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Article

Analysis of Dynamic Response Characteristics and Failure Pattern of Rock Slopes Containing X-Joints and Underlying Weak Interlayers

by
He Meng
1,2,
Yanjun Shang
1,2,3,*,
Liyun Zhou
3,
Yangfan Li
3,
Xuetao Yi
1,2 and
Qingsen Meng
1,2
1
State Key Laboratory of Lithospheric and Environmental Coevolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2
College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3
Xinjiang Key Laboratory of Geohazard Prevention, Xinjiang Institute of Engineering, Urumqi 830023, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(18), 10209; https://doi.org/10.3390/app151810209
Submission received: 21 July 2025 / Revised: 10 September 2025 / Accepted: 16 September 2025 / Published: 19 September 2025
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Abstract

Under the complex geological structural stress of the Western Himalayan syntaxis, the widespread distribution of hard and brittle rocks (such as sandstone and limestone) makes them prone to the formation of conjugate joints, also known as X-joints. These joints create weak structural planes in the slope rock mass, and when combined with weak interlayers within the slope, they result in a complex dynamic response and hazard situation in this region, which is further exacerbated by frequent seismic activity. This poses a serious threat to the planning, construction, and safe operation of the Belt and Road Initiative. To study the slope vibration response and instability mechanisms under these conditions, we conducted a shaking table test using the Iymek avalanche as a case study and performed Hilbert–Huang Transform (HHT) analysis. We also compared the results of the shaking table test on slope models without X-joints but containing weak interlayers. The findings show that the presence of X-joints leads to an earlier onset of plastic failure in the slope. During the failure development, X-joints cause stress concentration and the diversification of stress redistribution paths, delaying energy release. Ultimately, the avalanche failure mode in the X-joint slopes is more dispersed compared to the landslide failure mode in the model without X-joints. At the toe of the slope beneath the weak interlayer, low-frequency seismic waves can cause a significant amplification of acceleration, and the weak interlayer is often the shear outlets of the slope. These findings provide new insights into the seismic failure evolution of jointed slopes with weak interlayers and offer practical references for seismic hazard mitigation in mountainous infrastructure.

1. Introduction

The Western Himalayan syntaxis represents one of the most tectonically active zones in mainland China and forms a critical segment of the globally significant Eurasian Seismic Belt. These deformation patterns have led to the formation of a series of northward-convex arcuate fault zones, which exert a dominant control over the spatial distribution and recurrence of strong earthquakes in the region (see Figure 1) [1,2,3].
Due to intense tectonic activity, the widespread distribution of hard and brittle rocks in the Western Himalayan syntaxis often leads to the development of conjugate joints commonly referred to as X-joints. Extensive studies have shown that joints play a dominant role in earthquake-induced collapses and landslides [4,5,6,7], and weak interlayers also significantly influence the stability of rock slopes under seismic conditions [8,9,10]. Currently, shaking table tests have become a widely used and effective method for studying the dynamic characteristics and failure modes of slopes. However, previous research has mainly focused on homogeneous slopes or layered slopes with one or more sets of joints. Wang et al. [11] and Song et al. [12] each conducted shaking table tests on rock slopes with discontinuous structural planes, revealing a three-stage failure evolution in slopes with discontinuous joints—crack formation, surface crack propagation, and collapse sliding. Feng et al. [13] designed a physical model of an anti-dip rock slope containing two sets of structural planes for shaking table tests. Results demonstrated that under seismic loading, the slope model primarily manifested propagating shear and tensile cracks, which coalesced and developed step-path fractures, culminating in toppling and sliding failure. In studies on the seismic response of slopes with weak interlayers, shaking table tests conducted by Liu et al. [14], Chen et al. [15], and Liu et al. [16] have shown that the thickness of the weak interlayer plays a dominant role in the amplification of horizontal acceleration in the upper and lower slope sections, while the dip angle of the weak layer mainly affects the acceleration effect in the middle and lower slope sections. Fan et al. [17] differentiated the deformation modes in dip and anti-dip slopes with weak interlayer, where bedding sliding and compressive extrusion, respectively, predominated. Zhao et al. [18] conducted a shaking table test and analyzed using the HHT, concluding that weak interlayer selectively amplify seismic waves in the 5–10 Hz and 25–30 Hz bands, while attenuating those in the 15–20 Hz range.
Numerous cases have demonstrated that X-joints play a significant controlling role in the development of avalanches and landslides. Studies by Yu [19] on the relationship between multi-phase tectonic deformation and landslides in the Moutai Syncline in southeastern Sichuan Province; by Zhang et al. [20] on joint characteristics and collapse features in the Bailixia area of the Juma River in Hebei Province; and by Jiang [21] on the relationship between geohazards and regional geological environments in Guangxin District, Shangrao City, Jiangxi Province, all found that conjugate joints exert a clear controlling influence on the development of avalanches and landslides. In engineering construction, areas such as the Dadu River Jinchuan Hydropower Station dam area, the Yebatan Hydropower Station dam area on the Jinsha River, a highway tunnel in the Lvliang Mountain area, and high-road cuts are also influenced by conjugate joints [22,23,24]. However, research on the seismic response of rock slopes containing X-joints remains limited, and studies addressing the dynamic response of slopes combining X-joints with weak interlayers have not been fully explored. To address these gaps, we took the Iymek avalanche in the Western Himalayan syntaxis as a representative case and conducted shaking table experiments on rock slope models containing both X-joints and an underlying weak interlayer. The variation in acceleration amplification factors with slope elevation was examined under seismic excitations of varying strength in both horizontal and vertical directions, establishing the relationship between dynamic response and seismic wave frequency. Furthermore, the HHT analysis was employed to perform a refined time–frequency analysis of the slope response, allowing for a detailed characterization of the damage evolution and failure patterns. By comparing the macroscopic deformation characteristics and dynamic damage features of slope models with and without X-joints in the shaking table tests, this study elucidates the seismic response characteristics of rock slopes under the coupled effects of weak interlayers and X-joints, providing valuable insights for seismic hazard assessment in complex geological environments.

2. Geological Setting of the Study Slope

The Iymek avalanche source area is located at the northeastern margin of the Pamir active orogenic belt, with the center of the accumulation body situated in the northwestern corner of the Tarim Basin. The Main Pamir Thrust (MPT), a series of imbricate thrust faults trending nearly east–west and dipping northward, cuts through the central portion of the avalanche deposit (see Figure 2a). Geochronological evidence suggests that the MPT became active during the Middle Eocene to Late Oligocene periods [3,25,26,27], and the Holocene slip rate of ~6 mm/yr [28]. This high convergence rate has resulted in numerous strong earthquakes along the MPT over the past several million years [29,30,31,32]. However, due to the absence of historical records, the precise triggering mechanism of the Iymek avalanche remains uncertain [33]. Based on the geological setting and field observations, the event is most likely the result of an ancient earthquake. Several lines of evidence support this hypothesis. First, large-scale, long-runout rock avalanches are often associated with seismic or extreme rainfall triggers. However, the study area is characterized by a hyper-arid continental climate with minimal annual precipitation, rendering rainfall-induced triggers unlikely. Second, the MPT intersects the front edge of the avalanche deposit and has been seismically active throughout the Quaternary. Numerous large-scale avalanches are clustered along this fault zone. Third, there is no evidence of glacial modification within the deposits or surrounding valleys. The rugged back wall, highly fragmented rock mass in the source area, and a low apparent friction coefficient (H/L ≈ 0.14) further support the interpretation of a seismically triggered event [34].
Morphometric analysis based on Google Earth indicates that the avalanche covers an area of ~4.7 × 107 m2, with an average deposit thickness of ~30 m and an estimated volume of ~1.4 × 109 m3. The runout distance from source to toe reaches 16.3 km, meeting the criteria for classification as a massive rock avalanche. Field investigations show that the bedrock in the source area consists of Early Paleozoic metamorphic sedimentary rocks, including chlorite schist, marble, and metamorphic conglomerate, with the metamorphic conglomerate forming the weak interlayer in the slope (see Figure 2a). The slide direction is toward the northeast, opposite to the dip direction of the strata. The back scarp is sharply defined, measuring ~3 km in length, ~1.7 km in width, with a slope of 65–70° and a vertical height difference of ~1180 m (see Figure 2b). The chlorite schist and marble exhibit well-developed foliation, with bedding planes dipping at 15–40° toward the southwest. Two sets of joints are developed, with orientations of 113°∠60° (Joint1) and 325°∠45° (Joint 2), forming an X-joint (see Figure 2c). The debris mass contains widely distributed diamond-shaped rock blocks formed by X-joints cutting through the bedrock (see Figure 2d). Shi et al. [35] identified this event as the largest known avalanche in China to date. Utilizing established methodologies [36,37,38], they reconstructed pre-event topography through natural neighbor interpolation in ArcGIS and an 8 m spatial resolution digital elevation model (DEM). The newly generated topographic contours maintain continuous and consistent transitions with undisturbed terrain while conforming to geomorphic essence principles described by Jarman et al. [38], including general morphology of mountain slopes and valleys, and fundamental orientation of ridgelines. Results indicate a pre-avalanche summit elevation of approximately 4225 m.

3. Shaking Table Test

3.1. Similar Materials of Slope Model

The similarity theory forms the foundation for physical model testing, ensuring that scaled models accurately replicate the mechanical behavior of prototype systems. In slope shaking table experiments, geometric and mechanical similarity is particularly critical. Due to the complex geological conditions and large scale of the Iymek prototype, achieving full similarity across all parameters was impractical. Therefore, this study focused on key dynamic parameters—specifically, material density, elastic modulus, and Poisson’s ratio—to preserve the integrity of the seismic response simulation.
A newly developed geomechanical material, Iron Barite Sand Cementation Material (IBSCM), was selected as the model medium [39,40]. It consists of iron ore powder, barite powder, and quartz sand as aggregates, a rosin–alcohol solution as the binder, and gypsum as a regulator. This composition yields high density and low stiffness, ideal for modeling rock-like behavior. The materials are non-toxic, cost-effective, and easily processable. After multiple proportioning trials, the optimal mix ratios were determined as follows: (1) marble simulation: 20.65% iron ore powder, 29.50% quartz sand, 48.18% barite, 0% gypsum, 1.67% rosin; (2) metamorphic conglomerate simulation: 29.90% iron ore powder, 18.69% quartz sand, 44.85% barite, 6% gypsum, 0.56% rosin.
As shown in Table 1, although the elastic modulus exhibited some deviation due to a large similarity ratio, the material’s density and Poisson’s ratio met the similarity requirements. Moreover, the relative mechanical contrast between marble and conglomerate in the prototype was preserved.
The slope model consisted of two major components: the slope body and the base. To simulate X-joints, the slope model was assembled from prefabricated diamond-shaped modules (160 mm side length, 100 mm thickness, and 60° acute angle) representing rock blocks. The arrangement of these blocks was guided by joint orientations observed in the field (see Figure 3). Apply a layer of 1200 mesh talcum powder, 0.5 to 1 mm thick, between the modules to simulate a joint surface. The base was formed by manual compaction of IBSCM. A layer of 5 mm thick similar material was laid between the base and the module to ensure adhesion between them. The density and mechanical properties of each block were verified through repeated measurements during assembly.

3.2. Test Equipment and Model Boundaries

Figure 4 shows the instruments used in this experiment. The shaking table used in this experiment measures 3.0 × 3.0 m2 (see Figure 4a), with a load capacity of 10 t and a frequency range of 0.1–120 Hz. It supports six degrees of freedom, with maximum horizontal and vertical accelerations of 1.0 g and 0.7 g, respectively. A rigid model box (1.9 m × 0.9 m × 1.2 m) was used, with tempered glass panels on both sides and polyurethane foam seals to minimize rigid collisions. Polyethylene foam (50 mm) was attached to the front and rear walls to further reduce boundary interference. Gravelly soil was placed at the bottom over welded crossbeams to enhance friction and prevent displacement(see Figure 4b).
A total of twenty tri-axial accelerometers (measurement range: 50 g; frequency response: 0.5–100 Hz; sensitivity: 10.10 mV/ms2; size: 16.5 mm; mass: 17 g) were embedded along the central longitudinal section of the model (see Figure 4c and Figure 5), to capture vertical and horizontal acceleration response data. Acceleration data were recorded using a dynamic signal testing and analysis system (see Figure 4d). High-definition camera monitored slope model deformation and failure processes during shaking (see Figure 4e).

3.3. Loading Options

Two types of input seismic waves were used: Sine waves and natural earthquake records. This design allows natural earthquake waves to simulate the diversity and complexity of actual earthquakes, while sine waves can be used to study the slope response and failure mechanisms at specific frequencies. The Sine waves were tested at four frequencies: 5 Hz, 15 Hz, 25 Hz, and 35 Hz under varying amplitudes. The specific parameters of the natural seismic motions are shown in Table 2 and are derived from two significant earthquake events that occurred in the region: the Wuqia earthquake (Ms 6.8, 5 October 2008) and the Akto earthquake (Ms 6.7, 25 November 2016). Both waves included components in the EW, NS, and UD directions. Based on epicentral positioning, the SN component was assigned to the horizontal direction (X-direction) and the UD component to the vertical direction (Z-direction) for model excitation. Preprocessing steps—including baseline correction, filtering, and truncation—were applied to yield stable input records. Dominant frequencies were 2.09 Hz (Wuqia) and 0.39 Hz (Akto) in the X-direction, and 12.17 Hz and 0.74 Hz in the Z-direction, respectively (see Figure 6).
Eight seismic amplitude levels were applied: 0.1–0.5 g, 0.7 g, 0.9 g, and 1.1 g. Prior to each loading, Gaussian white noise (0.05 g amplitude) was used to determine the natural frequency of the model. The loading sequence followed a consistent protocol: Z-direction first, followed by X-direction, and finally combined bidirectional XZ-excitation. Considering that sine waves with multiple peaks in amplitude have greater power than the other two natural seismic waves, natural earthquake waves were applied first, followed by the sine waves. The entire test loading process was conducted a total of 119 times.

4. Results

4.1. Dynamic Response of the Slope

4.1.1. Transfer Function Analysis

The natural frequency is a key parameter characterizing the dynamic behavior of slopes. In slope model tests, the imaginary part of the acceleration transfer function at monitoring points is typically identified by inputting white noise into the model to determine its natural frequency [41,42]. The experiment was conducted with seven times white noise excitations. Based on the acceleration response data under white noise excitation, the transfer functions in both directions of the slope model were calculated.
Figure 7 shows the transfer functions in two directions under 0.2 g and 0.4 g seismic wave excitations. Analysis revealed that within the experimental frequency range (0–65 Hz), the predominant natural frequencies of the slope model in the X-direction were identified at 49.90 Hz and 39.94 Hz for the 0.2 g and 0.4 g conditions, respectively. Furthermore, the transfer function curve for the 0.4 g condition exhibited a minor secondary peak at 24.22 Hz (see Figure 7a,b). The frequency response in the Z-direction was more complex, with lower natural frequencies observed at 29.74 Hz and 31.35 Hz, and higher frequencies at 60.06 Hz and 61.91 Hz for the two excitations (see Figure 7c,d). The distinct natural frequencies identified in the two directions indicate differing dynamic characteristics and likely different modal responses when the slope model is excited along each direction, respectively.
Figure 8 shows that as the experiment progresses, the slope’s X-direction response initially demonstrated greater susceptibility to higher frequencies but shifted towards lower frequencies subsequently. Meanwhile, the higher and lower natural frequencies in the Z-direction remained stable at approximately 60 Hz and 30 Hz, respectively.

4.1.2. Response Characteristics Under Different Input Directions

The dynamic response characteristics of the slope mainly include acceleration, velocity, displacement, strain, and stress responses. Under seismic wave loading, the uneven changes in acceleration within the slope lead to stress differences in different regions of the slope, which is the primary cause of slope deformation and instability [43]. Therefore, the distribution and evolution of acceleration are key information for analyzing the dynamic response and instability characteristics of the slope. This study characterizes the slope’s dynamic response by analyzing the peak values extracted from acceleration time-history curves recorded by sensors at various monitoring points. Specifically, the peak horizontal acceleration (PHA) and peak vertical acceleration (PVA) are examined. To quantitatively evaluate the amplification of seismic waves through the slope model, dimensionless horizontal and vertical acceleration amplification factors are employed, defined as the ratio of the PHA to the peak input horizontal acceleration and the PVA to the peak input vertical acceleration, respectively.
(1)
Response characteristics in horizontal input direction
To investigate the spatial distribution of the horizontal peak ground acceleration (PHA) amplification factor under seismic loads, we conducted the study using seismic waves of different types and frequencies, with an amplitude of 0.3 g. The Kriging interpolation method was applied to generate contour maps of the PHA amplification factor (see Figure 9).
As shown in Figure 9, the slope generally exhibits a clear elevation amplification effect and a surface tendency effect. However, due to the presence of the weak interlayer, the acceleration amplification effect of the slope shows significant nonlinear variation. Specifically, (1) under low-frequency seismic waves (≤5 Hz), the slope response exhibits a distinct “seismic isolation effect,” where the acceleration response is significantly amplified beneath the weak interlayer (at the slope toe) (Figure 9a–c). (2) High-frequency seismic waves cause a more noticeable acceleration amplification at the slope crest (Figure 9d–f), with the amplification factor reaching 2.7 under excitation by the 25 Hz sine wave (Figure 9e).
Figure 10 illustrates the variation in amplification factors under different amplitudes of 5 Hz sine waves, aiming to explore the influence of seismic wave amplitude on the acceleration response and the “seismic isolation effect.” It is evident that the PHA acceleration amplification factor generally increases with the input seismic wave amplitude, showing a pronounced amplification effect (see Figure 10a). Moreover, the “isolation effect” is not influenced by amplitude, but since the weak interlayer does not extend through the slope back, the “isolation effect” is not observed at the slope back under high-amplitude seismic waves (see Figure 10b). The “seismic isolation effect” under low-frequency seismic waves is likely due to the significant impedance contrast between the weak interlayer and the high-modulus rock. Impedance contrast refers to the difference in wave propagation speed and density between different media. For low-frequency seismic waves, which have longer wavelengths, interference, reflection, and other wave effects are more likely to occur within the weak interlayer. When low-frequency waves encounter the weak interlayer, the poor elasticity of the weak layer prevents efficient wave transmission, causing the wave energy to accumulate beneath the interlayer and resulting in an amplification effect [44,45,46,47].
To further investigate the frequency dependence of the slope’s dynamic response, the relationship between the input wave frequency and the PHA amplification factor was evaluated using Sine waves of varying frequencies and amplitudes. The results show a clear correlation: under low-amplitude excitation, the amplification factor increases monotonically with increasing Sine wave frequency (see Figure 11a,b). However, at amplitudes ≥0.3 g, the amplification factor initially increases with frequency, reaching a maximum at 25 Hz and then declines (see Figure 11c,d). From Figure 7a,b, it can be observed that this phenomenon is associated with the appearance of a “minor secondary peak” in the transfer function curve around 25 Hz after being subjected to multistage seismic waves, resulting in a resonance effect.
(2)
Response characteristics in vertical input direction
Figure 12 presents the contour maps of PVA amplification factors under different seismic wave types at an input amplitude of 0.3 g. Figure 13 further illustrates the variation in PVA amplification factors with elevation along the slope surface and within the slope body, using the 5 Hz Sine wave as a representative case.
As shown in Figure 12 and Figure 13, the distribution of vertical acceleration amplification across the slope generally exhibits a nonlinear increase with slope height. However, when compared to the PHA amplification factors presented in Figure 9 and Figure 10, the PVA amplification factors under vertical excitation show the following significant differences: (1) Under the same intensity of excitation, the PVA amplification factor in the lower part of the slope is significantly higher than the PHA amplification factor, with the difference becoming more pronounced as the excitation intensity increases. (2) The coupling effect of vertical seismic waves with the weak interlayer differs from that of horizontal seismic waves. First, the weak interlayer enhances the PVA response, and there is no “seismic isolation effect.” This result is consistent with the observations of Liu et al. [14] in shaking table experiments on homogeneous slopes with retrograde weak interlayers. However, unlike their findings, in the current experiment, the vertical acceleration response above the weak interlayer exhibited a strong nonlinear elevation amplification effect. This phenomenon is related to the distribution of X-joints within the slope. The presence of X-joints complicates the vertical acceleration response of the slope. Therefore, in practical engineering, more attention should be given to the impact of vertical acceleration on slope failure.
The relationship between the PVA amplification factor and input wave frequency is shown in Figure 14. At low frequencies, the amplification effect is relatively weak, especially under an input of 0.1 g, where the amplification effect may even slightly decrease (see Figure 14a,b). Between 15 and 25 Hz, the PVA amplification factor increases sharply, but when the frequency reaches 35 Hz, the amplification either stabilizes or slightly decreases under higher amplitudes such as 0.3 g and 0.4 g (see Figure 14c,d). This behavior is likely attributed to the model’s low-order natural frequency, which occurs near 30 Hz in response to vertical (Z-direction) input, as indicated in Figure 7c,d.
(3)
Influence of different input directions
In this study, the ratio of acceleration amplification factors for horizontal and vertical seismic wave inputs (PHA amplification factor/PVA amplification factor) is defined as the RAAF index to analyze the impact of loading direction on seismic wave acceleration amplification effects. When RAAF > 1, it indicates that the dynamic response in that region is mainly controlled by horizontal seismic waves. If RAAF < 1, it suggests that vertical seismic waves have a greater influence. As shown in Figure 15, the following can be observed: (1) Under lower seismic amplitudes (0.2 g), the RAAF values within the slope model are all <1 (see Figure 15a,c,e). However, under seismic waves with 0.4 g amplitude, the RAAF values increase, with RAAF > 1 at the slope crest and shoulder (see Figure 15b,d,f). This indicates that under smaller amplitude excitation, the slope’s response to vertical seismic waves is more pronounced. (2) Under high-amplitude seismic waves, as the frequency increases, the RAAF value also increases, indicating that the slope model responds more significantly to high-frequency horizontal seismic waves under high-intensity seismic loading. (see Figure 15b,f). (3) The RAAF values in the lower part of the slope are generally smaller than those in the upper part, meaning that the lower slope exhibits a more significant response to vertical acceleration (see Figure 15a–f). Notably, the RAAF isolines show localized distortion near the weak interlayer, especially under low-amplitude excitation, where the RAAF values increase to varying degrees near the weak interlayer. This further confirms that the weak interlayer strongly reflects low-frequency horizontal seismic waves while having a limited influence on vertical seismic waves.

4.2. Phase Classification of Failure and Damage Identifications in the Slope

Seismic waves possess characteristics of non-stationarity, nonlinearity, and time-varying signals. Additionally, the seismic waves acquired by sensors encompass various frequency components that evolve during propagation. Therefore, the Fourier transform alone is insufficient for analyzing the characteristics of these frequency components. HHT, with its adaptive signal decomposition capability, is particularly effective for analyzing such complex signals, and is thus well-suited for studying seismic responses in slope models [48,49,50].

4.2.1. Hilbert Spectrum Analysis

In this study, monitoring points A12 (near the slope toe) and A14 (near the slope crest) were selected for HHT analysis. Figure 16a,b present the Hilbert spectra under low-amplitude (0.3 g) and high-amplitude (0.7 g) Wuqia seismic wave excitation, respectively. It can be seen that under the 0.3 g seismic wave, the dominant frequency of the Hilbert spectrum is in the range of 0–20 Hz, with fewer high-frequency components. The results show that the energy transfer in the slope is relatively concentrated under low-strength seismic waves, which are mainly affected by low-frequency seismic waves. In contrast, under 0.7 g amplitude excitation, the frequency content of the Hilbert spectrum becomes broader, particularly at point A14, where frequencies extend up to 30 Hz. This broader distribution implies a reduction in material stiffness, often associated with the initiation and propagation of microcracks. The peak amplitude value of the Hilbert spectrum (PAHS) reflects the sensitivity of the slope model to a specific frequency of seismic waves, indicating a significant increase in acceleration or deformation response caused by excitation at that frequency. Although the PAHS value remains between 6 and 7 Hz, the frequency components near the PAHS point are more diverse, exhibiting a multi-peak phenomenon. The presence of multiple peaks indicates that the slope structure is influenced not only by low-frequency seismic waves but also by high-frequency impacts, further exacerbating its damage. Figure 16c illustrates the evolution of PAHS with elevation under different seismic intensities. At low amplitudes (0.1–0.2 g), PAHS values across monitoring points remain relatively stable, corresponding to the elastic deformation stage. As the amplitude increases to 0.3–0.4 g, the growth rate of PAHS significantly accelerates, particularly at A15 (slope crest), where it increases from 0.0422 to 0.2314, an increase of five times. This indicates that deformation and failure within the slope are continuously increasing, especially at the slope crest. When the load amplitude exceeds 0.5 g, the decrease in PAHS at A14 and A15 indicates the entry into the plastic failure stage. In this stage, energy is gradually dissipated through mechanisms such as crack propagation, frictional sliding, or partial collapse, rather than being fully transmitted to the monitoring point. During the 0.5–0.7 g amplitude loading phase, the PAHS values at each monitoring point rapidly increase, indicating that structural changes have occurred within the slope, forming new energy transfer pathways. Subsequent seismic motion will trigger larger-scale destruction.

4.2.2. Marginal Spectrum Analysis

The marginal spectrum reflects the distribution of energy across different frequencies in seismic signals [51,52]. The Hilbert marginal spectrum under the 0.3 g and 0.7 g Wuqia earthquake wave loading was analyzed in this study, along with the changes in the peak marginal spectrum amplitude (PMSA) of the slope under different excitation amplitudes. The following conclusions can be drawn: (1) With the increase in the loading seismic wave intensity, the frequency distribution range of the marginal spectrum expands and exhibits a multi-peak phenomenon (e.g., A12, A15), indicating that damage occurred at these locations (Figure 17a,b), marking the transition from elastic to plastic deformation. (2) Figure 17c reveals the progressive failure process of the slope. At 0.4–0.5 g, the increase in PMSA starts to show divergence, indicating that local instability events begin to dominate the overall response. At 0.7 g, the synchronous high response at both the top and bottom monitoring points suggests the formation of a through-going slip surface in the slope.

4.3. Seismic-Induced Instability Mechanism of the Slope

To investigate the influence of X-joints on the failure process and pattern of rock slopes, a comparative model (Slope Model II) was constructed that excluded X-joints. All other parameters—including weak interlayer location, bedding orientation, model dimensions, similar material proportions, and seismic loading conditions—were kept consistent with the original model (Slope Model I), which incorporated X-joints.
(1)
Progressive failure evolution process of Slope Model I
Figure 18 illustrates the progressive failure of Slope Model I under increasing seismic intensities. The following can be observed: (1) Initial damage in the slope occurs at a 0.2 g amplitude, with tensile cracks forming at the slope toe within the weak interlayer and at the slope shoulder (see Figure 18a). (2) When the excitation amplitude increases to 0.5 g, cracks at the weak interlayer extend to the slope base, and surface cracks span the entire slope, accompanied by rock particle detachment (see Figure 18b). (3) At 0.7 g amplitude, the weak interlayer is fragmented, severely compromising its integrity (Figure 18c), marking the transition to macro-instability (see Figure 18c). (4) When the excitation amplitude reaches 1.1 g, the cracks at the slope shoulder extend towards the slope toe, the slope top subsides further, and the slope toe exhibits bulging. A large number of cracks, developed along the X-joints, form on the slope surface, leading to extensive block detachment. The failure is dispersed and exhibits the characteristics of an avalanche failure mode (see Figure 18d).
Therefore, based on the macroscopic failure phenomena of the slope model (see Figure 18) and the evolution of PAHS values (see Figure 16c), the failure process is divided into four stages: elastic stage (0.1–0.2 g), plastic stage (0.2–0.5 g), cumulative damage stage (0.5–0.7 g), and unstable failure stage (0.7–1.1 g).
(2)
Progressive failure evolution process of Slope Model II
The failure mode of Model II shows clear differences from Model I: (1) The initial failure of Slope Model II exhibits a delayed characteristic, with cracks only just beginning to appear at a 0.4 g amplitude (see Figure 19a). (2) When the seismic amplitude increases to 0.5 g, the cracks at the slope shoulder significantly widen (2–5 mm), and cracks also appear in the weak interlayer (see Figure 19b). (3) After a 0.7 g amplitude excitation, the cracks in the weak interlayer deepen and extend. The cracks at the slope shoulder extend toward the slope toe but have not yet connected with the cracks at the toe (see Figure 19c). (4) The failure process in Model II is faster than in Model I. When the amplitude reaches 0.9 g, the cracks at the slope shoulder and toe connect, forming a “sliding surface.” Cracks at the slope back connect and extend, forming a “failure cavity” within the slope. The slope top subsides by approximately 2 cm, while the slope toe rises, eventually sliding out from the weak interlayer. In terms of failure mode, Model II tends more towards a landslide failure (see Figure 19d).

5. Discussion

By comparing the differences in the failure process and final failure modes between Slope Model I and Slope Model II, it can be observed that the presence of X-joints significantly reduces the integrity of the rock mass, resulting in the formation of tensile and shear cracks in Slope Model I at a relatively low acceleration of 0.2 g. The X-joints network provides multiple pathways for crack propagation, creating a complex, multi-directional stress field with slower energy dissipation and continuous damage accumulation, requiring a longer time for plastic deformation to develop. At failure, the rock mass forms a blocky structure, with friction and interlocking between blocks necessitating a higher load (1.1 g) for complete detachment from the parent mass. The resulting debris is larger in scale and more loosely aggregated compared to Slope Model II, consistent with findings by the Iymek avalanche. In contrast, Slope Model II exhibits a more intact structure, requiring stress to accumulate to a higher amplitude (0.4 g) before initial failure is triggered. Cracks propagate rapidly along the slope shoulder towards the toe, with a single failure path and concentrated energy release, enabling a swift transition from plastic deformation to cumulative failure. When the potential sliding surface is fully intersected (0.9 g), the rock mass slides integrally along a single slip bed, exhibiting a more concentrated instability process and tending towards a landslide failure pattern.
In summary, the core impact of X-joints lies in their alteration of the slope’s structural characteristics:
  • Integrity reduction: X-joints network diminishes slope cohesion and accelerates crack propagation.
  • Stress field complexity: multi-directional joints promote diverse stress concentration paths and delayed energy release.
  • Dispersed failure patterns: fragmentation and multi-surface failure modes increase the likelihood of avalanche-type behavior.

6. Conclusions

This study, through a shaking table test, investigated the dynamic response characteristics of rock slopes containing X-joints and underlying weak interlayers under seismic loading. It compared the failure modes of slopes with and without X-joints and analyzed the mechanism of X-joint influence. The key conclusions are as follows:
(1)
Due to the presence of a weak interlayer, the horizontal acceleration of low-frequency seismic waves responds significantly at the slope toe (beneath the weak interlayer), exhibiting a distinct “seismic isolation effect,” which is not influenced by the amplitude of the input seismic waves. When the frequency of the input seismic waves approaches the natural frequency of the slope model, the acceleration amplification factor increases sharply, resulting in a “resonance” phenomenon. In the middle and lower parts of the slope, and under low-amplitude seismic excitation, the response to vertical seismic waves is more pronounced.
(2)
By combining the changes in PAHS values obtained from the HHT analysis with the macroscopic deformation and failure phenomena of the slope, the failure process of the rock slope containing X-joints and underlying weak interlayer is divided into four stages: elastic stage (0.1–0.2 g), plastic stage (0.2–0.5 g), cumulative damage stage (0.5–0.7 g), and unstable failure stage (0.7–1.1 g). Marginal spectrum analysis further identifies the location of the damage within the slope.
(3)
The presence of X-joints significantly reduces the integrity of the slope rock mass, leading to earlier initiation of failure and a shorter elastic failure stage. During the plastic failure stage, X-joints facilitate multi-directional stress redistribution and reflection within the slope, delaying energy dissipation, prolonging the duration of this stage, and resulting in a more dispersed failure pattern.

Author Contributions

Conceptualization, H.M. and Y.S.; methodology, Y.S.; investigation and data curation, H.M., X.Y. and Y.L.; validation and formal analysis, L.Z. and Q.M.; writing—original draft preparation, H.M.; writing—review and editing, Y.S. and X.Y.; supervision and project administration, Y.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Research Project of the Basic Scientific Research Special Funds for Higher Education Institutions in Xinjiang Uygur Autonomous Region (Grant No. XJEDU2023P134), the Third Xinjiang Scientific Expedition Program (Grant No. 2022xjkk1305) and the Science and Technology Partnership Program of the Shanghai Cooperation Organization and International Science and Technology Cooperation Program, the Xinjiang Department of Science and Technology (Grant No. 2023E01005).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original data supporting the conclusions of this article will be made available by the authors without undue reservation.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Location of the Iymek avalanche and geological setting of the studied area.
Figure 1. Location of the Iymek avalanche and geological setting of the studied area.
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Figure 2. Geological setting of the Iymek: (a) geological conditions of the Iymek avalanche; (b) longitudinal profile of the A-A′; (c) the rear wall of the Iymek avalanche; (d) the debris of the Iymek avalanche and the rock masses within it.
Figure 2. Geological setting of the Iymek: (a) geological conditions of the Iymek avalanche; (b) longitudinal profile of the A-A′; (c) the rear wall of the Iymek avalanche; (d) the debris of the Iymek avalanche and the rock masses within it.
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Figure 3. Construction process of the slope model with X-joints.
Figure 3. Construction process of the slope model with X-joints.
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Figure 4. Equipment used in the experiment: (a) shaking table; (b) rigid model box; (c) tri-axial accelerometers; (d) dynamic signal testing and analysis system; (e) HD camera.
Figure 4. Equipment used in the experiment: (a) shaking table; (b) rigid model box; (c) tri-axial accelerometers; (d) dynamic signal testing and analysis system; (e) HD camera.
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Figure 5. Slope model and distribution of the sensor: (a) slope model monitoring points layout (2D); (b) slope model monitoring points layout (3D).
Figure 5. Slope model and distribution of the sensor: (a) slope model monitoring points layout (2D); (b) slope model monitoring points layout (3D).
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Figure 6. Acceleration time curve and Fourier spectrum of loading natural seismic waves: (a) Wuqia seismic wave (X-direction); (b) Wuqia seismic wave (Z-direction); (c) Akto seismic wave (X-direction); (d) Akto seismic wave (Z-direction).
Figure 6. Acceleration time curve and Fourier spectrum of loading natural seismic waves: (a) Wuqia seismic wave (X-direction); (b) Wuqia seismic wave (Z-direction); (c) Akto seismic wave (X-direction); (d) Akto seismic wave (Z-direction).
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Figure 7. Transfer function curves of the slope model: (a) transfer function curve after 0.2 g seismic wave loading (X-direction); (b) transfer function curve after 0.4 g seismic wave loading (X-direction); (c) transfer function curve after 0.2 g seismic wave loading (Z-direction); (d) transfer function curve after 0.4 g seismic wave loading (Z-direction).
Figure 7. Transfer function curves of the slope model: (a) transfer function curve after 0.2 g seismic wave loading (X-direction); (b) transfer function curve after 0.4 g seismic wave loading (X-direction); (c) transfer function curve after 0.2 g seismic wave loading (Z-direction); (d) transfer function curve after 0.4 g seismic wave loading (Z-direction).
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Figure 8. The variations in the natural frequency of the slope model after seismic wave loading at different stages.
Figure 8. The variations in the natural frequency of the slope model after seismic wave loading at different stages.
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Figure 9. Distribution characteristics in PHA amplification factor under the effect of different seismic waves with 0.3 g amplitude: (a) Wuqia seismic wave; (b) Akto seismic wave; (c) 5 Hz Sine wave; (d) 15 Hz Sine wave; (e) 25 Hz Sine wave; (f) 35 Hz Sine wave.
Figure 9. Distribution characteristics in PHA amplification factor under the effect of different seismic waves with 0.3 g amplitude: (a) Wuqia seismic wave; (b) Akto seismic wave; (c) 5 Hz Sine wave; (d) 15 Hz Sine wave; (e) 25 Hz Sine wave; (f) 35 Hz Sine wave.
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Figure 10. Variations in PHA amplification factor under different amplitude seismic wave loading: (a) along the slope surface; (b) along the vertical section within the slope body.
Figure 10. Variations in PHA amplification factor under different amplitude seismic wave loading: (a) along the slope surface; (b) along the vertical section within the slope body.
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Figure 11. Variations in PHA amplification factor under sine wave of different frequencies: (a) under a loading amplitude of 0.1 g; (b) under a loading amplitude of 0.2 g; (c) under a loading amplitude of 0.3 g; (d) under a loading amplitude of 0.4 g.
Figure 11. Variations in PHA amplification factor under sine wave of different frequencies: (a) under a loading amplitude of 0.1 g; (b) under a loading amplitude of 0.2 g; (c) under a loading amplitude of 0.3 g; (d) under a loading amplitude of 0.4 g.
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Figure 12. Distribution characteristics in PVA amplification factor under the effect of different seismic waves with 0.3 g amplitude: (a) Wuqia seismic wave; (b) Akto seismic wave; (c) 5 Hz Sine wave; (d) 15 Hz Sine wave; (e) 25 Hz Sine wave; (f) 35 Hz Sine wave.
Figure 12. Distribution characteristics in PVA amplification factor under the effect of different seismic waves with 0.3 g amplitude: (a) Wuqia seismic wave; (b) Akto seismic wave; (c) 5 Hz Sine wave; (d) 15 Hz Sine wave; (e) 25 Hz Sine wave; (f) 35 Hz Sine wave.
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Figure 13. Variations in PVA amplification factor under different amplitude seismic wave loading: (a) along the slope surface; (b) along the vertical section within the slope body.
Figure 13. Variations in PVA amplification factor under different amplitude seismic wave loading: (a) along the slope surface; (b) along the vertical section within the slope body.
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Figure 14. Variations in PVA amplification factor under sine wave of different frequencies: (a) under a loading amplitude of 0.1 g; (b) under a loading amplitude of 0.2 g; (c) under a loading amplitude of 0.3 g; (d) under a loading amplitude of 0.4 g.
Figure 14. Variations in PVA amplification factor under sine wave of different frequencies: (a) under a loading amplitude of 0.1 g; (b) under a loading amplitude of 0.2 g; (c) under a loading amplitude of 0.3 g; (d) under a loading amplitude of 0.4 g.
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Figure 15. The value of RAAF under Sine waves: (a) under excitation of 0.2 g-5 Hz; (b) under excitation of 0.4 g-5 Hz; (c) under excitation of 0.2 g-15 Hz; (d) under excitation of 0.4 g-15 Hz; (e) under excitation of 0.2 g-25 Hz; (f) under excitation of 0.4 g-25 Hz.
Figure 15. The value of RAAF under Sine waves: (a) under excitation of 0.2 g-5 Hz; (b) under excitation of 0.4 g-5 Hz; (c) under excitation of 0.2 g-15 Hz; (d) under excitation of 0.4 g-15 Hz; (e) under excitation of 0.2 g-25 Hz; (f) under excitation of 0.4 g-25 Hz.
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Figure 16. Hilbert spectrum analysis under horizontal Wuqia seismic wave loading: (a) Hilbert spectrum at different measuring points with 0.3 g amplitude; (b) Hilbert spectrum at different measuring points with 0.7 g amplitude; (c) variations in PAHS in the slope model under different amplitudes.
Figure 16. Hilbert spectrum analysis under horizontal Wuqia seismic wave loading: (a) Hilbert spectrum at different measuring points with 0.3 g amplitude; (b) Hilbert spectrum at different measuring points with 0.7 g amplitude; (c) variations in PAHS in the slope model under different amplitudes.
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Figure 17. Marginal spectrum analysis under horizontal Wuqia seismic wave loading: (a) marginal spectrum at different measuring points with 0.3 g amplitude; (b) marginal spectrum at different measuring points with 0.7 g amplitude; (c) variations in PAMS in the slope model under different amplitudes.
Figure 17. Marginal spectrum analysis under horizontal Wuqia seismic wave loading: (a) marginal spectrum at different measuring points with 0.3 g amplitude; (b) marginal spectrum at different measuring points with 0.7 g amplitude; (c) variations in PAMS in the slope model under different amplitudes.
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Figure 18. The failure phenomena of Slope Model I subjected to multi-stage seismic excitations: (a) original state and after 0.2 g amplitude seismic wave loading; (b) after 0.5 g amplitude seismic wave loading; (c) after 0.7 g amplitude seismic wave loading; (d) after 1.1 g amplitude seismic wave loading. Note that the deformation and failure phenomena indicated by the numbers in the model diagram are shown in the corresponding photographs.
Figure 18. The failure phenomena of Slope Model I subjected to multi-stage seismic excitations: (a) original state and after 0.2 g amplitude seismic wave loading; (b) after 0.5 g amplitude seismic wave loading; (c) after 0.7 g amplitude seismic wave loading; (d) after 1.1 g amplitude seismic wave loading. Note that the deformation and failure phenomena indicated by the numbers in the model diagram are shown in the corresponding photographs.
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Figure 19. The failure phenomena of Slope Model II subjected to multi-stage seismic excitations: (a) original state and after 0.4 g amplitude seismic wave loading; (b) after 0.5 g amplitude seismic wave loading; (c) after 0.7 g amplitude seismic wave loading; (d) after 0.9 g amplitude seismic wave loading. Note that the deformation and failure phenomena indicated by the numbers in the model diagram are shown in the corresponding photographs.
Figure 19. The failure phenomena of Slope Model II subjected to multi-stage seismic excitations: (a) original state and after 0.4 g amplitude seismic wave loading; (b) after 0.5 g amplitude seismic wave loading; (c) after 0.7 g amplitude seismic wave loading; (d) after 0.9 g amplitude seismic wave loading. Note that the deformation and failure phenomena indicated by the numbers in the model diagram are shown in the corresponding photographs.
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Table 1. The physical and mechanical parameters of rock mass.
Table 1. The physical and mechanical parameters of rock mass.
Rock CharacterDensity (kg/m3)Compressive Strength (MPa)Tensile Strength (MPa)Elastic Modulus (GPa)Poisson’s Ratio (μ)Cohesion (MPa)Internal Friction Angle φ (◦)
MarblePrototype slope2.73903.3420.2216.539.5
Model slope2.653.7350.2160.3880.20.71128.3
Metamorphic conglomeratePrototype slope2.5355212.30.191033
Model slope2.50.4180.0440.1200.220.16534
Table 2. Parameters of natural seismic motions.
Table 2. Parameters of natural seismic motions.
Seismic EventsComponentsPredominant Frequency (Hz)PGA (cm/s2)
Wuqia Ms6.8EW1.93101.14
NS2.09139.06
UD0.3951.90
Akto Ms6.7EW20.2831.42
NS12.1727.03
UD10.7414.02
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Meng, H.; Shang, Y.; Zhou, L.; Li, Y.; Yi, X.; Meng, Q. Analysis of Dynamic Response Characteristics and Failure Pattern of Rock Slopes Containing X-Joints and Underlying Weak Interlayers. Appl. Sci. 2025, 15, 10209. https://doi.org/10.3390/app151810209

AMA Style

Meng H, Shang Y, Zhou L, Li Y, Yi X, Meng Q. Analysis of Dynamic Response Characteristics and Failure Pattern of Rock Slopes Containing X-Joints and Underlying Weak Interlayers. Applied Sciences. 2025; 15(18):10209. https://doi.org/10.3390/app151810209

Chicago/Turabian Style

Meng, He, Yanjun Shang, Liyun Zhou, Yangfan Li, Xuetao Yi, and Qingsen Meng. 2025. "Analysis of Dynamic Response Characteristics and Failure Pattern of Rock Slopes Containing X-Joints and Underlying Weak Interlayers" Applied Sciences 15, no. 18: 10209. https://doi.org/10.3390/app151810209

APA Style

Meng, H., Shang, Y., Zhou, L., Li, Y., Yi, X., & Meng, Q. (2025). Analysis of Dynamic Response Characteristics and Failure Pattern of Rock Slopes Containing X-Joints and Underlying Weak Interlayers. Applied Sciences, 15(18), 10209. https://doi.org/10.3390/app151810209

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