Constitutive Models With Elasto-plastic Damages For Rock-like Materials Subjected To High Confining Pressures And High Strain Rates

Because of the development of high-rise buildings and underground structures,more and more attentions have been paid to the constitutive modeling of rock-like materials under conditions of high confining pressures and high strain rates.The high in-situ stress is increasingly prominent as the underground mine gradually stepped into deep mining stage,which could cause rock burst,impact pressure increasing and a series of severe accidents.It caused a great threat to the deep exploitation for various natural resources.The dynamic characteristic of rock-like materials is the basis to study the mechanism of stress wave propagation and seismic engineering design.The classical rock strength criterions are mostly based on the assumption of low confining pressures and static conditions.Therefor,they are not suitable for high pressures and dynamic impact problems.The constitutive model of rock-like materials is an important theoretical basis for rock engineering design.The classical constitutive model of rock-like materials cannot accurately describe the nonlinear strength characteristics of the rock under high in-situ stress and dynamic loading.In addition,it has to consider how to describe the failure under the tensile loading conditions because the tensile strength of rock-like materials is much lower than the compressive strength.The constitutive model of material should have a simple function form and less material parameters when the constitutive model is used to numerically simulate the nonlinear deformation and failure behavior of rock-like material.Many constitutive models of rock-like materials have been proposed by researchers.However,very few studies take account of the combined effects of high confining pressure,high strain rates,and tensile and compressive damages.In this thesis,the phenomenological constitutive model of rock-like materials is established by using the theory of elasto-plastic damage mechanics.The following topics are studied in the thesis.1.A new constitutive model for rock materials accounting for the effects of high confining pressures and high strain rates is presented based on the extended Drucker-Prager strength criterion and the Johnson-Cook material model.The influence of the third deviatoric stress invariant is introduced.The non-associative plastic flow rule is used to describe the plastic deformation.Two internal damage variables are introduced to represent the tensile and compressive damage,respectively.It is of brittle failure when the rock subjected to the tensile loading,and the damage variable can be characterized by the volumetric strain.The evolution equation of tensile damage variable is defined as an exponential function in terms of the volumetric strain.The rocks undergo ductile failure caused mainly by plastic deformation when the rocks are subjected to the compressive loading.The compressive damage variable accumulates from equivalent plastic strain and plastic volumetric strain.2.The magnitude of the compressive damage of common concrete is greater than rock materials under the same loading conditions because of the strength of common concrete generally lower than that of rock.The associated plastic flow rule is utilized to evaluate plastic strains for concrete.The definition of tensile and compressive damage variables is the same as the rock material model.3.Due to the influence of friction and confining pressure,there is still a considerable residual strength after the rock failure caused by peak strength.The residual strength after the peak strength cannot be accurately described by any theoretical model.According to the triaxial compressive test data of rock-like materials,the relationship between confining pressure and residual strength is established by the curve fitting method.The new loading surface including the influence of residual strength is proposed.It is more accurate to consider the effect of confining pressure on the residual strength of the rock-like materials after the peak strength.The relationship between the confining pressure and the residual strength is fitted by a quadratic polynomials.The relationship between the confining pressures and the degradation index is fitted by the exponential function.The softening behavior after the peak strength of rock-like materials can be accurately simulated by the modified material model.4.The proposed constitutive models of rock-like materials are implemented into the nonlinear dynamic analysis code LS-DYNA through a user-defined material subroutine.The method on how to define the material parameters in the material model is presented.The reliability and accuracy of present constitutive models of rock-like materials are verified by numerical simulation of various standard experiments with different loading conditions(tensile,compression,Brazilian splitting,Hopkinson test).The numerical simulation results are in good agreement with the experimental results.The results show that the present material model can accurately describe pressure nonlinear hardening and strain rate hardening of rock-like materials.The present rock model is also applied to simulate the penetration of granite target plate by a hard projectile.The typical damage and failure on the granite target predicated by the proposed dynamic material model of rocks agree well with the experimental results.It demonstrates that the proposed rock material model is capable of capturing the failure of rock materials.The penetration depth calculated by numerical simulation is in good agreement with the experimental results.The tensile damage distribution of the rock target also agrees well with the crack distribution in the experiment.5.The reliability and accuracy of the concrete material model are verified by the numerical simulations of standard compression and tension tests with different confining pressures and strain rates.The ballistic test of ogive-nosed projectile penetrating into concrete target is simulated by using the present material model.The residual velocities and damage contours on the concrete target predicated by the proposed model agree well with the experimental results.The numerical simulation of the impact test of a 1/7.5 scale model of an aircraft penetrating into a half steel plate reinforced concrete(HSC)panel is carried out.The damage pattern of concrete slab and the predicted deformation of steel plate in the HSC panel are in good agreement with experimental results.The results also show that the steel plate at the HSC rear-face plate has a significant effect in preventing scattering of scabbed concrete debris from the rear face of the panel.6.Tunnel boring machines(TBMs)have been widely used in tunnel construction for a variety of purposes such as highways and subways.The cutter-head design is one of the critical aspects of the TBM manufacturing process.The cutting forces and appropriate cutter spacing are the main factors for governing cutting efficiency.Disc cutters are the main tools employed by TBMs for fragmenting rock.The rock material model,which can accurately consider the effects of high confining pressure and high strain rates,is the basis for numerical simulation of rock failure process induced by TBM disc cutters.The present rock material model is applied to simulate the rock failure process induced by disc cutters.The influence of penetration and confining pressure on cutting forces is determined.The simulation results show that the tensile damage distribution at the cross section of rock specimen can be applied to describe the radial crack produced by the cutters.The compressive damage region of rock is also obtained from the simulation of two disc cutters acting in tandem with different cutting spacing.The optimal cutter spacing is determined accounting to the compressive damage region of rock.The optimum cutter spacing determined from numerical modeling agrees well with that obtained by linear cutting machine test.The new elasto-plastic damage constitutive models of rock-like materials presented in the thesis can accurately and efficiently describe the effect of confining pressure and the dynamic failure of rock-like materials.Particular because of the consideration of the tensile damage,they are more accurate than the existing rock-like material models used in the commerical nonlinear dynamic software.Therefor,the present constitutive models of rock-like materials provide accurate and efficient dynamic material models for the numerical simulations of rock-like materials subjected to high confining pressures and high strain rates.