r7.01.18 Behaviour law of HOEK_BROWN amended

Summary

This document describes a law of behavior for rocks. The plasticization criterion is a Hoek-Brown parabolic criterion. It is written in main constraints. The evolution of plastic deformations is of the « non-associated » type, formulated on the basis of a Drucker-Prager criterion whose friction angle changes with plasticization.

This law can be used in pure mechanics as well as in coupled thermo-hydro-mechanical modeling.

In thermo-hydro-mechanical modeling, it can be used in effective stresses or in total stresses:

• In the first case, it is the actual constraints that are subject to meeting the Hoek and Brown criterion. Plastic deformations are calculated using the Drucker surface and the angle of friction in the space of the effective stresses

• In the second case, it is the total constraints that are subject to meeting the Hoek and Brown criterion. Plastic deformations are calculated using the Drucker surface and the angle of friction in the total stress space

• 1. Introduction
  • 1.1. Characteristics of the model
• 2. Ratings
  • 2.1. Generalities
  • 2.2. Model parameters
• 3. Continuous model
  • 3.1. Elastic behavior
  • 3.2. Plastic behavior
• 4. Incremental shape
  • 4.1. Calculation of \(\Delta \lambda\)
  • 4.2. Existence of the solution
• 5. Calculus of derivatives
  • 5.1. Derivative of the criterion with respect to the constraints
  • 5.2. Derivative of the stress tensor with respect to the principal stresses
  • 5.3. Derivative of the criterion with respect to the work-hardening variable
  • 5.4. Derivative of the parameters with respect to the work hardening variable
• 6. Calculation of the coherent tangent operator
  • 6.1. Calculation of \(\frac{\partial \sigma }{\partial \varepsilon }\)
  • 6.2. Special case of multiple eigenvalues for \({s}^{e}\)
  • 6.3. Calculation of \(\frac{\partial \mathrm{\sigma }}{\partial {\mathrm{\sigma }}_{p}}\)
• 7. Calculation of the tangent operator in speed
• 8. Algorithm
  • 8.1. Internal variables
  • 8.2. Algorithm
• 9. Bibliography
• 10. Features and verification
• 11. Description of document versions