A two‐dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing

Within the framework of our discontinuous deformation analysis for rock failure algorithm, this paper presents a two‐dimensional coupled hydromechanical discontinuum model for simulating the rock hydraulic fracturing process. In the proposed approach, based on the generated joint network, the calculation of fluid mechanics is performed first to obtain the seepage pressure near the tips of existing cracks, and then the fluid pressure is treated as linearly distributed loads on corresponding block boundaries. The contribution of the hydraulic pressure to the initiation/propagation of the cracks is considered by adding the components of these blocks into the force matrix of the global equilibrium equation. Finally, failure criteria are applied at the crack tips to determine the occurrence of cracking events. Several verification examples are simulated, and the results show that this newly proposed numerical model can simulate the hydraulic fracturing process correctly and effectively. Although the numerical and experimental verifications focus on one unique preexisting crack, because of the capability of discontinuous deformation analysis in simulating block‐like structures, the proposed approach is capable of modeling rock hydraulic fracturing processes. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

非饱和压实土率相关变形特征与时效模型

为研究高填方路堤压实土率相关变形特征,对不同压实度的非饱和压实土分别开展了不同加载速率以及不同围压条件下的CD三轴剪切试验,探讨了不同工况下压实土的剪切强度指标;借助GDS饱和土静态三轴仪的围压控制器来间接测定非饱和压实土体变的途径。试验结果表明：压实土强度及变形特征具有明显的时间相依性,加载速率越大,压实土的抗剪强度越高,超固结变形特性越强,抗剪强度指标黏聚力c值增幅较大、内摩擦角 值增幅较小;低围压下,压实土呈应变软化及剪胀变形,且压实度越高,应变软化及剪胀变形越显著,c值增加明显、 值增加缓慢。采用基于下负荷面的弹黏塑性本构模型对路基压实土的率相关变形特征进行表征,预测结果与试验数据吻合良好,表明该模型适用于高填方路堤长期沉降分析。     

A fully coupled simple model for unsaturated soils

Different phenomena influence the strength and volumetric behavior of unsaturated soils. Among the most important are suction hardening, hydraulic hysteresis, and the influence of volumetric strain on the soil-water retention curves. Fully coupled hydro-mechanical models require including all three phenomena in their constitutive relationships. Among these phenomena, suction hardening is the most influencing as it determines the apparent preconsolidation stress, the position of the loading-collapse yield surface, and the shift of both the isotropic consolidation and the critical state lines. In this paper, a fully coupled hydro mechanical model is presented. It is based on the modified Cam-Clay model but includes a yield surface with anisotropic hardening that takes account of the shift of the critical state line with suction. For highly overconsolidated materials, the sub-loading surface concept has been included in order to increase the precision of the model for these materials. The shift of the retention curves produced by volumetric strains is simulated using a hydraulic model based on the grain and current pore size distribution of the soil.     

Coupled computations for an elastic‐perfectly plastic soil using adaptive mesh refinement

An adaptive mesh refinement algorithm has been developed for non‐linear computations in geomechanics, based on a smoothed stress–strain finite element formulation. This uses estimates of error in the incremental shear strain invariant to guide the regeneration of unstructured meshes at regular intervals during loading. Following each mesh‐update, no re‐analysis of previous increments with the new mesh is necessary. Algorithm performance has been investigated by analysing a passive earth pressure problem using a linear elastic‐perfectly plastic Mohr–Coulomb soil model. Perfectly drained behaviour has been considered, as have partially drained situations using hydromechanical coupling, while undrained behaviour has been approximated using time steps close to zero. In all cases, mesh adaptivity has been successful in capturing regions of high strain gradient. The results have been compared with analytical solutions. Accurate computations of limit load and shear band orientation have been obtained for a wide range of material dilation angles. Copyright © 2000 John Wiley & Sons, Ltd.     

一种基于广义塑性力学的硬化剪胀土模型

分析弹塑性模型的特点之后,提出了一种以塑性功w^p和塑性剪应为εs^p作为硬化参量的双屈服面模型,它可以较好地反映硬化剪胀土的变形。模型符合广义塑性力学,可能方便地用于有限元计算。     

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 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.     

Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model

The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.     

An elastoplastic strainhardening model for soil allowing for hydraulic bonding–debonding effects

The paper presents a strainhardening constitutive model for unsaturated soil behaviour based on energy conjugated stress variables in the framework of superposed continua. The proposed constitutive law deals with hydro‐mechanical coupling phenomena. The main purpose is to develop within a consistent framework a model that can deal with possible mechanical instabilities occurring in partially saturated materials. The loss of capillary effects during wetting processes can, in fact, play a central role in unstable processes. Therefore, it will be shown that the bonding effects due to surface tensions can be described in a mathematical framework similar to that employed for bonded geomaterials to model weathering or diagenesis effects, either mechanically or chemically induced. The results of several simulations of common laboratory tests on partially saturated soil specimens are shown. The calculated behaviour appears to be in good qualitative agreement with that observed in the laboratory. In particular it is shown that volumetric collapse phenomena due to hydraulic debonding effects can be successfully described by the model. Finally, it will be highlighted the ability of the model to naturally capture the transition to a fully saturated condition and to deal with possible mechanical instabilities in the unsaturated regime. Copyright © 2008 John Wiley & Sons, Ltd.     

黏性土非线性弹性K-G模型的一种改进方法

为解决《土工试验规程》建议的K-G模型未考虑土体剪缩性问题并保持其简单性,在其基础上增加了一个剪缩模量,建议了一个3模量7参数K-G-D模型,给出了用 和 与 和 表示的完整的增量应力应变关系式;通过正常固结黏土的各向等压固结试验和等平均正应力的三轴压缩排水试验标定了模型参数;进行了黏土的常规三轴压缩排水试验,利用模型参数预测了相应路径下土样的体积与轴向变形,经与实测值对比,预测结果较好。该模型可考虑土体压硬性、剪缩性、应变强化特性,能较完善地描述欠固结和正常固结土及松砂和中密砂在等 和增 路径下的变形特性;模型并未在规程模型的基础上增加试验工作,且概念清晰、形式简单、便于实际应用。     

A multi‐mechanism constitutive model for plastic adaption under cyclic loading

As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi‐mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain‐hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.     

一种改进的粘土亚塑性本构模型

简要地介绍了Herle和Kolymbas针对黏土建立的亚塑性本构模型的方法。结合黏土的特性以及对响应包络线的分析,详细地列出了HK模型几个尚未解决的问题,并对该模型3个参数分别进行了改进,建立了改进后的HK亚塑性公式以及参数的确定方法。改进后的模型继承了HK模型参数少、易确定以及公式简洁等特点,使HK模型不仅具有严密的数学和力学基础,而且具有较好的实际意义。     

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.     

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.     

A new versatile constitutive law for modelling the monotonic response of soft rocks and structured fine-grained soils

This paper deals with a new critical state–based constitutive model for soft rocks and fine-grained soils. The model, formulated in the single-surface plasticity framework, is characterised by the following main features: (i) a generalised three-invariant yield surface capable of reproducing a wide set of well-known criteria, (ii) the dependency of the elastic stiffness on the current stress state by means of a hyperelastic formulation, (iii) the ability of simulating the plastic strain–driven structure degradation processes by a set of appropriate isotropic hardening laws, and (iv) a nonassociate flow rule in the meridian plane. The adopted formulation is hierarchical, such that the various features of the model can be activated or excluded depending on the specific kind of geomaterial to be modelled and on the quality and quantity of the related available experimental results. The constitutive model was implemented in a commercial finite element code by means of an explicit modified Euler scheme with automatic substepping and error control. The procedure does not require any form of stress correction to prevent drift from the yield surface. The performance of the model is first analysed by means of a wide set of parametric analyses, in order to highlight the main features and to evaluate the sensitivity of the formulation with reference to the input parameters. The model is then adopted to simulate the experimental response observed on three different geomaterials, ranging from soft clays to soft rocks.     

Numerical integration of an elastic–viscoplastic constitutive model for dry metamorphosed snow

A constitutive model for dry metamorphosed snow is proposed, within the framework of elasto‐viscoplasticity, which is able to reproduce the most relevant features of the macroscopic behaviour of snow, particularly its time and rate dependency. The basic ideas for modelling stem from the conceptual forms proposed for bonded geomaterials, such as cemented soils or soft rocks. The high viscosity of snow is accounted for by adopting an overstress approach, suitably modified. An evolution law for the curvature‐driven process of sintering, by which intergranular ice necks form and grow, is established. The system of constitutive equations is then numerically integrated via a fully implicit time stepping scheme. Selected results from finite element simulations of laboratory tests, available in the literature, are presented. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A coupled damage–plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification

The development of a coupled damage‐plasticity constitutive model for concrete is presented. Emphasis is put on thermodynamic admissibility, rigour and consistency both in the formulation of the model, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the model can be derived from two specified energy potentials, following procedures established beforehand. Based on this framework, a constitutive model featuring full coupling between damage and plasticity in both tension and compression is developed. Tensile and compressive responses of the material are captured using two separate damage criteria, and a yield criterion with a multiple hardening rule. A crucial part of this study is the identification of model parameters, with these all being shown to be identifiable and computable based on standard tests on concrete. Behaviour of the model is assessed against experimental data on concrete. Copyright © 2007 John Wiley & Sons, Ltd.