CALCULATING CAPILLARITY IN GRANULAR SOILS AS A FUNCTION OF GRAIN-SIZE PARAMETERS AND PACKING

Capillarity of a soil is known to be a function of the diameters of the pores, with the largest systematic pores limiting the capillarity of the total soil. Using the log-normal distribution of grain sizes in granular soils to guide sampling, a Monte Carlo simulation based on Soddy circular and spherical geometries was used to numerically determine the pore throat and pore body size distributions within 4-grain tetrahedra as a function of volumetric mean and standard deviation of the source soils. Using a log2 base, D_pt = D_s -2.684 - 0.0281 σ_gr + 0.155 σ_gr² – 0.0129 σ_gr³, where D_s = D_gr – ln(2) σ_gr² (= the grain size mean for total surface area), D_pt and D_gr are the logarithmic mean pore throat and grain diameters, and σ_gr is the logarithmic standard deviation of grain sizes. D_pb = D_s – 2.152 – 0.0311 σ_gr - 0.054 σ_gr² + 0.004527 σ_gr³, where D_pb is the logarithmic diameter of the pore body.

These values provide the parameters for understanding the sizing of the 4-grain tetrahedra that form the structural matrix of the soils. Assuming structural integrity of the soils, the pore body diameters within the less regular intervening system of larger pores can be closely constrained from the sizes of these tetrahedra and the packing density of the soils. It is these larger pores that control the capillarity of the soils. The mean diameters of the large pores decrease with increasing standard deviations and packing values, resulting in higher capillarity of the soils.