Site's Fundamental Period

Fundamental period of a layered soil column (fixed base, free surface) by the classical Rayleigh quotient with the static- deflection trial shape (e.g., Dobry, Oweis & Urzua 1976): under a uniform horizontal body force the shear strain at depth z is z / Vs(z)^2 (uniform density), the mode shape is its integral from the base, and $$T_s = 2\pi\sqrt{\sum h_i X_i^2 / \sum h_i X_i}$$ with X_i the shape at each layer midpoint. For a uniform profile this yields 3.974 H/Vs (exact: 4 H/Vs, -0.7 percent); across layered test profiles the error against the exact transfer-matrix solution is a few percent on the low side. Layer order (top-down or bottom-up) is irrelevant: layers are sorted internally by depth.

Usage

fitModel.Ts(VSm, hs, zm)

Arguments

VSm

Vector. Shear Wave Velocity profile in m/s (vector)

hs

Vector. Layer Thickness profile in m (vector)

zm

Vector. Layer mid-depth coordinates from the surface in m (vector)

Value

Double. Site's fundamental period Ts in seconds