Modeling cracking behavior of rock mass containing inclusions using the enriched numerical manifold method

In this study, the effects of weak and stiff circular inclusions on the overall mechanical behavior, in particular the cracking processes (crack initiation, propagation and coalescence) of a rectangular rock mass under uniaxial compression are investigated. The enriched method, which has been adopted by XFEM to treat the material interfaces, is incorporated into the numerical manifold method (NMM). By incorporating the modified Mohr-Coulomb crack initiation criterion and the crack evolution techniques, the cracking processes of specimens containing either one or two inclusions are successfully modeled by the developed NMM. Comparing the simulation and physical test results, the feasibility of the enriched method in treating inclusions is discussed. © 2013 The Authors.Link_to_subscribed_fulltex

A review of field occurrence of crack types and crack coalescence in rocks

This paper briefly reviews the literature on the general crack formation mechanisms and the typical occurrence of crack coalescence in natural rocks, but with no particular reference to specific locations or geologic settings. The field occurrences of tensile wing cracks, horsetail cracks, anticracks and shear cracks, as well as their coalescence are described. In contrast to the tensile wing cracks which develop in the tensile quadrant, anticracks develop from the pre-existing discontinuities in the compressive quadrant. The discussion will be illustrated with plenty of field examples, supplemented by a review of commonly used terminologies. © (2013) Trans Tech Publications, Switzerland.Link_to_subscribed_fulltex

Investigating the effects of micro-defects on the dynamic properties of rock using Numerical Manifold method

© 2014 Elsevier Ltd. All rights reserved. In this study, the Numerical Manifold method (NMM) is extended to investigate the effects of micro-defects on the dynamic mechanical properties of rock under different strain rates. The displacement decomposition technique is incorporated in the NMM to estimate the mixed mode stress intensity factors at the crack tip. A dynamic crack growth criterion is also incorporated in the NMM for crack growth analysis. The developed NMM is first validated by a simple sliding crack model. The developed model is then applied to investigate the effects of the micro-cracking properties such as initial micro-crack length, initial micro-crack inclination angle and initial micro-crack separation distance on the dynamic mechanical properties of a granite under different strain rates ranging from 10-4/s to 100/s. The effect of confining stress on the granite dynamic strength is also investigated. Simulation results illustrated that the initial micro-crack length and the confining stress have a significant effect on the dynamic strength. The effect of micro-crack separation distance, on the other hand, is heavily dependent on the ratio of separation distance to the initial micro-crack length.Link_to_subscribed_fulltex

Elastic-plastic cracking analysis for brittle-ductile rocks using manifold method

In this study, the formation of localized deformation band and failure processes of brittle-ductile materials (coarse and medium marbles) containing pre-existing flaws under various loading conditions are simulated numerically. By incorporating the modified Mohr-Coulomb crack initiation criterion and the crack evolution techniques, the cracking processes, such as crack initiation, propagation and coalescence are successfully modeled by the developed numerical manifold method. According to the results, the development of macro-shear cracks is preceded by the development of localized deformation bands, which are underlain by damage accumulation and material deterioration. The numerical results are comparable to the laboratory test results. © 2012 Springer Science+Business Media Dordrecht.Link_to_subscribed_fulltex

Influence of flaw inclination angle and loading condition on crack initiation and propagation

With reference to the experimental observation of crack initiation and propagation from pre-existing flaws in rock specimens under compression, the influences of pre-existing flaw inclination angle on the cracking processes were analyzed by means of finite element method (FEM) and non-linear dynamics method. FEM analysis on the stress field distribution induced by the presence of a pre-existing flaw provided better understanding for the influence of flaw inclination angle on the initiation position and initiation angle of the potential cracks. Numerical analysis based on the non-linear dynamics method was performed to simulate the cracking processes. The resultant crack types, crack initiation sequences and the overall crack pattern were different under different loading conditions. Under a relatively low loading rate or a small magnitude of maximum loading pressure, tensile cracks would tend to initiate prior to shear cracks. In contrast, under a relatively high loading rate and a large magnitude of maximum loading pressure, shear cracks would tend to initiate prior to tensile cracks instead. © 2012 Elsevier Ltd. All rights reserved.Link_to_subscribed_fulltex

The brazilian disc test for rock mechanics applications: Review and new insights

The development of the Brazilian disc test for determining indirect tensile strength and its applications in rock mechanics are reviewed herein. Based on the history of research on the Brazilian test by analytical, experimental, and numerical approaches, three research stages can be identified. Most of the early studies focused on the tensile stress distribution in Brazilian disc specimens, while ignoring the tensile strain distribution. The observation of different crack initiation positions in the Brazilian disc has drawn a lot of research interest from the rock mechanics community. A simple extension strain criterion was put forward by Stacey (Int J Rock Mech Min Sci Geomech Abstr 18(6):469-474, 1981) to account for extension crack initiation and propagation in rocks, although this is not widely used. In the present study, a linear elastic numerical model is constructed to study crack initiation in a 50-mm-diameter Brazilian disc using FLAC3D. The maximum tensile stress and the maximum tensile strain are both found to occur about 5 mm away from the two loading points along the compressed diameter of the disc, instead of at the center of the disc surface. Therefore, the crack initiation point of the Brazilian test for rocks may be located near the loading point when the tensile strain meets the maximum extension strain criterion, but at the surface center when the tensile stress meets the maximum tensile strength criterion. © 2012 Springer-Verlag.Link_to_subscribed_fulltex

Application of the numerical manifold method to model progressive failure in rock slopes

The present study develops the numerical manifold method as a tool to investigate the progressive failure in rock slopes. The entire processes of the progressive slide surface development related to crack initiation, propagation, coalescence and degradation to eventual catastrophic failure are successfully captured. To overcome the limitation of the original NMM associated with an improper removal of the interface cohesion of the discontinuities, the displacement-dependent cohesion removal method is adopted. Simple examples of failure of rock slopes containing different arrangements of discontinuities are modeled and their results are compared with those based on the popular limit equilibrium method proposed by famous pioneers Jennings (1970) [1] and Jaeger (1971) [2]. The present results illustrate that the types of crack propagation and coalescence obtained by the developed NMM can help explain the relevant cracking processes in nature and experimental studies. © 2014 Elsevier Ltd.Link_to_subscribed_fulltex

A Modified Correlation Between Roughness Parameter Z2 and the JRC

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Reply to comment by Saffet Yagiz on "point load test on meta-sedimentary rocks and correlations to UCS and BTS" by Diyuan Li and Louis Ngai Yuen Wong, rock mechanics and rock engineering, doi:10.1007/s00603- 012-0299-x

Uniaxial compressive strength (UCS) tests were conducted also at the Nanyang Technological University (NTU) on rock blocks collected from the same site under oven-dried and water-saturated conditions. Brazilian tensile strength (BTS) tests were conducted by another researcher under the supervision of the second author at NTU. The results have not been published yet. Anisotropy due to bedding planes was apparent in the hand specimens. However, the trace of the failure crack trace was mostly independent of the bedding orientation. The influence of the beddings on the trajectory of the failure crack was not very significant in the present study, in which a zigzag failure crack traverses at an angle with the beddings. In addition, P-wave velocity measurement was performed in this project and presented in the first manuscript submission. After the review process, one of the reviewers suggested to remove the relevant section from the manuscript.Link_to_subscribed_fulltex

Experimental studies on cracking processes and failure in marble under dynamic loading

The loading conditions influence not only the strength but also the cracking behaviors of rocks. The crack behavior study in various rock types containing artificially created flaws under the quasi-static loading condition has been extensively studied in the past. In the present study, the research of cracking processes in a natural rock is extended to dynamic loading conditions, which are then compared with the quasi-static results. Carrara marble specimens containing a single pre-existing open flaw are tested. The dynamic loadings are generated by the Split Hopkinson Pressure Bar (SHPB) system with the high-speed data acquisition subsystem and the high-speed video subsystem. Firstly, the influences of the flaw inclination angle on the compressive strength of the marble specimens are discussed and compared under these two loading conditions. Secondly, the cracking processes of marble are analyzed, which are found to consist of two stages-the development of white patches and the growth of macro-cracks. In the first stage, under these two loading conditions, the white patch patterns are generally similar with only minor differences. Significant differences with respect to the macro-crack types and the failure modes are found in the second stage. Under the quasi-static compression, the tensile wing and anti-wing white patches evolve into the closed tensile wing cracks (only for low flaw inclination angle specimens) and the open anti-wing cracks, subsequently leading to the specimen failure. In contrast, under dynamic compression, only the anti-wing and shear patches evolve into two symmetrical pairs of shear cracks, which result in the specimen failure. The flaw inclination angle appears not to influence the shape and orientation of the shear crack trajectories far away from the flaw tips. Therefore, the failure mode under quasi-static compression is dominantly diagonal, while the failure mode under dynamic compression is "X" shape regardless of the flaw inclination angle. © 2014 Elsevier B.V.Link_to_subscribed_fulltex