Modeling of inherent anisotropic behavior of partially saturated clayey rocks

Clayey rocks are frequently chosen as a geological barrier material for underground repositories. The inherent anisotropic mechanical behavior and the evolution of mechanical behavior with water content are two crucial material properties for the safety analysis of these structures. The present paper focuses on numerical modeling of the inherent anisotropy and the effect of water content, as well as the interactions of these properties in partially saturated clayey rocks with preferably oriented bedding planes. A discrete thermodynamic approach is adopted for describing the inherent anisotropic mechanical behavior, and the anisotropy of the elastic parameters, plastic evolution and damage evolution are considered. Capillary pressure is introduced to describe the effect of the water content with the help of the effective stress concept, and a procedure for the identification of the model parameters is presented. Finally, the proposed model is applied to a study of triaxial compression tests of argillite with different orientations of the bedding planes and variable water content. In summary, the main features of the studied material are well reproduced by the model.     

A constitutive model for unsaturated soil–structure interfaces

A constitutive model for simulation of the behavior of unsaturated interfaces is presented here. The model is an extension of an existing critical state compatible interface model for dry and saturated interfaces that was already proposed by one of the authors [Lashkari, A. 2013. Int. J. Numer. Anal. Meth. Geomech. 37 (8): 904–931]. For a proper simulation of the behavior of partially saturated interfaces, the extended model is formulated in terms of two pairs of work conjugate stress–strain‐like variables. The modified model simulations are compared with the existing data of dry, unsaturated, and saturated interfaces. For each interface type, it is shown that the proposed model can capture the essential elements of the behavior using a unique set of parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bed-parallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.     

Experimental study of poromechanical behavior of saturated claystone under triaxial compression

This paper presents experimental results of drained and undrained triaxial compression tests of saturated Meuse–Haute/Marne claystone. The emphasis is to study the evolution of pore pressure with growth of microcracks and the effect of pore pressure on mechanical behavior. Basic mechanical responses are first investigated through drained triaxial compression tests, showing nonlinear stress strain relations, volumetric dilatancy and pressure sensitivity. In undrained triaxial compression tests, the pore pressure exhibits a transition from increase to decrease due to the transition from volumetric compressibility to dilatancy caused by the growth of microcracks. The failure surfaces, determined by total stress and Terzaghi’s effective stress under undrained condition, are compared with the one under drained condition.     

非饱和土化学-塑性耦合本构行为的数值模拟

基于Hueckel提出的饱和黏土化学-塑性本构模型和Gallipoli提出的非饱和土弹塑性本构模型,提出了一个新的非饱和多孔介质的化学-塑性本构模型,并建立了该模型的隐式积分算法,算法中考虑了化学软化和非饱和吸力的影响。在已有的非饱和多孔介质有限元分析程序平台上进行了程序研发,对孔隙水中化学污染物浓度变化对非饱和土力学行为的影响进行数值模拟,使所研制的程序能够进行岩土工程问题的化学-力学耦合非线性分析。     

含液各向异性多孔介质应变局部化分析

工程中的含液多孔介质如饱和或非饱和岩土材料往往具有各向异性特性。采用Rudnicki建立的针对岩土材料的各向异性本构模型,对轴对称压缩试验中的含液多孔介质骨架的各向异性力学行为进行了分析;基于不连续分叉理论,导出了静态非渗流条件下处于轴对称应力状态的含液多孔介质应变局部化发生的临界模量、剪切带方向以及不连续速度矢量的显式表达式,在此基础上计算并讨论了材料参数变化和孔隙液体存在对各向异性多孔介质应变局部化的影响。     

On the constitutive modeling of partially saturated interfaces

Generalization of soil–structure interface models from dry/saturated states to consider partially saturated states is studied in this paper. For this purpose, basic constitutive equations of a conventional elasto-plastic interface model are firstly presented. Then, consideration is given to the effect of partial saturation on definition of effective stress, location of the critical state line as well as the impact of interface state on plastic hardening modulus and dilatancy. For each concern, proper independent approaches together with associated constitutive equations are discussed to be included in the basic model as complementary ingredients. Among many different possibilities to combine complementary constitutive equations for effective stress, relocation of the critical state line with degree of saturation, and impact of the interface state on plastic hardening modulus and dilatancy, six essential cases are selected. Evaluations show that all six cases can realistically consider the impact of partial degree of saturation on the peak and residual shear strengths as well as the volume change behavior of unsaturated interfaces.     

Unsaturated resilient behavior of a natural compacted sand

Granular materials are generally used in unbound layers of road pavement structures. The mechanical behavior of these materials is widely studied with repeated load triaxial tests (RLTT) in which the elastic response is defined as the resilient behavior. Usually observed under total stress conditions, the effect of pore pressure changes during loading are not usually included in design. Further, the unbound layers frequently exist under partially saturated conditions. The influence of the unsaturated state, i.e., the suction, on the mechanical behavior, of unbound granular materials for roads has not been sufficiently studied and is generally not taken into account in models used for these materials.     

Effect of suction on the mechanical behaviour of iron ore rock

The effect of suction on the behaviour of iron ore has been studied from both physical and mechanical points of view. The porosity and the suction phenomena have been analysed using different experimental techniques. Uniaxial compressive tests on partially saturated samples have shown that the suction is responsible for strength and cohesion improvement. Considering the theory of partially saturated porous soils of Coussy and Dangla (Mécanique des sols non saturés (2002 edn). Hermès Science: 2002; 390), we have proposed a constitutive law for partially saturated iron ore. The real increase in the apparent cohesion due to the capillary attraction forces is overestimated if the yield function is written in terms of effective stresses. The effect of the capillary cohesion has been modelled with a function in the expression of the apparent cohesion of the yield function. The effect of suction on the mechanical behaviour has been represented in the effective stresses space and in the total stresses space like the Alonso model (Géotechnique 1990; 40 :405–430). Copyright © 2005 John Wiley & Sons, Ltd.     

Performance of heavy structures founded upon loess at varying moisture conditions

Saye, S.R., Nass, K.H. and Easton, C.N., 1988. Performance of heavy structures founded upon loess at varying moisture conditions. Eng. Geol., 25: 325–339.

The site preparation for foundations and records of performance of three storage structures founded on loess are presented to illustrate the engineering problems and the range in compressibility of loess associated with different moisture conditions. The sites are located in western Iowa and eastern Nebraska. The structures are a 7500 m³ capacity steel water storage reservoir founded on dry collapsible loess along the bluff line of the Missouri River; a 7200 m³ capacity concrete grain elevator supported by a rigid mat founded on saturated and partially saturated loess; and a 10 m high soil preload for a 54 m diameter ammonia storage tank underlain by saturated and partially saturated loess.

The foundation design, the site preparation and the observed settlements are presented for each structure. The settlement behavior varies markedly with the individual moisture conditions and the apparent preconsolidation of the loess. The apparent preconsolidation is attributed to desiccation and appears to vary systematically.     

Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks

Microcracks in brittle rocks affect not only the local mechanical properties, but also the poroelastic behavior and permeability. A continuum coupled hydro-mechanical modeling approach is presented using a two-scale conceptual model representing realistic rock material containing micro-fractures. This approach combines a microcrack-based continuous damage model within generalized Biot poroelasticity, in which the tensors of macroscopic elastic stiffness, Biot effective stress coefficient and of overall permeability are directly related to microcrack growth. Heterogeneity in both mechanical and hydraulic properties evolves from an initially random distribution of damage to produce localized failure and fluid transmission. A significant advantage of the approach is the ability to accurately predict the evolution of realistic fracturing and associated fluid flow in permeable rocks where pre-existing fractures exert significant control. The model is validated for biaxial failure of rock in compression and replicates typical pre- and post-peak strength metrics of stress drop, AE event counts, permeability evolution and failure modes. The model is applied to the simulation of hydraulic fracturing in permeable rocks to examine the effects of heterogeneities, permeability and borehole pressurization rate on the initiation of fracturing. The results indicate that more homogenous rocks require higher hydraulic pressure to initiate fracturing and breakdown. Moreover, both the fracturing initiation pressure and breakdown pressure decrease with permeability but increase with borehole pressurization rate, and the upper and lower limit of the initiation pressure are seen to be given by the impermeable (Hubbert–Willis) and permeable (Haimson–Fairhurst) borehole wall solutions, respectively. The numerical results are shown to be in good agreement with the experimental observations and theoretical results. This coupled damage and flow modeling approach provides an alternative way to solve a variety of complicated hydro-mechanical problems in practical rock engineering with the process coupling strictly enforced.     

A hypoplastic constitutive model for debris materials

Debris flow is a very common and destructive natural hazard in mountainous regions. Pore water pressure is the major triggering factor in the initiation of debris flow. Excessive pore water pressure is also observed during the runout and deposition of debris flow. Debris materials are normally treated as solid particle–viscous fluid mixture in the constitutive modeling. A suitable constitutive model which can capture the solid-like and fluid-like behavior of solid–fluid mixture should have the capability to describe the developing of pore water pressure (or effective stresses) in the initiation stage and determine the residual effective stresses exactly. In this paper, a constitutive model of debris materials is developed based on a framework where a static portion for the frictional behavior and a dynamic portion for the viscous behavior are combined. The frictional behavior is described by a hypoplastic model with critical state for granular materials. The model performance is demonstrated by simulating undrained simple shear tests of saturated sand, which are particularly relevant for the initiation of debris flows. The partial and full liquefaction of saturated granular material under undrained condition is reproduced by the hypoplastic model. The viscous behavior is described by the tensor form of a modified Bagnold’s theory for solid–fluid suspension, in which the drag force of the interstitial fluid and the particle collisions are considered. The complete model by combining the static and dynamic parts is used to simulate two annular shear tests. The predicted residual strength in the quasi-static stage combined with the stresses in the flowing stage agrees well with the experimental data. The non-quadratic dependence between the stresses and the shear rate in the slow shear stage for the relatively dense specimens is captured.     

THE EFFECTIVE STRESS PRINCIPLE: INCREMENTAL OR FINITE FORM?

Different expressions of the effective stress principle can be found in the literature, in particular some are written in finite form and others in incremental form. For the purpose of the paper we take for granted that stress–strain relationships exist or can be obtained for the effective stress coming from both formulations. We investigate the consequences of the choice of particular finite or differential forms when they are introduced in a weak form of the linear momentum balance equation of two- of three-phase porous media for its numerical solution. For partially saturated geomaterials the importance of the capillary pressure–saturation relationship is pointed out.     

Impacts of saturation-dependent anisotropy on the shrinkage behavior of clay rocks

Geomaterials such as soils and rocks can exhibit inherent anisotropy due to the preferred orientation of mineral grains and/or cracks. They can also be partially saturated with multiple types of fluids occupying the pore space. The anisotropic and unsaturated behaviors of geomaterials can be highly interdependent. Experimental studies have shown that the elastic parameters of rocks evolve with saturation. The effect of saturation has also been shown to differ between directions in transversely isotropic clay rock. This gives rise to saturation-dependent stiffness anisotropy. Similarly, permeability anisotropy can also be saturation-dependent. In this study, constitutive equations accommodating saturation-dependent stiffness and hydraulic anisotropy are presented. A linear function is used to describe the relationship between the elastic parameters and saturation, while the relative permeability–saturation relationship is characterized with a log-linear function. These equations are implemented into a hydromechanical framework to investigate the effects of saturation-dependent properties on the shrinkage behavior of clay rocks. Numerical simulations are presented to demonstrate the role of saturation-dependent stiffness and hydraulic anisotropy in shrinkage behavior. The results highlight that strain anisotropy and time evolution of pore pressures are substantially influenced by saturation-dependent stiffness and hydraulic anisotropy.

     

A model for pore‐fluid‐sensitive rock behavior using a weathering state parameter

Chalk and other porous rocks are known to behave differently when saturated with different pore fluids. The behavior of these rocks varies with different pore fluids and additional deformation occurs when the pore fluid composition changes. In this article, we review the evidence that behavior in porous rocks is pore‐fluid‐dependent, present a constitutive model for pore‐fluid‐dependent porous rocks, and present a compilation of previously published data to develop quantitative relationships between various pore fluids and mechanical behavior. The model proposed here is based on a state parameter approach for weathering and has similarities to models previously proposed for weathering‐sensitive rocks in that the values for parameters that characterize material behavior vary as a function of weathering. Comparisons with published experimental data indicate that the model is capable of reproducing observed behavior of chalk under a variety of loading conditions and changes in pore fluid composition. Copyright © 2008 John Wiley & Sons, Ltd.     

The influence of the characteristics of quartz and mineral deterioration on the strength of granitic dimensional stones

It is important to have a thorough knowledge of the petrographic characteristics of rocks to evaluate and understand their mechanical behavior. This paper deals with the influence of the texture and the mineral characteristics of nine Portuguese granites employed as dimensional stones. This study evaluates different mineral characteristics, such as mineral deterioration, grain size, quartz fissuration and the contacts between quartz and others mineral groups. The main differences in the studied granites were identified, clarifying the relationship between the petrographic characteristics. The consequences on their respective mechanical behavior were subsequently evaluated. The physical and textural characteristics of quartz in the studied granites have proven to be very important for understanding the behavior of granitic rocks under compressive stress. Uniaxial compressive strength values are not proportional to the quartz–feldspar ratio or quartz content and there is a tendency for strength to decrease with the increase in quartz. This could be related to the increase in quartz-quartz contacts and the decrease in the rock capacity for accommodating the deformation.     

Morphological transitions for pore water and pore air during drying and wetting processes in partially saturated sand

Acta Geotechnica - Water retention characteristics are important for modeling the mechanical and hydraulic behavior of partially saturated sand. It is well known that the soil water characteristic...     

Poroplastic modelling of the excavation and ventilation of a deep cavity

A plastic deviatoric model with hardening is developed on the basis of geomechanical tests performed in the saturated case on low permeable porous material such as argillite. This model is a generalized Mohr–Coulomb plastic criterion combined with a Drucker–Prager plastic potential and the hardening parameter is the plastic distortion. Three different hardening functions have been introduced on the basis of triaxial tests: an increase of friction angle, a decrease of cohesion after a threshold and a contractancy to dilatancy transition for volumetric plastic strain. This plastic model has been adapted to the partially saturated case. The effective stress is expressed thanks to the equivalent interstitial pressure π. Numerical results are presented for the excavation and monotonous ventilation of a deep cylindrical cavity. A first plastification due to excavation is followed by a second one due to desaturation. The extent of the non-saturated zone provokes an extent of a plastic zone in the rock mass. Analysis shows that the origin of the plastification can be found in the deviatoric stresses because mean effective stresses are compressive during drying. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of Temperature on the Strength Parameters at the Plastic Domain for Unconsolidated Sandstones

Heavy and extra heavy oil reservoirs are subjected to high temperatures during thermal recovery processes like SAGD and CSS. In-situ temperature state changes throughout these operations may generate variations in the mechanical properties or strength parameters of the rock such as Young and Bulk’s modulus, internal friction angle, cohesion and dilation angle. This paper presents results about the variation of the elastic modulus and mechanical properties, in both elastic and plastic region due to changes in temperature and effective confining stress for reconstituted samples of Colombian unconsolidated sands. In order to study these changes, several drained triaxial tests are performed in a range of temperature between 50 and 230 °C and a range of effective confining stress between 0.4 and 8.2 MPa, these tests are carried out on reconstituted samples of oil sands recovered in an outcrop in the Magdalena middle valley of Colombia. The experimental results are analyzed with an analytical model based on the constitutive model of Mohr–Coulomb. The analysis is divided in two ways: First, the elastic region is analyzed calculating the variation of the elastic modulus (Young and bulk’s modulus) and the mechanical parameters (cohesion and internal friction angle) with temperature and effective confining stress, these calculus are done in the linear zone of the stress–strain curve. Then, the plastic region is analyzed using Mohr–Coulomb constitutive model with a non-associative flow rule in order to represent in a better way the dilatant/contractive behavior of the material, from this analysis is possible to obtain the behavior of the mechanical properties during plastic strains. The stress–strain curves obtained from the triaxial compression tests show that for the highest and medium effective confining stress (8.2 and 4.0 MPa), there is a hardening strain behavior after the yielding point that implies a loose sand behavior under confining conditions. Meanwhile, for lowest effective confining stress (0.4 MPa) the samples show a softening strain, a typical behavior for dense sands under confining conditions.     

不饱和土动弹塑性本构模型研究

以饱和度与有效应力为状态变量,通过引入描述不饱和与饱和土孔隙比差的状态变量,将Zhang等提出的饱和土体应力诱导各向异性动弹塑性本构模型推广到不饱和土体中,使其可描述不饱和土在动力循环荷载作用下的力学特性行为。通过对已有不饱和土体在完全不排水条件下的动三轴试验进行理论模拟,验证了所提出不饱和土本构模型的正确性。最后基于所提出本构模型,讨论了在不排水条件下初始饱和度对不饱和土动力特性研究。结果表明,不饱和土在动力荷载作用下,土体的孔隙比将减少,导致饱和度增加;当初始饱和度较高时,不饱和土会转化为饱和土,从而发生液化现象。该研究成果对研究不饱和土在地震等动力荷载作用下的力学特性行为具有重要意义。