Chun An Tang

Numerical studies of the influence of microstructure on rock failure in uniaxial compression — Part I: effect of heterogeneity

Abstract A numerical parameter-sensitivity analysis has been conducted to evaluate the effect of heterogeneity on the fracture processes and strength characterization of brittle materials such as rock under uniaxial compression loadings. This was done using the Rock Failure Process Analysis code (RFPA 2D ). Studying the details of macrofracture formation from specimen to specimen due to local variation in a heterogeneous material, a number of features were consistently obtained in the numerical simulations. In relatively homogeneous specimens, the macrofracture nucleated abruptly at a point in the specimen soon after reaching the peak stress. Prior to macrofracture nucleation, a small number of acoustic emission (AE) events or microfractures were distributed randomly throughout the specimen. It is difficult to predict where the macrofracture will initiate for the homogeneous rock type since the failure of the specimen is completely brittle. On the other hand, relatively heterogeneous specimens show a somewhat different response. In this case, more diffused AE events or microfractures appear in the early stage of loading. As opposed to homogeneous specimens, macrofracture nucleation starts well before the peak stress is reached and the fracture propagation, as well as the coalescence, can be traced. These events are precursors for predicting unstable failure of the specimen. For specimens with the same property of heterogeneity, however, the numerical simulations show that the failure modes depend greatly on the fracture initiation location — which is found to be sensitive to local variations within the specimen. Peak strength is dependent on the heterogeneous nature of the specimens. Splitting and faulting failure modes often observed in experiments are also observed in the simulations under uniaxial compression. It is found that tension fractures are the dominant failure mechanism in both splitting and faulting processes. The numerical simulation shows that faulting is mainly a process of tensile fractures, often en echelon fractures, developed in a highly stressed shear band, just is as observed in actual uniaxial compression tests.

Analysis of crack coalescence in rock-like materials containing three flaws—Part I: experimental approach

Fractures in the forms of joints and microcracks are commonly found in natural rocks, and their failure mechanism strongly depends on the crack coalescence pattern between pre-existing flaws. However, the crack coalescence pattern of rock specimens containing three or more flaws has not been studied comprehensively. In this paper, we investigate experimentally crack coalescence and peak strength of rock-like materials containing three parallel frictional flaws. Three flaws are arranged such that one pair of flaws lines collinearly and the third flaw forms either a non-overlapping pattern or an overlapping pattern with the first flaw. It is found that the mechanisms of crack coalescence depend on the flaw arrangement and the frictional coefficient μ on the flaw surface. Two “rules of failure” for the specimens containing three flaws are proposed. Rule No. 1: the pair of flaws with a lower value of coalescence stress will dominate the process of coalescence. Rule No. 2: mixed and tensile modes of coalescence are always the dominant modes if the coalescence stress of the two pairs of flaws is very close (say within 5%). In addition, it is found that the peak strength of the specimens does not depend on the initial crack density but on the actual number of pre-existing flaws involved in the coalescence. Comparisons of pattern of crack coalescence with the numerical approach are given in Part II of this study, and the two results agree well. The research reported here provides increased understanding of the fundamental nature of rock failure in uniaxial compression.

Coupled analysis of flow, stress and damage (FSD) in rock failure

Abstract Rock is a heterogeneous geological material that contains natural weakness of various scales. When rock is subjected to mechanical loading, these pre-existing weaknesses can close, open, grow or induce new fractures, which can in turn change the structure of the rock and alter its fluid flow properties. Experimental results provide strong evidence that rock permeability is not a constant, but a function of stresses and stress-induced damage. A flow-stress-damage (FSD) coupling model for heterogeneous rocks that takes into account the growth of existing fractures and the formation of new fractures is proposed herein. Implemented with the Rock Failure Process Analysis code (F-RFPA 2D ), this FSD model is used to investigate the behaviour of fluid flow and damage evolution, and their coupling action, in samples that are subjected to both hydraulic and biaxial compressive loadings. The modeling results suggest that the nature of fluid flow in rocks varies from material to material, and strongly depends upon the heterogeneity of the rocks.

Numerical Simulation of Cumulative Damage and Seismic Energy Release During Brittle Rock Failure—Part I: Fundamentals

Abstract This paper presents a numerical approach for the simulation of damage initiation and propagation causing seismic energy release during unstable failure of brittle rock. With a newly developed numerical code, RFPA2D (Rock Failure Process Analysis), the progressive failure process leading to the development of a shear or fault zone, and the eventual collapse of a heterogeneous rock sample is modeled. Since the constitutive law for each element in the model is elastic–brittle, seismic energy is radiated whenever an element fails. It is assumed that the radiated energy is equal to the energy stored in the element before failure is triggered. Due to the heterogeneity of rock properties, seismic quiescence may occasionally occur within the nucleation zone. The cumulative seismic damage calculated based on the seismic event rate from the simulation can be used as a damage parameter to describe the damage evolution. It was found that significant decreases followed by sudden increases in radiated seismic energy may be an indicator of potentially unstable nucleation.

Numerical simulation of the rock fragmentation process induced by indenters

Rock fragmentation processes induced by single and double indenters were examined by a numerical method. The simulated results reproduce the progressive process of rock fragmentation in indentation. Rock deforms elastically at the initial loading stage. Then tensile cracks are initiated around the two corners of the truncated indenter and propagate in the well-known conical Hertzian manner. The rocks immediately under the indenter are in a highly tri-axial stress state, and some of them fail in the ductile cataclastic mode with the stress satisfying the ductile failure surface of the double elliptic strength criterion. With the tensile cone cracks and ductile cataclastic failure releasing the confining pressure, the rocks under the indenter are compressed into failure and the crushed zone gradually comes into being. With increasing loading displacement, the re-compaction behaviour of the crushed zone occurs. Side cracks initiated from the crushed zone or bifurcated from cone cracks are driven by tensile stress associated with the crushed zone to propagate in a curvilinear path and finally intersect with the free surface to form chips. It is pointed out that the curvilinear path is caused by heterogeneity. The simulated force-penetration curve is in fact the indication of the propagation of cracks, the crushing of microstructural grains and the formation of chips. It is found that the confining pressure has an important influence on the indentation results. With decreasing confining pressure, there is a decrease in the indentation strength and a change in the rock failure process from the formation of rock chips to a vertically axially splitting failure. The simulated fragmentation process in the double indenter test reproduces the side cracks, which are induced by two indenters, propagate, interact and finally coalesce, chipping the rock between the indenters. The line spacing is an important factor that affects the fragmentation efficiency in multiple indenter tests. It is pointed out that simultaneous loading with multiple indenters with an appropriate line spacing seems to provide a possibility of forming larger rock chips, controlling the direction of subsurface cracks and consuming a minimum total specific energy. According to the simulated results, it is believed that the numerical simulation method will contribute to an improved knowledge of rock fragmentation in indentation, which will in turn help to enhance mining and drilling efficiency through the improved design of mining tools and equipment.

NUMERICAL SIMULATION ON SHEAR FRACTURE PROCESS OF CONCRETE USING MESOSCOPIC MECHANICAL MODEL

Abstract The numerical simulation of the damage and fracture processes of concrete structures has evolved considerably in the past years. In this contribution, a newly proposed mechanical model is used to simulate the fracture behavior of double-edge notched (DEN) and double central notched (DCN) concrete specimens loaded in shear. In this numerical model, the concrete is assumed to be a three-phase composite composed of matrices, aggregates and matrix–aggregate interfaces. An elastic finite element program is employed as the basic stress analysis tool while the elastic damage mechanics is used to describe the constitutive law of meso-level element. The maximum tensile strain criterion and Mohr–Coulomb criterion are utilized as damage thresholds. The heterogeneous stress field is obtained from numerical simulation, thus it is found that heterogeneity of mechanical properties has significant effect on the stress distribution in concrete. The crack propagation processes simulated with this model shows good agreement with those of experimental observations. It has been found that the shear fracture of concrete observed at the macroscopic level is predominantly caused by tensile damage at the mesoscopic level.

Numerical investigation of particle breakage as applied to mechanical crushing : Part I, Single-particle breakage

Abstract A numerical approach to particle breakage is applied using the Rock Failure Process Analysis code, RFPA 2D . The numerical tool is validated by simulating the Brazilian test with a two-dimensional disk sample. Then two irregularly shaped particles with an exact geometry and exact mechanical properties are numerically modelled to investigate their breakage behaviour under unconfined and confined loading conditions. The numerical results indicate that the dominant mode of failure is catastrophic splitting and progressive crushing, which mainly depends on the loading conditions with respect to confinement. The analysis of the load–displacement curves obtained from the simulations suggests a brittle-ductile transition between the two cases. The lateral constraint increases the initial stiffness and the maximum breakage strength of the particle. Most of the energy released during the failure process comes from the crushing of highly stressed areas, particularly, in the vicinity of the contact points where a crushed zone forms. It is also found that the particle shape governs the breakage strength in addition to the material properties themselves, and that the heterogeneity of the particles governs the fracture propagation paths.

Numerical simulation of the cutting of inhomogeneous rocks

In this study, the possible modes of crack initiation and propagation leading to chip formation in rock cutting are studied numerically by using a rock failure process analysis code referred to as ...

Numerical Simulation of Damage Accumulation and Seismic Energy Release During Brittle Rock Failure—Part II: Rib Pillar Collapse

Abstract This paper presents an application of the numerical model presented in the companion paper (Part I) in which, by using a newly developed numerical code, RFPA2D (Rock Failure Process Analysis), a fundamental approach for the simulation of damage initiation and propagation causing seismic energy release during an unstable failure of brittle rock was presented. The influence of material and loading system properties including stiffness and strength on pillar failure and associated seismic patterns is studied. The results confirm that soft loading systems promote unstable failure or collapse of pillars. Weak pillar foundations and shear stresses on the pillar drastically reduce the pillars load bearing capacity, and the related seismic activity and seismic energy release is significantly altered by these factors. As expected, for a high strength pillar, shear failure occurs in the floor and roof close to the edges of the pillar, whereas failure zones inside the pillar are found for low strength pillars. It is demonstrated that the proposed model properly simulates the pillar failure process.

A double rock sample model for rockbursts

In this paper, a double rock sample model for studying the rockburst mechanism is presented. Based on the assumption that there exists a proportional relation between the number of microseismic events and microfractured elements, the theoretical microseismic event rate produced by the double rock sample loaded in series under uniaxial compression is obtained. By using a newly developed numerical code, RFPA2D, the progressive failure process and associated microseismic behavior of the twin rock samples are simulated, which shows that the spatial distribution of microseismic events develops progressively from disorder at the initial loading stage to order prior to the main shock. A laboratory experiment with the same setup as the double rock sample model is conducted in order to verify the theoretical results.