Three-dimensional Stability Analysis Research Articles

Three-Dimensional Discontinuum Modeling and Rigid Block Stability Analysis of a Group of Three Caverns for Hydroproject in Northeast India

Abstract This paper presents various methods for calculating the factor of safety (FOS) and utilizes the Isoblock method to analyze the stability of underground powerhouse caverns located in the North-East state of India. A three-dimensional discontinuum analysis simulates the stability of the downstream sidewall, upstream sidewall, and crown of the caverns. The results indicate that the powerhouse cavern contains approximately 2.36% unstable blocks, while the Main Inlet Valve (MIV) and Transformer Caverns exhibit 0.14% and 0.84% unstable blocks, respectively. A comprehensive parametric analysis investigates the impact of joint stiffness, joint friction angle, in-situ stress, cover depth, and the orientation of the cavern's longer axis on stability. The findings reveal that the cavern's stability is significantly influenced by variations in lateral stress ratio and the direction of in-situ principal stress. Stability is optimized at stress ratios between 1.2 and 1.8, with maximum instability observed in the powerhouse cavern, correlating with its larger size. Notably, the stability of the crown is greater than that of the sidewalls, particularly when the cavern orientation is aligned between N68°E and N78°E. The study underscores the importance of these factors in the design and stability assessment of underground structures, providing valuable insights to enhance their safety and reliability. This analysis highlights the necessity for considering joint stiffness and in-situ stress orientations in future designs to mitigate risks associated with instability.

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 novel finite element limit equilibrium method and its application in instability analysis for 3-D high core rockfill dams

The safe operation of high rockfill dams is an important issue related to human life and property safety. However, the stability analysis of high core rockfill dams with complex spatial morphology is mostly confined to two-dimensional, and appropriate stability analysis methods are scarce. Therefore, it is necessary to develop the three-dimensional stability analysis method for high core rockfill dams and study the spatial stability mechanism after impoundment. Firstly, a finite element limit equilibrium framework suitable for stability analysis of high rockfill dams is introduced, and the horn-shaped three-dimensional failure mechanism is presented for optimization. Then, according to the statistical results of the actual core rockfill dam above 100 m, 15 high dam models with actual Duncan-Chang parameters between 100 m and 300 m are established to study the three-dimensional instability mechanism. Meanwhile, grey relation analysis (GRA) is used for quantitative analysis of stability sensitive factors. Finally, the stability analysis of the Quxue core rockfill dam (173.2 m) was completed within the established stability framework. The results show that the combined failure mechanism with the horn-shaped is suitable for dam stability analysis, and with the increase of height and slope ratio of dam, the most dangerous sliding surface evolves to shallow layer. In addition, GRA results show that slope ratio is the most sensitive parameter compared to dam height and material parameters. The practical engineering stability results of Quxue show that the research results can provide a reliable reference for the stability of the high core rockfill dam.

Three-dimensional undrained stability analysis of circular tunnel heading in anisotropic and heterogeneous clay: FELA, ANN, MARS, and XGBoost

Three-dimensional undrained stability analysis of circular tunnel heading in anisotropic and heterogeneous clay: FELA, ANN, MARS, and XGBoost

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.

Three-Dimensional and Two-Dimensional Stability Analysis of Bentonite Slurry Trenches Using a Shear Strength Reduction Technique and Limit Equilibrium Methods

Bentonite slurry trenches are becoming increasingly popular in the excavation of trenches, especially for diaphragm wall construction. The problem that needs to be addressed is the stability of bentonite slurry trenches. This paper presents a stability analysis of trenches with temporary support from bentonite slurry, with unit weights ranging from 10.5 to 12.0 kN/m3 in the realistic stratum, and C3 in the Hue city area. Our analysis employs the Shear Strength Reduction Technique (SSR) with Mohr–Coulomb materials to numerically evaluate the factor of safety (FS). The finite element method (FEM) software program (RS2 v. 121 and RS3 v. 4.0) and the finite difference method (FDM) FLAC v. 7.0 software were used. Additionally, the limit equilibrium method (LEM) of Bell–Washbourne and three-dimensional (3D) Bishop were used to calculate trench stability. The results of the analysis show a good agreement between RS2 and FLAC2D, and between RS3 and FLAC3D. Secondly, upon comparison, it was noted that the factor of safety of the 3D software programs (RS3 v. 4.0, FLAC v. 7.0) was higher than that of the 2D software programs (RS2 v. 11.0, FLAC v. 7.0), ranging from 52.3 to 63.0% for trench lengths of 6 m. However, for trench lengths of 54 m, the factor of safety values in 2D and 3D configurations were nearly equal. Thirdly, the factor of safety of the Bell–Washbourne method (LEM) was lower than that of the numerical analysis methods (FLAC and RS programs). Using the three-dimensional numerical method appears to be effective for estimating stability.

The three-dimensional stability analysis of piled slopes in unsaturated and inhomogeneous soils with nonlinear failure criterion

Under the nonlinear Mohr-Coulomb (MC) failure criterion, based on the upper-bound limit analysis theorem, the three-dimensional(3D) stability of piled unsaturated inhomogeneous slopes is analyzed. By incorporating the nonlinear strength parameters c t and φ t, the energy balance equation is established, and the explicit expression of slope safety factor (F S) is derived by the gravity increase method (GIM). In addition, a genetic algorithm (GA) is used to calculate the minimum F S. The results obtained were compared with those of existing literature to verify the effectiveness of the method used in this paper. The influence of nonlinear parameters on slope stability was studied through parameter analysis. The results show that the nonlinear parameters of soil have a significant influence on the stability of piled slopes. The F S increases with the increase of nonlinear coefficient and uniaxial tensile strength and decreases with the increase of initial cohesion of soil. In addition, the critical slip surface of the slope becomes shallower with the weakening of soil nonlinearity. Furthermore, ignoring the suction effect will overestimate the slope stability, and the slope stability intensified with decreased soil inhomogeneity.

Spatio-Temporal Prediction of Three-Dimensional Stability of Highway Shallow Landslide in Southeast Tibet Based on TRIGRS and Scoops3D Coupling Model

National Highway G559 is the first highway in Southeast Tibet into Motuo County, which has not only greatly improved the difficult situation of local roads, but also promoted the economic development of Tibet. However, rainfall-induced shallow landslides occur frequently along the Bomi–Motuo section, which seriously affects the safe operation and construction work of the highway. Therefore, it is urgent to carry out geological disaster assessment and zoning along the highway. Based on remote-sensing interpretation and field investigation, the distribution characteristics and sliding-prone rock mass of shallow landslides along the Bomi–Motuo Highway were identified. Three-dimensional stability analysis of regional landslides along the Bomi-Motuo Highway under different rainfall scenarios was carried out based on the TRIGRS and Scoops3D coupled model (T-S model). The temporal and spatial distribution of potential rainfall landslides in this area is effectively predicted, and the reliability of the predicted results is also evaluated. The results show that: (1) The slope structure along the highway is mainly composed of loose gravel soil on the upper part and a strong weathering layer of bedrock on the lower part. The sliding surface is mostly a circular and plane type, and the main failure types are creep–tensile failure and flexural–tensile failure. (2) Based on the T-S coupling model, it is predicted that the potential landslide along the Bomi–Motuo Highway in the natural state is scattered. The distribution area of extremely unstable and unstable areas accounts for 4.92% of the total area. In the case of extreme rainfall once in a hundred years, the proportion of instability area (Fs < 1) predicted by the T-S coupling model 1 h after rainfall is 7.74%, which is 1.57 times that of the natural instability area. The instability area (Fs < 1) accounted for 43.40% of the total area after 12 h of rainfall. The potential landslides were mainly distributed in the Bangxin–Zhamu section and the East Gedang section. (3) The TRIGRS and T-S coupling model is both suitable for predicting the temporal–spatial distribution of rainfall-induced shallow landslides, but the TRIGRS model has the problem of over-prediction. The instability area predicted by the T-S coupling model accounted for 43.30%, and 74% of the historical landslide disaster points in the area were correctly predicted. (4) In terms of rainfall response, the T-S coupling model shows higher sensitivity. The %LRclass (Fs < 1) index of the T-S coupling model is above 50% in different time periods, and its landslide-prediction effect (%LRclass = 78.80%) was significantly better than that of the one-dimensional TRIGRS model (%LRclass = 45.50%) under a 12 h rainfall scenario. The research results have important reference significance for risk identification and disaster reduction along the G559 Bomi–Motuo Highway.

Three-dimensional stability analysis of tunnel face considering the upper partial failure in layered rock masses

Three-dimensional stability analysis of tunnel face considering the upper partial failure in layered rock masses

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.

Discretization-Based Kinematic Approach for Three-Dimensional Stability Analysis of Slurry Trenches in Cohesive–Frictional Soils

Discretization-Based Kinematic Approach for Three-Dimensional Stability Analysis of Slurry Trenches in Cohesive–Frictional Soils

Stability analysis of a vertical excavation reinforced with horizontal nails using three-dimensional finite elements limit analysis

Three-dimensional stability analysis of a vertical excavation, reinforced with grouted horizontal nails, has been carried out by using the three dimensional lower and upper bounds based finite elements limit analysis (FELA) using Optum G3. The nail along with the surrounding grouted cementitious material is assumed to behave as a single monolithic cylindrical block which was assumed to be either rigid or an elasto-plastic material following the Von-Mises yield criterion. The excavation is assumed to fail on account of either an interface shear slippage between nails and surrounding soil mass or on an account of axial tensile rupture of the composite nail material for a few typical cases as well. The soil unit weight has been varied to induce the ultimate shear failure of the soil nailed excavation. The unit weight of the soil mass at which the failure of the nailed wall occurs is termed as γcr. Two different types of boundary conditions along the base of the excavation have been considered. In the first case, the in-situ soil mass behind the excavation is extended below the base as well (Case 1) and in the second case, the excavation is assumed to simply lie on a hard stratum (Case 2). The results have been provided in the form of a non-dimensional stability number N=γcrHc as a function of soil friction angle φ, Sv/H, SH/H, d/H, L/H and m; where H refers to height of the wall, d is diameter of the grouted nail, Sv and SH imply centre to centre vertical and horizontal spacing of the nails, and m is the mobilization factor between grouted nails and adjoining soil mass. The results from the analysis have been found to compare well with the data reported in literature. All the results have been presented in the form of non-dimensional stability charts, which will be useful for design for any given values of height H and cohesion c. From the observed failure mechanisms, an analysis has also been carried out to determine the optimized lengths of nails. The optimized lengths of nails for both Cases 1 and 2 have been also provided. The type of failure mechanism, base or face failure, dictates the optimized lengths of the nails.

A new analytical method for stability analysis of rock blocks with basal erosion in sub-horizontal strata by considering the eccentricity effect

Abstract. The basal cavity of a rock block formed due to differential weathering is an important predisposing factor for rockfall in hard–soft interbedded rocks, which induces an eccentricity situation at the base of the rock block. Rock block falling due to the non-uniform distribution with the failure modes of toppling or sliding is defined as biased rockfall in this study. Taking into account the non-uniform stress distribution due to the eccentricity effect, a new analytical method is proposed for three-dimensional stability analysis of biased rockfall. The development of non-uniform stress distribution stress calculated by this analytical method was verified by numerical simulation. The biased rockfall progresses from partial damage of the soft underlying layer, caused by non-uniform distributed stress, to toppling and sliding of overhanging hard rock block due to overall unbalanced force. Therefore, a set of factors of safety (Fos's) against partial damage (compressive and tensile damage of the soft underlying layer) and overall failure (toppling and sliding of the hard rock block) are used to determine the rockfall susceptibility level. The analytical method is applied and validated using biased rockfalls on the northeastern edge of the Sichuan Basin in southwest China, where a significant number of rockfalls consisting of overhanging thick sandstone and underlying mudstone occur. The evolution process of biased rockfalls is divided into four stages, initial state, basal cavity formation, partially unstable and failure. The proposed method is validated by calculating Fos's of the typical unstable rock blocks in the study area. As the cavity continues to grow, the continuous retreat of mudstone causes stress redistribution between the hard and soft rock layers. This results in damage to the underlying soft rock layer due to the development of the non-uniform distribution, ultimately leading to the failure of the hard rock block. The critical retreat ratio is determined to be 0.33, which is used to classify the low and moderate rockfall susceptibility in the eastern Sichuan Basin. The proposed analytical method provides insights into the evolution of biased rockfall and a means for early identification and susceptibility assessment of rockfall.

Roof stability analysis of cylindrical tunnels in hard soil/soft rock with reduced tension strength

Three-dimensional roof stability analyses of cylindrical tunnel segments limited along the tunnel direction were performed based on the modified Mohr–Coulomb failure criterion with reduced tensile strength. A wedge-shaped region of the classical Mohr–Coulomb envelope, where unrealistic tensile and shear strengths are predicted, is truncated by a Mohr circle associated with the true tensile strength. This revised failure criterion with partial nonlinearity allows geomaterials deep into the roof to deform with large velocity gradients under the normality plastic flow rule, observed in field investigations. Using the kinematic approach of limit analysis, rigorous bounds for three quantitative stability measures–stability number, factor of safety, and supporting pressure–were calculated. The roof failure mechanism adopted is relatively elaborate, involving three-dimensional geometry intersecting with a cylindrical tunnel segment; thus, an efficient approach was presented for tunnels with long length constraints. With respect to extremely short tunnel lengths, a modified roof failure mechanism with distinct ridges was proposed. The factor of safety with accommodation of the nonlinear pressure dependency was estimated by a consistent procedure associated with a reduced elliptic failure criterion. The results show that roof stability distinctly depends on the magnitude of the true tensile strength, internal friction angle, and length constraint.

Three-dimensional reliability stability analysis of earth-rock dam slopes reinforced with permeable polymer

Polymer is a new repair and reinforcement material for earth-rock dams developed in recent years. Models are developed where spatial variability is incorporated into the analytical framework to evaluate the stability and reliability of reinforced three-dimensional dam slopes. The Karhunen-Loeve (K-L) expansion method is employed to generate three-dimensional random fields. The simplified Bishop method and Monte Carlo method are used to calculate the safety factors and failure probabilities of the dam slopes. With the implementation of polymer grouting reinforcement, the safety factors are improved and the failure probabilities are reduced. The reinforcement effect will be affected by the amount of polymer dosing, dam slope characteristics, and polymer grouting parameters. The impact of various longitudinal autocorrelation distances on reliability is influenced by the length of the dam slope itself. An increase of the safety factor by approximately 37% can be achieved through a polymer dosing of around 3%. Nevertheless, with the elevation of dam slope height and slope ratio, the effectiveness of polymer reinforcement is diminished.

Rainfall infiltration and three-dimensional stability analyses of fractured rock slopes considering preferential flow

Rainfall infiltration and three-dimensional stability analyses of fractured rock slopes considering preferential flow

Global Stability Analysis of Full-Aircraft Transonic Buffet at Flight Reynolds Numbers

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier–Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft.

Three-dimensional stability analysis of tunnel face based on unified strength theory

The impact of cyclic footage and intermediate principal stress on the stability of the tunnel-face area are analyzed in this study using the theory of limit analysis. The study introduces the unified strength theory and proposes three-dimensional logarithmic spiral failure modes with corresponding velocity fields. The influence of various parameters on the tunnel-face area stability is analyzed, and it is found that when the internal friction angle is less than 30°, the internal friction angle parameters should be improved first to enhance stability, while when the internal friction angle is greater than 30°, cohesion should be prioritized. When using the double shear uniform strength theory in the tunnel-face area, the intermediate principal stress can improve the stability of the tunnel face. Results show that Mohr–Coulomb criterion calculations are conservative in the good surrounding ground, but no similar conclusion has been obtained for the poor surrounding ground, and specific problems must be analyzed during construction.

Numerical Study of the Effect of Ground Improvement on Basal Heave Stability for Deep Excavations in Normally Consolidated Clays

The ground-improvement technique is commonly used to restrain the wall displacement induced by excavation and resist the basal heave for deep excavations in soft clays. In this paper, a three-dimensional finite-element stability analysis was conducted to evaluate the effect of different ground-improvement properties and patterns on enhancing the factor of safety against basal heave in deep excavations. The results showed that a large downward movement of soil behind the wall could induce a large upward movement below the excavation, which is mainly resisted by the weight of the interior soil mass and the frictional resistance acting on the contact surface area between the wall and the soil inside the excavation. When the ground improvement was not contacted with the wall, the failure initially occurred on the wall interface, causing the soil inside the excavation to move upward along with the ground improvement, which resulted in an insignificant increase in the factor of safety. Hence, the ground improvement should be contacted to the wall to establish a higher basal heave resistance, where the increase of the safety factor was governed by the amount of the ground improvement that contacted the wall. Furthermore, a simplified method was proposed to calculate the factor of safety with and without ground improvement, which was validated by the results from the finite-element method.

3D limit analysis of rock slopes based on equivalent linear failure criterion with tension cut-off

Hoek-Brown (HB) failure criterion is widely used to predict the strength of intact or heavily jointed rock mass. For stability analysis of rock slopes governed by the HB failure criterion, the equivalent linearity to Mohr-Coulomb (MC) criterion is often adopted, leading to the well-known equivalent Mohr-Coulomb method (EMCM). Existing studies on EMCM analysis mainly consider the shear strength of rock material, while consideration of the tensile strength is rare. This contradicts the fact that the underlying tensile strength of rock mass has considerable impact on the rock slope stability in real world. In this regard, this paper proposes a limit analysis-based approach that can account for tension in the three-dimensional (3D) stability analysis of HB rock slope. This approach is established on the equivalent linearity of the HB criterion with consideration of tensile strength, known as the equivalent tension cut-off MC method (ETMCM), and using a horn-like 3D mechanism of limit analysis. The safety factor solutions given by the proposed approach are validated by previous studies and numerical results. Parametric studies are conducted to investigate the effect of rock tensile strength on slope stability. Results show that the consideration of tension leads to a more conservative safety factor and a sharper curvature of the failure surface, and these impacts tend to be more obvious with the increases in slope inclination and slope width. Finally, the stability of the HB rock slope under seepage conditions is studied using the proposed approach. The results indicate that the effect of tensile strength is highly remarkable in seepage circumstances.