Instability of wave propagation in saturated poroelastoplastic media

In the present work, stationary discontinuities and fluttery instabilities of wave propagation in saturated poro‐elastoplastic media are analysed in the frame of Biot theory. The generalized Biot formulations are particularly employed for simulating non‐linear coupled hydro‐mechanical behaviour of the media. Inertial coupling effect between the solid and the fluid phases of the media is also taken into account. The non‐associated Drucker–Prager criterion to describe non‐linear constitutive behaviour of pressure dependent elasto‐plasticity for the solid skeleton of the media is particularly considered. With omission of compressibility of solid grains and the pore fluid, the critical conditions of stationary discontinuities and flutter instabilities occurring in wave propagation are given in explicit forms. It is shown that when the stationary discontinuity is triggered at the surface of discontinuity there still may exist real wave speeds. The wave speeds across the stationary discontinuity surface entirely cease to be real only in non‐associated plasticity, certain ranges of value of Poisson's ratio and when compression stress normal to the surface of discontinuity dominates the stress state at the surface. It is also indicated that the fluttery instabilities, under which some wave speeds cease to be real even in strain hardening stage, may occur prior to stationary discontinuities only for non‐associated plasticity under certain conditions. These conditions are: (1) both the porosity and the Poisson's ratio possess relatively low values and (2) the deviatoric part of the effective stress normal to the surface of discontinuity is compressive. A region in the porosity–Poisson's ratio plot, in which fluttery instabilities are possible to occur, is given. Copyright © 2002 John Wiley & Sons, Ltd.     

Validating the ability of the discontinuous deformation analysis method to model normal P‐wave propagation across rock fractures

The effects of fractures on wave propagation problems are increasingly abstracting the attention of scholars and engineers in rock engineering field. This study aims to fully validate the ability of discontinuous deformation analysis (DDA) to model normal P‐wave propagation across rock fractures. The effects of a single fracture and multiple parallel fractures are all tested. The results indicate that DDA can accurately reflect the fracture effects, including the fractures stiffness, the fracture spacing and the fracture number, and the effects of incident wave frequency on one‐dimensional P‐wave propagation problems. Thus, DDA is able to deal well with normal incident P‐wave propagation problems. Copyright © 2017 John Wiley & Sons, Ltd.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.     

A general viscous‐spring transmitting boundary for dynamic analysis of saturated poroelastic media

A time‐domain viscous‐spring transmitting boundary is presented for transient dynamic analysis of saturated poroelastic media with linear elastic and isotropic properties. The u–U formulation of Biot equation in cylindrical coordinate is adopted in the derivation. By this general viscous‐spring boundary, the effective stress and pore fluid pressure on the truncated boundary of the computational area are replaced by a set of continuously distributed spring and dashpot elements, of which the parameters are defined assuming an infinite permeability and considering the two dilatational waves. Numerical examples demonstrate good absorption of both the two cylindrical dilatational waves by the proposed ‘drained’ boundary. For general two‐dimensional wave propagation problems, acceptable accuracy can still be achieved by setting the proposed boundary relatively far away from the scatter. Numerical comparison shows that the results obtained by using this boundary are more accurate for all permeability values than those by the traditional viscous‐spring or viscous boundaries established for u–U formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

The recognition of former melt flux through high‐strain zones

High‐strain zones are potential pathways of melt migration through the crust. However, the identification of melt‐present high‐strain deformation is commonly limited to cases where the interpreted volume of melt “frozen” within the high‐strain zone is high (>10%). In this contribution, we examine high‐strain zones in the Pembroke Granulite, an otherwise low‐strain outcrop of volcanic arc lower crust exposed in Fiordland, New Zealand. These high‐strain zones display compositional layering, flaser‐shaped mineral grains, and closely spaced foliation planes indicative of high‐strain deformation. Asymmetric leucosome surrounding peritectic garnet grains suggest deformation was synchronous with minor amounts of in situ partial melting. High‐strain zones lack typical mylonite microstructures and instead display typical equilibrium microstructures, such as straight grain boundaries, 120° triple junctions, and subhedral grain shapes. We identify five key microstructures indicative of the former presence of melt within the high‐strain zones: (a) small dihedral angles of interstitial phases; (b) elongate interstitial grains; (c) small aggregates of quartz grains with xenomorphic plagioclase grains connected in three dimensions; (d) fine‐grained, K‐feldspar bearing, multiphase aggregates with or without augite rims; and (e) mm‐ to cm‐scale felsic dykelets. Preservation of key microstructures indicates that deformation ceased as conditions crossed the solidus, breaking the positive feedback loop between deformation and the presence of melt. We propose that microstructures indicative of the former presence of melt, such as the five identified above, may be used as a tool for recognising rocks formed during melt‐present high‐strain deformation where low (<5%) volumes of leucosome are “frozen” within the high‐strain zone.     

Theoretical and numerical study of the steady‐state flow through finite fractured porous media

This paper investigates the two‐dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady‐state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi‐region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked. Copyright © 2013 John Wiley & Sons, Ltd.     

Breaking wave‐induced response and instability of seabed around caisson breakwater

Breaking‐wave‐induced dynamic response and instability of seabed around a caisson breakwater are investigated. A seabed‐rubble‐breakwater system is modeled using finite elements. The impact response of the porous seabed and rubble foundation is assumed to be governed by the coupled Biot equations, and three possible formulations are considered with respect to the inclusion of inertial terms. The response is presented in terms of shear stress and pore pressure distributions at three locations underneath the breakwater. The effect of seabed and wave parameters and the inertial terms on the impact response is investigated through parametric studies. Analyses show that usually partly dynamic formulation yields the largest response amplitudes as compared to the fully dynamic formulation, which is the most complete form. The instability of seabed and rubble mound as a result of instantaneous liquefaction is also studied. Breaking wave‐induced pressures in some cases are found to cause liquefaction in the rubble and the seabed. The effect of some parameters on the instability is found to be significant. Copyright © 2011 John Wiley & Sons, Ltd.     

A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical analysis of 1‐D compression wave propagation in saturated poroelastic media

A numerical procedure is presented for the simulation of 1‐D compression wave propagation in saturated poroelastic media. The media are modelled as a two‐phase system consisting of compressible fluid and solids. Viscous coupling forces resulting from the relative motion between phases are characterized as Darcy type. The numerical procedure can account for effects of axial strain, nonlinear material behaviour, and various drained and undrained boundary conditions. Time integration is carried out explicitly and isothermal conditions are assumed. The method is capable of modelling shock wave fronts without introducing artificial viscosity. Numerical results are in close agreement with analytical solutions for several simplified cases and indicate that mass coupling may have important effects on fluid velocity and wave speed. Corresponding effects on solid velocity and wave speed are much smaller. Numerical results also indicate that damping occurs in a saturated poroelastic column and is dependent on the value of hydraulic conductivity. Copyright © 2007 John Wiley & Sons, Ltd.     

Calculating the internodal transmissibilities using finite analytic method and its application for multi‐phase flow in heterogeneous porous media

In the traditional numerical reservoir simulations, the internodal transmissibility is usually defined as the harmonic mean of the permeabilities of the adjacent grids. This definition underestimates the phase flux and the speed of the saturation front, especially for the strong heterogeneous case. In this article, the internodal transmissibility is recalculated according to the nodal analytic solution. The redefined internodal transmissibility can be used directly to calculate the multiphase flow in the numerical reservoir simulations. Numerical examples show that, compared to the traditional numerical methods, the proposed scheme makes the convergences much faster as the refinement parameter increases, and the accuracy is independent of the heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd.     

An elasto‐plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling

This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two‐phase soil model is sufficient, the simulation of compressed air support demands the use of a three‐phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil—the soil skeleton, the fluid and the gaseous phase—and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto‐plastic, cam–clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY 's law and the soil–water characteristic curve after VAN GENUCHTEN . Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. Copyright © 2009 John Wiley & Sons, Ltd.     

Transverse and longitudinal fluid flow modelling in fractured porous media with non‐matching meshes

A new discrete fracture model is introduced to simulate the steady‐state fluid flow in discontinuous porous media. The formulation uses a multi‐layered approach to capture the effect of both longitudinal and transverse permeability of the discontinuities in the pressure distribution. The formulation allows the independent discretisation of mesh and discontinuities, which do not need to conform. Given that the formulation is developed at the element level, no additional degrees of freedom or special integration procedures are required for coupling the non‐conforming meshes. The proposed model is shown to be reliable regardless of the permeability of the discontinuity being higher or lower than the surrounding domain. Four numerical examples of increasing complexity are solved to demonstrate the efficiency and accuracy of the new technique when compared with results available in the literature. Results show that the proposed method can simulate the fluid pressure distribution in fractured porous media. Furthermore, a sensitivity analysis demonstrated the stability regarding the condition number for wide range values of the coupling parameter.     

爆炸应力波作用下缺陷介质裂纹扩展的动态分析

采用透射式焦散线测试系统,进行爆炸应力波作用下缺陷介质裂纹扩展试验,研究了含与炮孔共线的预制裂隙介质裂纹扩展速度、加速度、裂纹尖端动态应力强度因子和动态能量释放率的变化规律以及它们之间的变化关系。试验结果表明,在爆炸应力波作用下裂隙两端产生了两条翼裂纹A、B,翼裂纹A的长度较翼裂纹B长,两条翼裂纹向相反的方向扩展;在翼裂纹扩展过程中,存在着加速与减速的过程,扩展速度瞬间达到峰值,其后逐渐振荡下降;动态应力强度因子也呈现瞬间达最大值到逐渐减小连续振荡变化的趋势,动态应力强度因子 > ;翼裂纹尖端的动态能量释放率对裂纹扩展具有驱动作用。     

Numerical analysis of a one‐dimensional infiltration problem in unsaturated soil by a seepage–deformation coupled method

A multiphase coupled elasto‐viscoplastic finite element analysis formulation, based on the theory of porous media, is used to describe the rainfall infiltration process into a one‐dimensional soil column. Using this framework, we have numerically analyzed the generation of pore water pressure and deformations when rainfall is applied to the soil. A parametric study, including rainfall intensity, soil–water characteristic curves, and permeability, is carried out to observe their influence on the changes in pore water pressure and volumetric strain. From the numerical results, it is shown that the generation of pore water pressure and volumetric strain is mainly controlled by material parameters α and n′ that describe the soil–water characteristic curve. A comparison with the laboratory results shows that the proposed method can describe very well the characteristics observed during the experiments of one‐dimensional water infiltration into a layered unsaturated soil column. Copyright © 2010 John Wiley & Sons, Ltd.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

Discontinuous deformation analysis with second‐order finite element meshed block

The discontinuous deformation analysis (DDA) with second‐order displacement functions was derived based on six‐node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second‐order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright © 2006 John Wiley & Sons, Ltd.     

A four‐node plane parametric element based on quadrilateral area coordinate and its application to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials

A four‐node plane parametric element AQGβ6‐I is constructed on the basis of the quadrilateral area coordinate, the generalized conforming principle and the projection technique with a penalty factor β within an interval of 0–1. When β = 0, the element has excellent bending performance. When β = 1, the element can pass patch test strictly; its performance is as good as many famous elements. When β value is between 0 and 1, such as β = 0.5, the element can arrive at a compromise between (relatively) low sensitivity to mesh distortion and perfect convergence. The work provides an illuminating method to alleviate a difficult problem in finite element modelling using the four‐node quadrilateral element, which can pass the strict patch test, but has poor performance in bending dominated problem; on the contrary, it has excellent performance in bending dominated problem but cannot pass the strong patch test. The AQGβ6‐I with the convergence formulation (β = 1) is then applied to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials. The computational examples are carried out to demonstrate that the AQGβ6‐I (β = 1) element is not only stable, reliable and efficient but also of high accuracy. The present study provides a good applicable element for finite element simulations of solid‐deformation/fluid‐flow for porous geomaterials. Copyright © 2014 John Wiley & Sons, Ltd.