Method to estimate the initial landslide failure surface and volumes using grid points and spline curves in MATLAB

Abstract

This paper presents a new method to estimate a landslide failure surface and its volume based on a digital elevation model (DEM) using spline curves by assuming values of the tangent of the failure surface along with transversal vertical profiles. The model will give the depth of the probable failure surface plotted using the 2D grid function. We can easily visualize the results by running the codes; the display will show the step-by-step processes involved. The model requires fundamental data inputs, which are readily available online throughout the world, such as a DEM of the study area and a KML file of contour limits of the landslide as input. The calculation procedure is simple; it evaluates the depth of the failure surface at each point of the grid. The cross-section for each point is estimated perpendicular to the slope line joining the highest elevation point and the lowest elevation point within the contour limits. A cubic spline curve is calculated using two endpoints and the first derivative at these points. The Z value is calculated using these parameters at each grid point (centre of a grid), and finally, a 3D failure surface is generated, enabling the volume calculation. MATLAB code has been written to execute this process automatically. This model can easily use input data with very little fieldwork, and the processing can produce a result in a few minutes. We can enrich a real scenario by imposing more constraints on the variation in the cross-section angle based on the limit of the landslide using field measurements. This model is also helpful in predicting the area affected by the mass of the failure surface, and we can determine a predefined hazard zone to avoid any casualties in the future.