Application of Fluid-Structure Interaction Algorithms to Seismic Analysis of Liquid Storage Tanks Zuhal OZDEMIR, Mhamed SOULI Université des Sciences et Technologies de Lille Laboratoire de Mécanique de Lille University of Bosphor, Istanbul

Outline of the Presentation General Objective of the Studies Carried out on Tanks Difficulties in the Analysis of Tanks Analysis Methods for Tanks Fluid-Structure Interaction for Tank Problems 2D Rigid Tank 3D Flexible Tank

- Limit the tank damages observed during earthquakes - Determine the response parameters in order to take precautions - sloshing wave height (freeboard) - uplift displacement (flexible attachments for pipes) General Objective of the Studies Carried out on Tanks

Difficulties in the Analysis of Tanks - Three different domains * Structure * Fluid * Soil - Material and geometric nonlinearities - Complex support condition * Anchored * Unanchored

- Large amplitude wall deformations (Buckling) - Violent sloshing which causes damage at the tank wall and shell General Performance of Tanks during Earthquakes - High plastic deformation at the tank base Sloshing damage

Diamond Shape Buckling (Elastic Buckling) Elephant-Foot Buckling (Elasto-Plastic Buckling) Tank Shell Buckling

Analysis Methods for Tanks Irrotational flow, incompressible and inviscid fluid (potantiaql flow theory) - Simplified Analytical Methods Fluid : Laplace equation Spring-Mass Equivalent Analogue Most of the provisions recommended in the current tank design codes employ a modified version of Housner’s method Structure : rigid tank Base Shear and Overturning Moment Ordinary Beam Theory Shell Stresses (Axial Compressive and Hoop)

Analysis Methods for Tanks (cond) - Numerical Methods FEM is the best choice, because -structure, fluid and soil can be modelled in the same system -proper modelling of contact boundary conditions -nonlinear formulation for fluid and structure -nonlinear formulation for fluid and structure interaction effects * 2D finite difference method * FEM * BEM * Volume of fluid technique (VOF)

Structure Fluid Lagrangian Formulation Dynamic Structure equation Navier Stokes equations in ALE Formulation Fluid-Structure Interaction for Tank Problems

2D Tank Problem width = 57 cm height = 30 cm H water = 15 cm Sinusoidal harmonic motion non-resonance case resonance case The sketch of the 2D sloshing experiment (Liu and Lin, 2008)  o = rad/s

2D Tank Problem Lagrangian

ALE 2D Tank Problem

 =  o  = 1  o non-resonance case resonance case amplitude = m

3D Tank Problem Cylindrical tank size: - radius of 1.83 m - a total height of 1.83 m - filled up to height of m Maximum ground acceleration = 0.5 g in horizontal direction (El Centro Earthquake record scaled with )

3D Tank Problem Change of free surface in time

3D Tank Problem Von Mises stresses on the anchored tank shell

3D Tank Problem Von Mises stresses on the unanchored tank shell (displacements magnified 10 times)

3D Tank Problem Comparisons of the time histories of pressure for the numerical method and experimental data

3D Tank Problem Comparisons of the time histories of pressure for the numerical method and experimental data

3D Tank Problem Comparisons of the time histories of surface elevation for the numerical method and experimental data

3D Tank Problem Comparisons of the time histories of tank base uplift for the numerical method and experimental data

Conclusions (1) ALE algorithm lead highly consisted results with the experimental data in terms of peak level timing, shape and amplitude of pressure and sloshing. (2) Method gives reliable results for every frequency range of external excitation. (3) ALE method combined with/without the contact algorithms can be utilized as a design tool for the seismic analysis of rigid and flexible liquid containment tanks. (4) As a further study, a real size tank will be analysed

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3D Tank Problem Pressure distribution inside the tank

Analysis Methods for Tanks (cond) - Experimental Methods * Static tilt tests * Shaking table tests Schematic view of static tilt test A cylindrical tank mounted on the shaking table