Fully coupled hydraulic fracture simulation using the improved element partition method     

Shujun Peng  Zhennan Zhang  Jianye Mou  Bing Zhao  Zhiyuan Liu  Jiading Wang 《国际地质力学数值与分析法杂志》2019,43(1):441-460

The improved element partition method (IEPM) is a newly developed fracture simulation approach. IEPM allows a fracture to run across an element without introducing extra degrees of freedom. It can also simulate any number of fractures in a prescribed mesh without remeshing. In this study, the IEPM is extended to hydraulic fracture simulation. First, the seepage and volumetric storage matrix of a cracked element are derived using virtual nodes (the intersection points of a crack with element edges). Subsequently, the fully coupled hydromechanical equation is derived for this cracked element. To eliminate the extra degrees of freedom (virtual nodal quantities), the water pressure and displacement of the virtual nodes are associated with their adjacent nodes through least squares interpolation. Finally, the fully coupled equation in terms of nodal quantities is obtained. The verification cases validate the method. By using this method, the field-scale hydraulic fracturing process is well simulated. The proposed approach is simple and efficient for field-scale hydraulic fracture simulation.  相似文献   

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

Ramin Pakzad  Shanyong Wang  Scott W. Sloan 《国际地质力学数值与分析法杂志》2020,44(10):1472-1494

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.  相似文献   

Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law          下载免费PDF全文

Ahmad Hajjar  Luc Scholtès  Constantin Oltéan  Michel Antoine Buès 《水文研究》2018,32(16):2510-2525

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.  相似文献   

基于GPS应变、地震应变率与震源应力场对帕米尔高原现今构造变形特征的分析          下载免费PDF全文

潘正洋  邵志刚  周云  王洵  解孟雨  艾萨·伊斯马伊力 《地球物理学报》2020,63(3):1143-1154

研究帕米尔高原的构造变形特征对于理解印度板块向北推挤过程中的应变分配方式以及应力转换模式具有重要的意义.本文利用区域GPS应变场、地震应变场与震源应力场分析帕米尔高原的构造形变特征.主要结论为:(1)该区域变形主要以NNW-SSE或近N-S向的挤压为主,在高原内部伴有明显的近ENE-WSW或E-W向拉张,应力方向在帕米尔高原与塔吉克盆地区域呈现逆时针旋转的趋势,而在塔里木盆地则显示几乎与帕米尔高原的一致的应力状态,这可能与两侧盆地块体的强度差异有关.(2)安德森断层参数A∅显示帕米尔高原北缘与西侧区域为逆断层应力状态,在高原内部为正断层应力状态,这与GPS应变的结果显示的应变主要集中在主帕米尔断裂与阿莱谷地附近而在高原内部应变较低是一致的,另外应力在喀喇昆仑断裂北段的方向基本平行于断层走向,以及断层北端较低的滑动速率,这说明了地壳挤压缩短可能是帕米尔高原主要的的构造变形特征,并不支持由于边界走滑断裂导致的应变分异或者块体挤出的模式.(3)综合考虑地震应变方向与SHmax从帕米尔北部NNW-SSE方向到天山北部的近N-S方向的转换,GPS应变方向在帕米尔高原两侧盆地都存在不同程度的旋转,应力场安德森参数A∅显示的应力状态以及SKS的结果显示的近ENE-WSW方向,我们认为印度板块向北推挤与天山造山带碰撞导致帕米尔高原不对称的径向逆冲是帕米尔高原现今构造变形的主要成因与构造模式.  相似文献   

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials          下载免费PDF全文

Cássio B. Aguiar  Samir Maghous 《国际地质力学数值与分析法杂志》2018,42(16):2018-2046

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.  相似文献   

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock          下载免费PDF全文

N. Zolfaghari  E. Dontsov  A. P. Bunger 《国际地质力学数值与分析法杂志》2018,42(4):587-617

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.  相似文献   

Surficial fractures in the Navajo sandstone,south-western USA: the roles of thermal cycles,rainstorms, granular disintegration,and iterative cracking     

David B. Loope  Garrison R. Loope  Caroline M. Burberry  Clinton M. Rowe  Gerald C. Bryant 《地球表面变化过程与地形》2020,45(9):2063-2077

Deep (> 5 m) sheeting fractures in the Navajo sandstone are evident at numerous sites in southern Utah and derive from tectonic stresses. Strong diurnal thermal cycles are, however, the likely triggers for shallow (< 0.3 m) sheeting fractures. Data from subsurface thermal sensors reveal that large temperature differences between sensors at 2 and 15 cm depth on clear summer afternoons are as great as those that trigger sheeting fractures in exposed California granite. Extensive polygonal patterns in the Navajo sandstone are composed of surface-perpendicular fractures and were produced by contractile stresses. Numerous studies have shown that porewater diminishes the tensile strength of sandstone. Based on our thermal records, we propose that cooling during monsoonal rainstorms triggers polygonal fracturing of temporarily weakened rock. On steep outcrops, polygonal patterns are rectilinear and orthogonal, with T-vertices. Lower-angle slopes host hexagonal patterns (defined by the dominance of Y-vertices). Intermediate patterns with rectangles and hexagons of similar scale are common. We posit that outcropping fractures are advancing downward by iterative steps, and that hexagons on sandstone surfaces (like prismatic columns of basalt) have evolved from ancestral orthogonal polygons of similar scale. In lava flows, fractures elongate intermittently as they follow a steep thermal gradient (the source of stress) as it rapidly moves through the rock mass. In our model, a steep, surficial thermal gradient descends through unfractured sandstone, but at the slow pace of granular disintegration. Through time, as the friable rock on stable slopes erodes, iterative cracking advances into new space. Hexagonal patterns form as new fractures, imperfectly guided by the older ones, propagate in new directions, and vertices drift into a configuration that minimizes the ratio of fracture length to polygon area. © 2020 John Wiley & Sons, Ltd.  相似文献   

Static and dynamic conceptual model of a complexly fractured crystalline rock aquifer     

Evan Earnest  David Boutt  Larry Murdoch  William P. Clement 《水文研究》2019,33(20):2691-2710

A conceptual model of anisotropic and dynamic permeability is developed from hydrogeologic and hydromechanical characterization of a foliated, complexly fractured, crystalline rock aquifer at Gates Pond, Berlin, Massachusetts. Methods of investigation include aquifer‐pumping tests, long‐term hydrologic monitoring, fracture characterization, downhole heat‐pulse flow meter measurements, in situ extensometer testing, and earth tide analysis. A static conceptual model is developed from observations of depth‐dependent and anisotropic permeability that effectively compartmentalizes the aquifer as a function of foliation intensity. Superimposed on the static model is dynamic permeability as a function of hydraulic head in which transient bulk aquifer transmissivity is proportional to changes in hydraulic head due to hydromechanical coupling. The dynamic permeability concept is built on observations that fracture aperture changes as a function of hydraulic head, as measured during in situ extensometer testing of individual fractures, and observed changes in bulk aquifer transmissivity as determined from earth tides during seasonal changes in hydraulic head, with higher transmissivity during periods of high hydraulic head, and lower transmissivity during periods of relatively lower hydraulic head. A final conceptual model is presented that captures both the static and dynamic properties of the aquifer. The workflow presented here demonstrates development of a conceptual framework for building numerical models of complexly fractured, foliated, crystalline rock aquifers that includes both a static model to describe the spatial distribution of permeability as a function of fracture type and foliation intensity and a dynamic model that describes how hydromechanical coupling impacts permeability magnitude as a function of hydraulic head fluctuation. This model captures important geologic controls on permeability magnitude, anisotropy, and transience and therefor offers potentially more reliable history matching and forecasts of different water management strategies, such as resource evaluation, well placement, permeability prediction, and evaluating remediation strategies.  相似文献   

京西北地区地震重定位及构造特征     

刘燕翔  卫俊  李金  王妍  李峰  王曰风  蔡玲玲 《地震地磁观测与研究》2019,41(1):19-24

采用双差定位法对京西北地区（39.5°—41.5° N，113°—117° E）2013年1月1日至2017年12月31日6 223次有效地震进行精确定位，得到该区震源分布的精细图像和震源深度剖面图。结果显示，重新定位后地震的水平分布更集中，沿断裂带分布特征更加明显，震中在断裂带呈更明显的条带状、簇状分布，地震与线状的深浅断裂构造的关系密切；大部分地震发生在中上地壳，震源分布为典型震源密集区的空间形态，呈纵深约15 km、直径20—40 km的近圆形“厚饼状”。  相似文献   

Seismic fracture evaluation of diaphragm joints in welded beam-to-box column moment connections     

Ching-Yi Tsai  Keh-Chyuan Tsai  Chao-Hsien Li  Chung-Che Wu  Ker-Chun Lin  Sheng-Jhih Jhuang 《地震工程与结构动力学》2020,49(13):1344-1362

Steel box columns are widely used in steel building structures in Taiwan due to their dual strong axes. To transfer the beam-end moment to the column, diaphragm plates of the same thickness and elevations as the beam flanges are usually welded inside the box column. The electro-slag welding (ESW) process is widely used to connect the diaphragms to the column flanges in Taiwan because of its convenience and efficiency. However, ESW may increase the hardness of the welds and heat-affected zones (HAZs), while reducing the Charpy-V notch strength in the HAZ. This situation can cause premature fracture of the diaphragm-to-column flange welds before a large plastic rotation is developed in the beam-to-box column joints. To quantify the critical eccentricity and the effectiveness of fracture prediction, this study uses fracture prediction models and finite element model (FEM) analysis to correlate the test results. In this study, two beam-to-box column connection subassembly tests are conducted with different loading protocols and ESW chamber shapes. To implement a fracture prediction model, the material parameters are established from circumferential notched tensile tests and FEM analysis. Test results indicate that the fracture instances can be predicted on the basis of the cumulative plastic deformation in the HAZs. Analytical results indicate that fracture instances and locations are sensitive to the relative locations of the ESW joints and beam flange. Tests also confirm that the possible fracture of the diaphragm-to-column flange joints can be mitigated by enlarging the chamber of the ESW joint.  相似文献