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Article

Analysis of Failure Mechanism of Medium-Steep Bedding Rock Slopes under Seismic Action

by
Xiuhong Zheng
1,
Qihua Zhao
1,*,
Sheqin Peng
1,
Longke Wu
2,*,
Yanghao Dou
1 and
Kuangyu Chen
1
1
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China
2
Guangxi Communications Design Group Co., Ltd., Nanning 530025, China
*
Authors to whom correspondence should be addressed.
Sustainability 2024, 16(17), 7729; https://doi.org/10.3390/su16177729
Submission received: 10 August 2024 / Revised: 1 September 2024 / Accepted: 3 September 2024 / Published: 5 September 2024
(This article belongs to the Special Issue Sustainability in Natural Hazards Mitigation and Landslide Research)
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Abstract

:
Medium-steep bedding rock slopes (MBRSs) are generally considered relatively stable, because the dip angle of the rock layers (45–55°) is larger than the slope angle (40–45°). However, the stability of MBRSs was significantly impacted during the 1933 Diexi earthquake, leading to slope instability. Field investigations revealed that no continuous sliding surface was recognized in the failure slopes. Instead, the source areas of landslides present a “reverse steps” feature, where the step surfaces are perpendicular to the bedding surface, and their normal directions point towards the crest of the slopes. These orientations of “reverse steps” differ significantly from those of steps formed under static conditions, which makes it difficult to explain the phenomenon using traditional failure mechanism of the slope. Therefore, a large-scale shaking table test was conducted to replicate the deformation and failure processes of MBRSs under seismic action. The test revealed the elevation amplification effect, where the amplification factors of the acceleration increased with increasing elevation. As the amplitude of the input seismic wave increased, the acceleration amplification factor initially rose and subsequently decreased with the increase in the shear strain of the rock mass. The dynamic response of the slope under Z-direction seismic waves is stronger than that under X-direction seismic waves. The deformation and failure were mainly concentrated in the upper part of the slope, which was in good agreement with the field observations. Based on these findings, the deformation and failure mechanism of MBRSs was analyzed by considering both the spatial relationship between the seismogenic fault and the slope, and the propagation characteristics of seismic waves along the slope. The seismic failure mode of MBRSs in the study area was characterized as flexural–tensile failure. This work can provide a reference for post-earthquake disaster investigation, as well as disaster prevention and mitigation, in seismically active regions.

1. Introduction

Earthquake-induced landslides are one of the most destructive natural hazards and lead to an enormous loss of property and human lives [1]. Understanding the failure mechanisms of the slope under seismic action is crucial for the sustainable development of the region. On 25 August 1933 at 5:45 (Beijing time), a disastrous earthquake with a magnitude of 7.5 occurred in Diexi Town, Sichuan province, China. The epicenter was located at 32°2′2″ N, 103°41′5″ E, at a depth of 15 km. The seismic intensity was Level X on the Chinese Seismic Intensity Scale [2]. This earthquake destroyed the ancient town of Diexi and caused landslides, collapses, river blockages, dam breaks, and other disasters. These earthquake damages were primarily distributed in the valleys, with the majority concentrated in Songping Valley, forming a seismic deformation zone approximately 30 km in length along Songping Valley [3].
A detailed field investigation of the slopes was conducted in the main valley of Songping Valley, and it was found that the deformation and failure of the slopes were controlled by the seismogenic fault (the Songpinggou Fault). The failure slopes are linearly distributed along the fault, mainly concentrated in the middle and SE segments of the fault (Figure 1). These slopes are located within a horizontal distance of less than 3 km from the seismogenic fault. Among them, the medium-steep bedding rock slopes (MBRSs) are generally considered relatively stable, because the dip angle of the rock layers (45–55°) is larger than the slope angle (40–45°). However, these MBRSs were extensively damaged during the 1933 Diexi earthquake.
At present, many scholars have conducted extensive research on the seismic failure mechanisms of MBRSs using various methods, including field investigation analyses [7,8,9], numerical simulations [10,11], laboratory model testing [12,13], and analytical methods [14,15]. They have categorized the deformation and failure modes of MBRSs under seismic action into the following two types: tensile fracturing–sliding and sliding–buckling. The main characteristics of these modes are the tensile fracturing at the rear of the slope, sliding along the bedding planes, and failure at the front in the form of shearing or buckling.
However, through field investigations and analysis, a new dynamic deformation and failure mode—the flexural–tensile failure—has been discovered in the MBRSs of Songping Valley. Previous studies have indicated that the flexural–tensile failure generally occurs in bedding and anti-dip layered slopes where the rock layer dip angle exceeds 60° [16,17,18], whereas it is rarely observed in MBRSs. Given the particularity of the flexural–tensile failure in MBRSs, it is necessary to study the instability mechanisms of this type of slope under seismic action.
Shaking table model tests, as a method for directly observing the slope failure process, are repeatable and have been widely adopted by researchers [19,20,21,22,23]. Based on field investigations, this paper conducted a large-scale shaking table test to simulate the deformation and failure process of MBRSs. Furthermore, the deformation and failure mechanism of the slopes was analyzed by considering both the spatial relationship between the seismogenic fault and the slope, and the propagation characteristics of seismic waves along the slope. The results can provide a theoretical reference for the early identification of deformation and failure in MBRSs located in areas of high seismic intensity.

2. Study Area

2.1. Geological Background

The study area, located in the Songping Valley watershed of Mao County, Sichuan Province, is situated at the transition zone between the Qinghai–Tibet Plateau and the northwest Sichuan Basin (Figure 2) [24]. This region is distinguished by its moderate-to-high elevation, a result of tectonic erosion, and the valley forms a distinctive “V” shape. The strata exposed in the area are attributed to the Triassic period, specifically the Zagunao (T2z) and Zhuwo (T3zh) formations, which are predominantly metamorphic sandstone (see Figure 1) [4,5].
The neotectonic movement in the study area is intense, which primarily manifests as intermittent crustal uplift and fault activity [27]. Due to this fault activity, seismic activity in the study area has been frequent since the Holocene. From 1872 to 2017, there were 27 earthquakes with magnitudes between Ms5.0 and 5.9, as well as 6 earthquakes with magnitudes between Ms6.0 and 7.0, within a 300 km radius of the study area [28]. Notable earthquakes exceeding MS7.0 include the Diexi earthquake (Ms7.5, 1933), the Songpan earthquake (Ms7.2, 1976), the Wenchuan earthquake (Ms8.0, 2008), and the Jiuzhaigou earthquake (Ms7.0, 2017) (Figure 2). Among them, the Diexi earthquake had the most significant impact on the study area. The seismogenic fault responsible for this earthquake is the Songpinggou Fault, which develops along the Songping Valley and has a NW strike, with a dip angle of 55–80°. It is composed of NW, middle, and SE segments, where the NW segment dips NE and the others dip SW [6] (Figure 1). The fault is a strike–slip reverse fault dominated by counterclockwise horizontal dislocation.

2.2. Deformation and Failure Characteristics of Slope

The bedding slopes in the study area are primarily located on the left bank of Songping Valley. Given that the gradients of these slopes are 40–45° and the dip angles of the rock layers are 45–55°, they are referred to as MBRSs. Through field investigations, it was found that the rear edge of these failure slopes exhibits “reverse steps”, composed of residual rock layers. The step surfaces are perpendicular to the bedding surface, and their normal directions point towards the crest of the slope (Figure 3). Among them, the landslide at the entrance of Songping Valley (SPVE landslide) is a typical example (Figure 4a–c). The DEM (digital elevation model) image shows that the rear edge of this landslide is stepped, 3–6 m in width, with an east–west extension length of 60–240 m (Figure 4d,e).
At the same time, small steps were identified on the exposed bedding planes at the rear edge of the SPVE landslide. Based on the Digital Orthophoto Map (DOM), the steps at the rear edge of the landslide were identified, and the lengths and orientations of each step were measured using ArcMap 10.2 software. It was found that 202 steps were developed on the bedding plane, which is roughly 12,000 m2 (Figure 5a,b). These steps exhibit a jagged or undulating extension, with lengths of 2–25 m. The predominant strike of these small steps is N70–80° E (Figure 5c), which is the same as the strike of the “reverse step” observed on the 3D and DEM images (Figure 4). Additionally, a series of densely packed, linear, and parallel scratches was discovered on the bedding plane, oriented in the direction of N29° E (Figure 5a,b). These scratches are generally shallow and their depth at either end is not significantly different.
Topographically, the two “reverse steps” at the rear edge of the SPVE landslide (places A and B in Figure 4 and Figure 6) are both located at the transition zones between steep and gentle slopes (Figure 6). The relative slope height ratio of these locations to the adjacent gentle slope platforms is 0.7–0.8. Previous studies have indicated that these transition zones exhibit a more intense seismic response compared to other areas [29]. Furthermore, combined with the development of nearby vegetation, it is further confirmed that these two “reverse steps” were formed during the 1933 Diexi earthquake. They are identified as the source areas of SPVE landslides.
Based on the field investigation, the above-mentioned steps and scratches were found exclusively in the landslide source areas. Apart from the bedding planes, no other structural planes have been observed within the slopes. In addition, the orientations of these “reverse steps” significantly differ from those of steps formed under static conditions (Figure 7), which makes it difficult to explain the phenomenon with traditional failure mechanisms of the slope. Consequently, it can be concluded that the “reverse steps” and scratches in the landslide source areas were formed under seismic action.

3. Shaking Table Test

Shaking table tests can visually reflect the deformation and failure processes of slopes under seismic action, which is an important means for revealing the seismic response and failure mechanisms of slopes [20,30]. Therefore, a shaking table test was conducted to study the deformation and failure mechanism of MBRSs. The shaking table model test was carried out at the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology. The shaking table, with three dimensions and six degrees of freedom, is capable of achieving loading in the horizontal, vertical, and horizontal–vertical coupled directions. The main technical parameters of the shaking table are listed in Table 1.
The entire test process includes calculating the similarity ratio, determining the ratio of similar material, designing and creating the slope model, arranging acceleration sensors, and determining the loading conditions.

3.1. Similarity Relations and Similar Materials

The similarity design of the test model is necessary as the test cannot meet the geometric dimensions of the prototype slope [23]. The determination of the similarity relation is a crucial factor for the success of the shaking table test [31]. In this test, dimension (L), density (ρ), and gravitational acceleration (g) were selected as the control parameters. The density (ρ) and gravitational acceleration (g) of the model remained the same as those of the prototype, so the similarity ratios for both were set to 1. Meanwhile, considering the actual slope height and the size of the model box, the dimension (L) similarity ratio was determined to be CL = 200. Additionally, the other physical quantities were deduced by the Buckingham theorem π [32] and dimensional analysis [33], as shown in Table 2.
The physical–mechanical parameters of the prototype slope were obtained from the Geological Engineering Handbook [34]. The corresponding physical–mechanical parameters of the model slope were determined based on the similarity ratios presented in Table 2. The physical and mechanical parameters for both the prototype slope and the model slope are listed in Table 3. According to the previous research on the properties of similar materials [35], iron powder, barite powder, quartz sand, gypsum, rosin, and alcohol were selected as similar materials of the slope model in this test. Among them, alcohol is volatile, which is conducive to faster drying of the model slope and a shorter test period. Meanwhile, through an orthogonal test, the mass ratio of iron powder, barite powder, quartz sand, gypsum, rosin, and alcohol was determined to be 12.8:51.1:21.3:9.5:0.3:5. Furthermore, plastic film was used to simulate the bedding planes in the model slope [36].

3.2. Model Design and Model Construction

Based on the dimension similar ratio and the characteristics of MBRSs in the study area, a simplified model slope was designed, as shown in Figure 8. The model measures 1650 mm in length, 1480 mm in height, 950 mm in width, and has a slope angle of 40°. Both the model slope angle and the rock layer dip angle were set to the average values of the natural slope angle and the rock layer dip angle, which were 40° and 50°, respectively. According to the dimension similarity ratio, the calculated thickness of the rock layers is less than 1 cm. Thus, considering the feasibility of model production, the thickness of the rock layers was set to 10 cm. To overcome the rigid boundary effect on the test results, the foam boards with a thickness of 10 cm were pasted on both ends of the model box. These foam boards can absorb the energy of the seismic wave at the boundary [37,38,39]. Simultaneously, a 10 cm-thick buffer layer was laid at the bottom of the model box to reduce bottom boundary effects. The buffer layer materials are identical to those of the model. The designed model slope is shown in Figure 6. Furthermore, transparent plexiglass was installed along the length of the model box to facilitate the observation of the deformations of the slope during the tests.
Before constructing the model, the outline of the model was sketched on the sidewall of the model box (Figure 9a). The model slope was constructed using a layer-by-layer compaction method. The specific steps are as follows: (1) weighing similar materials proportionally and blending them evenly; (2) pouring the mixed materials into the model box and compacting to the desired density; (3) after completing a layer, scraping the surface, covering it with plastic film to simulate the bedding plane (Figure 9b,c), and marking the position of the bedding plane with a 5 mm-thick black material at the interface between the bedding plane and the plexiglass (Figure 9b); and (4) embedding accelerometers at specified locations. The above steps were repeated until the model reached its designed height. The completed model is illustrated in Figure 10.
Nineteen three-component accelerometers (named A1 through A19) were installed in the model slope to monitor its dynamic response. To minimize the side boundary effect, these sensors were embedded into the center of the model slope [40]. Meanwhile, accelerometer A0 was affixed to the shaking table to monitor the actual input seismic waves. The specific locations of the accelerometers are shown in Figure 6. All of these accelerometers are three-component capacitive types, with a sensitivity of 98 mV/g, a measurement range of ±50 g, and a frequency response ranging from 0.5 to 7000 Hz.

3.3. Seismic Loading Schemes

To investigate the dynamic response of slopes to various ground motion parameters, the test utilized sine waves and field-measured natural waves. The sine waves have frequencies of 5 Hz, 8 Hz, and 15 Hz. At the time of the 1933 Diexi earthquake, the Chinese Seismological Network had not yet been established, resulting in no recorded seismic wave data. The seismogenic fault of the 2017 Jiuzhaigou earthquake has the same characteristics as that of the 1933 Diexi earthquake. Both faults are strike–slip reverse faults dominated by counterclockwise horizontal displacement [3,6,41,42,43,44]. Therefore, the test selected the seismic waves recorded at the Diexi seismic station during the 2017 Jiuzhaigou earthquake (referred to as the DX wave), which included both south–north (SN) and up-down (UD) directional components. The compressed and normalized acceleration time history and the Fourier spectrum of the horizontal (SN) and vertical (UD) DX wave are illustrated in Figure 11. The loading duration for both the DX waves and sine waves is set at 20 s.
The input amplitudes for both the sine waves and DX waves were set at 0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, and 0.6 g. Small-amplitude (0.1 g–0.2 g) sine waves were utilized to study the seismic response of the slope, while large-amplitude (0.3 g–0.6 g) sine waves were conducted to investigate the failure mechanisms of the slope under seismic loading. Concurrently, it is considered that the destructive effect of a large-amplitude sine wave on the model is usually greater than that of a natural wave of the same amplitude. Therefore, in the test, small-amplitude sine waves and DX waves were first applied alternately. Subsequently, after the application of the sine wave with an amplitude of 0.2 g, all the DX waves were applied. Finally, large-amplitude sine waves were loaded until the model slope was completely destroyed. Furthermore, given that the strike of the slope is roughly parallel to that of the seismogenic fault, the seismic waves were vertically incident into the slope. Consequently, seismic waves excited the model slope in the horizontal (X), vertical (Z), and coupled horizontal–vertical (XZ) directions during the testing. The horizontal direction (X) is perpendicular to the slope strike. The loading sequences are listed in Table 4. In Table 4, DX represents the DX waves, S represents the sine waves, Z represents the vertical loading direction, X represents the horizontal loading direction, and XZ represents the coupled horizontal–vertical loading direction. Additionally, prior to loading each seismic wave listed in Table 4, the model was excited with white noise to determine the natural frequency and damping ratio of the slope [45]. After each input wave excitation was applied, there was a pause of about 10 min for observing and recording the deformation process of the model.

3.4. Analysis of Test Results

During the test, the deformation and failure of the model were recorded using a high-speed camera, a GoPro, a digital camera, and an unmanned aerial vehicle (Figure 12). Based on the observed deformation and failure phenomena, as well as the acceleration monitoring data, the deformation and failure process of the model slope was analyzed and can be summarized into the following three stages.
(1) Tensile fracturing stage of the rock layers in the middle-upper part of the slope
During the initial loading phase, the slope remained intact with no obvious cracks, which indicated that the rock mass was in the elastic stage. When a sine wave with an amplitude of 0.2 g and a frequency of 15 Hz was applied, localized rock peeling occurred on the middle to upper surface of the slope. At the 3/4 height of the slope, a large crack became visible, but the crack had not yet fully propagated (Figure 13a,b). Simultaneously, black discolorations were observed on both sides of the bedding planes in the middle-upper part of the slope (at places A, B, C, and D in Figure 13a). The width of these discolorations was 3–5 cm, and they gradually narrowed from the slope surface to the slope interior. The lengths of the discolorations were 15 cm (Figure 13d), 55 cm (Figure 13e), 45 cm (Figure 13f), and 20 cm (Figure 13g), respectively. Furthermore, the discolorations exhibited a consistent directionality, all of which were perpendicular to the bedding planes.
Figure 14 illustrates the variation curves of peak ground acceleration (PGA) amplification factors at different elevation monitoring points in the slope during the loading phase. The general trend of these curves is similar, and the amplification factors increase with increasing elevation. Moreover, the amplification factors increase with the increasing frequency of the input sine waves. When subjected to a sine wave with an amplitude of 0.2 g and a frequency of 15 Hz, the amplification factors exceed 2 in the middle-upper part of the slope, and reached 2.8 at the top of the slope. This is likely associated with the natural frequency of the model slope. The analysis of the white noise monitoring data revealed that the natural frequency of the slope model was 25.6 Hz (see Figure 15). The frequency of the seismic wave (15 Hz) is relatively close to the natural frequency of the slope, which is prone to resonance and makes the PGA amplification factor increase. Notably, the amplification factors sharply increase from the 3/4 slope height to the top of the slope, which leads to tensile fracturing along the bedding planes in the middle-upper part of the slope (Figure 13).
(2) Stage of crack expansion and interconnection in the slope
Under the action of DX waves with amplitudes of 0.3 g–0.6 g, the primary deformations of the slope were the formation and the expansion of cracks (Figure 16). Subsequently, under the action of sine waves with amplitudes of 0.3 g–0.5 g, these cracks gradually interconnected, and localized rock peeling on the slope surface resulted in the formation of cavities (Figure 17).
Figure 18 displays the variation curves of the PGA amplification factors at different elevation monitoring points within the slope during the loading phase. The general trend of these curves is similar, and the amplification factor increases with increasing elevation. As the amplitude increases, the amplification factors gradually decrease. When a sine wave with an amplitude of 0.5 g is applied, the amplification factors decrease significantly. This is primarily due to the fact that with the continuous loading of seismic waves, the shear strain of the rock mass increases and the shear modulus decreases, which leads to an increased dissipation of seismic wave energy within the slope [45]. Consequently, the amplification factor is reduced.
(3) Failure stage of slope
When the amplitude of the sine wave reached 0.6 g, the upper part of the slope experienced a failure. In the failure area, transverse steps (Figure 19a), parallel to the slope’s strike, and locally exposed bedding planes (the plastic film in Figure 19b) were distinctly observed. The orientation of these steps was consistent with that observed within the source areas of the SPVE landslide. The rear edge of the failure area featured a scarp with a height of 3–5 cm (Figure 19c). Additionally, the slope experienced an overall settlement of 3–6 cm, accompanied by the occurrence of partial surface spalling (Figure 19d). The landslide deposit exhibited well-defined sorting characteristics, with an average particle size of 11.5 cm × 1 cm × 1 cm, and a maximum particle dimension of 4 cm × 3 cm × 2 cm (Figure 19e).
It is noteworthy that the rock layers of the prototype slope have a thickness of 30–50 cm. Based on the dimension similarity ratio (CL = 200), the theoretical thickness of the rock layers in the model slope should be scaled down to 0.15–0.25 cm. Due to the practical considerations of model production, the actual thickness of the rock layers was set to 10 cm in the model slope. Additionally, although seismic waves in the horizontal (X), vertical (Z), and coupled horizontal–vertical (XZ) directions were applied individually to the model during the test, the actual seismic motion involves complex three-dimensional, random vibrations [46]. These discrepancies led to some differences between the test results and the prototype slope. Nevertheless, the failure location and the characteristics of the steps in the model slope are essentially consistent with those observed in the field. This test effectively simulated the deformation and failure processes of the MBRSs under seismic action.

4. Discussion

In the study area, the rock layer is characterized by a monocline structure, which has a strike that is approximately parallel to the seismogenic fault. During an earthquake, seismic waves enter the MBRSs perpendicular to the strike of the rock layers. Hence, this scenario is analogous to the application of seismic waves in the X and Z directions to the model in the shaking table tests.
Figure 20 illustrates contour maps of the acceleration amplification factors (AAFs) under the loading of DX waves in different directions. In the figure, AAF-X and AAF-Z represent the AAFs in the horizontal (X) and vertical (Z) directions, respectively. The slope displays the difference in dynamic response subject to seismic waves in different directions. Figure 20a shows that AAF-X increases with increasing elevation and reaches a maximum value at the slope crest. At the same elevation, the variation of AAF-X within the slope is not significant. Conversely, AAF-Z initially decreases and then increases with increasing elevation from the toe to the crest along the slope surface (Figure 20b). AAF-Z also reaches a maximum value at the slope crest. At the slope toe and in the middle-upper part of the slope, AAF-Z exhibits significant slope surface amplification effects and decreases gradually inward from the slope surface. In addition, AAF-Z is greater than AAF-X, which indicates that the MBRSs exhibit a stronger dynamic response subject to Z-direction seismic waves.
At the initial stage of the earthquake, the first-arriving P-waves induce the vertical movement of the rock mass. Due to the relatively compact structural state of the rock mass at this time, the slope experiences an intense reciprocating motion along the bedding planes because of P-waves. This leads to the formation of scratches on the bedding planes that are parallel to the dip direction of the rock layers (as shown in Figure 5).
After the S-wave arrives, under the combined action of both the P-wave and the S-wave, the rock mass moves towards the free face when the resultant direction is outward. This movement causes the rock layers to undergo bending deformations similar to those of cantilever plates, resulting in the separation of the rock layers from each other (Figure 21a). Once the rock layers have bent to a certain extent and the bending moment exceeds their flexural strength, the rock layers fracture, forming fracture surfaces that are perpendicular to the bedding planes (Figure 21b). As the earthquake continues, the fracture surfaces extend and interconnect, which leads to the progressive fracturing and disintegration of the rock mass. These fracture surfaces and bedding planes constitute the boundary separating the intact rock mass from the fragmented areas. When the seismic force reaches a sufficient magnitude, the fragmented rock masses detach from the parent rock and are thrown upward at a certain initial velocity and angle, which leads to slope instability (Figure 21c). The preserved “reverse steps” in the landslide source area further confirm the above-mentioned projectile failure mechanism.
Based on the above analysis and the modeling results of the shaking table test, the failure mode of MBRSs in the study area during strong earthquakes can be summarized as flexural–tensile failure. It is worth noting that the flexural–tensile failure typically occurs in bedding and anti-dip layered slopes where the rock layer dip angle exceeds 60° [47]. However, the rock layer dip angle of the MBRSs is less than 60° (45–55°), the slope gradient ranges from 40° to 45°, and the typical flexural–tensile failure still occurred in the study area. The main reason is that the MBRSs are located on both sides of the seismogenic fault and are in close proximity to it (less than 3 km horizontally). This leads the MBRSs to experience intense seismic effects [48,49,50]. At the same time, the strikes of the MBRSs are roughly parallel to that of the seismogenic fault. During earthquakes, the seismic waves incident vertically into the slopes, which has an enhanced seismic amplification effect [51,52]. Therefore, under strong seismic forces, the rock layers experience flexural–tensile failure, which is similar to that of a cantilever plate towards the free face. Additionally, the deformation and failure of the slope may also be related to the left-lateral strike–slip movement of the seismogenic fault.
This study analyzed the failure mechanisms of the MBRSs under seismic action using a large-scale shaking table test. If the bedding direction of the model slope is changed, the dynamic response characteristics and modes of deformation and failure are expected to differ under identical seismic wave conditions. Therefore, in future studies, it may be considered to set different bedding directions in the model for comparative analysis.

5. Conclusions

Based on field investigations, the failure mechanism of the medium-steep bedding rock slope was studied with a large-scale shaking table test. The main conclusions are summarized as follows:
(1) Under seismic action, the MBRSs exhibit a significant elevation amplification effect, and the PGA amplification factors increase with increasing elevation. In particular, the amplification factors sharply increase from the 3/4 slope height to the top of the slope. When the seismic wave amplitude is less than or equal to 0.3 g, the amplification factors within the slope increase with the increasing amplitude. However, as the amplitude of the seismic wave continues to increase, the amplification factors decrease due to the increase in the shear strain of the rock mass. The dynamic response of the MBRSs under Z-direction seismic waves is stronger than that under X-direction seismic waves.
(2) The elevation amplification effect caused the deformation and failure to concentrate in the upper part of the slope, where failure source areas exhibited “reverse steps”. The deformation and failure mode of the MBRSs under seismic action were categorized as flexural–tensile failure. That is, under seismic action, the rock mass moved towards the free face, which caused the rock layers to bend and fracture. As the fracture surfaces extended and interconnected, the slope ultimately failed.
(3) The MBRSs are in close proximity to the seismogenic fault, and their strikes are parallel to that of the fault, which leads the MBRSs to experience intense seismic effects during earthquakes. This provides the dynamic conditions necessary for the flexural–tensile failure of the MBRSs.

Author Contributions

Investigation, data curation, and writing—original draft, X.Z.; investigation, methodology, and writing—review and editing, Q.Z.; conceptualization, supervision, and project administration, S.P.; writing—review and editing, formal analysis, and validation, L.W.; methodology and data curation, Y.D. and K.C. All authors have read and agreed to the published version of this manuscript.

Funding

This study was supported by the National Natural Science Foundation of China (Grant No. 41272333).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

Longke Wu is an employee of Guangxi Communications Design Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Geological overview map of the study area. The basic geological maps are sourced from the 1:200,000 geological maps [4,5]; the Songpinggou Fault is based on Zhao et al. [6].
Figure 1. Geological overview map of the study area. The basic geological maps are sourced from the 1:200,000 geological maps [4,5]; the Songpinggou Fault is based on Zhao et al. [6].
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Figure 2. Geological structures and historical earthquakes near study area. (Adapted from Ren et al. [25] and Pei et al. [26]).
Figure 2. Geological structures and historical earthquakes near study area. (Adapted from Ren et al. [25] and Pei et al. [26]).
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Figure 3. Schematic diagram of “reverse step” at the rear edge of landslide.
Figure 3. Schematic diagram of “reverse step” at the rear edge of landslide.
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Figure 4. “Reverse steps” at the rear edge of the SPVE landslide (A and B are the failure areas). (a–c) Aerial 3D images (0.2 m resolution) captured by an unmanned aerial vehicle (UAV). (d,e) Digital elevation model (DEM) images (Gauss–Krüger projection, 0.2 m resolution) captured by an UAV. These images are provided by Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chendu, China.
Figure 4. “Reverse steps” at the rear edge of the SPVE landslide (A and B are the failure areas). (a–c) Aerial 3D images (0.2 m resolution) captured by an unmanned aerial vehicle (UAV). (d,e) Digital elevation model (DEM) images (Gauss–Krüger projection, 0.2 m resolution) captured by an UAV. These images are provided by Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chendu, China.
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Figure 5. Small steps at the rear edge of the SPVE landslide. (a) Digital Orthophoto Map (DOM) (Gauss–Krüger projection, 0.2 m resolution). (b) Sketch drawing. (c) Strike rosette plot of steps. Aerial orthophoto image was provided by Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chendu, China.
Figure 5. Small steps at the rear edge of the SPVE landslide. (a) Digital Orthophoto Map (DOM) (Gauss–Krüger projection, 0.2 m resolution). (b) Sketch drawing. (c) Strike rosette plot of steps. Aerial orthophoto image was provided by Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chendu, China.
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Figure 6. Geological cross-section along line I-I′ of the SPVE landslide (A and B are the failure areas). Aerial 3D image (0.2 m resolution) was provided by Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chendu, China.
Figure 6. Geological cross-section along line I-I′ of the SPVE landslide (A and B are the failure areas). Aerial 3D image (0.2 m resolution) was provided by Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chendu, China.
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Figure 7. Schematic diagram of steps. (a) Steps formed under static conditions (red arrow indicates the direction of movement). (b) “Reverse steps” in the source areas of the SPVE landslide.
Figure 7. Schematic diagram of steps. (a) Steps formed under static conditions (red arrow indicates the direction of movement). (b) “Reverse steps” in the source areas of the SPVE landslide.
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Figure 8. Sketch of the model slope and layout of the accelerometers (unit: mm).
Figure 8. Sketch of the model slope and layout of the accelerometers (unit: mm).
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Figure 9. Main process of making the model. (a) Sketching the outline of the model. (b) Scraping the surface. (c) Covering with plastic film.
Figure 9. Main process of making the model. (a) Sketching the outline of the model. (b) Scraping the surface. (c) Covering with plastic film.
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Figure 10. Lateral view of model slopes.
Figure 10. Lateral view of model slopes.
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Figure 11. Acceleration time history and Fourier spectrum of the DX wave in both the SN and UD directions.
Figure 11. Acceleration time history and Fourier spectrum of the DX wave in both the SN and UD directions.
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Figure 12. Location map of test model and data acquisition equipment.
Figure 12. Location map of test model and data acquisition equipment.
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Figure 13. Illustration and photographs of slope deformation under the excitation of a 0.2 g sine wave (A–D indicate the numbered black discolorations).
Figure 13. Illustration and photographs of slope deformation under the excitation of a 0.2 g sine wave (A–D indicate the numbered black discolorations).
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Figure 14. Curve of amplification factor with elevation under the excitation of seismic waves with amplitudes of 0.1 g and 0.2 g.
Figure 14. Curve of amplification factor with elevation under the excitation of seismic waves with amplitudes of 0.1 g and 0.2 g.
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Figure 15. Transfer function curve of the model slope under white noise excitations.
Figure 15. Transfer function curve of the model slope under white noise excitations.
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Figure 16. Illustration and photographs of slope deformations under the excitation of DX waves with amplitudes ranging from 0.4 g to 0.6 g.
Figure 16. Illustration and photographs of slope deformations under the excitation of DX waves with amplitudes ranging from 0.4 g to 0.6 g.
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Figure 17. Illustration and photographs of the slope deformations under the excitation of sine waves with amplitudes ranging from 0.3 g to 0.5 g.
Figure 17. Illustration and photographs of the slope deformations under the excitation of sine waves with amplitudes ranging from 0.3 g to 0.5 g.
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Figure 18. Curve of the amplification factor with elevation under the excitation of seismic waves with different amplitudes.
Figure 18. Curve of the amplification factor with elevation under the excitation of seismic waves with different amplitudes.
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Figure 19. Illustration and photographs of the slope deformation under the excitation of a 0.6 g sine wave. (a) Schematic diagram of the model. (b) Exposed bedding planes. (c) The scarp at the rear of the failure area. (d) Partial surface spalling of the model. (e) Landslide deposit.
Figure 19. Illustration and photographs of the slope deformation under the excitation of a 0.6 g sine wave. (a) Schematic diagram of the model. (b) Exposed bedding planes. (c) The scarp at the rear of the failure area. (d) Partial surface spalling of the model. (e) Landslide deposit.
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Figure 20. Contour maps of AAFs under the loading of DX waves in different directions. (a) Horizontal (X) direction. (b) Vertical (Z) direction.
Figure 20. Contour maps of AAFs under the loading of DX waves in different directions. (a) Horizontal (X) direction. (b) Vertical (Z) direction.
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Figure 21. Deformation and failure process of the MBRSs under seismic action. (a) Bending of rock layers towards the free face. (b) Fracture of rock layers. (c) Slope failure (arrow indicates the direction of movement).
Figure 21. Deformation and failure process of the MBRSs under seismic action. (a) Bending of rock layers towards the free face. (b) Fracture of rock layers. (c) Slope failure (arrow indicates the direction of movement).
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Table 1. Technical parameters of the shaking table test system.
Table 1. Technical parameters of the shaking table test system.
ParametersTechnical Specification
Table size4 m × 6 m
Maximum bearing capacity40 t
Maximum accelerationX, ±1.5 g; Y, ±1.2 g; Z, ±1.0 g
Maximum velocityX, ±1.5 m/s; Y, ±1.2 m/s; Z, ±1.0 m/s
Maximum velocityX, ±300 mm; Y, ±250 mm; Z, ±150 mm
Range of operating frequency0.1–60 Hz
Table 2. Similarity ratios for the model slope.
Table 2. Similarity ratios for the model slope.
No.Physical ParametersDimensionSimilarity RelationSimilarity Ratio
1Length (L)[L]Controlling parameter, Cl200
2Density (ρ)[M] [L]–3Controlling parameter, Cρ1
3Gravitational acceleration (g)[L] [T]–2Controlling parameter, Cg1
4Elastic modulus (E)[M] [L]–1 [T]–2CE = Cl Cρ Ca200
5Poisson’s ratio (μ)/11
6Cohesion (c)[M] [L]–1 [T]–2Cc = Cl Cρ Ca200
7Internal friction angle (φ)/11
8Stress (σ)[M] [L]–1 [T]–2Cσ = Cl Cρ Ca200
9Strain (ε)/11
10Displacement (u)[L]Cu = Cl200
11Velocity (v)[L] [T]–1Cv = (Ca Cl)1/22001/2
12Acceleration (a)[L] [T]–2Ca = Cg1
13Time (t)[T]Ct = (Cl/Ca)1/22001/2
14Frequency (f)[T]–1Cf = (Ca/Cl)1/2200−1/2
15Damping ration (λ)/11
Table 3. Physical and mechanical parameters of the prototype and model slope.
Table 3. Physical and mechanical parameters of the prototype and model slope.
Material TypeDensity
(g/cm3)		Elastic Modulus
(MPa)		Cohesion
(kPa)		Internal Friction Angle
(°)
Prototype slope2.3–2.48000–10,0004000–600030–40
Similarity ratio12002001
Calculated value2.3–2.440–5020–3030–40
Model slope2.348.824.332
Table 4. The loading scheme in the shaking table test.
Table 4. The loading scheme in the shaking table test.
NumberWavesDirectionAmplitude (g)NumberWavesDirectionAmplitude (g)
1DXZ0.122S (15 Hz)Z0.2
2DXX0.123S (15 Hz)X0.2
3DXXZ0.124S (15 Hz)XZ0.2
4S (5 Hz)Z0.125DXZ0.3
5S (5 Hz)X0.126DXX0.3
6S (5 Hz)XZ0.127DXXZ0.3
7S (8 Hz)Z0.128DXZ0.4
8S (8 Hz)X0.129DXX0.4
9S (8 Hz)XZ0.130DXXZ0.4
10S (15 Hz)Z0.131DXZ0.5
11S (15 Hz)X0.132DXX0.5
12S (15 Hz)XZ0.133DXXZ0.5
13DXZ0.234DXZ0.6
14DXX0.235DXX0.6
15DXXZ0.236DXXZ0.6
16S (5 Hz)Z0.237S (5 Hz)X0.3
17S (5 Hz)X0.238S (8 Hz)X0.3
18S (5 Hz)XZ0.239S (15 Hz)X0.3
19S (8 Hz)Z0.240S (5 Hz)X0.4
20S (8 Hz)X0.241S (5 Hz)X0.5
21S (8 Hz)XZ0.242S (5 Hz)X0.6
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Zheng, X.; Zhao, Q.; Peng, S.; Wu, L.; Dou, Y.; Chen, K. Analysis of Failure Mechanism of Medium-Steep Bedding Rock Slopes under Seismic Action. Sustainability 2024, 16, 7729. https://doi.org/10.3390/su16177729

AMA Style

Zheng X, Zhao Q, Peng S, Wu L, Dou Y, Chen K. Analysis of Failure Mechanism of Medium-Steep Bedding Rock Slopes under Seismic Action. Sustainability. 2024; 16(17):7729. https://doi.org/10.3390/su16177729

Chicago/Turabian Style

Zheng, Xiuhong, Qihua Zhao, Sheqin Peng, Longke Wu, Yanghao Dou, and Kuangyu Chen. 2024. "Analysis of Failure Mechanism of Medium-Steep Bedding Rock Slopes under Seismic Action" Sustainability 16, no. 17: 7729. https://doi.org/10.3390/su16177729

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