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Ravi Shankar B – Soil-structure

Ravi Shankar Badry received his  doctorate in Civil Engineering (CE). His research work was supervised by Prof. Pradeep Kumar R. Here’s a summary of her research work on Numerical modelling of soil-structure interaction using efficient radiating boundary conditions:

Since the 1964 Niigata earthquake, dynamic soil-structure interaction has been considered as an import factor in many important structures such as tall buildings, bridges, nuclear power plants, etc. As the 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 the 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 the boundary to 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 outward propagating waves with minimum 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 were made by the researchers, the challenge to develop a computationally efficient Absorbing Boundary Condition (ABC) to resemble the Sommerfeld radiation condition is not well addressed. 

Local Absorbing Boundary Conditions (ABC) are simple and computationally efficient, but they produce spurious reflections when the wave impinges on to the boundary other than normal direction. Absorbing layer techniques are efficient in absorbing outward propagating wave energy, but these techniques require many layers. Researchers have also attempted to combine the Local Absorbing Boundary Conditions (ABC) with Absorbing 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 impedance mismatch.

In this thesis, a new absorbing boundary condition for the wave propagation in viscoelastic medium (VABC) is proposed. The method is an extension to the standard ABC proposed by Lysmer and Kuhlemeyer (1969). The proposed method does not converge to Kelvin type of viscoelastic materials but can be applied to Maxwell type of viscoelastic material i.e., mass proportional damping is only 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 normal direction and reflections increases as the angle between the wave propagation and normal direction increases.

The study extends to provide an efficient absorbing method by combing VABC boundary condition with Absorbing Layers by Increase in Damping (ALID). The main objective of ALID is to attenuate the reflected waves from VABC in case 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 in absorbing the propagation wave energy at various loading frequencies. ALID+VABC has been found numerically efficient across vide range of loading frequencies when compared to the other methods. The method also requires less absorbing region lengths which allows to model with a smaller number of absorbing layers. However, all the absorbing layer methods ALID, ALID+VABC, SRM and PML are poor in allowing smooth propagation of the wave through layers when waves are entering at higher incident angle.

Dynamic Soil-Structure-Interaction analysis is carried out on a three-dimensional high rise tall building with 20 story using ABC, ALID, ALID+VABC as a radiating boundary condition. The complete 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 does not influence the analysis. Later, nonlinear dynamic analysis is carried out using El Centro earthquake loading. 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 this force 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 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 shows that  ALID and ALID+VABC performs better than ABC boundary conditions. The study also  shows that the ALID and ALID+VABC works well even if the absorbing medium length  is 0.33 λ. However, a minimum of 30 layers are recommended in the absorbing region.

February 2023