Stability Analysis of Steep Bedding Rock Slope with Strength Reduction Method

Hydraulic fracture initiation and propagation in deep coalbed methane reservoirs considering weak plane: CT scan testing

Laminated shale reserves various natural weak planes involving some bedding planes, natural fractures and mineral dykes. The obvious phenomenon of the interactions between hydraulic fractures and bedding weak planes were observed involving arrest, crossing, and diversion in previous works. Moreover, the bedding angles, cement mineral compositions of natural weak planes, and net pressure of hydraulic fracture were considered as the primary factors to determine the type of interaction. However, the rock failure modes and characterization of weak planes from micromechanics has been yet addressed. In this paper, a Particle Flow Code (PFC) model on natural weak planes of laminated shale was proposed by considering micromechanical properties including the cohesive strength, stiffness, elastic modulus, and friction angle. The PFC model was validated by the three-point bending tests on a typical laminated shale. The influence of weak plane angles, elastic modulus, and strength of weak planes on tensile fracture propagation were obtained. Their interaction types and dominant failure mode from tensile to shear were analyzed. It concludes that fractures divert in the inclined angles and low strength of natural weak planes, crossing occurs in the opposite case. Introduction Shale oil and gas formation normally reserves various natural weak planes involving the weak bedding planes, natural fractures and mineral dykes. It is evident that the natural weak planes affect hydraulic fracture geometry. The obvious phenomenon of the interactions between hydraulic fractures and bedding weak planes were observed involving arrest, crossing, and diversion in previous works. Moreover, the bedding angles, cement mineral compositions of natural weak planes, and net pressure of hydraulic fracture were considered as the primary factors to determine the type of interaction. However, the rock failure modes and characterization of weak planes from micromechanics has been yet addressed.

Taking a bedding rock slope with weak structural plane as the prototype, a shaking table test with a similarity ratio of 1:10 is designed and carried out. By analyzing the acceleration and displacement responses at different positions of the slope, the seismic response and instability mechanism of rock bedding slope under different seismic amplitudes, frequencies, and durations are studied. Before the failure of the slope, the rock bedding slope shows an obvious “elevation effect” and “surface effect” under the action of Wenchuan Wolong earthquake wave with different amplitudes. With the increase of the amplitude of the input seismic wave, the elevation effect and the surface effect gradually weaken. When the amplitude of the seismic wave reaches 0.9 g, the rock bedding slope begins to show damage, which demonstrates that the difference of PGA amplification coefficients on both sides of the weak structural plane increases significantly. Compared with the Kobe seismic wave and Wenchuan Wolong seismic wave, the excellent frequency of EL Centro seismic wave is closer to the first-order natural frequency of slope model and produces resonance phenomenon, which leads to the elevation effect of PGA amplification coefficient more significantly. Through the analysis of the instability process of rock bedding slope, it can be found that the failure mechanism of the slope can be divided into two stages: the formation of sliding shear plane and the overall instability of the slope.

Roadway deformation failure is often related to the presence of weak structural planes (WSPs) in the surrounding rock mass. Especially in coastal mining environments, WSP-induced deformation can create pathways that connect faults with seawater, accelerating groundwater seepage and inrush hazards. This study employs an optimized Finite–Discrete Element Method (Y-Mat) to simulate WSP-driven fracture evolution, introducing an elastoplastic failure criterion and enhanced contact force calculations. The results show that the farther the WSP is from the roadway, the lower its influence; its existence alters the shape of the plastic zone by lengthening the failure zone along the fault direction, while its angle changes the shape and location of the failure zone and deflects fracture directions, with the surrounding rock between the roadway and WSP suffering the most severe failure. The deformation failure of roadway surrounding rock is influenced by WSPs. Excavation unloading reduces the normal stress and shear strength in the weak structural plane of surrounding rock, resulting in slip and deformation. Additionally, WSP-induced fractures act as groundwater influx conduits, especially in fault-proximal roadways or where crack angles align with hydraulic gradients, so mitigation in water-rich mining environments should prioritize sealing these pathways. The results provide a theoretical basis for roadway excavation and support engineering under the influence of WSPs.

To investigate the influence of weakly structured formations on wellbore stability in deep coal seams within the Lufeng Block, this study establishes an innovative predictive model for coal seam wellbore collapse pressure. The model integrates mechanical parameter variations along weak structural planes with the Mohr–Coulomb criterion, leveraging experimental correlations between mechanical properties and bedding angle. Key findings reveal that the coal sample demonstrates enhanced compressive strength and elastic modulus under elevated confining pressures. A distinctive asymmetric “V” pattern emerges in mechanical parameter evolution: compressive strength, elastic modulus, cohesion, and internal friction angle initially decrease before recovering with increasing bedding angle, reaching minimum values at a 60° bedding angle. Comparative analysis demonstrates that the proposed model predicts a higher collapse pressure equivalent density than conventional Mohr–Coulomb approaches, particularly when accounting for mechanical parameter alterations along weak structural planes. Field validation through coal seam data from the operational well confirms the model’s effectiveness for stability analysis in weakly structured coal formations within the Lufeng Block. These findings provide critical theoretical support for wellbore stability management in deep coal seam engineering applications.

Open pit slope stability analysis has been performed to assess the slope deformation, state of stresses at critically instable failure zones, different failure modes and safe & functional design of excavated slopes using the numerical modeling technique, finite difference method. The purpose of slope stability analyses by numerical modeling in rock mechanics is not only to provide specific values of stress and strain at specific points but is also to enhance our understanding of the processes involved to finding instable zones, investigation of potential failure mechanisms, designing of optimal slopes with regard to safety, reliability, economics, and designing possible remedial measures. As part of the rock mass, the discontinuities inherently affect the strength and the deformational behavior of slopes in rock mass containing sets of ubiquitous joints. In this paper the finite difference method, FLAC (Fast Lagrangian Analysis of Continua) of numerical modeling technique is used to predict the stress-strain behavior of pit slope and to evaluate the stability analysis of open pit slope. Ubiquitous joint model, which is an anisotropic plasticity model that includes weak planes of specific orientation embedded in Mohr-Coulomb solids, has been adopted to account for the presence of weak planes, such as weathering joints, bedding planes, faults, joints in FLAC Mohr-Coulomb model. Thus by studying the distribution of stress, displacement and factor of safety, the stability analysis of pit slope has been evaluated and suggestions based on the numerical analysis has been presented.

In order to fully understand the different effect of strength reduction method on slope stability analysis in different instability criterion, and solve the problems related to the instability of slope, this paper uses the platform of the finite element software ABAQUS to carry out the research that finite element strength reduction method analyzes the stability of homogeneous soil slope in different instability criterion. Moreover, in detail, this paper analyzes the difference between slope safety factor and the soil strength parameters change on the effect by using strength reduction method in different instability criterion. The research shows that by using the strength reduction method, the safety factor has been affected by different instability criteria, but its influence affected by the soil strength in a certain range of the parameters are decided, at the same time, soil cohesion, internal friction angle, Poisson ratio and other parameters for the development of the plastic zone and the shape of the sliding surface also have some influence on the critical state of the slope.

In slope stability evaluation, it is common that a potential tensile sliding surface is not accurately positioned. In this paper, the strength reduction method considering shear and tensile failure with a strain-softening model is adopted to simulate the deterioration of the strength parameters of geomaterials during failure. Based on the initial stress method, a new quantitative display index of the full sliding surface is proposed. This method was applied to the stability analysis of a heterogeneous slope and a homogeneous slope. The results show that the plastic zone determined with the strain-softening model is much smaller than that determined with the Mohr-Coulomb model, and the difference is 34–40%. The safety factor obtained without considering tensile failure is 3.1% larger than that obtained considering tensile failure. The index can be used to quantitatively display the shear failure zone and tensile failure zone of a sliding surface.

Based on an example of a basalt fiber gabion ecological slope protection project, this paper uses ABAQUS finite element software to conduct seepage-stress coupling modeling and calculation for the undisturbed slope and gabion protection under two conditions of low water level and design water level. Based on the theory of direct coupling method and strength reduction method, the slope instability evaluation criterion is based on the displacement mutation of the model and the formation of the plastic penetration zone of the soil. The safety factor of the coupled gabion protection is greater than that of the original slope. The results show that the overall stability of the slope after being supported by stone cages and grid protection pads is enhanced, which shows the feasibility and good application prospects of the engineering practice of stone cage slope protection. The research conclusions of this paper can provide reference for the study of seepage-stress coupling in water conservancy projects and provide reference for the stability analysis of similar engineering slopes.

Rock slope reliability analysis based on distinct element method and random set theory

A new instability criterion based on the strength reduction method (SRM) is proposed, where the slope is in the limit equilibrium state when the critical slope contour determined by the sl...

The instability process of bedding rock slope with weak interlayer may be induced under rainfall infiltration conditions. Due to this, we conducted a research of model test for the instability process, based on the similarity theory. With use of the recent 50 years’ rainfall data of Changsha, China, we analyzed the seepage characteristics, mechanical characteristics, and deformation laws of the slope under the conditions of long‐time heavy rain and short‐time rainstorm, respectively. The test results show that the original seepage characteristics of the slope were changed by the existence of weak interlayer, presented the “double seepage” effect, resulted in the seepage characteristics of rock and soil in the shallow layer and weak interlayer of the slope showed a sickle “Γ” distribution, and the adjacent rock layer presented a curve‐type “S” distribution. With the increase of rainfall duration, the weak interlayer gradually became muddy and softened, and then the plastic flow zone was formed locally. The stress concentration phenomenon was gradually generated in the weak interlayer due to the influence of the gravitational field of the upper rock mass. The large infiltration of rainwater led to the phenomenon of plastic flow extrusion of the slope at the weak interlayer extrusion. With the further penetration of the tensile cracks in the upper part of the weak interlayer, the slope had a large settlement displacement and gradually formed sliding shear deformation along the weak structural plane. Under the condition of equal rainfall amount, the condition of long‐time heavy rain has a greater influence on the stability of the bedding rock slope with weak interlayer than that of short‐time rainstorm. The failure form of slope could be divided into four stages: prechange stage, interlayer extrusion stage, slip‐pull‐fracture stage and plastic flow‐shear failure stage.

Slope stability analysis is vital in geotechnical and highway engineering due to its direct implications on infrastructure safety and serviceability. This study employs the Strength Reduction Method (SRM) in PLAXIS 3D, a finite element-based software, to assess the stability of highway embankments under various slope geometries, embankment heights, and groundwater table (GWT) positions. A total of 72 cases were analysed, involving six slope ratios (1.25H:1V to 3.5H:1V), six embankment heights (1 m to 10 m), and two groundwater conditions (−4 m and 0 m). Results show that the Factor of Safety (FOS) decreases with increasing slope steepness and embankment height, while gentler slopes consistently exhibit higher FOS values. Rising the GWT to ground level reduced FOS values by up to 35%, highlighting the destabilizing role of elevated pore-water pressures. Comparative analysis revealed that gentler slopes improved FOS by up to 50% compared to steep slopes at higher embankments. The findings underscore the importance of adopting flatter slopes and effective drainage strategies in highway embankment design to ensure long-term stability.

It is faulty to analyze the jointed rock slopes’ stability susceptible to a combination of modes of failure composed of sliding around the toe region and toppling of the rock blocks on the upper part of the slope based on the current analytical methods, which are based on assumption that the distribution of the potential failure surface bounding the potential mixed failure runs predictably from crest to toe of the slope. An Analytical model that takes into consideration the kinematic mechanism of the discontinuous rock slope with counter-tilted weak plane subjected to a combination of failure mechanisms involving sliding and toppling has hence been presented in this chapter. This involves an iterative process which involves the calculations of the dimensions of all the individual blocks as well as the forces acting on them, and then stability of every block is examined, starting at the uppermost block. The stability analysis of each block is determined. The blocks may either be stable, topple or slide. The proposed analytical methods could curtail errors incurred due to the acceptance of the single weak plane for quantifying the failure mechanisms composed of slide head toppling rock slopes in physical situations with two planar weak planes.

A simplified method of predicting the shape and location of the potential failure surface in steep rock slopes is suggested. The 1988 updated Hoek and Brown failure criterion is used with Priest and Brown m and s values and Bieniawski's jointed rock mass classification system. This method is demonstrated by an application to the design of slope reinforcement by rock anchoring and by a case study. The validity of the method is assessed by reference to the variational calculus approach, using the linear Mohr–Coulomb failure criterion. Key words: benches, bench design, bench anchoring, quarrying, slope stability, ground control, rock mass rating.