Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.     

浙西北江山─绍兴断裂带构造演化特征

江山—绍兴断裂带是中国南方最重要的构造带之一。它是江南陆块与华夏陆块神功运动形成的碰撞拼贴带。它表现出明显的多期变形、构造叠加的特征：神功运动形成近东西向平卧褶皱；印支运动沿断裂带有向北西强烈的推覆挤压。断裂带不同时期的活动反映了不同特征的构造环境，形成不同的构造变形特征，并对两侧的地质历史具有明显的控制作用。     

元岭金矿蚀变破碎带特征及其找矿意义

根据对元岭金矿三条蚀变破碎带一般地质特征、微量元素特征的对比研究，并借鉴邻近矿区蚀变破碎带的矿化特征，本文阐明了元岭蚀变破碎带矿化的有利构造部位，总结了蚀变破碎带特征与矿化强度之间的关系，指出蚀变破碎带的矿化蚀变元素为中低温组合，矿化蚀变愈强则参与元素的种类愈多、数量愈大。围岩性质对矿化蚀变有一定影响，围岩中的易迁移亲铜元素和亲硫铁族无素对矿化有利。据此，为进一步成矿预测、评价蚀变破碎带的含矿性提供依据。     

从辽宁东、西部地质对比论郯庐断裂的平移运动

辽宁东、西部地质上诸多差异并非是原地升降运动造成的，而是二个异地岩块经郯庐断裂大规模左旋平移运动迁移到一起的结果。辽东半岛原曾与鲁西－徐淮地区处于相同的古纬度。郯庐断裂北延的主干断裂应是抚顺－敦化断裂，它在辽宁境内是地层区划的重要界线。郯庐断裂在太古宙末期即已出现，曾多次变换其平移方向，最近一次大规模左行平移活动的高峰期是在晚侏罗世晚期－早白垩世，结束于孙家湾组或泉头组堆积之前。     

密度和压缩系数的散射层析成像法

本文在速度成像的基础上研究了同时对密度和压缩系数成像的散射波层析成像法.对不同散射角度的计算可以得到一系列反演图像,拟合这些图像,从而可以有效地达到对密度和压缩系数（或速度）成像的目的.与单纯的速度成像相比,增加了反演的难度.首先是对资料的方位性要求增加;其次是对资料的利用率下降.即便如此,从对较少量的炮点和检波点资料的数值计算来看,仍取得了满意的成像结果.我们对组成字母“A”的散射体结构进行了成像计算,结果能够同时再现密度和压缩系数,成像清晰,表明了方法的可行性,并能应用于复杂结构的成像问题.