Transfer Functions for Rigid Rectangular Foundations

Abstract

SUMMARYClosed-form expressions and comprehensive numerical solutions are presented for the transfer functions of surfacesupported, rigid, rectangular foundations excited by horizontally polarized, incoherent shear waves for which the motions are parallel to one of the foundation sides. The free-field ground motion is specified stochastically in terms of a local power spectral density function and an orthotropic incoherence function which decays exponentially with the square of the excitation frequency and the separation distance. The response quantities examined include the lateral and torsional components of the foundation motion. Displayed graphically, the results elucidate the effects and relative importance of the numerous parameters involved. For vertically incident incoherent wave fields, the lateral transfer function of a rectangular foundation is related to that of a judiciously selected square foundation, and the interrelationship of the results is examined.

Kinematic soil-structure interaction effects on maximum inelastic displacement demands of SDOF systems

“…Analytical solutions for base-slab averaging in various incident waves have been developed for circular and rectangular foundations (Scanlan 1976;Newmark et al 1977;Luco and Wong 1986;Luco and Mita 1987;Veletsos and Prasad 1989;Veletsos et al 1997;Kim and Stewart 2003). Figure 1a shows the transfer function proposed by Veletsos et al (1997) for vertically incident incoherent waves, where a and b are the full footprint dimension of rectangular foundations, andã 0 is a dimensionless frequency parameter. In FEMA-440 document,ã 0 is approximate estimation as follows for rectangular foundations.…”

“…It has been shown that doing a running average to the free-field motion in time domain is exactly equal to using the following low pass filter in frequency domain (Holloway 1958;Hudson 1979). |H(f)| ap.,Tw=0.04s ap.,Tw=0.08s ap.,Tw=0.12s ex., be=20m ex., be=43m ex., be=72m Veletsos et al (1997) for vertically incident incoherent waves; (b) Comparison between approximate transfer functions (ap.) and the transfer functions (ex.)…”

“…and the transfer functions (ex.) derived by Veletsos et al (1997) for vertically incident incoherent waves…”

“…Figure 1b compares the approximate transfer function and the transfer function proposed by Veletsos et al (1997) for vertically incident incoherent waves with n 2 = 0.65. It can be seen from this figure that the approximate method (equally-weighted running average) gives good predictions of the foundation input motion for foundations with dimension b e < 72 m. In addition, the relationship between the filtering interval (T w ) and the foundation dimension b e in Fig.…”

Quasi-Kinematic Response of Embedded Foundations: Evidence of Foundation Mass Effect From Numerical Analyses and Instrumented Structures

“…It is well known that the dynamic behavior of buildings can be affected by the presence of a deformable soil-foundation system, which possibly makes the seismic response of a flexibly-supported structure different from that of the rigidly-supported counterpart [1] by: (i) lengthening the fundamental period of the structure; (ii) allowing additional dissipation of energy into the soil by radiation and hysteresis; (iii) filtering the signal transmitted to the structure by incident waves, as a result of both base slab averaging [2] and embedment effects [3].…”