A RE-ASSESSMENT OF FACTOR OF SAFETY ANALYSIS FOR PREDICTING SLOPE FAILURE: INSIGHTS FROM DISCRETE ELEMENT SIMULATIONS OF LANDSLIDING

Factor of Safety (FS) is commonly used as a measure of slope stability, and is defined as the ratio of resisting to driving forces acting on a slope. FS >1 implies stable conditions, while FS~1 implies instability and incipient slope failure. Theoretically, FS< 1 cannot be achieved. Here we carry out numerical simulations using the Discrete Element Method to better understand the mechanics of slope failure and the transition to unstable conditions. We find that natural landslide geometries only develop under “unphysical” conditions of FS< 1, whereas FS~1 conditions produce unnaturally small failures.

We modeled 2D cohesive slopes constructed of spheres interacting at frictional bonded contacts, simulating mechanically homogeneous materials. Slope height (H) was fixed at 1000m; initial slope angles of 30, 45 and 70 degrees were tested for a range of material strength (S) conditions to reproduce a range of FS values. Landslide size was quantified in terms of landslide surface length (l), and maximum landslide thickness above the sliding surface (t). All failures initiated at the slope-foot and propagated upwards to form discrete sliding planes. Landslide deposits varied from disintegrative to blocky with increasing S. With low S, landslides encompassed the entire slope height. With increasing S, slumps activated decreasing proportions of the lower slopes, until vanishing at FS=1. Regardless of size, landslide shapes were self-similar yielding a constant ratio of t/l for a given slope angle, with t decreasing with slope angle.

Considering the above observations, if all failures occur at FS=1, we would expect very small landslides (l<< H) along the lower parts of the slopes. This is rarely observed in nature, where slumps typically encompass the entire slope height (H), and l is commonly close to H. The geometry of natural slumps suggests that they develop under FS< 1 rather than FS~1 conditions. We argue that the simplified FS approach to slope stability overlooks the real mechanics of slope-failure, in which material properties, and therefore FS, change with time. Although failure may initiate when FS=1, progressive slope weakening occurs as the slip plane propagates, enabling much larger slumps to form than predicted under FS=1 conditions. The degree of slope weakening will influence the final geometry of the landslide.