15-12-2012, 05:05 PM
SOIL-STRUCTURE INTERACTION
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INTRODUCTION
The estimation of earthquake motions at the site of a structure is the most important
phase of the design or retrofit of a structure. Because of the large number of
assumptions required, experts in the field often disagree by over a factor of two as to
the magnitude of motions expected at the site without the structure present. This
lack of accuracy of the basic input motions, however, does not justify the
introduction of additional unnecessary approximations in the dynamic analysis of the
structure and its interaction with the material under the structure. Therefore, it will
be assumed that the free-field motions at the location of the structure, without the
structure present, can be estimated and are specified in the form of earthquake
acceleration records in three directions. It is now common practice, on major
engineering projects, to investigate several different sets of ground motions in order
to consider both near fault and far fault events.
If a lightweight flexible structure is built on a very stiff rock foundation, a valid
assumption is that the input motion at the base of the structure is the same as the
free-field earthquake motion. This assumption is valid for a large number of
building systems since most building type structures are approximately 90 percent
voids, and, it is not unusual that the weight of the structure is excavated before the
structure is built.
SITE RESPONSE ANALYSIS
The 1985 Mexico City and many recent earthquakes clearly illustrate the importance
of local soil properties on the earthquake response of structures. These earthquakes
demonstrated that the rock motions could be amplified at the base of a structure by
over a factor of five. Therefore, there is a strong engineering motivation for a sitedependent
dynamic response analysis for many foundations in order to determine the
free-field earthquake motions. The determination of a realistic site-dependent freefield
surface motion at the base of a structure can be the most important step in the
earthquake resistant design of any structure.
For most horizontally layered sites a one dimensional pure shear model can be used
to calculate the free-field surface displacements given the earthquake motion at the
base of a soil deposit. Many special purpose computer programs exist for this
purpose. SHAKE [1] is a well-known program, based on the frequency domain
solution method, which iterates to estimate effective linear stiffness and damping
properties in order to approximate the nonlinear behavior of the site. WAVES [2] is
a new nonlinear program in which the nonlinear equations of motion are solved by a
direct step-by-step integration method. If the soil material can be considered linear
then the SAP2000 program, using the SOLID element, can be used to calculate
either the one, two or three dimensional free-field motions at the base of a structure.
In addition, a one dimensional nonlinear site analysis can be accurately conducted
using the FNA option in the SAP2000 program.
KINEMATIC OR SOIL-STRUCTURE INTERACTION
The most common soil-structure interaction SSI approach, used for three
dimensional soil-structure systems, is based on the "added motion" formulation [3].
This formulation is mathematically simple, theoretically correct, and is easy to
automate and use within a general linear structural analysis program.
The method requires that the free-field motions at the base of the
structure be calculated prior to the soil-structure interactive analysis.
In order to develop the fundamental SSI dynamic equilibrium equations consider the
three dimensional soil-structure system shown in Figure 16.1.
ANALYSIS OF GRAVITY DAM AND FOUNDATION
In order to illustrate the use of the soil-structure interaction option several
earthquake response analyses of the Pine Flat Dam were conducted with different
foundation models. The foundation properties were assumed to be the same
properties as the dam. Damping was set at five percent. Ten Ritz vectors,
generated from loads on the dam only, were used. However, the resulting
approximate mode shapes, used in the standard mode superposition analysis,
included the mass inertia effects of the foundation. The horizontal dynamic loading
was the typical segment of the Loma Prieta earthquake defined in Figure 15.1a. A
finite element model of the dam on a rigid foundation is shown in Figure 16.2.