Análisis tridimensional de presas de arco de concreto armado mediante el método de elementos finitos

International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC 2014)
Three-dimensional Finite Element Analysis for
Concrete Arch Dam of Tianshengqiao
Reservoir
Liu Keding
Hunan Urban Construction College
Xiangtan, China
297298755@qq.com
thickness to height is 0.37.On the left of dam valley appear
stepped. After setting up the gravity pier on the left bank,
it becomes an ideal rectangle valley
Abstract—The stress and strain of dam structure not only
are the index of dam structure rigidity, but also are the basis
of identifying whether the dam structural damage occur.
Static analysis of dam is the foundation of design and
construction of dam, includes the calculation and analysis of
stress and strain of dam. The dam is a higher order
statically indeterminate structure, and the variation of the
temperature obviously affects the stress and displacement of
the structure, therefore, it is very important to consider the
randomness of the temperature change load in the static
analysis of arch dam.Concrete arch dam is a common
hydraulic structures .This article gives the stress and
deformation distribution during construction and operation
which has done the simulation analysis for concrete arch
dam structure of Tianshengqiao Reservoir using the finite
element method. The results show that Concrete Arch Dam
Structure of Banjiang Reservoir satisfy the design
requirements. Research for the design and construction of
concrete singles arch dam provide some reference.
II. CALCULATION MODEL
A
Model Parameters
Concrete arch dam structure of Tianshengqiao
Reservoir uses concrete strength grade of C15, elastic
modulus E1  22 GPa, poisson ratio 1  0.167 [3-4], bulk
density  1  24 kN/m3. The rock of dam is permian Qixia
limestone, medium thickness layer, hard lithology, basic
integrity. Rock trend to upstream, and the karst of dam site
is not developed, no leakage worries. Elastic modulus of
rock is E2  12 GPa, and poisson ratio is  2  0.28 [5].
B
Model Element
Concrete arch dam and bedrock structure model uses
isoparametric block element which has 8-node. The
element is applied to three-dimensional model of the
entity structure, have properties of plasticity, creep,
swelling, stress stiffening, large deformation and large
strain. The element has eight nodes and each node has
three translational degrees of freedom[6-7] .
Keywords-Tianshengqiao reservoir ； Concrete arch
dam； Finite element method； Simulation analysis, Operation
period.
I. ENGINEERING SITUATION
Tianshengqiao Reservoir is located in Laliu River,
Nandan County, Guangxi Zhuang Autonomous Region,
which is a reservoir to generate electricity, combined with
irrigation water resources and hydropower engineering[1].
Hub engineering is composed of dams, left bank gravity
pier, shore spillway, water penstock, power plants, bottom
outlet and other buildings. The total capacity of reservoir
is 4.02 million m3, normal water level 24m, design water
level 28.1m, check flood level 30.3m[2].The dam is
singles concrete arch dam, and the largest dam is
31.6m.The crest arc length is 43.44m, and the crest width
is 1.2m.The dam bottom thickness is 1.7m,and the ratio of
© 2014. The authors - Published by Atlantis Press
C
Model Element
The size of the entire calculation model is that it takes
90m along the direction of the river, 75m the direction of
across the river, 76m the vertical direction. The simulation
range of model is 90m × 75m × 76m(along the river×
across the river×the vertical direction) [8]. The element
division of arch and rock is shown in Fig .1.
1223
Figure 1.
Arch and bedrock FEM division
upstream of the arch crown. We will select a calculation
key point every 5m from the bottom to the top of the dam.
D
Calculation Condition
Considering the mechanical characteristics of arch
structure during operation[9]，the following five cases are
taken into account mainly: case1(structural weight and
normal water level), case2(structural weight, design water
level and tail water level), case3(structural weight,
checking flood level and tail water level).
A Stress Analysis
The circumferential and vertical stress has shown in
table1on the key points of concrete arch dam sectional
crown.
III. ANALYSIS PATH
While doing the finite element analysis of
Tianshengqiao concrete arch dam, the analysis path is
defined on the arch crown cross section and located
TABLE I. EACH CONDITION OF ARCH DAM SECTIONAL CROWN STRESS ON KEY POINTS（MPA）
Location
1
2
3
4
5
6
7
case1
Circumferential
stress
0.386
-0.418
-1.513
-1.229
-0.425
-0.070
0.034
Vertical stress
1.871
0.522
-0.861
-0.405
0.117
0.116
0.001
0.455
-0.095
-1.821
-1.862
-1.057
-0.377
0.067
case2
Circumferential
stress
Vertical stress
1.850
1.089
-0.981
-0.583
-0.092
0.056
0.001
0.559
-0.513
-2.219
-2.226
-1.452
-0.736
-0.137
case3
Circumferential
stress
Vertical stress
2.666
0.969
-0.138
-0.098
-0.058
-0.020
0.005
As can be seen from Table 1, circumferential stress of
arch crown′s upstream face is stress normally, but vertical
stress is tensile stress mainly. Especially at the junction of
the bedrock and dam, tensile stress value is larger. This is
mainly caused by the stress concentration. The larger
tensile stress value can be reduced by the equivalent stress
finite element method [10].
The contour map of the first principal stress and
circumferential stress can be seen in Fig .2 to Fig .7.
1224
BB
B
BB
B
B
B B
B
BB
BB
B
B
BBB B
B
B
B
C
CB B
B
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CBB C
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B B
B
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BB
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B B B
B
BB
B
B
B
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BB
B
C
C
C
D
D
D
B
C C C C C C C C
D
D
D
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D C B
B C
CC D C
DB C B
B
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C
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B FB
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B C C B
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BD
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D
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C B
B
C
C C
D DB CC
E
F B
FCHGDGF
E CEE
BBBDC
B
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
S1
(AVG)
TOP
DMX =.001968
SMN =-306738
SMX =.208E+07
A
=-174324
B
=90506
C
=355336
D
=620165
E
=884995
F
=.115E+07
G
=.141E+07
H
=.168E+07
I
=.194E+07
E GG G
G
H
G
F
F
G G
G
G
F
F
G
F GF
GG
GF
F
G
G
G
GF
F F
F
F F
F F
E
E
E
E
FE
D
DE D D
D
D
D D
D
EFC D C C
C
CC
D
F
DC
GE
C B
B
BB
E B
D
B
GC
F CD B
C
E B
D
CB
C B
G EDC E
F
C
C
C D
D DD
C
D
E EE E
E
D
G
F E
E
F
EF F F E FEE
G F
FF FGF F
GC
E
HG
DE
F G
D
F
EG F
E
H
F
G
H
G
F
H F
G
G H G
B
BB B B C
B
B B
B
C
BC
C
BBBB
B
B BB
B BB
B
B
B
B
B
B
B
B
B
B
C
CB B
C
B
B
C
CC
D
C
D
B D
CB B CD
AA E
E
A
E
A
D
C E
C
C B
B
C
D
B CCD D E B D
B
E
F
C
B
B EFC
DG
B EHCG
F MX
B
G ED A
I
H
B
DFE
C
DC
B
BB
CD
B
C EC
DF C
B
E
D
B B
CC
D D
BC
D
C B
C
B D C
B
E
A
A
C
D
E
FF
G C
HA
E
D
C
EA C
D
BH B
G
F
E
D
G
F
B
B
B
B
B
B
C
C
BC
D D D D D
B CB
D
D C
D A D
E E E EA
B
A
A BC
D B DC CB
C C C
C
C
B B B BDB
C B
A
E
MN AA B
B DBD BCCDBEFD
C
C C C CC
C
C
B
D D D DB D D C
D
B
E
F E E E
F E E E B C
G
EE B C
G
CA H AH
GBA C
F
G
F B
B
F FD B
D
B
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
S1
(AVG)
TOP
DMX =.002597
SMN =-282353
SMX =.231E+07
A
=-138102
B
=150399
C
=438901
D
=727402
E
=.102E+07
F
=.130E+07
G
=.159E+07
H
=.188E+07
I
=.217E+07
BB
BB
B
B
B
BB
B
B
B
B
B
B
B BB
B
B
B
B
B B B
B
C
B
C
C
C
CB B C
D
D
D
B
C
D
D
D
C
C
C BB
B
D DB
C D D
C
B
BB C
E BF
D
CCD
B EB
FC D CG
ED
G
I
HG D C D D A
D
C
B
F
B
ED
C
B
C
B
B
EF B
E
C
G
F
B DE C
BFC B
GHA C
E
B
B
B
B
B
B B B B B B
C C C C C
B
D D D D D DD
C
D
C
B
B B
C
B
CC C
A
D A
A CA A A
AC
DA D
C
C C
B
D E
E
E
F G
F G
F
H
I
H B
A
F G
E
I
H
DMX
D
MN
C E
F
DB H
I
GB
D
IHC
B
B
BC
B
C
BCB
B C
B
D
C BCB
B B
C
C
B
C
C
B C CB
CDB
GH
F
BB B
B
CED
B
C
C DC C C
EE B
D
B B
B
FHG
E
FGF
D
C B BCB
G
F
E
D
C
B
C
E
EE
HF
G
GG FG
G
F
G
G
F
F
G
G F
F G
G
G
F F
G
F
F
FF
F
F
E
E E
E
F
E
E
E
E
D
ED
E FG
D
C
C DC CE
C
D
C BD
B
B
G
F
E
C
A H
BADEFGH
D
AA A
MN
D
DCC BC
C
B A
H
G
F
E
B C
BD
B B C D
B
D FGH
C
DCEC
D
D D D
D
E
DD
E
EF EEEEF E
F FE
F
MX
EE E
F
FE
E D FHI
E
G
F
EGH
F EF
F
F
F F FH
G
G G
G
G
HGF FH H G GH GH G G G
DG
FGG FG
HGG H H H
HHH H G HG GGF EG
F
I I
I HI
H
EE G HF
H
HF F G
H
F H G
H
G
GF
F G
GH
G GG G
F
GF
G
F
F
G
G
G
G F
G
F
G F G
F
F
F
FF F
F
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F EF
F FF E F F F F
F
F
E
E
E
E
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E
F
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E
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DE D D
FG
E
EDEED
D
D
D E
D
D
D D
C
C G
GF DC
C
C C D
C C
D
B
D
CD CD
C
DB
E
GB B C
F
F
C
B B
B AE
E
C
BB
B B
C CD
D
BA FG
H
D
B
AA
MNA
HGFED C
D
C
A
CDB
GHE
EI
E
B
D
C
HB B B
G
F
F
C B
EBDC CI
D
CB B
C E
E DBD
C
C
E
B B B FG
C DC
EC
H
C
C
C
D
CE
E D F
D D D
DC
D
D
F
C
E
HGDF E F E D D
D
E FGH
E
EF
E
E
E
F
E
E
F
F
F
D
F
F
F
F
F
F
F
G
G
F
G
F
F
G GG
G G F GG G G GFF
HFH
GG H G H FEFF
GGG
G
GG G IMX
G
H
GG
G
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FH
G
G
H
G
H
H
H
G
G
H
H
H
H
G
G
H
H
HH
H
H
H
H
H
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
S1
(AVG)
TOP
DMX =.003232
SMN =-402559
SMX =.294E+07
A
=-217129
B
=153729
C
=524588
D
=895446
E
=.127E+07
F
=.164E+07
G
=.201E+07
H
=.238E+07
I
=.275E+07
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SY
(AVG)
TOP
RSYS=15
DMX =.001968
SMN =-.182E+07
SMX =698701
A
=-.168E+07
B
=-.140E+07
C
=-.112E+07
D
=-839361
E
=-559713
F
=-280066
G
=-418.234
H
=279229
I
=558877
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SY
(AVG)
TOP
RSYS=15
DMX =.002597
SMN =-.239E+07
SMX =649867
A
=-.222E+07
B
=-.189E+07
C
=-.155E+07
D
=-.121E+07
E
=-871870
F
=-533707
G
=-195543
H
=142621
I
=480785
Figure 5. Arch’s contour map of circumferential stress under case 2
（Pa）
Figure 4. Arch’s contour map of first principal stress under case 2（Pa）
BB BB
B
H
G
G
Figure 3. Arch’s contour map of circumferential stress under case 1
（Pa）
Figure 2. Arch’s contour map of first principal stress under case 1（Pa）
BB B
B
B B
B
B
H
G H
G GF G
ED FG F
F
G
F
G
F EF G
E
F
F F
E
FF
E E F
F
F EE
E
E
E E
E
E
D
F
D
D
E D
D
C CD
D
F
DD
C
D
C D
FE
BDB
B BB C
E
D
GC CCD
D
GF
BB B
B C
F
E
D ED C
C D
GC CD
C
D
EE
D
GF
E E EE
E
F EF F
EE E
F
G
FG G F F
GE
E
F
F
HD G
FF
E
G
F
G
H
F F
GH H G
Figure 6. Arch’s contour map of first principal stress under case 3（Pa）
From Fig .2, Fig .4 and Fig .6 it can be seen, arch
contour maps of the first principal stress are similar, and
the maximum principal tensile stresses appear at the
junction of the bedrock and the dam。 The first primary
stress also significantly increased with the rise of water
level, and the distribution range of the main tensile stress
also increases. From Fig .3, Fig .5 and Fig .7 can be seen,
the circumferential stress of the arch is stress mainly, and
the stress distribution is very complex. But in the bottom
of the arch emerges a range of tensile stress, and its value
is not high.
H H
G
G HG
GGF
G
FE
E
E
D
C
D D
C
C C
B
BC
C
D
D
E E
F FF
F
G
G
G
H H G
C
D
F
H
G
HG
GF G
F GF
FE
EDF
G
F E
F
G
F G G
F GF F
E F F
F
E
F
E
EF
EF
E E
DD
F
E E E E
DE
D
D D
E
D
G
D
D
C
E
C
F
D DCBBBG
D
B
D
FE
C
D
B
C
BB
A
AE H
G
D
B CB BD
C
GH
F
MN
D
CAD FE
C
CA
C
BD
EB
D ED
H
G
C B
C
D C
E C
F
D
D CCGH
E
E
EF E E E F
MX
FF
F G FFFEF
EF FF
H
I
F
GG
F
F
F
H
G GF
G
G
G
F
H
G
GG
H
G
H
G H H
HGHG G
H
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SY
(AVG)
TOP
RSYS=15
DMX =.003232
SMN =-.290E+07
SMX =914744
A
=-.268E+07
B
=-.226E+07
C
=-.184E+07
D
=-.141E+07
E
=-990636
F
=-567218
G
=-143800
H
=279618
I
=703035
Figure 7. Arch’s contour map of circumferential stress under case 3
（Pa）
B Deformation Analysis
By deformation analysis of Tianshengqiao Reservoir,
we calculate the radial displacement value on the key
points of Arch Dam sectional crown, and its results of
stress are shown in table 2. For case 2 the arch contour of
displacement is shown in Fig .8 and Fig .9.
1225
TABLE 2. EACH CONDITION OF ARCH DAM SECTIONAL CROWN RADIAL DISPLACEMENT ON KEY POINTS（MM）
Location
1
2
3
4
5
6
7
case1
0.160
0.766
1.785
1.638
0.869
0.443
0.306
case2
0.057
0.579
2.177
2.446
1.734
1.049
0.640
case3
0.222
1.087
2.774
3.055
2.383
1.673
1.159
I
G
I H
I I MX
I I H
G
FF
G
H
H
G F F
HH H GG F F
E
GG
F E
HH
FF
D
E
D D
H
F
F F EE D D
C
H
E DD
C C
C
G GF
B B
CC
B
FE
B
H F
G
B
AA
H
E ED D C B B
A
FG
C
AA
C B
GH F
B BB
E ED DD C C
B
H
C C
C
E
F
D
GG
D
E
F
G
G
EE
F F
H G G
F F
G GG G
H
G GG
H
H H
H
H HHH
GGG HH
I III
G HH
G
H
H
G
F
F
E E
GGG H
E
G HHH
E
D DD
E FFFF
F GG G
D
C
EE
CC
H
D F
C
B B
E FH
BB C
G
EFG
A A
B C E FG
CD D
AA B B C
H
D
MN
H
D
A
A
A
C EFG
E FG
B
B
C
B B
H
C
DD E
C C
D
D
F
D
D D D
H
E E E F FG
E E
F F
F
G
HH
G
GG
GG
H
H
F
E
B
A
C
D
F
FF
H
HH H
H
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
UX
TOP
RSYS=15
DMX =.002597
SMN =-.002595
SMX =.455E-03
A
=-.002425
B
=-.002086
C
=-.001747
D
=-.001409
E
=-.00107
F
=-.731E-03
G
=-.392E-03
H
=-.532E-04
I
=.286E-03
G
G
F
F
H
GHGF
F
F
E
G
E
H
G
F
F
F F F
F
G E
E G
F
G
D
HC
F
GD D
F
B
G
I
I
A
F D CH
A
A
EG B H H
B
G
F FE E C
E C
DF
E
GB
G
EC B
D FC
B
ED C F
EDD
From Table 2 and Fig .8 and Fig .9 can be seen that
with the increase of the water level, the radial
displacement significantly increased on the key points of
Arch Dam sectional crown, but the biggest radial
displacement appear in the middle of the arch crown,
while the radial displacement is small at the top and
bottom of the arch crown. For arch dam the value of radial
displacement is larger than the value of vertical
displacement, and the largest vertical displacement
appears in the top of the arch crown.
H
G
I
F
I
E
HH
E
G
H
F
E
F H
G
G
Figure 8. Arch’s contour map of radial displacement under case 2（m）
F
I
H
F
D
H
C
I
F
G
G F
E
B
I
H
A
I
A
B
G
A H
GB G
C F
E E
D
G
H
F G
H F HG
H
F
H
I F
F G
I
F
H G
I
I
F
H
I
H F
F G
G
G
G
F
G
G G
G
F
F GF F F G
G F FF
E
E
E
D
D
C I I IC
HD E F
C
I
B
BMX
G
I
H
F
A
IB
H H
B H H HB H HC C D G E F
HMN
B BAB
HA C
B BHCHC D E
E F G
D G GF
H
AH
GF G
F
G
G
G
D
E
FB
F
C
DEF EE FF FFFG
EC
DED
ANSYS 10.0
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
UZ
TOP
RSYS=15
DMX =.002597
SMN =-.464E-03
SMX =.101E-03
A
=-.433E-03
B
=-.370E-03
C
=-.307E-03
D
=-.244E-03
E
=-.181E-03
F
=-.119E-03
G
=-.557E-04
H
=.716E-05
I
=.700E-04
Figure 9. Arch’s contour map of vertical displacement under case 2
（m）
[2]
Bans Sevim,Ahmet Can Altunisik,Alemdar Bayraktar et al.
Earthquake Behavior of Berke Arch Dam Using Ambient
Vibration Test Results [J]. Journal of Performance of Constructed
Facilities,2012,26(6):780-792.
[3] SL191-2008. Design Code for Hydraulic Concrete Structure[S].
China Water Conservancy and Hydropower Press, 2008.
[4] Li Shouyi,Ding Lujun,Zhao Lijuan et al. Optimization design of
arch dam shape with modified complex method [J]. Advances in
Engineering Software,2009,40(9):804-808.
[5] Seyed Mohammad Seyedpoor,Javad Salajegheh,Eysa Salajegheh
et al. Shape optimal design of materially nonlinear arch dams
including dam-water-foundation rock interaction using an
improved
PSO
algorithm
[J].
Optimization
and
engineering,2012,13(1):79-100.
[6] Xucheng Wang. Finite Element Method [M]. Tsinghua University
Press, 2003.
[7] Bofang Zhu. Finite Element Method Principle and Application
[M]. China Water Conservancy and Hydropower Press, 1998.
[8] Bans Sevim,Alemdar Bayraktar,Ahmet Can Altunisik et al.
Investigation of water length effects on the modal behavior of a
prototype arch dam using operational and analytical modal
analyses
[J].
Structural
engineering
and
mechanics,2011,37(6):593-615.
[9] SL282-2003. Design Code for Concrete Arch Dam [S]. China
Water Conservancy and Hydropower Press, 2003.
[10] Bofang Zhu, Jizhang Gao, Zuyu Chen, Yisheng Li. Arch Dam
Design and Research [M]. China Water Conservancy and
Hydropower Press, 2002.
IV. CONCLUDING REMARKS
In summary, using concrete arch dam scheme of
Banjiang
reservoir
is
reasonable.
Basically,
circumferential stress of arch dam upstream face is
compressive stress. Furthermore, the arch′s first principal
stress which is small can meet the strength requirements,
so the structure is safe and reliable.
REFERENCES
[1]
F
GH F
G
F
H
F
G
G
Bans Sevim,Ahmet Can Altunisik,Alemdar Bayraktar et al.
Estimation of Elasticity Modulus of a Prototype Arch Dam Using
Experiments" Methods [J]. Journal of Materials in Civil
Engineering,2012,24(4):321-329.
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