A Unified Constitutive Model for Rock Based on Newly Modified GZZ Criterion
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ORIGINAL PAPER
A Unified Constitutive Model for Rock Based on Newly Modified GZZ Criterion Haohua Chen1 · Hehua Zhu2 · Lianyang Zhang1 Received: 4 May 2020 / Accepted: 26 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract This paper proposes a unified constitutive model for rock based on the newly modified generalized Zhang-Zhu (GZZ) criterion. The constitutive model adopts a non-associated plastic flow rule and a continuous potential function that takes the three effective principal stresses into account. To reflect strain-softening, strain-hardening, and elastic-perfectly plastic behavior of rock in a unified way, a general expression is proposed to model the post-failure behavior of rock using the deviatoric plastic shear strain as the fundamental variable. The proposed constitutive model has been successfully implemented in a 3D finite-difference code and validated using it to simulate the true triaxial test of two types of rocks and comparing the simulation results with the experimental data. Finally, a 3D numerical model based on the proposed constitutive model is constructed to simulate a highway rock tunnel during construction. The results show that the predicted displacements of the rock tunnel are in good agreement with the field measurements. Keywords Rock · 3D hoek–brown criterion · Constitutive model · Strain-softening · Strain-hardening List of Symbols Erm Young’s modulus of rock mass I1∗ , I2∗ , I3∗ Transformed first, second and third stress invariants J2, J3 Second and third deviatoric stress invariants mb, s, a Material constant for rock masses defined in Hoek–Brown criterion mbi, mbr Initial and residual value of mb md Material constant defining potential function mdi, mdr Initial and residual value of md mi Material constant for the intact rock p′ Mean effective stress si, sr Initial and residual value of s 𝜀f A parameter controlling the softening/hardening of the yield function * Lianyang Zhang [email protected] 1
Department of Civil and Architectural Engineering and Engineering Mechanics, The University of Arizona, Tucson, AZ 85716, USA
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
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𝜀g A parameter controlling the evolution of the potential function p 𝜀q Plastic deviatoric shear strain 𝜀x , 𝜀y , 𝜀z , 𝜀xy , 𝜀xz , 𝜀yz Six basic strain components 𝜃𝜎 Lode’s angle 𝜎1′ , 𝜎2′ , 𝜎3′ Maximum, intermediate, and minimum effective principal stresses 𝜎c Unconfined compressive strength of intact rock ′ Effective mean stress 𝜎m,2 𝜎x′ , 𝜎y′ , 𝜎z′ , 𝜏xy , 𝜏xz , 𝜏yz Six basic stress components 𝜏oct Octahedral shear stress D Disturbance factor reflecting the level of blast damage and stress relaxation to rock mass E, v Young’s modulus and Poisson’s ratio GSI Geological strength index K, G Bulk modulus and shear modulus f, g Yield function and potential function λ [Plastic multiplier for flow ] rule 𝜀x , 𝜀y , 𝜀z , 2𝜀xy , 2𝜀xz , 2𝜀yz 𝜀 [ ] 𝜎x′ , 𝜎y′ , 𝜎z′ , 𝜏xy , 𝜏xz , 𝜏yz 𝜎
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