3D Slope Research Articles

Physics-guided neural network-based framework for 3D modeling of slope stability

Physics-informed neural networks (PINN) have gradually attracted attention in the field of geotechnical engineering. This paper proposes a novel PINN-based framework for the three-dimensional (3D) stability analysis of soil slopes. Based on the fundamental theorem of plasticity and limit analysis, the partial differential equations (PDE) with regard to slope collapse are derived and integrated into the physics-guided loss function. A kinematically admissible failure mechanism that rigorously satisfies the Mohr-Coulomb associated flow rule is obtained by minimizing the loss function, thereby circumventing complex mathematical calculations. The discrete points generated by PINN are selected and refined through a series of procedures to represent the failure block of slopes using a two-dimensional matrix. The entire training process of the PINN-based framework is conducted without the need for any labeled data. The resulting discretized failure mechanism is meshfree and capable of accommodating spatially discrete data. A validation exercise is performed to verify the proposed framework by comparing it with the classical 3D rotational failure mechanism. To further consider the impact of external excitation on slope stability, a hybrid PINN framework is developed to assess the stability of slopes subjected to complex external environments. In addition to the PINN to generate a failure mechanism, a parallel PINN is employed to acquire the corresponding spatially discrete data of specified external excitations. The hybrid PINN framework for seismic stability assessment of slopes is demonstrated by way of example, indicating favorable feasibility and applicability of the developed approach. The proposed PINN-based framework provides innovative and promising avenues for 3D slope stability analysis.

A modified solution for evaluating the sliding direction and stability of 3D slopes

In this paper, we present an improved and efficient analytical solution for evaluating the stability of 3D slopes based on the minimum potential energy method. The equilibrium equation of the landslide is employed to determine the shear stress on the failure surface, and a new formulation for shear potential energy is introduced. The vector-combined direction of the force acting on the landslide is considered equivalent to the sliding direction (SD). Two classic examples are reanalyzed to validate the accuracy and performance of the proposed method. The analysis demonstrates that the obtained results align well with reference solutions and tend to be conservative in engineering applications. Parameter investigations are conducted to explore the influences of SD, shear strength parameters, slope angle, and soil unit weight on the safety factor (SF) of 3D slopes. The findings indicate that a larger SD corresponds to a less stable slope. Finally, the effects of optimization parameters, landslide volume, and surcharge on the location of the failure surface, SF, and SD are also examined. The developed analytical approach offers a novel and straightforward solution with sufficient accuracy and eliminates the need for iteration in determining the SF, making it a valuable complementary method for assessing the stability of 3D slopes.

Computational modeling of three-dimensional slope reinforcement by anchor cable micropile group considering coordinated deformation

The application of anchor cable micropile group (ACMPG) in small and medium-sized slope support is gradually widespread. However, the coordination deformation of the structure and the resistance of the soil in front of the piles are less considered in the existing calculation models. Therefore, based on the load transfer approach and according to the structural characteristics of the ACMPG, the calculation method was provided for the resistance of the soil in front of the pile and the tension of the anchor after deformation. And the equations for calculating the resistance of the ACMPG were established. Based on the method of upper bound limit analysis, the display equation had been established for the safety factor of reinforcing the 3D slope of the structure. And finite element models were developed to validate the theoretical model. Finally, a parametric study was conducted to investigate the influence of slope angle, soil friction angles, location, 3D effects, on the slope safety factor and the support effect of piles and anchor cables supporting the structure. The results showed that the theory proposed in this paper can accurately calculate the safety factor of slopes, which is helpful for the design and construction of slope reinforcement.

Three-dimensional slope stability analysis based on irregular ellipsoid sliding surface

The determination of the critical sliding surface is a crucial aspect of slope stability analysis. In reality, the environment in which slopes are located is often very complex, and the sliding surfaces have different shapes. Therefore, a three-dimensional stability study is proposed, using irregular ellipsoidal shapes as the sliding surface. By constructing the equation of the irregular ellipsoid and applying spatial geometric transformations, an irregular ellipsoid controlled by six parameters, (semi-axis length (a), width (b), height (c), rotation angle (θ), and spatial displacements (tx and tz)), is obtained. The interpolation method is employed to apply the irregular ellipsoid to 3D slopes, thereby generating irregular ellipsoidal sliding surfaces. The slope stability coefficient is calculated by using the residual thrust method and genetic algorithm to determine the critical sliding surface. A comparative stability analysis is conducted between the standard ellipsoidal sliding surface and the irregular ellipsoidal sliding surface through a classic case study. The results show that the Type II irregular ellipsoidal sliding surface aligns well with the mining area. Finally, the research findings are applied to the 3D slope stability analysis of the Shengli West No.2 Open-Pit Coal Mine in China, validating the feasibility of the proposed method.

Multi-dimensional error figuring model for ion beams in X-ray mirrors

X-ray mirrors are core optical elements in synchrotron light sources, which are typically figured by ion beams. However, traditional ion beam figuring (IBF) methods cannot effectively correct both the height and 2D slope errors. Thus, what we believe to be a novel multi-dimensional error figuring model (MEFM) is proposed to integrate the height and 2D slope errors into a linear system of equations for simultaneous multi-dimensional error convergence. The weight values are determined based on specific manufacturing errors. The simulation results show that MEFM can achieve lower 2D slope and height errors than a single height or 2D slope errors in the figuring method. The power spectral density (PSD) curves before and after simulated figuring demonstrate that the low- and mid-frequency errors are corrected simultaneously. Figuring experiments on a 270 mm × 15 mm X-ray reflector showed that the height and 2D slope errors effectively converged. The results of the PSD curves indicate that MEFM is more effective than the traditional height figuring model in correcting mid-frequency errors, which further proves the validity of the solution model. This study provides an algorithmic reference for the IBF of ultra-high precision X-ray reflectors, thereby promoting the development of physics, medicine, materials, and other fields.

Influence of 3D subsurface flow on slope stability for unsaturated soils

The occurrence of rainfall-induced slope failures has become more frequent due to the effect of climate change. Hence, various studies have been conducted to analyse the effect of rainfall infiltration on slope stability. Physically-based hydrological models have been commonly used with slope stability models such as the infinite slope model to develop slope susceptibility maps. However, a combination of three-dimensional (3D) water balance model with 3D limit equilibrium method (LEM) has not been commonly used. Hence, in this study, a water balance model, GEOtop was used to investigate the influence of subsurface flow in unsaturated soil under extreme rainfall conditions on regional slope stability in 3D directions. The results from the GEOtop model were used as inputs for 3D LEM slope stability analysis performed using the Scoops3D software to obtain the factor of safety (FOS) map for the region. Four slopes within the region were then selected to be modelled in the two-dimensional (2D) seepage and slope stability analyses, SEEP/W and SLOPE/W. Results from the detailed study showed that the pore-water pressures (PWPs) from the 3D water balance analyses were found to be higher than the 2D seepage analyses. Under similar PWP conditions, the FOS from the 2D slope stability analysis was observed to be lower than the 3D analysis for two out of the four slopes. However, the combined 3D water balance and slope stability analyses produced lower FOS compared to the 2D seepage and slope stability analyses due to the higher PWPs in the 3D water balance analyses. Therefore, this study highlights the importance of considering the 3D subsurface flow in unsaturated soil given that it has a significant influence on the FOS of slopes.

Probabilistic analysis of width-limited 3D slope considering spatial variability of Hoek–Brown rock masses

Probabilistic analysis of width-limited 3D slope considering spatial variability of Hoek–Brown rock masses

2D and 3D numerical modelling for preliminary assessment of long-term deterioration in Irish glacial till geotechnical slopes

ABSTRACT Long-term geotechnical slope deterioration, influenced by weathering and meteorological factors, presents stability challenges to infrastructure. Wetting and drying cycles lead to pore water pressure variations, causing deformations and slope failure. Studies on glacial tills which investigate deterioration in geotechnical slopes focus on variables like pore water pressure, soil water retention, compaction, freeze–thaw cycles and cracking. This research conducts a preliminary assessment of an Irish glacial till-cut slope, establishing a data-driven foundation for long-term slope behaviour studies. Data analysis, geospatial modelling and numerical simulations were performed on a cut slope in Castleblayney (Ireland), considering short-term/undrained and long-term/drained conditions. FLAC/Slope and Scoops3D were used for 2D and 3D slope stability analyses, applying the First-Order Second Moment (FOSM) probabilistic approach to assess how minor soil property changes affect slope stability, including long-term deterioration scenarios. The study underscores the importance of precise instrument placement within Irish glacial till geotechnical cut slopes, particularly at the uppermost part where shallow and deep failures coincide under long-term and short-term scenarios. This informs strategic instrument positioning for accurate slope deterioration investigations. This research lays the groundwork for understanding mechanisms driving geotechnical slope deterioration and provides insights for future studies on geotechnical asset deterioration models in Irish glacial tills.

3D slope stability analysis considering strength anisotropy by a micro-structure tensor enhanced elasto-plastic finite element method

This article presents a micro-structure tensor enhanced elasto-plastic finite element (FE) method to address strength anisotropy in three-dimensional (3D) soil slope stability analysis. The gravity increase method (GIM) is employed to analyze the stability of 3D anisotropic soil slopes. The accuracy of the proposed method is first verified against the data in the literature. We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90° turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions. Based on our numerical results, the end effect significantly impacts the failure mechanism and safety factor. Anisotropy degree notably affects the safety factor, with higher degrees leading to deeper landslides. For concave slopes, they can be approximated by straight slopes with suitable boundary conditions to assess their stability. Furthermore, a case study of the Saint-Alban test embankment A in Quebec, Canada, is provided to demonstrate the applicability of the proposed FE model.

Failure pattern of dispersive soil slopes under the action of rainfall conditions

Dispersive soil slopes are widely distributed in Northeast China. To analyze the failure caused by such slopes under various rainfall conditions, section K27 of the road-cutting slope of the Sui-Da Expressway in Heilongjiang Province, China, is considered an example. A 3D slope model was created using the similarity theory and visualized through close-range photogrammetry in a self-made model box. Six model tests were conducted under varying rainfall conditions to investigate the failure modes of dispersive soil slopes. Test results revealed that dispersive soil slopes are subject to two types of failure depending on the rainfall intensity. Slope erosion was divided into three stages by surface random roughness (SRR): initial erosion, constant velocity erosion, and accelerated erosion. Similarity theory suggests that the slope enters the accelerated erosion stage in the actual project when the SRR reaches around 31.95–46.5 cm. Furthermore, the reciprocal of the SRR change rate during the accelerated erosion stage exhibits a linear correlation with time. The time of the slope’s complete failure can be estimated when the reciprocal of the SRR change rate is 0 min/cm. The research findings are significant for comprehending the failure process of dispersive soil slopes.

Recent advances in stability analysis and design of 3D slopes

Slope failures in nature and engineering are typically three-dimensional (3D). The rotational failure mechanism derived from the variational limit equilibrium (LE) method shows superior performance in the stability analysis of the 3D slope. In contrast to the traditional LE methods, it avoids arbitrary kinematical and statical assumptions. Stability charts obtained by the variational LE method are used to derive explicit expression equations of the safety factor, also known as the stability equations, for both 3D reinforced and unreinforced slopes. These equations are highly accurate and can provide a convenient means to assess slope stability in practical engineering. An example of a convex reinforced slope with a turning arc is illustrated in this study to investigate the effect of the 3D effects on the required reinforcement length for design. The results indicate that the 2D method underestimates the required reinforcement length when dealing with a 3D reinforced slope problem. Furthermore, a forensic analysis of the Yeager Airport reinforced slope is conducted within the framework of the variational LE method. The required strength for stability is found to be significantly less than the allowable strength of reinforcements without considering the decrease in soil shear strength. However, the required strength greatly exceeds the allowable strength when the decrease in soil shear strength is considered. The results verify that the decrease in shear strength of the weak layer is responsible for the collapse.

Analysis of 2D and 3D Slope Stability Using the Bishop Simplified Method

Analysis of 2D and 3D Slope Stability Using the Bishop Simplified Method

Optimization design method of 2D + 3D slope shape for landslide prevention in open-pit coal mine

In order to improve the stability of the slope and prevent the occurrence of landslide disasters, taking the east slope of the first mining area of Zhundong Open-pit Coal Mine as the engineering background, a combination of the 2-Dimensional (2D) limit equilibrium method and 3-Dimensional (3D) numerical simulation is used to optimize the shape of the east slope. By selecting a typical calculation profile based on the Bishop method and the residual thrust method in the 2D rigid body limit equilibrium method, the stability analysis of the profile slope is carried out, and the slope shape of the profile position meeting the requirements of the safety reserve coefficient and stripping ratio is preliminarily designed. Based on the 3D finite element strength reduction method, aiming at the slope shape that does not meet the requirements of safety reserve coefficient and stripping ratio, the width of the transport plate is reasonably changed, and a 3D numerical simulation model of various schemes is established. The influence of different tracking distances and slope angles on slope stability is studied. The 3D stability of the slope under different spatial forms is calculated, and the optimal tracking distance and optimal slope angle are determined. The slope stability and stripping ratio are further optimized. The results show that when the width of the transport plate of the DBS3 section slope is 8 ​m, it does not meet the requirements of safety reserve coefficient 1.2. When the width of the transport plate is set to 24 ​m, it meets the requirements of a safety reserve coefficient of 1.2 and an economic stripping ratio of not more than 8.0 ​m3/t. The 3D numerical simulation results show that the optimal tracking distance on the east side is 50 ​m, and the optimal slope angle is 35°. After the optimization design of a 2D and 3D slope shape, 2.456 million tons of coal resources were mined, creating a profit of about 21.1268 million yuan. While preventing landslide disasters, the recovery rate of coal resources was further improved.

Analysis of three-dimensional slope stability combined with rainfall and earthquake

Abstract. In the current context of global climate change, geohazards such as earthquakes and extreme rainfall pose a serious threat to regional stability. We investigate a three-dimensional (3D) slope dynamic model under earthquake action, derive the calculation of seepage force and the normal stress expression of slip surface under seepage and earthquake, and propose a rigorous overall analysis method to solve the safety factor of slopes subjected to combined with rainfall and earthquake. The accuracy and reliability of the method is verified by two classical examples. Finally, the effects of soil permeability coefficient, porosity, and saturation on slope stability under rainfall in a project located in the Three Gorges Reservoir area are analyzed. The safety evolution of the slope combined with both rainfall and earthquake is also studied. The results indicate that porosity has a greater impact on the safety factor under rainfall conditions, while the influence of permeability coefficient and saturation is relatively small. With the increase of horizontal seismic coefficient, the safety factor of the slope decreases significantly. The influence of earthquake on slope stability is significantly greater than that of rainfall. The corresponding safety factor when the vertical seismic action is vertically downward is smaller than that when it is vertically upward. When considering both horizontal and vertical seismic effects, slope stability is lower.

Analytical Solution for Seismic Stability of 3D Rock Slope Reinforced with Prestressed Anchor Cables

Currently, the study of analytical solutions for the seismic stability of slopes under anchorage conditions is one of the hottest subjects in engineering. In this paper, an analytical solution for the seismic safety of the three-dimensional (3D) two-stage rock slope reinforced with prestressed anchor cables governed by the nonlinear Hoek–Brown criterion was deduced, in which the analyses of seismicity were performed by the latest modified pseudo-dynamic method. This method supplements the consideration of the damping effect of the rock medium on seismic waves, which is more in line with the real seismic situation. A mathematical geometric model was developed for calculating the external forces work and internal energy dissipation acting on 3D rotating rock masses reinforced with prestressed anchor cables, in which the seismic work rate was calculated using a new layer-by-layer superposition summation method. The analytical solution of the safety factor could be collated as an explicit function of several variables, and then, the optimal value was obtained by the Particle Swarm Optimization (PSO) algorithm. To corroborate the accuracy of new analytical solutions, the results were contrasted with those of the pertinent literature. The results of the two comparisons were very close. Ultimately, the sensitivity analyses and coupling effects of seismic pseudo-dynamic factors and prestressing anchorage factors were carried out. It was found that even small seismic intensities had a large effect on the stability of rock slopes with developed joints. Increasing the number of steps and prestressing anchors can effectively improve the stability of rock slopes under seismic effects. The conclusions have significant implications for the anchorage design of the 3D two-stage rock slope as seismic events occur.

Pseudo-static analysis of 3D unsaturated bench slopes stabilized by multiple rows of piles

Bench slopes incorporated with multiple rows of anti-slide piles remain an effective technique in landslide disaster preventions and are widely employed in the design of new subgrades and embankments. To provide more realistic results for engineering guidance, the three-dimensional (3D) effect and suction in soils require explicit considerations. Employing the upper bound limit analysis method, a 3D limit analysis of bench slopes stabilized by multiple rows of piles is performed in this paper. The upper bound solutions of several illustrative slopes are optimized and compared with the published ones, indicating the validity of the optimization program and the proposed method. A series of parameter analyses are conducted regarding the roles of suction and anti-slide piles in slope safety assessments. The results show that the suction effect and pile reinforcement increase continually as the pile location increases and the influence of bench width can be ignored. The stability of bench slopes stabilized by multiple rows of piles differ with that of slopes stabilized by single row of piles dramatically. The maximum pile reinforcement reaches 70% for sandy soil slopes but only 30% for clayey soil slopes. The influences of surcharge load and seismic load on the pile reinforcement can nearly be neglected.

Investigation of the stability of a fly ash pond facility using 2D and 3D slope stability analysis

A numerical investigation of the effect of pore pressure regime on the safety factor and the critical failure mechanism is presented for fly ash storage facility. Pore pressures’ measurements from standpipe piezometers and pore pressure estimated from seepage analysis are used to compare the factor of safety for a fly ash slope. This was applied for considering static and seismic scenarios. A probabilistic approach was applied to account for the uncertainties resulting from the limited data available and support a qualitative risk assessment evaluation. Slope stability analysis is conducted in two and three dimensions, adopting the limit equilibrium analysis approach, and also a finite element seepage analysis, to assess the stability of the slope. The two-dimensional cross-sections were extruded to three-dimensional models to estimate the factor of safety and associated shear failure. The results from the performed analysis suggest an increase in safety factor values of 5%.

Three-dimensional stability analysis of two-layer slope based on GIS under rainfall conditions

ABSTRACT Geographical Information System (GIS), as a computer-based tool, allows easy data processing, and complex geospatial data management and analysis, making it a suitable environment for 3D slope stability analysis. The study proposed an integral scheme for 3D stability analysis of a two-layer slope under rainfall conditions based on GIS. To construct the 3D model of the slope and the sliding surface in GIS, a method was proposed in which a grid is divided into four sections to improve the accuracy of calculation, and the extension of the Hovland model and the Janbu model in unsaturated soil was discussed. The transformation equations between the global coordinates and the ellipsoid local coordinates were derived to locate the critical sliding surface, and how to apply constraints of parameters to improve search efficiency was put forward. An infiltration model for a two-layer slope was built so that the changes in water content in slope at the both stages of rainwater infiltration and redistribution can be determined, and the model was integrated into the GIS-based scheme to assess the impact of rainfall on slope stability. Finally, two case studies were implemented to demonstrate the validity and correctness of the proposed scheme.

Effect of Rock Mass Disturbance on Stability of 3D Hoek–Brown Slope and Charts

The present study performs a stability analysis of a three-dimensional (3D) rock slope in disturbed rock masses following the Generalized Hoek–Brown (GHB) failure criterion. The factor of safety (FoS) of the slope is derived and the optimal solution is captured combining the limit analysis method and the strength reduction technique. It is indicated by the parametric analysis that the 3D geometric characteristics have a significant impact on slope stability such that FoS decreases sharply with the increase in the width-to-height ratio B/H within 0<B/H≤2.0 and thereafter reaches a constant value asymptotically. The FoS decreases more than 60% linearly when the disturbance factor D increases from 0 to 1.0. Stability charts and slope angle weight factor fβ_3D for 3D slopes are proposed to provide a convenient and straightforward approach to obtain the FoS solutions of 3D slopes. A case study was carried out to apply the stability charts on practical engineering cases, which showed that slope stability under two-dimensional (2D) plane strain will lead to conservative results, and a 3D stability analysis of slope is more appropriate, especially for a slope with a limited width.

Landslide Risk Assessment and Preventive Measures of Selected Locations in the Rangamati District, Bangladesh

Detecting landslides and unstable slopes is one of the most crucial responsibilities in the emergency response to resist landslides. Having a wide range of hilly terrines in the southeast region of Bangladesh, the risk of landslide disasters is becoming a critical issue. In Chittagong, especially in the Rangamati hill tracts, there have been several losses of life and property due to landslides in the recent past. This research attempts to evaluate the landslide risk in Rangamati hill tracts and provide suggestions to mitigate the landslide hazard by modifying the hill slope. Soil specimens from different hill locations were collected from three areas in the Rangamati district. Several laboratory experiments were conducted to determine the soil properties, and 2D slope stability analysis using Bishop's simplified method was used to evaluate the landslide potential. Different preventative measures, for example, soil nailing, anchors, and cutting slopes like stairs, are also implemented to mitigate the landslide potential by increasing the slope stability was assessed and suggested. Weighted Overlay Model (W.O.M.) was implemented for the Landslide Susceptibility Analysis in ArcGIS to confirm the potential hazard in the study areas, and hazard maps were suggested based on the slope stability results and current slopes in Rangamati. The slope stability analysis of the three spots showed that spot 3 is the most vulnerable spot, which had a low factor of safety value. Even with different mitigation techniques, spot 3 showed a lower factor of safety value, which was verified with the Weighted Overlay Method. It was also seen that among the mitigation techniques, anchoring the slopes is the most effective one that drastically increases the factor of safety value.