Stress
Stress is the force applied per unit area within a material. In subsurface formations, stresses result from the weight of overlying rock and tectonic forces.
Where:
- \(\boldsymbol{\sigma}\): stress
- \(\boldsymbol{F}\): applied force
- \(\boldsymbol{A}\): area
Strain
While stress describes the forces acting on a material, strain describes how the material actually deforms in response. Strain is a dimensionless measure of deformation.
Where:
- \(\boldsymbol{\varepsilon}\): strain
- \(\boldsymbol{\Delta L}\): change in length
- \(\boldsymbol{L_0}\): original length
Rock deformation can occur in two ways:
- Elastic deformation: Recoverable deformation. When stress is removed, the material returns to its original shape. Governed by Hooke’s Law.
- Plastic deformation: Permanent, irrecoverable deformation. Occurs once stress exceeds the elastic limit (yield strength).
When stress exceeds rock strength, fracturing occurs instead of deformation.
Pore Pressure and Effective Stress
Reservoir rocks contain fluids within their pore spaces. Pore pressure is the pressure exerted by these fluids.
The stress actually carried by the rock framework is called effective stress.
Where:
- \(\boldsymbol{\sigma'}\): effective stress
- \(\boldsymbol{\sigma}\): total stress
- \(\boldsymbol{P_p}\): pore pressure
- \(\boldsymbol{\alpha}\): Biot Coefficient (accounts for compressibility of the grains)
Shear vs. Tension:
Rock failure can occur in two main ways:
- Tensile Failure: occurs when rock is pulled apart.
- Shear Failure: occurs when sliding happens along a plane due to shear stress.
Shear failure can be described by the Mohr–Coulomb failure criterion:
Where:
- \(\boldsymbol{\tau}\): shear stress
- \(\boldsymbol{c}\): cohesion
- \(\boldsymbol{\phi}\): friction angle
- \(\boldsymbol{\sigma_n}\): normal stress
