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Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads
Journal Pre-proof Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads
Zhijian Wu, Dan Zhang, Shengnian Wang, Chao Liang, Duoyin Zhao PII:
S0013-7952(19)31634-5
DOI:
https://doi.org/10.1016/j.enggeo.2020.105507
Reference:
ENGEO 105507
To appear in:
Engineering Geology
Received date:
30 August 2019
Revised date:
20 December 2019
Accepted date:
22 January 2020
Please cite this article as: Z. Wu, D. Zhang, S. Wang, et al., Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads, Engineering Geology (2019), https://doi.org/10.1016/j.enggeo.2020.105507
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© 2019 Published by Elsevier.
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Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads Zhijian WU1 *, Dan ZHANG2 , Shengnian WANG1 , Chao LIANG1 , Duoyin ZHAO3 1
College of Transportation Science and Engineering, Nanjing Tech University, Nanjing, Jiangsu
211816, China Gansu Construction Investment (Holdings) Group Corporation Steel Structure Co., Ltd., Lanzhou,
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Chengdu Surveying Geotechnical Research Institute Co., Ltd. of MCC, Chengdu, Sichuan 610000,
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Gansu 730000, China
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China
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* Corresponding Author: Zhijian WU; email: [email protected]
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Abstract: The Loess Plateau is one of the most seismically and geologically ac tive regions in China. The related catastrophic earthquakes and geological disasters have caused more than 1.4 million
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deaths in the plateau. In this study, the slopes on the edge of the loess tableland in Pingliang City,
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Gansu Province—the core area of the Loess Plateau—are investigated. Based on large-scale shaking-table model tests and discrete-element numerical simulation—particle flow code (PFC 2D), the dynamic-response characteristics and deformation evolution process of fissured and non-fissured loess slopes under different seismic loads are studied. The test results show that with increasing seismic load input, the peak ground displacement (PGD) of the loess slopes increases gradually with increasing slope height. For the two types of slopes, the acc eleration amplification effects in the slope with horizontal direction load are larger than those of the vertical direction load. The amplification factor of the peak ground acceleration (PGA) at the shoulder of the fissured slope is significantly 1
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larger than that of the non-fissured slope. According to the numerical simulation results of the fissured slope, when the seismic load is small, the bond-failures are distributed densely in the initial fissured structural plane and at the model bottom. Regarding the non-fissured slope, the bond-failures in the slope are mainly distributed at the bottom of the model. With increasing acceleration amplitude, the number of bond-failures in the slopes increases rapidly. When the input load increases to 0.40g, two
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potential slip surfaces occur in the shallow surface of the fissured slope and a potential slip surface
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appears at the back edge of the non-fissured slope.
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Key words: loess slope; shaking-table test; fissure; deformation evolution; PFC.
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Introduction
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The Loess Plateau is one of the main areas in which strong earthquakes and geological
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disasters frequently occur in China. Strong earthquakes have caused more than 1.4 million deaths in this area. The large quantity of landslides induced by earthquakes is the primary
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cause of huge casualties. The fissures in the (shallow) loess surface layer in this area are
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extremely developed and widely distributed, and they frequently induce landslides, collapses, and other geological disasters. Thus, the fissured loess layer constitutes a potential slip surface with the occurrence of landslides. Therefore, it is necessary to study the influence of fissures on the stability of slopes. Some researchers have investigated the fissured slope of the soil. For instance, Skempton et al. (1993) discovered that the fissures in the soil can soften the clay structure, thereby reducing the stability of the slope. André et al. (2013) considered that the development of surface fissures is an important indicator
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for understanding and forecasting slope movements. Li and Yang (2016) investigated the effects of vertical tension fissures and ground water on stability of slopes based on Power-Law nonlinear failure criterion. However, there are few studies on fissured loess slopes, and the influence of fissures on loess slopes under the action of earthquakes has not been studied.
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Shaking-table tests and numerical simulations are effective methods to study the
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dynamic response characteristics of slopes. Many researchers have done many scientific
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through the two methods and have obtained a lot of valuable results.
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Shaking-table tests can directly reflect the deformations and failure mechanisms of
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slopes under vibrations, and are therefore an important mean for studying the seismic
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dynamic-response and instability failure mechanisms of slopes (Lin and Wang, 2006). Recently, many researchers have designed shaking-table model tests to study the
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dynamic-response characteristics of slopes during earthquakes (Liu et al., 2014; Li et al.,
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2019). Feng et al. (2018) studied the dynamic-response characteristics of anti-dip, bedding, and homogeneous rock slopes with large-scale shaking- table tests. Furthermore, a large-scale shaking-table test was performed on a rock slope with discontinuous joints to study the dynamic characteristics under the combined action of earthquakes and rapid water draw-down (Song et al., 2017). Che et al. (2016) conducted a series of shaking table tests to evaluate the influence of wave propagation on the stability of a high and steep rock slope with bedding discontinuity joints. Srilatha et al. (2017) studied the effect of the slope
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angle on the seismic response of unreinforced and reinforced soil slopes through laboratory shaking- table tests. Li et al. (2018) studied the dynamic behavior of a dip slope with various geometric conditions under different external excitatio ns. However, there is no study on the shaking table tests of fissured loess slopes. Cundall and Strack proposed the discrete-element method (DEM) to study the structure
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and motion law of discontinuous particulate matter in 1979. In contrast to the description of
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particulate matter with the continuum theory, the DEM is a widely applied method and
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suitable for studying the macroscopic characteristics of materials from microscopic point
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of view. The Particle Flow Code (PFC) software is based on Newton's second law and the
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theory of force displacement. The software is used to simulate the motion of circular
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particle media and their interactions. Because the landslide block is not a rigid body and generally behaves like a quasi-rigid body (Tang et al., 2009), researchers frequently use the
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PFC model to analyze granular assemblages with purely frictional or bonded circular
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particles represented by discs (Tang et al., 2013). Furthermore, Wang et al. (2017) applied the particle DEM to predict deformation failures and unstable motion processes in landslide accumulations and landslide impact disasters. By using the PFC, Zhang et al. (2017) simulated the slide mechanism of the Zhengjiamo landslide and determined the features of the landslide dynamics with a five-stage model. Chang et al. (2004) simulated the mechanical process and accumulation behavior of the JiufenErshan landslide in Taiwan. Moreover, the dynamic response of a
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falling accumulation slope with different parameters under the action of the horizontal shear wave of the 2008 Ms8.0 Wenchuan earthquake was simulated. Yuan et al. (2014) concluded that the eroded underlying layer can increase the maximal migration distance of the slide body based on simulations of the Donghekou landslide induced by the Wenchuan earthquake. Feng et al. (2017) established a numerical modeling approach by coupling
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PFC and Fast Lagrangian Analysis of Continua (FLAC) codes to examine the
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characteristics of seismic signals induced by the Xiaolin landslide and to perform a
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parametrical study. Scaringi et al. (2018) used PFC to reproduce the Xinmo landslide and
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to simulate the kinematics and runout of the potentially unstable mass, which could cause a
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new catastrophic event. Moreover, Zhang et al. (2019) conducted field investigations and
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numerical modeling with PFC to investigate the characteristics of the Jiweishan rock avalanche and their implications for the fragmentation mechanisms. Due to the
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particularity of loess structure, the general numerical simulation methods have limitations
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for analyzing loess slopes. When studying the dynamic processes of these landsides, discrete element methods can be used as a powerful tool for failure analysis of fissured loess slope. In this study, shaking- table model tests on fissured and non- fissured loess slopes were conducted. The deformation of the slope surface was measured with high precision and in real time with a three-dimensional optical measurement and analysis system. The dynamic-response characteristics of the two slope types under different seismic loading
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conditions were analyzed considering the slope surface displacement and slope acceleration. Moreover, to study the discontinuous phenomena (crack propagation and failure) inside the slope body and to validate the shaking-table model tests, the particle flow dispersion elements were numerically analyzed. The results provide information on the deformation instability evolution laws of the two loess slope types.
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1. Shaking-table tests
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1.1 Test equipment and model
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The shaking-table model tests were conducted with two loess slope types in the Key
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Laboratory of Loess Earthquake Engineering of the China Earthquake Administration.
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The shaking table is driven by 28 servo motors, which can produce horizontal and
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vertical bidirectional vibrations. The main technical parameters are listed in Table 1. Rigid soil box is commonly used in shaking table model tests to study the dynamic
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characteristics of soil, but it also has disadvantages. The rigid boundary has effect on the
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dynamic response of the soil such as reflecting seismic waves and affecting soil deformation modes. Generally, some scholars have stuck flexible materials on the inner wall of the rigid box to reduce those effects. In comparison, the shear model box is more capable of simulating the shear deformation of the soil under dynamic loads. However, due to structural strength and size limitations, it is not applicable to large model tests. A rigid model box with a length of 2.8 m, width of 1.4 m, and height of 1.8 m was adopted for large loess slope model in this study. The box was fixed on the table and
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rigidly connected to it. To observe the deformations of the slip surface and lateral view of the slope during the tests, two transparent plexiglass plates with a thickness of 30 mm were installed along the length of the model box. In addition, closed-hole foam material (polyethylene) with a thickness of 3 cm was pasted onto both box ends to reduce the influence of the model box boundaries and the rigid reflections of the seismic waves on
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the side walls on the test results.
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1.2 Similitude design and material ratio
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Based on the similarity theory (Lu et al., 2015), the similarity constants of the basic
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dimensions were the geometric similitude ratio CL=25, density similarity constant Cρ=1,
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similarity constant of the vibration acceleration Ca =1, and similarity constant of the gravitational acceleration Cg =1. The similar constants of the remaining physical
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quantities were derived through the Buckingham π theorem and a dimensional analysis
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(Table 2). Cohesion similarity constant Cc= CLCρCg =25, elastic modulus similarity
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constant CE= CLCρCg =25, shear modulus similarity constant CG= CLCρCg =25, stress similarity constant Cσ= CLCρCg =25. The similarity ratio of other dimensionless quantities is 1, so Cφ=Cμ=Cε=1. According to the similarity ratio obtained, many direct shear tests and tr iaxial tests were carried out to determine the material ratio of the model slope. Finally, the material ratio closest to the target value is obtained by the above tests. The model slope in final was composed of loess, barite powder, fly ash, sawdust, and water at a ratio of
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5:2:2.1:0.3:0.6. The physical parameters of the prototypical and similar materials are listed in Table 3. 1.3 Model The test model is based on a fissured slope on the plateau edge of Pingliang, Gansu Province, the center of the Loess Plateau, and a non-fissured slope on the tableland is
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used as a contrast model. The prototype slope (Fig. 1) with Q3 loess is a typical fissured
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loess slope on the Loess Plateau. Q 3 loess is a typical unsaturated, special soil with large
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pores, under-compacted, and vertical fissures. There are two fissures, one deep and
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another shallow, developed on the edge of the tableland at the top of the slope. The model
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had two comparable slopes with equal material ratios, a gradient of 55°, and a height of
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110 cm. The underlying formation of the slopes was 10 cm thick. The left slope had two fissures: one was 50 cm long, 3 mm wide, and 20 cm deep; the other fissure was 100 cm
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long, 5 mm wide, and 30 cm deep. They were 10 cm and 20 cm away fro m the slope
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shoulder, respectively. The right reference model had no fissures. To build the model, the soil sample was screened, and large particles were removed. Next, the materials were stirred evenly based on the mix ratio to form the model. Afterward, the mixture was covered with a polyethylene plastic cloth and left to rest for 24 h. Finally, layered compaction was applied to fill the model; each layer was 10 cm thick. The next layer was added after the surface of the completed layer had been roughened.
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The weighed soil samples were poured into the model box and rolled to the designed compactness. After each layer was completed, the density was checked with cutting ring sampling to control the density and compactness of each layer. The moisture content was also checked to control it at 6.4%, which is consistent with the ratio of the water obtained in the above tests (Section 1.2). The slope surface was supported with shuttering to obtain
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the designed slope angle. Furthermore, two equally sized division p lates as design
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fissures were wrapped in plastic wrap, smeared with Vaseline, embedded into the left
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slope, and finally removed 24 h after the slope model had been formed. The completed
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model is illustrated in Fig. 2.
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1.4 Displacement and acceleration measurements
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The three-dimensional optical deformation measurement and analysis system was used to measure the slope displacements subjected to seismic loads. This method exhibits a
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high precision, fast speed, and an easy operation. In addition, it enables non-contact and
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full- field multi-data measurements (Song et al., 2018). The system is mainly composed of two cameras with a resolution of 2 million pixels, 2 illuminators, and a beam bracket (the length of the bracket is approximately 1 m). The highest acquis ition frequency is 340 Hz (340 frames per second, 6–8 m field of view at 5 m distance), and the measurement error is approximately 0.05–0.1 mm within a range of 5 m from the surface of the slope model. The illuminators were symmetrically arranged in front of and behind the model, and the
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camera was installed approximately 2.5 m above the measured model with scaffolds (Fig. 3). Based on the binocular stereo vision technology, two high-speed cameras were used to collect the real-time images of the object deformation during all stages. Based on the parallax of images recorded by the two cameras at different positions and the spatial
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geometric relationship between the camera positions, the accurate recognition of the
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marker points or digital speckle points, including the coding and non-coding marker
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points, can be used to achieve stereo matching to reconstruct the three-dimensional
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spatial coordinates and displacements of the surface points.
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After calibrating the camera, 42 non-coding marking points were set on the surfaces of
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the two slope models, as illustrated in Fig. 4, and the collected marking points were identified, located, and numbered, as illustrated in Fig. 5. The three-dimensional
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coordinates were reconstructed by solving the corresponding image coord inates in the
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camera images. Based on the three-dimensional coordinates of the marking points, the deformation states of each point on the surface of the slope model were analyzed. As the input seismic load increases, there will be a relative displacement between the slope model and the model box. The displacement caused by the relative motion will affect the accuracy of the measurement results of the slope monitoring points. To avoid the impact of relative displacement between the slope model and model box, we designed two reference cross-bars rigidly connected to the model box and placed 12 marking
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points on the cross-bars to obtain a reference displacement of the slope model; two cross-bars were installed in width direction of the model box and 5 cm above the front edge of the slope top (Fig. 4a). The measurement points of the acceleration sensors are illustrated in Fig. 6. The sensors are three-phase capacitive with sensitivity of 680 mV/g in X direction, 680 mV/g
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in Y direction, 680 mV/g in Z direction and ±2 g in range. The size of each acceleration
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sensor is 13mm×15mm×8mm. Eight accelerometers were symmetrically installed along
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the surfaces of the two slopes to compare the dynamic-response characteristics of the
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slope surface. The acceleration sensor A0 was installed on the shaking table to monitor
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the actual input seismic wave. The sensors A3, A7, A11, A15, A3', A7', A11', and A15'
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were used to analyze the variations in the acceleration response subjected to seismic
1.5 Input motions
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loads along the slope surface.
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Two loading wave types were adopted in the shaking-table model test: the Wenchuan earthquake wave recorded in Tangyu, Sichuan, China and the El Centro wave, the time history and Fourier spectrum of which are illustrated in Fig. 7 and 8, respectively. They were inputted in horizontal X and vertical Z directions, respectively. To study the dynamic response of the slope for different acceleration amplitudes of the seismic loads, working conditions with the input accelerations of 0.05 g, 0.10g, 0.20g, and 0.40g were
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applied step by step (Fig. 9). A total of 16 tests (16 different input motions) have been performed on the model. 2. Dynamic-response of loess slopes 2.1 Dynamic displacement response The peak ground displacement (PGD) distribution nepho grams were obtained by
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calculating the PGD values of each measurement point of the slopes under different
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working conditions. Fig. 10 illustrates the horizontal PGD distributions of the
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measurement points of the slopes for the Wenchuan Tangyu wave in X direction.
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According to the results, the PGD distributions are similar under different seismic
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intensity loads. With increasing slope height, the PGD increases gradually, i.e., the
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displacements at the slope foot and slope shoulder are the smallest and largest, respectively. Regarding the fissured slope, the PGDs are approximately 1.32 cm, 2.19 cm,
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3.63 cm, and 5.05 cm for input accelerations of 0.05g, 0.10g, 0.20g, and 0.40g at the
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slope shoulder, respectively. Regarding the non-fissured slope, the PGDs are approximately 0.85 cm, 1.46 cm, 2.49 cm, and 4.05 cm for input accelerations of 0.05g, 0.10g, 0.20g, and 0.40g at the slope shoulder, respectively. Thus, it can be seen the amplification effect of the fissured slope is greater than that of the non- fissured slope under horizontal loads. The experimental results indicate a small slope deformation. Furthermore, the slope is in a stable state when the seismic intensity of the input load is below 0.20g. With
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increasing seismic load, the deformation of the slope model increases, and the deformation displacement of the slope model exhibits a cumulative effect. The stronger the input ground motion, the larger are the cumulative deformations of different positions on the slope surface and the PGD. The fissures at the slope top develop gradually with increasing seismic load, and the PGD on the slope shoulder is approximately 1.5 times
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larger than that at the same position of the non-fissured slope under the same load.
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Fig. 11 illustrates the PGD distribution on the slope surface of the slope model under
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vertical loads. For a Wenchuan Tangyu wave in Z direction, the PGD distributions on the
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slope surface of the vertical and horizontal excitations are similar. Thus, the PGD
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increases with increasing slope height, and the amplification effect of the fissured slope is
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greater than that of the non-fissured slope. Regarding the fissured slope, the PGDs are approximately 1.03 cm, 1.76 cm, 3.08 cm, and 4.53 cm for input accelerations of 0.05g,
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0.10g, 0.20g, and 0.40g at the slope shoulder, respectively. Regarding the non- fissured
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slope, the PGDs are approximately 0.85 cm, 1.17 cm, 2.13 cm, and 3.51 cm for input accelerations of 0.05g, 0.10g, 0.20g, and 0.40g at the slope shoulder, respectively. The PGDs of the loess slopes under horizontal seismic load are slightly larger than those under vertical seismic load (approximately 1.1–1.3 times those of vertical seismic load). 2.2 Dynamic acceleration response By taking the dynamic responses of two slopes under the action of the Wenchuan Tangyu wave as an example, the acceleration distribution characteristics of the
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monitoring points of the model slope were analyzed. Fig. 12 shows time-history curves of A3, A15, A3', and A15' under horizontal load with an input acceleration o f 0.40g. In the fissured slope, the peak ground acceleration (PGA) of the shoulder is 2.9 times that at the slope foot. In the non-fissured slope, the PGA of the shoulder is 2.4 times that at the slope foot. There is a clear trend of increasing PGA from the foot of the slope to the shoulder.
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Fig. 13 illustrates the variations in the PGA amplification factor at each monitoring point
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of the slope under horizontal load. The slope height has an evident amplification effect on
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the seismic acceleration under equal seismic loads, and the amplification factor increases
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with increasing height. Along the slope measurement points A11 to A15, the acceleration
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amplification factor increases significantly, thereby exhibiting an evident free- face
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amplification effect. Thus, the shoulder of the slope is at the intersection of the two free faces of the slope and the top. At this point, the seismic wave is reflected and
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superimposed many times, which aggravates the amplification of the seismic waves.
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According to Fig. 13, the PGA amplification factor of the measurement point A15 is much larger than that of A15' (approximately 1.6 times that of the non- fissured slope), thereby indicating that the existence of fissures is more likely to cause damage to the slopes, particularly to the slope shoulders. The PGA amplification factor gradually increases from foot to shoulders of both slopes. This trend is more evident for the fissured slopes. Moreover, the amplification factor decreases with increasing input acceleration. The decreasing trend is very weak in the non- fissured slopes and more evident for the
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fissured slopes. On the shoulder of the fissured slope, the PGA amplification factor at 0.40g is approximately 1.3 lower than that at 0.05g (3.6). Nevertheless, the PGA amplification factor on the shoulder of the fissured slope is still larger than that of the non-fissured slope. Fig. 14 illustrates the variations in the PGA amplification factor at each monitoring
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point of the slope under vertical load. The variations in the peak acceleration
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amplification factors of the fissured and non-fissured slopes are similar to those under
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horizontal excitation. Both slopes exhibit elevation amplification and free- face
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amplification effects. However, the amplification effect is smaller than that under
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horizontal excitation (2/3 times that of a horizontal loading). Similarly, under a vertical
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load, the PGA amplification factor on the shoulder of the fissured slope is significantly larger than that of the non-fissured slope.
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In addition, Fig. 15 shows the PGA amplification factors of four different monitoring
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points in the middle of each slope under horizontal and vertical seismic loads. The internal PGA amplification factors of the two types of slopes tend to increase gradually along the height. The PGA amplification factors in the fissured slope are larger than that in the non- fissured slope. This magnification is more obvious under horizontal loads. In the fissured slope, the PGA amplification factor near the initial fissures increases more significantly, which is different from the non- fissured slope. Fig. 16 shows the PGA amplification factors of three monitoring points at the back of each slope under horizontal
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load. It indicates that the PGA amplification factors at back of the non- fissured slope are evidently larger than that of the fissured slope. Due to the reflection of the seismic wave at the initial fissures and the low-density soil near initial fissures absorbed most of the energy, the initial fissures have become barriers to prevent the propagation of the seismic wave, which greatly attenuated the energy at the back edge.
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By comparing the variations in the displacement and acceleration response of the two
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slope types, it can be concluded that the amplification factors of PGD and PGA exhibit
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the elevation effect and free-face amplification effect under seismic loads. In the
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elevation effect, with increasing slope height, the amplification factors of PGD and PGA
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increase and reach their maxima on the slope shoulder. The free-face amplification effect
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shows that the closer the slope shoulder, the more evident are the increases in the slope displacement and acceleration. In addition, the fissures have a certain influence on the
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effect.
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slope displacement and acceleration response, which exhibits an evident amplification
2.3 Failure characteristics After investigating the seismic loads of each working condition, the fissures and deformations on the model side were documented with photos and sketches (Fig. 17). For an input acceleration of 0.05g, the slope model exhibits no significant changes, only a small amount of soil particles fall down at both slope surfaces. For an acceleration of 0.10g, a small number of fissures occur near the initial fissures on the fissured slope, and
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few fissures occur at both slope tops and on the slope surfaces. However, the fissured slope has more new fissures than the non-fissured slope. For an acceleration of 0.20g, more new fissures appear near the fissured slope surface and the initial fissures. Under the initial fissure near shoulder of the fissured slope, several fissures develop and form a through potential slip surface. Large settlement occurs at the shoulder of fissured slope.
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New fissures in the non- fissured slope only appear in the shallow surface and at the slope
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top, and the settlement at shoulder of the non-fissured slope is small. Shallow-surface
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particles slip along the slopes and accumulate at the both slope feet. For an acceleration
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of 0.40g, the fissures continue to increase and expand inside both slopes. Shear failure
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appears at the fissured slope foot, and the shallow landslide occurs. Besides, fissures
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behind shallow landslide form a new potential slip surface, and large settlement and several settlement differences occur on the top of the fissured slope. Although the
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non- fissured slope also exhibits many new fissures, the upper settlement at the shoulder is
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less than that of the non- fissured slope, and there isn’t obvious settlement difference appearing. The non- fissured slope is relatively stable, but fissures at back edge quickly extend to interior and approach to form a potential slip surface. In the deformation process of two slopes, at the same excitation level, there is no significant difference in settlement caused by horizontal and vertical loads, but the horizontal seismic loads have greater influence on the development of fissures in slopes than vertical seismic loads. In addition, there are influence differences in the size of
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initial fissures in the fissured slope. The deep fissure (left fissure) extends downward to form a deeper potential slid surface and the shallow fissure (right fissure) expands to the surface of the slope. According to the developments of the lateral fissures in both slope types in Fig.17, with increasing seismic loads, the fissures mainly concentrate around the fissured structure plane of the fissured slope, which increases and propagates along the
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position of the initial fissures and gradually forms potential slip surface in the fissured
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slope. Regarding the non-fissured slope, the fissures first appear near the free face near
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the slope body side and gradually extend into the slope. When the seismic load reaches
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up to 0.40g, fissures at back edge extend quickly into the interior of slope and approach
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the tops and sides of two slopes.
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to form a potential through slip surface. Fig.18 shows the final damage phenomenon of
3. Simulation of seismic dynamic failure process
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3.1 Numerical modelling
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The slope model was simulated with PFC 2D according to the shaking-table model tests. The steps were as follows: (1) the software built- in command "wall generate" was used to construct the boundary of the enclosed area (i.e. "wall") based on the designed model size. In the process of modeling, the wall could constrain the generation range of particles, and the wall could also be used as the boundary to impose constraints ; (2) the meso-parameters of the model were determined based on PFC 2D biaxial compression simulations (Table 4); In combination with the parameters in Table 4, the "ball distribute"
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command was used to generate particles; the gravity acceleration was set for all particles; the iterative calculation under gravity was conducted until the set equilibrium state was reached; (3) the floating point in the particle group was calibrated; the particles outside the slope profile were eliminated based on the required model size; and (4) the parallel bonding model and smooth-joint contact model were applied to the particles; the fissure
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structure surface was generated (Fig. 19). After each step, the internal stress of the model
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was balanced.
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In order to ensure that the slope was in the initial equilibrium state, the velocity field
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and displacement field of the slope model were reset. In addition, the meso-parameters
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such as the particle bonding strength were assigned to the slope model. Simulated
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Wenchuan Tangyu wave and applied the horizontal direction seismic load to the slope model. To simplify the loading of the seismic waves in PFC 2D, an acceleration time
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history curve was integrated to obtain the velocity time history curve. Afterward, instead
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of applying the seismic load, the velocity time history curve was applied to the “wall”. 3.2 Contact model and calibration of micro-parameters The PFC model simulates the movements and interactions of many finite-sized particles. The particles are rigid bodies with finite masses that move independently and can translate and rotate. The particles interact through pair-wise contacts through an internal force and moment (Potyondy 2015). The interaction between the particles reflects the micro- mechanical behavior of the matrix of the bulk media, which is
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generally described with a particle contact constitutive model, for which the contact bonding and parallel bonding models are the most commonly applied models (Potyondy et al., 2004). Currently, the parallel bonding model is the most commonly used particle contact constitutive model to establish a PFC 2D model of rock and soil (Lee et al., 2011;
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Ghazvinian et al., 2012). The parallel bonding model was chosen as constitutive model
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for the particle contact in this study. For the simulation of cracks in slopes, the “dfn”
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command was used. Furthermore, the smooth-joint model was used to represent the
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contact modes of the joints and cracks. Joints can be added to the base material with the
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smooth-joint logic (Itasca, Consulting Group Inc., 2014; Mas Ivars et al., 2008) by which
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each joint is associated with an interface consisting of a collection of smooth-joint contacts between grains upon opposite sides of the joint. The smooth-joint contact model
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simulates the behavior of an interface, regardless of contact orientations along the
interface.
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interface by effectively modifying the surfaces of the contacting grains to align with the
In general, the parameters of the particles and bonds in the particle flow model are quite different from the macroscopic parameters. Therefore, when establishing the model, the micro-parameters must be calibrated by matching the soil parameters obtained from the numerical and indoor tests. Thus, the micro-parameters must be inferred from the known soil parameters (e.g., cohesion, internal friction coeffic ient, elastic modulus, and
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Poisson's ratio). The stress-strain relationship measured curve and the calculation curve are obtained through triaxial tests and the simulation of biaxial compression tests (Fig. 20). It shows that the measured value is basically consistent with the calculated value. In this study, the micro-parameters of the model were determined based on PFC 2D biaxial compression simulations (Table 4).
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3.3 Evolution process of bond-failures in slopes
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Fig. 21 illustrates the evolution process of the bond- failures in the two slopes.
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Evidently, the slopes experience significant bond-failure generations and slope failure
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developments. The number of bond- failures increases rapidly with gradually increasing
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seismic loads. For a seismic intensity of 0.05g, bond- failures appear at the slope bottoms.
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In the left, fissured slope, the new bond- failures appear around the two original fissures on the slope top and begin to enter the slope. The left slope exhibits a total of 419
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bond- failures; the right slope has only 187 bond- failures. For an intensity of 0.10g, the
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number of bond-failures in the slopes increases rapidly (2348 bond- failures). The fissures are dense at the structural plane and trailing edge of the left slope model. However, the bond- failures are mainly concentrated at the bottom of the right slope model. In addition, the upper part of the right slope exhibits no bond-failures. For an acceleration intensity of 0.20g (3753 bond- failures), the bond-failures in the left and right slopes develop rapidly and densely on the slope surface. Moreover, most particles are not bonded anymore. The structural fissure plane of the left slope is nearly destroyed, and many bond- failures are
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distributed on the surface, foot, and rear edge of the slope. Furthermore, bond- failures begin to appear at the trailing edge of the right slope. For an input intensity of 0.40g (5035 bond- failures), the numbers of bond- failures of the two slopes are similar. Finally, the particles in the slope are not bonded anymore. The slope collapses along the failure surface, and the shallow-layer particles of the slope surface slip.
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The entire bond- failures development is as follows: In the fissured slope, a small
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number of bond-failures first occur near the initial fissures and at the slope bottom. With
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increasing acceleration input, new bond-failures occur along the position of the initial
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fissures and propagate toward the slope interior. In the non-fissured slope, the
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bond- failures first appear at the slope bottom and then move upward. However, the
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development of the bond-failures does not occur as fast as that of the non-fissured slope. When a local seismic wave propagates through both slopes, it is reflected and refracted in
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the fissure. When the seismic wave propagates to the slope surface, it is reflected and
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refracted at the slope surface. As a result, the seismic wave in the slope becomes locally superimposed, which makes the slope more prone to a plastic deformation. 3.4 Simulation and analysis of motion process Fig. 22 indicates the results of the numerical simulations of the deformation and instability process of the fissured slope (left model) and non- fissured slope (right model) induced by seismic loads. The red dashed line in the figure is the contour line of the slope model before the seismic loads. For a seismic intensity of 0.05g, the displacements of the
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particles on the top of the fissured slope are significantly larger than those of the non- fissured slope, particularly around the structural plane of the fissure in the left model. The displacements of the particles in horizontal direction are generally larger than those in vertical direction. Thus, the direction of the particle motion is mainly horizontal. For both loess slope types, the particle displacements on the shoulder and in the surface layer
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are the largest, followed by the displacement at the slope center, the displacement of the
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trailing edge, and the displacement of the underlying layer (Fig. 22a).
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According to Fig. 22b, the value and range of the particle displacement increases at the
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shoulder and surface of the two slopes for a seismic intensity of 0.10g. Moreover, some
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particles close to the structural plane of the fissure of the left model and in the shallow
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surface of the slope are not bonded anymore. The particles in the shallow surfaces of both slope types are loosened, and a small number of particles slip down the slope. In addition,
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a slight seismic subsidence occurs on the slope shoulders.
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Fig. 22c illustrates that the top location of the slope is evidently lower than the red dashed line for a seismic intensity of 0.20g. Thus, the seismic subsidence occurs at the slope top, and the seismic subsidence of the left slope is slightly larger than that of the right slope. In addition, the particles on the shallow surface of the slopes slip down the slope and accumulate at the slope foot. Finally, for a seismic load of 0.40g, the bonds between the particles in both slopes continue to break, and two potential circular slip surfaces are generated; the shallow slip
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surface spreads along the propagation direction of the two fissures in the left slope. However, a potential circular slip surface appears at the back edge of the right non- fissured slope. Seismic subsidence occurs in both slopes; the seismic s ubsidence of the left slope is stronger than that of the right slope. In conclusion, the bonding between particles is controlled by the cohesive strength and
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their friction coefficients in the PFC model. If the actual tension or tangential force
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among particles is greater than the corresponding cohesive strength, the bonding among
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particles disappears. The fissures appear between particles owing to the appearance of a
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cohesive strength failure. The cohesive strength in the initial fissures is weakened owing
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to the stress concentration, which leads to the expansion of the fissures and to a potential
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slip surface. Thus, the potential slip surface of a fissured slope is shallower than that of a non- fissured slope, and the initial fissures affect the position o f the final slip surface. In
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general, the slope experiences a gradual failure under a seismic force. The occurrence of
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landslides is closely related to the development of fissures. A seismic force will induce fissures that expand and extend, thereby forming a potential slip surface in the slope structure, which could result in landslides. 4. Conclusions A large-scale shaking-table model test was performed to study the dynamic-response characteristics of fissured and non- fissured loess slopes under seismic loads. In addition, PFC 2D was used to analyze the displacement and deformation process of the slope
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model. These results suggest that the two types of loess slopes have different dynamic-response characteristics and deformation process under seismic loads. The conclusions are as follows: The PGDs in the fissured and non- fissured loess slopes increase gradually with increasing slope height under seismic loads. The shoulder of the fissured slope
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experiences a bigger PGD than that of the non-fissured slope (approximately 1.5 times
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larger). When the seismic- input direction is horizontal, the PGD of the slope surface is
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slightly larger than that of the vertical loading (1.1–1.3 times larger).
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The acceleration amplification effect under horizontal input loads is greater than that
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under vertical loads. Both slopes reach the maximum on their shoulders. Hence, the
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elevation amplification and free- face amplification effects occur. Regarding the fissured slope, the amplification of PGA is significantly larger than those of the shoulder and
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slope surface of the non-fissured slope (approximately 1.6 times larger).
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With increasing seismic loads, the number of fissures continues to increase, and the loess slopes experience a gradual failure (transition from local to globa l failure) under seismic loads. The fissures propagate along the initial fissures in the fissured slope and the initial fissures are extremely easy to form potential slip surfaces. When the seismic load reaches to 0.40g, large deformation and potential slip surfaces occur on two types of loess slopes which could result in landslides. Acknowledgements
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This study is financially supported by the National Natural Science Foundation of China (No. 41472297), The Second Tibetan Plateau Scientific Expedition and Research (STEP) program (Grant No. 2019QZKK0905) ， the scientific research foundation for the introducing talent of Nanjing Tech University, and the Key Project of Natural Science Foundation of China (No.41630636).
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References
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André S., Jean-Philippe M., Norman K., Uwe N., Sabrina R., 2013. Image-based mapping of surface fissures for the investigation of landslide dynamics. Geomorphology, 186,12-27 Chang K.J., Taboada A., 2009. Discrete element simulation of the Jiufengershan rock-and-soil
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avalanche triggered by the 1999 Chi-Chi earthquake, Taiwan. J. Geophys. Res. 114, 1029-1037
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Che A., Yang H., Wang B., Ge X., 2016. Wave propagations through jointed rock masses and their effects on the stability of slopes. Eng. Geol. 201, 45-56 Feng X.X., Jiang Q.H., Zhang X.B., Zhang H.C., 2018. Shaking Table Model Test on the Dynamic
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Response of Anti-dip Rock Slope. Geotechnical and Geological Engineering 37(3),1211-1221 Feng Z.Y., Lo C.M., Lin Q.F., 2017. The characteristics of the seismic signals induced by lands lides
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using a coupling of discrete element and finite difference methods. Landslides 14(2),661-674. Ghazvinian A., Sarfarazi V., Schubert W., Blumel M., 2012. A study of the failure mechanism of planar mon-persistent open joints using PFC2D. Rock Mech. Rock Eng. 45(5), 677-693. Itasca, Consulting Group Inc., 2014. PFC (particle flow code in 2 and 3 dimensions), version 5.0
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[User's manual]. Minneapolis, MN: ICG.
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Li L.Q., Ju N.P., Zhang S., Deng X.X., 2019. Shaking table test to assess seismic response differences between steep bedding and toppling rock slopes. Bull. Eng. Geol. Environ. 78(1), 519-531 Li H. H., Lin C.H., Zu W., 2018. Dynamic response of a dip slope with multi-slip planes revealed by shaking table tests. Landslides 15,1731-1743 Li Y.X., Yang X.L., 2016. Stability analysis of crack slope considering nonlinearity and water pressure. KSCE J. Civ. Eng., 20 (6), 2289-2296 Lin M.L., Wang K.L., 2006. Seismic slope behavior in a large-scale shaking table model test[J]. Eng. Geol. 86(2), 118-133 Liu H.X., Xu Q., Li Y.R., 2014. Effect of Lithology and Structure on Seismic Response of Steep Slope in a Shaking Table Test. J. Mt. Sci 11(2), 371-383 Lu P., Wu H., Qiao G., 2015. Model test study on monitoring dynamic process of slope failure through spatial sensor network. Environ. Earth Sci. 74(4), 3315-3332 Lee H., Jeon S., 2011. An experimental and numerical study of fissure coalescence in pre-cracked specimens under uniaxial compression. Int. J. Solids Struct. 48(6), 979-999. 26
Journal Pre-proof Mas Ivars D., Potyondy D.O., Pierce M., Cundall P. A., 2008. The smooth-joint contact model. Proceedings of WCCM8-ECCOMAS Potyondy D.O., Cundall P. A., 2004. A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 41(8), 1329-1364. Potyondy D.O., 2014. Material-modeling support in PFC. Technical memorandum ICG7766-L, October 20, 2014. Minneapolis, MN: Itasca Consulting Group. Potyondy D.O., 2015. The bonded-particle model as a tool for rock mechanics research and application: currenttrends and future directions. Geosyst. Eng. 18(1),1-28 Scaringi G., Fan X., Xu Q., 2018. Some considerations on the use of numerical methods to simulate past landslides and possible new failures: the case of the recent Xinmo landslide (Sichuan, China). Landslides 15(7), 1359-1375.
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Skempton A.W., Vaughan P.R., 1993. The failure of carsington dam. Geotechnique 43(1), 151-173 Song D.Q., Che A.L., Zhu R.J., 2017. Dynamic response characteristics of a rock slope with discontinuous joints under the combined action of earthquakes and rapid water drawdown. Landslides 15(6), 1109-1125
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Srilatha N., Latha G., Madhavi, Puttappa C.G., 2017. Effect of Slope Angle on Seismic Response of
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Unreinforcedand Reinforced Soil Slopes in Shaking Table Tests. Indian Geotech. J. 47(3), 326-337 Tang C.L., Hu J.C., Lin M.L., 2009. The Tsaoling lands lide triggered by the Chi-Chi earthquake,
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Taiwan: insights from a discrete element simulation. Eng. Geol. 106, 1-19. Tang C.L., Hu J.C., Lin M.L., 2013. The mechanism of the 1941 Tsaoling landslide, Taiwan: insight
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from a 2D discrete element simulation. Environ. Earth Sci. 70(3), 1005-1019. Wang S.N, Xu W.Y., Shi C., 2017. Run-out prediction and failure mechanism analys is of the Zhenggang deposit in southwestern China. Landslides 14(2), 719-726 Yuan R.M., Tang C.L., Hu J.C., 2014. Mechanism of the Donghekou landslide triggered by the
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2008 Wenchuan earthquake revealed by discrete element modeling. Nat. Hazard. Earth Sys.
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14(5), 1195-1205 Zhang M., Wu L.Z., Zhang J.C., 2019. The 2009 Jiweishan rock avalanche, Wulong, China: deposit characteristics and implications for its fragmentation. Landslides 16(5), 893-906. Zhang Z.L., Wang T., Wu S.R., 2017. The role of seismic triggering in a deep-seated mudstone landslide, China: Historical reconstruction and mechanism analysis. Eng. Geol. 226, 122-135 Table 1 Technical parameters of shaking table test system Parameters
Technical specification
Table size
4m×6m
M ode of motion
Horizontal one-way, vertical one-way, horizontal and vertical coupling
Input waveform
Regular wave, random wave, seismic wave, artificial wave
M aximum bearing capacity
X、Z(single vibration): X, 20t; Z, 15t X、Z(combined vibration): X, 15t; Z, 15t 27
Journal Pre-proof M aximum displacement
X、Z(single vibration): X, ± 250 mm; Z, ± 100 mm X、Z(combined vibration): X, ±150mm; Z, ±100mm
M aximum velocity
X、Z(single vibration): X, 1500mm/s; Z, 700mm/s X、Z(combined vibration): X, 1000mm/s; Z, 700mm/s
M aximum acceleration
X、Z(single vibration): X, 1.7g; Z, 1.2g X、Z(combined vibration): X, 1.2g; Z, 1.0g
Range of operating frequency
X、Z(single vibration): X, 0.1～70Hz; Z, 0.1～50Hz X、Z(combined vibration): X, 0.1～50Hz; Z, 0.1～50Hz
Table 2 Similarity relations of model Similarity relations
Similarity constants
Length (L)
CL
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Density (ρ)
C
Acceleration (a)
Ca
Elastic modulus (E)
CE CLC Cg
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Shear modulus (G)
CG CLC Cg
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Stress (σ)
C CLC Cg
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Physical parameters
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1 1
C
1
Cc CLC Cg
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Internal friction angle ( )
C
1
Strain (ε)
C 1
1
Gravitational acceleration (g)
Cg
1
Time (t)
Ct CL1/ 2Cg 1/ 2
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Cohesion (c)
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Poisson's ratio (μ)
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Table 3 Similarity parameters of soil Elastic modulus, M aterial type E (M Pa)
Cohesion, c(kPa)
Density, ρ(g/m3)
Internal friction angle, φ(°)
Prototype
72
22.27
1.36
14.5
M odel
20.8
7.44
1.36
20.2
Table 4 M icro-parameters obtained by calibration. Parameters
Description
Value
ball_kn
Ball normal stiffness（Pa）
2.3e7
ball_ks
Ball shear stiffness（Pa）
2.3e7
r_max
M aximum ball radius（mm）
15
r_min
M inimum ball radius（mm）
8
ball_fric
Ball friction coefficient
0.2
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1
pb_fa
Parallel bond friction angle（°）
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pb_ten
Parallel bond tense strength（Pa）
6e4
pb_coh
Parallel bond cohesive strength（Pa）
1.2e5
pb_fric
Parallel bond friction coefficient
0.4
pb_rmul
Parallel bond radius multiplier
0.8
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Fig.1 The prototype slope
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Fig.2 Lateral view of model slopes
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Fig.3 Layout position of optical measurement system
(a)
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Fig.4 Layout of mark points of surface displacement. (a) M odel slope, and (b) sketch map
(a)
(b)
Fig.5 (a) Image Recognition and Location, and (b) Reconstruction of three-dimensional coordinates
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Fig.6 Layout of accelerometers on slope surface of model
（b）
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(a) Fig.7 WenchuanTangyu loading wave. (a) Time history, and (b) Fourier spectrum
(a) Fig.8 El-Centro loading wave. (a) Time history, and (b) Fourier spectrum
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（b）
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（a）0.05g
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Fig.9 Loading sequence of the shaking table test
（b）0.10g
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（c）0.20g
（d）0.40g
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Fig.10 PGD distribution on the slope surface of the slope model under horizontal loads (unit:mm)
（a）0.05g
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（b）0.10g
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（c）0.20g
（d）0.40g Fig.11 PGD distribution on the slope surface of the slope model under vertical loads (unit:mm)
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(b) A3'
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（a）A3
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(c) A15 (d) A 15' Fig.12 Acceleration time history curves of A3, A15, A3', and A15' under horizontal load with input load of 0.40g
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(a) (b) Fig.13 Variations in the PGA amplification factor at each monitoring point of the slope surface under horizontal load. (a) Fissured slope, and (b) Non-fissured slope
(a) (b) Fig.14 Variations in the PGA amplification factor at each monitoring point of the slope surface under vertical load. (a) Fissured slope, and (b) Non-fissured slope
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(a) (b) Fig.15 PGA amplification factors in the middle of the slopes. (a) horizontal load, and (b) vertical load
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Fig.16 PGA amplification factors in the back of the slopes under horizontal load. (a) Fissured slope, and (b) Non-fissured slope
（a）0.05g 38
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（c）0.20g
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（d）0.40g Fig.17 Deformation evolution process of slope models (shaking table test) 39
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(a) Fissured slope Fig.18 The final damage phenomenon of two slopes
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Fig.19 Contact model
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(b) Non-fissured slope
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（a）0.05g
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Fig.20 the results of the calibration test (solid lines indicate measured value, and dotted lines indicate calculated value.)
（b）0.10g
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（c）0.20g
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（d）0.40g Fig.21 Evolution process of the bond-failures in the two slopes
（a）0.05g
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（c）0.20g
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（d）0.40g Fig.22 Deformation evolution process of slope models (numerical simulation)
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The large-scale shaking-table model tests for the fissured and non-fissured loess slopes are conducted.
The deformations evolution processes of the two types of slope models are simulated based on a numerical calculation model established with the particle flow code (PFC 2D).
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The deformation evolution characterictics of the fissured and non-fissured loess slopes are revealed.
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CRediT author statement Zhijian
Wu:
Conceptualization,
Methodology,
Formal
Writing-Review & Editing Dan Zhang: Writing-Original Draft, Software, Visualization
Chao Liang: Investigation, Data Curation
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Duoyin Zhao: Investigation, Data Curation
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Shengnian Wang: Software, Writing-Review & Editing
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analysis,
Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may
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be considered as potential competing interests:
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Zhijian Wu, Dan Zhang, Shengnian Wang, Chao Liang, Duoyin Zhao PII:
S0013-7952(19)31634-5
DOI:
https://doi.org/10.1016/j.enggeo.2020.105507
Reference:
ENGEO 105507
To appear in:
Engineering Geology
Received date:
30 August 2019
Revised date:
20 December 2019
Accepted date:
22 January 2020
Please cite this article as: Z. Wu, D. Zhang, S. Wang, et al., Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads, Engineering Geology (2019), https://doi.org/10.1016/j.enggeo.2020.105507
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© 2019 Published by Elsevier.
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Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads Zhijian WU1 *, Dan ZHANG2 , Shengnian WANG1 , Chao LIANG1 , Duoyin ZHAO3 1
College of Transportation Science and Engineering, Nanjing Tech University, Nanjing, Jiangsu
211816, China Gansu Construction Investment (Holdings) Group Corporation Steel Structure Co., Ltd., Lanzhou,
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Chengdu Surveying Geotechnical Research Institute Co., Ltd. of MCC, Chengdu, Sichuan 610000,
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Gansu 730000, China
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China
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* Corresponding Author: Zhijian WU; email: [email protected]
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Abstract: The Loess Plateau is one of the most seismically and geologically ac tive regions in China. The related catastrophic earthquakes and geological disasters have caused more than 1.4 million
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deaths in the plateau. In this study, the slopes on the edge of the loess tableland in Pingliang City,
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Gansu Province—the core area of the Loess Plateau—are investigated. Based on large-scale shaking-table model tests and discrete-element numerical simulation—particle flow code (PFC 2D), the dynamic-response characteristics and deformation evolution process of fissured and non-fissured loess slopes under different seismic loads are studied. The test results show that with increasing seismic load input, the peak ground displacement (PGD) of the loess slopes increases gradually with increasing slope height. For the two types of slopes, the acc eleration amplification effects in the slope with horizontal direction load are larger than those of the vertical direction load. The amplification factor of the peak ground acceleration (PGA) at the shoulder of the fissured slope is significantly 1
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larger than that of the non-fissured slope. According to the numerical simulation results of the fissured slope, when the seismic load is small, the bond-failures are distributed densely in the initial fissured structural plane and at the model bottom. Regarding the non-fissured slope, the bond-failures in the slope are mainly distributed at the bottom of the model. With increasing acceleration amplitude, the number of bond-failures in the slopes increases rapidly. When the input load increases to 0.40g, two
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potential slip surfaces occur in the shallow surface of the fissured slope and a potential slip surface
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appears at the back edge of the non-fissured slope.
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Key words: loess slope; shaking-table test; fissure; deformation evolution; PFC.
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Introduction
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The Loess Plateau is one of the main areas in which strong earthquakes and geological
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disasters frequently occur in China. Strong earthquakes have caused more than 1.4 million deaths in this area. The large quantity of landslides induced by earthquakes is the primary
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cause of huge casualties. The fissures in the (shallow) loess surface layer in this area are
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extremely developed and widely distributed, and they frequently induce landslides, collapses, and other geological disasters. Thus, the fissured loess layer constitutes a potential slip surface with the occurrence of landslides. Therefore, it is necessary to study the influence of fissures on the stability of slopes. Some researchers have investigated the fissured slope of the soil. For instance, Skempton et al. (1993) discovered that the fissures in the soil can soften the clay structure, thereby reducing the stability of the slope. André et al. (2013) considered that the development of surface fissures is an important indicator
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for understanding and forecasting slope movements. Li and Yang (2016) investigated the effects of vertical tension fissures and ground water on stability of slopes based on Power-Law nonlinear failure criterion. However, there are few studies on fissured loess slopes, and the influence of fissures on loess slopes under the action of earthquakes has not been studied.
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Shaking-table tests and numerical simulations are effective methods to study the
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dynamic response characteristics of slopes. Many researchers have done many scientific
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through the two methods and have obtained a lot of valuable results.
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Shaking-table tests can directly reflect the deformations and failure mechanisms of
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slopes under vibrations, and are therefore an important mean for studying the seismic
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dynamic-response and instability failure mechanisms of slopes (Lin and Wang, 2006). Recently, many researchers have designed shaking-table model tests to study the
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dynamic-response characteristics of slopes during earthquakes (Liu et al., 2014; Li et al.,
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2019). Feng et al. (2018) studied the dynamic-response characteristics of anti-dip, bedding, and homogeneous rock slopes with large-scale shaking- table tests. Furthermore, a large-scale shaking-table test was performed on a rock slope with discontinuous joints to study the dynamic characteristics under the combined action of earthquakes and rapid water draw-down (Song et al., 2017). Che et al. (2016) conducted a series of shaking table tests to evaluate the influence of wave propagation on the stability of a high and steep rock slope with bedding discontinuity joints. Srilatha et al. (2017) studied the effect of the slope
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angle on the seismic response of unreinforced and reinforced soil slopes through laboratory shaking- table tests. Li et al. (2018) studied the dynamic behavior of a dip slope with various geometric conditions under different external excitatio ns. However, there is no study on the shaking table tests of fissured loess slopes. Cundall and Strack proposed the discrete-element method (DEM) to study the structure
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and motion law of discontinuous particulate matter in 1979. In contrast to the description of
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particulate matter with the continuum theory, the DEM is a widely applied method and
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suitable for studying the macroscopic characteristics of materials from microscopic point
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of view. The Particle Flow Code (PFC) software is based on Newton's second law and the
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theory of force displacement. The software is used to simulate the motion of circular
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particle media and their interactions. Because the landslide block is not a rigid body and generally behaves like a quasi-rigid body (Tang et al., 2009), researchers frequently use the
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PFC model to analyze granular assemblages with purely frictional or bonded circular
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particles represented by discs (Tang et al., 2013). Furthermore, Wang et al. (2017) applied the particle DEM to predict deformation failures and unstable motion processes in landslide accumulations and landslide impact disasters. By using the PFC, Zhang et al. (2017) simulated the slide mechanism of the Zhengjiamo landslide and determined the features of the landslide dynamics with a five-stage model. Chang et al. (2004) simulated the mechanical process and accumulation behavior of the JiufenErshan landslide in Taiwan. Moreover, the dynamic response of a
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falling accumulation slope with different parameters under the action of the horizontal shear wave of the 2008 Ms8.0 Wenchuan earthquake was simulated. Yuan et al. (2014) concluded that the eroded underlying layer can increase the maximal migration distance of the slide body based on simulations of the Donghekou landslide induced by the Wenchuan earthquake. Feng et al. (2017) established a numerical modeling approach by coupling
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PFC and Fast Lagrangian Analysis of Continua (FLAC) codes to examine the
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characteristics of seismic signals induced by the Xiaolin landslide and to perform a
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parametrical study. Scaringi et al. (2018) used PFC to reproduce the Xinmo landslide and
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to simulate the kinematics and runout of the potentially unstable mass, which could cause a
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new catastrophic event. Moreover, Zhang et al. (2019) conducted field investigations and
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numerical modeling with PFC to investigate the characteristics of the Jiweishan rock avalanche and their implications for the fragmentation mechanisms. Due to the
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particularity of loess structure, the general numerical simulation methods have limitations
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for analyzing loess slopes. When studying the dynamic processes of these landsides, discrete element methods can be used as a powerful tool for failure analysis of fissured loess slope. In this study, shaking- table model tests on fissured and non- fissured loess slopes were conducted. The deformation of the slope surface was measured with high precision and in real time with a three-dimensional optical measurement and analysis system. The dynamic-response characteristics of the two slope types under different seismic loading
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conditions were analyzed considering the slope surface displacement and slope acceleration. Moreover, to study the discontinuous phenomena (crack propagation and failure) inside the slope body and to validate the shaking-table model tests, the particle flow dispersion elements were numerically analyzed. The results provide information on the deformation instability evolution laws of the two loess slope types.
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1. Shaking-table tests
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1.1 Test equipment and model
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The shaking-table model tests were conducted with two loess slope types in the Key
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Laboratory of Loess Earthquake Engineering of the China Earthquake Administration.
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The shaking table is driven by 28 servo motors, which can produce horizontal and
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vertical bidirectional vibrations. The main technical parameters are listed in Table 1. Rigid soil box is commonly used in shaking table model tests to study the dynamic
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characteristics of soil, but it also has disadvantages. The rigid boundary has effect on the
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dynamic response of the soil such as reflecting seismic waves and affecting soil deformation modes. Generally, some scholars have stuck flexible materials on the inner wall of the rigid box to reduce those effects. In comparison, the shear model box is more capable of simulating the shear deformation of the soil under dynamic loads. However, due to structural strength and size limitations, it is not applicable to large model tests. A rigid model box with a length of 2.8 m, width of 1.4 m, and height of 1.8 m was adopted for large loess slope model in this study. The box was fixed on the table and
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rigidly connected to it. To observe the deformations of the slip surface and lateral view of the slope during the tests, two transparent plexiglass plates with a thickness of 30 mm were installed along the length of the model box. In addition, closed-hole foam material (polyethylene) with a thickness of 3 cm was pasted onto both box ends to reduce the influence of the model box boundaries and the rigid reflections of the seismic waves on
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the side walls on the test results.
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1.2 Similitude design and material ratio
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Based on the similarity theory (Lu et al., 2015), the similarity constants of the basic
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dimensions were the geometric similitude ratio CL=25, density similarity constant Cρ=1,
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similarity constant of the vibration acceleration Ca =1, and similarity constant of the gravitational acceleration Cg =1. The similar constants of the remaining physical
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quantities were derived through the Buckingham π theorem and a dimensional analysis
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(Table 2). Cohesion similarity constant Cc= CLCρCg =25, elastic modulus similarity
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constant CE= CLCρCg =25, shear modulus similarity constant CG= CLCρCg =25, stress similarity constant Cσ= CLCρCg =25. The similarity ratio of other dimensionless quantities is 1, so Cφ=Cμ=Cε=1. According to the similarity ratio obtained, many direct shear tests and tr iaxial tests were carried out to determine the material ratio of the model slope. Finally, the material ratio closest to the target value is obtained by the above tests. The model slope in final was composed of loess, barite powder, fly ash, sawdust, and water at a ratio of
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5:2:2.1:0.3:0.6. The physical parameters of the prototypical and similar materials are listed in Table 3. 1.3 Model The test model is based on a fissured slope on the plateau edge of Pingliang, Gansu Province, the center of the Loess Plateau, and a non-fissured slope on the tableland is
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used as a contrast model. The prototype slope (Fig. 1) with Q3 loess is a typical fissured
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loess slope on the Loess Plateau. Q 3 loess is a typical unsaturated, special soil with large
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pores, under-compacted, and vertical fissures. There are two fissures, one deep and
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another shallow, developed on the edge of the tableland at the top of the slope. The model
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had two comparable slopes with equal material ratios, a gradient of 55°, and a height of
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110 cm. The underlying formation of the slopes was 10 cm thick. The left slope had two fissures: one was 50 cm long, 3 mm wide, and 20 cm deep; the other fissure was 100 cm
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long, 5 mm wide, and 30 cm deep. They were 10 cm and 20 cm away fro m the slope
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shoulder, respectively. The right reference model had no fissures. To build the model, the soil sample was screened, and large particles were removed. Next, the materials were stirred evenly based on the mix ratio to form the model. Afterward, the mixture was covered with a polyethylene plastic cloth and left to rest for 24 h. Finally, layered compaction was applied to fill the model; each layer was 10 cm thick. The next layer was added after the surface of the completed layer had been roughened.
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The weighed soil samples were poured into the model box and rolled to the designed compactness. After each layer was completed, the density was checked with cutting ring sampling to control the density and compactness of each layer. The moisture content was also checked to control it at 6.4%, which is consistent with the ratio of the water obtained in the above tests (Section 1.2). The slope surface was supported with shuttering to obtain
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the designed slope angle. Furthermore, two equally sized division p lates as design
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fissures were wrapped in plastic wrap, smeared with Vaseline, embedded into the left
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slope, and finally removed 24 h after the slope model had been formed. The completed
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model is illustrated in Fig. 2.
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1.4 Displacement and acceleration measurements
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The three-dimensional optical deformation measurement and analysis system was used to measure the slope displacements subjected to seismic loads. This method exhibits a
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high precision, fast speed, and an easy operation. In addition, it enables non-contact and
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full- field multi-data measurements (Song et al., 2018). The system is mainly composed of two cameras with a resolution of 2 million pixels, 2 illuminators, and a beam bracket (the length of the bracket is approximately 1 m). The highest acquis ition frequency is 340 Hz (340 frames per second, 6–8 m field of view at 5 m distance), and the measurement error is approximately 0.05–0.1 mm within a range of 5 m from the surface of the slope model. The illuminators were symmetrically arranged in front of and behind the model, and the
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camera was installed approximately 2.5 m above the measured model with scaffolds (Fig. 3). Based on the binocular stereo vision technology, two high-speed cameras were used to collect the real-time images of the object deformation during all stages. Based on the parallax of images recorded by the two cameras at different positions and the spatial
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geometric relationship between the camera positions, the accurate recognition of the
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marker points or digital speckle points, including the coding and non-coding marker
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points, can be used to achieve stereo matching to reconstruct the three-dimensional
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spatial coordinates and displacements of the surface points.
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After calibrating the camera, 42 non-coding marking points were set on the surfaces of
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the two slope models, as illustrated in Fig. 4, and the collected marking points were identified, located, and numbered, as illustrated in Fig. 5. The three-dimensional
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coordinates were reconstructed by solving the corresponding image coord inates in the
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camera images. Based on the three-dimensional coordinates of the marking points, the deformation states of each point on the surface of the slope model were analyzed. As the input seismic load increases, there will be a relative displacement between the slope model and the model box. The displacement caused by the relative motion will affect the accuracy of the measurement results of the slope monitoring points. To avoid the impact of relative displacement between the slope model and model box, we designed two reference cross-bars rigidly connected to the model box and placed 12 marking
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points on the cross-bars to obtain a reference displacement of the slope model; two cross-bars were installed in width direction of the model box and 5 cm above the front edge of the slope top (Fig. 4a). The measurement points of the acceleration sensors are illustrated in Fig. 6. The sensors are three-phase capacitive with sensitivity of 680 mV/g in X direction, 680 mV/g
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in Y direction, 680 mV/g in Z direction and ±2 g in range. The size of each acceleration
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sensor is 13mm×15mm×8mm. Eight accelerometers were symmetrically installed along
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the surfaces of the two slopes to compare the dynamic-response characteristics of the
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slope surface. The acceleration sensor A0 was installed on the shaking table to monitor
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the actual input seismic wave. The sensors A3, A7, A11, A15, A3', A7', A11', and A15'
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were used to analyze the variations in the acceleration response subjected to seismic
1.5 Input motions
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loads along the slope surface.
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Two loading wave types were adopted in the shaking-table model test: the Wenchuan earthquake wave recorded in Tangyu, Sichuan, China and the El Centro wave, the time history and Fourier spectrum of which are illustrated in Fig. 7 and 8, respectively. They were inputted in horizontal X and vertical Z directions, respectively. To study the dynamic response of the slope for different acceleration amplitudes of the seismic loads, working conditions with the input accelerations of 0.05 g, 0.10g, 0.20g, and 0.40g were
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applied step by step (Fig. 9). A total of 16 tests (16 different input motions) have been performed on the model. 2. Dynamic-response of loess slopes 2.1 Dynamic displacement response The peak ground displacement (PGD) distribution nepho grams were obtained by
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calculating the PGD values of each measurement point of the slopes under different
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working conditions. Fig. 10 illustrates the horizontal PGD distributions of the
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measurement points of the slopes for the Wenchuan Tangyu wave in X direction.
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According to the results, the PGD distributions are similar under different seismic
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intensity loads. With increasing slope height, the PGD increases gradually, i.e., the
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displacements at the slope foot and slope shoulder are the smallest and largest, respectively. Regarding the fissured slope, the PGDs are approximately 1.32 cm, 2.19 cm,
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3.63 cm, and 5.05 cm for input accelerations of 0.05g, 0.10g, 0.20g, and 0.40g at the
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slope shoulder, respectively. Regarding the non-fissured slope, the PGDs are approximately 0.85 cm, 1.46 cm, 2.49 cm, and 4.05 cm for input accelerations of 0.05g, 0.10g, 0.20g, and 0.40g at the slope shoulder, respectively. Thus, it can be seen the amplification effect of the fissured slope is greater than that of the non- fissured slope under horizontal loads. The experimental results indicate a small slope deformation. Furthermore, the slope is in a stable state when the seismic intensity of the input load is below 0.20g. With
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increasing seismic load, the deformation of the slope model increases, and the deformation displacement of the slope model exhibits a cumulative effect. The stronger the input ground motion, the larger are the cumulative deformations of different positions on the slope surface and the PGD. The fissures at the slope top develop gradually with increasing seismic load, and the PGD on the slope shoulder is approximately 1.5 times
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larger than that at the same position of the non-fissured slope under the same load.
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Fig. 11 illustrates the PGD distribution on the slope surface of the slope model under
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vertical loads. For a Wenchuan Tangyu wave in Z direction, the PGD distributions on the
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slope surface of the vertical and horizontal excitations are similar. Thus, the PGD
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increases with increasing slope height, and the amplification effect of the fissured slope is
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greater than that of the non-fissured slope. Regarding the fissured slope, the PGDs are approximately 1.03 cm, 1.76 cm, 3.08 cm, and 4.53 cm for input accelerations of 0.05g,
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0.10g, 0.20g, and 0.40g at the slope shoulder, respectively. Regarding the non- fissured
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slope, the PGDs are approximately 0.85 cm, 1.17 cm, 2.13 cm, and 3.51 cm for input accelerations of 0.05g, 0.10g, 0.20g, and 0.40g at the slope shoulder, respectively. The PGDs of the loess slopes under horizontal seismic load are slightly larger than those under vertical seismic load (approximately 1.1–1.3 times those of vertical seismic load). 2.2 Dynamic acceleration response By taking the dynamic responses of two slopes under the action of the Wenchuan Tangyu wave as an example, the acceleration distribution characteristics of the
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monitoring points of the model slope were analyzed. Fig. 12 shows time-history curves of A3, A15, A3', and A15' under horizontal load with an input acceleration o f 0.40g. In the fissured slope, the peak ground acceleration (PGA) of the shoulder is 2.9 times that at the slope foot. In the non-fissured slope, the PGA of the shoulder is 2.4 times that at the slope foot. There is a clear trend of increasing PGA from the foot of the slope to the shoulder.
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Fig. 13 illustrates the variations in the PGA amplification factor at each monitoring point
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of the slope under horizontal load. The slope height has an evident amplification effect on
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the seismic acceleration under equal seismic loads, and the amplification factor increases
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with increasing height. Along the slope measurement points A11 to A15, the acceleration
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amplification factor increases significantly, thereby exhibiting an evident free- face
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amplification effect. Thus, the shoulder of the slope is at the intersection of the two free faces of the slope and the top. At this point, the seismic wave is reflected and
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superimposed many times, which aggravates the amplification of the seismic waves.
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According to Fig. 13, the PGA amplification factor of the measurement point A15 is much larger than that of A15' (approximately 1.6 times that of the non- fissured slope), thereby indicating that the existence of fissures is more likely to cause damage to the slopes, particularly to the slope shoulders. The PGA amplification factor gradually increases from foot to shoulders of both slopes. This trend is more evident for the fissured slopes. Moreover, the amplification factor decreases with increasing input acceleration. The decreasing trend is very weak in the non- fissured slopes and more evident for the
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fissured slopes. On the shoulder of the fissured slope, the PGA amplification factor at 0.40g is approximately 1.3 lower than that at 0.05g (3.6). Nevertheless, the PGA amplification factor on the shoulder of the fissured slope is still larger than that of the non-fissured slope. Fig. 14 illustrates the variations in the PGA amplification factor at each monitoring
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point of the slope under vertical load. The variations in the peak acceleration
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amplification factors of the fissured and non-fissured slopes are similar to those under
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horizontal excitation. Both slopes exhibit elevation amplification and free- face
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amplification effects. However, the amplification effect is smaller than that under
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horizontal excitation (2/3 times that of a horizontal loading). Similarly, under a vertical
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load, the PGA amplification factor on the shoulder of the fissured slope is significantly larger than that of the non-fissured slope.
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In addition, Fig. 15 shows the PGA amplification factors of four different monitoring
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points in the middle of each slope under horizontal and vertical seismic loads. The internal PGA amplification factors of the two types of slopes tend to increase gradually along the height. The PGA amplification factors in the fissured slope are larger than that in the non- fissured slope. This magnification is more obvious under horizontal loads. In the fissured slope, the PGA amplification factor near the initial fissures increases more significantly, which is different from the non- fissured slope. Fig. 16 shows the PGA amplification factors of three monitoring points at the back of each slope under horizontal
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load. It indicates that the PGA amplification factors at back of the non- fissured slope are evidently larger than that of the fissured slope. Due to the reflection of the seismic wave at the initial fissures and the low-density soil near initial fissures absorbed most of the energy, the initial fissures have become barriers to prevent the propagation of the seismic wave, which greatly attenuated the energy at the back edge.
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By comparing the variations in the displacement and acceleration response of the two
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slope types, it can be concluded that the amplification factors of PGD and PGA exhibit
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the elevation effect and free-face amplification effect under seismic loads. In the
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elevation effect, with increasing slope height, the amplification factors of PGD and PGA
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increase and reach their maxima on the slope shoulder. The free-face amplification effect
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shows that the closer the slope shoulder, the more evident are the increases in the slope displacement and acceleration. In addition, the fissures have a certain influence on the
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effect.
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slope displacement and acceleration response, which exhibits an evident amplification
2.3 Failure characteristics After investigating the seismic loads of each working condition, the fissures and deformations on the model side were documented with photos and sketches (Fig. 17). For an input acceleration of 0.05g, the slope model exhibits no significant changes, only a small amount of soil particles fall down at both slope surfaces. For an acceleration of 0.10g, a small number of fissures occur near the initial fissures on the fissured slope, and
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few fissures occur at both slope tops and on the slope surfaces. However, the fissured slope has more new fissures than the non-fissured slope. For an acceleration of 0.20g, more new fissures appear near the fissured slope surface and the initial fissures. Under the initial fissure near shoulder of the fissured slope, several fissures develop and form a through potential slip surface. Large settlement occurs at the shoulder of fissured slope.
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New fissures in the non- fissured slope only appear in the shallow surface and at the slope
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top, and the settlement at shoulder of the non-fissured slope is small. Shallow-surface
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particles slip along the slopes and accumulate at the both slope feet. For an acceleration
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of 0.40g, the fissures continue to increase and expand inside both slopes. Shear failure
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appears at the fissured slope foot, and the shallow landslide occurs. Besides, fissures
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behind shallow landslide form a new potential slip surface, and large settlement and several settlement differences occur on the top of the fissured slope. Although the
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non- fissured slope also exhibits many new fissures, the upper settlement at the shoulder is
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less than that of the non- fissured slope, and there isn’t obvious settlement difference appearing. The non- fissured slope is relatively stable, but fissures at back edge quickly extend to interior and approach to form a potential slip surface. In the deformation process of two slopes, at the same excitation level, there is no significant difference in settlement caused by horizontal and vertical loads, but the horizontal seismic loads have greater influence on the development of fissures in slopes than vertical seismic loads. In addition, there are influence differences in the size of
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initial fissures in the fissured slope. The deep fissure (left fissure) extends downward to form a deeper potential slid surface and the shallow fissure (right fissure) expands to the surface of the slope. According to the developments of the lateral fissures in both slope types in Fig.17, with increasing seismic loads, the fissures mainly concentrate around the fissured structure plane of the fissured slope, which increases and propagates along the
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position of the initial fissures and gradually forms potential slip surface in the fissured
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slope. Regarding the non-fissured slope, the fissures first appear near the free face near
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the slope body side and gradually extend into the slope. When the seismic load reaches
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up to 0.40g, fissures at back edge extend quickly into the interior of slope and approach
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the tops and sides of two slopes.
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to form a potential through slip surface. Fig.18 shows the final damage phenomenon of
3. Simulation of seismic dynamic failure process
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3.1 Numerical modelling
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The slope model was simulated with PFC 2D according to the shaking-table model tests. The steps were as follows: (1) the software built- in command "wall generate" was used to construct the boundary of the enclosed area (i.e. "wall") based on the designed model size. In the process of modeling, the wall could constrain the generation range of particles, and the wall could also be used as the boundary to impose constraints ; (2) the meso-parameters of the model were determined based on PFC 2D biaxial compression simulations (Table 4); In combination with the parameters in Table 4, the "ball distribute"
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command was used to generate particles; the gravity acceleration was set for all particles; the iterative calculation under gravity was conducted until the set equilibrium state was reached; (3) the floating point in the particle group was calibrated; the particles outside the slope profile were eliminated based on the required model size; and (4) the parallel bonding model and smooth-joint contact model were applied to the particles; the fissure
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structure surface was generated (Fig. 19). After each step, the internal stress of the model
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was balanced.
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In order to ensure that the slope was in the initial equilibrium state, the velocity field
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and displacement field of the slope model were reset. In addition, the meso-parameters
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such as the particle bonding strength were assigned to the slope model. Simulated
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Wenchuan Tangyu wave and applied the horizontal direction seismic load to the slope model. To simplify the loading of the seismic waves in PFC 2D, an acceleration time
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history curve was integrated to obtain the velocity time history curve. Afterward, instead
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of applying the seismic load, the velocity time history curve was applied to the “wall”. 3.2 Contact model and calibration of micro-parameters The PFC model simulates the movements and interactions of many finite-sized particles. The particles are rigid bodies with finite masses that move independently and can translate and rotate. The particles interact through pair-wise contacts through an internal force and moment (Potyondy 2015). The interaction between the particles reflects the micro- mechanical behavior of the matrix of the bulk media, which is
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generally described with a particle contact constitutive model, for which the contact bonding and parallel bonding models are the most commonly applied models (Potyondy et al., 2004). Currently, the parallel bonding model is the most commonly used particle contact constitutive model to establish a PFC 2D model of rock and soil (Lee et al., 2011;
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Ghazvinian et al., 2012). The parallel bonding model was chosen as constitutive model
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for the particle contact in this study. For the simulation of cracks in slopes, the “dfn”
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command was used. Furthermore, the smooth-joint model was used to represent the
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contact modes of the joints and cracks. Joints can be added to the base material with the
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smooth-joint logic (Itasca, Consulting Group Inc., 2014; Mas Ivars et al., 2008) by which
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each joint is associated with an interface consisting of a collection of smooth-joint contacts between grains upon opposite sides of the joint. The smooth-joint contact model
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simulates the behavior of an interface, regardless of contact orientations along the
interface.
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interface by effectively modifying the surfaces of the contacting grains to align with the
In general, the parameters of the particles and bonds in the particle flow model are quite different from the macroscopic parameters. Therefore, when establishing the model, the micro-parameters must be calibrated by matching the soil parameters obtained from the numerical and indoor tests. Thus, the micro-parameters must be inferred from the known soil parameters (e.g., cohesion, internal friction coeffic ient, elastic modulus, and
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Poisson's ratio). The stress-strain relationship measured curve and the calculation curve are obtained through triaxial tests and the simulation of biaxial compression tests (Fig. 20). It shows that the measured value is basically consistent with the calculated value. In this study, the micro-parameters of the model were determined based on PFC 2D biaxial compression simulations (Table 4).
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3.3 Evolution process of bond-failures in slopes
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Fig. 21 illustrates the evolution process of the bond- failures in the two slopes.
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Evidently, the slopes experience significant bond-failure generations and slope failure
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developments. The number of bond- failures increases rapidly with gradually increasing
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seismic loads. For a seismic intensity of 0.05g, bond- failures appear at the slope bottoms.
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In the left, fissured slope, the new bond- failures appear around the two original fissures on the slope top and begin to enter the slope. The left slope exhibits a total of 419
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bond- failures; the right slope has only 187 bond- failures. For an intensity of 0.10g, the
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number of bond-failures in the slopes increases rapidly (2348 bond- failures). The fissures are dense at the structural plane and trailing edge of the left slope model. However, the bond- failures are mainly concentrated at the bottom of the right slope model. In addition, the upper part of the right slope exhibits no bond-failures. For an acceleration intensity of 0.20g (3753 bond- failures), the bond-failures in the left and right slopes develop rapidly and densely on the slope surface. Moreover, most particles are not bonded anymore. The structural fissure plane of the left slope is nearly destroyed, and many bond- failures are
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distributed on the surface, foot, and rear edge of the slope. Furthermore, bond- failures begin to appear at the trailing edge of the right slope. For an input intensity of 0.40g (5035 bond- failures), the numbers of bond- failures of the two slopes are similar. Finally, the particles in the slope are not bonded anymore. The slope collapses along the failure surface, and the shallow-layer particles of the slope surface slip.
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The entire bond- failures development is as follows: In the fissured slope, a small
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number of bond-failures first occur near the initial fissures and at the slope bottom. With
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increasing acceleration input, new bond-failures occur along the position of the initial
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fissures and propagate toward the slope interior. In the non-fissured slope, the
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bond- failures first appear at the slope bottom and then move upward. However, the
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development of the bond-failures does not occur as fast as that of the non-fissured slope. When a local seismic wave propagates through both slopes, it is reflected and refracted in
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the fissure. When the seismic wave propagates to the slope surface, it is reflected and
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refracted at the slope surface. As a result, the seismic wave in the slope becomes locally superimposed, which makes the slope more prone to a plastic deformation. 3.4 Simulation and analysis of motion process Fig. 22 indicates the results of the numerical simulations of the deformation and instability process of the fissured slope (left model) and non- fissured slope (right model) induced by seismic loads. The red dashed line in the figure is the contour line of the slope model before the seismic loads. For a seismic intensity of 0.05g, the displacements of the
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particles on the top of the fissured slope are significantly larger than those of the non- fissured slope, particularly around the structural plane of the fissure in the left model. The displacements of the particles in horizontal direction are generally larger than those in vertical direction. Thus, the direction of the particle motion is mainly horizontal. For both loess slope types, the particle displacements on the shoulder and in the surface layer
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are the largest, followed by the displacement at the slope center, the displacement of the
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trailing edge, and the displacement of the underlying layer (Fig. 22a).
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According to Fig. 22b, the value and range of the particle displacement increases at the
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shoulder and surface of the two slopes for a seismic intensity of 0.10g. Moreover, some
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particles close to the structural plane of the fissure of the left model and in the shallow
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surface of the slope are not bonded anymore. The particles in the shallow surfaces of both slope types are loosened, and a small number of particles slip down the slope. In addition,
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a slight seismic subsidence occurs on the slope shoulders.
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Fig. 22c illustrates that the top location of the slope is evidently lower than the red dashed line for a seismic intensity of 0.20g. Thus, the seismic subsidence occurs at the slope top, and the seismic subsidence of the left slope is slightly larger than that of the right slope. In addition, the particles on the shallow surface of the slopes slip down the slope and accumulate at the slope foot. Finally, for a seismic load of 0.40g, the bonds between the particles in both slopes continue to break, and two potential circular slip surfaces are generated; the shallow slip
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surface spreads along the propagation direction of the two fissures in the left slope. However, a potential circular slip surface appears at the back edge of the right non- fissured slope. Seismic subsidence occurs in both slopes; the seismic s ubsidence of the left slope is stronger than that of the right slope. In conclusion, the bonding between particles is controlled by the cohesive strength and
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their friction coefficients in the PFC model. If the actual tension or tangential force
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among particles is greater than the corresponding cohesive strength, the bonding among
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particles disappears. The fissures appear between particles owing to the appearance of a
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cohesive strength failure. The cohesive strength in the initial fissures is weakened owing
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to the stress concentration, which leads to the expansion of the fissures and to a potential
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slip surface. Thus, the potential slip surface of a fissured slope is shallower than that of a non- fissured slope, and the initial fissures affect the position o f the final slip surface. In
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general, the slope experiences a gradual failure under a seismic force. The occurrence of
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landslides is closely related to the development of fissures. A seismic force will induce fissures that expand and extend, thereby forming a potential slip surface in the slope structure, which could result in landslides. 4. Conclusions A large-scale shaking-table model test was performed to study the dynamic-response characteristics of fissured and non- fissured loess slopes under seismic loads. In addition, PFC 2D was used to analyze the displacement and deformation process of the slope
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model. These results suggest that the two types of loess slopes have different dynamic-response characteristics and deformation process under seismic loads. The conclusions are as follows: The PGDs in the fissured and non- fissured loess slopes increase gradually with increasing slope height under seismic loads. The shoulder of the fissured slope
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experiences a bigger PGD than that of the non-fissured slope (approximately 1.5 times
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larger). When the seismic- input direction is horizontal, the PGD of the slope surface is
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slightly larger than that of the vertical loading (1.1–1.3 times larger).
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The acceleration amplification effect under horizontal input loads is greater than that
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under vertical loads. Both slopes reach the maximum on their shoulders. Hence, the
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elevation amplification and free- face amplification effects occur. Regarding the fissured slope, the amplification of PGA is significantly larger than those of the shoulder and
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slope surface of the non-fissured slope (approximately 1.6 times larger).
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With increasing seismic loads, the number of fissures continues to increase, and the loess slopes experience a gradual failure (transition from local to globa l failure) under seismic loads. The fissures propagate along the initial fissures in the fissured slope and the initial fissures are extremely easy to form potential slip surfaces. When the seismic load reaches to 0.40g, large deformation and potential slip surfaces occur on two types of loess slopes which could result in landslides. Acknowledgements
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This study is financially supported by the National Natural Science Foundation of China (No. 41472297), The Second Tibetan Plateau Scientific Expedition and Research (STEP) program (Grant No. 2019QZKK0905) ， the scientific research foundation for the introducing talent of Nanjing Tech University, and the Key Project of Natural Science Foundation of China (No.41630636).
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Li L.Q., Ju N.P., Zhang S., Deng X.X., 2019. Shaking table test to assess seismic response differences between steep bedding and toppling rock slopes. Bull. Eng. Geol. Environ. 78(1), 519-531 Li H. H., Lin C.H., Zu W., 2018. Dynamic response of a dip slope with multi-slip planes revealed by shaking table tests. Landslides 15,1731-1743 Li Y.X., Yang X.L., 2016. Stability analysis of crack slope considering nonlinearity and water pressure. KSCE J. Civ. Eng., 20 (6), 2289-2296 Lin M.L., Wang K.L., 2006. Seismic slope behavior in a large-scale shaking table model test[J]. Eng. Geol. 86(2), 118-133 Liu H.X., Xu Q., Li Y.R., 2014. Effect of Lithology and Structure on Seismic Response of Steep Slope in a Shaking Table Test. J. Mt. Sci 11(2), 371-383 Lu P., Wu H., Qiao G., 2015. Model test study on monitoring dynamic process of slope failure through spatial sensor network. Environ. Earth Sci. 74(4), 3315-3332 Lee H., Jeon S., 2011. An experimental and numerical study of fissure coalescence in pre-cracked specimens under uniaxial compression. Int. J. Solids Struct. 48(6), 979-999. 26
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Taiwan: insights from a discrete element simulation. Eng. Geol. 106, 1-19. Tang C.L., Hu J.C., Lin M.L., 2013. The mechanism of the 1941 Tsaoling landslide, Taiwan: insight
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14(5), 1195-1205 Zhang M., Wu L.Z., Zhang J.C., 2019. The 2009 Jiweishan rock avalanche, Wulong, China: deposit characteristics and implications for its fragmentation. Landslides 16(5), 893-906. Zhang Z.L., Wang T., Wu S.R., 2017. The role of seismic triggering in a deep-seated mudstone landslide, China: Historical reconstruction and mechanism analysis. Eng. Geol. 226, 122-135 Table 1 Technical parameters of shaking table test system Parameters
Technical specification
Table size
4m×6m
M ode of motion
Horizontal one-way, vertical one-way, horizontal and vertical coupling
Input waveform
Regular wave, random wave, seismic wave, artificial wave
M aximum bearing capacity
X、Z(single vibration): X, 20t; Z, 15t X、Z(combined vibration): X, 15t; Z, 15t 27
Journal Pre-proof M aximum displacement
X、Z(single vibration): X, ± 250 mm; Z, ± 100 mm X、Z(combined vibration): X, ±150mm; Z, ±100mm
M aximum velocity
X、Z(single vibration): X, 1500mm/s; Z, 700mm/s X、Z(combined vibration): X, 1000mm/s; Z, 700mm/s
M aximum acceleration
X、Z(single vibration): X, 1.7g; Z, 1.2g X、Z(combined vibration): X, 1.2g; Z, 1.0g
Range of operating frequency
X、Z(single vibration): X, 0.1～70Hz; Z, 0.1～50Hz X、Z(combined vibration): X, 0.1～50Hz; Z, 0.1～50Hz
Table 2 Similarity relations of model Similarity relations
Similarity constants
Length (L)
CL
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Density (ρ)
C
Acceleration (a)
Ca
Elastic modulus (E)
CE CLC Cg
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Shear modulus (G)
CG CLC Cg
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Stress (σ)
C CLC Cg
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C
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Cc CLC Cg
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Internal friction angle ( )
C
1
Strain (ε)
C 1
1
Gravitational acceleration (g)
Cg
1
Time (t)
Ct CL1/ 2Cg 1/ 2
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Cohesion (c)
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Poisson's ratio (μ)
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Table 3 Similarity parameters of soil Elastic modulus, M aterial type E (M Pa)
Cohesion, c(kPa)
Density, ρ(g/m3)
Internal friction angle, φ(°)
Prototype
72
22.27
1.36
14.5
M odel
20.8
7.44
1.36
20.2
Table 4 M icro-parameters obtained by calibration. Parameters
Description
Value
ball_kn
Ball normal stiffness（Pa）
2.3e7
ball_ks
Ball shear stiffness（Pa）
2.3e7
r_max
M aximum ball radius（mm）
15
r_min
M inimum ball radius（mm）
8
ball_fric
Ball friction coefficient
0.2
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Journal Pre-proof Parallel bond normal/shear stiffness ratio
1
pb_fa
Parallel bond friction angle（°）
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pb_ten
Parallel bond tense strength（Pa）
6e4
pb_coh
Parallel bond cohesive strength（Pa）
1.2e5
pb_fric
Parallel bond friction coefficient
0.4
pb_rmul
Parallel bond radius multiplier
0.8
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Fig.1 The prototype slope
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Fig.2 Lateral view of model slopes
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Fig.3 Layout position of optical measurement system
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Fig.4 Layout of mark points of surface displacement. (a) M odel slope, and (b) sketch map
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Fig.5 (a) Image Recognition and Location, and (b) Reconstruction of three-dimensional coordinates
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Fig.6 Layout of accelerometers on slope surface of model
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(a) Fig.7 WenchuanTangyu loading wave. (a) Time history, and (b) Fourier spectrum
(a) Fig.8 El-Centro loading wave. (a) Time history, and (b) Fourier spectrum
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（b）
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（a）0.05g
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Fig.9 Loading sequence of the shaking table test
（b）0.10g
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（c）0.20g
（d）0.40g
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Fig.10 PGD distribution on the slope surface of the slope model under horizontal loads (unit:mm)
（a）0.05g
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（b）0.10g
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（d）0.40g Fig.11 PGD distribution on the slope surface of the slope model under vertical loads (unit:mm)
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(b) A3'
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（a）A3
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(c) A15 (d) A 15' Fig.12 Acceleration time history curves of A3, A15, A3', and A15' under horizontal load with input load of 0.40g
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(a) (b) Fig.13 Variations in the PGA amplification factor at each monitoring point of the slope surface under horizontal load. (a) Fissured slope, and (b) Non-fissured slope
(a) (b) Fig.14 Variations in the PGA amplification factor at each monitoring point of the slope surface under vertical load. (a) Fissured slope, and (b) Non-fissured slope
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(a) (b) Fig.15 PGA amplification factors in the middle of the slopes. (a) horizontal load, and (b) vertical load
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Fig.16 PGA amplification factors in the back of the slopes under horizontal load. (a) Fissured slope, and (b) Non-fissured slope
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（c）0.20g
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（d）0.40g Fig.17 Deformation evolution process of slope models (shaking table test) 39
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(a) Fissured slope Fig.18 The final damage phenomenon of two slopes
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Fig.19 Contact model
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(b) Non-fissured slope
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（a）0.05g
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Fig.20 the results of the calibration test (solid lines indicate measured value, and dotted lines indicate calculated value.)
（b）0.10g
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（c）0.20g
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（d）0.40g Fig.21 Evolution process of the bond-failures in the two slopes
（a）0.05g
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（c）0.20g
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（d）0.40g Fig.22 Deformation evolution process of slope models (numerical simulation)
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The large-scale shaking-table model tests for the fissured and non-fissured loess slopes are conducted.
The deformations evolution processes of the two types of slope models are simulated based on a numerical calculation model established with the particle flow code (PFC 2D).
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The deformation evolution characterictics of the fissured and non-fissured loess slopes are revealed.
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CRediT author statement Zhijian
Wu:
Conceptualization,
Methodology,
Formal
Writing-Review & Editing Dan Zhang: Writing-Original Draft, Software, Visualization
Chao Liang: Investigation, Data Curation
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Duoyin Zhao: Investigation, Data Curation
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Shengnian Wang: Software, Writing-Review & Editing
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analysis,
Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may
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be considered as potential competing interests:
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