Abaqus Fluid Structure Interaction Graz-Austria

8/11/2019 Abaqus Fluid Structure Interaction Graz-Austria

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T HEME AFluid Structure Interaction

Arch Dam – Reservoir at Seismic loading

Formulator:

Graz University of Technology

Institute of Hydraulic Engineering and Water Resources Management



1.1 Focus of this benchmark example

The focus of this benchmark is to carry out the Dynamic Fluid Structure Interaction for

a large arch dam. Every participant may choose his own order of details in modeling.

The main goal of this example is the application of different approaches like:

Added mass technique ( Westergaard, Zangar,…)

Acoustic Elements (compressible, incompressible)

Fluid Elements (compressible, incompressible)

Further on, the usage of different Boundary Conditions is possible for:

Reservoir - Foundation

- Reflecting (on the bottom and the sides)

- Non-reflecting (at the end of the reservoir)

The modeling of the block joint opening – due to tensile stresses and nonlinear effects -

is not focus of this benchmark example. However, to carry out this analysis in the time

domain will provide the opportunity for further non-linear analyses.

1.2 General basic assumptions

The following general basic assumptions and boundary conditions for the investigations

should be used:

Same spatial discretization (Model/Mesh) of the Structure, Foundation and

Reservoir

Same Material Parameters

Acceleration-Time-History in X-,Y-,Z-Direction

Reservoir is infinite in length (non-reflecting)

Rayleigh Damping

Results to be compared - Visualization

Based on these basic assumptions and results gained the contributors are encouraged to intensify

and focus their effort to achieve results with higher profound physical justification and explain

the differences. (E.g.: different spatial discretization, more appropriate modeling of the

interaction; different length of the reservoir; need for nonlinear effects).

An interpretation of the evaluated results from an engineering point of view should be given.



2. Modell and Geometry

An Arch Dam, Foundation and Reservoir Model layout for the benchmark has been generated

and is available for downloading.

2.1 Arch Dam Model

Symmetric Geometry

Total Height: 220 Meters

Valley width (crest): ~ 430 Meters

Valley width (bottom): ~ 80 Meters

2.1.1 Arch Dam Geometry

The Arch Dam Geometry has been generated with the Program “Arch Dam Design”, which was

developed as part of the Master-Thesis by DI Manuel Pagitsch.

Arch Dam Model Plan View



View from the upstream Main Section

2.2 Foundation ModelSymmetry is used for the foundation too.

Height: 500 Meters

Length: 1000 Meters

Width 1000 Meters



2.3 Reservoir Model

Length: assumed minimum of 460 Meters (> 2x Height of the Dam)

Modeling the interaction with Acoustic- or Fluid Elements



2.4 Acceleration Time History

Transient Acceleration (amax ≈ 0.1g)

X-,Y-,Z- Direction

Artificially generated time history

3. Material Parameters

The Material properties are defined for isotropic and homogenous conditions.

Rock mass

Density: 0 kg/m3

Poisson - ratio: 0,2

Youngs - modulus: 25000 MPaWater

Density: 1000 kg/m3

Bulk - modulus: 2200 MPa



Dam

Density: 2400 kg/m3

Poisson - ratio: 0,167

Youngs - modulus: 27000 MPa

4. Mesh Properties

4.1 Coarse Mesh

Arch Dam

Total number of nodes: 2083

Total number of elements: 356

312 quadratic hexahedral elements of type C3D20R (ABAQUS CAE)

44 quadratic wedge elements of type C3D15 (ABAQUS CAE)

Foundation



quadratic hexahedral elements of type C3D20R (ABAQUS CAE)

Reservoir



quadratic hexahedral elements of type AC3D20 : A 20-node quadratic acoustic brick.

(ABAQUS CAE)



4.3 Elements and Node Numbering in ABAQUS/CAE

The provided input-files are containing a list of the nodes and elements of the mesh and also

predefined “node sets” for the different sections which should be investigated. The Node

numbering of ABAQUS/CAE is plotted in the following figures.



These figures are showing the node numbering for the two different element types which are

used in the provided input-files.

5. Loading

The following loading sequence is intended to be used.

Gravity

Hydrostatic Water Pressure (full supply water level = Crest Height)

Seismic Loading

Modal Superposition or

Direct time integration (Implicit/Explicit)



Fluid Structure Interaction

Arch Dam – Reservoir at Seismic loading

Dam-Water InteractionInteraction of an arch dam with the impounded water leads to an increase in the

dam vibration periods. This is because the dam cannot move without displacing the water in

contact with it. The fact that water moves with the dam increases the total mass that is in

motion. This added mass increases the natural periods of the dam, which in turn affects the

response spectrum ordinates and hence the effective earthquake inertia forces. It can also

cause an increase in damping due to partial absorption of pressure waves at the reservoir

boundary and radiation towards the upstream. These effects tend to change the earthquake

response of the dam with respect to that for the dam with empty reservoir, with the net

result depending on the characteristics and component of earthquake ground motion and on the

dam-water interaction model used. In this article, dam-water interaction during earthquake

is modelled using added-mass concept which was first formulated by Westergaard.

Loads Dead loads

The dead load of an arch dam can be calculated form the volume of the arch dam timesthe specific weight of concrete. To gain the maximum value of the dead load, the weight of all

appurtenances must be added too.

Dead load of an arch dam



Hydrostatic Pressure

The hydrostatic pressure, which is applied to the arch dam, can be calculated from the

hydrostatic pressure distribution. As the distribution does only depend on the height z , the

maximum value of hydrostatic pressure occurs at the bottom of the arch dam. Water pressure is

applied in direction perpendicular to the surface and therefore a curved surface causes vertical

and horizontal water pressure.

H ydrostatic pressure of an arch dam

EarthquakeEarthquake caused loads applied to an arch dam depend on the magnitude and the frequency of

the earthquake and the resonant frequency of the dam itself. To analyse earthquake originated

loads, complex dynamic models, processed with Finite Element software, are necessary.

THE CALCULATION OF STRESSES AND DISPLACEMENTS WITH ABAQUS CAE

Abaqus CAE is Finite Element software. Finite Element can be used to calculate the strains and

displacements of loaded structures approximately, by using a numerical calculation method. As

the calculated geometry of the arch dam is imported into Abaqus, several steps must be done

before the analysis of the stresses and displacements. The discretisation of the model and the

definition of the material as well as the setting of the boundary conditions are just a few of them.

As the analysis is done the stresses and displacements can be visualised within the results screen

of the program.



Abaqus CAE user in terf ace

Finite element method (FEM)

The Finite Element Method (FEM) is a key technology in the modeling and simulation of

advanced engineering systems.

The FEM is a numerical method which distributes field variables in the problem domain,

harder to obtain analytically. For instance, it is applied to determine the distribution of some field

variables: the temperature or heat flux in thermal analysis, the electrical charge in electrical

analysis etc. (Liu & Quek, 2003).

The FEM divides the problem domain into several sub domains. The smaller elements

usually have a very simple geometry. A continuous function of an unknown field variable is

approximated using piecewise linear functions in each sub-domain, called an element formed by

nodes. Next principles helped the elements “tied” to one another. This process leads the entire

system can be solved easily to yield the required field variable (Liu & Quek, 2003).

The behavior of a phenomenon in an engineering system depends upon the geometry or

domain of the system, the property of the material or medium, and the boundary, initial and

loading conditions. Normally the geometry or domain can be very complex. Further, the



boundary and initial conditions can also be complicated. Therefore, it is very difficult to solve

the governing differential equation via analytical means. Thus, in practice, most of the problems

are solved using numerical methods. Amongst these, the FEM is the most popular one, due to its

practicality and versatility (Liu & Quek, 2003).

Four steps are included in the procedure of computational modeling by using the FEM

broadly:

Modeling of the geometry

Real structures, components or domains have to be reduced to a manageable geometry, as

generally they are very complex. The geometry is eventually represented by a collection of

elements and the accuracy of representation is controlled by the number of elements used. It is

obvious that more elements we have, the more accurate the solution shall be. Unfortunately,

more elements demand a longer the computational time is required. Hence, the number of the

elements is always being limited, due to constrain on computational hardware and software.

Graphic interfaces are often used to create and manipulate of the geometrical objects, such as

computer aided design (CAD) software which can significantly save time to create the geometry

(Liu & Quek, 2003).

Knowledge, experience and engineering judgment are very important in modeling the geometry

of a system. An example of the having sufficient knowledge in the simplification required by the

mathematical modeling: a plate has three dimensions geometrically. However, the plate theory ofmechanics is represented mathematically only in two dimensions. Hence plate elements will be

used in meshing surfaces. A similar situation can be found in shells. The beam element has to be

used to mesh the lines in models; this is also true for truss structure (Liu & Quek, 2003).

Meshing (discretization)

Mesh generation is very important in the pre-process. Proper theories are needed for

discretizing the governing differential equations based on the discretized domains. The domain

has to be meshed into elements of specific shapes such as triangles and quadrilaterals. During the

mesh process, some information must prepared, such as elements connectivity, due to the later

formation process of the FEM equations.

Based on the mesh generated, a few types of approach are provided to establish the

simultaneous equations. The first is based on energy principles; the second is weighted residual

method. The third approach is based on the Taylor series, which leads to the formation of the



traditional finite difference method (FDM). The fourth approach is based on the control of

conservation laws on each finite element in the domain. The Finite Volume Method (FVM) is

established using this approach. Another approach is integral representation, used in some mesh

free methods.

It is so far shown that the first two are often used for solids and structures, and the others often

used for fluid flow simulation (Liu, 2002).

Specification of material property

The engineering system always consists of several materials. For each individual elementor a group of elements, materials properties must be defined. Different sets of material properties

are required in different simulated phenomena. For example , Young’s modulus and Poisson’s

ration are required in the stress analysis of solids and structures, whereas the thermal

conductivity coefficient will be required in a thermal analysis (Liu & Quek, 2003).

Specification of boundary, initial and loading conditions

Boundary, initial and loading conditions are crucial parts in solving the simulation.

Again, to accurately simulate these conditions for actual engineering systems requires

experience, knowledge and proper engineering judgments. They are different from problem to

problem and usually done easily by using commercial pre-processors (Liu & Quek, 2003).



MODELLING AND CALCULATION WITH ABAQUS CAE

a. AN I NTRODUCTION I NTO THE CALCULATI ON WITH ABAQUS CAE

This part of this master thesis is concerned with the calculation of the stresses anddisplacements of the arch dam, created with the Arch Dam Design – Input Manager. As the

model is imported ABAQUS CAE, some steps are necessary before starting the investigation of

the displacements and stresses. Beside the definition of surfaces, which simplify the evaluation

of the results, the discretisation of the model, the adding of loads and materials and the setting of

boundary conditions, have to be done. The sub chapters from below would detail the procedure

to complete to model until starting the calculation.

b. DEF I NE SURFA CES

Surfaces and sets are created to simplify the investigation of the calculation results of the

structural analysis. On the one hand, the surfaces of the partitions are used to display the surface

only, when evaluate the results and on the other hand, the definition of the surface of the

abutment and the upstream and downstream side is used to facilitate the assigning of loads or

boundary conditions.

The sur faces and sets of t he arch dam



c. CREATE A M ESH – MODEL DI SCRETI SATI ON

Coarse mesh is used in this Benchmark.

As the structural analysis of the arch dam considers static loads only, the number of elements

is appropriate regarding the calculation time. When performing an analysis considering dynamic

loads like earthquake accelerations the number of elements should be reduced significantly.

Arch Dam



312 quadratic hexahedral elements of type C3D20R (ABAQUS CAE)

44 quadratic wedge elements of type C3D15 (ABAQUS CAE)

Foundation



quadratic hexahedral elements of type C3D20R (ABAQUS CAE)

Reservoir (used in extract frequency step)



quadratic hexahedral elements of type AC3D20 : A 20-node quadratic acoustic brick.

(ABAQUS CAE)

Th e mesh of the calcul ation model



d. SET M ATERIA L AND SECTI ON PARAM ETERS

After the discretisation of the model, the material and section parameters have to be set for

the arch dam and the foundation. Beside the density, which is necessary to calculate the dead

weight of the parts, the Young’s Modulus and the Poisson’s Ratio have to be de termined to set

the structural behaviour of the different parts. As these material parameters are chosen, the

section parameters have to be assigned to the different parts.

d.1. CONCRET E

The material, which is assigned to the arch dam, is concrete. The density of the taken

concrete is 2400kg/m³ and the Young’ Modulus is 2 7000 MPa . The chosen Poisson’s Ratio is

0.167. The chosen section category is solid and the type is homogenous.

d.2. ROCK

The material, which is assigned to the foundation, is rock, with a density of 0 kg/m³, a

Young’ Modulus of 2 5000 MPa and a chosen Poisson’s Ratio of 0.2. Additionally the chosen

section category is solid and the type is homogenous.

d.3. WATER

The material, which is assigned to the water, is water, with a density of 1000 kg/m³, a

Bulk Modulus of 2200 MPa. Additionally the chosen section category is solid and the type is

homogenous.

e. CREATE L OADS

The loads, which are assigned to the arch dam to investigate the structural behaviour are the

dead weight, the water pressure and three different transient acceleration (a max =0.1g), X-

direction, Y-direction, Z-direction.

e.1. DEA D WEI GHT

The dead weight is assigned to the whole arch dam and created by using the mass of the

arch dam and the acceleration of ‐9,81 m/s in the z direction. To simplify the modelling and

calculation, the deadweight is assigned monolithic.



The dead weigh t of t he arch dam

e.2. WATER PRE SSURE

The Water pressure is assigned to the upstream surface of the arch dam only. To set the

water pressure the distribution hydrostatic and the magnitude 2158000Pa, which can be

calculated from the dam height and the specific weight of water, has to be chosen. Further the

zero pressure height, which is the height at the crest elevation and the reference pressure height,

which is the height at the base elevation of the dam.

The hydrostatic di str ibuti on of the water pressur e



e.3. SEI SM I C LOAD S

The three components of the ground accelerations (X-, Y-, Z- direction) during the earthquake

were used as an input to linear finite element acceleration time history method respectively. The

earthquake was 0.1g and the duration of the earthquake was 20 seconds.

For the dynamic analysis the damping type needs to be specified. The damping ratio which

determines the behavior of the system was set to 0.02.

Due to the ability of taking small time intervals of the earthquake duration in the analysis, the

finite element acceleration time history method was used to determine the linear dynamic

responses of the gravity arch dam in the attempt of giving more accurate information. In this

study the time interval was used to be 0.01 second.

For seismic analysis, three stochastically independent acceleration time histories are used

according to the data provided by the formulator. These accelerations are scaled according to the peak ground accelerations of these components are:

Downstream-upstream (X- direction) = 0.1 g

Vertically upwards (Y- direction) = 0.1 g

Cross valley direction (Z- direction) = 0.1 g

For the seismic analysis direct time history approach is used and hydrodynamic pressure is

computed by Westergaard’s added mass method. According to westergaard, the hydrodynamic

pressures that the water exerts on the dam during an earthquake are the same as if a certain body

of water moves back and forth with the dam whiles the remainder of the reservoir is left inactive.

The added mass per unit area of the upstream wall is given in approximate form by the

expression

where ρ w is the density of water.

It should be mentioned that in calculating the interface forces between dam and wedge, only

the stiffness of foundation is considered and density of it is taken as zero. In other words amassless foundation is considered.



f . SET B OUNDARY CONDI TI ONS BCS AND CONSTRAI NTS

The last step before starting the calculation of the stresses and displacements is the definition

of the boundary conditions and constraints. The boundary conditions have to be set for the edges

of the whole model, whereas the constraints describe the conditions between two parts within the

model. The boundary conditions are set by locking the displacements of the direction orthogonal

to the surface of each edge and the constraints are set by determining the abutment surface

between the arch dam and the foundation to be tied.

The foundation boundaries are fixed everywhere except along the foundation surface at the

dam crest elevation.

Documents

Abaqus Fluid Structure Interaction Graz-Austria