Abstract
In this paper, the rock behavior before yielding is analyzed by using the theory of continuum mechanics. The nonlinearly elastic constitutive equation of rock medium is derived and compared satisfactorily with the available experimental data. Moreover, the substitution of the linearly elastic hypothesis used in the conventional cap model with the nonlinearly one leads to the development of a new nonlinearly elastic-hardening plastic cap model as presented herein.
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Abbreviations
- σ:
-
Stress tensor
- σ ij :
-
Cartesian component form of stress tensor
- s ij :
-
Cartesian component form of deviatoric stress
- ɛ:
-
Strain tensor
- s ij :
-
Cartesian component form of strain tensor
- ε ij :
-
Cartesian component form of deviatoric strain
- ε ij :
-
Cartesian component form of elastic strain tensor
- ε E ij :
-
Cartesian component form of plastic strain tensor
- de E ij :
-
Cartesian component form of elastic strain increment
- de P ij :
-
Cartesian component form of plastic strain increment
- e P V ·e P kk :
-
Plastic volumetric strain
- de P V ·de P kk :
-
Increment of plastic volumetric strain
- e z :
-
Axial strain in triaxial compression test
- e 8 :
-
Circumferential strain in triaxial compression test
- σ ij :
-
Kronecker delta
- I 1 :
-
First invariant of stress tensor
- I 2 :
-
Second invariant of stress tensor
- I 3 :
-
Third invariant of stress tensor
- J 2 :
-
Second invariant of deviatoric stress
- J 3 :
-
Third invariant of deviatoric stress
- A, B, C, D, H, L :
-
Nonlinearly elastic constants
- K :
-
Bulk modulus in linearly elastic body
- G :
-
Shear modulus in linearly elastic body
- E :
-
Young's modulus
- ν:
-
Poisson's ratio
- c :
-
Cohesion
- ϕ:
-
Angle of internal friction
- V d :
-
Nonlinearly elastic volumetric dilatancy
- F :
-
Yielding function
References
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Communicated by Chien Wei-zang.
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Shou-I, T., Ken-ta, C. The elasto-plastic constitutive relation of generalized cap model for rock medium. Appl Math Mech 4, 385–394 (1983). https://doi.org/10.1007/BF01875671
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DOI: https://doi.org/10.1007/BF01875671