Temperature increase in saturated porous media under undrained condition leads to thermal pressurization of the pore fluid due to the discrepancy between the thermal expansion coefficients of the pore fluid and the solid skeleton. Such pore pressure variation induces a reduction of the effective stress that can lead to shear failure or hydraulic fracturing. This phenomenon is important in many industrial domains such as: reservoir rock and well cement lining under sudden temperature change; exothermal radioactive waste disposal in deep clay geological formation (Armand et al., 2017); rapid fault slip events when shear heating tends to increase the pore pressure that causes the decrease of the effective compressive stress and the shearing resistance of the fault material (Rice, 2006).

This page provides to readers an online tool to calculate the thermal pressurization coefficient of a material. The variation of pore pressure is linearly related to the variation of the temperature and the confining stress such as (Coussy, 2004; Ghabezloo and Sulem, 2009):
dp = Π * dσ + Λ * dT
where Π is the Skempton’s coefficient and Λ is a thermal pressurization coefficient those are functions of the thermo-poroelastic properties of the porous medium.
They can be expressed such as:

Π = b/K/(b^{2}/K + (b-φ)/K_{s} + φ/K_{f});
Λ = 3φ(α_{f}-α)/(b^{2}/K + (b-φ)/K_{s} + φ/K_{f})

where φ is the porosity; K, K_{s} and K_{f}
the drained bulk modulus and the bulk moduli of the solid phase and fluid, respectively;
b = 1-K/K_{s} the Biot's coefficient; α_{f} and α the linear thermal expansion coefficients of the fluid phase and the drained linear thermal expansion coefficient of the porous medium, respectively.

**References**

Coussy O (2004): Poromechanics, John Wiley & Sons.

Rice JR (2006): Heating and weakening of faults during earthquake slip. Journal of Geophysical Research, 111, B05311.

Ghabezloo S, Sulem J (2009). Stress dependent thermal pressurization of a fluid-saturated rock. Rock Mechanics and Rock Engineering, 42:1-24.

Armand G, Bumbieler F, Conil N, de la Vaissière R, Bosgiraud JM, Vu MN (2017). Main outcomes from in situ thermo-hydro-mechanical experiments programme to demonstrate feasibility of radioactive high-level waste disposal in the Callovo-Oxfordian claystone. Journal of Rock Mechanics and Geotechnical Engineering 9 (3), 415-427.