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.     

松辽盆地西部张裂缝预测的应力场方法

以松辽盆地地质资料为基础，介绍了应力场和张裂缝预测的计算方法。通过了各种岩性的张破裂概率隶属函数，预测松辽盆地酉部张裂缝区的分布。据此，为今后的油气勘探提出了几点认识和建议。     

Magnetic anomalies in the canary basin and the Mesozoic evolution of the central North Atlantic

The data from a recent magnetic compilation by Verhoefet al. (1991) off west Africa were used in combination with data in the western Atlantic to review the Mesozoic plate kinematic evolution of the central North Atlantic. The magnetic profile data were analyzed to identify the M-series sea floor spreading anomalies on the African plate. Oceanic fracture zones were identified from magnetic anomalies and seismic and gravity measurements. The identified sea floor spreading anomalies on the African plate were combined with those on the North American plate to calculate reconstruction poles for this part of the central Atlantic. The total separation poles derived in this paper describe a smooth curve, suggesting that the motion of the pole through time was continuous. Although the new sea floor spreading history differs only slightly from the one presented by Klitgord and Schouten (1986), it predicts smoother flowlines. On the other hand, the sea floor spreading history as depicted by the flowlines for the eastern central Atlantic deviates substantially from that of Sundvik and Larson (1988). A revised spreading history is also presented for the Cretaceous Magnetic Quiet Zone, where large changes in spreading direction occurred, that can not be resolved when fitting magnetic isochrons only, but which are evident from fracture zone traces and directions of sea floor spreading topography.Deceased 11 November 1991     

多源遥感数据综合解译鄂尔多斯盆地杭锦旗地区地质构造

利用多源遥感数据假彩色合成、融合及纹理分析等增强处理方法提取研究区构造信息,进而对研究区进行综合解译;通过分析水系、色调、纹理、地貌及岩性等特征,判断出杭锦旗地区存在一小一大、内外相套的2个环形构造,发育的北西向、北东向2组共轭断层和一组北北西向断层,与环形构造相互构架,构成研究区特殊的构造体系。经分析预测,这些构造是受周边南北向构造应力共同挤压而形成。     

葛店矿双庙扩大区三维地震勘探

葛店煤矿双庙扩大区位于豫、皖两省交界处。勘探区为一轴向北北东向的不对称向斜构造,地层倾角26°～30°,测区深部有岩浆岩侵入体,严重影响煤层赋存形态;地表条件复杂,村庄密集、河流较多,测区东侧塌陷区水塘大面积分布．三维地震勘探野外施工难度大。本区地震勘探观测系统设计为12线18炮制,为避免偏移归位及叠加次数降低等问题,在向斜轴部两侧、村子周边及河岸处适当加密炮点,并在塌陷区利用钢钎插置检波器以保证CDP点完整性。数据处理采取了叠前反褶积、叠前时间偏移等技术,数据处理效果显著。遵循多波组对比、多个数据体综合解释的原则,以纵向、横向和任意时间剖面相结合,充分利用三维可视化技术进行地震资料解释。本次勘探成果查明了主采煤层三2^2、二2煤层的构造形态及埋藏深度;解释落差5m以上断层34条,其中修改原有断层5条;另外新发现小于5m的异常断点22个。经巷道验证煤层底板标高误差0．43％～1．96％,巷道已揭露断层7条,与解释成果基本一致。