Fluido

Draft Dated: Monday, August 25, 2003

Contents of Chapter 23
1. Introduction 2. Fluid-Structure Interaction 3. Finite Element Model Of Dam-Foundation Interface 4. Loading Due To Uplift And Pore Water Pressure 5. Pore Water Pressure Calculation Using Sap2000 6. Selection Of Gap Element Stiffness Value 7. Fundamental Equations In Fluid Dynamics 8. Relationship Between Pressure And Velocity 9.Equilibrium At The Interface Of Two Materials 10. Radiation Boundary Conditions 11. Surface Sloshing Modes 12. Vertical Wave Propagation 13. The Westergaard Paper
14. Dynamic Analysis of Rectangular Reservoir 15. Finite Element Modeling of Energy Absorptive Reservoir Boundaries 16. Relative Versus Absolute Form 17. The Effect Of Gate Setback On Pressure 18. Seismic Analysis of Radial Gates 19.Final Remarks

FLUID STRUCTURE INTERACTION

23-1

23. FLUID-STRUCTURE INTERACTION
A Confined Fluid can be considered as a Special Case of a Solid Material. Since, Fluid has a Very Small Shear Modulus Compared to it’s Compressibility Modulus

23.1

INTRODUCTION
The static and dynamic finite element analysis of systems, such as dams, that contain both fluid and solid elements can be verycomplex. Creating a finite element model of fluid-solid systems that accurately simulates the behavior of the real physical system, requires the engineer/analysts to make many approximations. Therefore, the purpose of this chapter is to present a logical approach to the selection of the finite element model and to suggest parameter studies in order to minimize the errors associated with variousapproximations. Figure 23.1 illustrates a typical fluid/solid/foundation dam structural system and illustrates the several approximations that are required in order to create a realistic finite element model for both static and dynamic loads.

23-2 STATIC AND DYNAMIC ANALYSIS
Surface Waves ?

Gate
Damping ? Incremental Construction ?

Quiet or Fixed Upstream Boundary ?

Reservoir

EnergyAbsorption ?

Dam

Pore Water Pressure and Uplift Forces ? Location of Boundaries ?

Foundation

Radiation Boundary Conditions ?

Earthquake Displacements ?

Figure 23.1. Approximations required for the Creation of a Finite Element Model For Fluid/Solid Systems This example involves, in many cases, the use of orthotropic, layered foundation. The dam is constructed incrementally, oftenover a several month period, where the material properties, temperature and creep are a function of time. Therefore, the determination of the dead-load stress distribution within the dam can be relatively complicated. For gravity dams the dead load stresses from an incremental analysis may not be significantly different from the results of an analysis due to the dead load applied to the completedam instantaneously. However, for narrow arch dams the instantaneous application of the dead load to the complete dam can cause erroneous vertical tension stresses near the abutments at the top of the dam. SAP2000 has an incremental construction option that can be activated by the user in order to accurately model the construction sequence. In addition, SAP2000 has the ability to model most of theboundary conditions shown in Figure 23.1. Also, frame elements, solid elements and fluid elements can be used in the same model; hence, it is possible to capture the complex interaction between foundation, dam, reservoir and attached structures such as gates, bridges and intake towers.

FLUID STRUCTURE INTERACTION

23-3

23.2

FLUID-STRUCTURE INTERACTION
It has been standard practice toassume that fluid is incompressible for many fluid-structure interaction problems. As a result of the assumptions of incompressible fluid and a rigid structure, many dynamic fluid-structure interaction problems have been approximately solved replacing the fluid with an added mass. Also, the incompressible approximation allowed many problems, of simple geometry, to be solved in closed form using...