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Normal stress ( σ n ) under compression-shear conditions significantly affects crack propagation and failure modes of specimens containing non-persistent joints (NPJs). Crack propagation and failure modes of specimens vary for different σ n . In the present study, we adopt a strength-based local maximum stress criterion (SLMS) to describe tensile and shear cracks formed during shear and model crack propagation processes via the finite element method. Two classical cases are performed to validate the SLMS criterion for describing tensile and shear cracks under shear conditions. After that, crack initiation, propagation, and coalescence processes are modeled for specimens containing a pair of horizontal NPJs in coplanar and non-coplanar cases at different σ n . Variations of crack propagation and failure modes of specimens containing coplanar and non-coplanar NPJs are investigated for σ n ranging from low to high. Effects of rock bridge inclination angle (β ) on crack propagation and failure mode of specimens containing non-coplanar NPJs are investigated. Also, the effects of σ n on critical shear load ( τ sc ) for crack initiation in specimens containing coplanar and non-coplanar NPJs are examined. Results indicate that failure modes of specimens with coplanar NPJs transform from tensile to mixed tensile-shear, then to shear, and finally to pure shear as σ n increases. The increase of β promotes the appearance of tensile failure of specimens containing coplanar NPJs under high σ n while suppressing the appearance of shear failure. The modeling results provide a reference for understanding crack propagation and failure modes in rocks containing NPJs under compression-shear conditions. [ABSTRACT FROM AUTHOR]

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (Ka) of shale. In addition, the effects of specimen size and geometry on the Ka and the selection of fracture criterion on the prediction of the inherent fracture toughness (KIc) were also studied. The results show that the Ka increases with the increase of specimen size, and the difference between KIc of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of Ka of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of Ka of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α). Highlights: Fracture toughness is closely related to the size and configuration of the specimen, which is ultimately attributed to the inconsistent tangential stress distribution at the crack tip. The further improved maximum tangential stress criterion has the best effect on apparent fracture toughness prediction, and higher-order terms of the Williams expansion should be considered in apparent fracture toughness prediction of small-size specimens. The fracture criterion for determining the fracture process zone length should be consistent with the prediction criterion of apparent fracture toughness. The effective establishment of size effect law requires high accuracy tested data, especially for the configuration with large variation of the dimensionless stress intensity factor with normalized crack length. [ABSTRACT FROM AUTHOR]

Previous studies showed that the modified maximum tangential stress (MMTS) criterion considering two stress terms (containing r−1/2 and r1/2) of the well-known Williams series expansion can better assess the mode I fracture toughness (KIc) of rocks than the traditional maximum tangential stress (MTS) criterion. However, this study indicates that in some cases, only using the two stress terms cannot fully describe the tangential stress at the critical distance for rock specimens, and the higher order, non-singular stress terms can also play important roles in the tangential stress. The MMTS fracture criterion might still induce non-negligible errors for assessing mode I rock fracture. Thus, we propose a further improved MTS (FIMTS) criterion. The FIMTS criterion emphasizes that the number of non-singular stress terms used in a MTS-based criterion should be carefully chosen according to the following principle: the tangential stress at the critical distance can be accurately described using the selected stress terms. Mode I fracture tests on two kinds of rocks are conducted using a newly proposed V-notched short rod bend (VNSRB) specimen. The specimen- or loading-configuration-dependence of KIc indicated by the experimental data is theoretically assessed using the traditional MTS, the MMTS and the FIMTS criteria, and the last criterion is shown to be the best. Therefore, considering non-singular stress terms of the Williams expansion can better assess mode I fracture of rocks. Our study calls for more attention to the effects of non-singular stress terms on mode I fracture of rocks, especially for small-size specimens and for rocks with relatively large critical distances. [ABSTRACT FROM AUTHOR]

The geo-mechanical properties of reservoirs, especially the morphology of the rock surface and the fracture properties of rocks, are of great importance in the modeling and simulation of hydraulic processes. To better understand these fundamental issues, five groups of mixed-mode fracture tests were conducted on sandstone using edge-cracked semi-circular bend specimens. Accordingly, the fracture loads, growth paths and fracture surfaces for different initial mixities of the mixed-mode loadings from pure mode I to pure mode II were then determined. A surface topography measurement for each rough fracture surface was conducted using a laser profilometer, and the fractal properties of these surfaces were then investigated. The fracture path evolution mechanism was also investigated via optical microscopy. Moreover, the mixed-mode fracture strength envelope and the crack propagation trajectories of sandstone were theoretically modeled using three widely accepted fracture criteria (i.e., the MTS, MSED and MERR criterions). The published test results in Hasanpour and Choupani (World Acad Sci Eng Tech 41:764-769, ) for limestone were also theoretically investigated to further examine the effectiveness of the above fracture criteria. However, none of these criteria could accurately predict the fracture envelopes of both sandstone and limestone. To better estimate the fracture strength of mixed-mode fractures, an empirical maximum tensile stress (EMTS) criterion was proposed and found to achieve good agreement with the test results. Finally, a uniformly pressurized fracture model was simulated for low pressurization rates using this criterion. [ABSTRACT FROM AUTHOR]