Introduction

On December 16, 1920, an earthquake of magnitude Ms 8.5 occurred near Ganyanchi, Haiyuan County, Ningxia, China (named Haiyuan earthquake). This earthquake triggered widespread disaster events, including the landslides mainly distributed in areas such as Xiji, Jingning, and Huining Counties (see Fig. 1), where Mercalli seismic intensities (Dowrick 1996) of VIII and IX were primarily concentrated (Zhuang et al. 2018; Xu et al. 2020). Survey results and satellite images revealed that landslides in zones with seismic intensities between IX to XI covered an area of around 218 km2, with around 5384 landslides. According to Xu et al. (2018), the Haiyuan earthquake and landslide disasters it triggered caused numerous residential houses to collapse simultaneously, with 32,000 casualties in the zones with intensity IX to XI. Zhang and Wang (1995) conducted a comprehensive investigation on the area of landslide concentration resulting from the 1920 Haiyuan earthquake and the 1718 Tongwei earthquake. They found that these landslides caused by the seismic activity on the Loess Plateau show various sliding forms and failure mechanisms. Combining the field investigation results and laboratory test analyses, Zhang (1999) classified these loess landslides into seismic subsidence, loess liquefaction, and loess earthquake-induced landslides. Jingning County is located in the northern of the Longxi Basin in China, about 120 km from the Haiyuan earthquake epicenter (see Fig. 1). It is one of the typical areas where the Haiyuan earthquake-induced landslides heavily. Differ from other loess earthquake landslides classified by Zhang (1999), most of the landslides in this region show low-angle slopes and low water contents but exhibit the characteristics of long run-out landslides, such as substantial sliding scales and extensive disaster range, which implies a unique initiation mechanism.

Fig. 1
figure 1

Isoseismal map of the 1920 Haiyuan earthquake. The seismic intensity in this figure is the Mercalli seismic intensities (Dowrick 1996)

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Much progress has been achieved in studying the mechanisms of earthquake-induced landslides over the past decades. Mechanisms such as air cushion, soil particle fragmentation, and liquefaction effects have recently been proposed (Sassa et al. 1996, 2004, 2005; Wang et al. 2000; Yin et al. 2011a, b; Zhang et al. 2011; Tang et al. 2015). In addition, numerous researchers have conducted many field investigations and experimental analyses to study the initiation mechanisms of low-angle loess seismic landslides. Based on shaking table experiments, Wu et al. (2015, 2020a,b) found that the top of loess slopes with low angles exhibit typical seismic subsidence landslide characteristics under IX intensity seismic loading and stated that this phenomenon is one of the critical factors responsible for slope failure. Zhang et al. (2016, 2017) concluded that the high velocity of seismic loess landslide at the initial stage is the combined contribution of fluctuation, vibration, progressive damage of the slope body, and peak-residual strength drop of the locked-segment section. Furthermore, Li et al. (2020) demonstrated that there are certain micro-convex bodies on the sliding surface of loess landslides, and the movement of the slide body along the slide surface is not linear. Such studies illustrate that the damage at the top of the slope, the evolution of the sliding surface, and the high-speed initiation characteristics of low-angle loess landslides under seismic action are critical to reveal the initiation mechanism. Generally, the failure of such low-angle slopes under seismic activity is often controlled by multi-factors, such as macroscopic slope structure and microscopic soil properties. A clear understanding of the initiation mechanism and sliding pattern of loess landslides is essential for preventing disasters. However, current research on the mechanisms of earthquake-triggered low-angle loess-mudstone interface landslides still needs to be improved; there is still some ambiguity about the mechanism of such landslides. Therefore, a method is required to research the initiation mechanism of earthquake-triggered low-angle loess landslides based on the macro- and microscopic damage characteristics.

In recent years, geotechnical engineers have favored the DEM numerical model for seismic instability analysis because form variables do not limit it and can simulate discontinuities such as cracking and fracture of geotechnical materials. In this study, we performed a detailed field investigation of the Sunjiagou landslide in Jingning caused by the 1920 Haiyuan earthquake. We detected the slope’s initial sliding process via the DEM simulation. The initiation mechanism of low-angle loess-mudstone interface seismic landslides is discussed by integrating the slope macro-damage characteristics, the evolution pattern of micro-crack in the sliding zone, the velocity and stress variations characteristics, and the seismic PGA amplification effect. Finally, we proposed a new initial mechanism containing locked segment effects for this earthquake-triggered low-angle loess-mudstone interface landslides.

Geological and geomorphologic setting

History landslide events

The 1920 Haiyuan earthquake had a Ms magnitude of 8.5, with an epicenter at 36.7° N and 105.7° E, a Mercalli seismic intensity of XII, and a source depth of 17 km. The macroscopic epicenter is located in Shaomaying between Xi’an State and Ganyanchi, which is also situated in Haiyuan County (Fig. 1). The areas with severe landslide disasters caused by the earthquake mainly include the Counties of Xiji, Jingning, Huining, Haiyuan, Guyuan, and Tongwei. The Jingning, Xiji, and Huining areas have a more apparent seismic subsidence phenomenon. Figure 1 shows the seismic intensity and landslide distribution of the Haiyuan earthquake. Landslides induced by the Haiyuan earthquake are mainly located in the IX degree and X degree regions around the epicenter. There, Jingning County is about 120 km from the epicenter, which experienced a seismic intensity of IX during the Haiyuan earthquake.

This study selected a typical landslide concentration area in Jingning County as the study site. A region of 1700 × 3075 m was chosen for analysis (Fig. 2). The thickness of loess cover in the study area is 20–50 m. The geomorphology is mainly represented by a loess ridge and loess hill, a typical loess hilly landform. The slope gradient in the area is mainly 15–20°, allowing for the development of landslides along both sides of the loess ridge. In this case, multiple landslides sliding in the same direction are interconnected to form a large landslide complex. Based on Fig. 2, there are many residential buildings and engineering projects in areas where landslides are densely distributed. These buildings and settlements are at constant risk from earthquake-induced landslides. Therefore, it is essential to study the mechanism of initiating such landslides under the effect of earthquakes, thus proposing scientific and practical preventive measures to improve the seismic defense capacity of the towns in the area.

Fig. 2
figure 2

Extensive landslides in the study area, Jingning County, Gansu Province, China. The black arrow indicates the direction of landslide movement

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Sunjiagou landslide

Sunjiagou landslide is located west of Jingning County, Pingliang City, Gansu Province, China, in the northern part of the Longxi Basin (Figs. 1 and 2). It is one of the most typical landslides formed in the Jingning area by the Haiyuan earthquake of 1920. The Sunjiagou landslide consists of two giant landslides (see regions A and B in Fig. 3) sliding along the same loess ridge. Our investigation results indicate that shear sliding occurred along the loess-mudstone interface, a typical loess-mudstone junction-type landslide. The original slope angle of the landslide is 17°, the slope height is 185 m, the slope width is 400 m, the sliding area is about 2.4 × 105 m2, and the total volume is about 1.0 × 105 m3. The slide faces up through the overlying loess layer to the top of the ridge, which is steep and nearly upright with many vertical cracks. The lower part of the gentle slopes of the sliding surface lies on the loess-mudstone interface, and the soils of the sliding zone are mostly loess and broken mudstone. The back edge of the landslide is well-defined, with the back wall extending some 34 m high and showing numerous vertical cracks. In contrast, the sidewalls are large, gently angled, and have noticeable sliding scratches. When the landslide occurred, the mobilized soil diverted the river in the valley and washed away the village. The landslide deposits have now been leveled for farming or converted to terraces.

Fig. 3
figure 3

Characteristics of Sunjiagou landslide. (a) Overview of the Sunjiagou landslide, different colored dots represent locations sampled in Fig. 3a and b. (b) loose loess in the upper part of the slope. (c) loess-mudstone interface of this landslide

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Due to the region’s arid climate and gullies, soil moisture content tends to be low, at most 15%. The upper part of loess slopes is a wind-accumulated, under-compacted soil, typical of arid and semi-arid regions whose structural characteristics include an ample pore space. In contrast, the lower part consists of a basal mudstone layer. Based on the slope of the surrounding terrain and the original slope of the landslide determined by the restoration method of the principle of equal volume, combined with the results of on-site measurements, the profile of the landslide before land sliding was drawn (Fig. 4). As a result of long-term agricultural activities, the original landslide deposit has been modified several times, and the current topographic line of the slope as measured in the field is shown in Fig. 4.

Fig. 4
figure 4

Geological profile of the Sunjiagou landslide results from the field investigation

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The slope strata consist of (a) Quaternary loess layer (Fig. 3b): The overlying loess layer in the area is Upper Pleistocene, Quaternary (Qeol3), which is characterized by a yellowish-brown color, loose soil structure, large pore space development, and low average moisture content. (b) Neoproterozoic mudstone (Fig. 3c): The Neoproterozoic mudstone in the landslide area is brick-red in color, dense, with good water tightness, no apparent stacking, and high compressive and shear strength. Field exploration cores show that the contact with loess is more strongly weathered, and outcrops are observed on both sides of deep-cut river valleys and steep slopes with severe loess denudation.

Methodology

Principle of DEM

In a DEM model, the essential components are particles, walls, and contacts (Fig. 5a), used to simulate various materials (Cundall and Strack 1979). Particles are rigid bodies with mass that can translate and rotate, and they interact with each other through contact forces through internal inertial forces, moments, etc. Each contact corresponds to an interface between two particles, allowing the particles to interact with each other according to Newton’s laws of motion to update the forces and displacements. In this study, the Particle Flow Code is employed to run the failure process of the Sunjiagou loess slope. Then, the parallel bonding model is used to simulate the mechanical behavior of the loess and mudstone materials, where the bonding behavior is mainly achieved by placing cement between the particles (Fig. 5b). This cement is capable of transmitting forces and moments between different particles, where moments include bending moments (Fig. 5c) and torsional moments (3D only). Currently, the parallel bond model is commonly used to model geotechnical materials with cementing properties in engineering geology, also including the study of loess and mudstone with cementing and cohesive properties (Jiang et al. 2017; Wu et al. 2020a,b; Chang et al. 2021a, b, 2022; Sun et al. 2023).

Fig. 5
figure 5

DEM model and the linear parallel bond model. In Fig. 5b, \(A\) denotes the cross-sectional area of the cement

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The force-displacement update of parallel bond forces and moments includes the following steps. First, update the cross-sectional properties of the bond and update the parallel bond normal stiffness (pb_Fn); when the relative normal displacement exceeds the parallel-bond surface gap (gn), the cement is damaged (Fig. 5d). Second, update the parallel bonded shear stiffness (pb_Fs) when the relative shear-displacement exceed the parallel-bond shear-gap (gs), the cement is damaged (Fig. 5e). Third, update parallel bond bending moment (Mb), if the cumulative bend-rotation increment reaches the bending strength (gb), cement breaks (Fig. 5f). Fourth, update the maximum normal stress and shear stress at the parallel bond edge and determine whether the maximum normal stress exceeds the strength limit. If the maximum normal stress exceeds the normal strength limit, the tension damages the contact. If not, determine whether the shear stress exceeds the shear strength, and if so, the contact is damaged by shear.

Micro-mechanical parameters

During the investigation of the Sunjiagou landslide site, samples of in-situ loess and mudstone were collected from several locations within the slope (see Fig. 3a). The average cohesion of the loess specimen was 78.1 kPa, and the internal friction angle was 25.3°. Meanwhile, the average cohesion of the mudstone specimen was 2.27 MPa, and the internal friction angle was 43.4°, as measured by the laboratory triaxial compression test. In the DEM model, the macroscopic physico-mechanical parameters of particles do not directly correspond to the micro-parameters, and corresponding numerical simulation experiments usually link both of them. A numerical parameter calibration program was used to reproduce laboratory triaxial compression experiments to obtain the relationship between microscopic and macroscopic mechanical indices. The microscopic parameters are inferred from the target mechanical index to obtain the basic parameters of the slope model particles. For the calibration of the loess particles, the particle radius is 0.0005–0.0015 m in a 2D biaxial numerical model, and the model size is 0.1 m × 0.2 m, which generates 5149 particles in total. A servo mechanism was used to control the confining pressure during compression of the specimens, and several experimental calculations were performed to obtain the strength parameters of the soil under different confining pressures. The stress-strain data during the simulation were obtained. The stress-strain curves of the numerical specimens were plotted at 50, 100, and 150 kPa for the confining pressure (Fig. 6). The strength parameters of the loess were obtained by plotting the damaged envelope according to the Mohr-Coulomb strength theory. The results (c = 76.3 kPa, \(\varphi=26.2^{\circ}\)) were close to those of the loess specimens obtained from the indoor tests (c = 78.1 kPa, \(\varphi=25.3^{\circ}\)). The micro-parameters of the mudstone in the lower part of the slope model were obtained using the same method described above.

Fig. 6
figure 6

Biaxial compression test with different confining pressures in the DEM model

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As the actual slope model of Sunjiagou is large, modeling with particles of the size used for the above calibration would result in an unmanageable number of generated particles, and the calculation could not be performed. Therefore, the modeling process requires equal scaling of the size of the particles. Potyondy and Cundall (2004) analytically calculated that the macroscopic elastic Young’s modulus of the material in the 2D DEM model is independent of the particle size. At the same time, the normal stiffness of the particles and the cement correspond to their Young’s moduli.

$$k_n=2 E_c$$
(1)
$$p b_{-} k_n=\frac{p b_{-} E_c}{R_a+R_b}$$
(2)

Where kn and pb_kn are the normal stiffness of the particle and the cement, Ec and pb_Ec are Young’s moduli of the particle and cement, respectively. Ra and Rb are the radii of the particles on both sides of the cement (see Fig. 5b). According to the above correspondence, the micro-mechanical parameters of the numerical test model and the slope model were determined, as shown in Table 1.

Table 1 Micro-mechanical parameters of the DEM slope model
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Earthquake Loading

Since no relevant seismic wave data were recorded for the 1920 Haiyuan earthquake, 70s-band seismic wave data from the 2013 Min-Zhang earthquake in Gansu Province were used as a proxy in this study. The 2013 Gansu Min-Zhang Ms 6.6 earthquake was one of the largest earthquakes in the Loess Plateau in the last decade, which caused many landslides and other geologic hazards (Xu et al. 2013). Accordingly, the 2013 Min-Zhang earthquake data is usually used as a reference when studying seismic hazards in the Loess Plateau. The seismic wave data are the acceleration times recorded at the Minxian station 18 km from the epicenter of the 2013 earthquake. Peak acceleration amplitudes of the original seismic waves in the NS (North-South) and UD (Up-Down) directions were 0.96 m/s2 and 2.16 m/s2, respectively. The acceleration data of the Min-Zhang earthquake were scaled up to the earthquake’s intensity in the Jingning area during the Haiyuan earthquake. The acceleration amplitudes in the NS and UD directions after processing were 1.92 m/s2 and 4.32 m/s2, respectively, as shown in Fig. 7. NS- and UD-oriented seismic waves were employed to simulate horizontal and vertical seismic loads. Acceleration data were integrated into the velocities for ease of loading. The bottom boundary of the model is selected as the seismic input source, and the propagation direction is bottom-up, with transmission boundaries at and around the bottom of the model.

Fig. 7
figure 7

Seismic acceleration time curve of the Min-Zhang earthquake in 2013. Here, NS indicates the North–South direction and UD indicates the Up–Down (vertical) directions of the seismic data

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In the DEM model, boundary forces are applied to boundary particles, causing the boundary to absorb the kinetic energy of the incident wave, thus simulating an infinite medium. The relationship between the boundary and the particle velocity can be described as

$$F = 2R\rho C\dot u$$
(3)

where R is the particle radius, ρ is the particle density, C is the seismic wave velocity and \({\dot u}\) is the particle velocity. During the transmission of seismic waves at the boundary, the incident wave (\(\dot{\text{U}}\text{(t)}\)) amplitude is doubled to prevent the amplitude from being halved when the energy is absorbed. At this point, the contact force F between the boundary particles is

$$F = 2R\rho C[2\dot U({\rm{t}}) - \dot u]$$
(4)

Finally, the damping coefficients of the normal viscous and shear viscous dampers of the particles in the model were set to 0.16, according to the existing research results (Yang 2011; Murugaratnam et al. 2015).

Slope Numerical model

The dimensions of the DEM slope model in the study are the same as the slope dimensions of the geologic profile in Fig. 4. After generating a wall with a slope profile, particles with corresponding characteristics will be generated at different locations. When the stresses within the slope reached equilibrium, the final discrete unit slope model was produced (Fig. 8). The slope model was 690 m long and 185 m high, with the upper loess particles ranging from 0.25 to 0.75 m in size, totaling 23,729 particles, while the lower mudstone particles ranged from 0.3 to 0.75 m in size, totaling 51,695 particles. During the simulation, four measurement circles (S1-S4) with a radius of 10 m were laid on the contact surface of the loess-mudstone to monitor the changes in soil stresses during the slope failure. Twelve velocity monitoring points (V11-V43) were also set up on the four vertical profiles of the slope to monitor changes in soil velocity. The sides of the slope model were set up as viscous transport boundaries, and the bottom of the model was a seismic wave input boundary.

Fig. 8
figure 8

DEM model and the monitoring points configuration of the Sunjiagou landslide. The region between the two white dotted lines represents the sliding zone

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Results

Macro-damage characteristics

The initial failure processes of the slope under the seismic activity are shown in Fig. 9. During the simulation, the distribution of micro-cracks in the slope was monitored, with shear cracks demonstrated in black and tensile cracks in red. Five seconds after the earthquake, the acceleration amplification effect near the top of the slope resulted in the loosening of the slope shoulder and the formation of a distinct tensile fracture (Fig. 9a). At this point, a large number of red tensile cracks were distributed on the top of the slope. As a result of the collapse of the structure at the top of the slope, severe fragmentation and disintegration of the loess in this area was produced (see region a-1 in Fig. 9a). In contrast, only a tiny portion of the soil at the toe and surface of the slope face was damaged. As the intensity of seismic activity increases, the cracks inside the slope gradually increase, and the broken soil at the top of the slope gradually sinks and forms a small groove (Fig. 9b). At t = 10 s, the intensity of seismic activity applied to the slope model reaches the maximum value. By this time, the upper slope body had produced more extensive damage, creating a large amount of extensively fragmented soil (see region b-1 in Fig. 9b), with damaged crack groups extending slightly downward along the loess-mudstone interface.

Fig. 9
figure 9

Failure process of the Sunjiagou landslide from the DEM results. The black dashed line indicates the localized damage interface

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Afterward, the small groove at the top of the slope gradually widens as the tensile and fragmentation damage on the slope shoulder gradually increases (10–20 s). With time, the soil on the upper slope surface of the slope began to show visible damage, which macroscopically manifested itself as structural damage, such as seismic subsidence of the slope body (see region c-1 in Fig. 9c). Although the top of the slope and the upslope surface are severely damaged at this moment, the whole slope is still in a relatively stable state (Fig. 9c). We believe that cracks in the slopes continue to propagate down the contact while accumulating slope damage and potentially creating a locking effect in the lower and middle section of the slope. We elaborate on this further in Analysis of slope locked segment. At t = 30 s, the crack on the slope loess-mudstone interface extends entirely to the foot of the slope through a circular shear zone formed inside the slope (see black arrows in Fig. 9d). The groove at the top of the slope gradually widened as the overlying loess on the contact surface continued to slide downward. At 40 s, the soil at the top of the slope was broken entirely (see region e-1 in Fig. 9e), the upper part of the slope experienced significant tensile damage, and then the sliding body began to detach from the slope toe (Fig. 9e).

Figure 10 illustrates the subsequent accumulation process of the Sunjiagou landslide. Finally, the sliding mass was mainly accumulated near the original slope toe (t = 120 s), and the maximum thickness of the accumulation was about 40 m. To validate the numerical model, we analyzed the results of the field investigation and DEM simulation (Fig. 10c). In the DEM model, the distance between the leading edge of the final deposit and the original slope toe is 826.6 m, which is close to the results of the field investigation (900 m). It should be noted that within 102 years after the occurrence of the Sunjiagou landslide, the original deposit of the landslide has undergone several human excavations for agricultural land and construction, so it cannot be directly used as the post-landslide topography for comparison with the numerical results. Nevertheless, the final runout distance of the sliding mass in the numerical model proves the validity of the DEM model.

Fig. 10
figure 10

Accumulation characteristics of the Sunjiagou landslide from the DEM simulation. Figure 10c shows the final deposit of the Sunjiagou landslide

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Analysis of slope locked segment

Crack evolution in the sliding zone

Based on the presumption of deformation accumulation during the formation of the sliding surface mentioned in Macro-damage characteristics, the change in the number of cracks in the sliding zone of the slope was monitored during the simulation. The monitoring region of cracks extends 15 m on each side of the loess-mudstone interface, as shown in the white dotted line in Fig. 8.

According to the simulation results in Macro-damage characteristics, it can be determined that the sliding surface within the slope was formed by cracks before the 30 s seismic activity. Therefore, the total crack number change within the sliding zone 30 s before the seismic activity was investigated. In Fig. 11, the crack number in the sliding zone shows a sharp increase from 0 s to 10 s (slope of cut line K1 = 338.0), which is attributed to the severe seismic damage at the top of the slope during the first 10 s, resulted in severe soil damage and rapid crack growth. After the destruction of most of the soil at the top of the slope (slope of cut line K2 = 88.7), the cracks in the sliding zone grow slower between 10 and 21.5 s, which indicates the deformation damage of the slope decreases in the period 10–21.5 s. The time point of 21.5 s is the critical point for the growth rate of the crack number; after that, the crack number in the sliding zone increases again at a higher rate (slope of cut line K3 = 280.3). This phenomenon suggests that the cumulative deformation within the sliding zone reaches a certain threshold at 21.5 s, followed by the downward acceleration of the slope body along the interface. The increase in the crack number within the sliding zone is reminiscent of a particular damage mechanism in slopes, i.e., the locked segment effect. Specifically, the slope destabilization process produces a high-intensity zone in the stress concentration area, which plays a controlling role in the stability of the slope. Many scholars believe that this zone represents the locked portion of the slope (Yin et al., 2011a; Tang et al. 2015; Xue et al., 2014; Liu et al. 2020). Based on the above analysis, the crack propagation process in the sliding zone was plotted in Fig. 12. Two-time points, t = 10 s and t = 21.5 s, were employed to determine the crack group front expanding location. The results indicate that the damage crack group within the sliding zone extended to 254 m and 390 m, respectively (see Fig. 12b and d). Therefore, the 254 to 390 m range of the sliding zone is determined as the locked segment of the Sunjiagou slope.

Fig. 11
figure 11

Characterization of the variation in the mirco-crack number in the sliding zone, denoted by the blue curve

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Fig. 12
figure 12

Evolution characteristic of micro-crack in the sliding zone at different moments

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Stress evolution of the locked segment

The stress variations within the locked segment during slope failure were analyzed to validate the above points. The stress variation curves of the slope body within the four measurement circles (see Fig. 8) are shown in Fig. 13, and the given stresses represent the combined stresses in the horizontal and vertical directions.

Fig. 13
figure 13

Stress variation characteristic of the locked segment. S1–S4 represent the stress measurement circles set in Fig. 8

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According to Fig. 13, the stress trends in the four circles measured within 30 s tend to be similar. During the first 10 s of the earthquake, the loess and mudstone structure was not damaged because the cracks in the contact surface did not extend into the locked segment (254–390 m). As a result, the stress changes within the soil during this stage show large fluctuations with seismic activity and are generally in a growth mode. At 10–18 s, the damage stage of the locked segment is started. During this stage, the stress in the locked region continued to increase, but with small fluctuations. At 18 s, the stress in the locked segment region suddenly increased and decreased quickly after reaching the limit value at 21.5 s. The stress variation results indicate that during seismic activity, the slope is susceptible to stress concentration in the locked segment, and cumulative damage occurs continuously, which can rapidly increase stress in the locking section within a short period (18–21.5 s). When the internal stress concentration reaches a specific value and exceeds the limit shear strength of the locked segment (at t = 21.5 s), the locked segment shows brittle damage mode, and then the slope damage starts to accelerate. Therefore, the locked segment of the slope has an energy accumulation effect; that is, it stores a large amount of elastic strain energy before it is damaged. When the locked segment undergoes brittle disruption, the energy is converted into slope kinetic energy, which may be one of the reasons why such low-angle landslides are characterized by high-speed initiation.

Velocity and acceleration responses

Seisimic amplification effect

The velocity profiles of the slope body in different slope locations were extracted during the simulation. The acceleration-time profiles of different places of the slope before damage were obtained by converting the average velocity of particles at different monitoring points. This study defines the ratio of the peak ground acceleration (PGA) at the measurement point to the PGA at the reference point as the PGA amplification factor. The PGA amplification factor curves on the four vertical profiles of the slope model are plotted in Fig. 14. The horizontal coordinate of the curve is the ratio (h/H) of the actual elevation (h) at the monitoring point to the total elevation (H) of the vertical profile.

Fig. 14
figure 14

Seismic PGA amplification factor of the Sunjiagou landslide

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The PGA amplification factors on all four vertical profiles show varying forms increase with elevation. In addition, the loess mudstone interface significantly affects the acceleration amplification of the slope. The PGA amplification factor curve accelerates as height increases toward the loess-mudstone interface. Overall, the PGA amplification factor is more significant in the upper part of the slope than in the lower part (2.4, 3.6). The PGA amplification factors (1.4, 1.6) in the lower part of the slope also increased with the elevation gradient, though the increase is slight. The PGA analysis results show that the amplification effect is consistent with the severe damage in the upper part of the initial slope, which made the top of the slope the first area to be damaged under seismic action.

Initial velocity characteristics

The velocity variations of the overlying loess at four different locations on the slope (V13, V23, V33, and V43 in Fig. 8) are shown in Fig. 15. Comparing the velocity variations curves at the four different locations, the soil velocities at the upper part of the slope (Fig. 15a and b) are significantly more significant during the first 20 s, showing a robust seismic amplification effect. In contrast, the velocities of the soil in the lower part of the slope (Fig. 15c and d) are small within the first 20 s and show a relatively stable character. As the deformation damage extends along the loess-mudstone interface, the movement of the lower part of the slope begins to accelerate in a relatively short period as the sliding surface continues to form downward. That is, soils with low velocity (V < 0.5 m/s) motion acquire high velocity (V = 4.75 m/s) in a short period (25–27.5 s), and this phenomenon is more pronounced near the slope toe. Generally, low-angle loess landslides (< 20º) rarely have such high initiation velocities. Figure 15a and c shows that the start-up acceleration effect characterizes soils in the upper and middle parts of the slope. The velocity characteristics of the soil movement verify the ideas in Analysis of the Initiation Mechanism from another perspective. That is, the damage of this earthquake-triggered landslide at the loess-mudstone interface is related to a kind of sudden initiation mode following the failure of the locked segment.

Fig. 15
figure 15

Velocity characteristics of the sliding mass during the slope failure process

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Analysis of the initiation mechanism

Analysis of slope locked segment and Velocity and acceleration responses analyzed the initiation mechanism of the low-angle loess-mudstone seismic landslides via macroscopic damage, micro-crack evolution, as well as the stress-velocity variations characteristics of the slopes, respectively. This section outlines the mechanisms of formation of this type of slope. As shown in Fig. 16, the initiation of slope failure is categorized into three sequential mechanisms: seismic amplification effect, locked segment effect, and start-up acceleration effects, as described in detail below.

Fig. 16
figure 16

Diagram of initiation mechanism of the Sunjiagou landslide

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In the initial state, the slope is in an equilibrium condition under the forces of the slope’s gravity () and the internal slip resistance. The slope is considered stable (Fig. 16a). When the seismic activity started, many loess overhead structural bodies were destroyed due to the continuous effect of seismic pulsation. In particular, the soil at the top of the slope undergoes severe tensile damage due to strong seismic amplification at the top of the slope (Fig. 16b). At the same time, soil fragmentation occurs on the surface and foot of the slope, followed by the gradual evolution of the severely fragmented section in the top of the slope into a groove. The powerful seismic amplification effect at the top of the slope mainly causes this process. As seismic activity continues, the groove at the top of the slope becomes progressively wider, and the damage extends progressively downward along the loess-mudstone interface. Deformation in the upper part of the slope gradually accumulates in the locked segment of the slope, which results in a constant concentration of stress in the locking section until the locked segment is damaged (Fig. 16c). This stage is referred to as the locked segment effect during slope failure. After the failure of the locked segment of the slope, the formation of the sliding surface is accelerated until the damaged crack group propagates to the slope toe. During this stage, the slide body is in a limited equilibrium state until the sliding surface is fully formed. Meanwhile, the soil in the upper part of the slope was tensioned entirely and damaged, producing a high degree of fragmentation. Finally, the entire overlying loess slope begins to slide along the sliding surface at a high rate (Fig. 16d). This stage is known as the start-up acceleration effect of the slope initial process.

Conclusions

This study analyzes the initiation mechanism of low-angle loess-mudstone interface landslides formed by the 1920 Haiyuan earthquake in the Jingning area of China. The initial macro-damage process, the micro-crack evolution characteristics, the stress and velocity variations, and the seismic PGA amplification effect of the Sunjiagou landslide in Jingning County are analyzed via the DEM model. The main findings are as follows. First, the top of the Sunjiagou slope shows apparent tensile damage due to the seismic amplification effect, which made the soil in this region undergo intense fragments and evolve into a sinking groove. Meanwhile, during the propagation of the micro-crack group in the sliding zone, the loess in the slope surface shows the damage phenomena of dynamic fragmentation and seismic subsidence. When the damaged micro-cracks propagate to the slope toe, the loess slope body begins to slide along the loess-mudstone interface. Second, based on the micro-crack number variation curves and the micro-crack evolution results, the middle section of the Sunjiagou slope is determined as a locked segment of the landslide. Specifically, the growth rate of the micro-crack number in the sliding zone begins to decrease during a period (10–21.5 s), and the micro-crack evolution results revealed the range (254–390 m) of this locking section, named locked segment in the landslide study. Third, the stress variation results suggest that during the failure process of the locked segment, the stress within the locked segment continues to increase to a specific limit value and then begins to decrease rapidly, which causes the locked segment to exhibit a brittle failure mode. Fourth, velocity variation curves indicate that the velocity of the slope body began to increase sharply during 25–27.5 s, which was completed in a short period after the locked segment was damaged (t = 21.5 s) and reveals the start-up acceleration feature of the Sunjiagou landslide. Finally, the initiation mechanism of this earthquake-triggered loess-mudstone interface landslide is concluded as the sequential action of seismic amplification effect, locked segment effect, and start-up acceleration effect. The findings of this study provide insights into the mechanisms of seismic landslides with similar geological structures.