Because of the limitations of testing facilities and techniques, the seismic performance of soil-structure interaction (SSI) system can only be tested in a quite small scale model in laboratory. Especially for long-span bridge, a smaller tested model is required when SSI phenomenon is considered in the physical test. The scale effect resulting from the small scale model is always coupled with the dynamic performance, so that the seismic performance of bridge considering SSI effect cannot be uncovered accurately by the traditional testing method. This paper presented the implementation of real-time dynamic substructuring (RTDS), involving the combined use of shake table array and computational engines for the seismic simulation of SSI. In RTDS system, the bridge with soil-foundation system is divided into physical and numerical substructures, in which the bridge is seen as physical substructures and the remaining part is seen as numerical substructures. The interface response between the physical and numerical substructures is imposed by shake table and resulting reaction force is fed back to the computational engine. The unique aspect of the method is to simulate the SSI systems subjected to multisupport excitation in terms of a larger physical model. The substructuring strategy and the control performance associated with the real-time substructuring testing for SSI were performed. And the influence of SSI on a long-span bridge was tested by this novel testing method.
In the seismic analysis of a structure founded on ground, the ground motion passes to the base of structure and then loads on structure. The response of the foundation system affects the response of the structure and vice versa, which is called dynamical soil-structure interaction (SSI). Theoretical results [
The method of real-time substructuring derived from hardware-in-the-loop test [
In the research presented in this paper, a framework of substructuring for SSI system with bridge was established firstly; after that the control strategies for the real-time dynamic substructuring testing were analysed. Finally, the influence of SSI on a long-span bridge was tested through this novel testing method.
The development of advanced computation and control techniques resulted in the great progress of real-time substructure [
Generally schematic representation of RTDS using shaking table.
Importantly, the most significant advantage of real-time substructuring is that the process is implemented as a time-stepping routine in real-time, which allows that not only can the nonlinear and uncertain behaviour of physical substructure be accurately tested, but also the time-dependent nonlinearity of numerical substructure can be adopted in the testing. The test method mentioned above supplies a novel solution for the SSI testing. As known, compared with soil-foundation system, the behaviour of structure is relatively easily modelled, especially, the nonlinearity including gapping between the foundations and soil and nonlinear stress-strain response of the soil, and so on. However, the real interest in SSI is the response of structure under earthquake loading; meanwhile, the complexity of structural form and material, geometrical, and contacting nonlinearity of structure are also not well described theoretically. Therefore, both the two kinds of substructuring (soil-foundation system or structure modelled numerically) for SSI need to be developed. In this work, the soil-foundation system is treated as numerical substructure and simulated in computer, while the bridge seems as the physical substructure and tested in the laboratory. A diagrammatic representation of RTDS for a bridge is shown in Figure
Substructuring system for bridge subject to earthquake excitation.
Whole soil-structure system under multisupport excitation
Substructured system:soil-foundation system represented as numerical substructure
The ground motion imposing on superstructure caused by earthquake includes three portions (as illustrated in Figure
Numerical model of soil-pile-foundation system.
Deformation of soil-pile-foundation
Time-domain difference model
In order to overcome this disadvantage, two main methods [
So as to take the full advantage of the two models and make up for their deficiency as well, a time-domain difference model (TDDM) for soil-foundation system was proposed by Du and Zhao [
Herein, we assume that the bridge pier is constructed on a 3 × 3 pile group foundation, and the parameters are as follows: damping ratio of soil is 0.05, Poisson’s ratio of soil is 0.4, ratio of pile spacing and diameter is 5, Young Modulus ratio of pile to soil is 1000, mass density ratio of pile to soil is 1.42, and ratio of pile length and diameter is 15. Normalized by single pile static stiffness, the impedance function of the pile group foundation can be expressed as
Parameters of the used TDD model.
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
1.198 | −0.013 | −0.415 | −0.127 | 0.02 | 0.004 | 0.659 | 0.011 |
|
|||||||
|
|
|
|
|
|
— | — |
|
|||||||
−0.681 | −0.205 | 0.433 | 0.028 | −0.029 | −0.003 | — | — |
Normalized dynamic stiffness of pile group foundation reported by Du and Zhao [
In commonly used RTDS system, displacement or force was used to be target signal to drive transfer system; however in some SSI systems, such as sandy soil, the effect of SSI on the acceleration of structure is noticeable, but the effect on displacement is inconspicuous. In that case, the acceleration of interface cannot be reproduced well by using displacement control. In this work, the acceleration driving was attempted to be used in the RTDS for SSI of this work. In this RTDS system, shaking table array was used as the transfer system to produce the interface response of foundation, resulting from the dynamics of which, the response between physical and numerical substructure is always asynchronous, even causing the instability, especially for the low damping system [
Based on TDDM presented in Section
Framework of RTDS for SSI simulation.
Emulated system
Substructured system
To formulate the synthesis procedure of RTDS dynamics and control, a framework of linear substructuring controller (LSC) [
MLSC-MCSEF controlled RTDS system.
For verifying the validity of the RTDS for SSI simulation, further tests of a one-story steel frame including SSI considerations were performed. The parameters for the soil model are shown in Table
Specifications of shake table array in BJUT.
Table size | 1 m × 1 m ( |
Operation mode |
|
Maximum specimen mass | 5 ton |
Velocity | ±80 cm/s |
Frequency of operation | 0.1 |
Table mass | 1 ton |
Number | 9 |
Displacement | ±7.5 cm |
Acceleration (full load) | ±1.5 g ( |
Control mode | TVC |
Shake table array in BJUT.
Acceleration of physical substructure measured from the RTDS for one-story frame.
The dynamic response of a large-span bridge with the considerations of SSI subjected to earthquake excitation was tested using RTDS method developed in this work. In this RTDS test, the specimen (see in Figure
Dimensions of specimen.
Photo of specimen.
Seismic wave used in the test.
El Centro
Wenchuan
Before conducting RTDS test, a conventional shaking table test with white noise excitation was carried on to identify the dynamic parameters of the physical substructure. The Fourier spectrums of the acceleration measured at pier2 were shown in Figure
Flourier spectrum of the acceleration at the top of pier2.
To evaluate the effect of SSI on the dynamic response of long-span bridge, the soft soil-foundation system with the shear wave velocity
In the experiment, the MLSC-MCSEF strategy was adopted. Figure
Control performance of the table below pier2.
The tested results of acceleration and strain response excited by Wenchuan earthquake were presented in Figures
Dynamic response of bridge.
Acceleration at the top of pier2
Strain at the bottom of pier2
Acceleration response of the table below pier2.
Time history
Fourier spectrum
Table
Maximum strain at the bottom of Pier2 and Pier3.
|
Infinity | 400 | 200 | 100 | |
---|---|---|---|---|---|
El Centro | Pier2 ( |
269 | 559 | 601 | 272 |
Pier3 ( |
193 | 416 | 505 | 216 | |
Wenchuan | Pier2 ( |
345 | 710 | 643 | 185 |
Pier3 ( |
289 | 725 | 513 | 118 |
Flourier spectrum of the seismic wave used in the test.
El Centro
Wenchuan
The purpose of this work is to establish a potential testing method for the simulation of soil-structure interaction based on real-time dynamic substructuring (RTDS), testing bridge experimentally and modelling the remainder part numerically, which make the long-span bridge testing with consideration of SSI possible. The “size effect” resulting from the scaled model in whole system tests because of the size and power of the testing facilities is weakened; meanwhile the nonlinear dynamics of the SSI system can be investigated using this method. The feasibility of this method has been verified experimentally.
The influence of SSI on a long-span bridge was tested through RTDS method. The SSI effect enlarged the dynamic response of bridge when the shear wave velocity of soil is 400 m/s and 200 m/s, while the SSI effect reduced the dynamic response of bridge when the shear wave velocity of soil is too low (e.g.,
The authors declare that they have no conflicts of interest.
The authors gratefully acknowledge the support of the National Science Foundation of China, Grant no. 51608016, and the support of the Beijing Natural Science Foundation (8164050) in the pursuance of this work.