## Research into the Seismic Response of a Cantilever Retaining Wall

The seismic loads acting on the structural wedge of a cantilever retaining wall are illustrated in Figure 1-3. The structural wedge consists of the concrete wall and the backfill above the base of the wall (i.e., the backfill to the left of a vertical section through the heel of the cantilever wall). The resultant force of the static and dynamic stresses acting on the vertical section through the heel (i.e., heel section) is designated as PaE, heel, and the normal and shear base reactions are N' and T, respectively. Seismically induced active earth pressures on the heel section, PAE, heel, are used to evaluate the global stability of the structural wedge of a cantilever retaining wall, presuming there is sufficient wall movement away from the backfill to fully mobilize the shear resistance of the retained soil. The relative slenderness of the stem portion of a cantilever wall requires structural design consideration. In Figure 1-3 the seismically induced shear and bending moments on a section of the stem are designated as s and m, respectively. The resultant force of the static and dynamic stresses acting on the stem of the wall shown in Figure 1-3 is designated as PE, stem. The A is not included in the subscript because the structural design load is not necessarily associated with active earth pressures.

A dry site (i.e., no water table) will be analyzed in this first of a series of analyses of cantilever retaining walls using FLAC (Fast Lagrangian Analysis of Continua). This allows the researchers to gain a full understanding of the dynamic behavior of the simpler case of a cantilever wall retaining dry backfill

Cantilever Retaining Wall

before adding the additional complexities associated with submerged or partially submerged backfills.

This report summarizes the results of detailed numerical analyses performed on a cantilever wall proportioned and structurally detailed per Corps guidelines given in Engineer Manuals (EM) 1110-2-2104 (HQUSACE 1992) and 1110-22502 (HQUSACE 1989)) for global stability and structural strength under static loading. The objective of the analyses was to identify trends and correlations between PAE heel and PE, stem and their respective points of application. The identification of such trends allows the displacement-controlled design procedure, which can be used to estimate PAE heel, to be extended to estimate PE stem, which is required for the structural design of the stem.

The detailed numerical analyses were performed using the commercially available computer program FLAC. The nonlinear constitutive models, in conjunction with the explicit solution scheme, in FLAC give stable solutions to unstable physical processes, such as the sliding or overturning of a retaining wall. FLAC allows permanent displacements to be modeled, which is inherently required by the displacement-controlled design procedure. The resultant forces acting on the heel sections and their points of applications as determined from the FLAC analyses were compared with values computed using the Mononobe-Okabe equations in conjunction with the displacement-controlled design procedure (e.g., Ebeling and Morrison 1992).

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