A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction.This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures.The issue stems from the pressure independent hardening law in the classical deviatoric hardening model.To overcome this problem,we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations.Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands.Furthermore,to examine the importance of the improved deviatoric hardening model,it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures.It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Assessment of cyclic deformation and critical stress amplitude of jointed rocks via cyclic triaxial testing

Jointed rock specimens with a natural replicated joint surface oriented at a mean dip angle of 60were prepared,and a series of cyclic triaxial tests was performed at different confining pressures and cyclic deviatoric stress amplitudes.The samples were subjected to 10,000 loading-unloading cycles with a frequency of 8 Hz.At each level of confining pressure,the applied cyclic deviatoric stress amplitude was increased incrementally until excessive deformation of the jointed rock specimen was observed.Analysis of the test results indicated that there existed a critical cyclic deviatoric stress amplitude(i.e.critical dynamic deviatoric stress)beyond which the jointed rock specimens yielded.The measured critical dynamic deviatoric stress was less than the corresponding static deviatoric stress.At cyclic deviatoric stress amplitudes less than the critical dynamic deviatoric stress,minor cumulative residual axial strains were observed,resulting in hysteretic damping.However,for cyclic deviatoric stresses beyond the critical dynamic deviatoric stress,the plastic strains increased promptly,and the resilient moduli degraded rapidly during the initial loading cycles.Cyclic triaxial test results showed that at higher confining pressures,the ultimate residual axial strain attained by the jointed rock specimen decreased,the steadystate dissipated energy density and steady-state damping ratio per load cycle decreased,while steadystate resilient moduli increased.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON’S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.

A generalized three-dimensional failure criterion for rock masses

The smooth convex generalized failure function, which represents 1/6 part of envelope in tile deviatoric plane, is proposed. The proposed function relies on four shape parameters （L, a, b and c）, in which two parameters （a and b） are dependent on the others. The parameter Ls is called extension ratio. The proposed failure function could be incorporated with any two-dimensional （2D） failure criteria to make it a three-dimensional （3D） version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion tbr geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering （1） constant extension ratio and （2） variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio （L~） that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters （c~. and m） are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameterfis introduced. The modified extension ratio is related tofand extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range off varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression betweenfand Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.

Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials

Discrete element method(DEM)has been intensively used to study the constitutive behaviour of granular materials.However,to what extent a real granular material can be reproduced by virtual DEM simulations remains unclear.This study attempts to answer this question by comparing DEM simulations with typical features of experimental granular materials.Three groups of models with spherical and clumped particles are investigated from four perspectives:(i)deviatoric stress and volumetric behaviour;(ii)critical state behaviour;(iii)stress-dilatancy relationship;and(iv)the evolution of principal stress ratio against axial strain.The results demonstrate that DEM with spherical or clumped particles is capable of qualitatively describing macroscopic deviatoric stress responses,volumetric behaviour,and critical state behaviour observed in experiments for granular materials.On the other hand,some qualitative deviations between experiments and the investigated DEM simulations are also observed,in terms of the stress-dilatancy behaviour and principal stress ratio against axial strain,which are proven to be critical for constitutive modelling.The results demonstrate that DEM with spherical or clumped particles may not necessarily fully capture experimental features of granular materials even from a qualitative perspective.It is thus encouraged to thoroughly validate DEM with experiments when developing constitutive models based on DEM observations.

Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.

Discussion on “A generalized three-dimensional failure criterion for rock masses”

There are many methods to construct true triaxial strength criteria for rocks.Jaiswal and Shrivastva(2012)proposed a strength criterion,named J–S criterion,in the deviatoric plane,which provides nearly the same misfts for true triaxial test data as the exponential criterion.It is diffcult to calculate the strength at given2and3using the J–S criterion,and the multiple solutions to the nonlinear equation may induce confusion and mistake.Strength envelopes in deviatoric planes are not geometric similar;therefore,true triaxial test data cannot be grouped in the mean stress to check strength criteria in the deviatoric plane.

Mechanical Analysis of Viscous-Elastic Fluid Acting on Residual Oil in the Micro Pore

In order to analyze the normal deviatoric stress that viscous-elastic fluid acting on the residual oil under the situation of different flooding conditions and different permeabilities, Viscous-elastic fluid flow equation is established in the micro pore by choosing the continuity equation, motion equation and the upper-convected Maxwell constitutive equation, the flow field is computed by using numerical analysis, the forces that driving fluid acting on the residual oil in micro pore are got, and the influence of flooding conditions, pore width and viscous-elasticity of driving fluid on force is compared and analyzed. The results show that: the more viscous-elasticity of driving fluid increases, the greater the normal deviatoric stress acting on the residual oil increases;using constant pressure gradient flooding, the lager the pore width is, the greater normal deviatoric stress acting on the residual oil will be.

Use of the Cam-Clay Model in Finite Element Calculations after Identification of Soils from Simple Mechanical Tests

In order to make the use of complex elasto-plastic behavior models more accessible, we attempted to identify the Cam-Clay model in two samples of tropical and lateritic soils (from Senegal/West Africa) from casagrande box shear and oedometric tests. This methodology was used as a substitute for triaxial trials. In this article, we first verify the test results by the finite element method with the Optum software. We use a simulation of the tests with the modified Cam Clay model as the behavior model. Then, we simulate the oedometric test on tropical soils with the Castem software and also use the modified Cam Clay model. These calculations make it possible to write the criterion of plasticity of the material starting from the expression of the surface of load while passing by the calculation of the volumetric and deviatoric stresses.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

Experimental study on the dynamic modulus of compacted loess under bidirectional dynamic load

The dynamic characteristics of compacted loess are of great significance to the seismic construction of the Loess Plateau area in Northwest China,where earthquakes frequently occur.To study the change in the dynamic modulus of the foundation soil under the combined action of vertical and horizontal earthquakes,a hollow cy-lindrical torsion shear instrument capable of vibrating in four directions was used to perform two-way coupling of compression and torsion of Xi'an compacted loess under different dry density and deviator stress ratios.The results show that increasing the dry density can improve the initial dynamic compression modulus and initial dynamic shear modulus of compacted loess.With an increase in the deviator stress ratio,the initial dynamic compression modulus increases,to a certain extent,but the initial dynamic shear modulus decreases slightly.The dynamic modulus gradually decreases with the development of dynamic strain and tends to be stable,and the dynamic modulus that reaches the same strain increases with an increasing dry density.At the initial stage of dynamic loading,the attenuation of the dynamic shear modulus with the strain development is faster than that of the dynamic compression modulus.Compared with previous research results,it is determined that the dynamic modulus of loess under bidirectional dynamic loading is lower and the attenuation rate is faster than that under single-direction dynamic loading.The deviator stress ratio has a more obvious effect on the dynamic compression modulus.The increase in the deviator stress ratio can increase the dynamic compression modulus,to a certain extent.However,the deviator stress ratio has almost no effect on the dynamic shear modulus,and can therefore be ignored.

J^＊ INTEGRAL OF THE SPECIFIC DEVIATOR STRAIN ENERGY AND ITS APPLICATION

First the deviator strain energy is introduced, then the problem of plane-crack critical growth was discussed, a path independent line integral J* was defined, furthermore its conservation was proved strictly. As application examples, Mode-I stress intensity factors of cracked beams were obtained with present approach. The results are shown to agree well with those available in the open literature.

Characteristics and geological significance of the stress state of the lithosphere in the Qinghai-Tibetan Plateau and its neighboring areas

The present-day lithospheric stress state of the Qinghai-Tibetan Plateau and neighboring areas is controlled by both the lithosphere itself and the underlying mantle.In other words,the stress is affected by the gravitational potential energy(GPE)difference caused by the change in the density distribution within the lithosphere and the drag force on the base of the lithosphere caused by mantle convection.The study of the lithospheric stress state plays an important role in further understanding the dynamic background and mechanism for the evolution of the Qinghai-Tibetan Plateau.In this study,the Crust1.0 crustal density model combined with the S40RTS mantle shear wave velocity variation model was used to calculate the GPE.The EGM2008gravity field model was used to calculate the drag force from mantle convection at the base of the lithosphere.The lithospheric and joint stress fields of the two sources were obtained by solving the force balance under the thin sheet approximation.This way,we could comprehensively analyze the characteristics of the stress state within the Plateau.Six regions were classified according to the GPE stress field,mantle drag force stress field,the relative magnitude of the two stress fields,and correlation between the two stress fields and surface deformation.The lithospheric stress fields of the Tarim Basin and other stable blocks are mainly controlled by the GPE difference.The lithospheric stress field in the collision zone between the Indian Plate and the QinghaiTibetan Plateau is predominantly controlled by the deep mantle drag force.The lithospheric stress field in the interior of the Plateau is controlled by both GPE and mantle drag.The correlation between the lithospheric stress field and surface deformation at the southeast margin of the Qinghai-Tibetan Plateau is poor.It is hypothesized that the presence of lower crustal flow with lower effective viscosity leads to crust-mantle decoupling,and the mantle drag force has a weaker influence on the shallow crust,resulting in the inconsistency between the average lithospheric stress field and surface deformation.

DEM SIMULATION OF LIQUEFACTION FOR GRANULAR MEDIA UNDER UNDRAINED AXISYMMETRIC COMPRESSION AND PLANE STRAIN CONDITIONS

Based on three dimensional （3D） Discrete Element Method （DEM）, the paper presents simulation results of undrained tests on loose assemblies of polydisperse spheres under axisymmet- ric compression and plane strain conditions using a periodic cell. In the present work, undrained tests were modelled by deforming the samples under constant volume conditions. The undrained （effective） stress paths are shown to be qualitatively similar to experimental results in literature. A microscopic parameter in terms of redundancy factor （RF） is used to identify the onset of lique- faction （or temporary liquefaction）, with the condition of RF equal to unity defining the transition from ＇solid-like＇ to ＇liquid-like＇ behaviour. It is found that the undrained behaviour is governed by the evolution of redundancy factor under both undrained axisymmetric compression and plane strain conditions, and a reversal of deviatoric stress in stress path for medium loose systems oc- curs due to the fact that the system becomes a structural mechanism （RF 〈 1） transiently at the microscopic level during the evolution.

A GENERALIZED MODELING FOR CEMENT-BASED MATERIALS UNDER LARGE RANGE OF COMPRESSION STATE

The aim of this study is to describe the main behavior of cement-based materials under large compression state based on the recent experimental research. In this paper, the strainstress relations are firstly analyzed and confining pressure state is regarded as low/medium/high state. A generalized cup modeling is introduced by a coupled deviatoric shearing, pore collapse and damage mechanism within thermodynamic framework. A series of numerical simulations are performed for the considered cement paste and concrete. Comparisons between numerical predictions and experimental results show that the proposed model is able to describe the main features of mechanical behavior under large range of compression state.