LITERATURE REVIEW
2.3 Soil-Structure Interaction
2.3.1 Analysis of pile-soil-pile interaction
Poulos (1971) analyzed the behavior of laterally loaded piles. For single piles an analysis is presented for the horizontal displacement and rotation of a vertical pile subjected to lateral loading and moment, and situated in an ideal elastic mass.
Influence factors are presented for a wide range of pile flexibilities and length-to- diameter ratios, for both free-head and fixed-head piles. Comparisons between the elastic solutions and .the corresponding solutions obtained from the subgrade reaction theory show that the latter considerably overestimates the displacement and rotation of the pile, but give a reasonable estimate of the moments in the pile. The elastic analysis is extended to include the effect of local yield between the soil and the pile;
the load-displacement relationship for relatively flexible piles is found to be markedly influenced by local yield.
Poulos (1971) also analyzed the behavior oflaterally loaded pile groups. In the paper an elastic analysis is presented for the horizontal displacement and rotation of a laterally loaded pile group and the distribution of horizontal forces within the group.
The interaction between two identical equally loaded piles is analyzed first, and the increases in displacement and rotation ofthe piles, in relation to the single pile values, are expressed in terms of interaction factors. Using these interaction factors, a method for calculating the displacement and rotation of a general pile group, based on the principle of superposition, is described. An examination of the behavior of square groups of piles reveals that the displacement, rotation, and load distribution in the group is largely influenced by the length-to-diameter ratio of the piles and the relative pile flexibility. It is also found that the displacement depends on the breadth of the group rather than the number of piles in the group. A reasonable measure of agreement is found between a limited number of reported measurements and theoretical predictions of group displacements.
Novak et al. (1978) studied the dynamic soil reactions for plane strain case.
Resistance of soil to harmonic motion of an infinitely long cylinder is investigated theoretically in terms of linear viscoelasticity. Closed-form solution is obtained from which the complex stiffness can be evaluated. The numerical results agree with those obtained by means ofthe correspondence principle.
Velez et al. (1983) utilized an efficient finite-element formulation to study the dynamic response characteristics of single constrained-head piles embedded in a soil stratum whose modulus is proportional to depth from the surface. The excitation consists of a harmonic horizontal force or moment applied at the pile head, and the soil is modeled as a linear hysteretic medium. The results of a comprehensive parametric study are presented in the form of non-dimensional graphs from which static and dynamic stiffnesses and effective damping ratios of piles in many practical situations can readily estimated. For flexible piles, in particular, simple, yet sufficiently accurate, algebraic formulae are derived, valid for a wide range of problem parameters. Finally, the concept of an effective soil modulus is introduced to elucidate the importance of soil nonhomogeneity and to gain valuable insight to the mechanics ofthe problem.
Gazetas and Dobry (1984) developed an inexpensive and realistic procedure for estimating the lateral dynamic stiffness and damping of flexible piles embedded in arbitrarily layered soil deposits. Starting point is the determination of the pile deflection profile for a static force at the top using any reasonable method -- beam-on- Winkler foundation, finite elements, well-instrumented pile load tests in the field, etc.
Material as well as radiation damping due to waves emanating at different depths from the pile-soil interface are rationally taken into account; the overall equivalent damping at the top of the pile is then obtained as a function of frequency by means of a suitable energy relationship. The method is applied to study the dynamic behavior of three different piles embedded in two idealized and one actual layered soil deposit;
the results of the method, obtained by hand computations, compare favorably with the results of three dimensional dynamic finite element analyses.
Nogami and Konagai (1988) developed a simple mechanical soil model for the time domain flexural response analysis of dynamically loaded single piles, adopting a Winkler assumption. The model is defined by examining a frequency-domain analytical expression of the dynamic response of a massless cylinder in an infinite previously developed medium. The expression is based on the plane strain assumption. Using this soil model, the time-domain transfer matrix is developed for the flexural response of a single pile. The steady-state harmonic response of a single pile is computed by both the present approach and a previously developed frequency-
domain solution. Good agreement between the two computed results validates the present approach. The dynamic response of single piles subjected to the lateral impulse load is computed for piles in both homogeneous and inhomogeneous soil, in order to demonstrate the capability of the present approach. It is confirmed that the developed soil model and pile response formulation are very efficient in numerical computation.
Fan et al. (1991) studied the kinematic seismic response of single piles and pile groups. The paper includes the results of a numerical study on the kinematic response of groups of vertical floating piles connected through rigid massless caps and subjected to vertically propagating harmonic S-waves. Pile-soil and pile-pile interaction effects are modeled rigorously. Parametric results for the "effective seismic pile-cap motion," normalized by the "free-field" ground-surface motion, are displayed in dimensionless form for a number of typical pile-group configurations, in three idealized soil profiles: a homogeneous half-space, a half-space with modulus proportional to depth, and a two-layered stratum. It is shown that, whereas the influence of the nature of the soil profile is profound at all frequencies, the effects of pile-group configuration, number of piles in the group, and relative spacing between piles are usually insignificant for lateral displacements, but quite important for pile- cap rotations. Pile-head "fixity" conditions and the pile/soil modulus ratio are found to affect appreciably and in a similar way the seismic response of a single pile and of a pile group.
Konagai and Nogami (1998a) developed an analog circuit to simulate dynamic soil- structure interaction in shake table test where a soil medium at. the side of an embedded structure is treated as mutually uncoupled horizontal layers of a unit thickness and a plane strain condition is assumed within each individual layer such that the medium responses do not vary along the thickness. A new formulation is given here that the impedance of the above layer at the structure can be produced by frequency-independent simple mechanical models for all three modes of foundation responses. Similar frequency-independent models are also presented for the impedance at the foundation base. These models are made of two different basic elements and a mass interconnected in series. Their arrangements directly indicate the wiring of electric circuits which generate signals corresponding to the transient soil-
structure interaction responses. To all intents and purposes, electric circuits do not loose time in responding to the inputs, which allow simulating the soil-structure interaction response in shake table model tests, commonly conducted at relatively high excitation frequencies for earthquake simulation.
Konagai et al. (l998b) formed a simulation of soil-structure interaction effects in shaking table test. In this study, a soil-structure. system is divided into two substructures, the superstructure and the unbounded soil extending to infinity. A shaking table represents exactly the latter substructure of soil. The multi-step method is used to describe two primary causes of soil-structure interaction - the
inability of the foundation to match the free-field deformation, and the effect of the dynamic response of the superstructure on the movement of its supporting soil- foundation system. The expression for the soil stiffness obtained is eventually a complex function of circular frequency. Its real part is a downward open parabola to the right, whereas its imaginary part increases linearly with increasing frequency.
Though it is based on oversimplified conditions, but gives an idea that the stiffness for any of lateral, vertical or rotational response mode will be approximately described by a limited number of simple frequency-independent parameters.
The ring-pile analysis for a grouped pile foundation subjected to base motion by Takemiya (1986) aims at developing an effective and efficient formulation for the dynamic analysis of grouped-pile foundations. Grouped piles are analyzed based on the "ring-pile" concept which assumes that piles are in a concentric arrangement. The paper represents a FEM application. The investigation is addressed to the pile head impedance functions and the associated input forces due to pile-soil-pile interaction for the base motion, and the inertial interaction between foundation and structure, by taking a bridge pier on a grouped pile foundation as an example.
A simplified expression is derived for the dynamic stiffness of grouped piles in sway motion by Konagai et al. (2000). A computer program, based on the thin layer element method is used for this purpose. The idealization of grouped piles as a single equivalent uproright beam and the concept of the active pile length have facilitated the derivation of pile-cap stiffness in terms of frequency-independent mass, damping and stiffness parameters.
A new method to simulate soil-structure interaction effects in shaking table tests has recently been presented by Konagai and Ahsan (2002). In this method, analog circuits or digital signal processors are used to produce soil-foundation interaction motions in real time. Their expressions of soil-structure interaction motions are based on published rigorous formulations of impulse response functions or flexibility functions of foundations resting on or embedded in homogeneous or layered soils of semi- infinite extent. The method is further extended to take the "far field" soil non-linearity into account. An example of non-linear soil-structure interaction simulation using the present method is also described.
Single beam analogy for describing soil-pile group interaction has been offered by Konagai et al. (2000). Most laterally loaded piles are flexible in the sense that they are not deformed over their entire lengths. Instead, pile deflections become negligible below an 'active pile length' La. Here piles closely grouped together beneath a superstructure are viewed as a single equivalent upright beam whose stiffness matrix determines La. This idea is verified for different cases of pile spacing, and is further extended for nonlinear behavior of soils surrounding grouped piles.