Step-path Failure Research Articles

An Experimental and Numerical Study on Mechanical Behavior of Ubiquitous-Joint Brittle Rock-Like Specimens Under Uniaxial Compression

Rock engineers often encounter materials with a large number of discontinuities that significantly influence rock stability. However, the strength and failure patterns of ubiquitous-joint rock specimens have not been examined comprehensively. In this study, the peak uniaxial compressive strength (UCSJ) and failure patterns of ubiquitous-joint rock-like specimens are investigated by combining similar material testing and numerical simulation using the two-dimensional particle flow code. The rock-like specimens are made of white cement, water, and sand. Flaws are created by inserting mica sheets into the fresh cement mortar paste. Under uniaxial compressional loading, the failure patterns of ubiquitous-joint specimens can be classified into four categories: stepped path failure, planar failure, shear-I failure, and shear-II failure. The failure pattern of the specimen depends on the joint-1 inclination angle α and the intersection angle γ between joint-1 and joint-2, while α strongly affects UCSJ. The UCSJ of specimens with γ = 15° or 30° shows similar tendencies for 0° ≤ α ≤ 75°. For specimens with γ = 45° or 60°, UCSJ increases for 0° ≤ α ≤ 30° and decreases for α > 30°. For specimens with γ = 75°, the UCSJ peaks when α = 0° and increases for 60° ≤ α ≤ 75°. The numerical and experimental results show good agreement for both the peak strength and failure patterns. These results can improve our understanding of the mechanical behavior of ubiquitous-joint rock mass and can be used to analyze the stability of rock slopes or other rock engineering cases such as tunneling construction in heavily jointed rock mass.

Numerical simulations of failure behavior around a circular opening in a non-persistently jointed rock mass under biaxial compression

Pre-existing discontinuities change the mechanical properties of rock masses, and further influence failure behavior around an underground opening. In present study, the failure behavior in both Inner and Outer zones around a circular opening in a non-persistently jointed rock mass under biaxial compression was investigated through numerical simulations. First, the micro parameters of the PFC3D model were carefully calibrated using the macro mechanical properties determined in physical experiments implemented on jointed rock models. Then, a parametrical study was undertaken of the effect of stress condition, joint dip angle and joint persistency. Under low initial stress, the confining stress improves the mechanical behavior of the surrounding rock masses; while under high initial stress, the surrounding rock mass failed immediately following excavation. At small dip angles the cracks around the circular opening developed generally outwards in a step-path failure pattern; whereas, at high dip angles the surrounding rock mass failed in an instantaneous intact rock failure pattern. Moreover, the stability of the rock mass around the circular opening deteriorated significantly with increasing joint persistency.

Numerical simulation of a jointed rock block mechanical behavior adjacent to an underground excavation and comparison with physical model test results

Mechanical behavior of a jointed rock mass with non-persistent joints located adjacent to a free surface on the wall of an excavation was simulated under without and with support stress on the free surface using approximately 0.5m cubical synthetic jointed rock blocks having 9 non-persistent joints of length 0.5m, width 0.1m and a certain orientation arranged in an en echelon and a symmetrical pattern using PFC3D software package. The joint orientation was changed from one block to another to study the effect of joint orientation on strength, deformability and failure modes of the jointed blocks. First the micro-mechanical parameters of the PFC3D model were calibrated using the macro mechanical properties of the synthetic intact standard cylindrical specimens and macro mechanical properties of a limited number of physical experiments performed on synthetic jointed rock blocks of approximately 0.5m cubes. Under no support stress, the synthetic jointed rock blocks exhibited the same three failure modes: (a) intact rock failure, (b) step-path failure and (c) planar failure under both physical experiments and numerical simulations for different orientations. The jointed blocks which failed under intact rock failure mode and planar or step-path failure mode produced high and low jointed block strengths, respectively. Three phases of convergence of free surface were discovered. The joint orientation and support stress played important roles on convergence magnitude. The average increment of jointed block strength turned out to be about 10, 7.9 and 6.6 times the support stress when support stresses of 0.06MPa, 0.20MPa and 0.40MPa were applied, respectively. The modeling results offer some guideline in support design for underground excavations.

Mechanical Behavior of Brittle Rock-Like Specimens with Pre-existing Fissures Under Uniaxial Loading: Experimental Studies and Particle Mechanics Approach

Joints and fissures with similar orientation or characteristics are common in natural rocks; the inclination and density of the fissures affect the mechanical properties and failure mechanism of the rock mass. However, the strength, crack coalescence pattern, and failure mode of rock specimens containing multi-fissures have not been studied comprehensively. In this paper, combining similar material testing and discrete element numerical method (PFC2D), the peak strength and failure characteristics of rock-like materials with multi-fissures are explored. Rock-like specimens were made of cement and sand and pre-existing fissures created by inserting steel shims into cement mortar paste and removing them during curing. The peak strength of multi-fissure specimens depends on the fissure angle α (which is measured counterclockwise from horizontal) and fissure number (Nf). Under uniaxial compressional loading, the peak strength increased with increasing α. The material strength was lowest for α = 25°, and highest for α = 90°. The influence of Nf on the peak strength depended on α. For α = 25° and 45°, Nf had a strong effect on the peak strength, while for higher α values, especially for the 90° sample, there were no obvious changes in peak strength with different Nf. Under uniaxial compression, the coalescence modes between the fissures can be classified into three categories: S-mode, T-mode, and M-mode. Moreover, the failure mode can be classified into four categories: mixed failure, shear failure, stepped path failure, and intact failure. The failure mode of the specimen depends on α and Nf. The peak strength and failure modes in the numerically simulated and experimental results are in good agreement.

Conceptual Numerical Modeling of Large-Scale Footwall Behavior at the Kiirunavaara Mine, and Implications for Deformation Monitoring

Over the last 30 years, the Kiirunavaara mine has experienced a slow but progressive fracturing and movement in the footwall rock mass, which is directly related to the sublevel caving (SLC) method utilized by Luossavaara-Kiirunavaara Aktiebolag (LKAB). As part of an ongoing work, this paper focuses on describing and explaining a likely evolution path of large-scale fracturing in the Kiirunavaara footwall. The trace of this fracturing was based on a series of damage mapping campaigns carried out over the last 2 years, accompanied by numerical modeling. Data collected from the damage mapping between mine levels 320 and 907 m was used to create a 3D surface representing a conceptual boundary for the extent of the damaged volume. The extent boundary surface was used as the basis for calibrating conceptual numerical models created in UDEC. The mapping data, in combination with the numerical models, indicated a plausible evolution path of the footwall fracturing that was subsequently described. Between levels 320 and 740 m, the extent of fracturing into the footwall appears to be controlled by natural pre-existing discontinuities, while below 740 m, there are indications of a curved shear or step-path failure. The step-path is hypothesized to be activated by rock mass heave into the SLC zone above the current extraction level. Above the 320 m level, the fracturing seems to intersect a subvertical structure that daylights in the old open pit slope. Identification of these probable damage mechanisms was an important step in order to determine the requirements for a monitoring system for tracking footwall damage. This paper describes the background work for the design of the system currently being installed.

A DEM analysis of step-path failure in jointed rock slopes

A numerical analysis of step-path failure mechanisms in rock slopes is provided based upon simulations performed using a discrete element method specifically enhanced for the modeling of jointed rock masses. Fracturing of the intact rock as well as yielding within discontinuities can be simulated to determine the failure surface without any a priori assumption on its location. For both coplanar and non-coplanar sets of discontinuities, failure is the result of the propagation of tensile microcracks that develop in the rock bridges from the tips of pre-existing discontinuity planes in a way similar to wing cracks extensions that can eventually coalesce to form extended step-path failure surfaces. Sensitivity analyses are performed to better understand the critical mechanisms that lead to slope failure and to discriminate between the respective roles played by intact rock and planes of weakness at the onset of failure. For a randomly distributed set of joints that share the same preferential orientation, failure is shown to be dependent on the frictional strength mobilized on the joint surfaces. The results confirm the critical need for a comprehensive and extensive characterization of both mechanical and geometrical properties of discontinuities when assessing the stability of a rock mass.

Step-path failure of rock slopes with intermittent joints

Step-path failure is a typical instable mode of rock slopes with intermittent joints. To gain deeper insight into the step-path failure mechanism, six rock slopes with different intermittent joints are studied using the 2D Particle Flow Code (PFC). Three different step-path failure modes, i.e., shear, tensile, and mixed tensile–shear failure, are observed by focusing on the crack initiation, propagation, and coalescence in the rock bridges. The cracks develop progressively in the rock bridges, which induce the intermittent joints to coalesce one by one from bottom to top under the action of gravity. The tensile cracks that often appear in the main body and at the crown are nearly vertical to the step-path failure surface. The step-path failure in a rock slope with intermittent joints can be divided into four stages in terms of both stress and crack development in the rock bridges, i.e., elastic deformation, failure of rock bridges at a lower position, progressive failure of rock bridges upward, and final block slide. Therefore, reinforcement is suggested to be applied to the lower part of the slopes. Three equations for calculating the factors of safety are derived with respect to the three failure modes, in which the degree of joint coalescence is considered.

Block caving-induced strata movement and associated surface subsidence: a numerical study based on a demonstration model

The block cave mining mechanism and associated subsidence present one of the most challenging engineering problems in rock mining. Although block caving has been in use for many years, there has been limited research on the impact caving angles have on surface settlement and failure profiles, specifically when associated with deep caves and surface propagation (i.e., not as part of caving into an existing open pit). We analyse in this study block caving-induced step-path failure development in a large-scale demonstration model utilizing a numerical code based on a finite element technique that incorporates an elasto-brittle fracture mechanics constitutive criterion. Fracture initiation, propagation and coalescence, as well as the breaking of the intact rock bridge and the evolution of a pressure-balancing arch in the stressed strata, are represented visually during the whole caving process. Based on numerical results, surface impacts of block caving, such as subsidence profiles, break angles, fracture initiation angles and subsidence angles at different initial caving depths, are illustrated in this study.

Application of the discrete element method for modeling of rock crack propagation and coalescence in the step-path failure mechanism

The present study evaluates the discrete element method (DEM) as a tool for understanding the step-path failure mechanism in fractured rock masses. Initially, the study simulates crack propagation and coalescence in biaxial and triaxial laboratory tests. The results of this analysis show that the DEM accurately represents these processes in comparison to other studies in the technical literature. The crack propagation and coalescence processes are important in the step-path failure mechanism for slopes. Simple examples of this mechanism were modeled, and their results were compared with those of the analytical model proposed by Jennings (1970). Among the possibilities suggested by Jennings, modeling with DEM did not provide a good approximation for the case of coplanar cracks, for which failures in the intact rock bridges should only be caused by shear forces. In modeling with DEM, tensile failures occur within the sliding block, generating forces that are not considered in the Jennings model. The non-coplanar crack condition provided a better approximation, since the Jennings model formulation for this case includes the tensile failure of the rock. The main advantage of the DEM over other computational tools is its micromechanical representation of discontinuous media, which permits a better understanding of the step-path failure mechanism. However, good calibration of the macroscopic parameters of the rock and its discontinuities is necessary to obtain good results.

Numerical Analysis of Block Caving-Induced Instability in Large Open Pit Slopes: A Finite Element/Discrete Element Approach

This paper addresses one of the most challenging problems in mining rock engineering—the interaction between block cave mining and a large overlying open pit. The finite element modeling/discrete element modeling (FEM/DEM) approach was utilized in the analysis of block caving-induced step-path failure development in a large open pit slope. The analysis indicated that there is a threshold percentage of critical intact rock bridges along a step-path failure plane that may ensure the stability of an open pit throughout caving operations. Transition from open pit to underground mining at Palabora mine presents an important example of a pit wall instability triggered by caving. Using combined FEM/DEM-DFN (discrete fracture network) modeling, it was possible to investigate the formation of a basal failure surface within an open pit slope as a direct result of cave mining. The modeling of Palabora highlighted the importance of rock mass tensile strength and its influence on caving-induced slope response.

The role of tectonic damage and brittle rock fracture in the development of large rock slope failures

Rock slope failures are frequently controlled by a complex combination of discontinuities that facilitate kinematic release. These discontinuities are often associated with discrete folds, faults, and shear zones, and/or related tectonic damage. The authors, through detailed case studies, illustrate the importance of considering the influence of tectonic structures not only on three-dimensional kinematic release but also in the reduction of rock mass properties due to induced damage. The case studies selected reflect a wide range of rock mass conditions. In addition to active rock slope failures they include two major historic failures, the Hope Slide, which occurred in British Columbia in 1965 and the Randa rockslides which occurred in Switzerland in 1991. Detailed engineering geological mapping combined with rock testing, GIS data analysis and for selected case numerical modelling, have shown that specific rock slope failure mechanisms may be conveniently related to rock mass classifications such as the Geological Strength Index (GSI). The importance of brittle intact rock fracture in association with pre-existing rock mass damage is emphasized though a consideration of the processes involved in the progressive-time dependent development not only of though-going failure surfaces but also lateral and rear-release mechanisms. Preliminary modelling data are presented to illustrate the importance of intact rock fracture and step-path failure mechanisms; and the results are discussed with reference to selected field observations. The authors emphasize the importance of considering all forms of pre-existing rock mass damage when assessing potential or operative failure mechanisms. It is suggested that a rock slope rock mass damage assessment can provide an improved understanding of the potential failure mode, the likely hazard presented, and appropriate methods of both analysis and remedial treatment.

Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques

Recent advances in the characterization of complex rock slope deformation and failure using numerical techniques have demonstrated significant potential for furthering our understanding of both the mechanisms/processes involved and the associated risk. This paper illustrates how rock slope analyses may be undertaken using three levels of sophistication. Level I analyses include the conventional application of kinematic and limit equilibrium techniques with modifications to include probabilistic techniques, coupling of groundwater simulations and simplistic treatment of intact fracture and plastic yield. Such analyses are primarily suited to simple translational failures involving release on smooth basal, rear and lateral surfaces where the principle active damage mechanisms are progressive failure and/or asperity breakdown. Level II analyses involve the use of continuum and discontinuum numerical methods. In addition to simple translation, Level II techniques can be applied to complex translational rock slope deformations where step-path failure necessitates degradation and failure of intact rock bridges along basal, rear and lateral release surfaces. Active damage processes in this case comprise not only strength degradation along the release surface (e.g., asperity breakdown) but also a significant component of brittle intact rock fracture. Level III analyses involve the use of hybrid continuum–discontinuum codes with fracture simulation capabilities. These codes are applicable to a wide spectrum of rock slope failure modes, but are particularly well suited to complex translation/rotational instabilities where failure requires internal yielding, brittle fracturing and shearing (in addition to strength degradation along release surfaces). Through a series of rock slope analyses the application of varied numerical methods are discussed. Particular emphasis is given to state-of-the-art developments and potential use of Level III hybrid techniques.

Prediction of step path failure geometry for slope stability analysis : Call, R D; Nicholas, D E Paper to 19th US Symposium on Rock Mechanics, Stateline, Nevada, 1–3 May 1978, 8P

Prediction of step path failure geometry for slope stability analysis : Call, R D; Nicholas, D E Paper to 19th US Symposium on Rock Mechanics, Stateline, Nevada, 1–3 May 1978, 8P