L.C. Li

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.

Slope stability analysis by SRM-based rock failure process analysis (RFPA)

The fundamental principles of the strength reduction method (SRM) are incorporated into the rock failure process analysis (RFPA) code to produce an RFPA–SRM method for analysing the failure process and stability of rock and soil slopes. The RFPA–SRM method not only satisfies the global equilibrium, strain-consistent, and non-linear constitutive relationship of rock and soil materials but also takes into account the heterogeneous characteristics of materials on the micro- and macro-scales. When the proposed method is used for slope stability analysis, both the critical failure surface and the safety factor can be obtained directly without any assumptions regarding the shape and location of the failure surface. The numerical results agree well with those obtained using conventional limit equilibrium and other FEM strength reduction methods. The proposed technique is applied to a number of more complex cases, including slopes in mixed rock–soil formations, rock layer formations, and highly jointed rock masses. It is shown that the RFPA–SRM method can describe the mechanism of failure of slopes and has potential applications in a large range of geoengineering problems.

Numerical Study of the Influence of Material Structure on Effective Thermal Conductivity of Concrete

A two-dimensional numerical model is presented to examine meso- and macroscopic structure effects on the effective thermal conductivity of concrete. The heterogeneity of concrete is considered at a mesoscopic level by Weibull distribution assumption. Simulations on several heterogeneous samples show that the effective thermal conductivity strongly depends on the degree of heterogeneity. Higher homogeneity indicates a greater effect on the effective thermal conductivity. Numerically simulated results also indicate that the size and shape of individual coarse aggregate appear to have negligible influence on the effective thermal conductivity of concrete. However, that greatly depends on the thermal conductivity and volume fraction of coarse aggregate. Modeling suggests that heat conductivity decreases when there is a drop in strength due to the damages creating a thermal barrier across the cracks and thus preventing heat flow through the matrix, that is, resulting in reduction of effective thermal conductivity. Moreover, the formation of cracks in the interfacial transition zone also leads to significant reduction of heat flow in coarse aggregates.

Three-Dimensional Micro Flow-Stress-Damage (FSD) Model and Application in Hydraulic Fracturing in Brittle and Heterogeneous Rocks

In order to investigate the hydraylic fracture development of the specimens and simulate the cracks drived by fluid flow in rocks, a flow-stress-damage (FSD) model, implemented with parallel Rock Failure Process Analysis code (parallel -RFPA3D), is presented. The numerical code is based on linear elastic damage mechanics on mesoscopic scale and FEM. For simulating the complete progressive 3D failure and macroscopic mechanical behaviors of rock materials, rock properties such as elastic constants, peak strength, and poisson ratio are randomly distributed to reflect the initial random distributed weakness in mesoscopic scale. The FSD model is used to represent the permeability variation at the two stages, that is stress-dependent permeability for pre-failure and deformation-dependent permeability for post-peak stage of rock at the elemental scale. The results of the simulation with 680,000-element cylindrical rock specimen coincide well with reported experimental results and the process of crack from initiation to the instability extensions is captured vividly. The results and the process indicate that the FSD model works well and parallel-RFPA3D incorporated with FSD model is a valid tool of understanding the physical essence of the evolution of fracture with large-scale elements and fluid flows in rocks.

An Integrated Parallel System for Rock Failure Process Analysis Using PARDISO Solver

With the multi-core processors developing, the computational power of PC is becoming more and more powerful and researchers and engineers expected to utilize the increased computational power of PC to enlarge studied scale and quicken solution time. This study deals with the parallelization of 2D solid static linear finite element code using shared memory s Parallel Sparse Direct Linear Solver (Pardiso). The code is fully parallelized with OpenMP directives. The parallel efficiency is evaluated. Then the parallelized FEM code is integrated with Rock Failure Process Analysis system (RFPA). The entire system is described. To demonstrate the performance and reliability of the code, an application of rock failure under uniaxial compression is performed.

Strength Reduction Method on Stability Analysis of Tunnel

Strength reduction method and elastic-plastic FEM technique are reduced into RFPA codes. The RFPA code not only satisfies the global equilibrium, strain consistent and nonlinear constitutive relationship of rock and soil materials but also takes into account the heterogeneous characteristics of materials at mesoscopic and macroscopical level. As the proposed method is used to conduct the stability analysis of tunnel, the safety factor of tunnel is defined as the ratio of actual shear strength parameter to critical failure shear strength parameter. Not only the safety factor of tunnel with specific physics meaning can be obtained, but also the overall failure process and the location of failure surface may also be determined at the same time, so the present method is obviously superior to those traditional methods. The calculated results of a few engineering examples prove that the proposed method is effective in analyzing the stability of tunnel.

NUMERICAL APPROACH TO MINING INDUCED INSTANTANEOUS OUTBURSTS

Instantaneous outburst in underground coal mines has been the cause of major disasters in the world mining industry and has plagued underground mining op- erations of gassy coal seams in many countries for over a century. In this paper, a numerical quantitative model for the coupled gas flow in coal and rock failure is proposed to simulate and visualize mining induced instantaneous outbursts and associated stress fields. Numerical simulations on instantaneous outburst reveal that using the proposed numerical model to investigate the instantaneous out- bursts and attempt to gain insight into the mechanisms of outbursts is appropriate and practical.