Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand.This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand.Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment(i.e.dilatancy rate).Lack of an article that gathers these formulas is clear in the literature.Thus,this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands.Stress-dilatancy relation is usually not the same under compression and extension conditions.Furthermore,it may also be different under loading and unloading conditions.Therefore,the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading.Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship,more weight is allocated to stress-dilatancy relationship in this research.

Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used.

Improved slope safety analysis by new Druker-Prager type criterion

Based on Mohr-Coulomb （M-C） criterion, the parameters of Druker-Prager （D-P） criterion for geomaterial were determined under non-associated flow rule, and thus a new D-P type criterion was presented. Two assumptions were employed during the derivation： 1） principal strains by M-C model and D-P model are equal, and 2） the material is under plane strain condition. Based on the analysis of the surface on rt plane, it is found that the proposed D-P type criterion is better than the D-P criterion with M-C circumscribed circle or M-C inscribed circle, and is applicable for stress Lode angle less than zero. By comparing the predicted results with the test data of sand under plane strain condition and other D-P criteria, the proposed criterion is verified and agrees well with the test data, which is further proved to be better than other D--P type criteria in certain range of Lode angle. The criterion was compiled into a finite difference package FLAC3D by user-subroutine, and was used to analyze the stability of a slope by strength reduction method. The predicted slope safety factor from the proposed criterion agrees well with that by Spencer method, and it is more accurate than that from classic D-P criteria.

Simple approach for solution of the quasi-plane-strain problem in a circular tunnel in a strain-softening rock mass considering the out-of-plane stress effect

The out-of-plane stress is sometimes the major or intermediate principal stress in a circular tunnel opening.The influences of the outof-plane stress and axial strain are often neglected in the stability analyses of tunnel excavation,which can induce significant errors in the determination of surrounding rock deformations.In this paper,the use of a simple approach is proposed to solve the quasi-plane-strain problem of circular tunneling considering the effect of the out-of-plane stress,which is deformation-dependent and influenced by the in situ stress.As the intermediate principal stress is deformation-dependent,to obtain the numerical solution of the intermediate principal stress,the quasi-plane-strain problem is defined based on assumptions that the initial axial total strain is a nonzero constant(e0)and that the axial plastic strain is nonzero.With the numerical solution for the plastic strain,obtained using the plastic potential functions based on the three-dimensional failure criteria,the formula for the intermediate principal stress can be derived using Hooke’s law.The proposed approach can be utilized to obtain the numerical solution for the intermediate principal stress,which is deformationdependent,and the numerical results can be simplified as the solution presented by Pan and Brown.The proposed approach can also be used to obtain the solution for the strain softening of the surrounding rock.To verify its validity and accuracy,the results obtained using the proposed approach are compared with the solution of Pan and Brown.In addition,parametric studies are performed to address the influences of the out-of-plane stress on the stress and displacement in the circular tunnel.