On computation of strain‐dependent permeability of rocks and rock‐like porous media

Determination of transport properties of geomaterials is an important issue in many fields of engineering analysis and design. For example, in petroleum engineering, in situ permeability of an oil reservoir may be crucial in establishing its viability for exploitation, whilst prevention of leakage from underground storage facilities for oil and gas, nuclear waste as well as viability of CO₂ sequestration projects crucially depends on its long‐term values. Permeability is indirectly related to the porosity, pore‐size distribution and pore architecture of the porous media. These parameters evolve when a strain field is imposed. Physical measurement of permeability under a strain field in laboratory conditions is difficult, expensive and prone to a number of uncertainties. In the past, pore network models have been used to compute permeability of materials under stress/strain‐free conditions. In this paper, we propose an enhanced pore network model to compute permeability of rocks and rock‐like porous media under a stress/strain field. Data of pore‐size distribution obtained from mercury intrusion porosimetry are used to compute permeability of rock samples from various unspecified oilfields in the world. It is shown that the two permeabilities can be predicted from the model with sufficient accuracy. A hypothesis for change in porosity, pore‐size distribution and pore architecture as a result of imposed mechanical strains is then proposed. Based on this, permeability is computed again for one of the rock samples under uniaxial and triaxial compressive and tensile strain fields. It is shown that depending on the state of strain field imposed, permeability evolves in an anisotropic manner. Permeability under tensile strain field increases dramatically compared with the reduction that takes place under compressive strain field of the same magnitude. Copyright © 2014 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.     

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.     

Analytical study of mine closure behaviour in a poro‐visco‐elastic medium

This paper is interested in the hydro‐mechanical behaviour of an underground cavity abandoned at the end of its service life. It is an extension of a previous study that accounted for a poro‐elastic behaviour of the rock mass (Int. J. Comput. Geomech. 2007; DOI: 10.1016/j.compgeo.2007.11.003 ). Deterioration of the lining support with time leads to the transfer of the loading from the exterior massif to the interior backfill. The in situ material has a poro‐visco‐elastic constitutive behaviour while the backfill is poro‐elastic, both saturated with water. This loading transfer is accompanied by an inward cavity convergence, thereby compressing the backfill, and induces an outward water flow. This leads to a complex space–time evolution of pore pressures, displacements and stresses, which is not always intuitive. In its general setting, a semi‐explicit solution to this problem is developed, using Laplace transform, the inversion being performed numerically. Analytical inversion leading to a quasi‐explicit solution in the time domain is possible by identifying the characteristic creep and relaxation times of volumetric strains with those of the deviatoric strains, on the basis of a parametric study. A few numerical examples are given to illustrate the hydro‐mechanical behaviour of the cavity and highlight the influence of key parameters (e.g. stiffness of backfill, lining deterioration rate, etc.). Further studies accounting for more general material behaviours for the backfill and external ground are ongoing. Copyright © 2008 John Wiley & Sons, Ltd.     

High‐grade metamorphism and partial melting of basic and intermediate rocks

Rocks of basic and intermediate bulk composition occur in orogenic terranes from all geological time periods and are thought to represent significant petrological components of the middle and lower continental crust. However, the former lack of appropriate thermodynamic models for silicate melt, amphibole and clinopyroxene that can be applied to such lithologies at high temperature has inhibited effective phase equilibrium modelling of their petrological evolution during amphibolite‐ and granulite facies metamorphism. In this work, we present phase diagrams calculated in the Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O–TiO₂–O₂ (NCKFMASHTO) compositional system for a range of natural basic and intermediate bulk compositions for conditions of 2–12 kbar and 600–1050 ^°C using newly parameterized activity–composition relationships detailed in a companion paper by Green et al. in this issue. Particular attention is given to mid‐ocean ridge basalt (MORB) and diorite protolith bulk compositions. Calculated subsolidus mineral assemblages in all basic and intermediate rock types are modally dominated by hornblende and plagioclase, with variable proportions of epidote, clinopyroxene, garnet, biotite, muscovite, quartz, titanite or ilmenite present at different pressures. The H₂O‐saturated (wet) solidus has a negative P?T slope and occurs between ～620–690 ^°C at mid‐ to lower‐crustal pressures of 5–10 kbar. The lowest‐T melts generated close to the wet solidus are calculated to have granitic major‐element oxide compositions. Melting at higher temperature is attributed primarily to multivariate hydrate‐breakdown reactions involving biotite and/or hornblende. Partial melt compositions calculated at 800–1050 ^°C for MORB show good correlation with analysed compositions of experimental glasses produced via hydrate‐breakdown melting of natural and synthetic basic protoliths, with Niggli norms indicating that they would crystallize to trondhjemite or tonalite. Diorite is shown to be significantly more fertile than MORB and is calculated to produce high‐T melts (>800 ^°C) of granodioritic composition. Subsolidus and suprasolidus mineral assemblages show no significant variation between different members of the basalt family, although the P?T conditions at which orthopyroxene stabilizes, thus defining the prograde amphibolite–granulite transition, is strongly dependent on bulk‐rock oxidation state and water content. The petrological effects of open‐ and closed‐system processes on the mineral assemblages produced during prograde metamorphism and preserved during retrograde metamorphism are also examined via a case‐study analysis of a natural Archean amphibolite from the Lewisian Complex, northwest Scotland.     

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.     

Influence of different strain rates on hydro-mechanical behaviour of reconstituted unsaturated soil

The hydro-mechanical behaviour of a reconstituted unsaturated soil under different suctions and strain rates was studied through various rate-controlled unsaturated/undrained triaxial tests. The fully saturated reconstituted specimens were desaturated to four different initial suctions (s₀?=?0, 100 kPa, 200 kPa and 300 kPa) and then triaxially sheared (conventional triaxial compression) at three different strain rates in undrained conditions (\(\dot{\varepsilon }_{1} = 0.001\) h^?1, 0.01 h^?1, and 0.1 h^?1). The observed hydro-mechanical behaviour during shearing including the volumetric strain, deviatoric stress, degree of saturation and suction is presented and discussed in this paper. The results indicate that when the strain rate rises at the given initial suctions (or pore water pressures), the maximum deviatoric stress (q_max), critical net stress ratio (M) and critical state suction (s_c) increase but the degree of saturation (S_rc) and volumetric strain at the critical state (ε^c_v ) reduce. The critical effective stress ratio (M′) is not dependent on the strain rate for saturated and unsaturated samples. The critical state lines for unsaturated soils with the constant strain rates are parallel with each other in the e???lnp′ space.

     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison of the characteristics of rock salt exposed to loading and unloading of confining pressures

Rock mechanical behaviors and deformation characteristics are associated with stress history and loading path. Unloading conditions occur during the formation of a salt cavity as a result of washing techniques. Such conditions require an improved understanding of the mechanical and deformation behaviors of rock salt. In our study, rock salt dilatancy behaviors under triaxial unloading confining pressure tests were analyzed and compared with those from conventional uniaxial and triaxial compression tests. The volume deformation of rock salt under unloading was more than under triaxial loading, but less than under uniaxial loading (with the same deviatoric stress). Generally, under the same axial compression, the corresponding dilatancy rate decreased as the confining compression increased, and under the same confining compression, the corresponding dilatancy rate increased as the axial compression increased. The dilatancy boundary of the unloading confining pressure test began with unloading. This is different from the dilatancy of the uniaxial and triaxial compression tests. The accelerated dilatancy point boundary stress value was affected by confining and axial compressions. The specimens entered into a creep state after unloading. The associated creep rate depends on the deviatoric stress and confining compression values at the end of the unloading process. Based on unloading theory and the experimental data, we propose a constitutive model of rock salt damage. Our model reflects the dilatancy progression at constant axial stress and reduced lateral confinement.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

A coupled chemo‐thermo‐hygro‐mechanical model of concrete at high temperature and failure analysis

A hierarchical mathematical model for analyses of coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible–miscible levels. The thermo‐induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo‐thermo‐hygro‐mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non‐self‐adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes subjected to fire and thermal radiation. Copyright © 2005 John Wiley & Sons, Ltd.     

Petrogenesis of Late Cretaceous Jiangla’angzong I-Type Granite in Central Lhasa Terrane, Tibet, China: Constraints from Whole-Rock Geochemistry, Zircon U-Pb Geochronology, and Sr-Nd-Pb-Hf Isotopes

The Jiangla'angzong granite in the northern part of the Central Lhasa Terrane is composed of syenogranite and adamellite. LA-ICP-MS zircon U-Pb analyses suggest that syenogranite has a weighted mean ~(206) Pb/~(238) U age of 86±1 Ma(mean square weighted deviation=0.37), which is in accordance with the muscovite Ar-Ar age(85±1 Ma) of Cu-Au ore-bearing skarns and the zircon U-Pb age(84±1 Ma) of adamellite. This suggests that the Jiangla'angzong magmatism and Cu–Au mineralization events took place during the Late Cretaceous. The granite contains hornblende, biotite, and pyroxene, and does not contain Al-bearing minerals, such as muscovite, cordierite, and garnet. It has high contents of SiO_2(65.10–70.91 wt%), K_2O(3.44–5.17 wt%), and total K_2O+Na_2O(7.13–8.15 wt%), and moderate contents of A_(12)O_3(14.14–16.45 wt%) and CaO(2.33–4.11 wt%), with a Reitman index(σ43) of 2.18 to 2.33, and A/CNK values of 0.88 to 1.02. The P_2O_5 contents show a negative correlation with SiO_2, whereas Pb contents show a positive correlation with SiO_2. Th and Y contents are relatively low and show a negative correlation with the Rb contents. These characteristics suggest that the Jiangla'angzong granite is a high K calc–alkaline metaluminous I–type granite. It is enriched in light rare earth elements(LREE) and large ion lithofile elements(LILE), and depleted in heavy rare earth elements(HREE) and high field strength elements(HFSE), with LREE/HREE ratios of 11.7 to 18.1. The granite has negative Eu anomalies of 0.58 to 0.94 without obvious Ce anomalies(δCe=1.00–1.04). The relatively low initial 87 Sr/86 Sr ratios of 0.7106 to 0.7179, positive εHf(t) values of 1.0 to 4.1, and two-stage Hf model ages(TDM2) ranging from 889 Ma to 1082 Ma, These geochemical features indicate that the granite derived from a juvenile crust. The(~(143) Nd/~(144) Nd)_t values from the Jiangla'angzong granite range from 0.5121 to 0.5123, its εNd(t) values range from-10.17 to-6.10, its(~(206) Pb/~(204) Pb)_t values range from 18.683 to 18.746, its(~(207) Pb/~(204) Pb)_t values range from 15.695 to 15.700, and its(~(208) Pb/~(204) Pb)_t values range from 39.012 to 39.071. These data indicate that the granite was formed by melting of the upper crust with the addition of some mantle materials. We propose that the Jiangla'angzong granite was formed during the postcollision extension of the Qiangtang and Lhasa terranes.     

Photoelastic and numerical investigation of stress distributions around fault models under biaxial compressive loading conditions

This paper presents the results of a photoelastic and numerical study of stress distributions (contours and trajectories) around fault models of various geometries, submitted to a biaxial compressive load. It aims to describe typical biaxial stress behaviours and emphasize the existing differences with the well-known uniaxial compressive load case. Stress trajectories are sometimes shown by joint sets acting as markers of a paleostress field, and they can be interpreted by particular shallow tension–compression situations. At depth fractures can be reactivated, or can dilate under conditions of triaxial compression, and behaviour is essentially controlled by a high stress ratio (high σ₃/σ₁ ratio). In spite of the potential importance of such stress states on fracture permeability and fluid flow, and although they are frequently found at depth in a reservoir context, such stress conditions are poorly investigated, particularly in terms of stress perturbations.The presented analogue experiments consisted of compression tests done on polymethylmethacrylate (PMMA) plates; this material has mechanical properties comparable to those of brittle rocks in the upper crust, and presents birefringence. The samples contained open defects acting as faults, and the stress trajectories around these faults were investigated using a photoelastic device. Comparable numerical experiments were realised with a finite-element code (Franc 2D), using frictionless fault models.First, the effect of an increasing biaxial compressive load ratio σ₃/σ₁ on stress trajectories around an isolated open defect was explored. It was shown that the stress trajectories were drastically modified when σ₃/σ₁ increased from 0.2 to 0.4, this result being consistent with previous studies. In particular, when σ₃/σ₁ was superior or equal to 0.4, external isotropic points around where trajectories diverged (called repulsive isotropic points) appeared near the tips, but away from the defects. They tended to move away from the defects towards the main load direction when σ₃/σ₁ increased. The described isotropic points were points of stress trajectory divergence, i.e. points where stress decreased, implying that zones around them were strongly unfavourable to shear reactivation.Second, stress trajectories around fault models of various geometries (oblique isolated defect, dilational jog, compressive jog, and complex patterns) were studied, the applied biaxial compressive load ratio being 0.7. These biaxial stress trajectories were compared with similar uniaxial stress trajectories in order to explore the existing differences between the two regimes. It enabled new stress trajectory geometries to be described and interpreted. In particular, numerous external repulsive isotropic points were observed, and defect tips were shown to be zones of high convergence of stress trajectories. Furthermore, in contrast to the uniaxial compressive load case, stress trajectories and stress contours were geometrically similar within dilational and compressive jogs under biaxial compressive load. For both jog types, the centre of the overlapping zone, and the areas along the wall of a jog-defining fault and facing the overlapping tip of the other fault, proved to be zones of low mean stress, implying that fluids may migrate towards them from the tips of the faults, in response to mean stress gradients. Furthermore, the centre of the jogs exhibiting a high differential stress was a favourable area in terms of fracture reactivation, which may facilitate fluids transfer and storage.It was also observed that for both the uniaxial and biaxial compressive loads, isotropic zones were localised at the acute angle between branching defects.     

Experimental and theoretical investigation of the high‐pressure behavior of concrete

The results of an experimental study aimed at characterizing the behavior of concrete for high confining pressures (up to 500 MPa) are reported. The main characteristics of the response under deviatoric conditions are quasi‐linearity in the elastic regime, stress‐path dependency, and gradual change from compressibility to dilatancy under increasing deviatoric stress. By performing the cyclic triaxial compression tests with several load–creep–unload and reload cycles, the time influence on the overall behavior was detected. Further, whether the main features of the observed behavior can be described within the framework of elastic/viscoplasticity theory was investigated. For this purpose, Cristescu's (Rock Rheology. Kluwer Academic Publishers: The Netherlands, 1989) approach was used. It was shown that the proposed elastic/viscoplastic model captures the main features of concrete behavior at high pressures. Copyright © 2008 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.     

Stress‐dependent hardening and failure surfaces of dry sand

During several triaxial compression experiments on plastic hardening, softening, and failure properties of dense sand specimens, it was found on various stress paths that the size of the failure surface was not constant. Instead, it changed depending on the current state of hydrostatic pressure. This finding is in contrast to the standard opinion consisting of the fact that the failure surface remains constant, once it has been reached during an experiment or in situ. In general, the behaviour of cohesionless granular‐material‐like sand is somehow characterised in between fluid and solid, where the solid behaviour results from the angle of internal friction and the confining pressure. Although the friction angle is an intrinsic material property, the confining pressure varies with the boundary conditions, thus defining different solid properties like plastic hardening, softening, and also failure. Based on our findings, it was the goal of the present contribution to introduce an improved setting for the plastic strain hardening and softening behaviour including the newly found yield properties at the limit state. For the identification of the material parameters, a complete triaxial experimental analysis of the tested sand is given. The overall elasto‐plasticity concept is validated by numerical computations of several laboratory foundation‐ and slope‐failure experiments. The performance of the proposed approach is compared with the standard concept of a constant failure surface, where the corresponding yield surfaces are understood as contours of equivalent plastic work or plastic strain. Copyright © 2012 John Wiley & Sons, Ltd.     

A macroscopic damage‐plastic constitutive law for modeling quasi‐brittle fracture and ductile behavior of concrete

A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response:

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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.     

A solution around a backfilled cavity in a low‐permeability poroelastic medium with application in in situ heating tests

Thermo‐hydro‐mechanical responses around a cylindrical cavity drilled or excavated in a low‐permeability formation are studied when the cavity is subjected to a time‐dependent thermal loading. The cavity is considered backfilled after it is supported by casing or lining. Solutions of temperature, pore water pressure, stress, and displacement responses are analytically formulated based on Biot's consolidation theory with the assumption that the backfilling material, supporting material, and surrounding low‐permeability formation are poroelastic media. The solution is expressed in Laplace space, and numerical inversion techniques are used to find field variables in the real‐time domain. After the solution is verified with the numerical results, it is applied in a large‐scale in situ heating test – PRACLAY heating test – for a predictive reference calculation and an extensive parametric study. Another medium‐scale in situ heating test – ATLAS III heating test – is also analyzed using the solution, which provides reasonable agreement with measurements. The new analytical solution proves to be a convenient tool for a good understanding of the resulting coupled thermo‐hydro‐mechanical behavior and is therefore valuable for the interpretation of measured data in engineering practices and for a rational design of potential radioactive waste repositories. Copyright © 2016 John Wiley & Sons, Ltd.     

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and time-dependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10?6 s?1 to 1×10?3 s?1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value (about 0.1 to 0.2), soon reaches its minimum (about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.