Model errors caused by rigid-foundation assumption in soil-structure interaction: a comparison of responses of a soil-st
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Model errors caused by rigid‑foundation assumption in soil‑structure interaction: a comparison of responses of a soil‑structure‑flexible foundation system and a rigid foundation system Fu Jia1 · Liang Jianwen2 · Ba Zhenning2 Received: 13 January 2020 / Accepted: 8 October 2020 © Springer Nature B.V. 2020
Abstract This study investigates model errors caused by the rigid-foundation assumption in dynamic Soil-Structure Interaction (SSI), which has been widely accepted in the past decades to reduce computational effort. A linear two-dimensional model is used for a qualitative analysis that compares the dynamic responses of a rigid system, comprising a rigid foundation embedded in a layered half-space with a superstructure mounted on top, and a corresponding flexible system with the same parameters but a flexible foundation with a variable stiffness. The Indirect Boundary Element Method combined with non-singular Green’s functions of distributed line loads is employed to calculate the system responses accurately. Transfer functions computed for a range of parameters show that the rigid-foundation assumption leads to overestimating the system natural frequency and changes the peak deformations to a different extent. It is also shown through a case study of 42 earthquakes that the rigid-foundation assumption may either overestimate or underestimate the system responses by up to approximately 50%, and in some cases even by approximately 100%, depending on the frequency content of excitation and SSI dynamic characteristics. Keywords Soil-structure interaction · Flexible foundation · Foundation of variable stiffness · Structure responses · Layered half-space · System frequency · Indirect boundary element method List of symbols βb, βf, βj, βR Shear-wave velocity of the structure, the foundation, the jth sub-layer, the bedrock, respectively 𝛽b∗ , 𝛽f∗ , 𝛽j∗ , 𝛽R∗ Complex valued shear-wave velocity of the structure, the foundation, the jth sub-layer, the bedrock, respectively νb, νf, νj, νR Poisson’s ratio of the structure, the foundation, the jth sub-layer, the bedrock, respectively * Fu Jia [email protected] 1
Department of Civil Engineering, Northwestern Polytechnical University, Xi’an 710072, China
2
Department of Civil Engineering, Tianjin University, Tianjin 300354, China
13
Vol.:(0123456789)
Bulletin of Earthquake Engineering
ρb, ρf, ρj, ρR Mass density per unit length of the structure, the foundation, the jth sublayer, the bedrock, respectively ξb, ξf, ξj, ξR Damping ratio of the structure, the foundation, the jth sub-layer, the bedrock, respectively H Structure height a Foundation half-width c Foundation embedment D Soil-layer thickness ω Circular frequency of incident wave θ Incident angle Γ1 Foundation-soil interface Γ2 Two vertical outlines of the superstructure Ω1 Domain of half-space except foundation Ω2 Domain of superstructure with foundation N1, N2 Total elements along two boundaries, respectively pj, rj Horizontal and vertical fictitious loads, respectively i Imaginary unit
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