Discussion of “Seismic Earth Pressures on CantileverRetaining Structures” by Linda Al Atik and Nicholas Sitar

Abstract

This paper correctly identifies that the maximum active earth pressure developed by a retained soil wedge occurs during the passive direction of ground motion (base motion acceleration toward the retained side of the wall). Interestingly, the maximum active earth pressure is opposite the inertial movement and maximum moment of the wall itself (which is reported occurring in the active direction; base motion toward the lower side of the wall). The commonly illustrated active acceleration of the wedge [Fig. 1(a)] is, in fact, shorthand for the actual behavior. From the point of view of free-body interaction, the assumed acceleration in Fig. 1(a) produces forces equivalent to the actual behavior, and the soil wedge and the base block undergo relative acceleration in the passive direction [Fig. 1(b)]. The wedge will never develop its own significant independent active acceleration without input from the underlying base. The same reversal is often illustrated for sliding block analysis. The maximum displacement in sliding block analysis always occurs when the underlying ground is accelerating in the uphill (passive) direction, at which time the sliding block develops relative movement by being unable to accelerate uphill at the same rate as the base motion. The paper presents detailed results of dynamic earth pressure at the same instant as the maximum dynamic wall movements, which is reported occurring during acceleration in the active direction (e.g., Fig. 6). It would be of value for the authors to present the results of the maximum seismic active pressure from their experiment in the passive direction because it is likely to contribute to several other modes of stability, such as sliding, overturning, and permanent displacements other than wall bending. Second, although the authors present in their Fig. 6 a summary of the earth pressure coefficients for wall bending in the centrifuge modeling performed, it is useful to compare the authors’ results with the pressures calculated with the Mononobe-Okabe equation or similar wedge theory results, as redrawn in Fig. 2. The backcalculated maximum dynamic earth pressure component, which adds to the maximum bending moment and which includes the wall inertial force in the active shaking direction, is shown in Fig. 2. The Mononobe-Okabe earth pressure increment is superimposed using the horizontal coefficient equal to the peak ground acceleration, 0.65 of the peak ground acceleration as recommended in the discussed paper, and as commonly applied, 0.50 of the peak ground acceleration. The Mononobe-Okabe results using half of the peak ground acceleration show a reasonable, slightly conservative relationship for the flexible wall model and are comparable to only a slightly unconservative relationship for the rigid wall model.