Numerical  Analysis  of  Contra  Dam  using  Real  Earthquake  Accelerogram

Name:  Efthymios Nikoltsios 0909173n Supervisor:  Dr Lukasz  Kaczmarcyk

AimThe aim of the project was to analyse the response of the ContraDam using a real accelerogram of strong ground motion, analysethe effect of numerical damping in the results and optimise thevariables used in the FEA software MoFEM to adequately capturethe response of the structure.

MethodologyAnalysis Parameters: The model was designed using Cubit 13.0and based on the limited computer resources for the FEA, itincluded the dam body (220m height, 380m length) that was fixed atthe nodes in contact with the foundation. The physical dampingapplied was 4% and the material parameters were set for C50/60concrete.

The design earthquakes are studied and the ground motion used inthe current analysis was chosen with a maximum acceleration of1.1G acting towards the stream direction which causes the largestdeformations.

Parameters used were optimised by running the analysis multipletimes for different cases and comparing the results. The effect thatmesh discretisation, polynomial order of elements, time stepsize, integration scheme method, amount of numerical dampingand material nonlinearity have on the response and theadvantages and disadvantages of each are explained.

Figure  1  -­ Cubit  Model  of  Contra  Dam

Figure  2  -­ Accelerogram of  Nahanni  Earthquake

IntroductionEarthquakes can have big impact in the design life and safety of alarge arch dam, because the large forces created can producesignificant damage. This can deem the structure unsafe for usageand require a lot of money to repair. Also, numerical damping cancreate artificial error in FEA results [1] and needs to be considered.

ResultsThe Principal stress 1 in the dam body was observed on the leftabutment, at 24.87MPa.

The max displacement calculated during the ground excitation wasat the middle node of the crest at 32.23cm.

The effect of numerical damping to counteract numerical dispersionis also important. The effect was visualised by removing physicaldamping in two different integration schemes, one damping bothhigh and low frequencies and the other not damping the importantlow frequencies, so that only the nonphysical damping will cause theenergy dissipation in the system. The result was dramatic andindicated that the Backward Euler method is not accurate enough inthis case because of the amount of numerical damping applied.

Figure  3  – Cases  Analysed  for  Optimisation  of  FEA  Parameters

Data  Visualisation  &  AnalysisPrincipal Stresses, Hydrostatic Pressure and maximumDisplacements were calculated, which were used in the currentanalysis. All results were compared to results from similar projectsand were found to be close to literature values confirming thevalidity 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  

ConclusionsEach Parameter in the FEA is important to be optimised because itcan introduce varying amounts of error in the results. Secondly,Numerical damping of high frequencies does not affect greatly theresults whereas when low frequencies are damped, energy is lostrapidly from the system. Finally, the position under maximum stressin the system is on the left abutment and the stress is within thestrength of the concrete used, although a more detailed analysisincluding dam-­water-­reservoir interactions would be needed forcritical use of the results.References1. Warren, G.S. & Scott, W.R., 1995. Numerical dispersion in the finite-­element method usingtriangular edge elements. Microwave and Optical Technology Letters, M(2), pp.49–51.