Li Ren

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

Extensive research has shown that fluid flow through rock fractures is greatly influenced by surface roughness. For a single rock fracture, the roughness of the upper and bottom surfaces is the same in the initial condition and then its deformation occurs with normal stress and shear stress imposed on the natural rock. Previous researchers have paid considerable attention to describing the roughness of the single fracture and its effects on fluid flow. However, few studies have explained the fluid flow with shear displacement and the direction of the fluid flow velocity field. In this work, a more detailed 2D numerical model was developed using a laser scanner system with a spacing grid of 0.1xa0mm. To investigate the influence of shear displacement accurately, the COMSOL multiphase codes were applied. By applying the Navier–Stokes equations, the results of the procedure for shear displacement simulation illustrate the distribution of the absolute velocity and pressure drop under the constant pressure gradient. The velocities predicted at the vertical profiles of the inlet were similar to the parabolic velocity curve defined by the cubic laws. The mean mechanical aperture was usually larger than the hydraulic aperture from the measured flow rates, and a devised empirical equation was proposed to describe the relationship between the mechanical aperture and the hydraulic aperture values. The recirculation zones observed in directional fluid flow during shear explain the anisotropy of roughness of a single fracture, and the phenomenon argues the applicability of local cubic laws which overestimate the total fluid flow rate.

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.

Investigation on the Applicability of Several Fracture Criteria to the Mixed Mode Brittle Fractures

Mixed mode brittle fractures are very common failure behavior for cracked brittle materials under loading, and therefore, the prediction of the mixed mode brittle fractures is significant. In this paper, the authors attempt to make a detailed discussion on the applicability of several widely accepted fracture criteria to some brittle materials. By employing these criteria, several groups of experimental results of mixed mode brittle fractures were analyzed, and the applicability of each fracture criterion to some tested materials was also examined. The results show that many of the widely applied fracture criteria can provide a good estimation for predominately mode I fractures, but none of them can well predict predominately mode II fractures. Finally, the reasons of the failed prediction by these criteria were investigated, and several significant conclusions were presented.

Mixed-Mode Elastic-Plastic Fractures: Improved R-Criterion

AbstractFor elastic-plastic materials, the plastic core region around a crack tip generally has a limited dimension, and therefore, the corresponding radius rp from the crack tip to the elastic-plastic boundary can be considered as a critical parameter. However, neither the critical radius rpIc for mode I nor the critical radius rpIIc for mode II can be applied solely as the critical parameter to predict mixed-mode fractures well. In current work, a new parameter combining rpIc with rpIIc has been proposed, and accordingly, the preexisting R-criterion has been improved. The improved R-criterion not only can predict crack initiation angle but also can predict the critical load, which is more significant in predicting material fractures. A series of fracture tests using the semicircular bend specimens with different mode mixities were conducted on polycarbonate (PCBA), and the test results were compared with the predictions of several criteria. This comparison shows that the test results agree well with the...

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^{*}

Linear Elastic Fracture Mechanics Characterization of an Anisotropic Shale

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.

Strength Reduction Technique for Non-Linear Failure Criterion

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.