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.     

浅谈项目投资失败的原因及对策

地勘单位在向企业化经营转变的过程中 ,投资兴办了许多企业 ,但不少项目以失败告终。文章分析探讨了失败的原因 ,并提出相应的对策     

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。     

广西老厂铅锌矿床地质特征及其成因探讨

本文是在专题研究基础上,探讨广西老厂铅锌矿床地质特征和矿床成因。该矿床位于海洋山复式背斜南段的老厂穹窿构造核部,铅锌矿化受构造、地层和岩性控制。矿体呈脉状,产于NE向组张扭性断裂构造中;围岩为寒武系白云岩,板岩、砂岩;矿石类型以锌为主,矿物成分简单,以闪锌矿、方铅矿与石英、白云石为主,具充填、交代矿石结构、构造,矿石平均品位含Zn9.94%、Pb1.50%;围岩蚀变主要为硅化、绢云母化和碳酸盐化。据地层岩石元素丰度值、稀土元素配分和稳定同位素数据、资料,探讨了成矿物质来源于围岩,热液主要来自大气降水。因此,认为本矿床实属产于寒武系轻变质岩中的层控矿型大气降水热液铅锌矿床。     

Geological environment conflicts of Kunming Basin and its urban sustainable development

Kunming Basin locates middle of Yunnan altiplano and has a particularity in geography,topographic and geological environment.With the urban dilation quickly,add the reason of the unreasonable city layout,conflicts between environment and urban resources consumption become shrill increasingly.It is human being activities that lead to vulnerability and depravation of geological environment in local.Take a few examples on geological environment to expatiate relationship between urban construction and geological environment carrying capacity,and find a way how to make a better plan for urban sustainable development to achieve new balance between man and nature in local.     

山东省区域地质构造演化探讨

山东省区域地质构造演化分为5个阶段.①陆核形成阶段形成太古宙高级区,地壳分异成稳定的花岗岩穹窿和活动的绿岩带,第一次克拉通化完成.②陆块发生形成阶段地壳向刚性发展,在华北陆核硅铝壳的基础上先后有3次张开、闭合裂谷作用,第二次克拉通化完成.这一阶段演化在鲁西地区主要表现为挤压作用,形成大量造山花岗岩;鲁东地区则以拉张作用为主,形成海槽,产生沉积.③秦昆洋形成演化阶段四堡期沿鲁东南部地壳拉张,在华北板块与扬子板块间形成秦昆洋.晋宁期秦昆洋关闭,华北板块与扬子板块对接碰撞,沿胶南造山带产生大量同碰撞花岗岩,同时产生超高压变质作用及形成丰富多彩的碰撞构造.晋宁运动最终形成统一的原始中国古陆,第三次克拉通化完成.④陆块发展阶段鲁西地区地壳频繁升降,形成广泛的海相及海陆交互相沉积;鲁东地区则以造山抬升为主,地层沉积较少.⑤滨太平洋发展阶段该阶段的主要特征是断块构造发育,形成盆岭构造格局,产生大陆边缘花岗岩,构造体系由古亚洲构造域转向滨太平洋构造域.