Journal of Geography (Chigaku Zasshi)
Online ISSN : 1884-0884
Print ISSN : 0022-135X
ISSN-L : 0022-135X
Theoretical Analysis on the Process of Slope Development Based on Morphometric Measurements
Takeshi MIZUTANI
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1971 Volume 80 Issue 3 Pages 160-178

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Abstract

The mechanism of slope erosion and the process of slope formation have been studied by physical and morphometrical analysis.
In the previous study, a fundamental equation on slope erosion
E=Klm (sinθ-sinθc) n (1)
E : erosion depth at l
l : distance from the top of the slope
θ : slope angle k, m, n, θc : constant was derived by hydrological and physical considerations of erosional agents such as tracting force of flowing water and abrasion due to material of mass movement. Theoretical values of erosion depth obtained from equation (1) agree quite well with measured values at youthfully dissected strato-volcanoes in Japan.
In the present paper, erosional landforms of several strato-volcanoes in the stage of early maturity were measured and averaged profiles of initial and present landforms and altitudinal changes of average amount of erosion depth were obtained. Multiple regression coefficients log K, m and n were obtained with each slope by the method of least squares. The values of m and n are nearly 1 at most of slopes out of relation to location, erosional stage and scale of the slope. Theoretical values of erosion depth calculated from equation (1) with determined coefficients have also good agreements with measured values at these fairly highly dissected volcanoes.
The amounts of undercutting of valley beds at volcanoes are also given by equation (1). Theoretical basis of this agreement was obtained by physical consideration of erosional processes.
Equation (1) was derived supposing uniform sheet erosion all over the slope. This supposition, however, does not hold at highly dissected slope. The reason of applicability of equation (1) to highly dissected volcanoes can be explained by assumptions that erosional process at valley bed is dominating and the recession of valley wall proceeds in proportion to the amount of undercutting of valley bed keeping the gradient of slope almost constant.
Equation (1) can also be applied with success to the process of slope formation of abandoned coal slag heaps which are dissected by gullies. Thus, applicability of equation (1) to some of non-volcanic slopes was ascertained.
Gradient of the lower end of the slope where radial valleys nearly disappear decreases as dissection of the slope precedes. Then, θc is not a constant but a function of E.
Gradient and curvature of slope are thought to be regulating factors of slope erosion.However, multiple regression coefficients of these terms are entirely insignificant at several slopes. Gradient and curvature of slope are infered to be local and temporary factors.
From modifying equation (1), the following equation of slope development is derived,
∂y/∂t=f1 (x, y) xm {∂y/∂x+g (t)} +f2∂y/∂x
General process of slope development have been studied by solving the equation under various initial conditions.

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