Model for predicting the hydrostatic loading and unloading relationship of porous materials containing various amounts of fluid

An elastic-inelastic model is presented for the loading and unloading pressure-volume relationship of porous materials containing various amounts of fluid from 0 to 100% saturation. Distributions in both size and separation of connected and unconnected spherical and connected penny-shaped pores are assumed. The number of pores with a given size is assumed to be inversely proportional to the initial volume and independent of the separation between pores. The simple relationships relating the radius of a pore to the applied pressure are discussed. The pressure-volume relationship for the porous material with any saturation is calculated by using the input parameters, shear strength, shear modulus, matrix and fluid pressure-volume relationships, and the pressure-volume data for the dry material. Model predictions agree with the experimental data within experimental error for all saturations and at pressures up to 4 GPa (40 kbar) for Mt. Helen tuff