Manish Kumar Assistant Professor Department of Civil Engineering Indian Institute of Technology Bombay, Mumbai |
Structures subjected to earthquake motion are
generally analyzed using free field ground motions; that is, ground
motions at the location of structure if structure were not there.
This assumption, which simplifies the analysis, is although valid
for structure on rock or stiff soils, might not be appropriate for a
structure on soft soils. The fixed base assumption for the structure
founded on rock or stiff soils imply that high stiffness of elastic
soil media constrain the motion at the foundation of structure close
to the free field motion. However, there is always some
soil-structure interaction during earthquake shaking and the
interaction is particularly predominant for structures founded on
soft soils in which elastic media confining the foundation acts as
flexible column and overall response of structure is modified by
inertial and kinematic effects. SSI increases the fundamental period
of structure which generally reduces base shear, lateral forces, and
overturning moments but might increase the displacement demands.
Section 5.6 of FEMA 450(Council,
2003)
provides guidelines to account for the SSI in the analysis of
structure using equivalent lateral force procedures and response
spectrum procedure. Guidelines are not be used if the structure is
modeled as flexible-base, rather than rigid base, in the analysis of
structure. In both analysis procedures, it allows the reduction of
base shear obtained without considering SSI. Reduced base shear is
distributed over height using same procedure as used for fixed-base
structure. Time period of structure is modified using a simplified
model which takes into account the flexibility of soil-foundation
system as shown in
Figure 1.1. Hysteretic and radiation
damping of foundation systems contributes to the total damping of
structure and effective damping ratio is calculated as the sum of
viscous damping of structure and damping due to SSI. Radiation and
hysteretic damping is calculated using chart provided in the
guidelines. The modified shears, overturning moments, and torsional
effects are determined using same procedures as for structures
without SSI but using reduced lateral forces.
Structure on soil exhibits two kinds of
interaction effects known as kinematic and inertial effects.
Kinematic interaction effects exist due to change in wave
propagation media as a result of change in density and elasticity of
the media. It changes the wave propagation velocity and leads to
reflection and refraction of incoming seismic waves. Kinematic
effects of SSI represent the change in response of structure when
response is obtained using free-field motions and when the presence
of structure is considered. It doesn’t depend on the mass of
structure and is affected by the geometry and configuration of
structure, the foundation embedment, the composition of incident
free-field waves, and the angle of incidence of these waves(Villaverde,
2009).
Kinematic interaction can be neglected for structures with no
embedment excited by vertically propagating shear waves.
Inertial effects result from the combined
dynamic behavior of structure, foundation, and supporting soil
media. Soil media, owing to its elastic and inertial properties,
increases the degrees of freedom of structure and makes it possible
to dissipate energy of incoming seismic waves by the radiation of
waves away from the structure and hysteretic deformation of
supporting soil media. Inertial effect depends on the relative
flexibility of supporting soil media to the structure, which implies
that the effect is not significant for regular structure founded on
stiff soils or rock, but could be significant for stiff and massive
structures like nuclear power plants founded on soft-soils.
Some of the software programs used for SSI
analysis of structures are listed below:
1.
SHAKE
2.
SASSI
3.
FLUSH
4.
LSDYNA
There are two kinds of analysis methods that are used in contemporary software packages: 1) Direct method, and 2) Substructure method. Direct method models the soil and structure together and analyzes the combined system in a single step. Soil and structure are discretized in finite elements and nonlinear analysis can be performed. On the other hand, substructure method divides the analysis in three steps use the superposition to obtain the final response. It is solved in frequency domain analysis and assumes linear soil and structure behavior. Three steps used in substructuring method are:
Determination of foundation input motions.
Dynamic analysis of soil media to obtain stiffness and damping characteristic of foundation-soil interaction.
Analysis of structure supported on
springs represented by step 2 and subjected to base excitation
obtained in step 1.
SASSI and FLUSH use substructuring method
using frequency domain analysis. Although less computationally
expensive, these methods cannot perform nonlinear analysis and
equivalent linearization with iterations is used. SHAKE is used for
site response analysis to provide the input parameters required for
SSI analysis in SASSI.
LSDYNA and other finite element packages
(e.g, ABAQUS) use time domain methods and can perform nonlinear
analysis. They uses the direct method in which the soil and
structure is modeled and analyzed together. These software programs
are computationally extensive when compared to frequency domain
programs. Also, modeling a semi-infinite soil media is not possible
and transmitting boundaries are used to reproduce the behavior.
Moreover, there are identified issues with application of
three-dimensional coupled ground motions to structures in direct
methods.
Nuclear power plant layout consists of a
complex layout of heavy and massive structures at close distances.
Nuclear Island is supported on a very stiff and heavy basemat and
embedment of foundation might be significant. All these factors play
important role in increased kinematic and inertial interactions. The
rigidity and low height-width ratio dictates that rocking component
of structural response might not be neglected. Although, neglecting
SSI effects generally results in a conservative force demand, the
aim with the analysis of nuclear power plants is to be accurate
rather than conservative. Excessive mass and heavy size of nuclear
power plant dictates that even though if it is built on relatively
stiff soil, SSI effects might still be significant and needs to be
considered for the analysis and design.
References