Abstract
In this study, a new relation is presented to better describe the simultaneous dependence of dilation angle on the internal variable and the minimum principal stress for rocks. The model is based on the assumption that a separation of the influences of the internal variable and the minimum principal stress on dilation angle. The resulting expression is simplistic for practical purposes and has five parameters with fully clear physical meanings. Its accuracy is validated by fitting the published laboratory test data of a wide variety of rocks, showing that the proposed model has a good agreement with the experiments.
Highlights
-
A new dilation angle model is proposed for rocks.
-
The dilation angle model is simplistic for practical purposes and has five parameters with fully clear physical meanings.
-
The accuracy of the dilation angle model is validated by fitting the published laboratory test data of a wide variety of rocks.
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Abbreviations
- \(\psi\) :
-
Dilation angle
- \(\kappa\) :
-
Internal variable
- \(\sigma _3\) :
-
Minimum principal stress
- \(\sigma _n\) :
-
Normal stress
- \(\gamma _p\) :
-
Plastic shear strain
- \({\bar{\epsilon }}_p\) :
-
Equivalent plastic strain
- \(f(\frac{\sigma _3}{\sigma _c})\) :
-
Confining pressure function
- \(\sigma _c\) :
-
Unit stress
- \(\epsilon _1^p\) :
-
Axial (or major) plastic strain
- \(\epsilon _3^p\) :
-
Lateral (or minor) plastic strain
- k :
-
1—for plane-strain condition, 2—for triaxial condition
- \(\psi _{\text {max}}\) :
-
Peak dilatancy angle at \(\sigma _3=0\)
- \(\psi _{\text {lim}}\) :
-
Limit dilatancy angle at \(\sigma _3=0\)
- a :
-
Decay rate of \(\psi\)
- \(\kappa ^*\) :
-
Value of internal variable for which \(\psi _{\text {max}}\) is achieved
- \(\varvec{\epsilon }_p\) :
-
Plastic strain tensor
- t :
-
Pseudo-time
- \(c_1, c_2, c_3\) :
-
Fit coefficients in Eq. (6)
- \(\alpha\) :
-
Curvature of the pre-mobilization dilatancy
- \(\gamma _m\) :
-
Plastic shear strain at which \(\psi _{\text {max}}\) is achieved
- \(\gamma ^*\) :
-
Decay rate of \(\psi\) in Eq. (7)
- \(a_1, a_2\) :
-
\(\psi _{\text {max}}\) and \(\psi _{\text {lim}}\) at \(\sigma _3 = 0\), respectively
- \(b_1, b_2\) :
-
Decay rates of \(\psi _{\text {max}}\) and \(\psi _{\text {lim}}\) due to confinement, respectively
- b :
-
Decay rate of \(\psi\) due to confinement
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Zhao, R., Li, C. A New Dilation Angle Model for Rocks. Rock Mech Rock Eng 55, 5345–5354 (2022). https://doi.org/10.1007/s00603-022-02835-6
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DOI: https://doi.org/10.1007/s00603-022-02835-6