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Statistical damage constitutive model based on the Hoek-Brown criterion

Chen Yifan, Lin Hang, Wang Yixian, Xie Shijie, Zhao Yanlin, Yong Weixun

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 3

556--564

The constitutive models of rock are essentially the general depictions of the mechanical responses of rock mass under complex geological environments. Statistical distribution-based constitutive models are of great efficacy in reflecting the rock failure process and the stress–strain relation from the perspective of damage, while most of which were achieved by adopting Drucker–Prager criterion or Mohr–Coulomb criterion to characterize microelement failure. In this study, underpinned by Hoek–Brown strength criterion and damage theory, a new statistical damage constitutive model, which is simple in terms of model expression and capable of reflecting the strain softening characteristics of rock in post-peak stage, was established. First, the rock in the failure process was divided into infinite microelements including elastic part satisfying Hooke’s law and damaged part retaining residual strength. Based on strain equivalence hypothesis, the relation between rock microelement strength and damage variable was derived. By assuming the statistical law of microelement strength obeying Weibull distribution and the microelement failure conforming to Hoek–Brown criterion, the new statistical damage constitutive model based on Hoek–Brown criterion was, therefore, gained. The mathematical expressions of the corresponding model parameters were subsequently deduced in accordance with the geometric characteristics of the deviatoric stress–strain curve. Last, the existing conventional triaxial compression test data of representative rock samples under different confining stresses were employed to compare with the theoretical curves by proposed model, the consistency between which was quantified by utilizing the correlation factor evaluation method. The result indicated that the proposed model could well describe the entire stress–strain relationship of rock failure process and manifest the characteristics of rock residual strength. It is of great significance to the researches on rock damage and softening issues and rock reinforcement treatments.

Zmiany osiowej sztywności i rozwój uszkodzenia próbek piaskowca w teście konwencjonalnego trójosiowego ściskania

Cieślik J., Jakubowski J., Tajduś A.

Górnictwo i Geoinżynieria

2011

R. 35, z. 2

163-170

W referacie zaprezentowano wyniki badań laboratoryjnych, w których analizowano zmiany osiowej sztywności próbek piaskowca poddanego konwencjonalnemu trójosiowemu ściskaniu. Założono iż opisem zjawisk powstawania i propagacji szczelin w skałach, na poziomie reprezentatywnej objętości, zajmuje się kontynualna mechanika uszkodzeń. Na podstawie przeprowadzonych badań i analizy zmian osiowej sztywności próbek, dla analizowanych ciśnień zdefiniowano zmienną uszkodzenia i wyznaczono warunek zapoczątkowania procesu uszkodzenia. Wyniki badań obrazują charakter dwóch różnych procesów zniszczenia.

Results of laboratory investigations focusing on change of axial stiffness of sandstone samples made under a conventional triaxial compression test conditions has been presented in this paper. It was assumed, that fracture propagation and damage process of rock samples on representative volume element level follows continuum damage mechanics laws. Based on investigations and analysis of axial stiffness change of sandstone samples for applied confining pressures, a damage variable was determined and the condition for the initiation of damage process was proposed. The results of investigations show a phenomenon of two different failure processes.