To examine the influence of earthquake acceleration, numerical analysis was adopted to simulate the nonlinear dynamic behavior of soil-sheet pile structural interactions. Numerical simulations of the mechanical behaviors of soil materials were divided into two types. The first is the total stress analysis. The total stress analysis assumes that the constitutive laws for soil materials are based on the relationship between the total stress and strain. Therefore, if strain variation occurs in the soil, only the total stress is altered. The fluctuations of the effective stress in the soil cannot be described. Fluctuations in pore water pressure cannot be calculated if the changes in effective stresses in the soil during an earthquake cannot be described. The second type of numerical simulation is the effective stress analysis. The effective stress analysis indicates that under the effect of dynamic shear stress, the pore water pressure of soil increases with the dynamic shear stress of earthquakes. Thus, if a constitutive law based on effective stress is included in the numerical stress analysis, the distributions of pore water pressure, effective stress, and deformation in soil can be determined by conducting a dynamic effective stress analysis.

The effective stress analysis considers the pore water pressure excitation mode. This study employed the FLAC program embedded with the Finn [

24] model for effective stress analysis. The calculation is based on the explicit finite difference scheme to solve the full equations of motion, using lumped masses derived from the real density of surrounding zones. This formulation can be coupled to the structural element model, thus permitting analysis of soil-structure interaction brought about by ground shaking.

Coupled dynamic-groundwater flow calculations can be performed in the analysis. This mechanism is well-described by Martin et al. [

23], who also noted that the relation between irrecoverable volume-strain and cyclic shear-strain amplitude is independent of confining stress. They supply the following empirical equation, as shown in Equation (1), that relates the increment of volume decrease to the cyclic shear-strain amplitude (γ) where γ is presumed to be the engineering shear stain.

where

${C}_{1}$,

${C}_{2}$,

${C}_{3}$, and

${C}_{4}$ are constants.

${\Delta \mathsf{\epsilon}}_{vd}$ is the increment of volume strain and

${\mathsf{\epsilon}}_{vd}$ is the accumulated irrecoverable volume strain. An alternative, and simpler, formula is proposed by Byrne [

25] as shown in Equation (2). For the Byrne model,

${C}_{1}=8.7{\left({N}_{1}\right)}_{60}^{-1.25}$ and

${C}_{2}=0.4/{C}_{1}$. This study adopted the Finn and Byrne model [

25] which was revised from the model proposed by Martin et al. [

23]. The Finn and Byrne model was selected because only two parameters are needed for the analysis. Due to the difficulties and limitations for conducting geotechnical investigations in deep water, a two-parameter model such as the Finn and Byrne model is preferred in the planning stage. In addition, it is of importance that the two parameters of the model can be directly obtained from the standard penetration tests. To clarify the difference of the Martin model and the Finn and Byrne model, we first conducted a numerical experiment. The parameters for this test are listed in

Table 1. The width and the depth used in the experiment are 50 m and 5 m, respectively. A sine wave with a maximum amplitude of 0.005 m and a frequency of 5 Hz was used for the input of the cyclic loading. The total computing time is 10 s. The computed pore water pressures at three observed points at different depths were recorded during the computation. As one can see the results obtained from the Martin model and the Finn and Byrne model are almost consistent with each other as shown in

Figure 4.