Abstract
The failure and deformation mechanism of sandstone and mudstone has always been highlighted in research on mining engineering. To further investigate the failure and deformation mechanism of sandstone and mudstone, a damage definition was proposed to describe the failure mechanism of a rock specimen with micro-defects and inhomogeneity; the Weibull distribution function was used to illustrate the dispersion of mechanical properties (i.e. damage extent) of rock; the nonconstant terms of Z–P yield function was employed to describe the strength of rock elements. Based on the framework of the continuum damage mechanics and strain equivalence hypothesis, a continuous damage constitutive model was established. Finally, triaxial compression tests on sandstone and mudstone taken from the Chensilou coal mine were conducted to verify the reliability of the proposed model. The results show that the damage evolution curve presents the shape of a square root sign, The damage evolution of the rock specimens can be divided into six stages: (1) initial damage stage, (2) damage-weakening stage, (3) slight-increased damage stage, (4) rapidly-increased damage stage, (5) rock failure stage and (6) rock slippage stage. The proposed damage evolution contributes to establishing the constitutive model of the stress–strain relationship of sandstone and mudstone in the mining field.
Highlights
-
Processing a continuous damage statistical constitutive model for sandstone and mudstone based on triaxial compression tests.
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The damage evolution curve presents the shape of a square root sign.
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The damage evolution of the rock: initial damage-damage weakening-slight increased-rapidly increased-rock failure-rock slippage.
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Abbreviations
- V d :
-
Volume of damaged parts
- V u :
-
Volume of undamaged parts
- V tal :
-
Total rock elements volume
- D tal :
-
Total damage
- D nd, D wd, D sd :
-
Damage variables of natural damage, environmental damage and stress damage
- ΔD :
-
Damage increment
- [C]:
-
Stiffness matrices
- σ b :
-
Strength of rock micro-element
- λ, k :
-
Parameter of the Weibull function
- a 0, a 1, a 2, a 3, K, k 1 :
-
Parameter of Z–P yield function
- P faild :
-
Probability of failure
- σ 1, σ 2, σ 3 :
-
Maximum, intermediate and minimum nominal principal stresses
- σ rs :
-
Equivalent stress
- σ :
-
Nominal stress
- σ* :
-
Effective stress
- ε 1 :
-
Axial strain
- σ m :
-
Average nominal stress
- σ m * :
-
Average effective stress
- σ b :
-
Rock element strength
- σ ij :
-
Nominal stress tensor
- σ rs :
-
Stress state
- σ p, ε p :
-
Axial stress and strain of the peak point
- s ij *, s ji * :
-
Deviatoric effective stress tensor
- J 2 * :
-
Second invariant of the deviatoric stress tensor described by effective stress
- J 3 * :
-
Third invariant of the deviatoric stress tensor described by effective stress
- c :
-
Cohesion
- φ :
-
Internal friction angle
- F 0, F 1, F 2 :
-
Function about σ1 and ε1
- ρ :
-
Density
- E :
-
Elastic modulus
- ν :
-
Poisson’s ratio
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National Natural Science Foundation of China (NSFC) [Grant no. 51978634].
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Wu, Ly., Wang, Z., Ma, D. et al. A Continuous Damage Statistical Constitutive Model for Sandstone and Mudstone Based on Triaxial Compression Tests. Rock Mech Rock Eng 55, 4963–4978 (2022). https://doi.org/10.1007/s00603-022-02924-6
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DOI: https://doi.org/10.1007/s00603-022-02924-6