Numerical Simulation Study on Seepage-Stress Coupling Mechanisms of Traction-Type and Translational Landslides Based on Crack Characteristics

Abstract

This study examines the deformation and failure mechanisms of two reservoir bank landslides: the traction-type Baijiabao landslide and the translational Baishuihe landslide. Based on long-term monitoring data and a hydro-mechanical coupled numerical model of rainfall infiltration, we investigate the impact of crack depth on landslide stability. Results show that the Baishuihe landslide exhibits translational failure, initiated at the rear by tension cracks and rear subsidence, followed by toe uplift, whereas the Baijiabao landslide displays traction-type progressive failure, starting with toe erosion and later developing rear-edge cracks. Rainfall induces similar seepage patterns in both landslides, with infiltration concentrated at the crest, toe, and convex terrain areas. As crack depth increases, soil saturation near the cracks decreases nonlinearly, while the base remains saturated. However, displacement responses differ: Traction-type landslides exhibit opposing lateral movements with minimal vertical displacement. In contrast, translational landslides show displacement increasing with crack depth, dominated by gravity. These findings guide targeted mitigation: traction-type landslides require crack control and toe protection, while translational landslides need measures to block thrust transfer and monitor deep slip surfaces. This study offers new insights into the effect of crack depth on landslide stability, contributing to improved landslide hazard assessment and management.

1. Introduction

Reservoir bank landslides are a critical geohazard that threatens hydraulic infrastructure and regional stability [1,2,3]. In hydraulic engineering applications, reservoir bank instability can cause direct structural damage to critical infrastructure components, including dams and spillways, thereby disrupting normal reservoir operations. Furthermore, such instability may generate destructive surge waves, posing substantial risks to downstream populations and property [4,5,6]. Historical cases, including the 1985 Xintan landslide in China, the 1963 Vajont Reservoir landslide in Italy, and the 2021 Baihetan Reservoir landslides, exemplify the catastrophic consequences of sudden slope failures [7,8,9].

From a geohazard characterization perspective, reservoir bank landslides typically demonstrate large-scale magnitude, rapid onset mechanisms, and significant cascading failure effects [10,11,12]. In particular, for landslides with highly developed cracks, rainfall can infiltrate rapidly along these preferential pathways, significantly reducing the shear strength of the sliding mass and making sudden failure highly likely during intense precipitation events [13,14,15]. Cracks serve as preferential flow paths, accelerating infiltration and inducing a rapid increase in pore-water pressure, which not only softens the geotechnical material but also significantly influences slope stability and seepage distribution [16,17,18,19]. Consequently, monitoring pore-water pressure within the slope and the development of local cracks provides a critical basis for assessing localized slope instability. Moreover, the integration of modern monitoring techniques with numerical simulation methods provides an effective means for dynamically predicting and evaluating crack evolution and slope stability [20,21].

Case-specific investigations have further demonstrated the mechanisms of crack-induced instability. Chen et al. demonstrated that following intense rainfall, cracks exhibit varying geometric characteristics, transforming areas that were originally relatively stable into locally unstable zones [22]. Wang et al. demonstrated that crack formation induces preferential seepage channels within the shallow layers of the sliding mass, where rainfall infiltration along these cracks generates pore-water pressure, gradually evolving the landslide into a ‘step-like’ progressive deformation state [23]. Wei et al., through physical model experiments, investigated groundwater variations and deformation–failure patterns in landslides containing weak interlayers under varying reservoir water level fluctuation rates. They divided the deformation process into five stages: toe erosion, slope surface and interlayer crack development, localized toe collapses with crack propagation, localized toe micro-collapses accompanied by crack penetration through the sliding mass, and further crack extension leading to overall failure [24]. Miao et al. focused on the impact of tensile cracks on the stability of reservoir-bank landslides, developing a magnetically driven artificial crack apparatus to simulate crack closure and propagation. Coupled with multi-field monitoring, their study demonstrated that crack closure can induce progressive traction-type failure, whereas crack propagation triggers complex translational-type failure, with hydraulic erosion also altering the landslide morphology [25]. Collectively, these studies highlight the critical importance of understanding crack development for assessing and predicting landslide stability.

It is noteworthy that the distinct crack development characteristics of traction-type and translational landslides exert different influences on landslide stability; however, current research on this topic remains limited. Typically, traction-type landslides exhibit weaker resistance at the toe, with cracks usually initiating at this location and progressively extending backward. Localized toe collapses result in staged rearward expansion of the landslide mass [26,27,28]. In translational landslides, the middle to rear sections of the sliding surface often exhibit relatively steep inclinations. The downslope driving force generated by the sliding mass in these sections typically exceeds the shear resistance of the corresponding sliding surface. Consequently, a downslope thrust develops in the mid-to-rear slope, creating a tensile stress zone at the rear edge. Deformation generally initiates at the rear of the slope mass [29,30].

Existing studies often neglect the differential responses of cracks across various landslide types, failing to distinguish the distinct developmental patterns, seepage pathways, and stability effects of toe cracks in traction-type landslides and rear-edge cracks in translational landslides. This study analyzes the deformation characteristics and mechanisms of the Baijiabao and Baishuihe landslides based on macroscopic deformation features and monitoring data. A hydro-mechanically coupled numerical model under rainfall infiltration was established to examine the differential influence of crack depth on the stability of both landslide types. For the two typical cases, separate numerical models were developed: a translational landslide model characterized by rear-edge cracks, and a traction-type landslide model characterized by toe cracks. Crack depths of 1 m, 2 m, 3 m, and 4 m were simulated to examine the coupled evolution of seepage and stress fields under intense concentrated rainfall using numerical methods. The study focuses on analyzing how different crack depths affect the spatial distribution of pore-water pressure and the evolution patterns of displacement fields. The results provide scientific insights to support early warning, forecasting, and mitigation strategies for similar landslide types.

2. Landslide Crack Characteristics

2.1. Crack Characteristics of the Baijiabao Landslide

2.1.1. General Description and Geological Features

The Baijiabao landslide is situated in Xiangjiadian Village, Guizhou Town, Zigui County, Hubei Province, approximately 2.5 km from the estuary of the Xiangxi River. The landslide is geographically located at 110°45′33.4″ E and 30°58′59.9″ N. It is positioned on the right bank of the Xiangxi River, with the landslide toe reaching the riverbank at elevations between 125 and 135 m. The rear boundary is bedrock at approximately 265 m elevation, bounded to the south by a gully and to the north by a ridge’s lower bedrock. The landslide body extends approximately 700 m in length, with a front width of about 500 m and a middle-upper width of roughly 300 m. The total landslide area is about 23.4 × 10⁴ m². Its thickness ranges from 45 m on average to a maximum of 80 m, with a total volume of approximately 1053 × 10⁴ m³. The sliding mass primarily comprises colluvial deposits of variable thickness, which are thicker near the toe and consist of brecciated soil and rock fragments. The sliding surface is located at the interface between the colluvium and underlying bedrock, which consists of feldspar-quartz sandstone and mudstone with bedding striking 250°and dipping 30°, forming a reverse fault structure. Figure 1 presents the plan view and cross-sectional view of the Baijiabao landslide.

2.1.2. Field Investigation

Before May 2007, no significant surface deformation was detected on the Baijiabao landslide. In June 2007, tensile cracks emerged along the roadway on the right flank of the landslide (Figure 2a). By July 2007, arcuate tensile cracks developed at the rear edge of the landslide, with widths of approximately 1–3 cm on the right side (Figure 2b) and 1–5 cm on the left side accompanied by a vertical offset of 10 cm. The cracks on both sides connected to form an arcuate tensile crack approximately 160 m in length, delineating the rear boundary of the landslide. Furthermore, tensile cracks and severe pavement damage were observed on the road crossing the central portion of the landslide. In July 2008, cracks were observed on the road crossing the landslide’s central area and along its lateral boundaries, causing further road surface damage (Figure 2c). On May 2009, tensile deformation occurred on the right-side road surface at the front of the landslide (Figure 2d). By June 2009, significant bank collapse along the Xiangxi River adjacent to the landslide toe was evident, accompanied by various degrees of slope failures, ground deformations, and boundary cracks (Figure 2e,f). Between June and July 2012, pronounced surface deformation reappeared. New tensile openings developed along the northern boundary cracks, extending discontinuously toward the rear edge. The arcuate cracks at the rear edge showed trends of connectivity, indicating significant overall displacement of the landslide mass (Figure 2g,h). From July to August 2014, tensile and vertical offset cracks reappeared at an elevation of 262 m near the rear edge (Figure 2i). Cracks also developed in houses situated above the roadway at 190 m elevation. Analysis of macroscopic surface deformation indicates that tensile cracks appeared along the rear edge, accompanied by extensional deformation in the pre-existing boundary cracks on both sides. The peripheral cracks of the landslide effectively coalesced, reflecting coherent overall deformation characteristics. The locations corresponding to each photograph are indicated on the Baijiabao landslide plan (Figure 1a).

In summary, the macroscopic deformation process of the Baijiabao landslide clearly demonstrates the characteristic features of a traction-type landslide. The deformation first manifested in June 2007 as tensile cracks along the roadway on the right flank of the landslide. Subsequently, arcuate tensile cracks gradually developed and propagated with vertical offsets along the rear edge, indicating tensile deformation induced by instability at the front edge. Following significant bank collapse at the frontal toe in 2009, deformation further propagated toward the central and lateral regions. The overall deformation process exhibits a progressive failure pattern characterized by “front-edge traction-type and rear-edge tensile cracking”. Moreover, the deformation predominantly occurs from May to September each year, coinciding with rapid reservoir water level decline and intense rainfall, highlighting a pronounced correlation between landslide deformation and reservoir water level fluctuations as well as rainfall infiltration.

2.1.3. Monitoring Data Analysis

Significant step-like deformations are observed at the monitoring points during the annual reservoir drawdown period. As of 28 December 2024, the cumulative displacements at the front-edge monitoring point ZD1, the central point ZD2, and the rear-edge point ZD3 of the Baijiabao landslide were 385.9 mm, 427.6 mm, and 651.7 mm, respectively (Figure 3). The data indicate that the displacement at the front-edge point (ZD1) is smaller than that at the rear-edge point (ZD3). However, deformation at the front-edge point occurred earlier within the same step-like deformation period, suggesting that movement at the front edge drives subsequent deformation at the rear, consistent with the behavior of a traction-type landslide.

Additionally, four automatic surface crack displacement monitoring instruments were installed on the Baijiabao landslide, with monitoring commencing on 22 April 2017. As shown in Figure 4, the relative displacement monitoring curves of the surface cracks each exhibited a pronounced step-like increase between 2017 and June 2019. Monitoring point LF4 also exhibited a sharp increase in displacement in June 2021. All four cracks are situated along the rear edge of the landslide. The crack widths rank as LF2 > LF1 > LF4 > LF3, with LF3 notably narrower than the others, likely due to its shorter length. LF1 and LF2 are located on the same side and have comparable lengths, thus warranting comparative analysis. At the start of monitoring in April 2017, LF1 had a width of approximately 200 mm, whereas LF2 measured about 110 mm. During the rainfall period in June 2017, all four cracks experienced varying degrees of step-like deformation, with LF1 remaining wider than LF2. Beginning in August 2017, as the reservoir water level in the Three Gorges area gradually rose from 145 m to 160 m by October 2017, the cracks underwent another step-like deformation, during which LF2′s width surpassed LF1, reaching 350 mm. This deformation event was attributed to rainfall.

All four cracks exhibited significant step-like displacements during the rapid reservoir drawdown and rainfall periods each June, with the sequence of step deformations consistently occurring first in LF1, followed by LF4, and then LF2 during the drawdown periods of 2017, 2018, and 2019, indicating a traction-type displacement characteristic. LF4, which extends along the left boundary, exhibited overall tensile cracking, whereas the high-elevation crack LF3 experienced relatively minor deformation. However, the synchronous activity of LF3 with the other cracks suggests that deformation at the rear edge is governed by sliding at the front edge. These monitoring data corroborate earlier macroscopic deformation observations, revealing a traction-type landslide evolution process characterized by initial deformation at the front edge due to erosion, followed by stress transfer toward the rear, progressive tensile cracking at the rear edge, and finally the development of overall connectivity. This fully confirms that the landslide’s failure mechanism is driven by reservoir water level fluctuations and exhibits typical traction-type behavior.

2.2. Crack Characteristics of the Baishuihe Landslide

2.2.1. General Description and Geological Features

The Baishuihe landslide is situated in Baishuihe Village, Shazhenxi Town, Zigui County, Hubei Province, on the southern bank of the Yangtze River, approximately 56 km from the Three Gorges Dam. The landslide is geographically located at 110°32′09″ E and 31°01′34″ N. The landslide is situated within a broad river valley, sloping south to north and exhibiting a stepped profile toward the river. The rear elevation is around 410 m, while the landslide toe extends below the reservoir water level at 135 m. The eastern and western boundaries are defined by bedrock ridges. The overall slope angle is about 30°. The landslide spans approximately 600 m (N-S) by 700 m (E-W), with an average thickness of 30 m and a volume of 1260 × 10⁴ m³. The underlying strata consist of Jurassic thick-bedded sandstone interlayered with thin-bedded mudstone, with bedding planes striking 15° and dipping 36°. Due to significant deformation, an early warning zone was established in 2004, covering about 21.5 × 10⁴ m² with dimensions of 500 m by 430 m and an average thickness of 30 m. The main sliding direction is 20°, and the landslide is classified as a large, deep-seated soil slide. Figure 5 presents the plan and cross-sectional views of the Baishuihe landslide.

2.2.2. Field Investigation

Since the end of May 2003, water impoundment began in the Three Gorges Reservoir area, with the water level rising to 135 m by early June. By mid-July 2003, a series of transverse tensile cracks had appeared in the central and frontal sections of the eastern sliding mass. These cracks were oriented in the 320–330° direction, with widths of 5–20 mm and lengths ranging from 5 to 300 m. Numerous houses on the landslide mass exhibited severe tensile cracking and structural damage. Between mid-June and mid-July 2004, multiple cracks developed in the eastern section of the landslide, extending from the 200 m elevation on the east side to the Dashujing area at 150 m elevation on the west. These cracks caused leakage from water wells, with widths of 5–20 mm and maximum subsidence reaching 150 mm. In September 2005, new tensile cracks appeared along the rear edge and central section of the eastern sliding mass, as well as on the road surface at approximately 230 m elevation (Figure 6a–c). The most significant deformation occurred in 2007, when the reservoir water level decreased from 156 m to 145 m for the first time. During this period, the eastern and rear boundaries of the landslide were nearly fully connected by cracks. On the western side, feather-like intermittent cracks developed, although the western boundary had not yet fully connected (Figure 6d,e). From 2008 to 2010, landslide deformation was primarily concentrated during periods of intense seasonal rainfall. Apart from minor localized deformations, no large-scale displacements were observed. In 2014, intense rainfall triggered a slope collapse in the soil mass above the retaining wall of the Sha-Huang Highway at the rear edge of the landslide, with an estimated volume of about 30 m³ (Figure 6f,g). In July 2015, significant surface deformation was observed on the Baishuihe landslide. On the western boundary along the Sha-Huang Highway, tensile cracks and subsidence were clearly visible, with new cracks widening by 1–5 mm. On the eastern boundary, cracks had cumulatively widened by approximately 15 cm, with new openings of 2–8 mm. In 2016, significant deformation was again observed after May. Cracks developed in the central and front sections of the eastern landslide and along the western boundary, causing offset and disruption of the highway subgrade, which severely affected traffic conditions (Figure 6h,i). The locations corresponding to each photograph are indicated on the Baishuihe landslide plan (Figure 5a).

From the development characteristics of the cracks, it is evident that, since the impoundment of the Three Gorges Reservoir began at the end of May 2003, the Baishuihe landslide has exhibited typical features of a translational landslide in terms of macroscopic deformation. The cracks are primarily distributed in belt-like zones along the eastern flank, rear edge, and toe of the landslide. During the initial stages, cracks extended from the eastern and central sections toward the front, accompanied by tensile damage to houses, indicating localized extensional deformation. Between 2004 and 2007, cracks gradually extended from the higher-elevation eastern section to the lower-elevation western section, forming a continuous boundary. Feather-like, discontinuous cracks developed along the western flank, reflecting the overall east-to-west translational movement of the landslide. The deformation is closely associated with concentrated rainfall, indicating that the landslide is driven by variations in pore-water pressure. Under external influences such as rainfall infiltration, tensile cracking and subsidence occurred at the rear due to the loss of support, whereas compressive deformation developed at the toe as the sliding mass advanced, resulting in bulging or localized accumulation. This differential movement between the rear and front consequently caused uneven surface subsidence and structural damage. For instance, a cumulative settlement of 15 cm was recorded on the highway in 2015, attributed to compression and localized bulging or uplift of the soil due to blockage at the toe during forward movement. Nevertheless, as the sliding mass continued to advance, cumulative settlement persisted. Furthermore, structural damages, including tensile cracking and base rupture of the roadbed, further corroborate the horizontal translational mechanism of the landslide.

2.2.3. Monitoring Data Analysis

Significant step-like deformations are observed annually at the monitoring points when the reservoir water level decreases to approximately 160 m, coinciding with periods of intense rainfall. As of December 2024, the cumulative displacements at the front-edge monitoring points XD-01 and XD-03 within the Baishuihe landslide warning zone reached 4934 mm and 5206 mm, respectively, whereas the displacements at the rear-edge points ZG93 and ZG118 were approximately 3400 mm (Figure 7). Monitoring point ZG118 was damaged in November 2018; however, prior to this event, its cumulative displacement trend was consistent with that of ZG93, although slightly smaller. The data indicate that the displacements at the front-edge points (XD-01, XD-03) are substantially greater than those at the rear-edge points (ZG93, ZG118). Nevertheless, during the step-like deformation phases, displacement at the rear-edge points occurred earlier than at the front, suggesting that the deformation initiates at the rear and subsequently drives the movement of the front. Given that the front edge is adjacent to the water and more susceptible to sliding, it experiences larger displacements, exhibiting the characteristic features of a translational landslide.

2.3. Development Characteristics of Landslide Cracks

Traction-type landslides are typically characterized by relatively gentle slip surfaces and ample free space at the toe. These landslides are usually triggered by factors such as water erosion and incision, reservoir water level fluctuations, or engineering excavation, which reduce the anti-sliding force at the front, resulting in initial deformation [31]. Front-edge deformation is generally driven by gravitational forces. Following local sliding failure of the frontal rock-soil mass, a new free surface is generated, potentially inducing additional localized failures in the adjacent area. As the slope adjacent to the failed mass loses its structural support, new deformation gradually occurs, resulting in the formation of tensional cracks extending upslope. This process creates a secondary sliding block, and the sequence continues, ultimately forming a series of step-like arcuate tensile cracks, scarps, and multiple sliding masses progressing from the front to the back. Macroscopically, this manifests as a progressive “retrogressive” sliding pattern. The cracking characteristics of these landslides exhibit distinct zonation and mechanical differentiation. The rear of the landslide often develops a series of arcuate or en echelon tensile cracks arranged in a stepped pattern, with large crack widths, indicating gravitational tensile failure of the sliding mass. Shear cracks parallel to the sliding direction are frequently observed along the lateral boundaries, reflecting relative displacement between the sliding body and stable surrounding materials. Typical examples include the Baijiabao Landslide [32], Yangjiatuo Landslide [33], and Liangshuijing Landslide [34]. Figure 8a illustrates the deformation–failure process and crack development in a traction-type landslide.

In translational landslides, the primary driving force originates from the rear edge. Rainfall commonly infiltrates along permeable weak zones at the rear, gradually seeping toward the landslide toe. Consequently, the mechanical strength of these weak zones decreases progressively from the rear to the front, consistent with the infiltration path of rainwater. At the macroscopic scale, displacement generally initiate at the rear edge before propagating to the front. The sliding surface of such landslides commonly exhibits a two-stage composite morphology, characterized by a steep upper segment and a gentler lower segment [31]. At the toe, compressional resistance produces pronounced uplift, leading to the formation of transverse bulging and radial cracks. Tensional cracks also develop at the rear edge, though they are typically smaller in scale. Longitudinal shear cracks frequently emerge in the central portion of the landslide body, reflecting the forward-pushing movement of the sliding mass. Feather-like shear cracks may form along the flanks, indicating lateral expansion of the slide mass. If the landslide contains a rotational component, or if different sections of the slope move at varying rates, cracks may first develop on one side and subsequently extend to the other. With progressive deformation, tensional cracks increase in both number and spatial extent. Discontinuous cracks also gradually elongate, widen, and deepen over time. These crack characteristics collectively reveal a landslide kinematic pattern in which the toe deforms under rearward thrust, producing an overall forward-propagating motion, as exemplified by the Baishuihe Landslide [35], Xintan Landslide [36], and Bazimen Landslide [37]. Figure 8b illustrates the deformation–failure process and crack development of a translational landslide.

3. Landslide Numerical Simulation

3.1. Principles of Computation Using COMSOL Multiphysics

To describe the rainfall infiltration process, the Richards model is adopted in this study. The soil-water characteristic curve (SWCC) and unsaturated hydraulic conductivity involved in the model are fitted using the Van Genuchten equations [38,39], which are expressed as follows:

$$C{\displaystyle \frac{\partial \psi }{\partial t}}={\displaystyle \frac{\partial }{\partial z}}\left(K{\displaystyle \frac{\partial \psi }{\partial z}}+1\right)$$

(1)

$$\theta ={\theta }_r+{\displaystyle \frac{{\theta }_s-{\theta }_r}{{\left[1+{\left(\alpha \psi \right)}^n\right]}^m}}$$

(2)

$$K=K_s{S}_e^{0.5}{\left[1-{\left(1-S_e^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$m$}\right.}\right)}^m\right]}^2$$

(3)

In the equations, t denotes the time variable associated with changes in soil suction (s); z is the vertical depth of the soil (m); ψ is the matric suction (Pa); θ is the volumetric water content (cm³/cm³); θ_r is the residual water content (cm³/cm³), fixed at 0.02; θ_s is the saturated water content (cm³/cm³), fixed at 0.3; C is the specific water capacity, defined as C = dθ/dh, where h represents the hydraulic head (m); S_e is the effective saturation, defined as S_e = (θ − θ_r)/(θ_s − θ_r); α, n and m are fitting parameters related to the physical properties of the slope material, with values set to 1, 2, and 0.5, respectively; K is the unsaturated hydraulic conductivity; K_s is the saturated hydraulic conductivity.

To describe the deformation characteristics of the slope, the elastic behavior is defined by the generalized Hooke’s law [40], while the plastic behavior is modeled using the Mohr-Coulomb yield criterion. The governing equations are formulated as follows:

$$\left\{d\epsilon \right\}=\left\{d{\epsilon }^e\right\}+\left\{d{\epsilon }^p\right\}$$

(4)

$$d{\epsilon }^e={\left[D^e\right]}^{-1}\left\{d\sigma \right\}$$

(5)

$$\begin{array}{c}d{\epsilon }^p=\lambda {\displaystyle \frac{\partial Q}{\partial S}}, \lambda \ge 0\\ F\left(\sigma ,{\sigma }_{ys}\right)\le 0, \lambda F=0\\ F_{cone}=\sqrt{J_2}+\alpha I_1-k\\ \alpha ={\displaystyle \frac{\tan \varphi }{\sqrt{9+12{\tan }^2\varphi }}}, k={\displaystyle \frac{3c}{\sqrt{9+12{\tan }^2\varphi }}}\end{array}$$

(6)

In the equations: dε^e denotes the elastic strain increment and dε^p the plastic strain increment. [D^e] represents the elastic stiffness matrix. λ is the plastic multiplier. Q is the plastic potential function. S denotes the deviatoric stress tensor. σ is the stress. σ_ys is the yield stress, and F is the yield function. J₂ is the second invariant of the deviatoric stress tensor, and I₁ is the first invariant of the stress tensor. The symbols α and k are material parameters. c and φ represent the cohesion and internal friction angle, respectively.

3.2. Implementation of Numerical Model

Taking the Baijiabao landslide and Baishuihe landslide as examples, cross-sectional models of the landslides were constructed using AutoCAD 2022 and then imported into COMSOL Multiphysics 6.3 (COMSOL) for mesh generation. As shown in Figure 9 and Figure 10, the Baishuihe landslide is 610 m long and 281 m high, with a tension crack located along the Shahuang Highway at an elevation of approximately 230 m. The Baijiabao landslide is 736 m long and 300 m high, with a tension crack located along the Zixing Highway at an elevation of approximately 185 m. For the sliding body, the maximum mesh element size is set to 2 m with a maximum element growth rate of 1.05, while for the sliding bed, the maximum element size is 40 m with a growth rate of 1.1. The Baishuihe landslide model contains 16,230 mesh elements, and the Baijiabao landslide model contains 22,958 mesh elements.

Cracks in this study are modeled using the built-in fracture feature in COMSOL Multiphysics, with a thickness of 0.5 m, and hydraulic conductivity of 10 m/d, representing vertical surface cracks. Hydraulically, the fractures are fully coupled with the surrounding soil, allowing fluid exchange; the top is exposed to rainfall infiltration, while the bottom is hydraulically connected to the soil, enabling rapid drainage. Mechanically, fractures are assumed continuous with the surrounding soil, without separate stress boundary conditions on the fracture faces.

Boundary conditions were assigned during model setup: the left boundary is constrained in the horizontal direction, and the bottom boundary is constrained in both the horizontal and vertical directions. The initial subsurface flow field of the landslide models was established based on the groundwater table: the groundwater level at the slope toe corresponds to the reservoir water level of 145 m, gradually rising toward the slope crest. The soil below the groundwater table is assumed to be fully saturated, whereas the soil above it is unsaturated. The volumetric water content in the unsaturated zone is calculated using the van Genuchten soil–water characteristic curve. This distribution of the groundwater table and unsaturated water content was used as the initial hydraulic condition for the subsequent rainfall infiltration simulations. The slope toe is defined as a permeable boundary, and a rainfall boundary condition with an intensity of 100 mm/d is applied to the surface soil layer. Specific calculation conditions are shown in

Table 1. COMSOL numerical model working condition setting.

	Condition Design
Translational Landslide (Baishuihe Landslide)	145 m reservoir water level + 100 mm/d rainfall for 24 h + rear edge cracks of 1 m, 2 m, 3 m, and 4 m
Traction-type Landslide (Baijiabao Landslide)	145 m reservoir water level + 100 mm/d rainfall for 24 h + front edge cracks of 1 m, 2 m, 3 m, and 4 m

. The basic physical parameters of the landslides are listed in

Table 2. Numerical model parameters of Baijiabao landslide.

	Elastic Modulus E (MPa)	Poisson Ratio $\mathit{\upsilon }$	Cohesion c (kPa)	Internal Friction Angle $\mathit{\phi }$ (°)	Density $\mathit{\rho }$ (kg/m3)	Permeability Coefficient Ks (m/d)
sliding mass	16.7	0.35	16.5	20	1800	1.98
bedrock	3000	0.30	1950	22	2600	0.01

and

Table 3. Numerical model parameters of Baishuihe landslide.

	Elastic Modulus E (MPa)	Poisson Ratio $\mathit{\upsilon }$	Cohesion c (kPa)	Internal Friction Angle $\mathit{\phi }$ (°)	Density $\mathit{\rho }$	Permeability Coefficient Ks (m/d)
sliding mass	20.8	0.35	27.1	18	2000	1.08
bedrock	61,000	0.30	2000	35	2535	0.01

.

4. Numerical Results and Discussion

4.1. Crack Depth Effects on Seepage Fields

4.1.1. Traction-Type Landslides

As shown in Figure 11, under 24-h rainfall conditions, the saturation area on the slope surface of the Baijiabao landslide progressively expands. In the vicinity of the cracks, rainfall infiltrates the slope body, producing higher soil saturation at the crack base compared to the surrounding soil. As crack depth increases, the soil saturation on the slope surface adjacent to the crack decreases, while the soil saturation at the crack base remains approximately stable around 0.5. When the crack depths are 1 m, 2 m, 3 m, and 4 m, the saturation levels on the crack slope surface adjacent to the cracks are 0.426, 0.325, 0.272, and 0.246, respectively, and the saturation levels at the crack base are 0.549, 0.519, 0.529 and 0.553, respectively. The reduction in slope surface saturation with increasing crack depth are 0.101, 0.053 and 0.026 successively, indicating a diminishing trend in magnitude. This suggests that the influence of crack depth on slope surface saturation exhibits a nonlinear attenuation trend. At shallow crack depths, rainfall preferentially infiltrates along the cracks, leading to a substantial reduction in moisture retention on the slope surface and producing the greatest decrease in saturation. However, with further increases in crack depth, its regulatory effect on slope surface saturation gradually weakens, as moisture primarily infiltrates vertically into deeper layers, thereby stabilizing lateral water replenishment of the slope surface.

The distribution of the total Darcy velocity field in Figure 11 (represented by vector arrows) indicates that, under rainfall conditions, the Baijiabao landslide develops two concentrated seepage zones at the slope crest and slope toe. The maximum seepage velocity occurs at the slope crest near the 4 m-deep crack, with flow direction downward along the soil-bedrock interface. This results from the shorter seepage path and higher hydraulic gradient at the slope crest, resulting in the highest Darcy velocity. At the slope toe, which is close to the groundwater table, the seepage velocity comprises both the vertical component from rainfall infiltration and an outward component from groundwater exfiltration. The superposition of these seepage effects leads to water head accumulation at the slope toe, and the outward seepage velocity may trigger piping erosion and particle migration, thereby reducing slope stability. At the crack locations, the seepage velocity is relatively low, and it decreases gradually on the surface with increasing crack depth. This occurs because deeper cracks lengthen the infiltration path, thereby reducing the seepage velocity near the slope surface. Additionally, a localized perched water zone with high saturation develops at the crack base. Driven by gravity and matric potential, moisture in this zone diffuses into the surrounding soil, potentially affecting the stability of the deeper soil layers.

4.1.2. Translational Landslides

Figure 12 illustrates that, under the 24-h rainfall condition, the saturated area on the slope surface of the Baishuihe landslide gradually expands. Rainwater infiltrates through the cracks into the slope body, and the soil at the crack base exhibits higher saturation than the surrounding soil. As crack depth increases, surface saturation around the cracks decreases, while the crack-bottom saturation remains nearly constant at about 0.65. When the crack depths are 1 m, 2 m, 3 m, and 4 m, the surface saturations are 0.514, 0.391, 0.332 and 0.328, respectively, whereas the corresponding crack-bottom saturations are 0.669, 0.640, 0.641 and 0.663. The reductions in surface saturation with increasing crack depth are 0.123, 0.059, and 0.004, respectively, showing a progressively diminishing decrease.

As shown by the total Darcy velocity distribution in Figure 12 (represented by vector arrows), under rainfall conditions, the Baishuihe landslide exhibits four concentrated seepage zones located at the slope crest, the designated crack area, the terrain bulge at approximately 174 m elevation, and the slope toe. Similarly, the highest seepage velocity occurs at the slope crest near the 4 m deep crack, where the flow direction is predominantly downward along the slope surface. This is due to the presence of a certain thickness in the sliding body, differing from the Baijiabao landslide where the soil-rock interface intersects the slope surface. At the designated crack area (Zone 2), the surface seepage velocity decreases gradually with increasing crack depth, with a sharper reduction at shallow depths that diminishes at greater depths. Additionally, at the terrain bulge around 174 m elevation (Zone 3), seepage velocity is relatively high because rainfall accumulates in a local catchment area, where surface runoff converges and infiltrates intensively, resulting in elevated infiltration pressure.

Comparing the seepage fields of traction-type and translational landslides under rainfall reveals several common patterns: (1) Increasing crack depth decreases surface soil saturation around cracks, while saturation at the crack bottom remains relatively stable. (2) Concentrated seepage zones are present at the slope crest, slope toe, and terrain bulges, which warrant focused attention in landslide mitigation. (3) The influence of crack depth on slope stability is twofold: reduced surface saturation may lessen the self-weight and seepage forces of shallow soils, favoring local stability, whereas persistently high crack-bottom saturation may soften the slip-zone soils and elevate the risk of deep-seated sliding. Therefore, it is recommended to prioritize the installation of pore-water pressure sensors at the crack bottoms during landslide monitoring, rather than focusing solely on slope surface moisture content. Additionally, prevention and control designs should account for the differing effects of crack depth on shallow and deep stability, in order to develop more targeted engineering measures.

4.2. Crack Depth Effects on Displacement Fields

4.2.1. Traction-Type Landslides

Figure 13 illustrates the displacement field of the Baijiabao landslide under rainfall, which exhibits typical traction-type deformation characteristics: in the early stage of rainfall, displacement is initially concentrated at the landslide front edge, forming a primary sliding zone. As rainfall continues, the affected displacement area progressively expands toward the rear edge, indicating a retrogressive progressive failure pattern. During the deformation, secondary slip surfaces gradually develop in the rear region, eliciting pronounced displacement responses and ultimately producing a hierarchical deformation pattern.

The displacement fields of the landslide under varying crack depths exhibit similar regional deformation characteristics. Figure 14 shows the X-direction, Y-direction, and total displacement field of the Baijiabao landslide after 24 h of rainfall with a crack depth of 1 m. Six main regions exhibit notable displacement: the slope crest, a topographic bulge at approximately 220 m elevation, the left and right sides of the designated crack,, the area above the groundwater table near the slope toe, and the area below the groundwater table near the slope toe. In the X-direction displacement field (Figure 14a), regions 1, 2, 4, and 6 show positive displacement, indicating downslope movement consistent with the landslide’s shear sliding trend. Notably, region 6 shows negative displacement when the crack depth is 4 m, likely due to seepage-induced stress reversal. Regions 3 and 5 display negative displacement, the negative displacement in region 3 likely results from water infiltration filling the crack, where hydrostatic pressure pushes soil on both sides of the crack outward. The negative displacement in region 5 may stem from localized toe-soil uplift coupled with reverse horizontal movement. In the Y-direction displacement field (Figure 14b), regions 3 and 4 correspond to the crack location and the area near the crack toward the front of the sliding mass, respectively, whereas other regions are consistent with the X-direction field. Regions 1, 2, 4, and 5 exhibit negative displacement, whereas regions 3 and 6 exhibit positive displacement. The overall negative displacement on the slope indicates a general downslope movement under rainfall. The positive Y-displacement in region 3 likely results from water infiltration saturating the crack, producing hydrostatic pressure. As a preferential seepage channel, this crack facilitates rapid water percolation, generating excess pore-water pressure that reduces effective stress and induces a buoyancy effect. Moreover, the unsaturated soil absorbs water, reducing matric suction and inducing swelling deformation. The positive displacement in region 6 arises from bulging of the toe soil. In the total displacement field (Figure 14c), regions with larger displacements align with those in the X-direction field, with displacement concentrated at the slope crest, slope toe, and crack locations. Synchronous displacement increases in these critical areas may indicate the landslide is entering an accelerated deformation phase, highlighting the need for timely and targeted mitigation measures.

Figure 14d–f show the X-direction displacement, Y-direction displacement, and total displacement for regions 1 to 6 at different crack depths, respectively. Given that the scale of crack depth is much smaller than the overall landslide size, its impact on the large-scale displacement field of the landslide is relatively limited. Therefore, this study examines the local deformation characteristics around the crack, specifically regions 3 and 4. Figure 14d indicates that region 3 exhibits negative X-direction displacement, with its magnitude monotonically increasing as the crack depth increases. Region 4 shows positive X-direction displacement, which also gradually increases with crack depth. These observations suggest that increasing crack depth simultaneously enhances the opposite horizontal movements of the soil masses on both sides of the crack, reflecting soil expansion effects induced by rainfall infiltration. Figure 14e shows that region 3 has positive Y-direction displacement, whereas region 4 exhibits negative Y-direction displacement. The Y-direction displacements in both regions show minimal variation with increasing crack depth; however, region 3 displays a slight increasing trend overall, whereas the absolute value in region 4 slightly decreases. This suggests that crack depth has a limited influence on vertical displacement. From Figure 14f, the total displacement in region 3 is generally larger than in region 4, and displacement decreases with increasing crack depth in a stepwise manner. This nonlinear response indicates a threshold effect of crack depth on displacement field, consistent with the influence observed in the seepage field.

4.2.2. Translational Landslides

Based on the displacement field results of the Baishuihe landslide under rainfall (Figure 15), the landslide exhibits typical characteristics of translational deformation. At the onset of rainfall, displacement initially occurs in the rear slope region and is accompanied by a coordinated displacement response at the slope toe. As rainfall infiltration continues, the affected displacement area at the rear progressively expands, with secondary sliding bodies developing behind the initial sliding surface, significantly increasing the instability risk at the rear. Additionally, the displacement magnitude at the toe continuously increases as deformation progresses, indicating that the deformation of the Baishuihe landslide gradually propagates from the rear toward the front. This process characterizes a typical rear-driven translational landslide.

The displacement fields of the landslide under varying crack depths exhibit similar regional deformation characteristics. Figure 16 shows the X-direction, Y-direction, and total displacement fields of the Baishuihe landslide after 24 h of rainfall with a crack depth of 1 m. The landslide displays five main displacement zones: the slope crest, the left side of the terrain bulge at approximately 240 m elevation, the left and right sides of the set crack, and the slope toe area. In the X-direction displacement field (Figure 16a), zones 1, 3, and 4 exhibit positive displacement, whereas zone 3 shows negative displacement at the 1 m crack depth, possibly due to higher shallow seepage pressure caused by the shallow crack. The positive displacement zones reflect the overall downslope movement of the landslide mass. Zones 2 and 5 display negative displacement; the negative displacement in zone 2 results from the influence of a local sliding mass located above, with zone 2 representing the toe of this local sliding body and manifesting local soil uplift accompanied by reverse horizontal displacement, similar to zone 5. In the Y-direction displacement field (Figure 16b), zones 1 through 4 exhibit negative displacement, with zone 3 showing positive displacement at the 1 m crack depth, likely caused by seepage-induced soil expansion. Zone 5 shows positive displacement. This indicates that the rear slope moves downward, driving the overall deformation of the toe, consistent with the deformation pattern of a translational landslide. In the total displacement field (Figure 16c), zones 1, 3, and 4 at the rear slope show relatively large displacements. Zones 1 and 3 suggest a potential development of shallow sliding surfaces, while the displacement concentration at zone 4 is mainly near the rock-soil interface, forming a distinct deep-seated displacement concentration zone.

Figure 16d–f, respectively, show the X-direction displacement, Y-direction displacement, and total displacement of regions 1–5 under different crack depths. Figure 16d,e show that the X-direction displacements in regions 3 and 4 are mainly positive, while the Y-direction displacements are primarily negative. With increasing crack depth, the absolute values of displacement gradually increase, although the rate of increase gradually diminishes. This indicates that as crack depth increases, the influence of seepage on shallow soil weakens, and under the combined effects of rainfall and gravity, the slope body progressively slides downward. From Figure 16f, it is evident that total displacement in regions 3 and 4 increases with crack depth, with the growth rate in region 4 significantly exceeding that in region 3, indicating that greater crack depths induce more pronounced deformation in the deep soil layers.

5. Conclusions

This study comparatively analyzed the deformation evolution patterns and disaster mechanisms of the Baijiabao traction-type landslide and the Baishuihe translational landslide based on macroscopic deformation characteristics and long-term monitoring data. A hydro-mechanical coupled numerical model under rainfall infiltration conditions was established to investigate the differential effects of crack development depth on the stability of these two types of reservoir bank landslides. The main findings are as follows:

(1)

Analysis of crack characteristics and monitoring data indicates that the Baishuihe landslide exhibits a translational failure mode, initiated at the rear edge and driven by reservoir drawdown and rainfall. Cracks propagate from east to west, accompanied by rear-edge subsidence and frontal bulging. The Baijiabao landslide demonstrates a progressive traction-type failure, primarily triggered by rapid reservoir drawdown, beginning with frontal collapse and subsequently extending toward the middle and flanks.

(2)

Under rainfall and crack development, the seepage fields of both traction-type and translational landslides display similar patterns: increasing crack depth reduces slope-surface saturation in a nonlinear manner, while saturation at crack bottoms remains relatively stable. Shallow cracks promote rapid infiltration, causing a sharp decline in near-surface moisture, whereas deeper cracks exert a comparatively weaker effect. Seepage is concentrated at the slope crest, toe, and topographic protrusions, which should therefore be prioritized in landslide prevention and control strategies.

(3)

The influence of crack depth on displacement fields differs significantly between the two landslide types. In the traction-type landslide, soils adjacent to cracks undergo reverse horizontal movement, with displacements decreasing stepwise as crack depth increases. This behavior is mainly controlled by crack expansion and pore-water pressure induced by rainfall infiltration; Y-direction displacement is relatively minor. In contrast, the translational landslide undergoes overall rear-edge sliding, with displacement increasing with crack depth. This process is dominated by gravity and thrust transmission, and deep-seated deformation becoming more pronounced.

These findings highlight the distinct controlling mechanisms of traction-type and translational landslides. Accordingly, traction-type slopes require suppressing lateral crack propagation and toe shear, while translational slopes demand blocking rear-edge thrust transmission and monitoring deep slip surfaces.