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A continuum model of jointed rock masses based on micromechanics and its integration algorithm

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Abstract

The paper is devoted to proposing a constitutive model based on micromechanics. The joints in rock masses are treated as penny-shaped inclusion in solid but not through structural planes by considering joint density, closure effect, joint geometry. The mechanical behavior of the joints is represented by an elasto-plastic constitutive law. Mori-Tanaka method is used to derive the relationship between the joint deformations and macroscopic strains. The incremental stress-strain relationship of rock masses is formulated by taking the volume average of the representative volume element. Meanwhile, the behavior of joints is obtained. By using implicit integration algorithms, the consistent tangent moduli are proposed and the method of updating stresses and joint displacements is presented. Some examples are calculated by ABAQUS user defined material subroutine based on this model.

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Abbreviations

τ i :

stresses of the joint under local coordinates

g i :

relative displacement of joint under local coordinates

V m :

maximum closure of joint

K n0 :

initial normal stiffness

α 0 :

joint asperity surface angle

µ:

friction coefficient

λ :

plastic coefficient

K e ij :

joint elastic stiffness matrix under local coordinates

C R ijkl :

elastic stiffness tensor

T ij :

transformation matrix between joint local coordinates and global coordinates

ρ J :

quantity of one set of joints in per volume

[u J i ]:

relative displacements under global coordinate system

n i :

components of normal direction of joint

S J :

area of joint

a J :

radius of joint

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Authors and Affiliations

  1. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, China

    FuWei Zhu & GuanSuo Dui

  2. Department of Civil Engineering, Hohai University, Nanjing, 210098, China

    QingWen Ren

Authors
  1. FuWei Zhu
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  2. GuanSuo Dui
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  3. QingWen Ren
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Correspondence to GuanSuo Dui.

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Zhu, F., Dui, G. & Ren, Q. A continuum model of jointed rock masses based on micromechanics and its integration algorithm. Sci. China Technol. Sci. 54, 581–590 (2011). https://doi.org/10.1007/s11431-011-4289-0

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  • DOI: https://doi.org/10.1007/s11431-011-4289-0

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