Real-time dynamic hybrid testing for soil–structure interaction analysis

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element (FE) numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom (DOFs). Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

This paper investigates the seismic behavior of a wind turbine, including soil–structure interaction (SSI). A full-system finite-element model is introduced for dynamic analysis, including SSI. The model is based on the NREL 5 MW reference wind turbine that consists of a rotor blade system with three rotating blades, nacelle, and tower connected to a soil–foundation system. The proposed model is validated using the full-system natural frequencies of the reference wind turbine. In the soil foundation system, the foundation is modeled as a rigid gravity-based foundation with two DOFs and the SSI effect is considered using a cone model. Dynamic analyses are developed in frequency and time domains, and the model is subjected to earthquake excitation and wind loading for different soil types for parked and operational conditions. Transfer functions are obtained, and the modal frequencies of the soil foundation structure system are estimated. Results show that SSI plays an important role in the response of the wind turbine. We can conclude that for a parked wind turbine, the effect of SSI is beneficial while considering that SSI has a detrimental effect in the operational conditions of wind turbine. The participation of different input loads in total response of an operational wind turbine is also presented.

The dynamic responses of wind turbine towers subjected to earthquakes and winds are very complex and might cause significant damages. However, the reproduction of the dynamic response in a laboratory is not easy because the specimen shall be scaled very small to meet the space limits of wind tunnels and shaking tables. Real-time hybrid testing (RTHT) is an appealing option to solve this difficulty, which takes part of a structure as the specimen, while treats the rest numerically so that large scale specimen could be used. However, the application of RTHT to a wind turbine tower requires more complex boundary coordination to reproduce the coupled shear and bending behavior. This paper proposes a shaking-table substructure testing framework, where the lower part of the tower is fixed on the shaking table at the bottom and the top of the specimen is simultaneously loaded by a two-degree-of-freedom loading device. The loading facilities communicate in real time with the numerical substructure, and the superstructure including the wind turbine and blades is numerically simulated under the external excitations. Displacements and forces at the boundary are transferred between the numerical and physical substructures to realize boundary compatibility and equilibrium. A novel boundary loading device controls two masses to realize bending and shear equilibrium at the same boundary surface. Enhanced three-variable control is proposed to improve the performance of boundary coordination and the error-response negative feedback compensation method is proposed to reduce error transmission in RTHT, as demonstrated and introduced in a series of simulations and conceptual study.

Dynamic soil-structure interaction models for fragility characterisation of buildings with shallow foundations

Earthquake responses of a base-isolated structure on a multi-layered soft soil foundation by using shaking table tests

Performance evaluation of full-scale tuned liquid dampers (TLDs) for vibration control of large wind turbines using real-time hybrid testing

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.

Soil-structure interaction analysis of NPP containments: substructure and frequency domain methods

In hybrid substructuring, a structural system is partitioned into a numerical substructure and a physical substructure. Typically, the physical substructure consists of a system component whose behavior is difficult to model while the numerical substructure consists of a computational model of the remainder of the system. Hybrid substructuring has previously been shown to be an effective method to quantify the effect of parametric uncertainties in the numerical substructure on the response of the system. This paper proposes and implements a methodology where the effect of parametric uncertainty can also be incorporated into the physical substructure. This idea is implemented in a series of small-scale Real-Time Hybrid Substructuring (RTHS) tests on a magneto-rheological fluid damper used to control a two degree-of-freedom mass-spring system. The physical current supplied to the damper is treated as a random variable. Using the RTHS test results, a metamodel of the system’s frequency domain behavior is developed using Principal Component Analysis and Kriging. This metamodel is then used to evaluate probabilistic system performance.

Dynamic soil-structure interaction (SSI) effects have always been important in the context of assessing the seismic safety and vulnerability of large and complex infrastructures such as bridges, dams, power plants, industrial units etc. Although SSI problem has been under intensive investigations in the past several decades, relatively little is known about the SSI in the case of multi-layered half-space. Majority of previous researches dealing with SSI problems were conducted for rather simple soil profiles: elastic half-space, a soil layer bonded to rigid base, or a soil layer overlying elastic half-space. Very few papers appeared in the literature tackle the SSI problem having two or more soil layers overlying elastic half-space. This is probably due to the substantial computational effort required. Advantages and limitations of widely used current approaches such as finite element method (FEM), boundary element method (BEM) and thin-layer method (TLM) are discussed. Sponsored by the Science Foundation of Sino-German Center researches into SSI on layered soil carried out at Dalian University of Technology are briefly introduced. An advanced approach for dynamic SSI analysis of structures on multilayered half-space is proposed, which circumvent difficulties encountered by FEM, BEM and TLM with relative ease. The governing wave motion equations are solved in the frequency-wave-number domain analytically. The precise integration method (PIM) is employed to perform integration to obtain numerical results. Very high accuracy can be achieved. Analytical solution of wave motion equation is written in dual vector form, which enables efficient and convenient assembling of two adjacent layers into a new one without losing effective digits. Formulations dealing with dynamic impedance of arbitrary-shaped foundation on isotropic as well as arbitrary anisotropic multi-layered soil are presented. The solution is not difficult to extend to problems dealing with foundation embedment and throughthe- soil coupling of two or more foundations. Numerical results validate efficiency and accuracy of the proposed approach.

The influence of dynamic soil–structure interaction (SSI) on simply supported railway bridges is investigated. Impedance functions are calculated considering shallow foundations in soil strata limited by bedrock. The impedance functions are coupled to bridge models, and the assembled soil–bridge systems are investigated addressing the modal properties. A parametric study is performed on a large set of soil–bridge systems. Finally, the response to train loading is analysed. The study shows that the effects of SSI are essentially different depending on whether radiation damping is active or not. Shorter bridges are often affected by radiation damping and the response due to train loading may be significantly reduced when SSI is considered. However, for longer bridges (>15 m) the effect of SSI is often small. Due to the stiffness reduction of the impedance, some bridges may even have a detrimental effect from SSI and a reduction of the traffic speed is obtained.

Recent studies on design optimization of steel frames considering soil-structure interaction have focused on static loading scenarios, and limited work has been conducted to address the design optimization under dynamic soil-structure interaction. In the present work, first, a platform is developed to perform optimization of steel frames under seismic loading considering dynamic soil-structure interaction (SSI) in order to quantify the effects of earthquake records on the optimum design. Next, verification of the adopted modeling technique is conducted using comparison of the results with the reference solution counterparts in frequency domain. For time history analyses, records from past events are selected and scaled to a target spectrum using simple scaling approach as well as spectrum matching technique. For sizing of the steel frames, a recently developed metaheuristic optimization algorithm, namely exponential big bang-big crunch optimization method, is employed. To alleviate the computational burden of the optimization process, the metaheuristic algorithm is integrated with the so-called upper bound strategy. Effects of factors such as the building height, presence of soil domain, and the utilized ground motion scaling technique are investigated and discussed. The numerical results obtained based on 5- and 10-story steel braced frame dual systems reveal that, although dynamic SSI reduced the seismic demands to some extent, given the final design pertains to different load combinations, the optimum weight difference is not considerable.

A review study on seismic behavior of individual and adjacent structures considering the soil – Structure interaction

3D dynamic soil-structure interaction in layered, fluid-saturated, poroelastic half-space