The energy flow in a soil-pile-structure (SPS) system during an earthquake is an important consideration in seismic-resistant design. The energy input to the structure is formulated here in the frequency domain. The frequency-domain approach enables the exact and complete treatment of frequency-dependent stiffness and damping properties. It is shown that the input energy can be derived in a compact form through the frequency integration of the product of the ground-motion input component and the structural model component. By taking full advantage of this compact form, it is demonstrated that the formulation of earthquake input energy in the frequency domain is essentially appropriate for deriving the exact first and second-order sensitivities of the input energy with respect to an uncertain soil stiffness parameter. The sensitivity expressions derived for swaying-rocking models with independent uncertain parameters are used here for the efficient formulation in a new model. The exact second-order sensitivities facilitate the expression of input energy variation due to uncertainty in ground stiffness, which is useful seismic design data.
AIJ (2006). Seismic Response Analysis and Design of Buildings Considering Dynamic Soil-Structure Interaction. Architectural Institute of Japan.
2.
AkiyamaH. (1985). Earthquake Resistant Limit-state Design for Buildings. University of Tokyo Press, Tokyo, Japan.
3.
AndersonJ.C. and BerteroV.V. (1987). Uncertainties in establishing design earthquakes. Journal of Structural Engineering, ASCE, Vol. 113, No. 8, pp.1709–1724.
4.
ChangY.L. (1937). “Discussion on ‘lateral pile-loading test’ by L.B.Feagin”, Transition of ASCE, pp. 272–278.
5.
DrenickR.F. (1970). “Model-free design of aseismic structures”. Journal of Engineering Mechanics Division, ASCE, Vol. 96(EM4), pp. 483–493.
6.
FrancisA.J. (1964). “Analysis of pile groups with flexural resistance”, Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 90(SM3), pp.1–32.
7.
GazetasG. and DobryR. (1984). “Horizontal response of piles in layered soils”, Journal of Geotechnical Engineering, ASCE, Vol. 110, No. 1, pp. 20–40.
8.
HousnerG.W. (1959). “Behavior of structures during earthquakes”, Journal Engineering Mechanics Division, ASCE, Vol. 85, No. 4, pp.109–129.
9.
HousnerG.W. and JenningsP.C. (1977). “The capacity of extreme earthquake motions to damage structures”, Structural and Geotechnical Mechanics: A Volume Honoring NM Newmark edited by HallWJ, 102–116, Prentice-HallEnglewood Cliff, NJ.
10.
IyengarR.N. and ManoharC.S. (1987). “Nonstationary random critical seismic excitations”, Journal of Engineering Mechanics, ASCE, Vol. 113, No. 4, pp. 529–541.
11.
KishidaA. and TakewakiI. (2006). “Exact higher-order sensitivity and variation of earthquake energy input in soil-structure interaction system”, Advances in Structural Engineering, Vol. 9, No. 5, pp. 37–53.
12.
KuwamuraH.KirinoY. and AkiyamaH. (1994). “Prediction of earthquake energy input from smoothed Fourier amplitude spectrum”, Earthquake Engineering Structural Dynamics, Vol. 23, pp. 1125–1137.
13.
LucoJ.E. (1980). Linear Soil-structure Interaction. UCRL-15272, Lawrence Livermore Laboratory, Livermore, CA.
14.
LyonR.H. (1975). Statistical Energy Analysis of Dynamical Systems. The MIT Press, Cambridge, MA.
15.
ManoharC.S. and SarkarA. (1995). “Critical earthquake input power spectral density function models for engineering structures”, Earthquake Engineering Structural Dynamics, Vol. 24, pp. 1549–1566.
16.
OhiK.TakanashiK. and TanakaH. (1985). “A simple method to estimate the statistical parameters of energy input to structures during earthquakes”, Journal of Structural Construction Engineering, AIJ, Vol. 347, pp. 47–55 (in Japanese).
17.
OrdazM.HuertaB. and ReinosoE. (2003). “Exact computation of input-energy spectra from Fourier amplitude spectra”, Earthquake Engineering Structural Dynamics, Vol. 32, pp. 597–605.
18.
ShinozukaM. (1970). “Maximum structural response to seismic excitations”, Journal Engineering Mechanics Division, ASCE, Vol. 96, No. EM5, pp. 729–738.
19.
TakewakiI. (2001). “Probabilistic critical excitation for MDOF elastic-plastic structures on compliant ground”, Earthquake Engineering Structural Dynamics, Vol. 30, No. 9, pp. 1345–1360.
20.
TakewakiI. (2002a). “Critical excitation method for robust design: A review”, Journal of Structural Engineering, ASCE, Vol. 128, No. 5, pp. 665–672.
21.
TakewakiI. (2002b). “Robust building stiffness design for variable critical excitations”, Journal of Structural Engineering, ASCE, Vol. 128, No. 12, pp.1565–1574.
TakewakiI. (2004b). “Response spectrum method for nonlinear surface ground analysis”, Advances in Structural Engineering; Vol. 7, No. 6, pp. 503–514.
24.
TakewakiI. (2005). “Frequency domain analysis of earthquake input energy to structure-pile systems”, Engineering Structures, Vol. 27, No. 4, pp. 549–563.
25.
TakewakiI. (2006). “Worst-case analysis for earthquake energy input rate in SDOF and MDOF structures”, Advances in Structural Engineering, Vol. 9, No. 3, pp. 361–375.
26.
TakewakiI. and FujimotoH. (2004). “Earthquake input energy to soil-structure interaction systems: A frequency-domain approach”, Advances in Structural Engineering, Vol. 7, No. 5, pp. 399–414.
27.
TrifunacM.D.HaoT.Y. and TodorovskaM.I. (2001). On Energy Flow in Earthquake Response. Report CE 01–03, July 2001, University of Southern California.
28.
UangC.M. and BerteroV.V. (1990). “Evaluation of seismic energy in structures”, Earthquake Engineering Structural Dynamics, Vol. 19, pp. 77–90.
29.
WolfJ.P. (1985). Dynamic Soil-structure Interaction. Prentice-Hall, Inc.
30.
WolfJ.P. (1988). Soil-structure-interaction Analysis in Time Domain. Prentice-Hall, Inc.
