L.Z. Xie

Mixed-Mode Fracture Behavior and Related Surface Topography Feature of a Typical Sandstone

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, 2008) 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.

Fracture Behavior Investigation of a Typical Sandstone Under Mixed-Mode I/II Loading Using the Notched Deep Beam Bending Method

The brittle fracture behavior of rocks under mixed-mode loading is important in rock engineering. First, a new configuration called the notched deep beam (NDB) specimen was introduced for the fracture testing of rock materials under mixed-mode I/II loading, and a series of finite element analyses were performed to calibrate the dimensionless fracture parameters (i.e., YI, YII and

Progressive failure constitutive model for softening behavior of rocks based on maximum entropy theory

T^{*}

Effect of layer orientation on acoustic emission characteristics of anisotropic shale in Brazilian tests

T∗). The results showed that an NDB specimen subjected to three-point bending is able to generate pure mode I loading, pure mode II loading, and any mixed-mode loading in between. Then, several NDB specimens made of sandstone were used to investigate the brittle fracture behavior of rock under mixed-mode I/II loading. The fracture surfaces were theoretically described using a statistical method, and the results indicated that all the fracture surfaces generated under different mixed-mode loading were statistically identical; to some extent, these results experimentally showed that only tensile fracture occurs under mixed-mode I/II loading. The obtained fracture strengths were then analyzed using several brittle fracture criteria. The empirical criterion, maximum energy release rate criterion, generalized maximum tangential stress (GMTS) criterion, and improved R-criterion accurately predicted the fracture strength envelope of the sandstone. Finally, based on the concepts of point stress and mean stress, the micro-crack zones (MCZs) under different mixed-mode loading were theoretically estimated based on the MTS and GMTS criteria. The critical radius of MCZ in the crack propagation direction was not a constant for all mixed-mode loading conditions regardless of whether the T-stress was considered. This result suggests that the size of the core region used to predict the crack initiation direction and fracture strength based on the GMTS criterion should be chosen more carefully.

Numerical investigation of geometrical and hydraulic properties in a single rock fracture during shear displacement with the Navier–Stokes equations

Mixed mode fracture tests are conducted under various initial loading combinations of mode I and mode II (from pure mode I to pure mode II) on semicircular bend (SCB) specimens of dolomite rock. Damage zones are observed behind the fracture surfaces of the broken samples. Scanning electron microscope images of the fracture surfaces are used to study the failure manner. Using the conventional remesh method based on the finite element method (FEM), several widely accepted fracture criteria are employed to theoretically predict the fracture paths. These criteria include the maximum tangential stress criterion, minimum strain energy density criterion, maximum energy release rate criterion, maximum dilatational strain energy density criterion, and the distortional strain energy density criterion. The applicability of the five fracture criteria is examined. The results show that none of the criteria are successful in predicting the crack trajectories of the predominately mode II cracks; the differences among the predicted results of the crack growth paths are negligible for each crack inclined angle. The effect of Poisson’s ratio on the fracture criteria is also investigated and the results show that the predicted crack trajectories are not sensitive to Poisson’s ratio.

Coupling between the statistical damage model and permeability variation in reservoir sandstone: Theoretical analysis and verification

Considering that rock failure is a gradual process when subjected to triaxial stress conditions, a new statistical damage constitutive model is proposed to describe the progressive failure of rocks. The model is based on continuous damage mechanics and maximum entropy theory while the commonly used statistical damage model is based on continuous damage mechanics and the conventional Weibull distribution, which is used to describe the strength of mesoscopic rock elements. Weibull distribution is a distribution function with a specific assumption that the nth central moment and the geometric mean of the statistical variable are constant. The maximum entropy distribution is the only unbiased distribution and the Weibull distribution is a special case of the maximum entropy distribution. According to the maximum entropy theory, the damage variable is defined without any prior assumptions of the theoretical distributions. The rock is hypothesized to be divided into two parts: the damaged portion and undamaged portion. The bearing capacity of the damaged part is also considered in the new model so that it is more in accordance with the actual situation. The mesoscopic rock elemental strength is calculated based on energy release rate principles to avoid the deficiencies in using the conventional stress or strain criteria approaches, and the effect of rock initial fissures is emphasized. A new method is presented to determine the unknown parameters in the constitutive equations. The applicability of the new statistical damage constitutive model is verified by experimental data. It is shown that the theoretical model is in good agreement with the test data trend and can simulate the softening behavior of rock well. Admittedly, the proposed model proposed in this paper is a basic model without considering some important aspects of rock deformation mechanics, such as the absences of the complex stress conditions. The purpose of this paper was to illustrate that the constitutive model can be established in the framework of continuous damage mechanics and maximum entropy theory.

A thermodynamically consistent model accounting for viscoplastic creep and anisotropic damage in unsaturated rocks

Compressive fracture is one of the most common failure patterns in geotechnical engineering. For better understanding of the local failure mechanism of compressive fractures of brittle geomaterials, three compressive fracture tests were conducted on sandstone. Edge cracked semicircular bend specimens were used and, consequently, fresh and unfilled compressive fracture surfaces were obtained. A laser profilometer was employed to measure the topography of each rough fracture surface, followed by fractal analysis of the irregularities of the obtained compression-induced fracture surfaces using the cubic cover method. To carry out a contrastive analysis with the results of compressive fracture tests, three tension mode fracture tests were also conducted and the fractal features of the obtained fracture surfaces were determined. The obtained average result of the fractal dimensions of the compression-induced surfaces was 2.070, whereas the average result was 2.067 for the tension-induced fracture surfaces. No remarkable differences between the fractal dimensions of the compression-induced and tension-induced fracture surfaces may indicate that compressive fracture may occur, at least on the investigative scale of this work, in a similar manner to tension fracture.