Effect of Foundation Width on Subgrade Reaction Modulus

Abstract

Structures are subjected to vertical and horizontal loads. Vertical subgrade reaction acts on the foundation bottom surface, and in the case of an embedded structure, horizontal subgrade reaction acts on the embedded part. The subgrade reaction is obtained by multiplying the displacement of the foundation by the Subgrade Reaction Modulus (SRM). In practice, SRM is calculated using an equation that incorporates the negative power relationship of the Foundation Width (FW). If the structure is evaluated to be poorly seismic resistant, it is necessary to widen FW. However, when the FW is widened, the design value of SRM decreases. In this case, it is not possible to expect an increase in the subgrade reaction proportional to the increase of FW. Therefore, when the inertia force is very high, the FW has to be very wide. However, underestimating SRM can lead to structural overdesign. In this study, the relationship between SRM and FW, for a structure in which vertical and horizontal load act simultaneously, was analyzed. Compared with the design practice assumptions, the horizontal SRM was found to be highly dependent on FW while the vertical SRM was shown to be less dependent on FW.

Evaluation Methods of Vertical Subgrade Reaction Modulus and Rotational Resistance Moment for Seismic Design of Embedded Foundations

“…The SR shows a larger value as it moves closer to the foundation edge. Especially at the foundation edge, the initial SR value is larger than those at other positions, correlating with the results of [7]. Focusing on the SRs at 1m, after 5s, when B = 4m, and after 9s, when B = 10m, they show almost constant values.…”

“…The SRM calculation equation in the JSHB is shown in (11). The SRM calculation equation in this study has a weaker FW dependency than that in the JSHB, correlating with [7].…”

“…The legend is the distance from the foundation edge. At the foundation edge, the SR is large because of the influence of boundary conditions and the SRM is larger than those at other positions, correlating with the result in [7]. In the early stage of loading, the SRM shows a constant value because the ground does not exhibit nonlinear behavior.…”

“…However, the results of the horizontal loading test of pier models where the FW was changed revealed that the seismic resistance becomes extremely high by widening the FW because the vertical SR becomes large [6]. It has been also highlighted that the FW dependence of the vertical SRM is lower than that of the horizontal SRM [7]. Therefore, the horizontal and vertical SRMs should be evaluated differently, and the appropriate evaluation of the vertical SRM is critical to perform rational seismic design.…”

A Simplified Deformation Estimation Method for Anchor Piles of Sheet Pile Quay Walls under Kinematic Forces during Earthquakes

“…The current study used (2), assuming C-type of ground. The SRM is often considered to be dependent on the foundation width [29,30], however, in the design of anchor piles, this dependence is ignored [1].…”