The influence of the plastic potential on plane strain failure

The influence of the shape of the plastic potential in the deviatoric plane on plane strain collapse is investigated. The most commonly employed elastic‐perfect plastic models are considered, which adopt well‐known failure criteria for defining the yield and plastic potential surfaces, namely the von Mises, the Drucker–Prager, the Tresca, the Mohr–Coulomb and the Matsuoka–Nakai criteria. Finally, the conclusions are also extended to strain hardening/softening models. For simple constitutive models based on perfect plasticity, it is shown that the value of the Lode's angle at plastic collapse in plane strain conditions strongly depends on the specific failure surface adopted for reproducing the plastic potential surface. If the value of the Lode's angle at yield coincides with the failure value prescribed by the plastic potential, the stress–strain curves exhibit the typical perfect plastic behaviour with yield coinciding with failure, otherwise the stress changes after yield and the stress‐strain curves resemble those of strain hardening/softening models. The infinite strength which is in some situations exhibited by the Drucker–Prager model in plane strain condition is investigated and explained, and it is shown that this can also affect strain hardening/softening models. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

SPH procedures for modeling multiple intersecting discontinuities in geomaterial

A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system. The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.     

A two‐mechanism elastoplastic model for shakedown of unbound granular materials and DEM simulations

An elastoplastic model has been developed for the finite elements modelling of repeated load triaxial tests. This model is based on the shakedown theory established by Zarka for metallic structures. To the previous works, which were based on the Drucker–Prager yield surface and the plastic potential of Von Mises, a compression cap has been added to each one. The model straightforwardly determines the purely elastic state or the elastic shakedown state or the plastic shakedown state and calculates the deviatoric and the volumetric plastic strains. The calibration of the elastoplastic model has been carried out with DEM simulations and an unbound granular material for roads under repeated load triaxial tests using finite element method. The calculations underline the capabilities of the model to take into account, with a unique formalism, the accumulation of the deviatoric and volumetric plastic strains along the loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of rock failure behaviour on predictions in sand production problems

The mechanical strength of rock in terms of shear or compressive failure has been previously adopted as a criterion for sand production and when used solely has been proven to overestimate the process. On the other hand, ignoring the mechanical strength behaviour of the material increases the tendency for inaccurate estimations of the erosion process. In this work, an equally proportionated inclusion of the mechanical strength and erosion-based criteria in sanding predictions is proposed and assessed by numerical models. Several rock failure models and their influences on the sanding process have been analysed, including models such as the Drucker–Prager (DP), the Drucker–Prager hardening (DP hardening), the Mohr–Coulomb (MC) and the Mohr–Coulomb softening (MC softening). Modelling outcomes show distinct differences in rock response to operating and boundary conditions (e.g. flow rate and drawdown), and predictions of sand production. It was confirmed by modelling results that despite the low magnitude of stresses and strains developed at the well face and perforation regions, post-yield hardening behaviour increases the estimation of the amount and intensity of sand production. Also, incorporating a post-yield softening behaviour increases the magnitude of stresses and strains; however, this effect is observed to have a negligible impact on sand production. The role of void ratio has been recognised as a dominant factor, as its evolution significantly determines the pattern and intensity of sand production. A more cautious selection and rigorous coupling of rock strength models in sand production modelling is therefore essential if accuracy of predictions is to be improved.     

Three-dimensional elastic–viscoplastic consolidation behavior of transversely isotropic saturated soils

Acta Geotechnica - This paper investigates three-dimensional elastic–viscoplastic consolidation behaviors of transversely isotropic saturated soils. The Drucker–Prager yield criterion...     

Scratch hardness–strength solutions for cohesive‐frictional materials

In this paper we develop analytical solutions for scratch hardness–strength relations for cohesive‐frictional materials of the Mohr–Coulomb and Drucker–Prager type. Based on the lower bound yield design approach, closed‐form solutions are derived for frictionless scratch devices, and validated against computational upper bound and elastoplastic finite element solutions. The influence of friction at the blade–material interface is also investigated, for which a simple computational optimization is proposed. Illustrated for scratch tests on cement paste, we show that the proposed solutions provide a convenient way to determine estimates of cohesion and friction parameters from scratch data, and may serve as a benchmark to identify the relevance of strength models for scratch test analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Failure criteria for cohesive‐frictional materials based on Mohr–Coulomb failure function

This study presents two three‐parameter failure criteria for cohesive‐frictional materials based on the Mohr–Coulomb failure function. One proposed failure criterion can be linked to Mogi's empirical formula and incorporates the well‐known Von‐Mises, Drucker–Prager, and Linear Mogi criteria as special cases. Another one with smooth and convex cross sections contains a general Lode dependence in the deviatoric plane and includes the Matsuoka–Nakai and Lade–Duncan Lode dependences as special cases. The effect of the intermediate principal stress on the strength of the material can be taken into account in both criteria. The proposed criteria are numerically calibrated against polyaxial data sets of many different types of rocks and concrete_. The comparison results show that the performance of the proposed criteria is excellent, and the failure criterion with a general Lode dependence performs better than the other one for concrete. Copyright © 2015 John Wiley & Sons, Ltd.     

A Damage Mechanics Model for Porous Media

When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. This paper introduces the concept of effective stress and the modified Mohr–Coulomb criterion as a means for examining the problem of consolidation response of a damage-susceptible poroelastic geomaterial, which is considered to be a novel development in the application of damage mechanics to the study of poroelastic phenomena. Then, a damage mechanics model for porous media is established and applied to analyze the Biot’s consolidation problem of damaged soils. The comparison between the numerical predictions and the classical solutions shows that the computational damage model developed in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media.     

Determination of Yield Surfaces for Isotropic Non-Cohesive Particulate Materials by the Discrete Element Method

We perform numerical simulations using the discrete element method (DEM) to determine yield surfaces for large samples of randomly packed uniform spheres with constant normal and tangential contact stiffnesses (linear spring model) and uniform inter-particle friction coefficient μ, for a large range of values of the inter-particle friction coefficient μ. The beauty of DEM is that the micromechanical properties of the spheres, especially the inter-particle friction coefficient μ, are known exactly. Further, simulations can be performed with particle rotation either prohibited or unrestrained, which provides an effective means for evaluating analytical models that employ these assumptions. We compare the resulting yield surfaces to the Mohr–Coulomb, Matsuoka–Nakai, Lade–Duncan, and Drucker–Prager yield surfaces, and determine the relationship between the resulting material friction angle ? on the macroscale and the inter-particle friction coefficient μ (or the inter-particle friction angle ? _μ ) on the microscale. We find the Lade–Duncan yield surface provides the best agreement, by far, with the simulations in all cases. We also monitor inter-particle friction work and particle rotation within each specimen during the DEM simulations, both globally and on a particle-by-particle basis, and we compare the results obtained from DEM simulations in which the spheres were allowed full three-dimensional translational and rotational freedom of motion and DEM simulations in which particle rotation was prohibited.     

A generalized nonlinear failure criterion for frictional materials

A generalized nonlinear failure criterion formulated in terms of stress invariants is proposed for describing the failure characteristics of different frictional materials. This failure criterion combines a power function and a versatile function in the meridian and deviatoric plane, respectively, which is a generalization of several classic criteria, including the Tresca, Drucker–Prager, Mohr–Coulomb, Lade–Duncan and Matsuoka–Nakai failure criterion. The procedure for determination of the strength parameters was demonstrated in detail. Comparisons between the failure criterion and experimental results were presented for uncemented/cemented Monterey sand, normally consolidated Fujinomori clay, rockfill, concrete, Mu-San sandstone and granite, which reveal that the proposed failure criterion captures experimental trend quite well.     

Effect of plastic deformation on hydraulic fracturing with extended element method

The propagation of hydraulic fracture in elastic rocks has widely been investigated. In the paper, we shall focus on numerical modeling of hydraulic fracturing in a class of porous rocks exhibiting plastic deformation. The plastic strain of porous rocks is described by a non-associated plastic model based on Drucker–Prager criterion. The plastic deformation is coupled with fluid pressure evolution described by the lubrication theory. An extended finite element method is used for modeling the propagation of fracture. The fracture propagation criterion is based on the J-integral. The proposed numerical model is validated by comparisons with numerical and analytical results. The influence of plastic deformation on fracture propagation process is investigated.

     

Finite strain elastoplastic solutions for the undrained ground response curve in tunnelling

The instantaneous response of saturated low permeability grounds to tunnel excavation is important for deformations and stability close to the tunnel face. It is characterized by zero volume change in combination with the development of excess pore pressures. In tunnelling through poor quality ground under great depth of cover and high in situ pore pressure, heavily squeezing conditions (characterized by very large convergences) may occur soon after excavation. This paper presents exact finite strain analytical solutions for the undrained ground response around cylindrical and spherical openings that are unloaded from uniform and isotropic initial stress states, on the basis of the Modified Cam Clay (MCC) model and the Mohr–Coulomb (MC) model. The solution for a Drucker–Prager material is also given as it requires only a very small modification to the MC solution. The so‐called ground response curve, that is, the relationship between the support pressure and the cavity wall displacement, is derived in closed form for the MC model. The solution for the MCC problem is semi‐analytical in that it uses the trapezium rule for the computation of a definite integral. The influence of the significant parameters of the problem on the predicted deformation behaviour is shown by means of dimensionless charts. Finally, the practical usefulness of the solutions presented is illustrated by applying them to the breccia zones of the planned Gibraltar Strait tunnel – an extreme case of weak, low permeability ground under high pore pressure. The solutions can serve as a trustworthy benchmark for numerical procedures that incorporate material and geometric nonlinearities. Copyright © 2014 John Wiley & Sons, Ltd.     

Fully coupled solution for the consolidation of poroelastic soil around elastoplastic stone column

The paper presents a new fully coupled elastoplastic solution for the response of a poroelastic thick-walled soil cylinder around an elastoplastic stone column using Biot’s (J Appl Phys 12:155–164, 1941) consolidation theory. A unit cell concept is adopted for the soil–stone column analysis, and the problem is formulated in cylindrical coordinates. Expressions for excess pore pressure, stresses and displacements in the Laplace domain are derived analytically taking into account elastic or plastic behavior of the column. The inverse of the Laplace transform is evaluated numerically using an efficient scheme to obtain the final elastoplastic solution in time domain. The validity of the new solution has been checked against finite element solution and compared with some previously developed analytical methods for the stone column analysis. The results showing settlements, change in excess pore pressures and stresses with time are presented in terms of time factor. The proposed solution can be used to calculate transient state of settlements, distribution of deformations, stresses and excess pore pressures in soil and column under instantaneous or time-dependent monotonically increasing rigid vertical load.     

ELASTOPLASTIC ANALYSIS OF CYLINDRICAL CAVITY PROBLEMS IN GEOMATERIALS

A large-strain elastoplastic analysis is presented for a cylindrical cavity embedded in an infinite medium under uniform radial pressure. The investigation employs invariant, non-associated deformation-type theories for Mohr–Coulomb (M–C) and Drucker–Prager (D–P) solids, accounting for arbitrary hardening, with the equivalent stress as the independent variable. The M–C model results in a single first-order differential equation, whereas for the D–P solid an algebraic constraint supplements the governing differential equation. Material parameters and response characteristics were determined by calibrating the models with data from triaxial compression tests on Castlegate sandstone and on Jurassic shale. A comparison is presented between predictions obtained from the two models and experimental data from hollow cylinder tests under external loading. A sensitivity of the results to material parameters, like friction and dilation angles, is provided for the case of a cavity subjected to internal pressure in terms of limit pressure predictions. In all cases it has been found that the results of the D–P inner cone model are in close agreement with those obtained from the M–C model. © 1997 by John Wiley & Sons, Ltd.     

ELASTOPLASTIC RESPONSE OF PRESSURE SENSITIVE SOLIDS

Tensorially invariant constitutive relations are systematically derived for large strain elastoplastic response of geomaterials. The analysis centres on Mohr–Coulomb (MC) and Drucker–Prager (DP) models with arbitrary hardening and non-associated response. Both flow and deformation theories are constructed for each model with emphasis on linear incremental relations between the Eulerian strain rate tensor and the objective Jaumann stress rate tensor. Specifying the results for plane strain compression we find that deformation theory produces a much smaller tangent instantaneous shear modulus than flow theory. It follows that failure of ellipticity and onset of surface instabilities predicted by deformation theory for associated solids occur at much lower levels of strain than the corresponding flow theory results. On the other hand, flow theory predictions admit a considerable sensitivity to the level of non-associativity. In fact, at high levels of non-associativity flow theory predictions for loss of ellipticity can be at strains below those obtained from deformation theory. © 1997 John Wiley & Sons, Ltd.     

Application of a unified linear yield criterion in plane strain to study the strength theory effect in geotechnical engineering

The plane strain condition is a common, but polyaxial stress state for geotechnical structure designs, in which the selection of an appropriate yield or failure criterion is crucial to reasonably account for the intermediate principal stress. Under plane strain condition, a unified linear yield criterion for seven commonly used geotechnical yield criteria is presented in conjunction with the inductive method. These seven yield criteria considered in this study are the Mohr–Coulomb, Tresca, Drucker–Prager, Mogi–Coulomb, Extended Matsuoka–Nakai, Extended Lade–Duncan criteria, and the Unified Strength Theory. The generalized analytical solutions for earth pressure of retaining walls, critical load of strip foundations as well as stress and displacement of circular tunnels are derived on the basis of the proposed unified yield criterion, and their respective theoretical significance is analyzed. Thereafter, the critical load of strip foundations obtained herein is compared with two numerical results from the literature. Furthermore, the effect of strength theory on result differences of the three typical geotechnical problems by simply selecting constants, which conform to different yield criteria, is explored through a parametric study. It is found that the proposed unified yield criterion is convenient for investigating analytical solutions of the aforementioned geotechnical structures. The strength theory effect due to adopting different yield criteria is considerably significant, which cannot be ignored. Additionally, recommendations are provided on how to make use of these seven yield criteria for an optimum design.     

Numerical analysis of the installation effect of diaphragm walls in saturated soft clay

The construction of diaphragm wall panels can cause the stress change and soil movements in adjacent ground. In this paper, the construction sequence of a typical diaphragm wall panel in saturated soft clay is simulated with a 3D finite element program. The soil is assumed to behave as an isotropic linear elastic/Mohr–Coulomb plastic material with a soil–water coupled consolidation response. Influence of the pore water pressure is concerned to consider the consolidation behavior of the saturated soft clay. The analysis shows that the changes in effective horizontal stress and pore water pressure during diaphragm wall installation depend on arching mechanism and permeability. The variation in stresses and movements of ground computed by the coupled consolidation analysis and the total stress analysis are compared. Influences of the permeability coefficient on the installation effects are discussed by parametric studies. Finally, a case study of a diaphragm wall construction in Shanghai, in which the ground settlements were monitored, is presented to illustrate the prediction procedure of coupled consolidation analysis.     

Analytical and numerical analyses of the load‐bearing capacity of retaining walls laterally supported at both ends

This paper investigates the load‐bearing capacity of a perfectly smooth retaining wall laterally supported at both ends assuming that the wall fails by the development of three plastic hinges. The study considers the case of a cohesionless elastic–perfectly plastic backfill with a Mohr–Coulomb yield criterion and an associative flow rule in drained conditions. A kinematically admissible soil–structure failure mechanism is proposed and compared with the conventional solutions and with results from a numerical finite element modelling. The study shows that the proposed solution and the numerical solution are in good agreement. These solutions are found to be much more favourable for the wall than the conventional solutions. Copyright © 2010 John Wiley & Sons, Ltd.