NUMERICAL MODELLING OF SOIL-STRUCTURE INTERACTION USING EFFICIENT RADIATING BOUNDARY CONDITIONS

Abstract

Since the 1964 Niigata earthquake (the epicentre is located at the continental shelf off the northwest coast of Honshu, Japan), dynamic soil-structure interaction has been considered an important factor in many important structures such as tall buildings, bridges, nuclear power plants, etc. As soil-structure interaction analysis is a complex phenomenon, researchers have developed different techniques through experimental, analytical, and numerical approaches. Amongst all the techniques numerical methods are found more reliable in the design of structures to include the effects of soil-structure interaction. However, radiating waves from structure are one of the major concerns in numerical modelling of the soil-structure interaction. To solve the radiating wave propagation problems using finite element analysis (FEA), it is required that the boundary must be terminated at some finite location. This truncation of the model at the finite boundary will cause the reflection of radiating waves. The reflected waves from the boundary will affect the solution and may lead to instabilities in the numerical analysis. Therefore, it is necessary to provide an artificial boundary condition that will transmit the outwardly propagating waves with minimal or negligible reflections. The primary objective of this research is to develop an efficient radiating boundary condition for numerical simulation of wave propagation in nonlinear, unbounded spatial domains. Despite several attempts by the researchers, the challenge of developing a computationally efficient absorbing boundary condition (ABC) to resemble the Sommerfeld radiation condition has not been well addressed. Absorbing Boundary Conditions (ABC), also called Local Absorbing Boundary Conditions are simple and computationally efficient, but they produce spurious reflections when the wave impinges on the boundary in a direction other than the normal. Absorbing layer techniques are efficient in absorbing outwardly propagating wave energy, but these techniques require many layers. Researchers have also attempted to combine the Absorbing Boundary Conditions (ABC) with the Layers by Increasing Damping (ALID) to utilize the advantages of both methods. Since ABC is only applicable to wave propagation in elastic media, the attempt to combine the two techniques becomes unsuccessful due to an impedance mismatch. In this thesis, a new absorbing boundary condition for wave propagation in a viscoelastic medium (VABC) is proposed. The method is an extension of the standard ABC proposed by Lysmer and Kuhlemeyer (1969). The proposed method does not converge to Kelvin-type viscoelastic materials but can be applied to Maxwell-type viscoelastic materials, i.e., only mass proportional damping is considered. The accuracy of the method is studied for viscoelastic wave propagation problems, and the results are compared with the standard ABC and analytical solutions.  The analytical and numerical results show that the VABC boundary conditions are promising in absorbing the wave energy when the damping ratio is less than 20% and produces the reflections when damping ratio is more than 20% due to dropping the higher order terms in the expansion. The VABC produces spurious reflections when the waves are not impinging in the normal direction, and reflections increase as the angle between the wave propagation and the normal direction increases. The study extends to provide an efficient absorbing method by combining VABC boundary conditions with Absorbing Layers by Increase in Damping (ALID). The main objective of ALID is to attenuate the reflected waves from VABC in cases of angle incidence. The combination of ALID and VABC, i.e., ALID+VABC, is achieved by matching the impedance of VABC with the last layer of ALID. Results from ALID+VABC are compared with other methods such as ABC, ALID, and SRM (Stiffness Reduction Method). A sensitivity analysis is carried out to verify the efficiency of absorbing the propagation wave energy at various loading frequencies. ALID+VABC has been found to be numerically efficient across a wide range of loading frequencies when compared to the other methods. The method also requires shorter absorbing region lengths, which allows for a smaller number of absorbing layers. However, all the absorbing layer methods such as ALID, ALID+VABC, SRM, and PML are poor at allowing smooth propagation of the wave through layers when waves are entering at a higher incident angle. Dynamic Soil-Structure-Interaction analysis is carried out on a three-dimensional tall building with 20 stories using ABC, ALID, and ALID+VABC as a radiating boundary condition. The complete Soil-Structure-Interaction (SSI) analysis is carried out in two stages. First, a nonlinear static analysis is carried out with gravity loading. The absorbing layers in ALID and ALID+VABC were also present in the static analysis since the damping properties did not influence the analysis. Later, nonlinear dynamic analysis is carried out using El Centro earthquake loading. The Domain Reduction Method is used to apply the earthquake motion. 1D wave propagation is used to obtain the forces for free-field motion at the boundary interface, and these forces are applied in dynamic analysis. Static analysis results show that the model with absorbing layers, i.e., ALID and ALID+VABC, produces more displacements compared to ABC since the finite elements in the absorbing layers are subjected to gravitational loads (dead loads) from above. This proves that the absorbing layers can be used to reduce the actual model domain if they are modelled appropriately so that the size of the resulting model will not be increased with ALID and ALID+VABC. The time history response of the structure under El Centro earthquake loading (the earthquake occurred in the Imperial Valley in south-eastern Southern California in 1940) shows that ALID and ALID+VABC perform better than ABC boundary conditions. The study also shows that ALID and ALID+VABC work well even if the absorbing medium length is 0.33 λ. However, a minimum of 30 layers are recommended in the absorbing region.