1
Numerical Analysis of Contra Dam using Real Earthquake Accelerogram Name: Efthymios Nikoltsios 0909173n Supervisor : Dr Lukasz Kaczmarcyk Aim The aim of the project was to analyse the response of the Contra Dam using a real accelerogram of strong ground motion, analyse the effect of numerical damping in the results and optimise the variables used in the FEA software MoFEM to adequately capture the response of the structure. Methodology Analysis Parameters: The model was designed using Cubit 13.0 and based on the limited computer resources for the FEA, it included the dam body (220m height, 380m length) that was fixed at the nodes in contact with the foundation. The physical damping applied was 4% and the material parameters were set for C50/60 concrete. The design earthquakes are studied and the ground motion used in the current analysis was chosen with a maximum acceleration of 1.1G acting towards the stream direction which causes the largest deformations. Parameters used were optimised by running the analysis multiple times for different cases and comparing the results. The effect that mesh discretisation, polynomial order of elements, time step size, integration scheme method, amount of numerical damping and material nonlinearity have on the response and the advantages and disadvantages of each are explained. Figure 1 Cubit Model of Contra Dam Figure 2 Accelerogram of Nahanni Earthquake Introduction Earthquakes can have big impact in the design life and safety of a large arch dam, because the large forces created can produce significant damage. This can deem the structure unsafe for usage and require a lot of money to repair. Also, numerical damping can create artificial error in FEA results [1] and needs to be considered. Results The Principal stress 1 in the dam body was observed on the left abutment, at 24.87MPa. The max displacement calculated during the ground excitation was at the middle node of the crest at 32.23cm. The effect of numerical damping to counteract numerical dispersion is also important. The effect was visualised by removing physical damping in two different integration schemes, one damping both high and low frequencies and the other not damping the important low frequencies, so that only the nonphysical damping will cause the energy dissipation in the system. The result was dramatic and indicated that the Backward Euler method is not accurate enough in this case because of the amount of numerical damping applied. Figure 3 – Cases Analysed for Optimisation of FEA Parameters Data Visualisation & Analysis Principal Stresses, Hydrostatic Pressure and maximum Displacements were calculated, which were used in the current analysis. All results were compared to results from similar projects and were found to be close to literature values confirming the validity of the obtained response. Figure 4 – Max Principal Stress Path During Excitation Figure 5 – Max Displacement During Excitation Figure 6 – Numerical Damping in Backward Euler and Alpha Method Conclusions Each Parameter in the FEA is important to be optimised because it can introduce varying amounts of error in the results. Secondly, Numerical damping of high frequencies does not affect greatly the results whereas when low frequencies are damped, energy is lost rapidly from the system. Finally, the position under maximum stress in the system is on the left abutment and the stress is within the strength of the concrete used, although a more detailed analysis including damwaterreservoir interactions would be needed for critical use of the results. References 1. Warren, G.S. & Scott, W.R., 1995. Numerical dispersion in the finiteelement method using triangular edge elements. Microwave and Optical Technology Letters, M(2), pp.49–51.
