Y.B. Zhang

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.

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.

Numerical investigation of dynamic crack branching under biaxial loading

Dynamic crack growth and branching of a running crack under various biaxial loading conditions in homogeneous and heterogeneous brittle or quasi-brittle materials is investigated numerically using RFPA2D (two-dimensional rock failure process analysis)-Dynamic program which is fully parallelized with OpenMP directives on Windows. Six 2D models were set up to examine the effect of biaxial dynamic loading and heterogeneity on crack growth. The numerical simulation vividly depicts the whole evolution of crack and captured the crack path and the angles between branches. The path of crack propagation for homogenous materials is straight trajectory while for heterogeneous materials is curved. Increasing the ratio of the loading stress in x-direction to the stress in y-direction, the macroscopic angles between branches become larger. Some parasitic small cracks are also observed in simulation. For heterogeneous brittle and quasi-brittle materials coalescence of the microcracks is the mechanism of dynamic crack growth and branching. The crack tip propagation velocity is determined by material properties and independent of loading conditions.

Displacement Back Analysis for a High Slope of the Dagangshan Hydroelectric Power Station Based on BP Neural Network and Particle Swarm Optimization

The right bank high slope of the Dagangshan Hydroelectric Power Station is located in complicated geological conditions with deep fractures and unloading cracks. How to obtain the mechanical parameters and then evaluate the safety of the slope are the key problems. This paper presented a displacement back analysis for the slope using an artificial neural network model (ANN) and particle swarm optimization model (PSO). A numerical model was established to simulate the displacement increment results, acquiring training data for the artificial neural network model. The backpropagation ANN model was used to establish a mapping function between the mechanical parameters and the monitoring displacements. The PSO model was applied to initialize the weights and thresholds of the backpropagation (BP) network model and determine suitable values of the mechanical parameters. Then the elastic moduli of the rock masses were obtained according to the monitoring displacement data at different excavation stages, and the BP neural network model was proved to be valid by comparing the measured displacements, the displacements predicted by the BP neural network model, and the numerical simulation using the back-analyzed parameters. The proposed model is useful for rock mechanical parameters determination and instability investigation of rock slopes.

Influence of Heterogeneity on Direct Tensile Failure Process of Rocks and Associated Fractal Characteristic of AE

The investigation on the behavior of a specimen under uniaxial tension and the process of microfracture attracts considerable interest with a view to understanding strength characterization of brittle materials. Little attention has been given to the detailed investigation of influence of heterogeneity of rock on the progressive failure leading to collapse in uniaxial tension. In this paper, a numerical code RFPA3D (Realistic Failure Process Analysis), newly developed based on a three-dimensional model, to simulate the fracture process and associated fractal characteristic of heterogeneous rock specimen subjected to direct uniaxial tension. Specimens with different heterogeneity are prepared to study tension failure. In a relatively homogeneous specimen, the macrocrack nucleates abruptly at a point in the specimen soon after reaching peak stress. In more heterogeneous specimens, microfractures are found to appear diffusely throughout the specimen, and the specimens show more ductile failure behavior and a higher residual strength. Development of fractal theory may provide more realistic representations of rock fracture. The fractal dimension of distributed AE is computed during the fracture process. For all specimens, the fractal dimension increases as the loading proceeds, and it reaches the peak value when macrocrack nucleates abruptly. It is also found that fractures scatter more diffusely in relatively heterogeneous specimens, and the fractal dimension has a smaller value. The homogenous rock specimens have flat and smooth rupture faces which are consistent with the fractal results.

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.

3D MODELLING OF BRITTLE FRACTURE IN HETEROGENEOUS ROCKS

Owing to the vast developments in computer science and technologies, recent years have seen a renewal of interest in the computational modelling of ma- terial failure in meso-macro scale. The multi-scale capability of the method is recognized as a promising tool in attacking formidable problems in fracture me- chanics for heterogeneous media, such as rock, concrete or ceramic, and, indeed, has been successfully applied to the various engineering problems for industrial materials. These models have established themselves as a powerful and realistic alternative to the non-local continuum models for softening damage and frac- turing. However, the quantitative macro response (such as stress-strain) from most of the current meso-mechanical models is not close enough to the be- haviour of real materials. One reason for this shortcoming is that most of these models are two-dimensional. In this paper, a three-dimensional material failure process analysis model, MFPA 3D , is proposed. The failure behaviour of brit- tle materials can be simulated by this three-dimensional model. The model can realistically simulate the inelastic triaxial behaviour, strength limits, and post- peak response for both tension and compression. The capabilities of the MFPA 3D model to generate a wide range of damage morphologies are examined in this paper.