Probabilistic Assessment of Rocking Response for Simply-Supported Rigid Blocks

A probabilistic assessment of the rocking and overturning response of a simply-supported rigid block on a horizontal plane is reported. A two-dimensional rectangular block resting on a rough, horizontal, tensionless and cohesionless rigid base at ground surface is considered, subjected to far field horizontal earthquake excitations. The roughness of the interface is assumed to be sufficiently large to prevent sliding, while the flexibility of the block is neglected. Rocking response curves are calculated for increasing ground motion intensity (or, equivalently, decreasing uplift strength) via Incremental Dynamic Analysis (IDA), and results are summarised in the form of 16%, 50% and 84% fractile IDA curves. By employing non-linear regression analysis, simple expressions are developed for each fractile of peak response to offer a complete probabilistic characterisation of rocking behaviour. Generalised overturning criteria are proposed covering a wide set of excitations and block parameters.