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Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution 
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下载免费PDF全文 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
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The model proposed in this article relates permeability to porosity measurements that can easily be performed in the laboratory. The pore size distribution (PSD) curve is updated with strains and damage. The updated volumetric fractions of natural pores and cracks are introduced in the expression of permeability. Contrary to classical permeability models based on PSD integrations, the model proposed in this article accounts for possible changes in the porosity modes: one mode for undamaged samples and two modes for cracked samples. The proposed approach also accounts for varying states of damage, as opposed to classical fracture network models, in which the cracks pattern is fixed. The only material parameters that are required to describe the microstructure are the lower and upper bounds of the pores size for both natural pores and cracks. All the other PSD parameters involved in the model are related to macroscopic parameters that can easily be determined in the laboratory, such as the initial void ratio. The framework proposed in this article can be used in any damage constitutive model to determine the permeability of a brittle porous medium. Drained triaxial compression tests have been simulated. Before cracks initiation, permeability decreases while the larger natural pores are getting squeezed. After the occurrence of damage, permeability grows due to the increase of cracks density. The model performs well to represent the influence of the confining pressure on damage evolution and permeability variations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Xianda Shen Jihui Ding Chlo Arson Judith S. Chester Frederick M. Chester 《国际地质力学数值与分析法杂志》2021,45(1):28-44
The dependence of rock behavior on the deformation rate is still not well understood. In salt rock, the fundamental mechanisms that drive the accumulation of irreversible deformation, the reduction of stiffness, and the development of hysteresis during cyclic loading are usually attributed to intracrystalline plasticity and diffusion. We hypothesize that at low pressure and low temperature, the rate‐dependent behavior of salt rock is governed by water‐assisted diffusion along grain boundaries. Accordingly, a chemo‐mechanical homogenization framework is proposed in which the representative elementary volume (REV) is viewed as a homogeneous polycrystalline matrix that contains sliding grain‐boundary cracks. The slip is related to the mass of salt ions that diffuse along the crack surface. The relationship between fluid inclusion‐scale and REV‐scale stresses and strains is established by using the Mori–Tanaka homogenization scheme. It is noted from the model that a lower strain rate and a larger number of sliding cracks enhance stiffness reduction and hysteresis. Thinner sliding cracks (i.e., thinner brine films) promote stiffness reduction and accelerate stress redistributions. The larger the volume fraction of the crack inclusions, the larger the REV deformation and the larger the hysteresis. Results presented in this study shed light on the mechanical behavior of salt rock that is pertinent to the design of geological storage facilities that undergo cyclic unloading, which could help optimize the energy production cycle with low carbon emissions. 相似文献
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This paper deals with the evaluation of seismic site effects due to the local topographical and geotechnical characteristics. The amplification of surface motions is calculated by a numerical method combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The numerical technique is improved by time truncation. In the first part of this article, the accuracy and the relevance of this optimized method are presented. Moreover, parametric studies are done on slopes, ridges and canyons to characterize topographical site effects. The second part deals with sedimentary valleys. The complexity of the combination of geometrical and sedimentary effects is underlined. Extensive parametrical studies are done to discriminate the topographical and geotechnical effects on seismic ground movement amplifications in two-dimensional irregular configurations. Characteristic coefficients are defined to predict the amplifications of horizontal displacements. The accuracy of this quantitative evaluation technique is tested and discussed. 相似文献
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The damage model presented in this article (named ‘THHMD’ model) is dedicated to non‐isothermal unsaturated porous media. It is formulated by means of three independent strain state variables, which are the thermodynamic conjugates of net stress, suction and thermal stress. The damage variable is a second‐order tensor. Stress/strain relationships are derived from Helmholtz free energy, which is assumed to be the sum of damaged elastic potentials and ‘crack‐closure energies’. Damage is assumed to grow with tensile strains due to net stress, with pore shrinkage due to suction and with thermal dilatation. Specific conductivities are introduced to account for the effects of cracking on the intensification and on the orientation of liquid water and vapor flows. These conductivities depend on damage and internal length parameters. The mechanical aspects of the THHMD model are validated by comparing the results of a triaxial compression test with experimental measurements found in the literature. Parametric studies of damage are performed on three different heating problems related to nuclear waste disposals. Several types of loading and boundary conditions are investigated. The thermal damage potential is thoroughly studied. The THHMD model is expected to be a useful tool in the assessment of the Excavation Damaged Zone, especially in the vicinity of nuclear waste repositories. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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A method is proposed to calculate the distribution of energy during the quasi-static confined comminution of particulate assemblies. The work input, calculated by integrating the load-displacement curve, is written as the sum of the elastic deformation energy, the breakage energy and the redistribution energy. Experimental results obtained on samples subjected to compression stresses ranging between 0.4 and 92 MPa are used to calibrate the model. The elastic energy stored in the samples is obtained by simulating the compression test on the final particle size distributions (PSDs) with the discrete element method and by extracting the contact forces. A PSD evolution law is proposed to account for particle breakage. The PSD is related to the total particle surface in the sample, which allows calculating the breakage energy. The redistribution energy, which comprises the kinetic energy of particles being rearranged and the friction energy dissipated at contacts, is obtained by subtracting the elastic energy and breakage energy from the work input. Results show that: (1) at least 60% of the work input is dissipated by particle redistribution; (2) the fraction of elastic deformation energy increases, and the fraction of redistribution energy decreases as the compression stress increases; (3) the breakage energy accounts for less than 5% of the total input energy, and this value is independent of the compressive stress; (4) the energy dissipated by redistribution is between 14 and 30 times larger than the breakage energy. 相似文献
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This paper deals with the evaluation of seismic site effects due to the local topographical and geotechnical characteristics. The amplification of surface motions is calculated by a numerical method combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The numerical technique is improved by time truncation. In the first part of this article, the accuracy and the relevance of this optimized method are presented. Moreover, parametric studies are done on slopes, ridges and canyons to characterize topographical site effects. The second part deals with sedimentary valleys. The complexity of the combination of geometrical and sedimentary effects is underlined. Extensive parametrical studies are done to discriminate the topographical and geotechnical effects on seismic ground movement amplifications in two-dimensional irregular configurations. Characteristic coefficients are defined to predict the amplifications of horizontal displacements. The accuracy of this quantitative evaluation technique is tested and discussed. 相似文献