Environmental Engineering Reference
In-Depth Information
Structure
with
period
T 1 ~
25 s
0.25 g
0
k h
~
0.20 g
0.34 g
0.18 g
k h
k v
k v
k
0.20 g
Soils
FIGURE 11.46
Soil-structure interaction model for
half-space analysis. (From Seed, H.B.
et al., Report No. EERC 75-25,
Earthquake Engineering Center,
University of California, Berkeley,
August 1975. With permission.)
0.145 g
60 m
Rock
Limitations
As of 1974, the approach does not consider material damping, can only be applied to one-
or two-layer soil systems, and provides no means for determining strains induced in the
soils. These and other limiting factors are summarized in Table 11.19. The strains induced
in the soils greatly affect soil deformation moduli G used in the determination of the
spring constant.
Finite-Element Method of Analysis
Soil Profile Presentation
The model idealizes the soil continuum as a system of finite elements interconnected at a
finite number of nodal points (Figure 11.47) . Either triangular or rectangular elements can
be used, depending upon the geometry of the conditions being modeled.
In most cases, the soils are considered to be equivalent linear-elastic materials. Soil
response is described by formulating stiffness and mass matrices, and a nodal solution or
a time-marching integration is effected, depending upon the capability of the particular
computer program employed. Response-time histories of displacement, velocity, and
acceleration can be computed for each nodal point. Soil characteristics required include
shear modulus, Poisson's ratio, soil unit weight, and damping coefficients. The variations
of the shear moduli and damping coefficients with strain are considered.
Ground Motion
Control motion is based on actual earthquake data, or on synthetic records, to obtain verti-
cal and horizontal excitation in terms of g , and can be specified as located in the free field
at the surface, or at foundation level. A wide variety of ground response spectra has been
specified for the design of major facilities, such as nuclear power plants, major bridges,
and other critical structures such as LNG storage and processing plants. For nuclear power
plants the majority of the design ground response spectra is usually based on a statistical
analysis of earthquakes of different magnitudes and site distances.
Design spectra construction is usually based on statistical analysis of recorded motions,
frequently for a 50 to 84% non exceedence probability. Figure 11.48 compares several site-
independent ground response spectra used in the design or evaluation process in terms of
 
 
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