The seismic displacement of a block sliding on an inclined plane with resistance varying with the distance moved

The paper considers a rigid block on an inclined plane. First, the typical response measured along slip surfaces of sands and clays under both drained and undrained conditions is identified. Then, for any expression simulating this change in shear stress with displacement along the boundary between the block and the plane, the paper derives an equation which predicts the equivalent friction angle which, when applied, computes the same seismic displacement of the block. The paper also proposes, validates and calibrates a simple constitutive equation which simulates the typical shear stress-displacement response measured in ring shear tests for both sands and clays sheared under both drained and undrained conditions. Next, the paper for the constitutive law above simulating the change in shear stress with displacement along the slip surface, derives equations which predict the equivalent friction angle which, when applied, computes the same seismic displacement of the block. Finally, based on these equations, the paper proposes an easy-to-apply methodology predicting the seismic displacement of slopes along slip surfaces with strain softening with the aid of the seismic displacement predicted by the conventional sliding-block model and applies this methodology in order (a) to validate it against results of elaborate numerical analyses and (b) to modify the Ambraseys-Menu expressions predicting the seismic displacement of the conventional sliding-block model for soils exhibiting strain softening.