Stability Analysis and Treatment of Pebble Soil Slopes Under Rainfall and Earthquake Conditions

Abstract

In many mountainous areas of China, frequent geological disasters pose a serious threat to human life and property. The Luding “9.5” earthquake triggered a large number of landslide disasters, causing serious loss of life and property. Therefore, it is extremely urgent to carry out research on the stability analysis and treatment methods of landslides in the Luding area. In this paper, the Caiyangba landslide in Yanzigou Town, Luding County, is taken as the research object. The slope model is constructed by Midas to study the stability development law of Caiyangba landslide under different rainfall conditions and seismic conditions, and to explore the feasibility of the “anchor lattice treatment method”. The results show that the “anchor lattice treatment method” can effectively improve the stability of the slope under rainfall conditions. The improvement effect of slope stability decreases with the increase in rainfall duration and rainfall. The development law of the slope stability coefficient with rainfall duration in WMG (the working condition of not adopting the “anchor lattice treatment method” is referred to as WMG) and MG (the working condition of adopting the “anchor lattice treatment method” is referred to as MG) conditions conform to the development law of exponential function, and the expression of instantaneous change rate of slope stability coefficient is derived. The above function can also well explain the development law of X-direction displacement and Y-direction displacement of SP (school: monitoring point) and RP (road: monitoring point); the development law of the instantaneous change rate of displacement. Under the influence of ground motion, the improvement effect of the “anchor lattice treatment method” on the slope stability coefficient is limited, but the improvement effect of slope stability increases with the increase in seismic intensity. The slope stability coefficient and the displacement of SP and RP show obvious fluctuation with time, and the fluctuation law is similar to that of ground motion records. It is recommended to add a gravity-retaining wall at the foot of the slope. The teaching building reduces the number of floors and increases the number of pile foundations. Roads should restrict the passage of heavy vehicles, such as cars and strictly stacked items. The above results can provide a theoretical reference for the sustainable treatment and sustainable development of landslides in the Luding area.

1. Introduction

China is a country with frequent geological disasters. In the first half of 2025 alone, natural disasters led to a total of 25.37 million people being affected to varying degrees, 307 people died and disappeared, and direct economic losses were CNY 54.11 billion. Among them, affected by continuous rainfall, the landslide led to 34,000 people being affected to varying degrees, 84 people died and disappeared, and the direct economic loss was CNY 280 million. In mainland China, 57 earthquakes with a magnitude greater than 4.0 have occurred, and many landslides have been triggered. A total of 284,000 people have been affected to varying degrees, 126 people have died, and direct economic losses have reached 9.39 billion yuan [1]. It can be seen that the landslide has a great impact on human life and property. Therefore, many scholars have carried out a lot of research on the stability of the slope.

Slope stability analysis is an important research direction in the fields of geotechnical engineering [2,3,4], geological disaster prevention [5,6,7], and mine safety [8,9,10]. In recent years, with the development of computer technology, sensor monitoring, and artificial intelligence, slope stability analysis has made significant progress in theoretical methods [11,12], monitoring technologies [13,14], and engineering applications [15,16,17]. From the limit equilibrium method [18,19] based on static equilibrium conditions to the strength reduction method [20,21], machine learning [22,23], and AI early warning system [24,25], combined with multi-source data, the research on slope stability analysis has been greatly developed. At present, slope stability analysis has shifted from traditional empirical calculation to intelligent, high-precision, multi-source data fusion. Especially in the direction of multi-physics coupling analysis, many scholars have carried out a lot of research. Cai et al. [26] studied the temporal and spatial evolution of slope stability uncertainty during rainfall by first-moment analysis. The results show that under unsaturated and heavy rainfall conditions, the shallow layer of the slope will first appear in the low reliability area. Wang et al. [27] studied the safety evolution of the slope under the combined action of rainfall and earthquake, and found that the influence of earthquake on stability is significantly greater than that of rainfall. The simulation function of rock slope under rainfall is established by Pan et al. [28], which proves that this method can accurately reflect the mechanical behavior and stress–strain distribution of rock mass under rainfall conditions. Han et al. [29] studied the analytical relationship between rainwater infiltration with depth and time under heavy rainfall, and found that the change in hydraulic conductivity had a significant effect on infiltration and slope stability. Naidu et al. [30] A uses combined clustering and regression analysis to identify the rainfall threshold of the Ambri landslide event in Kerala, India. Based on the coupling of peridynamics and the finite element method, Gu et al. [31] propose a seepage-deformation field data exchange model and incorporate the influencing factors of fine particle erosion during rainfall. Chen et al. [32] simulate the influence of extreme rainfall on slope stability under different rainfall durations using a two-dimensional finite element model, and find that the potential slip depth of the tree slope is smaller than that of the shrub and grass slopes. Zhou et al. [33] evaluated the effectiveness of different treatment measures on slope stability during the earthquake, and the results showed that the slope displacement affected by the earthquake was significantly greater than that in natural conditions. Based on the established dynamic viscoelastic–plastic soil constitutive model, Ma et al. [34] calculated the safety seismic coefficient and sliding distance of soil slope under natural earthquake conditions. Ma et al. [35] proposed an optimized prediction model based on EO-LightGBM, which proved that the model can effectively reduce the error rate and improve the adaptability of slope stability prediction under complex seismic conditions. Xu and Yang [36] analyzed the stability of three-dimensional heterogeneous anisotropic slopes under earthquake or pore water pressure, and found that increasing the soil heterogeneity coefficient or reducing the anisotropy coefficient can improve the slope stability. Through the establishment of the weak weak-layer rock slope model, Zhang et al. [37] found that the influence of spatial variability of the weak layer on stability is greater than that of the rock material. Zhou and Qin [38] proposed a new method for seismic slope stability evaluation by combining the finite element upper bound method and the pseudo-dynamic method. Aiming at the interaction between earthquake and rainwater, Chen et al. [39] studied the slope safety factor and failure mode, and found that the influence of soil friction angle is stronger than that of cohesion.

In summary, many scholars have carried out a lot of research on the stability and treatment methods of different types of slopes, and have achieved rich results. However, the stability performance and treatment methods of slopes affected by different geographical environments are completely different. Affected by the Luding “9.5” earthquake, many areas in Luding County have experienced landslides of different degrees. However, the slope stability and treatment methods in the above landslide areas have not been studied and discussed in detail. Therefore, it is extremely important to carry out in-depth research on the slope stability and treatment methods of landslides in the above areas. This paper takes the Caiyangba landslide in Yanzigou Town, Luding County, as the research object, and deeply discusses the slope stability and treatment method of the Caiyangba landslide under rainfall and earthquake conditions through numerical calculation. The research results can provide some reference value for the monitoring and treatment of the Caiyangba landslide, and also improve the emergency response capacity of the region, which is an important embodiment of firmly implementing the sustainable development strategy.

2. Overview and Methods of the Study Area

2.1. Overview of the Study Area

Luding County is located in the western part of Sichuan Province (latitude 29°28′~30°06′ N, longitude 101°49′~102°27′ E), with a total area of 2165.35 km², a length of 69.2 km from north to south, and a width of 49.9 km from east to west. It is the traffic artery between the Sichuan–Tibet highway and railway. At 12:52 on 5 September 2022, a 6.8-magnitude earthquake (focal depth 16 km, epicenter north latitude 29.59°, east longitude 102.08°) occurred in the county, resulting in a large area of collapse and surface cracks in Yanzigou Town, which urgently needs engineering treatment.

Among them, the Caiyangba landslide was affected by the earthquake, mainly manifested as surface cracks and shallow landslides. The trailing edge of the landslide is the Moxi platform (altitude 1730–1766 m), and the leading edge is the Moxi river bank (altitude 1604–1639 m). The relative height difference is 90–125 m, the overall slope is 50–70°, and the local slope is more than 80°. Affected by rainstorms, earthquakes, and other factors, the stability of the landslide is poor, and there is a risk of further deformation or instability. In addition, there are roads and schools under construction on the top of the slope, so it is urgent to carry out stability research and engineering management. The actual location and site conditions of the landslide are shown in Figure 1.

Because Luding County is in a high altitude area, there is less water vapor in Luding County, and it is not easy to have a heavy rainfall climate. By counting the rainfall in Yanzigou Town, Luding County, in 2024, it can be seen that it is difficult for Yanzigou Town to have short-term heavy rainfall (see Figure 2). And according to the “Grade of precipitation (GB/T 28592-2012)” [40], it can be seen that Yanzigou Town is mainly dominated by light rain and moderate rain. However, short-term heavy rainfall occurred in Luding County in July 2025 (the rainfall reached 20 mm/h). Luding County issued a red warning signal for a rainstorm and took emergency measures [41]. Therefore, when exploring the stability of slopes under rainfall conditions, this paper will mainly consider extreme rainfall conditions. The rainfall in this paper is set to 10 mm/h, 20 mm/h, and 30 mm/h, respectively, and the rainfall duration is set to 5 h, 10 h, and 20 h, respectively.

Luding County is located at the intersection of the Xianshuihe seismic zone, Anninghe seismic zone, and Longmenshan seismic zone in the Qinghai–Tibet Plateau seismic zone. Among them, the seismic activity of the Xianshuihe seismic zone is the strongest, which has a great influence on the area, and the influence of the other two seismic zones is relatively weak. According to the statistics of seismic data, within 300 km of Luding County, since 1216 AD, a total of 7 earthquakes of 7.0~7.9 magnitude have been recorded; 21 earthquakes of 6.0–6.9 magnitude; there were 71 earthquakes of magnitude 5.0–5.9 [42]. It can be seen that the earthquake is one of the main natural disasters in Luding County. And Luding County belongs to the high altitude mountainous area, where there are a large number of unstable slopes. Therefore, it is necessary to study the influence of ground motion on slope stability. In this paper, the stability of the slope under different seismic intensities is studied by using the Luding “9.5” ground motion record recorded by the KMI station in Kunming, Yunnan Province [43]. According to “The Chinese seismic intensity scale (GB/T 17742-2020)” [44], the corresponding relationship between epicentral intensity and magnitude is shown in

Table 1. Correspondence table of epicentral intensity and magnitude.

Magnitude	2	3	4	5	6	7	8	>8
Epicentral intensity	1~2	3	4~5	6~7	7~8	9~10	11	12

. In recent years, the magnitude of earthquakes in Luding County has mainly been in the range of 3~7. Therefore, the seismic intensity of 9 degrees is adopted in this paper. The seismic conditions are shown in

Table 2. The peak acceleration of seismic waves under different seismic conditions [45].

Seismic Intensity	Frequent Earth-quake	Design Basis Earthquake	Maximum Considered Earthquake
9 degree	140 cm/s2	400 cm/s2	620 cm/s2
	0.14 g	0.41 g	0.63 g

. The adjusted ground motion records are shown in Figure 3.

2.2. Stratum Composition and Parameters

The main material of the Caiyangba landslide is pebble soil, which contains a large number of giant pebbles. The lithology is mainly granite and granodiorite. Pebble content accounted for more than 50%. Through the field test, it can be seen that the particle gradation of the Caiyangba landslide is shown in

Table 3. Soil particle composition.

Particle Size (mm)	Proportion (%)			Average Value
	Sample 1	Sample 2	Sample 3
>200	37.42	28.83	37.50	34.58
200~60	31.25	29.62	26.27	29.05
60~40	8.58	12.88	11.08	10.85
40~20	4.09	6.20	5.62	5.30
20~10	2.04	4.41	3.45	3.30
10~5	2.37	3.10	2.52	2.66
5~2	5.70	4.89	3.02	4.54
2~1	2.85	3.86	3.80	3.50
1~0.5	1.64	2.23	1.74	1.87
0.5~0.25	1.97	1.47	2.91	2.12
0.25~0.075	1.31	1.55	1.32	1.39
<0.075	0.77	0.95	0.77	0.83
$D_{60}$ (mm)	178.25	135.59	182.46	165.43
$D_{30}$ (mm)	57.66	43.76	49.78	50.40
$D_{10}$ (mm)	2.59	1.95	1.98	2.17
Uniformity coefficient $C_{\mathrm{c}}$	68.82	69.53	92.15	76.83
Curvature coefficient $C_{\mathrm{u}}$	7.20	7.24	6.86	7.10

. Soil mechanics parameters are shown in

Table 4. Soil mechanical parameters.

Soil	Elastic Modulus ${\mathit{E}}_{\mathbf{0}}$ (MPa)	Poisson Ratio $\mathit{\upsilon }$	Volume Weight $\mathit{\gamma }$ (kN/m3)	Saturated Volume Weight ${\mathit{\gamma }}_{\mathbf{s}}$ (kN/m3)	Initial Void Ratio $\mathit{e}$	Permeability Coefficient $\mathit{\kappa }$ (m/s)	Cohesion $\mathit{c}$ (kPa)	Internal Friction Angle $\mathit{\phi }$ (°)
pebble soil	90.60	0.28	19.91	20.31	0.50	0.000205	36.00	38.00

.

2.3. Study Method

This paper mainly studies the stability of the Caiyangba landslide through Midas finite element calculation, and then explores the slope treatment method of the Caiyangba landslide and the stability characteristics after treatment. Due to the sliding failure, the original structure of the landslide accumulation body has been lost, and the volume of the landslide accumulation body is small. Therefore, when conducting numerical modeling, the “9.5” earthquake landslide accumulation body is not considered (see Figure 4). In the numerical calculation, the boundary conditions are set as shown in Figure 5 [45,46]. The groundwater depth at the top of the slope in the study area is about 126 m, and the groundwater depth at the foot of the slope is about 3 m. Based on the relevant provisions of the “Load code for the design of building structures (GB 50009-2012)” [47] and “Technical Standard of Highway Engineering (JTG B01-2014)” [48], the load value of the school to the foundation is set to 48 kN/m, and the load value of the road to the foundation is set to 38 kN/m. The calculation conditions are shown in

Table 5. Rainfall calculation conditions in the study area.

Condition	Rainfall (mm/h)	Rainfall Duration (h)
JY1-1	10	5
JY1-2	10	10
JY1-3	10	20
JY2-1	20	5
JY2-2	20	10
JY2-3	20	20
JY3-1	30	5
JY3-2	30	10
JY3-3	30	20

and

Table 6. Seismic calculation conditions in the study area.

Condition	Seismic Intensity	PGA (g)	Direction
DZ-1	9-degree frequent earthquake	0.14	X
DZ-2	9-degree design basis earthquake	0.41	X
DZ-3	9-degree maximum considered earthquake	0.63	X

. At present, the slope is considered to adopt the “anchor lattice treatment method” (the working condition of adopting the “anchor lattice treatment method” is referred to as MG, and the working condition of not adopting the “anchor lattice treatment method” is referred to as WMG). The horizontal and vertical spacing of the lattice is 3 m, and the cross-section size of the lattice beam is 0.3 m × 0.3 m, using C25 reinforced concrete structure. The length of the anchor rod ranges from 6 m to 15 m, and the inclination angle of the anchor rod is 20°. The slope section diagram, numerical model and anchor lattice beam layout method of Caiyangba landslide are shown in Figure 4.

At present, two analysis methods are mainly used in the analysis of slope stability: the limit equilibrium method and the strength reduction method. However, the strength reduction method is one of the most widely used methods in slope stability analysis. The limit equilibrium method needs to assume the shape of the sliding surface (such as an arc or polyline), while the strength reduction method can automatically calculate the most dangerous potential sliding surface, which is especially effective for landslides with complex shapes. And the strength reduction method can be easily coupled with seepage, earthquake, retaining structure, and other complex factors to simulate the working state of the slope in the real environment [49]. The finite element strength reduction method uses the continuous iterative calculation of the finite element model to continuously reduce the shear strength parameters (cohesion ($c$) and internal friction angle ($\phi$)) of the soil, so that the rock and soil mass reaches the ultimate failure state to obtain the stability coefficient, and the failure sliding surface is found through the calculation result cloud diagram. The properties of the pebble soil slope in this paper conform to the Mohr–Coulomb criterion and are calculated by the strength reduction method. The specific calculation method is as follows.

Effective shear strength (${\tau }^{\prime }$):

$${\tau }^{\prime }=\tau /F_{\mathrm{s}}$$

(1)

According to the Mohr–Coulomb criterion,

$$\tau =c+\tan \phi$$

(2)

Bring Expression (2) into Expression (1):

$${\tau }^{\prime }={\displaystyle \frac{c}{F_{\mathrm{s}}}}+\sigma {\displaystyle \frac{\tan \phi }{F_{\mathrm{s}}}}=c^{\prime }+\sigma \tan {\phi }^{\prime }$$

(3)

In the formula, $c^{\prime }$ is the effective cohesion; $\tan {\phi }^{\prime }$ is the effective internal friction angle; and $F_{\mathrm{s}}$ is the strength reduction coefficient (stability coefficient). When the strength reduction coefficient continues to increase, $c^{\prime }$ and $\tan {\phi }^{\prime }$ will continue to decrease; that is, ${\tau }^{\prime }$ will continue to decrease. When $F_{\mathrm{s}}$ increases to a certain value, the internal sliding force of the slope is equal to the anti-sliding force, and the interior of the slope reaches a critical state.

The calculation process of slope stability under rainfall and earthquake conditions is shown in Figure 5.

3. Results and Discussions

3.1. Slope Stability Analysis Under Different Rainfall Conditions

The Caiyangba landslide treatment project is Grade I. Based on the relevant provisions of the “Code for the design of landslide stabilization (GB/T38509-2020)” [46] and “Technical code for building slope engineering (GB 50330-2013)“ [50], the safety coefficient of slope stability is shown in

Table 7. Stability safety coefficient of slope.

Condition	$\mathbf{Safety} \mathbf{Coefficient} {\mathit{F}}_{\mathbf{st}}$
Weight	1.30
Weight + Rainfall	1.25
Weight + Earthquake	1.15

. The slope stability state is shown in

Table 8. Slope stability state.

Stability coefficient $F_{\mathrm{s}}$	$F_{\mathrm{s}}<1.00$	$1.00\le F_{\mathrm{s}}<1.05$	$1.05\le F_{\mathrm{s}}<F_{\mathrm{st}}$	$F_{\mathrm{s}}\ge F_{\mathrm{st}}$
State	Instability	Under stability	Basic stability	Stability

.

In the absence of rainfall and earthquakes, there is no settlement and slip phenomenon in the Caiyangba landslide, so the initial displacement values of the school monitoring point (SP) and road monitoring point (RP) are both 0. Through numerical calculation, the stability coefficient ($F_{\mathrm{s}}$) of the original slope without rainfall is equal to 1.2563, which indicates that the Caiyangba landslide is currently in a basic stability state. At the same time, based on Table 5, the development law of the slope stability coefficient in the case of WMG and MG is explored. The specific results are shown in Figure 6.

Figure 6 shows that the slope stability coefficient decreases consistently with increasing rainfall duration and intensity. At the same time, with the increase in rainfall, the stability coefficient decreases as a whole. After adopting the “anchor lattice treatment method”, the slope stability coefficient reached 1.3281 without rainfall (see

Table 9. Change value of slope stability coefficient.

Rainfall	Working Condition	0 (h)	5 (h)	10 (h)	20 (h)
10 mm/h	WMG ($F_{\mathrm{s}}$)	1.2563	1.2313	1.2219	1.2188
	MG ($F_{\mathrm{s}}$)	1.3281	1.2594	1.2481	1.2375
	MG ($F_{\mathrm{s}}$)-WMG ($F_{\mathrm{s}}$)	0.0718	0.0281	0.0262	0.0187
20 mm/h	WMG ($F_{\mathrm{s}}$)	1.2563	1.2273	1.2203	1.2172
	MG ($F_{\mathrm{s}}$)	1.3281	1.2551	1.2406	1.2289
	MG ($F_{\mathrm{s}}$)-WMG ($F_{\mathrm{s}}$)	0.0718	0.0278	0.0203	0.0117
30 mm/h	WMG ($F_{\mathrm{s}}$)	1.2563	1.2219	1.2133	1.2094
	MG ($F_{\mathrm{s}}$)	1.3281	1.2473	1.2313	1.2148
	MG ($F_{\mathrm{s}}$)-WMG ($F_{\mathrm{s}}$)	0.0718	0.0254	0.0180	0.0054

). The stability coefficient exceeds 1.30, indicating that the Caiyangba landslide is stable. And under the influence of rainfall conditions, the time when the slope is in a stability state in the MG condition is much longer than that when the slope is in a stability state in the WMG condition. At the same time, the difference in slope stability coefficient between the MG condition and WMG condition is greater than zero, and the difference decreases with the increase in rainfall duration and rainfall (see Table 9). This shows that the “anchor lattice treatment method” can effectively improve the slope stability of the Caiyangba landslide. However, the improvement effect of slope stability decreases with the increase in rainfall duration and the rainfall itself. This may be due to the increase in hydraulic erosion, the cohesive force of the slope decreases continuously, and the friction force between the anchor rod and the slope rock and soil mass decreases continuously. Through fitting, it can be seen that the development law of the stability coefficient conforms to the development law of the exponential function (see Expression (4)), and the fitting coefficient is shown in

Table 10. Fitting coefficient.

Condition	${\mathit{A}}_{\mathbf{0}}$	$\mathit{\lambda }$	${\mathit{B}}_{\mathbf{0}}$	${\mathit{R}}^{\mathbf{2}}$ (Coefficient of Determination)
10 mm/h (WMG)	1.21836	0.03794	4.49540	0.99939
20 mm/h (WMG)	1.21684	0.03946	4.26761	0.99663
30 mm/h (WMG)	1.20892	0.04738	4.35506	0.99680
10 mm/h (MG)	1.23597	0.09213	4.87892	0.98147
20 mm/h (MG)	1.22712	0.10098	4.95242	0.98698
30 mm/h (MG)	1.21178	0.11632	5.47822	0.98345

.

$$F_{\mathrm{s}}=A_0+\lambda \exp \left(-t/B_0\right)$$

(4)

In the formula, $F_{\mathrm{s}}$ is the slope stability coefficient; $t$ is the duration of rainfall; and $A_0$, $\lambda$, and $B_0$ are fitting coefficients.

Based on Expression (4), the instantaneous change rate of slope stability coefficient is obtained (see Expression (5)).

$$F_{\mathrm{s}}^{\prime }=\left(-\lambda /B_0\right)\exp \left(-t/B_0\right)$$

(5)

In the formula, $F_{\mathrm{s}}^{\prime }$ is the instantaneous change rate of slope stability coefficient (The degree of change in the slope stability coefficient in a specific moment).

Based on Table 10 and Expression (5), the development law of the instantaneous change rate of slope stability coefficient is obtained (see Figure 7). It can be seen from Figure 7 that with the increase in rainfall, the value of $F_{\mathrm{s}}^{\prime }$ shows a decreasing law of development. This shows that the increase in rainfall will make the slope stability coefficient have a greater attenuation value, and further accelerate the occurrence of slope instability. And after the original slope adopts the “anchor lattice treatment method”, the value of $F_{\mathrm{s}}^{\prime }$ decreases. Combined with Figure 6, it can be seen that in the MG condition, the slope stability coefficient has been greatly improved, but this also increases the sensitivity of the slope stability coefficient to rainfall. At the same time, with the increase in rainfall duration, the difference in $F_{\mathrm{s}}^{\prime }$ value between the WMG condition and the MG condition is shrinking and approaches zero infinitely. This shows that the slope stability coefficient in the WMG condition and the MG condition will not always decrease under the influence of rainfall, but will gradually approach a limit value. Combined with Figure 6, the limit value may decrease with the increase in rainfall. Therefore, in the disaster prediction based on the slope stability coefficient, when the A curve of the slope is close to zero and tends to be stable, the dynamic development of the slope should be monitored to prevent sudden instability and failure of the slope.

Because there are schools and roads under construction on top of the Caiyangba landslide, it is very important to explore the displacement variation law of schools and roads. The X-and Y-direction displacement contours of the slope are shown in Figure 8 and Figure 9.

It can be seen from Figure 8 and Figure 9 that the original slope is mainly dominated by X-direction displacement under the influence of rainfall, and the displacement is mainly concentrated in the midslope. At this time, the X-direction displacement is more dispersed. Under the influence of school and road loads, the settlement phenomenon mainly occurs at the top of the slope. The lower right part of the slope has an obvious extrusion phenomenon, resulting in local uplift of the lower right part of the slope, and is mainly concentrated at the foot of the slope. After adopting the “anchor lattice treatment method”, the potential sliding surface of the slope is strengthened, which greatly increases the integrity of the slope, so that the X-direction displacement of the slope is mainly concentrated at the foot of the slope. At the same time, the extrusion phenomenon of the slope has also been greatly alleviated, so that the local uplift of the slope is mainly concentrated at the foot of the slope. This is mainly due to the lack of corresponding reinforcement measures at the foot of the slope, which is prone to stress concentration under the influence of gravity and environmental factors. And after the stress redistribution, the displacement deformation of the slope is generally consistent, which is conducive to the long-term stability of the slope. Therefore, after adopting the “anchor lattice treatment method”, a gravity retaining wall should also be added to the slope toe to reduce the displacement deformation of the slope toe. Based on the displacement calculation results of the slope, the displacement variation in SP and RP is shown in Figure 10 and Figure 11.

Through Figure 10 and Figure 11, it can be seen that the fitting results of X-direction displacement and Y-direction displacement of SP and RP conform to the function law of expression (4), and the fitting coefficients are shown in

Table 11. Fitting coefficient (X-direction displacement).

Condition	${\mathit{A}}_0$	$\mathit{\lambda }$	${\mathit{B}}_{\mathbf{0}}$	${\mathit{R}}^{\mathbf{2}}$ (Coefficient of Determination)
SP10 mm/h (WMG)	0.00071	−0.00071	5.03037	0.92540
SP20 mm/h (WMG)	0.00075	−0.00075	4.06402	0.95853
SP30 mm/h (WMG)	0.00081	−0.00081	4.73654	0.92855
SP10 mm/h (MG)	0.00600	−0.00600	2.62017	0.97648
SP20 mm/h (MG)	0.00620	−0.00620	1.22623	0.99717
SP30 mm/h (MG)	0.00620	−0.00620	2.61097	0.98186
RP10 mm/h (WMG)	0.00211	−0.00211	3.43634	0.97302
RP20 mm/h (WMG)	0.00230	−0.00230	1.66904	0.97920
RP30 mm/h (WMG)	0.00267	−0.00267	5.42868	0.96094
RP10 mm/h (MG)	0.02180	−0.02180	2.32747	0.98568
RP20 mm/h (MG)	0.02250	−0.02250	1.06895	0.99650
RP30 mm/h (MG)	0.02282	−0.02282	2.79754	0.97894

and

Table 12. Fitting coefficient (Y-direction displacement).

Condition	${\mathit{A}}_{\mathbf{0}}$	$\mathit{\lambda }$	${\mathit{B}}_{\mathbf{0}}$	${\mathit{R}}^{\mathbf{2}}$ (Coefficient of Determination)
SP10 mm/h (WMG)	−0.00651	0.00651	3.02874	0.97063
SP20 mm/h (WMG)	−0.00690	0.00690	1.44928	0.99079
SP30 mm/h (WMG)	−0.00720	0.00720	1.44270	0.98014
SP10 mm/h (MG)	−0.04870	0.04870	2.16545	0.98930
SP20 mm/h (MG)	−0.04980	0.04980	1.09545	0.99814
SP30 mm/h (MG)	−0.05021	0.05021	2.27475	0.99101
RP10 mm/h (WMG)	−0.00730	0.00730	1.18089	0.99532
RP20 mm/h (WMG)	−0.00770	0.00770	1.40633	0.98821
RP30 mm/h (WMG)	−0.00815	0.00815	3.95061	0.96417
RP10 mm/h (MG)	−0.05460	0.05460	0.89311	0.99986
RP20 mm/h (MG)	−0.05590	0.05590	1.11208	0.99804
RP30 mm/h (MG)	−0.05641	0.05641	2.40369	0.98903

. Therefore, the development law of the instantaneous change rate of SP and RP displacement also conforms to the function law of expression (5). It can be seen from Figure 12 that the development law of the instantaneous change rate of SP and RP displacement is similar to that of the instantaneous change rate of the slope stability coefficient. Similarly, with the increase in rainfall duration, the gap between the values of the instantaneous change rate of displacement is shrinking and approaches zero infinitely. This also shows that SP and RP may have stable displacement deformation under the influence of rainfall. Therefore, when the instantaneous change rate of displacement is close to zero and tends to be stable, the dynamic development of the slope should also be monitored to prevent the sudden instability of the slope. By exploring the displacement development law of SP and RP, it is found that the X-direction displacement value and Y-direction displacement value of SP and RP increase after adopting the “anchor lattice treatment method”. Combined with Figure 8 and Figure 9, it can be seen that this may be due to the stress concentration at the foot of the slope after the “anchor lattice treatment method” is adopted, which in turn leads to greater displacement deformation of the slope. Therefore, it is necessary to increase the gravity retaining wall at the foot of the slope. At the same time, combined with Figure 6, it can be seen that the stability of the slope has also been greatly improved after the “anchor lattice treatment method” is adopted. This shows that after adopting the “anchor lattice treatment method”, the slope can withstand greater displacement deformation and increase the usability of the slope.

3.2. Slope Stability Analysis Under Different Seismic Conditions

Through Figure 3, it can be seen that the peak ground acceleration of the Luding “9.5” ground motion record reaches the maximum value when the time is 9.0 s. Therefore, this paper mainly explores the development law of the slope stability coefficient of the Caiyangba landslide when the ground motion time is 8.8 s, 8.9 s, 9.0 s, 9.1 s, and 9.2 s, respectively. The calculation results of slope stability are shown in

Table 13. Slope stability coefficient under different seismic intensities.

Time (s)	${\mathit{F}}_{\mathbf{s}}$
	0.14 g (WMG)	0.14 g (MG)	0.41 g (WMG)	0.41 g (MG)	0.63 g (WMG)	0.63 g (MG)
8.8	2.1344	2.1313	1.2328	1.2344	1.1375	1.1844
8.9	2.2457	2.2500	1.4129	1.4125	1.2793	1.2856
9.0	3.5707	3.5750	1.6738	1.7000	1.0000	1.0500
9.1	4.7035	4.7156	2.4750	2.4750	1.5797	1.5828
9.2	2.6719	2.7000	1.7504	1.7836	1.4992	1.5012
Average value	2.7638	2.7833	1.6335	1.6556	1.2920	1.3220
MG-WMG	0.0195		0.0221		0.0300

and Figure 13.

It can be seen from Table 13 and Figure 13 that with the increase in PGA, the slope stability coefficient shows a decreasing trend as a whole. This shows that with the increase in seismic intensity, the probability of slope failure is also increasing. After adopting the “anchor lattice treatment method”, the slope stability coefficient has been slightly improved. At the same time, the difference in the slope stability coefficient between the MG condition and the WMG condition is greater than zero, and the difference increases with the increase in seismic intensity (see Table 13). This shows that under the influence of ground motion, the improvement effect of the “anchor lattice treatment method” on the slope stability coefficient is limited. And the improvement effect of slope stability increases with the increase in seismic intensity. Under the influence of ground motion, the variation in slope stability coefficient with time shows obvious fluctuation. When the duration of the earthquake reaches 40 s, the total displacement cloud map of the slope is shown in Figure 14.

It can be seen from Figure 14 that with the increase in seismic intensity, the total displacement of the slope also increases. In the WMG condition, the large deformation position of the slope is mainly located at the midsection and toe of the slope. In the MG condition, the large deformation position of the slope is mainly located at the toe of the slope, and the total displacement value of the slope also decreases as a whole. This shows that after adopting the “anchor lattice treatment method”, the displacement deformation of the slope is mainly concentrated at the foot of the slope. The “anchor lattice treatment method” can effectively reduce the large deformation range of the slope under the influence of ground motion, and also reduce the influence of ground motion on the slope deformation. However, in order to increase the seismic resistance and stability of the slope to a greater extent, the displacement of the slope toe can be reduced by adding a gravity retaining wall at the slope toe. Based on the calculation results of ground motion, the displacement variation in SP and RP is shown in Figure 15 and Figure 16.

It can be seen from Figure 15 and Figure 16 that the displacement of SP and RP shows obvious fluctuation with the development of ground motion duration, and its fluctuation law is similar to that of ground motion records. The X-direction displacement of SP decreases first and then increases. After 20 s, the displacement begins to approximate the linear development law. The X-direction displacement of RP is mainly positive. Similarly, after 20 s, the displacement begins to approximate the linear development law. Under the same seismic intensity, the X-direction displacement value in the MG condition is significantly lower than that in the WMG condition. And the difference between the two increases with the increase in duration. This shows that under the influence of the earthquake, the “anchor lattice treatment method” can effectively reduce the X-direction displacement of the slope. The Y-direction displacement of SP and RP shows more obvious fluctuation. And with the increase in time, the fluctuation range gradually decreases. However, the overall development trend of the Y-direction displacement of SP and RP shows a settlement phenomenon, and there is no uplift phenomenon. This shows that under the influence of ground motion, the slope may still exhibit a landslide phenomenon. After adopting the “anchor lattice treatment method”, the Y-direction displacement of SP increases as a whole. This may be due to the stress concentration phenomenon at the foot of the slope after the “anchor lattice treatment method” is adopted, which leads to greater displacement deformation inside the slope. However, after adopting the “anchor lattice treatment method”, the Y-direction displacement of the RP appears to decrease as a whole. This is mainly because the lower part of RP is the reinforcement area, which directly increases the ability of the road to resist settlement deformation. Combined with Figure 14, it can be seen that the total displacement of the slope increases with the increase in earthquake duration. Therefore, it is necessary to increase the gravity retaining wall at the foot of the slope to prevent the large deformation of the slope under the influence of the earthquake. At the same time, it is also suggested that school buildings near the slope should reduce the load of the building on the foundation by reducing the number of floors, and the number of pile foundations should be increased to enhance the anti-settlement ability of the building. Roads should restrict the passage of heavier vehicles, such as cars. And the road should also have carefully stacked items to reduce the load of the road on the roadbed.

4. Conclusions

Based on the field situation of the Caiyangba landslide, this paper explores the development law of slope stability and displacement of the Caiyangba landslide under rainfall and earthquake conditions through numerical calculation. The main results are as follows:

• The “anchor lattice treatment method” can effectively improve the stability of the Caiyangba landslide. The improvement effect of slope stability decreases with the increase in rainfall duration and the rainfall itself. Under the influence of rainfall, the development law of slope stability coefficient in WMG condition and MG condition with rainfall duration conforms to the development law of the exponential function ($F_{\mathrm{s}}=A_0+\lambda \exp \left(-t/B_0\right)$). At the same time, the expression ($F_{\mathrm{s}}^{\prime }=\left(-\lambda /B_0\right)\exp \left(-t/B_0\right)$) of the instantaneous change rate of the slope stability coefficient is derived. It is found that the slope stability coefficient will not always decrease under the influence of rainfall, but will gradually approach a limit value. When the $F_{\mathrm{s}}^{\prime }$ curve of the slope is close to zero and tends to be stable, the dynamic development of the slope should be monitored to prevent the sudden instability of the slope.
• After adopting the “anchor lattice treatment method”, the potential sliding surface of the Caiyangba landslide is reinforced, which greatly increases the integrity of the Caiyangba landslide, so that the X-direction displacement of the slope is mainly concentrated at the toe of the slope. At the same time, the extrusion phenomenon of the slope has also been greatly alleviated, so that the local uplift of the slope is mainly concentrated at the foot of the slope. Therefore, after adopting the “anchor lattice treatment method”, a gravity retaining wall should also be added to the slope toe to reduce the displacement deformation of the slope toe. And the development law of X-direction displacement and Y-direction displacement of SP and RP conforms to the development law of the exponential function ($F_{\mathrm{s}}=A_0+\lambda \exp \left(-t/B_0\right)$). The development law of the instantaneous change rate of the SP and RP displacements also conforms to the development law of the expression ($F_{\mathrm{s}}^{\prime }=\left(-\lambda /B_0\right)\exp \left(-t/B_0\right)$). And after adopting the “anchor lattice treatment method”, the Caiyangba landslide can withstand greater displacement deformation and increase the usability of the slope.
• With the increase in seismic intensity, the probability of instability and failure of the Caiyangba landslide also increases. Under the influence of ground motion, the effect of the “anchor lattice treatment method” on the improvement of the slope stability coefficient is limited. However, the improvement effect of slope stability increases with the increase in seismic intensity. Under the influence of ground motion, the variation in slope stability coefficient with time shows obvious fluctuation. The displacement of SP and RP shows obvious fluctuation with the development of ground motion duration, and its fluctuation law is similar to that of ground motion records. In the WMG condition, the large deformation position of the slope is mainly located at the midsection and toe of the slope. In the MG condition, the large deformation position of the slope is mainly located at the toe of the slope. Therefore, the displacement of the slope toe can be reduced by adding a gravity retaining wall at the slope toe. At the same time, it is also suggested that school buildings near the slope should reduce the load of the building on the foundation by reducing the number of floors, and the number of pile foundations should be increased to enhance the anti-settlement ability of the building. Roads should restrict the passage of heavier vehicles, such as cars. And the road should also be carefully stacked items to reduce the load of the road on the roadbed.
• At present, the treatment of the Caiyangba landslide is in progress. The research results of this paper fill the research gap of slope stability and displacement characteristics of the Caiyangba landslide under rainfall and earthquake conditions. It provides some suggestions and references for the follow-up treatment of the Caiyangba landslide. This paper mainly studies the pebble soil slope in Luding County. In the follow-up study, the Caiyangba landslide will be the core object of the study. The geotechnical mechanism research and verification research of pebble soil slope are carried out by collecting perfect actual data. Improve the treatment of Caiyangba landslide, explore the mechanical mechanism and economic effect of different treatment methods, and provide a perfect theoretical basis for the treatment of pebble soil slope in Luding County.