Is Harmonic Averaging of Shear Wave Velocity or the Simplified Rayleigh Method Appropriate to Estimate the Period of a Soil Profile?

Abstract

For soil sites with well-defined soil-rock interfaces and high impedance contrast, the maximum amplification of earthquake ground motion tends to occur at the fundamental period in shear of the soil profile, T. Analytical results are presented for the calculation of T for several idealized soil profiles as well as more realistic layered profiles using three simplified procedures. The first is the use of harmonic averaging of V S to estimate the value of the equivalent shear wave velocity of the profile, V eq, needed to calculate the correct value of T. Harmonic averaging tends to overestimate T for profiles where V S increases with depth, and to underestimate T in profiles where V S decreases with depth. The second is the Simplified Rayleigh Method proposed by the authors, which is easily implemented in a spreadsheet and gives values of T and effective shear wave velocity that are accurate within a few percent. The third method is the Simplified Gómez Method, which accounts for differences in density and has been incorporated into the Mexico City Code; it generally gives results superior to harmonic averaging but underestimates T for some profiles where V S increases with depth.