Numerical Simulation of Seismic Interaction of Pile Foundation and Structure

Continuum vs. Discrete Modeling of Spatial Dimension

Continuum modeling of soil-pile system essentially consists of four components (Figure 1): pile or pile group with pile cap, interface between pile and soil, near-field soil that can undergo plasticity, and far-field soil that accounts for the stiffness and damping effects of truncated semi-infinite soil. This continuum modeling can be computationally expensive, but it naturally simulates the a) wave propagation effects, b) soil plasticity, c) soil-pile separation, and d) pile group effects (Figure 2).

Figure 1.

Finite Element Mesh of a continuum model showing pile elements, Near-field soil elements and far-field soil elements: a) plan and b) isometric view

Figure 2.

Abilities of continuum models to simulate a) seismic wave propagation, b) soil plasticity, c) soil-pile slippage and gapping, and d) pile-group effects

For practical or design purposes that neither need modeling the seismic wave propagation effects nor require pile group effects, the simple alternative of discrete modeling of soil using Winkler springs exists. Again, Winkler modeling can use static or dynamic p-y curves with or without dampers. For modeling radiation damping, more complex series of springs and dampers can be used (Nogami, Otani, Konagai, & Chen, 1992). In all discrete models, pile is modeled as a beam with rotational degrees of freedom. Figure 3 shows the typical details of such models, with the pile properties (modulus of elasticity E and linear density m of pile material, radius r₀, cross-sectional area A, length L) and the near-field soil properties (soil density ρ, shear modulus G_s, radius of near-field r₁ stiffness proportional damping ξ_k, mass proportional damping ξ_m). In fact, such models are derived on the basis of experimental results or continuum modeling.

Figure 3.

Discrete modeling of soil-pile systems using complex soil springs