応答スペクトル法による表層地盤の非線形増幅特性の解析法

Abstract

This paper proposes a response spectrum method (RSM) for evaluating nonlinear amplification of surface strata (SS) overlying an engineering bedrock (EBR). The proposed RSM follows the procedures below. (1) Represent the response characteristics of SS on EBR by a multi-lumped mass model with shear springs and damping coefficients. (2) Calculate a period T1, a mode shape {U1} and a modal damping factor ƒA1 for the first vibration mode. (3) Evaluate the equivalent shear wave velocity Vse of SS. (4) Evaluate the amplification factor R1 of the surface to EBR at T1 using the Haskell matrix of two strata consisting of an equivalent SS with Vse and ƒA1 on EBR. (5) Evaluate the displacements in SS from R1{U1}, and hence evaluate the shear strains. (6) In accordance with nonlinear relations between shear modulus (G), damping factors (h) and shear strains, replace soil constants G and h by those corresponding to strains. (7) Return to step (1) with revised G and h. Iterate these procedures until T1 becomes stable. (8) After T1 is converged, calculate the response distributions in SS. The results obtained by the proposed RSM are compared with those by “SHAKE” in terms of the response spectrum at the surface as well as distributions of displacement, shear wave velocity and damping factor in SS. The applicability of the proposed RSM for evaluating the nonlinear amplification of SS is confirmed through the comparative studies.