Modelling chemo‐hydro‐mechanical behaviour of unsaturated clays: a feasibility study

Effective capabilities of combined chemo‐elasto‐plastic and unsaturated soil models to simulate chemo‐hydro‐mechanical (CHM) behaviour of clays are examined in numerical simulations through selected boundary value problems. The objective is to investigate the feasibility of approaching such complex material behaviour numerically by combining two existing models. The chemo‐mechanical effects are described using the concept of chemical softening consisting of reduction of the pre‐consolidation pressure proposed originally by Hueckel (Can. Geotech. J. 1992; 29 :1071–1086; Int. J. Numer. Anal. Methods Geomech. 1997; 21 :43–72). An additional chemical softening mechanism is considered, consisting in a decrease of cohesion with an increase in contaminant concentration. The influence of partial saturation on the constitutive behaviour is modelled following Barcelona basic model (BBM) formulation (Géotech. 1990; 40 (3):405–430; Can. Geotech. J. 1992; 29 :1013–1032). The equilibrium equations combined with the CHM constitutive relations, and the governing equations for flow of fluids and contaminant transport, are solved numerically using finite element. The emphasis is laid on understanding the role that the individual chemical effects such as chemo‐elastic swelling, or chemo‐plastic consolidation, or finally, chemical loss of cohesion have in the overall response of the soil mass. The numerical problems analysed concern the chemical effects in response to wetting of a clay specimen with an organic liquid in rigid wall consolidometer, during biaxial loading up to failure, and in response to fresh water influx during tunnel excavation in swelling clay. Copyright © 2005 John Wiley & Sons, Ltd.     

Data assimilation using the particle filter for identifying the elasto‐plastic material properties of geomaterials

A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto‐plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto‐plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto‐plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto‐plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto‐plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 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.     

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.     

Formulation of a three‐dimensional constitutive model for unsaturated soils incorporating mechanical–water retention couplings

Wheeler, Sharma and Buisson proposed an elasto‐plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three‐dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto‐plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three‐dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours. Copyright © 2013 John Wiley & Sons, Ltd.     

On some advanced thermo‐mechanical models for saturated clays

This paper aims to evaluate the performance of several recent constitutive models in simulating the thermo‐mechanical behaviour of saturated clays. A classic thermo‐mechanical test on natural Boom Clay, commonly used in constitutive modelling, was first clarified. Different methods commonly used to measure volumetric strain in drained heating tests were then discussed. Model evaluation was performed in terms of thermodynamic and elasto‐plastic requirements. The capability of the models to capture the observed behaviour was assessed on the basis of the experimental evidence. It was shown that all the models provide reasonable predictions of the thermo‐mechanical behaviour of saturated clays. However, each constitutive model has its own limitations or unclear points from the theoretical point of view. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of long‐term consolidation behavior of soft sensitive clay using an elasto‐viscoplastic constitutive model

The phenomenon of excess pore water pressure increase or stagnation and continuing large ground deformation in soft sensitive clay following the completion of construction of embankment is simulated for a case study at Saint Alban, Quebec, Canada. The present model employs an updated Lagrangian finite element framework and is combined with an automatic time increment selection scheme. The simulation based on an elasto‐viscoplastic constitutive model considers soil‐structure degradation effect. It is shown that without consideration for the microstructural degradation effect, it is not possible to reproduce the field responses of soft sensitive clay even during the construction of the embankment. When the soil‐structure degradation effect is considered, the present model can offer reasonably accurate prediction for the consolidation behavior of soft sensitive clay, including the so‐called anomalous pore water pressure generation and continuing large deformation even after the end of construction, which has been posing numerous uncertainties on the long‐term performance of earth structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Time‐scale analysis in unsaturated porous media under external wave loads

Extreme waves caused by tsunamis and storm surges can lead to soil failures in the near‐shore region, which may have severe impact on coastal environments and communities. Multiphase flows in deformable porous media involve several coupled processes and multiple time scales, which are challenging for numerical simulations. The objective of this study is to investigate the roles of the various processes and their interactions in multiphase flows in unsaturated soils under external wave loading, via theoretical time‐scale analysis and numerical simulations. A coupled geomechanics–multiphase flow model based on conservation laws is used. Theoretical analysis based on coupled and decoupled models demonstrates that transient and steady‐state responses are governed by pore pressure diffusion and saturation front propagation, respectively, and that the two processes are essentially decoupled. Numerical simulations suggest that the compressibility of the pore fluids and the deformation of the soil skeleton are important when the transient responses of the media are of concern, while the steady‐state responses are not sensitive to these factors. The responses obtained from the fully coupled numerical simulations are explained by a simplified time‐scale analysis based on coupled and decoupled models. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical analysis of seepage–deformation in unsaturated soils

A coupled elastic–plastic finite element analysis based on simplified consolidation theory for unsaturated soils is used to investigate the coupling processes of water infiltration and deformation. By introducing a reduced suction and an elastic–plastic constitutive equation for the soil skeleton, the simplified consolidation theory for unsaturated soils is incorporated into an in-house finite element code. Using the proposed numerical method, the generation of pore water pressure and development of deformation can be simulated under evaporation or rainfall infiltration conditions. Through a parametric study and comparison with the test results, the proposed method is found to describe well the characteristics during water evaporation/infiltration into unsaturated soils. Finally, an unsaturated soil slope with water infiltration is analyzed in detail to investigate the development of the displacement and generation of pore water pressure.     

边坡大变形弹塑性有限元分析[Ⅰ]: 理论

本文采用以物理坐标为变量的Ｕｐｄａｔｅｄ－Ｌａｇｒａｎｇｉａｎ描述方法,在考虑边坡非线性变形破坏的基础上,建立了边坡大变形破坏的弹塑性有限元模型,详细推导了有限单元方程和数值分析公式,并考虑了边坡的初始应力和超孔隙水压力。     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

Large deformation elastic electro-osmosis consolidation of clays

This paper presents the theoretical background of an elastic electro-osmosis consolidation model for saturated soils experiencing large strains, which considers volumetric strains induced by changes in both the hydraulic and electric driven pore water flows. Three fully coupled governing equations, considering the soil mechanical behaviour, pore water transport and electrical field, and their numerical implementation within an updated Lagrangian finite element formulation, are presented. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, various numerical examples are investigated to study the deformation characteristics and time dependent evolution of excess pore pressure. Finally, the importance of considering large strains in a consistent and proper way is demonstrated, and differences compared to models based on small strain theory are highlighted.     

A closed form analytical solution for two‐dimensional plane strain consolidation of unsaturated soil stratum

This paper discusses the excess pore‐air and pore‐water pressure dissipations and the average degree of consolidation in the 2D plane strain consolidation of an unsaturated soil stratum using eigenfunction expansion and Laplace transformation techniques. In this study, the application of a constant external loading on a soil surface is assumed to immediately generate uniformly or linearly distributed initial excess pore pressures. The general solutions consisting of eigenfunctions and eigenvalues are first proposed. The Laplace transform is then applied to convert the time variable t in partial differential equations into the Laplace complex argument s. Once the domain is obtained, a simplified set of equations with variable s can be achieved. The final analytical solutions can be computed by taking a Laplace inverse. The proposed equations predict the two‐dimensional consolidation behaviour of an unsaturated soil stratum capturing the uniformly and linearly distributed initial excess pore pressures. This study investigates the effects of isotropic and anisotropic permeability conditions on variations of excess pore pressures and the average degree of consolidation. Additionally, isochrones of excess pore pressures along vertical and horizontal directions are presented. It is found that the initial distribution of pore pressures, varying with depth, results in considerable effects on the pore‐water pressure dissipation rate whilst it has insignificant effects on the excess pore‐air pressure dissipation rate. Copyright © 2015 John Wiley & Sons, Ltd.     

Revisiting the thermodynamics of hardening plasticity for unsaturated soils

A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

A simple analytical solution to one‐dimensional consolidation for unsaturated soils

This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Solid–fluid transition modelling in geomaterials and application to a mudflow interacting with an obstacle

Given the contrasting behaviour observed for geomaterials, for example, during landslides of the flow type, this contribution proposes an original constitutive model, which associates both an elasto‐plastic relation and a Bingham viscous law linked by a mechanical transition criterion. This last is defined as the second‐order work sign for each material point, which is a general criterion for divergence instabilities. Finite element method with Lagrangian integration points is chosen as a framework for implementing the new model because of its well‐known ability to deal with both solid and fluid behaviours in large deformation processes. A first boundary model considering a sample of initially stable soil, a slope and an obstacle is performed. The results show the power of the constitutive model because the consistent evolution of initiation, propagation and arrest of the mudflow is described. A parametric study is led on various plastic and viscous parameters to determine their influence on the flow development and arrest. Finally, forces against the obstacle are compared with good agreement with those of other authors for the same geometry and a pure viscous behaviour. Copyright © 2014 John Wiley & Sons, Ltd.     

Chemo‐thermo‐mechanically coupled seismic analysis of methane hydrate‐bearing sediments during a predicted Nankai Trough Earthquake

In the present study, we have developed a numerical method which can simulate the dynamic behaviour of a seabed ground during gas production from methane hydrate‐bearing sediments. The proposed method can describe the chemo‐thermo‐mechanical‐seismic coupled behaviours, such as phase changes from hydrates to water and gas, temperature changes and ground deformation related to the flow of pore fluids during earthquakes. In the first part of the present study, the governing equations for the proposed method and its discretization are presented. Then, numerical analyses are performed for hydrate‐bearing sediments in order to investigate the dynamic behaviour during gas production. The geological conditions and the material parameters are determined using the data of the seabed ground at Daini‐Atsumi knoll, Eastern Nankai Trough, Japan, where the first offshore production test of methane hydrates was conducted. A predicted earthquake at the site is used in the analyses. Regarding the seismic response to the earthquake which occur during gas production process, the wave profiles of horizontal acceleration and horizontal velocity were not extensively affected by the gas production. Hydrate dissociation behaviour is sensitive to changes in the pore pressure during earthquakes. Methane hydrate dissociation temporarily became active in some areas because of the main motion of the earthquake, then methane hydrate dissociation brought about an increase in the average pressure of the fluids during the earthquake. And, it was this increase in average pore pressure that finally caused the methane hydrate dissociation to cease during the earthquake. Copyright © 2016 John Wiley & Sons, Ltd.     

Limitations of suction‐controlled triaxial tests in the characterization of unsaturated soils

Behavior of unsaturated soils is influenced by many factors, and the influences of these factors are usually coupled together. Suction‐controlled triaxial (SCTX) tests are considered to allow researchers to investigate influences of individual variables on unsaturated soils under specified stress path with controls of stresses, pore water, and air pressures. In the past 50 years, SCTX testing method has been established as a standard approach to characterize constitutive behavior of unsaturated soils. Most important concepts for modern unsaturated soil mechanics were developed upon results from the SCTX tests. Among these, one of the most important contributions in the constitutive modeling of elasto‐plastic behavior for unsaturated soils is the Barcelona basic model (BBM) proposed by Alonso et al. in 1990. The BBM successfully explained many features of unsaturated soils and received extensive acceptance. However, the SCTX tests are designed based upon the divide‐and‐conquer approach in which an implicit assumption is used: soil behavior is stress‐path independent. However, it is well‐established that unsaturated soil behavior is elasto‐plastic and stress‐path dependent. It is found that the SCTX tests in fact cannot control the stress path of an unsaturated soil during loading. This incapability, in combination with complicated loading/collapse behavior of unsaturated soils, makes the SCTX tests for characterizing unsaturated soil questionable. This paper discusses the limitations of the SCTX tests in the characterization of unsaturated soils. A possible solution to the problem was proposed based on a newly developed modified state surface approach. The discussions are limited for isotropic conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

循环荷载下非饱和结构性黏土的弹塑性双面模型

非饱和黏土的结构性能够显著影响其力学特性。基于非饱和土经典模型BBM（Barcelona basic model）和一种可描述循环塑性的硬化法则,引入体积破损率的作为标准土体结构破损的参数,建立了一个描述常吸力下非饱和结构性黏土静态及动态力学特性的弹塑性双面模型。模型在应力空间中包含与重塑非饱和土屈服面几何相似的结构性边界面和加载面,采用径向映射法则和可移动的记忆中心原理,通过结构性边界面和加载面在应力空间中的演化来反映循环加载过程中非饱和结构性黏土的循环塑性特征和结构损伤过程。通过与相关非饱和黏土控制吸力试验数据的比较,表明该模型能够较好地反映静态加载下非饱和结构性黏土的力学特性,而模型预测的循环荷载下的应力?应变特征也具有一定的合理性。