Simulation of Dynamic Soil-Foundation-Structure Interaction (SFSI)
Ronald Y. S. Pak
Department of Civil, Environmental & Architectural Engineering
University of Colorado, Boulder, CO 80308-0428, U.S.A.
(pak@colorado.edu)
Introduction
In both geotechnical and structural earthquake engineering, there is strong common
recognition that dynamic soil-foundation-structure interaction (SFSI) is a major research
area whose advancement is central to public interest (Seible et al. 2001). In the soil
dynamics community, recent focus lies mostly on liquefaction-related problems such as
pore-pressure developments near the foundation, dynamic bearing capacity, postearthquake settlements, ground rupture, lateral spreads and other soil failure conditions
(Pak and Yamamura 2000). In the structural engineering community, on the other hand,
the items of major concerns are the effective ground motion transmitted to the structures
through the foundation, the load-deformation characteristics of the soil-foundation
system, the resultant natural frequencies and damping of the structure and the effect of
spatial variations and coherence of the incident seismic wave motions (Celibi and Okawa
1998). Adding to this broad range of questions the need to relate them to various nondestructive in-situ soil characterization methods and ambient/force vibration tests, a
complete understanding of SFSI effects from infinitesimal to high response levels is
probably more critically needed than in any other non-interdisciplinary research areas.
Together with critical issues such as the influence of local topography and soil profile,
the unboundedness of the soil domain, foundation-soil-foundation interactions, the
nonlinear mechanical behavior of soils at both small and large strains, and the threedimensional nature of most problems, it should be apparent that many current
engineering concepts and design practice will be seriously challenged to accommodate
the full scope of soil-foundation-structure interaction problems. To truly dissect and
understand the underlying phenomena, full efforts to further develop our analytical and
experimental capabilities in both soil and structural dynamics are clearly needed.
Coupled such tools with rigorous inquisitive pursuits, serious opportunities for
fundamental discovery and solutions are available that can propel our current
understanding of SFSI problems to the next level.
Experimental Simulation and Analytical Modeling
In the last two decades, considerable progress in technology has been made in
experimental, theoretical as well as computational directions which can be used to assess
a number of SFSI problems. On experimental simulation techniques, the approach that
holds the most promise, especially for fundamental research, is perhaps the centrifuge
scaled modeling method. Because of its ability to produce the critical similitude of
gravity-induced stresses in the prototype environment by means of centrifugal
acceleration, the centrifuge approach can, via validated scaling laws, allow legitimate
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extrapolation of model response to full-scaled situations. Owing to the efficiency gained
in small-scale model testing, many tests can be performed at a fraction of the cost of a
corresponding full-scale test program even if the latter were technically feasible. The
result is a significant improvement in the confidence of the test data which can and
should always be repeated for more resolution and checked for consistency. For a
number of SFSI problems, not only have the necessary centrifuge simulation technologies
been developed (e.g. 1D shakers, laminar boxes, viscously damped containers, half-space
simulation methodologies), their usage have generated some serious new insights which
have altered the current interpretation of a number of SFSI problems (e.g., Pak and
Ashlock 2000). While more innovative developments are still needed to simulate a
number of important SFSI phenomena on a centrifuge, the scaled modeling approach is
certain to be a critical tool that can help bring the subject to the next level of scientific
understanding and comprehension. On the theoretical and computational side, the power
of continuum mechanics in the context of viscoelastic and elastoplastic constitutive
theories is now within an engineer’s reach by virtue of numerical methods such as finite
element and boundary element analysis. While their direct relevance and reliability as
the basis of engineering design can at times be legitimately challenged as do
experimental methods, the conceptual exercise generated by analytical methods,
especially if coupled with experimental research, is often a prerequisite to sorting out the
underlying structure of a complex problem. As illustrations of the virtue of such a
combined approach, a brief report will be given on some insights gained from a series of
integrated experimental and analytical investigations on a class of basic dynamic SFSI
problems. While they will serve well to highlight the complexities of even the simplest
of SFSI problems, these observations also outline a path of great opportunities for the
construction of a more effective framework beyond those used in the last century.
Some Physical and Analytical Observations
To explore the fundamental aspects of dynamic SFSI problems, a systematic research
program of dynamic scaled modeling has been ongoing at the University of Colorado,
Boulder using its large 400 g-ton geotechnical centrifuge. By means of a set of effective
half-space simulation methodologies (see Pak and Guzina 1994), complete frequencydomain characterizations of the dynamic characteristics of a variety of foundations under
multi-directional forced vibration have been proven to be feasible. Comparing such data
on granular soils with some of the popular theoretical models for instance, there are a
number of observations which could be of immediate interest and practical relevance
even without any advanced synthesis:
(1) Effect of foundation size and contact pressure:
From the data base, it has been consistently found that the static foundation contact stress
level has a major influence on the dynamic response of the soil-structure system. No
only does it affect the foundation impedance sensitively, it also moderates the degree of
nonlinearity in the response with respect to the dynamic excitation level. From the
experimental results, it was also found that the foundation dimension is an important
parameter to the foundation stiffness as well as its overall response.
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(2) Mode of vibration
From a comparison of the experimental data with the commonly-used homogeneous halfspace theoretical solution, it was found that the theory cannot describe concurrently all
modes of structure-foundation motion as observed in the physical tests. While the
vertical vibration mode can be handled by the mathematical solution by means of the
concept of an equivalent homogeneous shear modulus, the corresponding prediction for
the lateral and rocking motions is significantly stiffer with too high a natural frequency in
the earthquake frequency range than what was typically observed in the measurements.
(3) I.M.F.
To overcome the consistent deficiencies of the popular homogeneous half-space
approximation, the idea of Impedance Modification Factors (I.M.F.) was conceived and
validated for the experimental data base (Pak and Ashlock 2000). Created to represent
the part of the physical characteristics of the soil-foundation system not captured by the
theoretical model, the I.M.F.s can be derived from experimental measurements. The
concept is important not only because it provides a more correct picture of the SFSI
phenomena under multi-directional excitations, but also because it represents a more
sophisticated way of looking at the experimental data which can in turn lead to deeper
insights into the fundamental nature of this class of problems.
(4) Other Inhomogeneous half-space solutions
In view of the fundamental inadequacy of the homogeneous half-space solution for such
a fundamental SFSI problem, theoretical solutions which can better describe the depthdependent shear modulus variation of sandy soils such as those of the power-law format
(e.g, the square-root type) were also examined in terms of their abilities to better describe
the experimental results. Interestingly, almost in all cases, they fare even worse than the
homogeneous half-space solution in all modes of vibration.
Engineering Implications
From the foregoing observations, the following list of actions can be relevant to our
current research activities in SFSI:
(1) Foundation bearing pressure needs to be included in the synthesis of experimental lab
or field data analysis of SFSI, may it be centrifuge test, field vibration tests or
earthquake record case studies.
(2) Review past experimental syntheses to incorporate the effects of contact pressure,
foundation size and their relation to any observed nonlinearities.
(3) Representative values of I.M.F.s need to be determined for common soil-foundation
configurations.
(4) The underlying physical phenomena behind the I.M.F. effects need to be identified
and incorporated into the next-generation theoretical solution.
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(5) Explore fully the implications to seismic soil-foundation motion problems.
References
Celibi, M. and Okawa, I. (1998). Proc. UJNR Workshop on Soil-Structure Interaction,
USGS.
Pak, R.Y.S. and Guzina, B.B. (1994). Physical simulation of dynamic soil-foundation
systems on unbounded media, Centrifuge 94, Balkema, 271-276.
Pak, R.Y.S. and Guzina, B.B. (1995). Dynamic characterization of vertically loaded
foundations on granular soils, J. Geotech. Engrg., ASCE, 121 (3), 274-286.
Pak, R.Y.S. and Guzina, B.B. (1999). Seismic soil-structure interaction analysis
by direct boundary element methods, Intl. J. Solid. Struct., 36 (31-32), 4743-4766.
Pak, R.Y.S. and Ashlock, J.C. (2000). Fundamental dynamic behavior of foundations on
sand,'' Geotechnical Special Publication No.107, ASCE, 10-19.
Pak, R.Y.S and Yamamura, J. (2000). Soil Dynamics and Liquefaction, GSP 107, ASCE.
Seible, F., Ashford, S. Elgamel, A.and Filiatrault, A. (2001). NEES-2 NSF Workshop
Report, SSRP-2001/07, U. of Calif. San Diego.
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