Micromechanics analysis of thermal expansion and thermal pressurization of a hardened cement paste

The results of a macro-scale experimental study of the effect of heating on a fluid-saturated hardened cement paste are analysed using a multi-scale homogenization model. The analysis of the experimental results revealed that the thermal expansion coefficient of the cement paste pore fluid is anomalously higher than the one of pure bulk water. The micromechanics model is calibrated using the results of drained and undrained heating tests and permits the extrapolation of the experimentally evaluated thermal expansion and thermal pressurization parameters to cement pastes with different water-to-cement ratios. It permits also to calculate the pore volume thermal expansion coefficient f a which is difficult to evaluate experimentally. The anomalous pore fluid thermal expansion is also analysed using the micromechanics model

Effect of the volume of the drainage system on the measurement of undrained thermo-poro-elastic parameters

For evaluation of the undrained thermo-poro-elastic properties of saturated porous materials in conventional triaxial cells, it is important to take into account the effect of the dead volume of the drainage system. The compressibility and the thermal expansion of the drainage system along with the dead volume of the fluid filling this system, influence the measured pore pressure and volumetric strain during an undrained thermal or mechanical loading in a triaxial cell. The correction methods previously presented by Wissa (1969), Bishop (1976) and Ghabezloo and Sulem (2009) only permit to correct the measured pore pressures during an undrained isotropic compression test or an undrained heating test. An extension of these methods is presented in this paper to correct also the measured volumetric strain and consequently the measured undrained bulk compressibility and undrained thermal expansion coefficients during these tests. Two examples of application of the proposed correction method are presented on the results of an undrained isotropic compression test and an undrained heating test performed on a fluid-saturated granular rock. A parametric study has demonstrated that the porosity and the drained compressibility of the tested material, and the ratio of the volume of the drainage system to the one of the tested sample are the key parameters which influence the most the error induced on the measurements by the drainage system.Comment: International Journal of Rock Mechanics and Mining Sciences (2009) in pres

Stress dependent thermal pressurization of a fluid-saturated rock

Temperature increase in saturated porous materials under undrained conditions leads to thermal pressurization of the pore fluid due to the discrepancy between the thermal expansion coefficients of the pore fluid and of the solid matrix. This increase in the pore fluid pressure induces a reduction of the effective mean stress and can lead to shear failure or hydraulic fracturing. The equations governing the phenomenon of thermal pressurization are presented and this phenomenon is studied experimentally for a saturated granular rock in an undrained heating test under constant isotropic stress. Careful analysis of the effect of mechanical and thermal deformation of the drainage and pressure measurement system is performed and a correction of the measured pore pressure is introduced. The test results are modelled using a non-linear thermo-poro-elastic constitutive model of the granular rock with emphasis on the stress-dependent character of the rock compressibility. The effects of stress and temperature on thermal pressurization observed in the tests are correctly reproduced by the model

Theory of the two-dimensional Ising model with random impurities

The effects of random impurities on the various thermodynamic functions are studied with the aid of the two-dimensional Ising model. Of special interest are the limiting forms of these functions near the critical point. This problem is approached by a Green's function formulation as developed by Kadanoff. Since experiments only measure the average effects of impurities, we consider the average of the Green's function over all distributions of impurities and calculate it by perturbation theory. From this function we find the location of the new critical temperature and the temperature dependence of the coherence length. Thermodynamic and correlation functions are calculated by means of perturbation expansions and their functional dependence on the coherence length investigated. It is found that the magnetic properties such as the magnetization, susceptibility, and spin-spin correlations retain the same functional dependence on the coherence length. The specific heat is found to have a finite value at the critical point, and the T = Tc form of the energy-energy correlation c function is changed. The thermodynamic functions exhibit new critical indices very close to Tc. These renormalized exponents have been predicted c in literature and are found to satisfy the scaling laws predictions.U of I Onlythesi

Fluid pressures in deforming porous rocks

The constitutive relations describing the fluid pressure response of a porous medium to changes in stress and temperature must reflect the microscopic processes that are operative over the time scale allowed for the deformation. Short‐duration deformations are readily described by undrained moduli, and intermediate duration deformations by drained moduli, both of which are formulated through linear elastic theory. Long‐term deformations that operate over geologic time are normally dominated by irreversible processes and result in considerably larger deformations, for the same applied stress conditions, than would be expected from their elastic counterparts. Model constitutive equations are developed for both elastic and irreversible processes and the magnitude and interpretation of the relevant material properties examined. Although the theory is presented in general terms, a sample calculation shows that for sandstone the inelastic deformation is one and one half orders of magnitude greater than the elastic deformation at the same applied stress. This difference in magnitude has a significant effect on the effective hydraulic diffusivity, various pore pressure coefficients, and the prospective fluid pressure development of the sediment