ABSTRACT
Field measurements from 23 sites in California and from five other widely distributed locations on soil-mantled hillslopes reveal a strong inverse relation between maximum drainage area of unchannelized basins and their average hollow gradients. The area–slope product was found to equal about 4000 m2. Hollow length was also negatively correlated to average hollow gradient. These observations indicate that the number of sources and, consequently, drainage density increase with slope. The conservation of mass equation for a tipped triangular trough and a slope-dependent transport law are used to develop an expression for the rate of colluvium accumulation in hollows. Maximum colluvium depth is found to increase by the one-half power of time owing to the vertically increasing cross-sectional area of the trough. Rate of accumulation is proportional to side-slope gradient and to the difference between the side-slope and hollow gradient. The ratio of hollow to side-slope gradient is typically about 0.8. Models of shallow subsurface flow and deeper ground water flow are used to predict, via the Mohr–Coulomb failure criterion, the relation of hollow length to its gradient. It is not yet known which flow path plays the dominant role in controlling the position of the channel head, but both models predict that angle of internal friction ϕ' of the colluvium or weathered bedrock strongly influences the size and slope of the unchannelized basins and that basin size must rapidly decline above a gradient of 0.7 tan ϕ'.
