The Influence of Model Assumptions on the Dynamic Impedance Functions of Shallow Foundations
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TECHNICAL NOTE
The Influence of Model Assumptions on the Dynamic Impedance Functions of Shallow Foundations Johan Lind O¨stlund1,2 • Andreas Andersson1,3 • Mahir U¨lker-Kaustell1,2 • Jean-Marc Battini1 Received: 6 November 2019 / Revised: 12 April 2020 / Accepted: 12 May 2020 The Author(s) 2020
Abstract The influence of model assumptions on the dynamic impedance functions of shallow foundations is investigated using finite elements in two studies. The first investigates the effects of model assumptions in different combinations including embedment of the foundation, variation of modulus with depth, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load at varying soil depths and with different soil modulus coefficients. Shallow foundations in strata of frictional soil on top of bedrock are considered. Small-strain modulus and modulus reduction relationships are used in an iterative process to update the modulus due to the permanent load. The results show that model assumptions can have a large influence on impedance functions. The static stiffness coefficients differ, in some instances by more than 100%. The impedance functions, normalized with the static stiffness coefficients match each other well in the pre-resonance frequency range. However, in the frequency range above the fundamental frequency, the normalized impedance functions show a large variation. Further, the results show that the influence of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which can be increased up to 67%. The change in fundamental frequency was however minimal. Keywords Dynamic impedance functions Permanent load Dynamic soil–structure interaction Soil dynamics
1 Introduction
& Jean-Marc Battini [email protected] http://www.kth.se ¨ stlund Johan Lind O [email protected] http://www.kth.se Andreas Andersson [email protected] http://www.kth.se ¨ lker-Kaustell Mahir U [email protected]; http://www.tyrens.se 1
Division of Structural Engineering and Bridges, Royal Institute of Technology (KTH), Brinellva¨gen 23, 11428 Stockholm, Sweden
2
Tyre´ns AB, Peter Myndes Backe 16, 118 86 Stockholm, Sweden
3
Swedish Transport Administration, Solna, Sweden
In the context of modeling dynamic soil–structure interaction (SSI) systems, one method of substructuring the models is by calculation of impedance functions. Instead of computing the complete system, the model is subdivided and impedance functions are calculated from the soil– foundation subpart before being applied to the structure. In addition to efficiency, substructuring the system can also give better insight into the dynamic behavior of the soil– foundation system since it can be studied without the coupled effects of the structure. The impedance function is commonly expressed in complex numbers: ZðxÞ ¼ kd ðxÞ
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