## Seismic Earth Pressure on Basement Walls with Cohesionless Backfill

- Author(s): Wagner, Nathaniel Bryce
- Advisor(s): Sitar, Nicholas
- et al.

## Abstract

Earth retaining structures have historically performed well under seismic loading, including cases in which the structures were designed for less intense ground motion or only considering static loading. The few reported failures are often attributable to waterfront structures retaining saturated backfill where the main factor was liquefaction. The remaining failures are rare and generally involve more complex conditions, such as sloping backfill, or poor construction or design. These observations suggest that seismic design provisions for engineered retaining structures may be too stringent, and in some cases may not be necessary. The objective of this study was to extend previous efforts to understand the seismic interaction of backfill-wall systems using experimental and numerical modeling, with an emphasis on deep, stiff basement walls in cohesionless soil and the current design methods thereof.

The experimental phase of the study consisted of a dynamic centrifuge model of a deep, stiff basement structure with a dry, level, dense sand backfill. The results obtained in the centrifuge experiment were first used to develop and calibrate a two-dimensional, finite difference model using FLAC2-D. A non-linear, hysteretic constitutive model was used to model the cyclic behavior of the soil and linear elastic beam elements were used to model the structure. The numerical simulations captured the most important aspects of the centrifuge experiment, specifically the inertial response and dynamic soil-structure interaction. Special attention was given to the selection of model parameters, the boundary conditions, and the initialization process. The second part of the numerical modeling effort concentrated on analyzing the response of typical prototype basement structures of varying depth using the calibrated soil properties from the first phase of numerical modeling.

As would be expected, the results from the experimental and numerical analyses show that the observed seismic load increments are a function of the ground motion, wall type and the depth of embedment. The dynamic earth pressure increment distribution for deep basement structures is highly non-linear in contrast with shorter retaining structures (<6.5 m in height) for which the dynamic earth pressure increment was observed to increase linearly with depth. The point of application of the dynamic earth pressure resultant varies between 1/3 H and 0.6 H above the base of the wall, as recommended by most current design procedures. The depth of embedment can be incorporated in traditional limit equilibrium analyses by calculating a seismic coefficient, k_MHEA, as the maximum of the average acceleration within the backfill over the depth of the basement structure. Results from previous centrifuge experiments and the experimental results of this study were found to be in good agreement with the seismic earth pressure coefficient, ΔK_ae, obtained using the Okabe (1924) pseudo-static Coulomb wedge analysis and the methodology proposed by Seed & Whitman (1970). This suggests that current design procedures overestimate seismic loads on retaining structures not necessarily through inherent conservatism in the methods, but rather due to overly conservative choice of seismic demand input.

Current design methodologies for cantilever and gravity retaining structures in highway applications utilize a similar procedure wherein the seismic coefficient is the maximum of the average acceleration in an assumed failure wedge This method utilizes a maximum value of the seismic coefficient at one instant in time and introduces bias toward the ground motion at the surface if mass-weighted over a wedge of soil that is largest near the top. For retaining structures permitted to displace, in effect allowing a failure wedge to form, the current methodology is applicable although the experimentally and analytically obtained dynamic loads are significantly lower than is predicted by the traditionally used methods. For retaining structures not permitted to translate or rotate, the proposed seismic coefficient is more rational than that computed in the current methodology wherein the peak acceleration at the surface or some fraction thereof is used. Moreover, this definition of the seismic coefficient is consistent with that recommended by Anderson et al. (2008) and Bray et al. (2010).

Evaluating static and dynamic earth pressure on retaining structures is a complex problem with a variety of competing and complementary effects to consider. In this study, a centrifuge experiment replicated the basic response of an idealized soil-basement structure system. Ultimately, further observations of performance in future seismic events and data from instrumented, full scale structures are highly desirable in order to fully validate these results. Numerical modeling offers a means to identify important aspects of the earth pressure problem. However, the results are sensitive to the input parameters, the boundary conditions, and the initialization of the process. Therefore, numerical models should be calibrated against real data when possible.