-
Finite Element Simulative Analysis of Concrete Arch Dam
Structure Dongyu Ji1,a, Weixing Chen2,b
1Hunan Urban Construction College, Xiangtan, Hunan Province
411101, P.R. China 2Survey, Design & Research Institute of
Henan Petroleum Exploration Bureau (HPEB), SINOPEC,
Nanyang, Henan Province 473132, P.R. China [email protected],
[email protected]
Keywords: Concrete arch dam; Finite element method; Simulation
analysis; Stress distribution.
Abstract. In this paper, finite element simulative analysis is
proceeded for the concrete arch dam of Tianshengqiao reservoir.
Deducing variation law of the dam’s stress and displacement in
construction process and operational process. The analytic results
are shown: concrete arch dam of Tianshengqiao reservoir is
reasonable structure, and every index meets the requirements for
design.
Introduction Tianshengqiao reservoir is located Laliu River,
which is located Nandan county in the Guangxi
zhuang autonomous region. The main function of reservoir is
irrigation, and it is a comprehensive utilization water conservancy
and hydropower engineering. The main buildings include concrete
arch dam, left bank gravity pier, shore spillway, penstock, power
station and underport, etc. Total reservoir storage capacity is 402
million m3, reservoir’s normal storage level is 24 m, design level
is 28.1 m, flood level is 30.3 m. The dam is concrete single arch
dam, maximum dam high is 31.6 m, the arc length of dam crest is
43.44 m, thickness of dam crest is 1.2 m, thickness of dam bottom
is 1.7 m, hickness-to-height ratio of arch dam’s section is 0.07.
River valley of dam site is ladder-shaped, gravity pier is set at
the left bank, river valley is rectangular-shaped.
Calculation Model Model Parameters. Concrete strength grade of
Tianshengqiao reservoir concrete arch dam is
C15, elastic modulus E1=22 GPa[1], Poisson ratio 1μ =0.167,
density 1γ =24 kN/m3. The foundation of
dam is Qixia limestone of permian period, the limestone is
medium thickness seam, lithology is hard, it is basic complete.
Rock stratum tends to upstream, karst of dam site is not the
development, the rock stratum is not leaking. Rock’s elastic
modulus E2=12 GPa[2], Poisson ratio 2μ =0.28.
Model Element. Concrete arch dam and bedrock structure model is
divided by eight nodes isoparametric block element. The element is
often applied to three-dimensional model of entity structure, it
has plasticity, creep, expansion, stress rigidization, large
deformation and large strain characteristics. It has eight nodes,
each node has three translational degree of freedoms[3].
Model size. Calculation model simulation range is listed below,
calculation model along the river is 90 m, transverse of the river
is 75 m, vertical direction is 76 m. The simulation range of whole
calculation model is 90 m×75 m×76 m. Element division of dam and
bedrock is shown in Fig.1.
Calculation Cases. Considering mechanical characteristics of dam
structure in operating process[4], researching three calculation
cases as follows. Case 1, normal storage level and dam weight, case
2, design level, tail water level and dam weight, case 3, flood
level, tail water level and dam weight.
Arch Dam Structure Analysis Analysis Path. In order to analyzing
concrete arch dam of Tianshengqiao reservoir, one analysis
path is defined, on the upstream face of crown cantilever,
choosing one calculation point every 5 m
0844
2nd International Conference on Electronic & Mechanical
Engineering and Information Technology (EMEIT-2012)
Published by Atlantis Press, Paris, France. © the authors
-
from dam bottom to dam crest, there are seven calculation points
totally, these points assembled analysis path. Stress distribution
of the path is provided in the paper.
Fig.1 Element division of dam and bedrock
Stress Analysis. In order to researching stress distribution law
of crown cantilever, obtaining circumferential and vertical stress
values of analysis path under various cases, the stress values of
crown cantilever under various cases are listed in the table 1.
Table 1. Calculation point’s circumferential and vertical stress
values on the dam’s analysis path under various cases(MPa)
Calculation Point 1 2 3 4 5 6 7
Case 1 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
Case 2 Circumferential
stress 0.455 -0.095 -1.821 -1.862 -1.057 -0.377 0.067
Vertical stress 1.850 1.089 -0.981 -0.583 -0.092 0.056 0.001
Case 3 Circumferential
stress 0.559 -0.513 -2.219 -2.226 -1.452 -0.736 -0.137
Vertical stress 2.666 0.969 -0.138 -0.098 -0.058 -0.020 0.005 We
can see from table 1, under various cases, circumferential stress
of crown cantilever’s
upstream face is mainly compressive stress. But vertical stress
is mainly tensile stress, tensile stress value is larger especially
in the junction of dam bottom and bedrock, this is mainly because
the junction appears stress concentration phenomenon. These larger
stress values can be reduced by the finite element equivalent
stress method[5].
We obtain concrete arch dam’s contour maps of first principal
stress and circumferential stress under various cases, contour maps
are shown from Fig.2 to Fig.7.
We can see from Fig.2, Fig.4 and Fig.6, arch dam’s contour map
of first principal stress is similar under various cases, maximum
principal tensile stress appears the junction of dam bottom and
bedrock. And first principal stress values increase with water
pressure increases, distribution range of principal tensile stress
values also gradually increases. In the Fig.3, Fig.5 and Fig.7,
circumferential stress of arch dam is mainly compressive stress,
and stress distribution is more complex, near the arch dam’s bottom
appears tensile stress, but tensile stress values are smaller.
0845
2nd International Conference on Electronic & Mechanical
Engineering and Information Technology (EMEIT-2012)
Published by Atlantis Press, Paris, France. © the authors
-
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 S1 (AVG)TOP DMX =.001968 SMN
=-306738 SMX =.208E+07
BCC
BCC
BB
BB
B
B
C
B
B
B
C
CB
B
B
CD
B
BC
DC
B
B
C
B
D
C
BD
CB
B
A
DC
B
CB
BD
C
B
DC
D CB C B
B B
B BC
BC
D D
D D
C CBB
EF
BCDB
DC
D
B
C
D
B
EFCBCD
B
CDE
B
C
CD
B
B
C
B
C
B
B
B
CBC
CBC
B
B
B
B
B
BBBB
B BBBBBBBB
B BBB
BBBBBB B BB BBBBB BB
DB
C C
B
B
B
BC BCCDBCDFE
GHIDFC
EGHI
C
FE
DGHIFC
EGHIDC
FE
DGHFC
EFGDBC
EDCB
EC
DB
CDCCFHDEGFH CEG
IDCCD
CDEF
CDEF DEGFH
C
GCDEFH A A A
BAB
B
B
CBACB
B
B
BBB
BB
BBBB BB
AB
BB MNMX
A =-174324 B =90506 C =355336 D =620165 E =884995 F =.115E+07 G
=.141E+07 H =.168E+07 I =.194E+07
ANSYS 10.0 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 SY (AVG) TOP
RSYS=15 DMX =.001968 SMN =-.182E+07 SMX =698701
FGHEFGH
EFGHEFGH
FGF
EF
D
BCD
BCDEE
FDE
CD
E
DC
A
A
ED
BC
F
CDEB
CDAB
CD
E
D
B
C
E
E
B
A
CDE
B
EF
E
DC
A
E
D
F
DE
B
A
C
D
E
D
B
F
E
C
CD
DE
C
F
D
B
C
E
D
EC
B
D
F
C
E
F EDE
CD C
B B
B BC CD D
E EF F
E ED D
C CC
CD
CD D
E E
F F
G
C
E
F
D
D
E
G
DB
C
FEE
B
CD
F
E
GE
B
D
FE
CDE
BCD
EDC
D
F
C
B
DE
FG
FGEFGEFGEFE
F
FE
DC
BDCEDE
FGF
GG
F
FFF
FG GG
F GG
FF
F
GGF
FFG
GGGG
FGFGFG GG
FGGFGG
HGHGGGFEG G H FGGGGGH
G
F
G GGH
E
HGF
H
E
HGFE
HG
E
HFE
GFE
GF
GHGHGHIGH
GHH
FG
F
GH
EFGH F
E
FG F
F FE
G
F
G
F
G
F EFED
FEEFFFFEDC E
FEDEFFF G
MN
MX
A =-.168E+07 B =-.140E+07 C =-.112E+07 D =-839361 E =-559713 F
=-280066 G =-418.234 H =279229 I =558877
Fig.2 Arch dam’s contour map of first Fig.3 Arch dam’s contour
map of principal stress under case 1(Pa) circumferential stress
under case 1(Pa)
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 S1 (AVG) TOP DMX =.002597 SMN
=-282353 SMX =.231E+07
CBCDCDBC
CBB
B
B
B
A
BC
BACD
BC
B
DBA
C
D
B
C
AD
E
C
B
D
E
C
B
DB
E
DC
ABC
E
D
BC
D
BC
D
ECAB
D
CB
D
E EC B D C
BD
AC B
CB
E D DE
DDCC C
B B
FGDEBC
D
B
EHFCD
A
B
E
C
DG
A
BCDE
CD
B
EFC
A
C DE
BCD
B
B
C
A
BC
B
BC
CBC
CBCB
B
B
B
B
B
BBB BB
BB
BBBB B BB BBB
BBCB
BBB B BB B C C BBBBBBBC
CDB
B
B BB
BCBCBFGHECD
GEFDC
HED
FGHECD
GEFDC
EDC
FGEDC
FDE
C
DEF
C
DECD
C
CD
BCBCDEFHGCDEF
I
CDBC
DE
CDE FCDEFCDEG
FCDE CDEFGH A A A A
BA
B
B
B
B
B
B
B
B BAABB
A
MNMX
A =-138102 B =150399 C =438901 D =727402 E =.102E+07 F =.130E+07
G =.159E+07 H =.188E+07 I =.217E+07
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 SY (AVG) TOP RSYS=15 DMX
=.002597 SMN =-.239E+07 SMX =649867
GHFGHIFGHEI
FGHE FGFGF
EF
CDEBADCBD
E
DEF
CDE
DE
C
A
D
BC
E
DFCEBDCAB
DC
DE
G
B
BCD
F
EA
C
EE
FDB
A
E
FGEC
A
B
D
E
D
CDE
F
D
E
B
D
C
C
E
FG
DB
E
C
D
F
C
B
E
D
CDE
F
B
DE
C
GHF
G FDE DE
C CB B
BB B
C CD DE E
F FE E
DD
CD CC B
CD C
DE E
GH
DF
BC
E
D
E
FD
GF
E
HECB
D
F
E
G
CD
B
C
E
FDEBCD
BCD
G
EF
DC
D
E
GFGH
EFGHEFGH
EFGFGE
F
FDECBD
CBDE
DE
FFG
EFF
FG
FFF F F
G G
F FFG G
HFF
EFF
FGFGFF
G FF
GFG
FGF
HGFHFGFGEG GH
G HFGG
FGHFHGHG
IHGFGHGFGEDG H HH H I FEGFGGHGGHHHIHI
H
F
H
G
HHH
G
HG
G
HG
G
HHGH
G
H
G
HHHIHH
HH
G
H
G GGH
G G
G
G FF
G
GGGGGFEF
GFGG
MN
MX
A =-.222E+07 B =-.189E+07 C =-.155E+07 D =-.121E+07 E =-871870 F
=-533707 G =-195543 H =142621 I =480785
Fig.4 Arch dam’s contour map of first Fig.5 Arch dam’s contour
map of principal stress under case 2(Pa) circumferential stress
under case 2(Pa) ANSYS 10.0
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 S1 (AVG) TOP DMX =.003232 SMN
=-402559 SMX =.294E+07
BCC
BCC
BC
B
B
B
B
BC
BCB
B
B
C
DC
B
BCCB D
D
CB
D
CB
D
B
CA
D
C
B
D
C
B
D
C
B
A
D
C
B
DD BC BC
ABC
BC
D D
D D
C C
B B
EFGDCB
DEBCD
DC
B
FCB
D
C
B
ECDC
CD
B
B
BCB
B
CBC
CBC
CB
B
B
B
B
B
BBBBB
BBB
BB
BB
BB
BBBBBBB B BB BBBBBBB
DGCB
C
B
B
B
BBCCBCBEF
DC
DGHIEF
C
DGHI DEF
C
DGHIEF
CD
GHI
D
EF
C
DFGHE
C
FGDE
BC
DC CBD
BCCCEFDHGEFHDGI
CCB DE
CD
ECF
D
ECF
D
EGFH
CD
G
DCEFH
A A A AB
B
A B
BC
B
B
B
B B
B
C BB AB BBAAB MNMX
A =-217129 B =153729 C =524588 D =895446 E =.127E+07 F =.164E+07
G =.201E+07 H =.238E+07 I =.275E+07
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 SY (AVG) TOP RSYS=15 DMX
=.003232 SMN =-.290E+07 SMX =914744
GHFGHFEGHFEGHFEGF
E G
F
FEDCBD
CBDE
DE
ECD
D
EC
A
A
B
D
F
C
D
EBC
DABC
ABCD
EDC
BD
ECB
D
F
DBCD
EE
D
D
ECBD
D
E
F
C
B
D
C
E
D
B
C
C
D
E
B
D
C
E
FDC
CDE
F EF
DE DC C
B B
B BB
C CD D
EE EDD
CC
CC
DC
D DE
G
E
B
FE
D
D
G
C
D
F
E
D
B
C
E
F
D
D
GE
C
D
FECDB
CDB
CD
G
E
D
CD
EF
D
GFGFEGFEGFEFE
F
FECBDE
CDB
DC
EEF
EFEEEFEFEF
E EF F
EFF
F GFFEFF
D
EEFEE
FE
FFG
EFG
FGEFEF GG
F GEFFGGFGGF
HGFGFFGEFD GG H H FDEFEGFGFFGGHGHG
GG
GGGH
F
GH
F
H
F
GH
F
HGF
HH
FGF
HH
GHIGHHH
FGH
FGH
F
H
F
G
F
G
GF
GG
F
G
G F
F
EF E
G
F FFFED FFEGEF GFGGFG
MN
MX
A =-.268E+07 B =-.226E+07 C =-.184E+07 D =-.141E+07 E =-990636 F
=-567218 G =-143800 H =279618 I =703035
Fig.6 Arch dam’s contour map of first Fig.7 Arch dam’s contour
map of principal stress under case 3(Pa) circumferential stress
under case 3(Pa)
Displacement Analysis. Through displacement analysis of
Tianshengqiao reservoir concrete arch dam, getting radial
displacement of crown cantilever’s calculation points under various
cases, the radial displacement values of crown cantilever under
various cases are listed in the table 2, contour maps of
displacement under various cases are shown from Fig.8 to Fig.9.
Table 2. Calculation point’s radial displacement values on the
analysis path of arch dam’s crown cantilever under various
cases(mm)
Calculation Point 1 2 3 4 5 6 7
Case 1 0.160 0.766 1.785 1.638 0.869 0.443 0.306
Case 2 0.057 0.579 2.177 2.446 1.734 1.049 0.640
Case 3 0.222 1.087 2.774 3.055 2.383 1.673 1.159
0846
2nd International Conference on Electronic & Mechanical
Engineering and Information Technology (EMEIT-2012)
Published by Atlantis Press, Paris, France. © the authors
-
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 UX TOP RSYS=15 DMX =.002597
SMN =-.002595 SMX =.455E-03
HG
HG
H
F
FG
G
H
H
H
E
DEF
GH
FG
FG
G
F
CD
E
F
DE
E
FG
D
BC
DE
FE
C
DC
F
DE
B
CD
B
C
EF
DE
A
BC
DE
B
C
FDB
A
EC
A
B
D
BC
FD
A
C
E
BA
D
C
A
B
FD
C
E
BC
A
C
A
B
FDC
G FEF
DE DE
C BC
BB
AA
ABC B BD
CC
D
FG F
EDE DE
C BCB
A
B A
BA
D C B
D C
F E D
C
B
CDE
F
C
E
G
D
C
F
EDC
D
EF
G
D
D
E
F
G
E
E
F
FG
E
E
F
G
FG
FG
H
G
F
G
H
H
H
H
HG
HG
H
FGH
GHHHHH E D
F EGF
F EG EF
GHHHG
HFGHG
FG
E F
GEFFE
DEE
DE
III H FG FH G F H
HGHGG
FFFII
I H G IIIIHHGG
HH H
G G
H
G
HH
H
G
H
G
H
G
H
G G
H H
GHH
GG
GHH H H
MN
MX
A =-.002425 B =-.002086 C =-.001747 D =-.001409 E =-.00107 F
=-.731E-03 G =-.392E-03 H =-.532E-04 I =.286E-03
NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 UZ TOP RSYS=15 DMX =.002597
SMN =-.464E-03 SMX =.101E-03
F
G
F
F
GG
G
F
F
G
F
E
F
G
H
H
D
EFG
H
HIC
D
F
H
G
C
E
HI
GF
B
CD
I
HB
FG
I
H
IBCEF
H
I
GDF
H
I
B
FG
H
I
F
ABCEG
H G HI
G
III
H HG G
FF
FEE F
A B A BA A
B C BCD D
EEF F
G GH H
II
H
G
E
CDA
F
H
E
G
BC
DEF
H
H
G
E
E
CD
F
H
G
F
ED
G
F
G
F
F
E
FFF
G
G
F
FF
G
EHF
FG F
F
II
GGF
H
H
IF IF
I
FH
G F HFFGHFGG GF GGH H GHFGHFGHGH
EF
E
D
FF
EEEDEF
H
GH
F
H
GH
F
H
G
H
FG G
F
FFEF
E
G
E
G
FGE
GEF
H
BCAB A
D
B
C
AB
D
BC BC
ED
C
E
D ED
F
E
F
F
F GGGGABBC
BC BCD CDD D
MN
MX
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
Fig.8 Arch dam’s contour map of radial Fig.9 Arch dam’s contour
map of vertical
displacement under case 2(Pa) displacement under case 2(Pa) We
can see from table 2, Fig.8 and Fig.9, calculation point’s radial
displacement values of arch
dam’s crown cantilever obviously increase with water pressure
increases. But maximum radial displacement appears the middle of
crown cantilever, displacement values of crown cantilever’s top and
bottom are smaller. Arch dam’s radial displacement values are more
larger than vertical displacement values, maximum vertical
displacement appears crown cantilever’s top.
Conclusion From the above, Tianshengqiao reservoir adopts
concrete arch dam is economic and reasonable.
The arch dam’s circumferential stress is basically compressive
stress, and arch dam’s first principal stress values are smaller,
stress values can meet strength requirements, the arch dam
structure is safe and reliable.
References [1] SL191-2008: Design Code for Hydraulic Concrete
Structures(China Water Conservancy and Hydropower Press, China
2008)(in Chinese) [2] M.R. Shen, J.F. Chen: Rock Mechanics(Tongji
University Press, China 2006)(in Chinese) [3] X.CH. Wang, M. Shao:
Finite Element Method Basic Principle and Numerical Method(Tsinghua
University Press, China 1997)(in Chinese) [4] SL282-2003: Design
Code for Concrete Arch Dam(China Water Conservancy and Hydropower
Press, China 2003)(in Chinese) [5] B.F. Zhu, J.ZH. Gao, Z.Y. Chen,
Y.SH Li: Arch Dam Design and Research(China Water Conservancy and
Hydropower Press, China 2002)(in Chinese)
0847
2nd International Conference on Electronic & Mechanical
Engineering and Information Technology (EMEIT-2012)
Published by Atlantis Press, Paris, France. © the authors
