Numerical analysis of anisotropic stiffness and strength for geomaterials

In numerical modelling,selection of the constitutive model is a critical factor in predicting the actual response of a geomaterial.The use of oversimplified or inadequate models may not be sufficient to reproduce the actual geomaterial behaviour.That selection is especially relevant in the case of aniso-tropic rocks,and particularly for shales and slates,whose behaviour may be affected,e.g.well stability in geothermal or oil and gas production operations.In this paper,an alternative anisotropic constitutive model has been implemented in the finite element method software CODE_BRIGHT,which is able to account for the anisotropy of shales and slates in terms of both deformability and strength.For this purpose,a transversely isotropic version of the generalised Hooke’s law is adopted to represent the stiffness anisotropy,while a nonuniform scaling of the stress tensor is introduced in the plastic model to represent the strength anisotropy.Furthermore,a detailed approach has been proposed to determine the model parameters based on the stressestrain results of laboratory tests.Moreover,numerical analyses are performed to model uniaxial and triaxial tests on Vaca Muerta shale,Bossier shale and slate from the northwest of Spain(NW Spain slate).The experimental data have been recovered from the literature in the case of the shale and,in the case of the slate,performed by the authors in terms of stress-strain curves and strengths.A good agreement can be generally observed between numerical and experi-mental results,hence showing the potential applicability of the approach to actual case studies.Therefore,the presented constitutive model may be a promising approach for analysing the anisotropic behaviour of rocks and its impact on well stability or other relevant geomechanical problems in aniso-tropic rocks.

Particle flow code simulation of intact and fissured granitic rock samples

This study presents a calibration process of three-dimensional particle flow code(PFC3D)simulation of intact and fissured granite samples.First,laboratory stressestrain response from triaxial testing of intact and fissured granite samples is recalled.Then,PFC3D is introduced,with focus on the bonded particle models(BPM).After that,we present previous studies where intact rock is simulated by means of flatjoint approaches,and how improved accuracy was gained with the help of parametric studies.Then,models of the pre-fissured rock specimens were generated,including modeled fissures in the form of“smooth joint”type contacts.Finally,triaxial testing simulations of 1 t 2 and 2 t 3 jointed rock specimens were performed.Results show that both elastic behavior and the peak strength levels are closely matched,without any additional fine tuning of micro-mechanical parameters.Concerning the postfailure behavior,models reproduce the trends of decreasing dilation with increasing confinement and plasticity.However,the dilation values simulated are larger than those observed in practice.This is attributed to the difficulty in modeling some phenomena of fissured rock behaviors,such as rock piece corner crushing with dust production and interactions between newly formed shear bands or axial splitting cracks with pre-existing joints.

Validity of continuous-failure-state unloading triaxial tests as a means to estimate the residual strength of rocks

The residual strength of rocks and rock masses is an important parameter to be constrained for analysis and design purposes in many rock engineering applications.A residual strength envelope in principal stress space is typically developed using residual strength data obtained from compression tests on many different specimens of the same rock type.In this study,we examined the potential for use of the continuous-failure-state testing concept as a means to constrain the residual strength envelope using a limited number of specimens.Specifically,cylindrical specimens of three rock types(granodiorite,diabase,and Stanstead granite)were unloaded at the residual state such that a full residual strength envelope for each individual specimen was obtained.Using a residual strength model that introduces a single new strength parameter(the residual strength index,or RSI),the results of the continuous-failurestate unloading tests were compared to conventionally obtained residual strength envelopes.Overall,the continuous-failure-state residual strength data were found to be consistent with the conventional residual strength data.However,it was identified that the primary factor limiting an accurate characterization of the residual strength for a given rock type is not the amount of data for a given specimen,but the variety of specimens available to characterize the inherent variability of the rock unit of interest.Accordingly,the use of continuous-failure-state testing for estimation of the residual strength of a rock unit is only recommended when the number of specimens available for testing is very limited(i.e.<5).