The saturated hydraulic conductivity of soils with n-modal pore size distributions

A model for water retention in bi-modal soils (soils having structural and matrix porosity only) is further developed into a model for tri-modal soils so that the effects of macro-pores can also be included. This model is based on the exponential (Boltzmann) water retention function. It is suggested that this could be extended to include any number, n, of modes of porosity as may exist due to the hierarchical nature of soil structure. This is then used in combination with Marshall's pore model for hydraulic conductivity to produce a model for the saturated hydraulic conductivity, Ksat, of n-modal soils that appears as a very simple and elegant equation. This simple expression for Ksat allows for scaling of the porosity and also the characteristic pore size. The model is illustrated with a Polish data set (a sub-set of the POLHYDRO database). Measured values of water retention, bulk density and Ksat are used to estimate the parameters of the macro-pore term that explains the contribution of the soil macro-pores to Ksat. The mean values and distributions of these macro-pore parameters are presented for the 42 Polish arable soils. However, the existence of macro-pores does not necessarily imply that they are connected and that they contribute to the hydraulic conductivity. It is found that in normal agricultural fields at harvest time, they do not contribute to the hydraulic conductivity. Examination of measured and predicted values of Ksat showed that in the normal field conditions that were studied, water movement occurs almost entirely through the structural pores. However, it is predicted that flow through the macro-pore spaces occurs in freshly-tilled soil. The effects of compaction on Ksat are easily modelled using the new approach. Different scenarios may readily be compared. A simple one in which the characteristic size of the structural pores decreases as the soil becomes more dense is found not to be consistent with the observations. We are left with the conclusion that the number of structural pores and not their size decreases as soil becomes more dense. It is concluded that the multi-modal nature of soil pore size distributions has a big influence on water retention and on saturated hydraulic conductivity. Taking the multi-modal pore size distribution into account leads not only to physically-based predictions of soil hydraulic properties, but also to improved understanding of soil structure and function.