A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

Compaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo‐mechanical compaction results from Intergranular Pressure‐Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo‐mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed‐form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.     

A continuum‐discrete hydromechanical analysis of granular deposit liquefaction

A coupled continuum‐discrete hydromechanical model was employed to analyse the liquefaction of a saturated loose deposit of cohesionless particles when subjected to a dynamic base excitation. The pore fluid flow was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid phase particles. A well established semi‐empirical relationship was utilized to quantify the fluid–particle interactions. The conducted simulations revealed a number of salient micro‐mechanical mechanisms and response patterns associated with the deposit liquefaction. Space and time variation of porosity was a major factor which affected the coupled response of the solid and fluid phases. Pore fluid flow was within Darcy's regime. The predicted response exhibited macroscopic patterns consistent with experimental results and case histories of the liquefaction of granular soil deposits. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling landslides in unsaturated slopes subjected to rainfall infiltration using material point method

This paper presents a dynamic fully coupled formulation for saturated and unsaturated soils that undergo large deformations based on material point method. Governing equations are applied to porous material while considering it as a continuum in which the pores of the solid skeleton are filled with water and air. The accuracy of the developed method is tested with available experimental and numerical results. The developed method has been applied to investigate the failure and post‐failure behaviour of rapid landslides in unsaturated slopes subjected to rainfall infiltration using two different bedrock geometries that lie below the top soil. The models show different failure and post‐failure mechanisms depending on the bedrock geometry and highlight the negative effects of continuous rain infiltrations. Copyright © 2016 John Wiley & Sons, Ltd.     

Fully coupled modeling of seabed subsidence and reservoir compaction of North Sea oil fields

This paper focuses on the aspects of fully coupled continuum modeling of multiphase poroelasticity applied to the three-dimensional numerical simulations of the Ekofisk oil reservoir in the North Sea (56°29′–34′N, 03°10′–14′E). A systematic presentation is chosen to present the methodology behind fully coupled, continuum modeling. First, a historical review of the subsidence phenomena above an oil and gas reservoir is given. This will serve as a background against which the relevance of the present approach to compaction and subsidence modeling will be demonstrated. Following this, the governing equations for a multiphase poroelasticity model are briefly presented. Particular attention is paid to the analysis of the pore-compressibility term usually used in an uncoupled approach for characterising the host-rock deformation. A comparative numerical analysis is carried out to contrast and highlight the difference between coupled and uncoupled reservoir simulators. Finally, a finite-element numerical model of the Ekofisk field is presented and a significant result is a contour map of seabed subsidence which is in general agreement with the shape of the subsidence contours based on past bathymetric surveys. Analysis of the simulation reveals that, due to the downward movement of the overburden, oil migration occurs from the crest of the anticline in which the field is situated, towards the flank. The pore-pressure depletion in the reservoir is significantly delayed due to the replenishment of the reservoir energy via the formational compaction. Horizontal movement in the reservoir, which is neglected in traditional modeling, can be significant and comparable in magnitude to the vertical subsidence. Electronic Publication     

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

This paper studies the chemo‐mechanics of cemented granular solids in the context of continuum thermodynamics for fluid‐saturated porous media. For this purpose, an existing constitutive model formulated in the frame of the Breakage Mechanics theory is augmented to cope with reactive processes. Chemical state variables accounting for the reactions between the solid constituents and the solutes in the pore fluid are introduced to enrich the interactions among the microstructural units simulated by the model (i.e., grains and cement bonds). Two different reactive processes are studied (i.e., grain dissolution and cement precipitation), using the chemical variables to describe the progression of the reactions and track changes in the size of grains and bonds. Finally, a homogenization strategy is used to derive the energy potentials of the solid mixture, adopting probability density functions that depend on both mechanical and chemical indices. It is shown that the connection between the statistics of the micro‐scale attributes and the continuum properties of the solid enables the mathematical capture of numerous mechanical effects of lithification and chemical deterioration, such as changes in stiffness, expansion/contraction of the elastic domain, and development of inelastic strains during reaction. In particular, the model offers an interpretation of the plastic strains generated by aggressive environments, which are here interpreted as an outcome of chemically driven debonding and comminution. As a result, the model explains widely observed macroscopic signatures of geomaterial degradation by reconciling the energetics of the deformation/reaction processes with the evolving geometry of the microstructural attributes. Copyright © 2015 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.     

Coupled HM analysis using zero‐thickness interface elements with double nodes. Part I: Theoretical model

In recent years, the authors have proposed a new double‐node zero‐thickness interface element for diffusion analysis via the finite element method (FEM) (Int. J. Numer. Anal. Meth. Geomech. 2004; 28 (9): 947–962). In the present paper, that formulation is combined with an existing mechanical formulation in order to obtain a fully coupled hydro‐mechanical (or HM) model applicable to fractured/fracturing geomaterials. Each element (continuum or interface) is formulated in terms of the displacements (u) and the fluid pressure (p) at the nodes. After assembly, a particular expression of the traditional ‘u–p’ system of coupled equations is obtained, which is highly non‐linear due to the strong dependence between the permeability and the aperture of discontinuities. The formulation is valid for both pre‐existing and developing discontinuities by using the appropriate constitutive model that relates effective stresses to relative displacements in the interface. The system of coupled equations is solved following two different numerical approaches: staggered and fully coupled. In the latter, the Newton–Raphson method is used, and it is shown that the Jacobian matrix becomes non‐symmetric due to the dependence of the discontinuity permeability on the aperture. In the part II companion paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.730 ), the formulation proposed is verified and illustrated with some application examples. Copyright © 2008 John Wiley & Sons, Ltd.     

3D subsidence analyses above gas reservoirs accounting for an unconventional plasticity model

The coupled hydro‐mechanical state in soils coming from consolidation/subsidence processes and undergoing plasticity phenomena is here evaluated by means of the subloading surface model. The most important feature of this theory is the abolition of the distinction between the elastic and plastic domains, as it happens in the conventional elastoplastic models. This means that plastic deformations are generated whenever there is a change in stress and a smoother elastoplastic transition is produced. The plasticity algorithm has been implemented in the PLASCON3D FE code, coupling hydro‐thermo‐mechanical fields within a saturated (locally partially saturated) porous medium subjected to external loads and water/gas withdrawals from deep layers (aquifers/reservoirs). The 3D model has been first calibrated and validated against examples taken from the literature, and then subsidence analyses at regional scales due to gas extractions have been developed to predict the evolution of settlements and pore pressure in soils for long‐term scenarios. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of water seepage in a pavement system using the particulate approach

A particulate model has been developed to analyze the effects of transient and steady state seepage of water through a randomly-packed coarse-grained soil as an alternative to conventional seepage analysis based on continuum models. In this model, the soil skeleton and the pore water are volumetrically coupled in the transient and steady-state conditions. The concept of relative density has been used to define different compaction levels of the soil layers forming a pavement filter system and observe the seepage response to compaction. First, Monte–Carlo simulation is used to randomly pack discrete spherical particles from a specified particle size distribution (PSD) to achieve a desired relative density based on the theoretical minimum and maximum void ratios. Then, a water pressure gradient is applied across one two-layer unit to trigger water seepage. The interstitial pore water motion is idealized using Navier–Stokes (NS) equations with provision to incorporate the drag forces acting between the pore fluid and soil particles. The NS equations are discretized using finite differences and applied to discrete elements in a staggered, structured grid. The model predicted hydraulic conductivities are validated using widely used equations.     

Implementation of a hydromechanical elastoplastic constitutive model for fully coupled dynamic analysis of unsaturated soils and its validation using centrifuge test results

Prediction of unsaturated soil behavior during earthquake loading has received increasing attention in geotechnical engineering research and practice in recent years. Development of a fully coupled analysis procedure incorporating a coupled hydromechanical elastoplastic constitutive model for dynamic analysis of unsaturated soils has, however, been limited. This paper presents the implementation of a coupled hydromechanical elastoplastic constitutive model into a fully coupled dynamic analysis procedure and its validation using a centrifuge test. First, the fully coupled finite element equations governing the dynamic behavior of unsaturated soils with the solid skeleton displacement, pore water pressure, and pore air pressure as nodal unknowns are briefly presented. The closest point projection method is then utilized to implement the coupled hydromechanical elastoplastic constitutive model into the finite element equations. The constitutive model includes hysteresis in soil–water characteristic curves, cyclic elastoplasticity of the solid skeleton, and the coupling mechanisms between the SWCCs and the solid skeleton. Finally, the analysis procedure is validated using the results from a dynamic centrifuge test on an embankment constructed of compacted unsaturated silt subjected to base shaking. Reasonable comparisons between the predicted and measured accelerations, settlements, and deformed shapes are obtained.

     

Discussing the definition of the second‐order work for unsaturated soils

The volumetric compaction due to wetting processes is a phenomenon observed quite often in unsaturated soils. Under certain circumstances, saturation events can result into a sudden and unexpected collapse of the system. These phenomena are usually referred to as wetting‐induced collapses, without providing any detailed theoretical justification for this terminology. In order to predict in a general fashion the occurrence of coupled instabilities induced by saturation processes, a generalization of the theoretical approaches usually employed for saturated geomaterials is here provided. More specifically, this paper addresses the problem of hydro‐mechanical instability in unsaturated soils from an energy standpoint. For this purpose, an extension of the definition of the second‐order work is here suggested for the case of unsaturated porous media. On the basis of some examples of numerical simulations of laboratory tests, coupled hydro‐mechanical instabilities are then interpreted in the light of this second‐order energy measure. Finally, the implications of the theoretical results here presented are commented from a constitutive modelling perspective. Two possible alternative approaches to formulate incremental coupled constitutive relations are indeed discussed, showing how the onset of hydro‐mechanical instabilities can be predicted using an extended form of Hill's stability criterion. Copyright © 2010 John Wiley & Sons, Ltd.     

Coupled three-dimensional discrete element–finite difference simulation of dynamic compaction

Discrete element method has been widely adopted to simulate processes that are challenging to continuum-based approaches. However, its computational efficiency can be greatly compromised when large number of particles are required to model regions of less interest to researchers. Due to this, the application of DEM to boundary value problems has been limited. This paper introduces a three-dimensional discrete element–finite difference coupling method, in which the discrete–continuum interactions are modeled in local coordinate systems where the force and displacement compatibilities between the coupled subdomains are considered. The method is validated using a model dynamic compaction test on sand. The comparison between the numerical and physical test results shows that the coupling method can effectively simulate the dynamic compaction process. The responses of the DEM model show that dynamic stress propagation (compaction mechanism) and tamper penetration (bearing capacity mechanism) play very different roles in soil deformations. Under impact loading, the soil undergoes a transient weakening process induced by dynamic stress propagation, which makes the soil easier to densify under bearing capacity mechanism. The distribution of tamping energy between the two mechanisms can influence the compaction efficiency, and allocating higher compaction energy to bearing capacity mechanism could improve the efficiency of dynamic compaction.

     

Flow–stress coupled permeability tensor for fractured rock masses

In this paper a new analytical model is proposed to determine the permeability tensor for fractured rock masses based on the superposition principle of liquid dissipation energy. This model relies on the geometrical characteristics of rock fractures and the corresponding fracture network, and demonstrates the coupling effect between fluid flow and stress/deformation. This model empirically considers the effect of pre‐peak shear dilation and shear contraction on the hydraulic behavior of rock fractures and can be used to determine the applicability of the continuum approach to hydro‐mechanical coupling analysis. Results of numerical analysis presented in this paper show that the new model can effectively describe the permeability of fractured rock masses, and can be applied to the coupling analysis of seepage and stress fields. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of gas generation in electro‐osmosis consolidation

This paper presents a numerical model for the elasto‐plastic electro‐osmosis consolidation of unsaturated clays experiencing large strains, by considering electro‐osmosis and hydro‐mechanical flows in a deformable multiphase porous medium. The coupled governing equations involving the pore water flow, pore gas flow, electric flow and mechanical deformation in unsaturated clays are derived within the framework of averaging theory and solved numerically using finite elements. The displacements of the solid phase, the pressure of the water phase, the pressure of the gas phase and the electric potential are taken as the primary unknowns in the proposed model. The nonlinear variation of transport parameters during electro‐osmosis consolidation are incorporated into the model using empirical expressions that strongly depend on the degree of water saturation, whereas the Barcelona Basic Model is employed to simulate the elasto‐plastic mechanical behaviour of unsaturated clays. The accuracy of the proposed model is evaluated by validating it against two well‐known numerical examples, involving electro‐osmosis and unsaturated soil behaviour respectively. Two further examples are then investigated to study the capability of the computational algorithm in modelling multiphase flow in electro‐osmosis consolidation. Finally, the effects of gas generation at the anode, the deformation characteristics, the degree of saturation and the time dependent evolution of the excess pore pressure are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

爆炸挤淤筑堤沉降的Verhulst预测

沉降观测是爆炸挤淤筑堤质量检测的一个重要手段,目前其监测方法较多还是按传统的观测法,需要较长的观测时间,耗时耗力。通过分析灰色Verhulst模型的特点,根据实际观测资料运用灰色Verhulst模型预测了堤身各时刻的沉降量,与实际观测具有较好的符合性,并预测了堤身的最终沉降量和所需时间。结合实例预测表明,这一模型具有较好的适用性,可以在类似工程中推广应用。     

A constitutive model for the dynamic and high‐pressure behaviour of a propellant‐like material: Part I: Experimental background and general structure of the model

This paper is the first part of a work that aims at developing a mechanical model for the behaviour of propellant‐like materials under high confining pressure and strain rate. The behaviour of a typical material is investigated experimentally. Several microstructural deformation processes are identified and correlated with loading conditions. The resulting behaviour is complex, non‐linear, and characterized by multiple couplings. The general structure of a relevant model is sought using a thermodynamic framework. A viscoelastic‐viscoplastic‐compaction model structure is derived under suitable simplifying assumptions, in the framework of finite, though moderate, strains. Model development, identification and numerical applications are given in the companion paper. Copyright © 2001 John Wiley & Sons, Ltd.