An examination of simplified earthquake-induced displacement procedures for earth structures: Discussion

Abstract

The Discusser has read this paper with considerable interest, since its subject matter pertains to our work in embankment dam engineering at the U.S. Bureau of Reclamation. We generally use Newmark's sliding block model to estimate dynamic deformations of embankment dams and feel reasonably comfortable with the results. However, the Authors suggest that the procedure can give significantly unconservative results and that it should not be used. The Discusser questions some of the reasons for the concerns and recommendations against the use of the Newmark procedure for estimating seismic deformations of embankment dams. As pointed out by the Authors, there are many viewpoints, opinions, and ideas for estimating seismic deformations for earth structures. Therefore, it is essential to consider details of the problem under study and those of possible solution procedures in selecting an appropriate solution strategy and procedure. As engineers, we all tend to tamper with the rigors of mathematical models to include some of the entities considered important for our problems or exclude some of the entities considered not so important, for simplification. However, considerations for consistency across various aspects of engineering work are essential, especially when the results of one analysis feed into another. (1) An embankment dam is a deformable earth structure, whereas the Newmark model is a rigid block on a rigid inclined plane. However, it is consistent with other aspects of slope stability models as explained in item 2 below. In addition, the stick-slip type of movements envisioned in the sliding block model have been monitored in rock movements in open pit mines during blasting (Oriard 1972). For its performance on embankment dams during earthquakes, the sliding block model was used for displacement calculations in studies performed to analyse the observed performance of La Villita Dam, a 197 ft (60 m) high earth and rockfill dam in Mexico, which had been subjected to six major earthquakes of magnitudes 4.9–8.1 located at epicentral distances of 6–75 mi (10–121 km) from the dam, and for which seismically induced permanent deformations were recorded and also detected in recorded acceleration responses. Deformations in the dam were significant and the crest acceleration records asymmetric. Details of the dam performance data and those of the experimental and numerical models used to study the observed responses are given in Elgamal (1992) and Elgamal et al. (1990). The asymmetric character of the acceleration responses at the dam crest were attributed to stick-slip type of deformations in the dam and it was learned that plastic yielding does not allow acceleration peaks to exceed yield acceleration, that is, a yield acceleration imposes a physical barrier on the magnitude of inertial forces that can develop in a sliding zone. Response of structures to vibration effects using steady state harmonic motion depends on how close the period of the structure is to the period of the harmonic motion. Thus, agreement of a numerical model results with shaking-table experiments using sinusoidal input motions is necessary but may not be sufficient for gaining confidence in its application to earthquake loading. It would be helpful to apply the Authors' procedure to La Villita Dam and compare the results. (2) Earthquake forces result from erratic vibratory motion of the ground on which the structure is supported. For a rigid structure, rigidly coupled to its foundation, force on the structure equals the mass of the structure times acceleration of the ground (F = M × A) at any instant; for a flexible structure which deforms slightly, F may be less than M × A for short periods of time; and for a very flexible structure subjected to a ground motion whose period is near that of the structure, F may be much greater than M × A. In a slope stability model by the limit equilibrium method, a rigid soil mass rests on a curved slip surface with a rigid plastic glue which conforms to a shear strength criterion properties of the slide mass above the slip surface are not related to those of the soil it represents and the materials below the slip surface provide a rigid, nonyielding support to the slide mass. In this model, no deflection occurs before failure and when failure takes place, the slide mass slides slowly downwards without accelerating. Yield acceleration for the slide mass is