A general analytical expression for pore size distribution based on probability theory

The pore structure of soils and rocks plays a crucial role in geotechnical, geo-environmental and geological engineering, as it dominates the hydro-mechanical behaviour, gas- and liquid-permeability as well as material transport property of soils and rocks. A large amount of pore size distribution (PSD) data of porous materials have been experimentally determined in the past decades and are currently available in the literature. However, a general expression to parameterize these PSD curves is still missing. In this study, a general multimodal PSD model is developed based on the probability theory, which is a strong tool to quantify the complex soil microstructure precisely. The parameters in the model possess a clear physical meaning. The model is validated by reproducing the PSD curves of two clays and a sand-clay mixture having a complex pore structure. The parameterized PSD curves demonstrate a strong consistency with the measurements. In addition, the model is applied to predict the PSD evolution under hydro-mechanical processes (e.g., compaction, saturation- swelling-process), the water content – soil suction – dry density relationship of Boom clay after compaction and the time-dependent PSD evolution of MX80 Bentonite. Beside soils, the proposed general multimodal PSD relationship can describe the pore structure of any other porous and granular material, as all the underlying physics is the same for all of them. The proposed model can be incorporated into the existing effective stress parameter formulation, permeability models and constitutive models of unsaturated multimodal soils.