The diversion capacity of capillary barriers

An arrangement of unsaturated fine-grained soil overlying unsaturated coarse-grained soil along a sloping contact can, under appropriate circumstances, divert infiltrating water away from the coarser material. Such an arrangement is called a capillary barrier. The water diverted by a capillary barrier flows downdip above the contact. The volume of water moving laterally increases in the downdip direction as additional infiltration is diverted by the barrier. Sufficiently far downdip, the laterally moving water wets the contact to the point that an amount of water equal to the infiltration flows downward through the coarse soil. The lateral flow at such a point represents the diversion capacity of the capillary barrier because this flow will not increase farther downdip. If the width (measured in the direction of dip) of the system is large enough that total infiltration exceeds the diversion capacity, the downdip portion of the barrier will not be effective. The diversion capacity can be calculated exactly in the quasi-linear approximation where the relationship between relative permeability krel and pressure potential ψ takes the form krel = eαψ. This calculation shows that an upper bound on the width of capillary barriers is Ks tan o/qα, where Ks is the saturated hydraulic conductivity of the fine soil, o is the dip angle of the contact, and q is the infiltration rate.