Wedge Stability Research Articles

Exploring joint orientation effects on rock wedge stability: Experimental and discrete element analysis

The primary objective of this study was to examine and analyze the sliding behavior of rock wedge slopes with the interaction of three joint sets, considering the influence of plunge angles, included wedge angles between joints, and gravity conditions. The discontinuity planes with varying dip directions relative to the wedge's plunge direction were analyzed. The stability assessment of wedge failure was initially reviewed, explicitly focusing on limit equilibrium (LE) analysis and in-house physical tests. Centrifuge tests and discrete element analysis using the 3DEC software were then performed to explore the factors influencing the failure characteristics of the slopes. Additionally, two mitigation strategies were proposed to enhance the stability of the rock wedge slopes. The key findings include the significant impact of plunge angle on wedge slope stability compared to the included wedge angle between joints, the strong effect of gravitational conditions on the collapsing ratio of wedge units, and the higher risk posed by wedge slopes with discontinuity planes dipping out of the slope. The numerical simulation results highlighted the importance of considering joint spacing in slope stability assessments. Mitigation methods such as fixing key wedge blocks were found to effectively reduce the wedge collapsing ratio and improve rock slope stability under more realistic stress levels. This study provides valuable insights for formulating prevention and mitigation strategies, useful for enhancing safety and reducing the potential damage caused by rock wedge failure events.

Ice-buttressing-controlled rock slope failure on a cirque headwall, Lake District, UK

Abstract. Rock slope failures in the Lake District, UK, have been associated with deglacial processes after the Last Glacial Maximum, but the controls and timing of the failures remain poorly known. A cirque headwall failure was investigated to determine failure mechanisms and timing. The translated wedge of rock is thin and lies on a steep failure plane, yet the friable strata were not disrupted by downslope movement. Fault lines and a failure surface, defining the wedge, were used as input to a numerical model of rock wedge stability. Various failure scenarios indicated that the slope was unstable and would have failed catastrophically if not supported by glacial ice in the base of the cirque. The amount of ice required to buttress the slope is insubstantial, indicating likely failure during the thinning of the cirque glacier. We propose that, as the ice thinned, the wedge was lowered slowly down the cirque headwall, gradually exposing the failure plane. A cosmogenic 10Be surface exposure age of 18.0±1.2 ka from the outer surface of the wedge indicates Late Devensian de-icing of the backwall of the cirque, with a second exposure age from the upper portion of the failure plane yielding 12.0±0.8 ka. The 18.0±1.2 ka date is consistent with a small buttressing ice mass being present in the cirque at the time of regional deglaciation. The exposure age of 12.0±0.8 ka represents a minimum age, as the highly fractured surface of the failure plane has experienced post-failure mass-wasting. Considering the chronology, it appears unlikely that the cirque was reoccupied by a substantial ice mass during the Younger Dryas stadial.

Rock Wedge Stability Analysis by a Level III Reliability Method

In fractured rock masses, discontinuities control the mechanical response of rock slopes. They even define the geometry of a potential failure, known a kinematically controlled failure. Hence, a proper characterization and description are needed to assess their stability. Accordingly, in this work, a reliability assessment of rock wedges' stability was performed by a Monte Carlo simulation. The orientation of discontinuities was modeled as a random variable that follows the rotationally symmetric Fisher distribution. We developed an algorithm to define the modes of failure based on the orientation of planes, which was articulated within a methodology to compute the factor of safety of rock wedges explicitly. The algorithm systematically defines a set-up of joint planes. Then it verifies the relative location of the slope orientation on that set-up, which is related to the mode of failure of the rock wedge. The proposed algorithm was validated by comparison against commercial software; both yielded the same results. Besides, the probability of failure and the factor of safety probability function of removable wedges were computed for different concentration parameters. Reliability assessment showed the importance of properly characterizing the variability of joint orientation since the concentration highly influences the computed probability of failure. In addition, a proper definition of removable wedges by kinematic analysis is required before computing the factor of safety because many combinations of planes do not lead to unstable wedges, which reduces the probability of failure. Otherwise, it is overestimated. Finally, we recommend further work on rock wedge reliability assessment involving rotational nonsymmetric distribution.

Reliability and sensitivity analysis of wedge stability in the abutments of an arch dam using artificial neural network

Reliability and sensitivity analysis of wedge stability in the abutments of an arch dam using artificial neural network

Dual layer metamodel-based safety assessment for rock wedge stability of a free-crested weir

A key problem in gravity dams is providing sufficient stability to prevent sliding, and the difficulty increases with the number of weak structural planes in the dam foundation. Probabilistic methods allow different loading, material and geometric configurations to be considered, constituting the basis of more adequate design and assessment procedures. Metamodels drastically reduce the need for simulation runs, thereby decreasing the time and effort needed to simulate the structural response when analyzing a wide variety of dam-system scenarios. In this paper, a fragility-based safety assessment of a free-crested weir with respect to its rock foundation stability is performed using a dual-layer metamodel. The first layer emulates and replaces the continuous output of the software and allows the safety factor to be predicted, while the second layer provides the probability of not reaching this safety factor by generating parameterized multivariate fragility functions. To explicitly account for the effects of parameter uncertainties, multidimensional integration is implemented to update the fragility functions. Accordingly, recommendations can be formulated concerning the conditioning parameter’s minimum values to achieve the expected performance when additional information regarding the remaining parameters is acquired. The results show that improving the knowledge of the loading (seismic and reservoir) parameters reduces the uncertainties in parameters such as cohesion to meet the safety factor requirements.

Wedge Movement Effects on the Nonlinear Behavior of an Arch Dam Subjected to Seismic Loading

Arch dam abutment stability is regarded as a prominent part of designing concrete dams. In the present study, the seismic stability of the rock wedges in the foundation of the concrete arch dams is studied using limit state and finite-element methods. For this purpose, a double-curvature arch dam (the Bakhtiari dam), is taken into consideration. Each abutment has six wedges. The finite-element model (FEM) includes the dam, reservoir, wedges, and the rest of the foundation. The dam abutment seismic safety is analyzed using the time history analysis along with the Londe method. Subsequently, the wedges in the proximity of the critical state are identified. Afterward, the analysis of the critical wedges’ joints has been conducted via FEM, and the damage propagation in the dam body has been investigated. Moreover, the effects of the grout curtain efficiency, hazard level, and foundation flexibility on the nonlinear behavior of the arch dam with integrated foundation and foundation with joints are scrutinized. The outcomes reveal the remarkable effect of joints considered in the foundation on the dam behavior.

A stratigraphic record from syn to post subduction sedimentation in Marlborough, New Zealand, and implications for Gondwana breakup

Sediments that accumulate within marine basins at convergent plate margins can provide important insights into the evolution and tectonic stability of the subduction wedge. Long-term sediment dispersal and stratigraphic patterns can also be influenced by geodynamic reconfigurations of the plate margin, such as changes in plate dip or velocity, or the subduction of anomalous oceanic crust. An understanding of tectonic context and complexity is therefore critical for any interpretation of convergent margin stratigraphy. Unfortunately, ongoing subduction and wedge deformation tends to obscure or destroy the stratigraphic record of such events as sediments become progressively incorporated into the wedge.The Awatere Valley in New Zealand's South Island contains well-preserved forearc stratigraphic record that accumulated within coastal-plain and marine basins during the final stages of East Gondwana subduction. We assign seven facies associations (FA) to characterise post-subduction units, showing that a transition from syn to post-subduction deposition is contained within largely marine strata from the New Zealand Urutawan to Ngaterian stages (c. 108 to 95 Ma). In contrast to previous accounts of deposition within nascent rift-basins, restored basin geometries are most consistent with those of terraced subduction wedges. We find no evidence that extension affected deposition prior to 95 Ma. Our results instead document a transition from highly deformed sedimentary wedge (pre 108 Ma) to largely undeformed sedimentary cover units (∼100 Ma) that is predominantly gradational.Up to 2 km of basin fill documents a relative sea-level (RSL) rise and fall between 108 and 95 Ma. A period of relative sediment starvation during the Urutawan (108–103 Ma) was abruptly terminated by synchronous mass-wasting, including the remobilisation of metre-scale blocks and rafts, that signals a dramatic increase in depositional energy relative to preceding patterns. Within the context of a large RSL fluctuation, diminishing compressional tectonism and forearc volcanism (from 98 Ma), this increase is anomalous and appears to signal a significant change in underlying subduction dynamics.

Limit equilibrium analysis on the stability of rock wedges with linear and nonlinear strength criteria

The stability of a wedge is an important research topic for rock slopes. A rock wedge is formed by two sets of intersecting discontinuous structural surfaces distributed in a rock mass and cutting the rock slope. Hence, its stability is related to the occurrence of structural surfaces. To evaluate the stability of rock wedges, the limit equilibrium (LE) methods, which do not fully consider the shear forces on the slip surface of both sides of the rock wedge, are usually adopted. As a result, the calculated rock wedge factor of safety (FOS) may be overestimated. Here, a spatial model of a rock wedge is established from the occurrence parameters of the structural planes and slope surfaces. Moreover, reasonable assumptions of internal forces on both sides of a micro-unit body are adopted with the micro-unit body in the rock wedge as the analysis object. Subsequently, the analytical formulas for the normal and shear forces of the rock wedge with full consideration of the shear forces on the slip surface of both sides are derived by applying mechanical equilibrium conditions . Furthermore, the solution of the normal stress on the slip surface of a rock wedge under the assumption of a linear distribution is given. Afterwards, the formulas for calculating the FOS of a rock wedge under the linear Mohr–Coulomb strength criterion and nonlinear generalised Hoek–Brown strength criterion are derived. By comparing and analysing some rock slope examples, the feasibility of the proposed method is verified, and it is shown that the conventional LE methods overestimate the stability of rock wedges. In addition, stability charts of rock wedges are proposed to illustrate the influence trend of dips and dip directions of discontinuous structural planes on the rock wedge FOS when the structural planes have certain discreteness and distribution ranges. • A rigorous LE model is established for analysing the stability of rock wedges. • The FOS of a rock wedge under the nonlinear GHB strength criterion is calculated. • Stability charts of rock wedges are proposed and plotted.

Flight stability of wedges

Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments and simulations that analogous results hold in the two-dimensional context of solid wedges or triangular prisms in planar flows at Reynolds numbers Re∼102 to 103. Slender wedges are statically unstable with apex leading and tend to flip over or tumble, and broad wedges oscillate or flutter due to dynamical instabilities, but those of apex half angles between about 40° and 55° maintain stable posture during flight. The existence of “Goldilocks” shapes that possess the “just right” angularity for flight stability is thus robust to dimensionality. We also show that the stability is robust to moderate changes in shape and Reynolds number.

Numerical Analyses on the Rockbolt Behaviour in Rock Wedges Reinforcement Using 2D-DDA

One major concern in the design and construction of caverns in jointed rock mass is the potential failure of rock wedges falling from the roof or sliding out from the sidewalls. The rockbolts are commonly used to improve the stability and to prevent failure in the caverns. In this paper, the two-dimensional discontinuous deformation analysis (2D-DDA) method was used to analyse the stability of the rock wedge supported by rockbolts on the cavern roof. The joint relaxation method was adopted to represent a deformable rock joint under stresses. Parametric studies were conducted to investigate the effects of the confining pressure, the spacing and the angle between rockbolt and direction of wedge falling on the stability of the rock wedge. The numerical simulation results indicate that the wedge is self-supporting after stress redistribution if the confining pressure is larger than the critical confining pressure and the semi-apical angle of the wedge is less than the friction angle of rock joint. The force in rockbolt slightly decreases with reduced rockbolts spacing but increase when the rockbolt is not along the falling direction of rock wedge.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton—Bandis criterion

Based on the nonlinear Barton-Bandis (B–B) failure criterion, this study considers the system reliability of rock wedge stability under the pseudo-static seismic load. The failure probability (Pf) of the system is calculated based on the Monte–Carlo method when considering parameter correlation and variability. Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability. The relationships among the failure probability, safety factor (Fs), and variation coefficient are explored, and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn. The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability, but correlation increases system reliability or decreases system reliability affected by other parameters. Under the pseudo-static seismic action, sliding on both planes is the main failure mode of wedge system. In addition, the parameters with relatively high sensitivity are two angles related to the joint dip. When the coefficient of variation is consistent, the probability of system failure is a function of the safety factor.

Stability analysis of underground surrounding rock mass based on block theory

Evaluation of the performance of existing support in underground tunnels is of great importance for production and interests. Based on field investigation, the shape and number of joints and fractures were investigated in the mining area. Then, the stability of each structural blocks is analyzed by 3D wedge stability analysis software (Unwedge). Moreover, a new analysis method based on critical block theory is applied to analyze the stability of excavated laneways in continuous and discontinuous rock and monitor the stress changes in a fractured tunnel rock mass. The test results indicate that the 3D wedge stability analysis software for underground excavation can evaluate deep tunnel support. Besides, there is no direct relation between the size of the block and the instability of the tunnel. The support method, on large and thick key blocks, needs to be improved. In a broken tunnel section, U-shaped steel support can effectively promote the stress state of the surrounding rock. By monitoring the surrounding rock, it is proven that the vibrating string anchor stress monitoring system is an efficient and real-time method for tunnel stability evaluation.

A modified stability analysis method of landfills dependent on gas pressure.

Excessive gas pressure (GP) in landfills is a potential triggering mechanism for slope failure, which is rarely considered in analytical models. This paper presents a modified analytical model for landfill stability dependent on GP. A two-layered GP model is established to describe the GP above and below the leachate level. The distribution of GP is then used to calculate the factor of safety (FS) using a modified wedge stability analysis method. It is found that the lack of consideration of the GP in landfill stability analysis leads to serious overestimation of the FS. In addition, the GP gas pressure within the landfill accelerates the critical interface of a multilayer liner system shifting from one to another. A new estimation criterion for FS is proposed. The proposed criterion can directly estimate the stability of the landfill by the field-tested pore pressure. Finally, the proposed method is applied to estimate the slope failure of Xiaping landfill in Shenzhen, and the results verify the proposed method.

Effects of lateral opening wedge and medial closing wedge distal femoral osteotomies on axial load stability

BackgroundThe stability of the current distal femoral osteotomy is insufficient for early weight bearing and bone healing. The purpose of this study was to test the stability of medial closing wedge- (MCW-) and lateral opening wedge-distal femoral osteotomies (LOW-DFO), which have improved with the recent advances in technology. MethodsWe used composite bone models with MCW-DFO, improved with biplanar osteotomy technique and a Tomofix™ MDF plate, or LOW-DFO improved with biplanar osteotomy technique, a Tomofix™ LDF plate, and a β-TCP bone substitute, BONISH® graft. A cyclic axial loading test was employed to evaluate the strain on a plate and hinge point. The breaking axial load was measured. ResultsTensile strain on the plate produced by cyclic axial loading was significantly lower for LOW-DFO (2.0 ± 0.8 MPa) than for MCW-DFO (3.9 ± 1.6 MPa, P < .05). Compressive strain on the hinge point produced by cyclic axial loading was lower for LOW-DFO (6.6 ± 2.9 MPa) than for MCW-DFO (7.7 ± 4.6 MPa,). The maximum breaking axial load was significantly higher for LOW-DFO (5511 ± 945 N) than for MCW-DFO (4303 ± 518 N, P < .05). ConclusionsLOW-DFO improved with recent advanced technology was superior to MCW-DFO improved with advanced technology in both cyclic axial loading test and breaking axial load test. This suggests that LOW-DFO facilitates earlier weight bearing and bone healing than does MCW-DFO.

Stability analysis of rock wedge slide subjected to groundwater dynamic evolution

Heavy rainfall may increase the infiltration rate, raising the groundwater table after a short period time. Variation in the hydrostatic pressure on potential sliding surfaces and trailing edges of fissures in a rock slope may contribute to slope failure. The failure mechanisms of rainfall-triggered rock wedge slides have been widely studied in the literature. However, studies on the dynamic evolution of groundwater in rock failure are still limited. In this study, a typical rock wedge slide that occurred in Chengkou County, Chongqing, China is selected as a case study to analyze the stability of rock wedge with double planes and tension crack subjected to groundwater dynamic evolution. Model tests were designed and performed to reproduce the dynamic evolution of groundwater in the rock slope and analyze its role in wedge failure. Development and distribution characteristics of water pressure are investigated through monitoring the water pressure distributed along the surfaces of wedge failures. From the experimental study, it is found that the initial formation process of water pressure along the sliding surface consists of four types of distribution patterns, i.e., triangular distribution, Type I trapezoidal distribution, Type II trapezoidal distribution, and Type III trapezoidal distribution. Based on the model tests and theoretical analysis, the order of the calculated safety factors of the Chengkou rock wedge slide are: triangle > type I trapezoid > type II trapezoid > type III trapezoid. The existence of inflection points in the trapezoidal distribution mode significantly increases water pressure on both sides of rock wedge, which contributes instability. The new approach for investigation of the effect of dynamic evolution groundwater on stability of rock wedge slide is developed based on fundamental mechanism and experimental study. It can be adopted for stability assessment of similar rock wedge slides in other areas.

Analytical stochastic analysis of rock wedge stability using a JDRV method considering the residual factor as a random variable

The stability of a rock wedge is one of the main failure models of rock slopes. Although the strength parameters of the discontinuity planes are commonly deemed to be between the peak and residual strengths, the effect of a residual factor on the stability of a rock wedge still has not been considered. This paper presents an analytical stochastic method, considering the residual factor as a random variable, for determining the stability of a rock wedge. First, based on the Hoek–Bray method, this paper derives the formulas for evaluating the wedge stability in terms of the residual factor, and then, based on a jointly distributed random variables (JDRV) method, the calculation formulas for the probability distribution function of the safety factor is established. In the analytical method, the friction angle and cohesion are selected to satisfy the truncated normal distribution, and the residual factor is assumed to obey the generalized beta distribution. The study of a typical rock wedge shows that the results of the analytical method and the Monte Carlo simulation are almost consistent. Besides, it is also shown that the residual factor has a substantial influence on the estimation accuracy of the failure probability of the wedge.

Pseudo-static stability analysis of wedges based on the nonlinear Barton-Bandis failure criterion

This paper investigates the stability of a three-dimensional (3D) wedge under the pseudo-static action of an earthquake based on the nonlinear Barton-Bandis (B-B) failure criterion. The influences of the mechanical parameters of the discontinuity surface, the geometric parameters of the wedge and the pseudo-static parameters of the earthquake on the stability of the wedge are analyzed, as well as the sensitivity of these parameters. Moreover, a stereographic projection is used to evaluate the influence of pseudo-static direction on instability mode. The parametric analyses show that the stability coefficient and the instability mode of the wedge depend on the mechanical parameter of the rock mass, the geometric form of the wedge and the pseudo-static state of the earthquake. The friction angle of the rock φb, the roughness coefficient of the structure surface JRC and the two angles related to strikes of the joints θ1 and θ2 are sensitive to stability. Furthermore, the sensitivity of wedge height h, the compressive strength of the rock at the fracture surface JCS and the slope angle α to the stability are insignificant.

Instability Model of a Coal Wall with Large Mining Height under Excavation Unloading Conditions

On the basis of the stress field characteristics of surrounding rocks at a coal wall on a working face with a large mining height, the theories of unloading rock mass mechanics and fracture mechanics were used to establish a model of the excavation unloading field effect of the coal wall, and its instability mechanism under the action of unloading stress field was analyzed. Results show that the coal mining process is the unloading process of coal and rock masses, and the stress field of surrounding rocks at the coal wall turns into an unloading stress field that consists of original and unloading stresses. Under the action of unloading stress field, cracks in the coal wall will undergo instability, propagation, and combination in the form of composite‐type cracks and will gradually evolve into a wedge structure. The wedge stability is inversely related to roof pressure P0, unloading force T, and intersection angle φ of structural planes. Elevating the wall‐supporting force Ph, the initial supporting force of supports on the working face and the cohesion C of coal body can effectively control the occurrence of coal wall caving accidents and contribute to the safe mining of working faces with a large mining height.

Safety Assessment of Tunnel Portals for Site Selection Based on Spatial Information Geoprocessing

The evaluation of portal locations for mountain tunnels is among the most crucial considerations during route selection and structural layout planning. The development of spatial information technology has provided a more objective approach for assessing the slope stability of potential portal sites. The simulations in such studies have been performed to evaluate potential hazards and slope stability. However, potential instabilities resulting from excavation are seldom considered in these studies. Therefore, a method based on spatial information technology was developed in this study for considering the potential impact of the direction and depth of excavations on portal stability. An analysis method for an infinite slope was integrated into the geographical information system for evaluating the stability of critical wedges. The proposed method provides a reasonable estimation comparable with that provided by the conventional slice method. The results of applying this method to six mountain tunnel portals where slope instability occurred during construction indicate that the actual outcomes agreed with the predicted outcomes. For potential portal site evaluation, the proposed method facilitates the rapid estimation of safety factors for various slope designations, which is useful for site selection.

Focused fluid seepage related to variations in accretionary wedge structure, Hikurangi margin, New Zealand

AbstractHydrogeological processes influence the morphology, mechanical behavior, and evolution of subduction margins. Fluid supply, release, migration, and drainage control fluid pressure and collectively govern the stress state, which varies between accretionary and nonaccretionary systems. We compiled over a decade of published and unpublished acoustic data sets and seafloor observations to analyze the distribution of focused fluid expulsion along the Hikurangi margin, New Zealand. The spatial coverage and quality of our data are exceptional for subduction margins globally. We found that focused fluid seepage is widespread and varies south to north with changes in subduction setting, including: wedge morphology, convergence rate, seafloor roughness, and sediment thickness on the incoming Pacific plate. Overall, focused seepage manifests most commonly above the deforming backstop, is common on thrust ridges, and is largely absent from the frontal wedge despite ubiquitous hydrate occurrences. Focused seepage distribution may reflect spatial differences in shallow permeability architecture, while diffusive fluid flow and seepage at scales below detection limits are also likely. From the spatial coincidence of fluids with major thrust faults that disrupt gas hydrate stability, we surmise that focused seepage distribution may also reflect deeper drainage of the forearc, with implications for pore-pressure regime, fault mechanics, and critical wedge stability and morphology. Because a range of subduction styles is represented by 800 km of along-strike variability, our results may have implications for understanding subduction fluid flow and seepage globally.