SCALE-INVARIANCE OF SOIL-MOISTURE VARIABILITY AND ITS IMPLICATIONS FOR THE FREQUENCY-SIZE DISTRIBUTION OF LANDSLIDES

Power spectral analyses of soil moisture variability are carried out f rom scales of 100 m to 10 km on the microwave remotely-sensed data fro m the Washita experimental watershed during 1992. The power spectrum S (k) has an approximate power-law dependence on wave number k with the exponent -1.8. This behavior is consistent with the behavior of a stoc hastic differential equation for soil moisture at a point, and it has important consequences for the frequency-size distribution of landslid es. We present the cumulative frequency-size distributions of landslid es induced by precipitation in Japan and Bolivia as well as landslides triggered by the 1994 Northridge, California earthquake. Large landsl ides in these regions, despite being triggered by different mechanisms , have a cumulative frequency-size distribution with a power-law depen dence on area with an exponent ranging from -1.5 to -2. We use a soil moisture field with the above statistics in conjunction with a slope s tability analysis to model the frequency-size distribution of landslid es. In our model, landslides occur when a threshold shear stress depen dent on cohesion, pore pressure, internal friction and slope angle is exceeded. This implies a threshold dependence on soil moisture and slo pe angle since cohesion, pore pressure and internal friction are prima rily dependent on soil moisture. The cumulative frequency-size distrib ution of domains of shear stress greater than a threshold value with s oil moisture modeled as above and topography modeled as a Brownian wal k is a power-law function of area with an exponent of -1.8 for large l andslide areas. This distribution is similar to that observed for land slides. The effect of strong ground motion from earthquakes lowers the shear stress necessary for failure, but does not change the frequency -size distribution of failed areas. This is consistent with observatio ns. This work suggests that remote sensing of soil moisture can be of great importance in monitoring landslide hazards and proposes a specif ic quantitative model for landslide hazard assessment. (C) 1997 Elsevi er Science B.V.