Dynamic analysis of the coupled soil-structure system.

DOE-STD-1020-2002

Since the foundation medium relative to the structure dimensions is semi-infinite, dynamic

modeling of the foundation medium is generally accomplished using a halfspace model. Such a

model permits waves generated at the structural-foundation resulting from the dynamic response

of the structure to be dissipated into the far-field of the model. This leads to the phenomenon

called radiation damping. The three-dimensional phenomenon of radiation damping and

layering effects of foundation soil shall be considered. When significant layering exists in the

foundation medium, it should be modeled explicitly or its effects such as significant frequency

dependency of the foundation impedance functions and reduction of radiation damping should be

considered in the analysis.

When mathematical models are used, either the continuum halfspace or the discretized

halfspace may be employed. The discretized halfspace by finite element or finite difference

models requires the use of model-consistent wave transmitting boundaries to accurately simulate

radiation damping and to eliminate artificial wave reflections which are not negligible. The

lower boundary shall be located far enough from the structure that the seismic response at points

of interest is not significantly affected or a transmitting boundary below the model could be

used. Soil discretization (elements or zones) shall be established to adequately reproduce static

and dynamic effects.

Embedment of the foundation increases the foundation impedances. For structures that

are significantly embedded, embedment effects should be included in the SSI analysis. These

effects can be incorporated by using available simplified methods for some geometries (Refs.

C-39 and C-40). The potential for reduced lateral soil support of the structure due to tensile

separation of the soil and foundation should be considered when accounting for embedment

effects. One method to comply with this requirement (Section 3.3.1.9 of ASCE 4-98) is to

assume no connectivity between structure and lateral soil over the upper half of the embedment

or 20 feet, whichever is less. However, full connectivity may be assumed if adjacent structures

founded at a higher elevation produce a surcharge equivalent to at least 20 feet of soil. For

shallow embedments (depth-to-equivalent-radius ratio less than 0.3), the effect of embedment

may be neglected in obtaining the impedance function, provided the soil profile and properties

below the basemat elevation are used for the impedance calculations.

Dynamic analysis of the coupled soil-structure system. When the SSI system

parameters are assumed to be frequency-independent constants, the equations of motion may be

solved by time domain solution procedures, such as either the direct integration or the standard

modal time history response analysis methods. Due to relatively large soil radiation damping

which can cause relatively large modal coupling, the application of standard modal superposition

time history methods requires the determination of "composite" modal damping ratios. The most

frequently used are the stiffness-weighted method presented in Sections 3.1.5.3 and 3.1.5.4 of

ASCE 4-98 and the transfer function matching method (Ref. C-45). When the SSI system

parameters are frequency-dependent, the equations of motion are generally solved by complex

frequency response methods. The computation of the Fourier transform of the input motion

should be performed using sufficient time and frequency increments in order to allow for

frequency components of motion up to 25 hz to be accurately reproduced unless a lesser limit

can be justified.

C-27