The large number of intersecting surfaces in a volume divides the latter into small sub-volumes. Each of the sub-volumes is outlined or nearly outlined by parts of the intersecting surfaces. A number of simple geometrical conditions to be imposed on the intersecting surfaces determine a certain size distribution of the outlined sub-volumes. The approach based on these prerequisites was previously successfully applied to the multiple cracking and fragmentation of rocks, naturally and by blasting, as well as to soil fragmentation by shrinkage cracks. In both cases the intersecting surfaces are cracks, and sub-volumes are rock or soil fragments. The first application of the approach to the pore structure of soils was related to modelling the clay matrix pores and their size distribution. In this case the plate-like clay particles play the part of the intersecting surfaces, and the pore volumes play the part of the sub-volumes. The approach leads to the scale-invariant fragment- and pore-size distributions and permits one to take into account the superposition of the intersecting surfaces of a different physical nature and scale, the connectedness and tortuosity of the intersecting surfaces, the shape characteristics of sub-volumes, and the swelling-shrinkage of a system of clay particles. In general, soils contain, besides clay matrix pores, such sub-volumes as silt-sand grains and different types of clay aggregates and pores. The boundaries of the silt-sand grains and aggregates, along with cracks and clay particles, play the part of the intersecting surfaces. The objective of this work is to generalize the approach to model the different size distributions in sand and aggregated soil (in the last case we only consider the interaggregate, ie structural porosity). This development follows a brief summary of the approach including its previous applications as well as a consideration of the differences between such inter- secting surfaces as cracks, plate-like clay particles, boundaries of sand grains and aggregates. A comparison between the model predicted size distributions and relevant available data shows satisfactory agreement.