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December 2012
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Dynamic analysis of the Baozhusi dam using FEM
S UMMARY
The core issue of this thesis is a model analysis of the seismic activity of
the Baozhusi dam, exposed to the 8.0 Ms (Mercalli intensity scale)
earthquake in 2008. The intensity of the Wenchuan earthquake surpassed
the design level of the dam however, except minor injuries; the Baozhusi
dam was not destructively damaged.
The horizontal component of the ground motion predominate the
dynamic response of the dam, it is considered that the horizontal
component of the ground motion crossed the dam at its axis therefore
diminishing the seismic shockwaves.
The dynamical behavior of the dam has been modeled and analyzed by
the 2- dimensional finite element method with the help of ABAQUS
software package in order to ensure the safe operation of the dam. The
seismic response is evaluated for Wenchuan earthquake ground
acceleration data using finite element acceleration time history method.
This dynamical analysis has calculated the time history of the main
principal stresses and displacement in the dam section, and their
maximum values in the earthquake duration have been compared and
investigated.
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Dynamic analysis of the Baozhusi dam using FEM
S AMMARY IN SWEDISH
I denna avhandling genomförs en modal analys av inverkan av seismisk
akitvitet på Baozhuisdammen som 2008 drabbades av en jordbävning
som uppmätte 8,0 påMercalliskalan. Dammen fick inga allvarliga skador
trots att intensiteten i jordbävningen överskred den nivåsom dammen är
dimensionerad för.
Markrörelsens horrisontella komponent var riktad parallellt med
dammaxeln vilket medförde att de sesmiska vågorna i dammen inte
blev såomfattande.
Dammens dynamiska beteende har modellerats och analyserats med den
två-dimensionella finitaelementmetoden med hjälp av ABAQUS
mjukvarupaket. Den sesmiska responsen har evaluerats med hjälp av
tidshistorisk finitaelementmetod med utgångspunkt från jordbävningens
accelerationsdata.
Med hjälp av dynamisk analys har beräkningar av de påkänningar och
förskjutningar av dammsektionen som orsakats av jordbävningen
utförts, de maximala värdenna har identifierats och redovisas.
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Dynamic analysis of the Baozhusi dam using FEM
S UMMARY IN C HINESE
地震的发生会对基础设施如大坝的安全造成影响,大型水电站的
安全又与人类的生产生活息息相关。随着国家社会对水电站安全
的关注程度日益提高,必须对震后大坝进行安全复核分析。本文
是针对宝珠寺水电站进行汶川地震后的安全复核研究。
为了确保宝珠寺水电站汶川地震震后的安全使用,本文运用
ABAQUS 软件对宝珠寺大坝进行静动加载二维有限元分析。通过对
大坝主应力和位移的研究,证明大坝处于安全状态。
本文还针对汶川地震强度超过大坝设计强度大坝依然安全稳定进
行讨论,给出地震运动的水平分量沿大坝轴线因此一定程度削弱
了地震波的影响的结论。
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Dynamic analysis of the Baozhusi dam using FEM
A CKNOWLEDGMENTS
The project reported in this master degree thesis was carried out at the
Department of Hydraulic Engineering of Tsinghua University Beijing
from March to June 2012.
Our thoughts of appreciation go to Professor Jin Feng for inviting us to
the Hydraulic Department of Engineering at Tsinghua University, for his
patience and his passion for our topic of interest. We would also like to
devote our thanks to Miss Guan Ying for all the help offered during our
stay.
We would like to bring our thanks to Dr. James Yang from Vattenfall
R&D/KTH for making the trip possible and for all necessary
arrangements.
We are grateful to our examinator, Professor Hans Bergh from the Land
and Water Resources Engineering Department within the Royal Institute
of Technology (KTH) Sweden.
Our thanks go also to the Royal Institute of Technology (KTH) that
helped achieving the present project.
The present project, managed by James Yang, was funded by Elforsk AB
within the frame of dam safety, with Mr. Cristian Andersson as the
program director. Some funding was even obtained from KTH that
facilitated the accomplishment of the project.
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Dynamic analysis of the Baozhusi dam using FEM
T ABLE OF C ONTENTS
Summary ........................................................................................................................... iii
Sammary in swedish ...........................................................................................................v
Summary in Chinese........................................................................................................ vii
Acknowledgments ............................................................................................................ ix
Table of Contents ............................................................................................................. xi
Abstract .............................................................................................................................. 1
Introduction ....................................................................................................................... 1
Hydropower condition in China.................................................................................. 1
Baozhusi hydropower station ...................................................................................... 3
WenChuan earthquake................................................................................................. 3
Objectives and targets of the study ............................................................................. 4
Dam types ..................................................................................................................... 5
Dam parts and dam terminology ................................................................................ 6
Concrete gravity dams.................................................................................................. 6
Forces acting on gravity dams ..................................................................................... 7
Methodology ...................................................................................................................... 9
Gravity dams stability criteria ...................................................................................... 9
Finite element method (FEM) .................................................................................... 9
ABAQUS software ...................................................................................................... 11
Modeling of Baozhusi dam and material properties ............................................... 12
Load conditions and assumptions ............................................................................ 14
Self-weight, hydrostatic and silt pressure ............................................................................... 14
Up-lift pressure ..................................................................................................................... 14
Hydrodynamic pressure ........................................................................................................ 14
Seismic load .......................................................................................................................... 15
Dynamic methods of stress- strain analysis ............................................................. 15
Results .............................................................................................................................. 16
Discussion ........................................................................................................................ 19
Conclusion ....................................................................................................................... 19
References ........................................................................................................................ 21
Other References ............................................................................................................. 22
Appendix ........................................................................................................................... II
Appendix I -Equations................................................................................................ II
Equation of motion ................................................................................................................ II
Normal stresses ...................................................................................................................... II
Principal stresses ................................................................................................................... III
Reduced gravity formula ....................................................................................................... III
Silt pressure equation ............................................................................................................ IV
Westergaard hydrodynamic equation ..................................................................................... IV
Appendix II-Learning (ABAQUS) software ............................................................. IV
Equations used in the analytical solution ............................................................................... IV
Appendix III-Input file ............................................................................................... V
Part of static input file.............................................................................................................V
Part of static, dynamic integrated analysis input file ............................................................... XI
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Dynamic analysis of the Baozhusi dam using FEM
A BSTRACT
High magnitude earthquakes have devastating effects that leads to severe human and
material losses; when affecting concrete gravity dams, seisms devastate the
surrounding habitat through sudden release of reservoir. Dam safety is therefore
a significant issue to be accounted in order to prevent the failure of dams located in
seismic regions.
The Baozhusi dam, the case study of this thesis, was exposed to 8.0 Ms (at the
Mercalli scale) Wenchuan earthquake 2008 with intensity of (0.148 g) at the dam site.
The earthquake intensity exceeded the design level of the dam (0.1 g); yet, the
Baozhusi dam was not severely damaged as showed by tests.
The present study case is a modeling and analyzing of the dynamical behavior of the
Baozhusi dam during the earthquake duration.
The results show that the horizontal component of the ground motion predominate
the dynamic response of the dam. It is confirmed that the horizontal component of
the ground motion crossed the dam at its axis and therefore minimizing the damages
on the concrete gravity dam.
I NTRODUCTION
Hydropower condition in China
Water energy has been a force that humans tried to make use of since
the dawns of humanity. Parallels can be drawn between the technological
evolution of humanity and the use of water energy. If in ancient times,
water energy was used to grind flour and irrigate in time its use has
progressed to operating watermills, sawmills, cranes and domestic lifts,
to undertake the flood control, shipping, water mining etc.
The water is the cheapest and most at hands energy in nature, it is the
leading renewable and sustainable energy source in the world (Martinot
& Sawin, 2009).
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Dynamic analysis of the Baozhusi dam using FEM
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Fig. 4 Cross section of the non overflow monolith of the Baozhusi dam.
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Fig. 6 Fracture of the concrete near contraction joint at the top of Baozhusi dam after
Wenchuan Earthquake.
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Dynamic analysis of the Baozhusi dam using FEM
resists the forces acting on the dam (Fig. 8). Concrete gravity dams are
especially suited across gorges with very steep side slopes and where
good foundations are available. The particularity of this dam is that it
requires a lot of construction materials and therefore it may be costly.
It is still cheaper than earth dams if suitable soils are not available for the
construction of earth dams (USACE, 1995).
Forces acting on gravity dams
Different forces acting on gravity dams are (Fig. 8):
Self-weight of the dam
Water pressure
Uplift pressure
Silt pressure
Wave pressure
Ice pressure
Temperatures
Earthquake
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M ETHODOLOGY
Gravity dams stability criteria
The basic stability requirements for a gravity dam for all conditions of
loading are (Bergh, 2010):
Stability against overturning: it may occur if moment around the dam
toe of the stabilizing forces (mainly the self-weight of the dam) is
larger than the moment of the overturning forces (hydrostatic
pressure, uplift pressure etc.).
The stability can be estimated through dividing the stabilizing moment
with the overturning moment at any point in the dam body. The result
should be larger than the magnitude of the safety factor that is between
1.3 - 1.5.
Stability against sliding: the dam should be safe against sliding on any
horizontal or near-horizontal plane within the structure at the base or
surfaces in the foundation. This is expressed as ∑ H< ∑ v tanψ.
Overstressing: the allowable stresses in the concrete and in the
foundation material shall not be exceeded.
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).
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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 element or 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).
ABAQUS software
Realistically, up to thousands, and even several millions of elements and
nodes are included in the FEM problems, therefore they are usually
solved by using commercially available software packages. A large
number of commercial software packages (Table. 1) are available for
solving a wide range of problems which might be static, dynamic, linear
and nonlinear. Most of them use the finite element method or used in
combination with other methods (Liu & Quek, 2003).
The ABAQUS program applied in this project was developed by Hibbitt,
Karlsson & Sorenson.Inc. It is an indispensable software package due to
its abilities of dealing with nonlinear problems. There are several
modules in the ABAQUS finite element package: ABAQUS/Explicit
(mainly used for explicit dynamic analysis); ABAQUS/CAE is an
interactive preprocessor that can be used to create finite element models
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Table 4 Maximum and minimum displacement and principle stresses from static
analysis
Maximum Minimum
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Dynamic analysis of the Baozhusi dam using FEM
Seismic load
The horizontal and vertical components of the ground accelerations
during the Wenchuan earthquake were used as an input to linear finite
element acceleration time history method (Fig. 10, 11) respectively. The
earthquake was 0.148g and the duration of the earthquake was
158.2 seconds.
The amplitude of the vertical component was taken as two thirds of the
gravity acceleration according to Chinese specification for seismic design
of hydraulic structures.
For the dynamic analysis the damping type needs to be specified. In this
study Rayleigh damping has been used, where the damping ratio is larger
than 10% of the critical damping of the system. Rayleigh damping has
two factors: mass damping factor and stiffness damping factor (Table 3).
The damping ratio which determines the behavior of the system was set
to 0.05.
Dynamic methods of stress- strain analysis
The dam structure is under stress when subjected to loads or forces. In
general, the stresses are not uniform and lead to strains, which can be
observed as either deformation or displacement (Liu & Quek, 2003).
Solid mechanics and structural mechanics deal with the relationships
between stresses and strains, displacements and forces, stress (strains)
and forces for given boundary conditions of solids and structures. These
relationships are vital to the modeling, simulating and designing of
structural systems. Thus, the mechanics knowledge was reviewed and
been used in the comparison between analytical solution and simulated
solution (Apendix II) (Table. 1A) in the beam example.
The aim of the dynamic analysis is to determine the responses of the
structure concentrating on the maximum tension and compression
stresses and the displacements, based on the characteristic of the
structure and the nature of the earthquake. Dynamic methods usually
apply the model technique which is based on some simplified
assumptions i.e. the responses can be computed independently in each
natural mode of vibration followed by a combination of these responses
in order to obtain the total response (Chopra, 1987).
Two methods are recommended for the analysis of the stresses in gravity
dams by using the finite element method: finite element response
spectrum method and finite element acceleration time history method.
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
Baozhusi gravity dam in the attempt of giving more accurate
information. In this study the time interval was used to be 0.0005
second. The 2-dimensional finite element method it is generally regarded
as an appropriate analysis method to gravity dams with height of more
than 100 meters, therefore used in the present study (USACE, 2003).
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R ESULTS
Two analyses were applied to the dam, static analysis where only static
forces have been taken into account (Table. 4) and static dynamic
integrated analysis where static forces plus the hydrodynamic pressure
and seismic load are considered (Table. 5). The statics analysis can be
taken as a special case of dynamics where the static equations can be
derived by simply dropping out the dynamic terms in general, dynamic
equations (Liu & Quek, 2003), the following part only describes the
static, dynamic integrated case.
The contour lines of the minimum and maximum principal stresses due
to Wenchuan earthquake including the initial static loading represent the
distribution of the peak values of the maximum principal stress at each
point within the section. The positive values represent the tensile
stresses, while the negative values represent the compression stresses
(Fig. 12, 13 and 14).
According to the static dynamic integrated analysis, the main part of the
dam was subjected to compression stresses (minimum principal stress)
yet the maximum compression stress was 7.211(Mpa) located near to the
break point of the downstream slope (Fig. 12).
The highest value of the tensile stress (maximum principal stress) was
4.329 (Mpa) occurred at the heel of the dam (Fig. 13).
Fig. 14 Maximum tension stresses after eliminating the stresses with a radius 5% of
the dam height at the dam heel (Mpa).
(Note: The figure is distorted of layout reasons.)
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Dynamic analysis of the Baozhusi dam using FEM
D ISCUSSION
The results of the linear static dynamic integrated analysis showed that
the main part of the dam is subjected to compression stresses and its
highest value was located near to the break point of the downstream
slope. The maximum compression stress was 7.211 (Mpa) (Fig. 12)
(Table. 5) and does not exceed the allowable compressive strength of the
selected concrete which is 13.1 (Mpa) (Table. 3).
The results of the linear static dynamic integrated analysis show that the
maximum tension stress was 4.329 (Mpa) at the heel of the dam (Fig.13).
It is approximately three times the allowable tensile strength for the
selected concrete - 1.4 (Mpa) (Table. 3). Since the tension that occurs in
the vicinity of the dam foundation interface is largely fictitious
(Léger & Katsouli, 1989). Eliminating the maximum principal stresses
from the region at the dam heel by radius of 5% of the dam height has
been employed in order to get more accurate results (Feng, 2012).
After removing the maximum principal stresses at the heel of the dam
with radius of 5% of the dam height, the response results showed that
the maximum tension stress was 0.392 (Mpa) (Fig. 14) which did not
exceed the allowable tensile strength of the selected concrete.
The displacement result obtained through this model may not properly
represent the real situation of the dam. It is hard to define the initial
displacement of the dam before applying the loads. These results may be
affected by the assumptions of the model, for instance the depth of the
foundation and its material properties.
C ONCLUSION
Based on the intensity of the Wenchuan earthquake (0.148g) at the dam
site, which exceeded the design intensity of the Baozhusi gravity dam
(0.1g) and finite element acceleration time history method, the results of
the responses of the dynamic analysis of the 2D FEM model are
compatible with the real situation of the Baozhusi dam therefore the
objectives of this study have been achieved. Since no significant damages
have been reported and the dam resisted to the shock of the earthquake,
the results demonstrated that the vertical component of the earthquake
motion had relatively weaker excitation to the dam than the horizontal
component that predominates the dynamic response of the dam.
Therefore it is believed that the horizontal component of the ground
motion crossed the dam along the dam axis. It is probably the reason
that avoided the severe damaging of the dam (Feng, 2012).
With the combination of the seismic load, self-weight and water
pressure, it is normal for the dam heel and dam toe regions to have high
tensile and high compression stresses. The effect of the mesh in the
finite element method makes the dam heel and toe areas to have
maximum value of the stresses, thus more attention needs to be paid to
these regions.
In this study the mass less foundation model was applied in the finite
element simulation. In fact the infinite dam foundation radiation
damping effect will, to some extent, weaken the seismic energy that
creates the dynamic response of the structure decreased. This is
beneficial to the dam seismic safety (Feng, 2012).
The slight cracking of the dam contraction joints that occurred during
the earthquake can release high tensile stress that effectively mitigates the
destruction of the ground movement on the dam structure (Feng, 2012).
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The seismic load damages started from its upper part which has a thinner
section- the break slope. As the earthquake develops the cracks will
extend to the internal dam body, and will result in bigger cracks
throughout the upstream and the downstream of the dam.
Anchor cables or other protection means can also be used on the dam
face for preventing cracks from expanding.
Further study should be applied, due to the numerical simulation in this
project did not consider the dam seismic response caused by the infinite
dam foundation radiation damping effect.
In a practical analysis more load cases should be performed, such as
analyses based on different water level in the reservoir, accordingly
further research is recommended to extend the study case of Baozhusi
concrete gravity dam under Wenchuan earthquake.
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Dynamic analysis of the Baozhusi dam using FEM
R EFERENCES
Bergh H. 2010. Hydraulic Engineering Course Compendium (AE2609).
Land and Water Resources Engineering, KTH, Stockholm.
BP. 2012. The BP Statistical Review of World Energy 2012. BP plc.
(London). 45p.
China Water. 2008. Hydraulic Engineering in the Earthquake Area:
BaoZhuSi Hydropower Station. China and the Netherlands Water
Resource Management Innovation Seminar.
Chopra AK. 1987. Simplified Earthquake Analysis of Concrete Gravity
Dams. Journal of Structural Engineering New York. 113: 1688-1708.
Clough RW, Penzien J. 1995. Dynamic of Structures. Berkeley, USA.
16p.
Fatih B, Maria A. 1999. World Energy Prospects to 2020. Elsevier
Science Ltd. 24:905-918.
FERC (Federal Energy Regulatory Commission). 1999. Engineering
Guidelines for the Evaluation of the Hydropower Projects.
Washington (DC), USA: Federal Energy Regulatory Commission
Division of Dam Safety and Inspections. 104p.
George EP, John PC. 1989. Guidelines for Design of Dams. New York
State Department of Environmental Conservation. 32p.
Gosschalk EM. 2002. Reservoir Engineering Guidelines for Practice.
London: Thomas Telford. 327p
Hibbitt D, Karlsson B, Sorensen P. 2009 a. Abaqus User Manual.
Hibbitt, Karlsson & Sorensen, Incorporated.
Hibbitt D, Karlsson B, Sorensen P. 2009 b. ABAQUS 6.9/CAE User's
Manual. Hibbitt, Karlsson & Sorensen, Incorporated.
Liang JQ. 2010. The Impact of China’s Three Gorges Project: An
Evaluation of Its Effect on Energy Substitution and Carbon Dioxide
Reduction. American University. 27p.
Liu GR. 2002. A Conbined Finite Element/ Strip Element Method for
Analyzing Elastic Wave Scattering by Cracks and Inclusions in
Laminates. Computational Mechanics. 28:76-81.
Liu GR, Quek SS. 2003. The Finite Element Method: A Pratical Course.
Elsevier Science Ltd. 348p.
Li W, Zhang YQ, Wang WZ, Shi ZB, Shen JH, Li M, Xin Y. 2009.
Symptoms of Posttraumatic Stress Disorder Among Adult Survivors
Three Months after the Sichuan Earthquake in China. Journal of
Traumatic Stress. 22:445-450.
Léger P, Katsouli M. 1989. Seismic Stability of Concrete Gravity Dams.
Earthquake Engieering & Structural Dynamics. 18: 889-902.
Martinot E, Sawin JL. 2009. Renewables Global Status Report 2009
Updated.REN21 (Paris). 31p.
Shi MG, Mou HL, Zhou, MX. 2010. BaoZhuSi Gravity Dam Seismic
Review (in Chinese). Tsinghua University.
The Economist Report. 2003. Damming Evidence. The Economist
Newspaper Limited. 368:9-11.
Unicef. 2008. China- Hydropower As the Right Solution. United Nations
Chindren’s Fund.
USACE (US Army Corps of Engineer). 1995. Engineering and Design,
Gravity Dams Design. United States Army Corps of Engineer. 10p.
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O THER R EFERENC ES
Feng J. 2012. Professor & Chair at the Department of Hydraulic
Engineering, Tsinghua University, Beijing.
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A PPENDIX
Appendix I -Equations
Equation of motion
The dynamic equilibrium equation is formulated from the equilibrium of
the effective forces associated with each of its degree of freedom
(Clough & Penzien, 1995) and can be expressed as:
MÜ (t) +I-P=0
Where:
M: mass matrix of the structure
Ü (t): acceleration vector of the structure
I: internal force of the structure
P: applied external load vector
I=KU (t) +CÙ (t)
Where:
K: stiffness matrix of the structure.
U (t): nodal displacement
C: damping matrix for the structure
Ù (t): velocity of the structure
So the equation of motion can be written as (USACE, 2003):
MÜ (t) + KU (t) + CÙ (t) = P (t)
Normal stresses
The sum of the direct stress and the bending stress at any point on the
base of the dam gives the normal stress that can be calculated according
to this formula:
∑
* +
Where:
: Normal stress
∑ : Sum of the vertical forces
: Width of the dam base
: Eccentricity of the resultant force
The normal stress at the toe of the dam will be calculated by using the
positive sign in the above formula while the normal stress at the heel will
be calculated by using the negative sign.
(σMax) (UMax) ( )
(σMax)
Errors %
Errors %
Errors %
(UMax) ( )
[Mpa] [mm] [Mpa]
Model [Mpa] [mm] [Mpa]
Analytic Analytic Analytic
Simulated Simulated simulated
solution solution solution
Coarse
108 118 9.2 16.19 16.58 2.4 9 8.17 9.2
mesh
Dens
108 101 6.4 16.19 16.5 1.9 9 9.34 3.7
mesh
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When the eccentricity of the resultant force (e) is less than (b/6) the
compression stress occurs in both toe and heel of the dam, when it is
equal to (b/6), the maximum compression stress occurs at the toe of the
dam and it is equal to zero at the heel of the dam.
When the eccentricity of the resultant force (e) is larger than (b/6), the
negative compression stress or the tensile stress occurs at the heel of the
dam which is not allowed to the safety of the dam (Bergh, 2010).
Principal stresses
Principal stresses are the maximum and minimum stresses that occur at
any point within the dam which can be calculated according to this
formula:
[ ]
√* +
Where:
: Maximum and minimum principal stresses
: Normal stress on the horizontal plane
Normal stress on the vertical plane
: Shear stress
The shear stress is equal to zero at the upstream and downstream face of
the dam, therefore the upstream and downstream faces of the dam are
planes principal stresses.
The principal stresses at both upstream and downstream faces can be
computed by the following equations:
( )
( )
Where:
: Maximum principal stress at the upstream face of the dam
: Maximum principal stress at the downstream face of the dam
: Normal stress
: Intensity of hydrostatic pressure
: Intensity of hydrodynamic pressure due to earthquake
Reduced gravity formula
: Reduced gravity
: Water density
: Concrete density
Normal acceleration
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Where:
: Hydrodynamic pressure of one node on the dam face
: Water density
: Total depth of water acting on the structure
: Height of the node above the dam base
: Dam face nodal acceleration
Appendix II-Learning (ABAQUS) software
In order to familiarize oneself with the (ABAQUS) software and its
different features, begin with modeling a beam fixed at one end
(cantilever beam) with uniformly distributed load (Fig. 1A). After
computing the stresses and displacements in the models with different
mesh size, start to analyze the accuracy of the results that depend on the
number and the shape of the element in the model. Compare the results
with the analytical solutions (Table. 1A).
Equations used in the analytical solution
Where:
Maximum bending moment
= load per unit length
= span length of the bending member
IV
Dynamic analysis of the Baozhusi dam using FEM
Where:
= Maximum stress
= Distance from neutral axis
= Moment of inertia
=
= Beam width
= Beam height
= Maximum displacement
= Elastic modulus
Where:
Maximum shear stress
= shear force
= cross section area of the beam
Appendix III-Input file
These are parts of our modeling input file which include static analysis
and dynamic analysis input files. Parts of listing of nodes and elements
were removed due to the fact that they are more than 5000 raw.
Necessary explanation is only given to the static input file, as the static
and dynamic input file have similar syntax rules.
Dynamic analysis is starting with the part of added mass set representing
the elements that have been set to hydrodynamic pressure, followed by
material properties, boundary conditions, static steps analysis and
dynamic steps analysis. All the rows that have the symbol (*) are
considered during the model run, while the rows that have the symbol
(**) are used for describing and commenting on the code- they are not
included during the computation.
Part of static input file
**
*NODE
1, -494.763, 595. Nodal cards
2, -514.263, 595. It defines the coordinates of
3, -496.263, 595. the nodes in the model. The
4, -497.763, 595. first entry being the node ID
while the second and third
5, -499.263, 595.
entries are the x and y
** coordinates of the position
*ELEMENT, TYPE=CPS4 of the node, respectively.
1, 43, 57, 42, 32
2, 44, 58, 57, 43
3, 45, 59, 58, 44
4, 46, 60, 59, 45
5, 47, 61, 60, 46
**
** base
V
Zaid Alsuleimanagha & Jing Liang TRITA-LWR Degree Project 12:43
**
*ELSET, ELSET=BASE, GENERATE
1878, 2477, 1
Element (connectivity) card
**
It defines the element type
** damlayer and what nodes make up the
** element. CPS4 represents
*ELSET, ELSET=DAMLAYER that it is a plane stress, four
189, 199, 1 nodal, quadrilateral elements.
There are many other
1112, 1147, 1 element types in the
** ABAQUS element library.
** baselayer For example, if we were to
** use a plane strain element,
the element type would be
*ELSET, ELSET=BASELAYER
CPE4. The order of the
1402, 1424, 1 nodes for all elements must
1581, 1607, 1 be consistent and
** counterclockwise.
** add-concret
**
*ELSET, ELSET=ADD-CONCRET, GENERATE
1311, 1401, 1
**
** dam
**
*ELSET, ELSET=DAM, GENERATE
1, 1310, 1
1425, 1580, 1
1622, 1877, 1
**
** cutoff
**
*ELSET, ELSET=CUTOFF, GENERATE
1608, 1621, 1 The “ELSET= DAM”
** statement is simply for
** R200 naming this set of
elements so that it can be
**
referenced when defining
*ELSET, ELSET=R200, GENERATE the material properties. In
16, 33, 1 the subsequent data entry,
42, 47, 1 the first entry is from
which element ID this
54, 61, 1
element set applied, and
75, 83, 1 the following entry is end
91, 100, 1 up with which element
** planestress ID.
**
*ELSET, ELSET=PLANESTRESS, GENERATE
1, 1607, 1
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Dynamic analysis of the Baozhusi dam using FEM
1622, 1877, 1
**
** planestrain
**
*ELSET, ELSET=PLANESTRAIN, GENERATE
1608, 1621, 1
1878, 2477, 1
**
** uplift
**
*ELSET, ELSET=UPLIFT, GENERATE
24, 33, 1 Node sets
199, 199, 1 It sets of nodes defended to be
205, 208, 1 used for referencing when
264, 303, 1 defining boundary and loading
conditions. For example, the
363, 398, 1 nodes 2033, 2042, 2043 etc. are
** grouped up as a set labeled
*NSET, NSET=boundary_up “boundary_up”.
2033,2042,2043,2044,2045,2046,2047,2048,2049
**
*NSET, NSET=boundary_down
1997,2050,2069,2070,2071,2072,2073,2074
**
**
*NSET, NSET=boundary_bottom
2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,
2061,2062,2063,2064,2065,2066,2067,2068,2042,2050
**
*ELSET, ELSET=HYDRO_UP
199, 1147
*ELSET, ELSET=HYDRO_UP_1, GENERATE
24, 32, 1
264, 288, 1
289, 299, 1
1185, 1193, 1
*ELSET, ELSET=HYDRO_UP_2
33, 205, 300, 1148, 1194
*ELSET, ELSET=SAND
205, 300, 1148, 1194
*ELSET, ELSET=SAND_1
1147
*ELSET, ELSET=SAND_2, GENERATE
289, 299, 1
1185, 1193, 1
*Surface, type=ELEMENT, name=hydro_up
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Zaid Alsuleimanagha & Jing Liang TRITA-LWR Degree Project 12:43
HYDRO_UP, S2
HYDRO_UP_1, S4
HYDRO_UP_2, S3
*Surface, type=ELEMENT, name=sand
SAND, S3
SAND_1, S2
SAND_2, S4
**
**------------------------------------------------------------------------
**Section
*Solid Section, ELSET=BASE, material=rocko2-2-2
1., Property cards
*Solid Section, ELSET=R150, material=r150 It defines
1., properties to the
elements of set
*Solid Section, ELSET=R200, material=r200 ”r150”. It will
1., have the material
*Solid Section, ELSET=CUTOFF, material=r150 properties defined
1., under ” r150”.
*Solid Section, ELSET=ADD-CONCRET, material=r150
1.,
*Solid Section, ELSET=BASELAYER, material=baselayer
1.,
*Solid Section, ELSET=DAMLAYER, material=damlayer
1.,
**---------------------------------------------------------------------------
**Material
Material cards
*Material, name=r150
It defines material properties under
*Density
the name “r150 etc.” Density, elastic
2400., properties are defined.
*Elastic
2.15e10, 0.167
*Material, name=r200
*Density
2400.,
*Elastic
2.50e10, 0.167
*Material, name=rocko2-2-2
*Density
2650.,
*Elastic
2.00e10, 0.18
*Material, name=baselayer
*Density
2400.,
*Elastic
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Dynamic analysis of the Baozhusi dam using FEM
2.15e10, 0.167
Boundary Condition cards
*Material, name=damlayer
It defines boundary conditions. For
*Density example, the first one
2400., labeled”boundary_bottom” represents
*Elastic that nodes belonging to the set
“boundary_bottom” have its “1” and
2.15e10, 0.167
“2” directions constrained.
**--------------------------------
** BOUNDARY CONDITIONS
**
*Boundary
boundary_bottom, 1, 2
boundary_down, 1, 1
boundary_up, 1, 1
**-------------------------------------------------------------------------------
**INITIAL STRESS
*include,input=22#part-initial-geo.inp
**
Control card
*STEP,name=GEOSTATIC It indicates the analysis step. In this
*GEOSTATIC case it is a “Geostatic” analysis.
1.,1.
*CONTROLS, ANALYSIS=DISCONTINUOUS
*Dload
base, GRAV, 9.81, 0.,-1
** OUTPUT REQUESTS
*Output, field
*Element Output
S,PEEQ
*node output
U
**
*End Step
** ----------------------------------------------------------------
** STEP: Gravity
**
*Step, name=Gravity,inc=10000
*Static
0.1, 1., 1e-12, 1.
*CONTROLS, ANALYSIS=DISCONTINUOUS
** LOADS
** Load cards
** Name: Load-1 Type: Gravity “DLOAD” defines Gravity on
*Dload the element set “dam” defined
dam, GRAV, 9.81, 0., -1. earlier.
add-concret, GRAV, 9.81, 0., -1.
**
IX
Zaid Alsuleimanagha & Jing Liang TRITA-LWR Degree Project 12:43
*Output, field
*Element Output
S,PEEQ
*node output
U,COORD
**
*node file
U,COORD
*El file
S
*End Step
** ----------------------------------------------------------------
**
** STEP: hydro-static
**
*Step, name=hydro-static,inc=1000000
*Static
0.05, 1., 1e-12, 1.
*CONTROLS, ANALYSIS=DISCONTINUOUS
**
** LOADS
**
** Name: hydro_up Type: Pressure
*Dsload
HYDRO_UP, HP, 882000, 588, 498
**dam uplift
*Dload
uplift, GRAV, 4.0875, 0.,1.
** Name: sand_pressure Type: Pressure
*Dsload
sand, HP, 148182.46, 533.7, 498
**
** OUTPUT REQUESTS Output control cards
*Output, field It defines the output required. For
example for nodal output, we require
*Element Output the displacement “U”, while for
S,PEEQ element output, we require the stress,
*node output “S”.
U,Coord
**
*node file
U,COORD
*El file
S
*End Step
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Dynamic analysis of the Baozhusi dam using FEM
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Zaid Alsuleimanagha & Jing Liang TRITA-LWR Degree Project 12:43
XII
Dynamic analysis of the Baozhusi dam using FEM
XIII