Abstract
In order to study the process of slope failure caused by heavy rainfall, some large scale slope models of loamy and sandy materials were constructed. Artificial rainfall was applied to these models until a large scale failure occurred. Surface displacement were monitored by extensometers set on the models from the beginning of experiment to the final failure. Through analysis of the data, a rule on slope movement in the process of failure was found.
The increment of the logarithm of velocity of surface displacement is proportional to the logarithm of acceleration of the surface displacement in the final stage of the slope movement just before the failure. That is d2χ/dt2=a (dχ/dt) αwhere χ is downward surface displacement along the slope, t means time, d2χ and dχ/dt show acceleration and velocity of surface displacement, a and αa are constants. Usually, α took 1.5 to 2.2 in range in the experiments.
From the integration of the equation for the range of α>1, an equation, 1/υ = {a (α-1)} 1/ (α-1) (tγ-t) 1/ (α-1) is obtained, were 1/υ is 1/ (dχ/dt), that is inverse number of velocity and tγ is a constant of integration. The equation shows that the curve written by each point of t and 1/υ is linear if α=2, convex if α>2 and concave if 1<α<2 and that the value uniformly decreases. In the case of α=2, the failure time of a slope can be predicted exactly from the time (tγ) when 1/υ equals 0 (infinite velocity).
Furthermore, the equation can be modified as (1/υ) / (d (1/υ) /dt) = (α-1) (tr-t). The equation shows that the curve written by each point of t and (1/υ) / (d (1/υ) /dt) is linear for the range of α>1. Based on the relations mentioned above, the failure time of a slope can be predicted exactly in the case of α≠2. Also a graphical method to show the failure time, based on the equation, is proposed.
