Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution          下载免费PDF全文

Wencheng Jin  Hao Xu  Chloé Arson  Seth Busetti 《国际地质力学数值与分析法杂志》2017,41(2):223-250

We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

A methodology for regionalizing 3‐D effective porosity at watershed scale in crystalline aquifers          下载免费PDF全文

Benoît Dewandel  Yvan Caballero  Jérôme Perrin  Alexandre Boisson  Fabrice Dazin  Sylvain Ferrant  Subash Chandra  Jean‐Christophe Maréchal 《水文研究》2017,31(12):2277-2295

An innovative approach for regionalizing the 3‐D effective porosity field is presented and applied to two large, overexploited, and deeply weathered crystalline aquifers located in southern India. The method derives from earlier work on regionalizing a 2‐D effective porosity field in that part of an aquifer where the water table fluctuates, which is now extended over the entire aquifer using a 3‐D approach. A method based on geological and geophysical surveys has also been developed for mapping the weathering profile layers (saprolite and fractured layers). The method for regionalizing 3‐D effective porosity combines water table fluctuation and groundwater budget techniques at various cell sizes with the use of satellite‐based data (for groundwater abstraction), the structure of the weathering profile, and geostatistical techniques. The approach is presented in detail for the Kudaliar watershed (983 km²) and tested on the 730 km² Anantapur watershed. At watershed scale, the effective porosity of the aquifer ranges from 0.5% to 2% in Kudaliar and between 0.3% and 1% in Anantapur, which agrees with earlier works. Results show that (a) depending on the geology and on the structure of the weathering profile, the vertical distribution of effective porosity can be very different and that the fractured layers in crystalline aquifers are not necessarily characterized by a rapid decrease in effective porosity and (b) that the lateral variations in effective porosity can be larger than the vertical ones. These variations suggest that within a same weathering profile, the density of open fractures and/or degree of weathering in the fractured zone may significantly vary from a place to another. The proposed method provides information on the spatial distribution of effective porosity that is of prime interest in terms of flux and contaminant transport in crystalline aquifers. Implications for mapping groundwater storage and scarcity are also discussed, which should help in improving groundwater resource management strategies.  相似文献   

A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching          下载免费PDF全文

Y. Jia  H.B. Bian  S.Y. Xie  N. Burlion  J.F. Shao 《国际地质力学数值与分析法杂志》2017,41(18):1848-1869

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic‐plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.  相似文献   

On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales          下载免费PDF全文

Carmine Fallico  Samuele De Bartolo  Massimo Veltri  Gerardo Severino 《水文研究》2016,30(13):2366-2372

We study the scale dependence of the saturated hydraulic conductivity K_s through the effective porosity n_e by means of a newly developed power‐law model (PLM) which allows to use simultaneously measurements at different scales. The model is expressed as product between a single PLM (capturing the impact of the dominating scale) and a characteristic function κ^? accounting for the correction because of the other scale(s). The simple (closed form) expression of the κ^?‐function enables one to easily identify the scales which are relevant for K_s. The proposed model is then applied to a set of real data taken at the experimental site of Montalto Uffugo (Italy), and we show that in this case two (i.e. laboratory and field) scales appear to be the main ones. The implications toward an important application (solute transport) in Hydrology are finally discussed. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion          下载免费PDF全文

Jiazhong Qian  Lei Ma  Hongbin Zhan  Qiankun Luo  Xiao Wang  Mu Wang 《水文研究》2016,30(11):1718-1726

Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Re_c) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Re_c for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Re_c decreases with the increasing E, and the relationship between the logarithm of Re_c and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Re_c and d for a given E value is vague, and Re_c becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (J_i) of J increases monotonically with Re, whereas the viscous component (J_v) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Re_c, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

How preferential flow delivers pre‐event groundwater rapidly to streams     

Stephen R.H. Worthington 《水文研究》2019,33(17):2373-2380

Groundwater often accounts for a substantial fraction of flood hydrographs, but the processes responsible for this have been unclear. However, many aquifers have preferential flow and this explains how aquifers can be so responsive. In bedrock aquifers, weathering enhances the connectivity and apertures along the most efficient flow paths and hence enhances the permeability. This results in celerities and velocities of the preferential flow in these dual‐porosity aquifers that are two to three orders of magnitude higher than if the aquifers behaved as single‐porosity media. The celerities have been determined from artificial and natural flood pulses, from tidal lags, and from pumping tests. Preferential‐flow velocities have been calculated from tests using applied tracers. Celerities in bedrock aquifers are typically one to two orders of magnitude faster than velocities. The ubiquitous preferential flow in aquifers provides an additional explanation, besides groundwater ridging, for the rapid release of groundwater to streams during storm events.  相似文献   

Large‐scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method          下载免费PDF全文

A. Verde  A. Ghassemi 《国际地质力学数值与分析法杂志》2016,40(6):865-886

An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time‐marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large‐scale problems have accounted only for elastic rocks, neglecting the fluid leak‐off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large‐scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field‐scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

Cracking risk of partially saturated porous media—Part I: Microporoelasticity model     

Bernhard Pichler  Luc Dormieux 《国际地质力学数值与分析法杂志》2010,34(2):135-157

Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. This is the motivation to develop a thermodynamics‐based microporoelasticity model for the assessment of cracking risk in partially saturated porous geomaterials. The study refers to 3D representative volume elements of porous media, including a two‐scale double‐porosity material with a pore network comprising (at the mesoscale) 3D mesocracks in the form of oblate spheroids, and (at the microscale) spherical micropores of different sizes. Surface tensions prevailing in all interfaces between solid, liquid, and gaseous matters are taken into account. To establish a thermodynamics‐based crack propagation criterion for a two‐scale double‐porosity material, the potential energy of the solid is derived, accounting—in particular—for mesocrack geometry changes (main original contribution) and for effective micropore pressures, which depend (due to surface tensions) on the pore radius. Differentiating the potential energy with respect to crack density parameter yields the thermodynamical driving force for crack propagation, which is shown to be governed by an effective macrostrain. It is found that drying‐related stresses in partially saturated mesocracks reduce the cracking risk. The drying‐related effective underpressures in spherical micropores, in turn, result in a tensile eigenstress of the matrix in which the mesocracks are embedded. This way, micropores increase the mesocracking risk. Model application to the assessment of cracking risk during drying of argillite is the topic of the companion paper (Part II). Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

Displacement velocity effects on rock fracture shear strengths     

《Journal of Structural Geology》2016

Triaxial shear tests are performed to assess the effects of displacement velocity and confining pressure on shear strengths and dilations of tension-induced fractures and smooth saw-cut surfaces prepared in granite, sandstone and marl specimens. A polyaxial load frame is used to apply confining pressures between 1 and 18 MPa with displacement velocities ranging from 1.15 × 10⁻⁵ to 1.15 × 10⁻² mm/s. The results indicate that the shearing resistances of smooth saw-cut surfaces tend to be independent of the displacement velocity and confining pressure. Under each confinement the peak and residual shear strengths and dilation rates of rough fractures increase with displacement velocities. The sheared-off areas increase when the confining pressure increases, and the displacement rate decreases. The velocity-dependent shear strengths tend to act more under high confining pressures for the rough fractures in strong rock (granite) than for the smoother fractures in weaker rocks (sandstone and marl). An empirical criterion that explicitly incorporates the effects of shear velocity is proposed to describe the peak and residual shear strengths. The criterion fits well to the test results for the three tested rocks.  相似文献   

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation     

《Computers and Geotechnics》2016

A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions.  相似文献