Frequency–size relation of shallow debris slides on cut slopes along a railroad corridor: A case study from Nilgiri hills, Southern India

The probability of landslide volume, V L , is a key parameter in the quantitative hazard analysis. Several studies have demonstrated that the non-cumulative probability density, p(V L ), of landslide volumes obeys almost invariably a negative power law scaling of p(V L ) for landslides exceeding a threshold volume and a roll-over of small landslides. Some researchers attributed the observed roll-over to under-sampling of data, while others relate it to a geo-morphological (physical) property of landslides. We analyzed 15 sets of a complete landslide inventory containing shallow debris slides (2 ≤ V L ≤ 3.6 × 10 3 m 3 ) with sources located on cut slopes along a 17-km-long railroad corridor. The 15 datasets belong to individual years from 1992 to 2007. We obtained the non-cumulative probability densities of landslide volumes for each dataset and analyzed the distribution pattern. The results indicate that for some datasets the probability density exhibits a negative power law distribution for all ranges of volume, while for others, the negative power scaling exists only for a volume greater than 10 m 3 , with scaling exponent β varying between 0.96 and 2.4. When the spatial distribution of landslides were analyzed in relation to the terrain condition and triggering rainfall, we observed that the number of landslides and the range and the frequency of volumes vary according to the changes in local terrain condition and the amount of rainfall that trigger landslides. We conclude that the probability density distribution of landslide volumes has a dependency on the local morphology and rainfall intensity and the deviation of small landslides from power law, i.e., the roll-over is a “real effect” and not an artifact due to sampling discrepancies. Copyright Springer Science+Business Media B.V. 2012