Abstract
Two dimensional generalized Hoek et al. (2002) criteria is very popular for determining the strength of rock materials worldwide. While using this criterion, it is usually required to determine the minor principal stress first. Since, GHB criteria is a nonlinear function of minor principal stress, its solution is not very straightforward and simple. Few analytical and numerical solution to find out the value of minor principal stress already exist. Some solutions are unable to give acceptable value of minor principal stress for whole range of geological strength index (GSI) values of rocks. In the present paper, a solution strategy based on Newton–Raphson method to determine the value of minor principal stress from GHB criteria in two dimensions is presented. The obtained solution of minor principal stress for few problems are compared with the solutions from existing literature. The proposed solution strategy can determine the value of minor principal stress for whole range of GSI (0–100) very accurately with very less computational effort. Finally, the variation of various rock strength parameters such as angle of internal friction, cohesion and shear stress are investigated for different values of GSI and disturbance factor (D).
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Abbreviations
- \(\sigma_{1}\) :
-
Maximum effective stress at failure
- \(\sigma_{3}\) :
-
Minimum effective stress at failure
- \(\sigma_{ci}\) :
-
Uniaxial compressive strength of the intact rock material
- mb, s, a :
-
The empirical constants of the generalized Hoek–Brown criterion
- GSI:
-
The geological strength index of the rock mass
- D :
-
Disturbance factor of the rock mass
- \(m_{i}\) :
-
Hoek–Brown constant for intact rock
- \(\sigma_{n}\) :
-
Normal stress
- \(\tau\) :
-
Shear stress
- \(c\) :
-
Cohesion
- \(\phi\) :
-
The angle of internal friction
- \(\sigma_{nl} \;{\text{and}}\;\sigma_{nu}\) :
-
Lower and upper value of normal stresses
- f n :
-
Normal stress increment factor
- \(\sigma_{3l} \;{\text{and}}\;\sigma_{3u}\) :
-
Lower and upper value of minor principal stresses
- \(\tau_{l} \;{\text{and}}\;\tau_{u}\) :
-
Lower and upper value of shear stress
- \({\mathbf{\mathbb{R}}}\) :
-
Vector space of real numbers
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Kumar, V., Burman, A., Himanshu, N. et al. Solution of Minor Principal Stress for Generalized Hoek–Brown Rock Material in Two Dimension Using Newton–Raphson Method. Geotech Geol Eng 38, 1817–1837 (2020). https://doi.org/10.1007/s10706-019-01132-4
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DOI: https://doi.org/10.1007/s10706-019-01132-4