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Abstract
Based on the assumption that rock strength follows the log normal distribution statistically, this paper establishes a damage constitutive model of rock under uniaxial stress conditions in combination with the Mohr–Coulomb strength criterion and damage mechanical theory. Experiments were carried out to investigate the damage evolution process of rock material, which can be categorized into nondamaging, accelerated growth, constant‐speed, similar growth, and speed‐reducing growth stages. The evolution process had a good corresponding relationship with the rock stress‐strain curves. Based on the statistical damage constitutive model proposed in this paper, a numerical fitting analysis was conducted on the uniaxial compression testing data of laboratory sand rock and on experimental data from other literature, in order to validate the rationality of the constitutive equation and the determination of its parameters and to analyze the effect of internal friction variables on damage variables and compression strength. The research outcomes presented in this paper can provide useful reference for the theory of rock mechanics and for rock engineering.
Highlights
Experiments have shown that rock is a type of complex medium
Many investigators have tried to explain the relationship between the deformation of rock and external loading, i.e., the constitutive relationship of rock. e results of early research into rock mechanics include Hooke’s law, Newton’s law of viscosity, and Saint Venant’s ideal plasticity law. e continuous recognition of progress in understanding the mechanical properties of rock has led investigators to propose a variety of constitutive models by means of a subsequent viscoelastic plastic theory of continuum mechanics, such as that put forward by Liu et al [1]
E theoretical and experimental data curves were individually prepared as shown in Figures 3(a)–3(c) based on the damage constitutive model presented in this paper, and the correlation coe cients between modeling data and lab data are 0.9995, 0.8095, and 0.7867. e statistical constitutive equation matched the real uniaxial compression testing curves of the rock well. is latter observation indicated that the proposed constitutive equation was able to represent the elastic, yield, and softening stages of the uniaxial stress-strain curve of the rock, and that the
Summary
Experiments have shown that rock is a type of complex medium. Under the application of external loading, rock presents a very complex nonlinear deformation, and the complex deformation results in complexity and uncertainty of rock engineering . Based on the assumption that the crack growth of rock during the postpeak period is the process of cohesive instability and making use of the nonassociated plastic potential function of rock plastic deformation and expansion derived from the dilation angle, Pourhosseini and Shabanimashcool [8] developed a damage constitutive model to describe the nonlinear behaviors of intact rock under static load (including prepeaking elastic behaviors and postpeaking strain-softening behaviors). Ey proposed a plastic hole yield criterion by making use of Gurson’s criterion and a friction yield model to determine the matrix deformation of porous materials Combining these two criteria, they developed an elasticplastic damage constitutive model with two yield surfaces. Us, our research provides references for rock mechanics research and engineering
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