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Figure 6 provides the corresponding amplitude spectrum of maximum kinematic pile bending moment in the two-layer soil, owing to variation in the frequency ratio [omega]/[[omega].sub.1], among the FE, the BDWF, and the simplified approaches.
The good agreement of the factors [u.sub.p](0)/[u.sub.g] and [u.sub.p](0)/[u.sub.e](0) among the simplified approach, the FE method, and the BDWF solution has been attributed to the predominant effect of the free field soil displacement.
Figure 11 shows the comparison of kinematic pile bending between the simplified proposed approach and the BDWF formulation .
The simplified approach is generally valid to nonhomogeneous soil problems, in light of the good comparison with the dynamic FE method and BDWF solution.
The simplified method employs the soil-displacement-influence coefficients [I.sub.s] to consider the pile-soil interaction (resembling the spring constant [k.sub.x] in the BDWF).
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