–45.

Martino, S., A. Minutolo, A. Paciello, M. G. Scarascia, and V. Verrubbi(2006). Seismic microzonation of jointed rock-mass ridges througha combined geomechanical and seismometric approach, Nat. Hazards39, 419–449.

Qi, S. W., Q. Xu, H. X. Lan, B. Zhang, and J. Y. Liu (2010). Spatial dis-tribution analysis of landslides triggered by 2008512Wenchuan Earth-quake, China, Eng. Geol. 116, 95–108.

Razmkhah, A., M. Kamalian, and R. Golrokh (2008). Parametric analysis ofthe seismic response of irregular topographic features, GeotechnicalEarthquake and Engineering and Soil Dynamics IV Congress, Sacra-mento, California, 18–22 May 2008.

Rogers, A. M., L. J. Katz, and T. J. Bennett (1974). Topographic effects onground motion for incident Pwaves- a model study, Bull. Seismol. Soc.Am. 64, 437–456.

Sepúlveda, S. A., W. Murphy, and D. N. Petley (2005). Topograhic controlson coseismic rock slides during the 1999 Chi-Chi earthquake, Taiwan,Q. J. Eng. Geol. Hydrogeol. 38, 189–196.

Sepúlveda, S. A., W. Murphy, R. W. Jibson, and D. N. Petley (2005). Seis-mically induced rock slope failures resulting from topographic ampli-fication of strong ground motions: The case of Pacoima Canyon,California, Eng. Geol. 80, 336–348.

Shimizu, Y., ö. Aydan, and Y. Ichikaw (1986). A model study on dynamicfailure modes of discontinuous rock slopes, in Proc. of theInternational Symposium on Engineering in Complex Rock Forma-tions, Beijing, China, 3–7 November 1986.

Tang, C. A., Y. J. Zuo, S. F. Qin, J. Y. Yang, D. G. Wang, L. C. Li, and T. Xu(2009). Spalling and slinging pattern of shallow slope and dynamicsexplanation in the 2008 Wenchuan earthquake, in Proc. of the 10thConference on Rock Mechanics and Engineering, Weihai, Shandong,China, 28–30 July 2008.

Wang, K. L., and M. L. Lin (2011). Initiation and displacement of landslideinduced by earthquake—A study of shaking table model slope test,Eng. Geol. 122, 106–114.

Wen, Z. P., J. J. Xie, M. T. Gao, Y. X. Hu, and K. T. Chau (2010).Near-source strong ground motion characteristics of the 2008Wenchuan earthquake, Bull. Seismol. Soc. Am. 100, 2425–2439.

Xu, Q., X. J. Pei, and R. Q. Huang (2009). Large-Scale Landslides Inducedby the Wenchuan Earthquake, Science Press, Beijing (in Chinese).

Yang, J., T. Sato, S. Savidis, and X. S. Li (2002). Horizontal andvertical components of earthquake ground motions at liquefiable sites,Soil Dynam. Earthq. Eng. 22, 229–240.


http://www.mathworks.cn/cn/help/signal/ref/tfestimate.html

http://www.mathworks.cn/cn/help/signal/ref/tfestimate.html

Ye, B., G. L. Ye, W. M. Ye, and F. Zhang (2012). A pneumatic shakingtable and its application to a liquefaction test on saturated sand,Nat. Hazards 66, 375–388.

Yin, Y. P. (2009). Features of landslides triggered by the Wenchuanearthquake, J. Eng. Geol. 17, 29–38 (in Chinese).

Yin, Y. P., F. W. Wang, and P. Sun (2009). Landslide hazards triggered by the2008 Wenchuan earthquake, Sichuan, China, Landslides 6, 139–152.

State Key Laboratory of Geohazard Prevention and Geoenvironment Pro-tectionChengdu University of TechnologyNo. 1 Erxianqiao East RoadChengdu, Sichuan 610059, China

(H.L., Q.X., X.F.)

AGECON Ltd.Hong Kong, China, Block Rear12/F, 425Z Queen’s Road WestHong Kong, China

(Y.L.)

Manuscript received 27 February 2013


response of high-strength rock slope to seismic waves in a...

Documents