Numerical solutions for flow in porous media

A numerical approach is proposed to model the flow in porous media using homogenization theory. The proposed concept involves the analyses of micro‐true flow at pore‐level and macro‐seepage flow at macro‐level. Macro‐seepage and microscopic characteristic flow equations are first derived from the Navier–Stokes equation at low Reynolds number through a two‐scale homogenization method. This homogenization method adopts an asymptotic expansion of velocity and pressure through the micro‐structures of porous media. A slightly compressible condition is introduced to express the characteristic flow through only characteristic velocity. This characteristic flow is then numerically solved using a penalty FEM scheme. Reduced integration technique is introduced for the volumetric term to avoid mesh locking. Finally, the numerical model is examined using two sets of permeability test data on clay and one set of permeability test data on sand. The numerical predictions agree well with the experimental data if constraint water film is considered for clay and two‐dimensional cross‐connection effect is included for sand. Copyright © 2003 John Wiley & Sons, Ltd.     

黏性土渗透性温度效应实验研究

由于全球气候变暖、城市热岛效应加剧和核废料地质处置等原因,温度对黏性土工程性质的影响日益受到关注。本文在实验的基础上,采用直接测量法,对南京下蜀土、淤泥质土以及混合土3种试样,进行了5°～45°温度下的变水头渗透实验,分析了温度对黏性土渗透性的影响。实验结果表明:温度对3种试样的渗透性均有较大影响。温度越高,渗透性越大;试样的密度越大,渗透系数随温度变化率越低;在3种试样中,混合土的渗透系数高于淤泥质土和下蜀土的对应值,而淤泥质土的渗透系数又略大于下蜀土。最后对黏性土渗透性的温度效应机理进行了分析,认为水的动力黏滞性,黏粒的双电层厚度以及土的微结构三方面因素的共同作用引起了黏性土渗透性的温度效应。     

Simulation of damage–permeability coupling for mortar under dynamic loads

The results reported in this paper deal with the simulation of damage in cohesive geomaterials such as rocks or concrete subjected to dynamic loads. The practical objective is to stimulate the production of tight gas reservoirs with a technique that is an alternative to hydraulic fracturing. The principle is that when subjected to dynamic loads, cohesive materials such as concrete, rocks or ceramics exhibit distributed micro‐cracking as opposed to localised cracking observed under static loads. Hence, a low permeability rock containing gas trapped into occluded pores can be fragmented with the help of dynamic loads, and gas can be extracted in a much more efficient way compared with hydraulic fracturing, where only large macro cracks are formed with very few connections between occluded pores. At the stage of laboratory development of this technique, compressive underwater shock waves have been used to increase the intrinsic permeability of concrete specimens. In a previous study, pressure waves generated by pulsed arc electrohydraulic discharges in water were used in order to induce micro‐cracking and an increase of average permeability of concrete hollow cylinders subjected to confinement stresses (equivalent to geostatic stresses). We discuss here a 3‐D anisotropic constitutive model aimed at describing the dynamic response of these specimens. It is based on rate‐dependent continuum damage constitutive relations. Crack closure effects and damage‐induced anisotropy are included in the model. The directional growth of damage is related to the directional growth of material intrinsic permeability. Numerical simulations of damage induced by shock waves show good agreement with the experiments for various confinement levels of the specimens. Copyright © 2013 John Wiley & Sons, Ltd.     

碳酸盐岩储层参数对微观渗流的影响

针对碳酸盐岩油藏孔隙大小的双峰分布特征,首先利用计算机模拟建立了描述不同孔隙特征的大孔隙网络模型和微孔隙网络模型,在此基础上提出一种耦合算法构建出的同时描述大孔隙和微孔隙特征的碳酸盐岩双孔隙网络模型;然后,基于侵入-逾渗理论,模拟双孔隙网络模型中油水两相流体的一次驱替和二次吸吮过程,并建立了毛细管压力和相对渗透率的求解模型;最后,通过调整双孔隙网络结构参数,模拟水湿油藏条件下碳酸盐岩储层参数对相对渗透率曲线的影响. 结果表明,随着微孔隙比例因子和平均配位数的增加,油相相对渗透率曲线升高;随着双孔隙半径比的增加,油相和水相相对渗透率曲线下降,这对碳酸盐岩油藏渗流机理研究有着重要的指导意义.      

Characterization of clastic rock using a biconcave bond model of DEM

This paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.     

Computational mechanics of the steel–concrete interface

Concrete cracking in reinforced concrete structures is governed by two mechanisms: the activation of bond forces at the steel–concrete interface and the bridge effects of the reinforcement crossing a macro‐crack. The computational modelling of these two mechanisms, acting at different scales, is the main objective of this paper. The starting point is the analysis of the micro‐mechanisms, leading to an appropriate choice of (measurable) state variables describing the energy state in the surface systems: on the one side the relative displacement between the steel and the concrete, modelling the bond activation; on the other hand, the crack opening governing the bridge effects. These displacement jumps are implemented in the constitutive model using thermodynamics of surfaces of discontinuity. On the computational side, the constitutive model is implemented in a discrete crack approach. A truss element with slip degrees of freedom is developed. This degree of freedom represents the relative displacement due to bond activation. In turn, the bridge effect is numerically taken into account by modifying the post‐cracking behaviour of the contact elements representing discrete concrete cracks crossed by a rebar. First simulation results obtained with this model show a good agreement in crack pattern and steel stress distribution with micro‐mechanical results and experimental results. Copyright © 2001 John Wiley & Sons, Ltd.     

砂土力学性质的细观模拟

基于颗粒流理论,对砂土的室内双轴试验和砂土剪切带形成与发展进行了数值模拟,基本再现了砂土试样应力-应变关系。主要研究了颗粒粒径、颗粒摩擦系数等细观参数变化时试样宏观性质的变化情况。对比分析了室内试验和颗粒流数值模拟试验的砂土剪切带特征。同时对比研究了模型试样颗粒粒径、颗粒刚度和摩擦系数等细观参数的变化,对剪切带的形成与发展过程的影响。结果表明：通过颗粒流数值模型试验可以有效模拟砂土剪切带的形成与发展机理。     

Artificial Neural Network Prediction Models for Soil Compaction and Permeability

This paper presents Artificial Neural Network (ANN) prediction models which relate permeability, maximum dry density (MDD) and optimum moisture content with classification properties of the soils. The ANN prediction models were developed from the results of classification, compaction and permeability tests, and statistical analyses. The test soils were prepared from four soil components, namely, bentonite, limestone dust, sand and gravel. These four components were blended in different proportions to form 55 different mixes. The standard Proctor compaction tests were adopted, and both the falling and constant head test methods were used in the permeability tests. The permeability, MDD and optimum moisture content (OMC) data were trained with the soil’s classification properties by using an available ANN software package. Three sets of ANN prediction models are developed, one each for the MDD, OMC and permeability (PMC). A combined ANN model is also developed to predict the values of MDD, OMC, and PMC. A comparison with the test data indicates that predictions within 95% confidence interval can be obtained from the ANN models developed. Practical applications of these prediction models and the necessary precautions for using these models are discussed in detail in this paper.     

Kinematic models for non‐coaxial granular materials. Part I: theory

The purpose of this paper is to present a physically based plasticity model for non‐coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR² model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro‐analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micro‐pure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro–micro mechanical analysis shows that the APR is a non‐linear function of, among other quantities, the macro‐rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double‐sliding free‐rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR² model the APR tensor and the spin tensor are directly linked with non‐coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR² model for a class of dilatant materials, and analyse its material stability. Copyright © 2005 John Wiley & Sons, Ltd.     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Extension of plasticity theory to debonding,grain dissolution,and chemical damage of calcarenites

The mechanical properties of calcarenites are known to be significantly affected by water saturation: both stiffness and strength decrease for wetting in the short term and for chemical dissolution in the long term. Both processes mainly affect bonds among grains: immediately after inundation depositional bonds fall in suspension, whereas diagenetic bonds dissolve more slowly. In this paper, the authors started from the micro‐structural analysis of the weathering processes to conceive a strain hardening hydro‐chemo‐mechanical coupled elastoplastic constitutive model. The concept of extended hardening rules is here enriched: weathering functions have been determined by employing a micro to macro simplified upscaling procedure. Chemical damage is incorporated into the formulation by means of a scalar damage function. Its evolution is also described by using a multiscale approach. A new term is added to the strain rate tensor in order to incorporate the dissolution induced chemical deformations developing once the soft rock is turned into a granular material. A calibration procedure for the constitutive parameters is suggested, and the model is validated by using both coupled and uncoupled chemo‐mechanical experimental test results. Copyright © 2015 John Wiley & Sons, Ltd.     

Prediction of uniaxial compression PFC3D model micro‐properties using artificial neural networks

Artificial neural networks are used to predict the micro‐properties of particle flow code in three dimensions (PFC3D) models needed to reproduce macro‐properties of cylindrical rock samples in uniaxial compression tests. Data for the training and verification of the networks were obtained by running a large number of PFC3D models and observing the resulting macro‐properties. Four artificial networks based on two different architectures were used. The networks used different numbers of input parameters to predict the micro‐properties. Multi‐layer perceptron networks using Young's modulus, Poisson's ratio, uniaxial compressive strength, model particle resolution and the maximum‐to‐minimum particle ratio showed excellent performance in both training and verification. Adding one more variable—namely, minimum particle radius—showed degrading performance. Copyright © 2009 John Wiley & Sons, Ltd.     

Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities

This paper presents a non‐linear soil–structure interaction (SSI) macro‐element for shallow foundation on cohesive soil. The element describes the behaviour in the near field of the foundation under cyclic loading, reproducing the material non‐linearities of the soil under the foundation (yielding) as well as the geometrical non‐linearities (uplift) at the soil–structure interface. The overall behaviour in the soil and at the interface is reduced to its action on the foundation. The macro‐element consists of a non‐linear joint element, expressed in generalised variables, i.e. in forces applied to the foundation and in the corresponding displacements. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. Mechanisms of yielding and uplift are modelled through a global, coupled plasticity–uplift model. The cyclic model is dedicated to modelling the dynamic response of structures subjected to seismic action. Thus, it is especially suited to combined loading developed during this kind of motion. Comparisons of cyclic results obtained from the macro‐element and from a FE modelization are shown in order to demonstrate the relevance of the proposed model and its predictive ability. Copyright © 2001 John Wiley & Sons, Ltd.     

A distinct element method numerical investigation of compaction processes in highly porous cemented granular materials

In this paper, the results of an oedometric numerical test campaign, performed by means of a 3D Discrete Element Code on idealised cemented granular cylindrical specimens, are illustrated. The idealised microstructure taken into account is characterised by the following: (i) rigid grains bonded to one another; (ii) a high void ratio; and (iii) two different families of voids: the micro and the macro‐voids. The compaction process developing within the specimens, as well as the localization along tabular zones of pure compressive deformation (compaction banding) that in some cases takes place, are discussed. The influence on the evolution of this peculiar strain localization process of many microstructural/numerical parameters like material porosity, macro‐void size, the constitutive relationship adopted for the bonds and the bond damage rate is analysed. Tests for different values of porosity were run. Below a certain porosity threshold value, the onset of mixed modes of localisation was detected whereas the increase in the macro‐void size is observed to favour the onset of instability. Copyright © 2014 John Wiley & Sons, Ltd.     

Strength of two structured soils in triaxial compression

Oil sands are dense granular materials with interlocked structure and clay shales are heavily overconsolidated clays. They are classified as structured soil or weak rock, exhibiting high peak strength with severe softening and dilation, particularly at low confining stress. The triaxial compression test results indicate that both materials yield linear Mohr–Coulomb envelopes with an apparent cohesion for peak and residual strengths. However, the strength components mobilized from these two materials are very different. This paper investigates if these strength parameters are intrinsic properties or responses derived in triaxial compression conditions. Computer tomography scanning technique is used to aid in examining the micro‐structural features of the sheared specimens such as shear banding pattern, shear band thickness, spatial porosity distributions inside and outside shear bands. These micro‐structural features are used to explain the macro‐deformation response observed in the triaxial compression tests. Mobilization of strength components derived from interlocked structure, cementation, dilation, rolling and critical state are analysed for pre‐, post‐peak softening and residual stages. It is found that the empirical correlation such as Mohr–Coulomb failure criterion based on triaxial compression test results does not necessarily reflect the intrinsic properties of the test materials. Testing conditions are embedded in the empirical correlation. Copyright © 2001 John Wiley & Sons, Ltd.     

DEM–FEM analysis of soil failure process via the separate edge coupling method

The concurrent multiscale method, which couples the discrete element method (DEM) for predicting the local micro‐scale evolution of the soil particle skeleton with the finite element method (FEM) for estimating the remaining macro‐scale continuum deformation, is a versatile tool for modeling the failure process of soil masses. This paper presents the separate edge coupling method, which is degenerated from the generalized bridging domain method and is good at eliminating spurious reflections that are induced by coupling models of different scales, to capture the granular behavior in the domain of interest and to coarsen the mesh to save computational cost in the remaining domain. Cundall non‐viscous damping was used as numerical damping to dissipate the kinetic energy for simulating static failure problems. The proposed coupled DEM–FEM scheme was adopted to model the wave propagation in a 1D steel bar, a soil slope because of the effect of a shallow foundation and a plane‐strain cone penetration test (CPT). The numerical results show that the separate edge coupling method is effective when it is adopted for a problem with Cundall non‐viscous damping; it qualitatively reproduces the failure process of the soil masses and is consistent with the full micro‐scale discrete element model. Stress discontinuity is found in the coupling domain. Copyright © 2017 John Wiley & Sons, Ltd.     

Coupling between anisotropic damage and permeability variation in brittle rocks

In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd.     

考虑微观结构的非饱和渗透系数计算公式

分维理论是预测非饱和渗透系数的一种常用方法。在对有侧限条件下高庙子膨润土的非饱和渗透系数的试验结果分析后,发现分维理论并不适用,其缺陷在于不能够反映膨润土这种特殊粘土在水化过程中的微观结构变化。因为膨润土是一种纳米材料,其小孔隙和大孔隙分布在水化过程中都会发生变化,而一般性粘土和砂土没有这种特殊的物理化学特性。结合Kozeny—Carman关于多孔介质的半经验公式,提出了半经验一半理论的考虑微结构的膨润土的非饱和渗透系数计算公式。在对高庙子膨润土的扫描电镜试验和压汞试验资料分析的基础上,定性验证了所提出公式的正确性。     

Multi-scale characterisation of coastal sand aquifer media for contaminant transport using X-ray computed tomography

To be able to predict contaminant transport in groundwater, an accurate conceptual and physical understanding of aquifer properties at multiple scales is required. In this study, physical and hydraulic properties of a coastal sand aquifer were derived using micro and macro X-ray computed tomography (XCT) techniques. Qualitative and quantitative data improved conceptualisation of the aquifer structure at micro and macro scale. At the macro scale (50-mm diameter by 1,500-mm long core) XCT images of undisturbed drill core identified coarse grained laminae (not obvious to the naked eye) of increased porosity and permeability, variations in mineral assemblage and particulate organic matter distribution within the core. Micro-XCT analysis (16-mm diameter cores) of the three main aquifer layers provided quantitative micro-scale data on permeability, porosity, grain, pore and throat size distribution statistics, and grain sphericity. Ratios of mean pore to grain diameter were ~0.65–0.75 and ratios of mean throat to mean grain diameter were ~0.2. Multiple permeability and porosity values were derived from micro domains (~4.35 mm³) within each micro-XCT core. Permeability values varied between and within micro-XCT core samples reflecting the heterogeneity at the millimetre core scale in these sediments. Sphericity values were similar for all three layers (average ~0.4) which reflected SEM observations of the semi-spherical nature of the dominant quartz and feldspar grains. The results of this study indicate that models based on the assumptions of homogeneity in depositional structure below centimetre scale may not suitably address factors affecting flow and transport of contaminants.     

A technique for estimating permeability of a randomly fractured rock mass

Extensive field and laboratory testing programs were performed to develop a relationship between the permeability of a fractured limestone and the core recovery values. The studied limestone does not encompass any jointing system but is consistently and randomly fractured. Nineteen in situ falling head permeability tests were carried out to measure permeability of the fractured rock mass at a representative study area. Analysis of test results has led to the formulation of an empirical equation that estimates the permeability of the rock mass in terms of its solid core recovery value and the permeability of the fractures filling material. Unlike the existing equations for estimating the permeability of rock masses, the proposed equation is simple and utilizes parameters that can be easily determined in regular geotechnical field and laboratory investigations. A technique is also presented to estimate the permeability of a rock layer, the quality of which significantly changes with depth, using the proposed equation that utilizes a single value of core recovery. Analysis of well-documented pumping test results supported the validity of the proposed equation and technique.