Theoretical And Numerical Simulations Of Deformation Localization Of Geomaterials

Deformation localization is a commonly phenomenon in the failures of geomaterials under different loading conditions and it is also the precursor of catastrophic material failure. Accoding to the theory of deformation localization, stability of geomaterials attributes to occurrence of the localization. That is bifurcation occourence in characteristics of stress-strain relationship. As far as geomaterials is concerned, no mater what geometric nonlinearity or material nonlinearity is, bifurcation probably exists and this phenomenon have been already discovered and studied in laboratory.Bifurcation of geomaterials along different stress paths are always importants concerns in soil mechanics and engineering. Many analytical works have been conducted to understand the bifurcation of geomaterials under plane strain condition while very limited bifurcation results in true triaxial stress condition are available at present. Because the mechanical behaviour of geomaterials much depending on stress state and stress paths, bifurcation theory under plane strain condition cannot express accurately predictions of bifurcation points under true triaxial condition. So extending bifurcation theory to three dimensional stress conditions and applying it to deformation localization analysis are still a research hotspot.Overconsolidated clay and dense sand are two kinds of typical soil materials in geotechnical enineering, which display the hardening-softening and shear dilatancy features during shearing. But the constitutive models implemented in most of the commom finite element software cannot describe the above defotmation characteristics. In order to apply two elastoplastic constitutive models proposed by Yao et al. (2004, 2009) for overconsolidated clays and sands to numerical analysis of deformation localization, the subroutines are developed for the implementation of the models into a nonlinear finite element software ABAQUS by using the return mapping algorithm. Numerical simulations of triaxial compression, triaxial extension and plane strain tests are performed. The algorithm is verified by simulating the mechanical behaviour of overconsolidated clays and sands.Secondly, bifurcation features for the two constitutive models are probed. Analytical solutions to three-dimensional bifurcation are deduced. And the solution of the model along different stress paths under constant mean effective stress is resolved. Furthermore, numerical simulations for isotropically homogenous cubic true triaxial specimens along different stress paths under constant mean effective stress are carried out. The comparisons between the numerical results and theoretical solutions show that the numerical results agree with the theoretical solutions. Effects of overconsolidation ratio, initial void ratio, confining pressure, coupling of soil and water, flow rule and softening on bifurcation for geomaterial are discussed.Thirdly, because of limited analytical works for the shear bands of overconsolidated clay, numerical simulations have been conducted for an example of application. By using the implemented program, three-dimensional finite element analysis of shear band is carried out under triaxial compression, triaxial extension and plane strain stress paths by appling a nonlinear finite element software ABAQUS. Effects of shear dilatancy, shear rate and pore pressure on shear bands are discussed.Finally, the bifurcation exists in the constitutive models with description of softening developed within the framework of conventional continuum theory along some stress paths. As a result, the corresponding boundary value problem becomes no definite type and numerical modeling of bifurcation behaviour suffers from severe mesh-dependence. In order to avoid this problem, one available approach is to consider some regularization techniques. According to non-local theory, gradient term can be got by a Taylor series expansion through construction a weight function, which can keep the regularization techniques effective. So two extended non-local elastoplastic constitutive models are abtained by introducting the second order gradient term and consistent approach modulus is deduced.