Quantifying dynamic soil-structure interaction for railway induced vibrations

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.

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.

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

Seismic design and analysis of underground structures

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

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.

Dynamic soil-structure interaction (DSSI) plays a fundamental role in many geotechnical and/or structural design situations, as clearly shown by the damage which occurred during several recent earthquakes (Kobe 1995; Koaceli 1999; Chi-Chi 1999; L’Aquila 2009). For a long time civil engineering researchers have devoted increasing attention to this subject. Thanks to their efforts, several technical regulations, such as EC8 (2003), have taken DSSI into account. However, many steps are still necessary in order to increase our knowledge regarding this complex phenomenon, as well as to make all the results achieved known to academics and practitioners. This paper presents the results of a shaking table test performed on a scaled physical model consisting of a 3-D steel frame resting on a bed of sand. The experimental results are compared with the numerical ones obtained using a sophisticated elasto-plastic constitutive model recently implemented in the FEM code utilised. The solution of geotechnical problems requires the use of appropriate constitutive models. Many interesting constitutive models have been developed, but only a few of these have been implemented into commercial numerical codes; which is particularly so when dynamic analyses are required. The described experimental results, as well as the comparison between them and the numerical results, allow interesting considerations to be drawn on dynamic soil-structure interaction and on its numerical simulation.

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.

This paper presents the results of 3D nonlinear finite element modeling of seismic soil-foundation-structure interaction in fully integral abutment bridges using HP steel piles as bridge foundations. The soil’s stiffness has a significant effect on load distribution when the soil, HP piles, abutment, and superstructure act as a combined system to resist seismic forces on the bridge. Due to the lack of knowledge on dynamic soilstructure interaction during earthquakes, the real world design procedures are kept simple and conservative. A deeper understanding of soil-foundation-structure interaction mechanism will facilitate sustainable bridge design by optimizing the sizes of structural members and increasing the service life of bridges. In this paper, the seismic soil-structure interaction mechanisms are investigated for the bridge longitudinal direction as well as for the bridge transverse direction. Both simple span and two-span bridges are analyzed using the finite element program ANSYS. The research findings will provide the theoretical support to sustainable bridge design by optimizing the size and orientation of HP steel piles in fully integral abutment bridges.

본 논문에서는 열차가 주행할 때 궤도를 통해 전달되는 진동크기가 구조물의 안전성뿐 만아니라 선로 인근주민, 가축 및 건물에게 미치는 영향을 최소화하기 위해 규정된 진동한계범위에 도달하는 가를 다양한 지반과 궤도구조물의 상호작용에 의한 3D 수치해석을 통해 정확히 예측하고 다양한 지반에 적절한 진동저감을 가져오는 궤도의 단면 및 형태를 결정하는 방법에도 이결과를 사전에 활용할 수 있도록 하였다. 예로서 열차운행으로 인해 발생되는 터널, 성토 및 교량 3종류의 서로 다른 시설물의 진동을 지반-구조물의 상호작용에 의한 3D수치해석을 통해 Spec과 비교분석하여 평가하였으며 주변 환경에 적합한 토층의 변화를 통해 진동저감방법의 한예를 수행하였다. The paper describes four practical cases of railway structure concerning a three-dimensional numerical approach to analyse dynamic soil-structure interaction(SSI)of railway tracks on layered soil under transient load in the time domain. The SSI-Model has been implemented in TDAPIII accounting for nonlinear properties of the track and soil. The approach can be also be used to calculate vibration propagation in the soil and its effect on nearby buildings and structure. The Method is applied to analyse the dynamic response of railway tracks due to a moving wheel set. Finally some sample are given in order to reduce the vibration at the point of emission, at the transmission path and the structure itself.

Soil-structure interaction (SSI) plays a critical role in evaluating seismic performance and guiding damping design in earthquake-prone regions. This study investigates the influence of damping layers placed between the half-space and the foundation on dynamic SSI and the seismic response of the superstructure under plane SH waves. Therefore, an analytical solution is developed by coupling the wavefunction expansion method with the transfer matrix method, and it is verified by reducing the model to a published exact solution when the damping layers become sufficiently small. Parametric analysis reveals that seismic damping layers have a significant effect on the displacement response of both the foundation and superstructure, as well as the surface ground motions. Increasing the shear wave velocities and the number of damping layers, while decreasing the layer thickness, can attenuate the seismic response of the foundation and superstructure. In addition, the surface ground motions exhibit strong sensitivity to the incident angles. The results show that the structural response under earthquake excitation can be effectively mitigated by appropriately designing seismic damping layers. They also provide valuable insights for seismic design and earthquake resilience, extending and advancing previous analytical DSSI studies.

Shaking table test is an important method to study on the problem of the soil-structure dynamic interaction. The property of the soil container directly affects the accuracy of the result. A laminar shear container was designed for shaking table test. And a shaking table test on soil-underground structure dynamic interaction which structure lay in clay was conducted. The results of the test show that the container eliminated the boundary effect when the dynamic load was applied in only one horizontal direction. Meanwhile, the stiffness of the soil container could be changed according to the change of the model soil, which is applicable to decrease the boundary effect.

The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the finite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave field on the nodes of the substructure composed of elements that contain artificial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artificial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplified by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verified by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.

：Numerical simulation is an important approach to conduct soil-structure dynamic interaction analysis, while the realization of the seismic wave input determines the accuracy of the simulation. Wave method is one of the most commonly used methods for seismic wave input, which converts the input wave into the equivalent loads on the artificial boundaries. Comparing with other methods, the wave method has high precision, but the implementation is relatively complicated. Based on another form of equivalent input seismic loads in the finite element model, a new seismic wave input method was proposed. In the new method, by imposing the free-field displacements on the nodes of the substructure composed of the elements containing the artificial boundary nodes, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Afterwards, the equivalent input seismic loads are applied to the nodes of the artificial boundaries to complete the seismic wave input and the seismic analysis of the soil-structure dynamic interaction model are performed. In comparison with the original wave method, the new method avoids the complex processes of calculating the free field stress on the artificial boundaries and the additional forces caused by the artificial boundaries, and determining the directions of the loads on different artificial boundaries. Therefore, it is simple to calculate the equivalent input seismic loads and easy to implement the seismic wave input process in the new method. The validity of the new method is verified by the numerical examples of the seismic analysis of the elastic half-space and layered half-space under vertical and oblique incident seismic waves.

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