Simplified Procedures for Estimating Earthquake- Induced Deviatoric Slope Displacements

Simplified procedures are commonly employed to estimate seismic displacements of earth and waste fills. The landmark work of Makdisi and Seed (1978) has been widely adopted in practice. Although this work is widely used, it has a number of significant limitations such as decoupling the sliding block analysis from the seismic response analysis, use of a limited number of recorded earthquake motions in its development, and the requirement to use the highly variable crest peak ground acceleration (PGA) as an input parameter. The Bray and Rathje (1998) method was an advancement in that it took advantage of the large number of ground motions recorded since the mid-70's and used the less variable design rock PGA as the intensity input parameter. It also provided an assessment of the uncertainty in the estimated displacement and was adopted in the ASCE/SCEC guidance document by Blake et al. (2002) for implementing the Seismic Hazards Mapping Act in California. However, it too used the decoupled approximation, and it was not intended to be used rigorously in a probabilistic seismic hazard assessment. Both of these methods are critiqued, and then a more recent simplified procedure developed by Bray and Travasarou (2007) for estimating permanent displacements due to earthquake-induced deviatoric deformations is presented. The new method utilizes a nonlinear fully coupled stick-slip deformable sliding block model to capture the dynamic performance of an earth dam, natural slope, compacted earth fill, or municipal solid-waste landfill. The primary source of uncertainty in assessing the likely performance of an earth/waste system during an earthquake is the input ground motion. Hence, a comprehensive database containing 688 recorded ground motions is used to compute seismic displacements. A seismic displacement model is developed that captures the primary influence of the system's yield coefficient (k y), its initial fundamental period (T s), and the ground motion's spectral acceleration at a degraded period equal to 1.5T s. The model separates the probability of " zero " displacement (i.e., < 1 cm) occurring from the distribution of " nonzero " displacement, so that very low values of calculated displacement do not bias the model. The use of the seismic displacement model is validated through re-examination of 16 case histories of earth dam and solid-waste landfill performance. The proposed model can be implemented rigorously within a fully probabilistic framework or used deterministically to evaluate seismic displacement potential.