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Indian Seismic code IS1893-2002 suggests soil-structure interaction analysis for important and non-trivial structures, since the codal provisions do not consider such interactions in precise manner. The code merely gives the seismic design spectrum for structures resting on various kinds of soil. Design of pile foundations in soils, in general, and in liquefying soils has received great attention in the recent past due to the discovery of new failure modes. Analysis of pile- soil dynamics is especially complicated because of the presence of semi-infinite soil and a limited zone of nonlinearity. This is further complicated due to 1) liquefaction and consequent loss of lateral soil support, 2) passive earth pressures from moving soil mass and 3) destabilizing effect of axial loads on the pile (Madabhushi, Knappette, & Haigh, 2010). Both continuum modeling (Maheshwari & Emani, 2014; Emani & Maheshwari, 2009) and discrete or Winkler spring modeling of soils (Nogami, Otani, Konagai, & Chen, 1992; Wang, Kutter, Chacko, Wilson, Boulanger, & Abghari, 1998) is carried out by researchers for non-linear seismic analysis of soil-pile systems, even under liquefaction conditions (PhaniKanth, Choudhury, & Reddy, 2013) (Maheshwari, Truman, Truman, & El Naggar, 2005). Experimental studies are carried out by Miyamoto, Hijikata, & Tanaka (2004) using mining blast induced vibrations, on structures supported on 2 x 2 pile group, and the same are explained using 1D and 3D numerical models considering inelastic soil-pile-structure interaction analysis.
The present work is undertaken with a motivation to help foundation designer in considering the interactions of pile in inelastic soil for estimating the seismic loads. Using beam-on-nonlinear-Winkler (BNW) modeling, an inelastic design spectrum is developed for structures resting on pile foundations.
Soil-Pile Modeling
The soil-pile system consists of a single 10 m long circular pile of diameter 0.4 m, embedded completely in a nonlinear soil. The soil-pile system is modeled as a beam supported by nonlinear Winkler soil (BNW) springs in the near-field and by a series of dampers in the far-field. The spring stiffness values are taken from Nogami et al (1992) as also the damping of the far-field dampers. The inertia of the pile is consistently modeled while the inertia of the soil system is also appropriately modeled by point masses lumped at appropriate height of the pile beam (Maheshwari et al., 2005). The various aspects of the numerical (Finite Element) model of the soil-pile system are described in detail in the Table 1 below.
Table 1. Single Pile interaction with non-linear soil
| Feature | Description (Figure 1) |
| Pile |
| Geometry | Circular pile of length 10 m and 0.4m diameter |
| Material | E=25E9 Pa, ρ = 2500 kg/m3 |
| Meshing | Linear flexural beam element with consistent mass, and no damping. Ten elements are used in 10m length |
| Loading and Boundary conditions (described in detail latter in the paper) | For inelastic seismic response spectrum: Synthetic acceleration time history is applied to the base of the pile-soil system.
For verification problem: A horizontal displacement load is applied on the top of the pile with a harmonic time variation, while the base is kept fixed |
| Near-field soil |
| Geometry and meshing | Two-noded nonlinear springs are used to model the exponential degradation of soil stiffness due to plasticity. Also, lumped mass elements model the inertia of near-field soil. Lumped mass on pile side is 188 kg and on far-field side is 110 kg. No damping in near-field zone |
| Plasticity (Figure 2) | Exponential degradation of strain hardening is modelled as
where, Fy=6000 N, Q∞=600000N, b=0.3 are used, up is the plastic deformation of nonlinear spring |
| Far field soil |
| Geometry and meshing | The stiffness and damping of the far field soil is modelled by spring-dashpot assembly in series. The equivalent stiffness and damping are 1.9066e+007 N/m and 4.9968e++5 kg/s. Mass lumped on pile-side is 35 kg. |
| Soil – Pile interface |
| Elements | Gap elements are used to model the separation between soil and pile |
Figure 1. FE model of the single pile soil system
Figure 2. Force- displacement relation of non-linear near-field soil springs