Explicit integration of a porosity‐dependent hydro‐mechanical model for unsaturated soils

An adaptive substepping explicit integration scheme is developed for a porosity‐dependent hydro‐mechanical model for unsaturated soils. The model is referred to as the modified σ –Θ model in this paper, which features the employment of the subloading surface plasticity and the stress–saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ –Θ space may result in incorrect loading–unloading decisions during the integration. A new loading–unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ –Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ –Θ space within a set error level. The performance of the loading–unloading decision method for the modified σ –Θ model is discussed through comparing it with the conventional loading–unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p–Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

非饱和土化学-水力-力学耦合行为数值模拟

在描述非饱和土力学本构行为的Gens-Alonso模型[1]的基础上,结合化学浓度对前固结压力的软化公式[2],并考虑了化学浓度对黏聚力的软化作用,建立了描述非饱和土化学-水力-力学耦合行为的本构模型。对包括化学-水力-力学本构关系、流体流动和污染物传输的控制方程的平衡方程组进行有限元离散,并采用此非饱和土化学-水力-力学耦合行为的数值模型对非饱和土中隧道周围化学-水力-力学耦合过程进行了模拟,对纯粹的力学响应、弹性化学力学响应、弹塑性化学力学响应 3 种情况进行了分析,数值结果显示了化学浓度作用下隧道周围的体积变化量和应力状态比单纯的力学响应有较大的提高,隧道表面的收缩量也有明显的增大。数值模拟的结果显示了该方法对模拟非饱和土复杂的耦合行为的可行性。     

超固结非饱和土的试验研究

Farulla等[1]通过固结仪对不同轴应力下的超固结非饱和土进行了湿化变形研究,试验结果表明超固结非饱和土的湿化变形随轴应力的不同而不同,其规律与Alonso等[2]的假设并不完全相符。为了进一步验证这个试验现象,利用双压力室非饱和土三轴仪,在同一个前期固结压力下对不同程度的超固结非饱和土进行了湿化试验,研究其湿化变形特性;对某一吸力下的超固结非饱和土进行三轴排水剪切试验,研究其体变和强度特性。试验结果证明了Farulla等试验的正确性,最后用文中所提的模型进行了预测,其结果与试验现象一致     

A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling of deformation response and chemo‐mechanical coupling in chalk

A constitutive relation is derived for describing the mechanical response of chalk. The approach is based on a phenomenological framework which employs chemo‐plasticity. The properties of the material are assumed to be affected by the physico‐chemical processes that occur through the interaction between the skeleton and the pore fluid. The underlying mechanism is discussed by invoking a micromechanical analysis. The performance of the framework is illustrated by examining the evolution of mechanical characteristics in the presence of different pore fluids. Copyright © 2006 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.     

A thermo‐hydro‐mechanical model for unsaturated soils based on the effective stress concept

A simple thermo‐hydro‐mechanical (THM) constitutive model for unsaturated soils is described. The effective stress concept is extended to unsaturated soils with the introduction of a capillary stress. This capillary stress is based on a microstructural model and calculated from attraction forces due to water menisci. The effect of desaturation and the thermal softening phenomenon are modelled with a minimal number of material parameters and based on existing models. THM process is qualitatively and quantitatively modelled by using experimental data and previous work to show the application of the model, including a drying path under mechanical stress with transition between saturated and unsaturated states, a heating path under constant suction and a deviatoric path with imposed suction and temperature. The results show that the present model can simulate the THM behaviour in unsaturated soils in a satisfactory way. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional transient thermo‐hydro‐mechanical fundamental solutions of unsaturated soils

The governing differential equations of unsaturated soils considering the thermo‐poro‐mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three‐dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed‐form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed‐form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution. Copyright © 2009 John Wiley & Sons, Ltd.     

A hierarchical thermo‐hydro‐plastic constitutive model for unsaturated soils and its numerical implementation

Unsaturated soils are highly heterogeneous 3‐phase porous media. Variations of temperature, the degree of saturation, and density have dramatic impacts on the hydro‐mechanical behavior of unsaturated soils. To model all these features, we present a thermo‐hydro‐plastic model in which the hydro‐mechanical hardening and thermal softening are incorporated in a hierarchical fashion for unsaturated soils. This novel constitutive model can capture heterogeneities in density, suction, the degree of saturation, and temperature. Specifically, this constitutive model has 2 ingredients: (1) it has a “mesoscale” mechanical state variable—porosity and 3 environmental state variables—suction, the degree of saturation, and temperature; (2) both temperature and mechanical effects on water retention properties are taken into account. The return mapping algorithm is applied to implement this model at Gauss point assuming an infinitesimal strain. At each time step, the return mapping is conducted only in principal elastic strain space, assuming no return mapping in suction and temperature. The numerical results obtained by this constitutive model are compared with the experimental results. It shows that the proposed model can simulate the thermo‐hydro‐mechanical behavior of unsaturated soils with satisfaction. We also conduct shear band analysis of an unsaturated soil specimen under plane strain condition to demonstrate the impact of temperature variation on shear banding triggered by initial material heterogeneities.     

非饱和重塑黏土渗透性试验研究

工程中常常遇到非饱和土渗流问题,其渗透性是非饱和土的重要研究内容。采用常规压力板仪详细研究了重塑黏土在3种不同击实功和5种不同击实含水率下的土-水特征曲线,并用变水头法测量了相应的饱和土渗透系数。结合土水曲线和饱和渗透系数,基于Van Genuchten模型和Fredlund模型,详细探讨了重塑非饱和重塑黏土在不同击实条件下的渗透性。结果表明,土样饱和渗透系数随着击实含水率的增大而减小,且随着基质吸力的增大土样渗透性差别逐渐减小。当试样吸力达到1 MPa时,可认为不同击实含水率下试样的渗透性基本相同;在轻型击实和简化轻型击实下,试样渗透性很相似。重型击实功下试样的渗透系数和轻型击实下土样渗透系数的比值 随着吸力的增大而逐渐增大,在饱和状态时比值约为1/100,当吸力达到1 MPa时比值逐渐稳定在1/10右。     

Formulation of a unified constitutive model for clays and sands

This paper presents a new generalized effective stress model, referred to as MIT-S1, which is capable of predicting the rate independent, effective stress–strain–strength behaviour of uncemented soils over a wide range of confining pressures and densities. Freshly deposited sand specimens compressed from different initial formation densities approach a unique condition at high stress levels, referred to as the limiting compression curve (LCC), which is linear in a double logarithmic void ratio, e, mean effective stress space, p′. The model describes irrecoverable, plastic strains which develop throughout first loading using a simple four-parameter elasto-plastic model. The shear stiffness and strength properties of sands in the LCC regime can be normalized by the effective confining pressure and hence can be unified qualitatively, with the well-known behaviour of clays that are normally consolidated from a slurry condition along the virgin consolidation line (VCL). At lower confining pressures, the model characterizes the effects of formation density and fabric on the shear behaviour of sands through a number of key features: (a) void ratio is treated as a separate state variable in the incrementally linearized elasto-plastic formulation: (b) kinematic hardening describing the evolution of anisotropic stress–strain properties: (c) an aperture hardening function controls dilation as a function of ‘formation density’; and (d) the use of a single lemniscate-shaped yield surface with non-associated flow. These features enable the model to describe characteristic transitions from dilative to contractive shear response of sands as the confining pressure increases. This paper summarizes the procedures used to select input parameters for clays and sands, while a companion paper compares model predictions with measured data to illustrate the model capability for describing the shear behaviour of clays and sands. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical modelling of the hydro‐chemo‐mechanical behaviour of geomaterials in the context of CO2 injection

Safety assessment of geosequestration of CO₂ into deep saline aquifers requires a precise understanding of the study of hydro‐chemo‐mechanical couplings occurring in the rocks and the cement well. To this aim, a coupled chemo‐poromechanical model has been developed and implemented into a research code well‐suited to the resolution of fully coupled problems. This code is based on the finite volume methods. In a 1D axisymmetrical configuration, this study aims to simulate the chemo‐poromechanical behaviour of a system composed by the cement well and the caprock during CO₂ injection. Major chemical reactions of carbonation occurring into cement paste and rocks are considered in order to evaluate the consequences of the presence of CO₂ on the amount of dissolved matrix and precipitated calcium carbonates. The dissolution of the solid matrix is taken into account through the use of a chemical porosity. Matrix leaching and carbonation lead, as expected, to important variations of porosity, permeability and to alterations of transport properties and mechanical stiffness. These results justify the importance of considering a coupled analysis accounting for the main chemical reactions. It is worth noting that the modelling framework proposed in the present study could be extended to model the chemo‐poromechanical behaviour of the reservoir rock and the caprock when subjected to the presence of an acidic pore fluid (CO₂‐rich brine). Copyright © 2013 John Wiley & Sons, Ltd.     

ACMEG‐TS: A constitutive model for unsaturated soils under non‐isothermal conditions

This paper introduces an unconventional constitutive model for soils, which deals with a unified thermo‐mechanical modelling for unsaturated soils. The relevant temperature and suction effects are studied in light of elasto‐plasticity. A generalized effective stress framework is adopted, which includes a number of intrinsic thermo‐hydro‐mechanical connections, to represent the stress state in the soil. Two coupled constitutive aspects are used to fully describe the non‐isothermal behaviour. The mechanical constitutive part is built on the concepts of bounding surface theory and multi‐mechanism plasticity, whereas water retention characteristics are described using elasto‐plasticity to reproduce the hysteretic response and the effect of temperature and dry density on retention properties. The theoretical formulation is supported by comparisons with experimental results on two compacted clays. Copyright © 2008 John Wiley & Sons, Ltd.     

Modelling of unsaturated ground behaviour influenced by vegetation transpiration

Vegetation contributes to weak soil stabilisation through reinforcement of the soil, dissipation of excess pore pressure and increasing the shear strength by induced matric suction. This paper describes the way vegetation influences soil matric suction, shrinkage and ground settlement in the vadose zone through transpiration. A mathematical model for the rate of root water uptake, including the root growth rate considering ground conditions, type of vegetation and climatic parameters, has been developed. A finite element approach is employed to solve the transient coupled flow-deformation equations. The finite element mesh is built using partially saturated soil elements capable of representing the salient aspects of unsaturated permeability and the soil water characteristic curve. The model formulation is based on the effective stress theory of unsaturated soils. Based on this proposed model, the distribution of the ground matric suction profile adjacent to the tree is numerically analysed. Current field measurements of soil matric suction and moisture content collected from Miram site located in Victoria State, Australia by the authors are compared with the numerical predictions. The results indicate that the proposed root water uptake model incorporated in the numerical analysis can be used for prediction of ground properties influenced by tree roots.     

Thermo‐hydro‐mechanical modeling of damage in unsaturated porous media: Theoretical framework and numerical study of the EDZ

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.     

The role of pore water in the mechanical behavior of unsaturated soils

Deformation and failure of soils are governed by the stresses acting on the soil skeleton. The isotropic stress acting on the soil skeleton can be divided into two components. One is the stress component which is transmitted through the soil skeleton. This skeleton stress is influenced by the pore water (bulk water) in the soil. The other is the internal stress component which does not contribute to equilibrium with a given external force. The internal stress is induced by the capillary tension of meniscus water clinging to the contact point of soil particles and acts so as to connect the soil particles tightly. Therefore, in modeling the stress and strain relations for unsaturated soils, it is of much importance to quantitatively evaluate how the pore water exists in the soil. This paper discusses the role of pore water on the mechanical behaviour of the soil. In particular, the significance of the water retention curve is emphasized from a mechanical viewpoint. Essential features required in modeling of the constitutive relations for unsaturated soils are discussed and presented.     

Three‐dimensional elasto‐plastic model for unsaturated compacted soils with different initial densities

This paper presents an elasto‐plastic model for unsaturated compacted soils and experimental results obtained from a series of suction‐controlled triaxial tests on unsaturated compacted clay with different initial densities. The initial density dependency of the compacted soil behaviour is modelled by establishing experimental relationships between the initial density and the corresponding yield stress and thereby between the initial density and the location and slope of normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane are given by the extended SMP criterion. A considerable number of the isotropic compression, triaxial compression and extension tests on unsaturated compacted clay with different initial densities were performed using a suction‐controllable triaxial apparatus, to measure the stress–strain–volume change in different stress paths and wetting paths. The model has well‐predicting capabilities to reproduce the mechanical behaviour of specimens compacted under different conditions not only in isotropic compression but also in triaxial compression and triaxial extension. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling mechanical behaviour of limestone under reservoir conditions

High porosity and low permeability limestone has presented pore collapse. As fluid is withdrawn from these reservoirs, the effective stresses acting on the rock increase. If the strength of the rock is overcome, pore collapse may occur, leading to irreversible compaction of porous media with permeability and porosity reduction. It impacts on fluid withdrawal. Most of reservoirs have been discovered in weak formations, which are susceptible to this phenomenon. This work presents a study on the mechanical behaviour of a porous limestone from a reservoir located in Campos Basin, offshore Brazil. An experimental program was undergone in order to define its elastic plastic behaviour. The tests reproduced the loading path conditions expected in a reservoir under production. Parameters of the cap model were fitted to these tests and numerical simulations were run. The numerical simulations presented a good agreement with the experimental tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.