Dynamic triaxial constitutive model for rock subjected to initial stress

Junzhe Li,Xinlong Zhou,Guang Zhang,Shaohua Hu,Mingze Liu

doi:10.1515/phys-2020-0014

Abstract

AbstractBuilding on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

Highlights

With the massive development of deep earth resources and the wide construction of underground space projects, more and more attention has been paid to study the dynamic constitutive model of deep rock
Cao et al [7] established a dynamic triaxial damage constitutive model of rock based on the Kelvin–Voigt model and Weibull distribution, which consists of the Newton dashpot simulating dynamic stress component and the Hooke spring with statistical damage characteristics simulating the static stress component
Liu et al [8] performed a series of dynamic triaxial compression tests on amphibolite within a strain rate range of 50–170 s−1 and a confining pressure range of 0–6 Model parameter (MPa), and the aforementioned test results are used to verify the dynamic damage constitutive model of rock established by combining the statistical damage model and the Kelvin–Voigt model

Summary

Introduction

With the massive development of deep earth resources and the wide construction of underground space projects, more and more attention has been paid to study the dynamic constitutive model of deep rock. Xie et al [18] proposed the five-parameter generalized Maxwell model (i.e., the result of replacing the nonlinear spring of the ZWT model with a Hooke spring) to describe the isotropic viscoelasticity of rock-like materials and established a model describing the stress–strain behavior of the soil matrix under uniaxial impact loading by introducing damage to modify the five-parameter generalized Maxwell model. It is unreasonable to introduce damage to correct the entire model To solve this shortcoming, Xie et al [19,20] replaced three elastic elements in the ZWT model with three Hooke springs that may be damaged and established a damagetype viscoelastic dynamic constitutive model describing the stress–strain behavior under uniaxial impact loading. The model established in this article can provide reference and guidance for the study on the dynamic characteristics of deep rock

Model proposed by Xie et al and its improvement

Basic assumptions

Constitutive equation

Evolution equations of damage variables

Case analysis and discussion

Conclusions