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🌍 Soil-Structure Interaction Explorer

A fixed-base model assumes the foundation cannot move. Real soil deforms, adding sliding and rocking springs in series with the structure, and the period lengthens. The tempting conclusion is that this always helps — but on soft sites the spectrum may still be rising at the longer period, so lengthening can raise demand instead of lowering it. Watch which way it goes.

Site

Shear wave velocity V_s 160 m/s

Footing radius R 5.0 m

Structure

Fixed-base period T 0.80 s

Effective height h 12 m

Mass M 2000 t

Live Result

—

Flexible-base period T̃—

Lengthening ratio T̃/T—

Sliding stiffness K_x—

Rocking stiffness K_θ—

Rocking share of flexibility

Spectral demand ratio—

Powered by Gazetas impedance functions in the ASCE 41 / FEMA 440 framework (engine/ssi.js). Verified before publishing: the lengthening ratio converges toward 1.000 as soil stiffness grows (correct rigid-base limit, checked as a genuine trend rather than asserted as exact equality for a finite stiffness), the rocking term is confirmed to scale exactly as h², and doubling the footing radius is confirmed to give 2× sliding but 8× rocking stiffness — the R¹ versus R³ dependence. Crucially, the engine reports the demand ratio rather than assuming SSI helps; a deliberate test pins the adverse case where lengthening increases spectral demand.

Method

GazetasRigid circular footing on a halfspace: K_x = 8GR/(2−ν), K_θ = 8GR³/(3(1−ν)).

ASCE 41 / FEMA 440T̃/T = √(1 + k/K_x + kh²/K_θ) — structure, sliding and rocking flexibilities in series.

Scope: static (frequency-independent) impedances, rigid circular footing, homogeneous halfspace, SDOF structure. Does NOT model radiation or hysteretic foundation damping, embedment, piles, layered profiles, kinematic interaction, or soil nonlinearity. G here is derived from V_s and must be understood as the strain-compatible modulus, not small-strain G_max.

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