Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System
In contrast with modeling of the contraction joints, the performance and influence of lift joints are usually neglected in numerical analysis of concrete arch dams. In this paper, the seismic nonlinear response of a concrete arch dam– reservoir–foundation system is investigated with considerin...
Збережено в:
| Дата: | 2013 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2013
|
| Назва видання: | Проблемы прочности |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/112677 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System / M.A. Hariri-Ardebili, H. Mirzabozorg // Проблемы прочности. — 2013. — № 6. — С. 22-44. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-112677 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1126772020-12-17T17:35:52Z Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System Hariri-Ardebili, M.A. Mirzabozorg, H. Научно-технический раздел In contrast with modeling of the contraction joints, the performance and influence of lift joints are usually neglected in numerical analysis of concrete arch dams. In this paper, the seismic nonlinear response of a concrete arch dam– reservoir–foundation system is investigated with considering the effects of lift joints using orthotropic-based material. An anisotropic damage mechanics approach is introduced and modified to take into account the effects of weak horizontal planes between concrete lifts during the construction phase. This model is capable to consider the pre-softening behavior, the softening initiation criterion and anisotropic cracking behavior in mass concrete. The coupled equation of motion in dam–reservoir system is solved by staggered displacement method while the foundation rock is assumed as a mass-less and rigid mediums. The coupled system is excited using three-component ground motion in the maximum credible level. It is found that using orthotropic-based material increases crest displacements and also leads to more damage in the dam body in comparison with the case using the common isotropic-based material. В отличие от моделирования усадочных швов, при численном анализе бетонных арочных плотин работа и влияние строительных швов обычно не учитываются. Исследуется сейсмическая нелинейная реакция системы (бетонная) арочная плотина–резервуар–основание с учетом действия строительных швов на основе ортотропного материала. Представленный анизотропный подход к механике повреждения изменен для учета слабых горизонтальных плоскостей между слоями бетона в процессе строительства. Эта модель допускает учет характеристики предварительного размягчения, критерия возникновения размягчения и характеристики анизотропного растрескивания. С помощью метода ступенчатых перемещений, предполагая, что скальное основание состоит из невесомых жестких тел, решена система связанных уравнений движения в системе плотина–резервуар. Движение грунта по трехкомпонентной технологии возбуждает данную систему на максимально вероятном уровне. Обнаружено, что использование ортотропного материала увеличивает смещение гребня плотины и, как следствие, повреждение тела плотины в большей степени по сравнению с использованием распространенного изотропного материала. На відміну від моделювання усадкових швів, при чисельному аналізі бетонних арочних гребель робота і вплив будівельних швів зазвичай не враховуються. Досліджується сейсмічна нелінійна реакція системи (бетонна) арочна гребля–резервуар–основа з урахуванням дії будівельних швів на основі ортотропного матеріалу. Представлений анізотропний підхід до механіки руйнування змінено для урахування слабких горизонтальних площин між шарами бетону в процесі будівництва. Ця модель допускає урахування характеристики попереднього розм’якшення, критерію виникнення розм’якшення і характеристики анізотропного розтріскування. За допомогою методу східчастих переміщень, припускаючи, що скельову основу складають невагомі жорсткі тіла, розв’язано систему зв’язаних рівнянь руху в системі гребля–резервуар. Рух ґрунту за трикомпонентною технологією збуджує дану систему на максимально імовірному рівні. Установлено, що використання ортотропного матеріалу збільшує зміщення гребеня греблі і, як наслідок, пошкодження тіла греблі в більшій мірі порівняно з використанням розповсюдженого ізотропного матеріалу. 2013 Article Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System / M.A. Hariri-Ardebili, H. Mirzabozorg // Проблемы прочности. — 2013. — № 6. — С. 22-44. — Бібліогр.: 41 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/112677 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Научно-технический раздел Научно-технический раздел |
| spellingShingle |
Научно-технический раздел Научно-технический раздел Hariri-Ardebili, M.A. Mirzabozorg, H. Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System Проблемы прочности |
| description |
In contrast with modeling of the contraction
joints, the performance and influence of lift
joints are usually neglected in numerical analysis
of concrete arch dams. In this paper, the seismic
nonlinear response of a concrete arch dam–
reservoir–foundation system is investigated with
considering the effects of lift joints using
orthotropic-based material. An anisotropic damage
mechanics approach is introduced and modified
to take into account the effects of weak
horizontal planes between concrete lifts during
the construction phase. This model is capable to
consider the pre-softening behavior, the softening
initiation criterion and anisotropic cracking
behavior in mass concrete. The coupled equation
of motion in dam–reservoir system is
solved by staggered displacement method while
the foundation rock is assumed as a mass-less
and rigid mediums. The coupled system is excited
using three-component ground motion in
the maximum credible level. It is found that using
orthotropic-based material increases crest
displacements and also leads to more damage in
the dam body in comparison with the case using
the common isotropic-based material. |
| format |
Article |
| author |
Hariri-Ardebili, M.A. Mirzabozorg, H. |
| author_facet |
Hariri-Ardebili, M.A. Mirzabozorg, H. |
| author_sort |
Hariri-Ardebili, M.A. |
| title |
Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System |
| title_short |
Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System |
| title_full |
Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System |
| title_fullStr |
Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System |
| title_full_unstemmed |
Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System |
| title_sort |
orthotropic material and anisotropic damage mechanics approach for numerically seismic assessment of arch dam-reservoir-foundation system |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2013 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112677 |
| citation_txt |
Orthotropic Material and Anisotropic Damage Mechanics Approach for Numerically Seismic Assessment of Arch Dam-Reservoir-Foundation System / M.A. Hariri-Ardebili, H. Mirzabozorg // Проблемы прочности. — 2013. — № 6. — С. 22-44. — Бібліогр.: 41 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT haririardebilima orthotropicmaterialandanisotropicdamagemechanicsapproachfornumericallyseismicassessmentofarchdamreservoirfoundationsystem AT mirzabozorgh orthotropicmaterialandanisotropicdamagemechanicsapproachfornumericallyseismicassessmentofarchdamreservoirfoundationsystem |
| first_indexed |
2025-07-08T04:23:38Z |
| last_indexed |
2025-07-08T04:23:38Z |
| _version_ |
1837051275701649408 |
| fulltext |
UDC 539.4
Orthotropic Material and Anisotropic Damage Mechanics Approach for
Numerically Seismic Assessment of Arch Dam–Reservoir–Foundation
System
M. A. Hariri-Ardebili
a,1
and H. Mirzabozorg
b,2
a University of Colorado, Boulder, USA
b K. N. Toosi University of Technology, Tehran, Iran
1 mohammad.haririardebili@colorado.edu
2 mirzabozorg@kntu.ac.ir
ÓÄÊ 539.4
Îðòîòðîïíûé ìàòåðèàë è àíèçîòðîïíûé ïîäõîä â ðàìêàõ ìåõàíèêè
ïîâðåæäåíèÿ ê ÷èñëåííîé îöåíêå ñåéñìè÷åñêîé ðåàêöèè ñèñòåìû
ïëîòèíà–ðåçåðâóàð–îñíîâàíèå
Ì. À. Õàðèðè-Àðäåáèëè
à
, Õ. Ìèðçàáîçîðã
á
à Êîëîðàäñêèé óíèâåðñèòåò, Áîóëäåð, ÑØÀ
á Òåõíîëîãè÷åñêèé óíèâåðñèòåò èìåíè Ê. Í. Òóñè, Òåãåðàí, Èðàí
 îòëè÷èå îò ìîäåëèðîâàíèÿ óñàäî÷íûõ øâîâ, ïðè ÷èñëåííîì àíàëèçå áåòîííûõ àðî÷íûõ
ïëîòèí ðàáîòà è âëèÿíèå ñòðîèòåëüíûõ øâîâ îáû÷íî íå ó÷èòûâàþòñÿ. Èññëåäóåòñÿ ñåéñìè-
÷åñêàÿ íåëèíåéíàÿ ðåàêöèÿ ñèñòåìû (áåòîííàÿ) àðî÷íàÿ ïëîòèíà–ðåçåðâóàð–îñíîâàíèå ñ
ó÷åòîì äåéñòâèÿ ñòðîèòåëüíûõ øâîâ íà îñíîâå îðòîòðîïíîãî ìàòåðèàëà. Ïðåäñòàâëåííûé
àíèçîòðîïíûé ïîäõîä ê ìåõàíèêå ïîâðåæäåíèÿ èçìåíåí äëÿ ó÷åòà ñëàáûõ ãîðèçîíòàëüíûõ
ïëîñêîñòåé ìåæäó ñëîÿìè áåòîíà â ïðîöåññå ñòðîèòåëüñòâà. Ýòà ìîäåëü äîïóñêàåò ó÷åò
õàðàêòåðèñòèêè ïðåäâàðèòåëüíîãî ðàçìÿã÷åíèÿ, êðèòåðèÿ âîçíèêíîâåíèÿ ðàçìÿã÷åíèÿ è õà-
ðàêòåðèñòèêè àíèçîòðîïíîãî ðàñòðåñêèâàíèÿ. Ñ ïîìîùüþ ìåòîäà ñòóïåí÷àòûõ ïåðåìå-
ùåíèé, ïðåäïîëàãàÿ, ÷òî ñêàëüíîå îñíîâàíèå ñîñòîèò èç íåâåñîìûõ æåñòêèõ òåë, ðåøåíà
ñèñòåìà ñâÿçàííûõ óðàâíåíèé äâèæåíèÿ â ñèñòåìå ïëîòèíà–ðåçåðâóàð. Äâèæåíèå ãðóíòà ïî
òðåõêîìïîíåíòíîé òåõíîëîãèè âîçáóæäàåò äàííóþ ñèñòåìó íà ìàêñèìàëüíî âåðîÿòíîì
óðîâíå. Îáíàðóæåíî, ÷òî èñïîëüçîâàíèå îðòîòðîïíîãî ìàòåðèàëà óâåëè÷èâàåò ñìåùåíèå
ãðåáíÿ ïëîòèíû è, êàê ñëåäñòâèå, ïîâðåæäåíèå òåëà ïëîòèíû â áîëüøåé ñòåïåíè ïî ñðàâíå-
íèþ ñ èñïîëüçîâàíèåì ðàñïðîñòðàíåííîãî èçîòðîïíîãî ìàòåðèàëà.
Êëþ÷åâûå ñëîâà: àíèçîòðîïíîå ïîâðåæäåíèå, îðòîòðîïíûé ìàòåðèàë, âçàèìî-
äåéñòâèå â ñèñòåìå ïîòîê–êîíñòðóêöèÿ, àðî÷íàÿ ïëîòèíà, îöåíêà ñåéñìè-
÷åñêîé ðåàêöèè.
Introduction. Performance of concrete dams can be affected by various
phenomena in which one of the most important factors is earthquake shaking.
Various types of concrete dams show different failure modes under seismic loads.
Concrete arch dams are built as partially independent block where shear keys and
grouting the contraction joints leads to monolithic behavior of the structure.
© M. A. HARIRI-ARDEBILI, H. MIRZABOZORG, 2013
22 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
However the contraction joints are assumed to have very little tensile strength
under seismic loading and blocks can have opening and sliding with respect to the
adjacent ones. The important point which is usually neglected in seismic safety
evaluation of conventional and RCC arch dams is effects of weak planes between
concrete lifts formed during construction phase.
A lift joint is the horizontal joint between the old and fresh concrete pouring
layer, which its thickness varies between 2 to 3 m depending on the rate of
concrete pouring during a day. Lift joint is a key factor in successful construction
and operation of RCC arch dams because the quality of the bond between
successive layers of concrete determines the overall strength and seepage condition
of the dam. At lift joints, the coarse aggregate becomes segregated, and thus forms
a discontinuity from one lift to another through which water can flow. The
condition of the lower surface, time delay between placement of lifts, compaction
and consistency of the covering concrete are factors affecting the strength of lift
joints. Although all the necessary arrangements are considered for implementing
the lift joints in best condition, the strength of this part of the dam is less than the
intact concrete.
There is very little literature considering effect of lift joints on seismic
behavior of conventional and RCC arch dams. Hess [1] studied RCC lift joints
strength under various conditions as well as seismic loading. Arabshahi and Lotfi
[2] investigated the effects of contraction, peripheral and lift joints on seismic
response of arch dams. They used zero thickness interface element for modeling
the joints. Fronteddu et al. [3] studied static and dynamic behavior of concrete lift
joint interfaces experimentally. Puntel et al. [4] investigated the cyclic behavior of
concrete dam joints considering both experimental and numerical aspects. Mojtahedi
and Fenves [5] considered the effects of contraction and lift joints of the Pacoima
dam in 1994 Northridge earthquake based on uniform and non-uniform free-field
ground motions. Malla and Wieland [6, 7] studied the 3D behavior of an
arch-gravity dam due to earthquake loading and AAR effects considering the
horizontal crack generated first on the downstream (DS) face near the gallery
utilizing the discrete crack approach.
In the field of damage mechanics, many researchers have proposed damage-
based models for simulating the behavior of brittle materials as well as mass
concrete. Hansen and Schreyer [8], Doghri and Tinel [9], Menzel et al. [10],
Voyiadjis et al. [11] used continuum damage mechanics approach for description of
material behavior under various loading conditions. Isotropic damage mechanics
approach using one or two damage variables have been studied by researchers such
as Lee and Fenves [12], Jason et al. [13], Bonora et al. [14], Jason et al. [15],
Pirondi et al. [16], Wu et al. [17], Celentano and Chaboche [18]. Anisotropic
damage mechanics approach have been studied by Chaboche [19], Voyiadjis and
Abu-Lebdeh [20], Govindjee et al. [21], Halm and Dragon [22], Carol et al. [23],
Hansen et al. [24], Gatuingt and Pijaudier-Cabot [25], Brunig [26], Cicekli et al.
[27], Hammi and Horstemeyer [28].
On the other hand, some researchers used the methods based on damage
mechanics and combination of this method with theory of plasticity, discrete crack
approach and other techniques in order to simulation of crack and failure in
concrete dams. Ghrib and Tinawi [29, 30] and Mirzabozorg et al. [31] used damage
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 23
mechanics approach to study the static and dynamic behavior of concrete gravity
dams. Gunn [32, 33] used the damage mechanics approach in 3D space for
analyzing concrete structures under the static loads. Horii and Chen [34] illustrated
various methods to model the nonlinear behavior of mass concrete in gravity dams.
In their study, the problems in crack modeling; computational algorithm and
damping implementation were discussed in conjunction with safety assessment of
concrete dam against large earthquakes. Oliver et al. [35] presented a continuum
strong discontinuity approach to consider cracking of concrete. Criteria for onset
and propagation of material failure and specific finite elements with embedded
discontinuities were sketched and some numerical simulations of cracking in plain
and reinforced concrete specimens were presented. Pekau and Yuzhu [36] presented
a study on the dynamic behavior of the fractured Koyna dam during earthquakes
using the distinct element method. They modeled the hydrodynamic effect using
the added mass approach. Calayir and Karaton [37] presented a paper in which the
earthquake damage response of concrete gravity dams is considered including the
effect of reservoir interaction. In their work, 2D damage mechanics approach
similar to that introduced in Mirzabozorg et al. [31] was utilized to model the
nonlinear behavior of the dam body in 2D space and the reservoir was modeled in
the Lagrangian space. Ardakanian et al. [38] developed an anisotropic damage
mechanics approach to consider the nonlinear seismic response of concrete dams in
3D space when the reservoir is assumed compressible. Oliveira and Faria [39]
studied the failure scenarios of concrete dams. In their work, a continuum damage
mechanics model that incorporates two independent scalar damage variables in
tension and compression was adopted in which both in tension and compression
material softening is reproduced.
In the present study, the nonlinear response of an arch dam-reservoir system is
investigated under seismic loading. An anisotropic non-uniform damage mechanics
approach was used for cracking simulation of mass concrete under dynamic loads
considering fluid-structure interaction effects. Non-uniform cracking means that
cracks in the candidate element propagate within the Gaussian points.
The major efficiency of this method is the ability of evaluating nonlinear
seismic behavior of concrete dams in 3D space using large elements and also, its
ability of more accurate tracing crack paths within the dam body and reducing time
and saving analysis requirements. Considering that all previous investigations on
arch and arch RCC dams are just take into account the effects of contraction and in
some cases perimetral joints effects and also almost all of them used the discrete
crack approach for simulation of weak vertical planes, in the present paper the
effects of horizontal lines (lift joints) are simulated based on continuum mechanics
approach and assuming orthotropic characteristics for mass concrete in the direction
perpendicular to the lift surfaces.
1. Constitutive Relationship for Mass Concrete. In order to analysis of a
structural system utilizing the damage mechanics approach, the proposed method
should be able to simulate the behavior of the element in different states as follow;
Pre-softening behavior, fracture energy conservation, nonlinear behavior during the
softening phase and finally crack closing/reopening behavior. The following
sub-sections represent a brief review on general concepts of the utilized method in
this study.
24 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
1.1. Pre-Softening Relationship. In the general, the relationship of the stress
and strain vectors at the pre-softening phase is given as
{ } [ ] { },� �� D 0 (1)
where [ ]D 0 is the elastic modulus matrix and { }� and { }� are the vector of stress
and strain components, respectively. Assuming isotropic linear behavior at the
pre-softening phase, the modulus matrix of [ ]D
isotropic
0 is given as
[ ]
( )( )
.
D
E
sym
isotropic
0 1 1 2
1
1
1
0 0 0
1 2
2
�
� �
�
�
�
�
� �
�
� �
� � �
�
0 0 0 0
1 2
2
0 0 0 0 0
1 2
2
�
�
�
�
�
)
)
, (2)
where E and � are isotropic modulus of elasticity and Poisson’s ratio within
material. Similarly orthotropic elastic modulus matrix [ ]D
orthotropic
0 may be used
for simulating the linear behavior of materials such as RCC as following:
[ ]D
orthotropic
0 �
�
�
� �
�
1
1
� �
� � � � �
�
yz zy
y z
xy xz zy
z x
zx xz
z x
xz
E E
E E E E
sym
�
� �
.
� � � � � � �xy yz
x y
yz xz yz
x y
xy yx
x y
yz
E E E E E E
G
� � �
� �1
0 0 0 2
0 0 0 0 2
0 0 0 0 0 2
G
G
zx
xy
�
�
�
, (3)
in which,
��
� � � �1 2� � � � � � � � �xy yx yz zy zx xz xy yz zx
x y zE E E
, (4)
where �xy , � yx , �xz , � zx , � yz , and � zy are Poisson’s ratio respect to x , y , and z
axis, Ex , E y , and E z are the Young modulus, and Gxy , G yz , and G zx are shear
modulus in planes parallel to xy , yz , and zx planes, respectively.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 25
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
The above mentioned matrix is a symmetric and so we have
� �yz
y
zy
zE E
� ,
� �zx
z
xz
xE E
� ,
� �xy
x
yx
yE E
� . (5)
In addition, the shear modulus can be obtained as follow:
G
E
ij
j
ij
�
�2 1( )
,
� (6)
where i j x y z, , ,� are three orthogonal directions.
1.2. Softening Initiation Criterion. In the present model, the uniaxial strain
energy (the area under the stress–strain curve up to the peak stress point or
apparent tensile stress) is used as softening initiation criterion. The crack initiates
when uniaxial strain energy density, � �1 1 2, is greater than U 0 in static conditions
U d
i i
i
0
0
2
� �� �
� �
�
�
, (7)
where � i and � i are the apparent tensile strength and its corresponding strain,
respectively. Considering that the properties of material changes under dynamic
loads, the strain rate effect under dynamic loads is applied on the crack initiation
criterion as follow:
� �
�
�U
E
U DMF
i
e0
2
0
2�
( ) , (8)
where DMFe is dynamic magnification factor and the parameters with the prime
sign indicate properties in dynamic condition.
1.3. Softening Relationship. During the softening phase the elastic stress–
strain relationship is replaced using the damaged modulus matrix in each of the
three principal directions. In the present paper, the secant modulus stiffness (SMS)
approach is used for the stiffness matrix formulation. Based on this approach, the
constitutive law is defined in terms of total stresses and strains as shown in Fig. 1.
26 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
Fig. 1. SMS formulation of the modulus matrix.
Considering the energy equivalence principle and neglecting the coupling
between the three principal fracture modes, the damaged modulus matrix is given
as
[ ]
[ ]
[ ]
D
D
D
d
d
t
d
r�
�
�
�
0
0
(9)
where
[ ]
( )( )
D
E
d
t �
� �
�
1 1 2� �
�
� �
� � � �
�
( )( ) .
( )( ) ( )( )
( )(
1 1
1 1 1 1
1
1
2
1 2 2
2
1
�
� �
�
d sym
d d d
d 1 1 1 1 13 2 3 3
2� � � � �
�
�
�
d d d d) ( )( ) ( )( )
,
� �
(10)
[ ]
( ) ( )
( ) ( )
.
( )
D G
d d
d d
sym
d
d
r �
� �
� � �
�
2 1 1
1 1
0
2 1
1
2
2
2
1
2
2
2
2
2 ( )
( ) ( )
( ) ( )
( ) (
1
1 1
0 0
2 1 1
1 1
3
2
2
2
3
2
1
2
3
2
1
2
�
� � �
� �
� � �
d
d d
d d
d d3
2)
,
�
�
�
(11)
where d1 , d2 , and d3 are the damage variables corresponding to the principal
strains in the local directions. Satisfying the principle of energy equivalence and
assuming the linear stress–strain curve in the post-peak phase as shown in Fig. 1,
d i is given as
d i
i
i
f
� � �
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�1 1
0 0
0
�
�
� �
� �
, (12)
where �0 and � f are the stains corresponding to the crack initiation and no
resistance strain, respectively, and � i is the principal strain of the element in the
considered direction. The proposed modulus matrix includes all of the principal
fracture modes. However, as mentioned, in the proposed formulation, the interaction
between the three principal fracture modes and mixed modes is neglected.
The damaged modulus matrix shown in equation (9) is in the local coordinate
which is corresponding to the direction of the principal strains. This matrix should
be transformed to the global coordinate as following:
[ ] [ ] [ ] [ ]D T D TS
T
d� (13)
where [ ]T is the strain transformation matrix. Based on the maximum strain
reached in each principal direction, the secant modulus matrix is determined as
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 27
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
shown in Fig. 1. Clearly, increasing of the strain leads to increasing the
corresponding damage variable and finally, when the strain reaches to the fracture
strain, the element is fully cracked in the corresponding direction and the related
damage variable sets to be unit. In fact, any change in the principal strain or its
direction leads to update requirement of the global constitutive matrix, [ ]D S .
Satisfying the fracture energy conservation principle in the static and the dynamic
loading conditions, the no resistance strain is given as
�
�f
f
c
G
h
�
2
0
, � �
�
�
�
�f
f
c
G
h
2
0
, (14)
where hc is the characteristic dimension of the cracked Gaussian point and is
assumed equal to the third root of the Gaussian point’s contribution volume within
the cracked element. The primed quantities show the dynamic constitutive
parameters. The strain-rate sensitivity of the specific fracture energy is taken into
account through the dynamic magnification factor DMF f as follows:
� �G G DMFf f f . (15)
It is worth noting that DMF f is mainly contributed by DMFe .
1.4. Crack Closing/Reopening. In the current formulation, co-axial rotating
crack model (CRCM) is used to simulation of the cracked Gaussian point’s
behavior within the cracked elements. In this approach shear stiffness factors
[arrays of matrix in Eq. (11)] are determined based on the state of the Gaussian
point in each principal direction in the current time step. As softening within the
considered element progresses, the shear stiffness factor in the cracked Gaussian
point decreases corresponding to the state of the principle strains and may reach to
zero value and therefore, the constitutive matrices contributions of the cracked
Gaussian point and finally, the constitutive matrix of the considered element must
be updated as these factors are changed [40, 41].
Under the cyclic loading, there is residual strain in the closed Gaussian point.
This concept has been used in the element level approaches in which the total
strain in each Gaussian point is decomposed into the two components of the elastic
and the residual strain given as Ardakanian et al. [38]:
� � � � ��� � � �e in e
max , (16)
where �max is the maximum principal strain which the Gaussian point has reached
during the previous cycles and � is the ratio between the residual strain in the
closed Gaussian point and the maximum principal strain and is normally given as
0.2. Figure 2 summarizes the crack closing/reopening algorithm applied in the
present numerical approach.
2. Dam–Reservoir Interaction. In order to obtain accurate responses of dam
under dynamic loads it is required that an appropriate formulation is governed for
dam–reservoir interaction problem and suitable boundary conditions are defined
for reservoir medium.
28 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
2.1. Boundary Conditions. Hydrodynamic pressure distribution in reservoir is
governed by pressure wave equation. Assuming that water is linearly compressible
and neglecting viscosity, small-amplitude irrotational motion of water is governed
by Helmholtz equation given as
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 29
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
Fig. 2. The closing/reopening algorithm for cracked Gaussian point [40].
� �2
2
1
p x y z
C
p x y z t( , , ) ��( , , , ), (17)
where p is hydrodynamic pressure and C is velocity of pressure wave in water.
The boundary conditions required for solving the above differential equation is
given in Fig. 3. In addition, this figure represents the coupled equations governing
the dynamic behavior of the structure and the reservoir stored in its upstream (US).
2.2. Solving the Coupled Equation. The coupled equations of dam–reservoir–
foundation system are solved using the staggered displacement method in which
the direct integration scheme is used to determine the displacement and
hydrodynamic pressure at time increment i�1. The �-method is utilized for
discretization of both equations (implicit–implicit method). In this method, the
velocity and displacement at time step i�1 can be written as
30 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
Fig. 3. Mathematical definition of reservoir various boundary conditions.
{ �} { �} { ��} ,
{ �} { �} ( )
U U t U
U U
i i
p
i
i
p
i
� � �
�
� �
� � �
1 1 1
1 1
�
�
�
�t U i{ ��} ,
(18)
{ } { } { ��} ,
{ } { } { �} (
U U t U
U U t U
i i
p
i
i
p
i i
� � �
�
� �
� � �
1 1
2
1
1
��
� 0 5 2. ) { ��} ,� � �t U i
(19)
where � and � are the integration parameters. The similar equations can be
written for determining { �} ,P i
p
�1 { } ,P i�1 and { } .P i
p
�1 The terms with superscript p
represent displacement, velocity and pressure quantities at time step i�1 which
are obtained using the pertinent quantities at time step i. The governing field
equations at time i�1 can be written as
[ ]{ ��} [ ]{ �} ( )[ ]{ }M U C U K Ui i i� � �� � � �1 1 11 �
� � �� �{ } [ ]{ } [ ]{ } ,F Q P K Ui i i1 1 1 � (20)
[ ]{ ��} [ ]{ �} ( )[ ]{ }G P C P K Pi i i� � �� � � � � �1 1 11 �
� � � �� �{ } [ ] { ��} [ ]{ } ,F Q U K Pi
T
i i2 1 1� � (21)
where � is related to the numerical damping of the solver algorithm. The coupled
field Eqs. (20) and (21) are solved using the staggered displacement solution
scheme [41]. In this method, Eq. (20) is approximated as
[ ]{ ��} { } [ ]{ } ( )[ ]{ } [*M U F Q P K Ui i i
p
i
p
� � � �� � � � �1 1 1 1 11 � � K U i]{ } . (22)
Combining Eqs. (20) and (22) using Eqs. (18) and (19) gives
[ ]{ ��} [ ]{ ��} [ ]{ ��} [ ]{ ��
*M U M U t Q P t ci i i� � �� � �1 1
2
1� �� � U i} � �1
� � �( ) [ ]{ ��} .1 2
1� ��t K U i (23)
The lumped mass results in a diagonal mass matrix. This property is utilized
in modifying Eq. (23) such that
[ ]{ ��} [ ]{ ��} [ ]{ ��} .*M U M U t Q Pi i i� � �� �1 1
2
1�� (24)
Substituting Eq. (24) into Eq. (21), then
([ ] [ ] [ ] [ ]){ ��} [ ]{ �} ( )[C t Q M Q P C PT
i i� � � � ��
� ��� �� 2 1
1 1 1 � ��K P i]{ } 1
� � � �� �{ } [ ] { ��} [ ]{ } .*F Q U K Pi
T
i i2 1 1� � (25)
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 31
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
In Eq. (25), the right hand side terms are known; thus, { }P i�1 is obtained. In
order to correct the approximation made in Eq. (24), { }P i�1 is substituted in Eq.
(13) to calculate { }U i�1 and its derivatives. The procedure of the staggered
displacement method is summarized by the following steps:
Step 1: Knowing the displacement, velocity and pressure at time i, { ��}*U i�1 is
obtained from Eq. (22).
Step 2: { ��}*U i�1 is introduced in Eq. (25) to calculate { } .P i�1
Step 3: { }P i�1 is substituted into Eq. (20) to calculate { }U i�1 and its
derivatives.
3. Numerical Model and Finite Element Implementation. Karadj double
curvature arch dam, located in Iran, is selected to obtain the effects of the
orthotropic material on the nonlinear seismic response of the structure. The height
of dam is 168 m and its crest length is 390 m. Its thickness at the base and crest
level are 32 and 7.85 m, respectively. The normal water level for this dam is 1760 m
in summer condition and corresponding reservoir capacity is 203 Mm3. The
vertical arches in this dam are consisting of quadratic curves where their equations
are presented in Fig. 4a. In addition the radii of horizontal arches and
corresponding central angle of arcs are shown in Fig. 4b. The general view and
developed finite element model of dam–reservoir–foundation system are depicted
in Fig. 5. The dam structure is modeled with 72 isoparametric twenty-node
elements and its foundation medium surrounding the dam body is simulated using
980 elements. The depth of the foundation model is about twice of the dam height
in the three global directions. The fluid is modeled using 1024 isoparametric
eight-node fluid elements and is extended about twice of the dam height in the
upstream direction.
The twenty-node isoparametric solid finite elements are implemented to
model the structure, mathematically. The requirement for integration and generation
of the mass, stiffness and damping matrices for this type of element is 27 Gaussian
points in 3 3 3� � order within each element. Figure 6a shows the ordering of the
Gaussian points within the solid elements. Reservoir domain is modeled using
eight-node isoparametric fluid elements with 2 2 2� � Gaussian integration points
32 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
a b
Fig. 4. Characteristics and equation of vertical arcs in central block (a) and geometric characteristics
of the horizontal arcs (b).
(Fig. 6b). For the interface elements between the structure and the liquid, 3 3�
Gaussian integration points are used (Fig. 6c) and for the other surface elements on
the boundary of liquid, 2 2� Gaussian integration points are employed. For
implementation of appropriate interaction in boundaries of reservoir domain, 64
surface elements are used on the reservoir–dam interface. Also 384 and 64 surface
elements are used for modeling the reservoir–foundation interface and reservoir
far-end boundary, respectively.
Material properties of mass concrete in isotropic and orthotropic conditions
are extracted based on appropriate test as reported in Table 1. It is noteworthy that
orthotropic material was considered in present study for take into account the
effects of lift joints under static and seismic loads. In this paper the properties of
orthotropic material is assumed to be same with isotropic material properties in two
horizontal directions (horizontal dam section) and the new properties is defined for
concrete in vertical direction (perpendicular to the lift surfaces).
For the foundation medium, the modulus of elasticity, Poisson’s ratio, and the
unit weight are taken as 16.3 GPa, 0.15, and 29.4 kN/m3, respectively. The
velocity of wave propagation and the unit weight of water in the reservoir are
assumed 1436 m/s and 9.807 kN/m3, respectively. The wave reflection coefficient
of the reservoir bottom and sides is given as 0.8, conservatively.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 33
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
a b
Fig. 5. General view of Karadj arch dam and its valley (a) and finite element model of the dam body,
foundation, and reservoir (b).
a b c
Fig. 6. Ordering of Gaussian points within twenty-node solid elements (a); eight-node fluid
elements (b); four-node solid-fluid interface elements (c).
The stiffness proportional damping is used in the conducted analyses in which
the damping ratio for the fundamental mode is taken to be 10%. Applied loads on
the system are the self weight, the hydrostatic pressure and the seismic load. The
values of the integration parameters in the �-method are taken as ���0 2. ,
��0 36. , and � �0 7. . The quasi-linear damping mechanism is used for the
structure in the dynamic analysis in which the stiffness proportional damping is
updated during the element cracking within the dam body.
34 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
T a b l e 1
Isotropic and Orthotropic Properties of Mass Concrete
Characteristic Isotropic material Orthotropic material*
Static
condition
Dynamic
condition
Static
condition
Dynamic
condition
Modulus of elasticity (GPa) 26.0 32.5 21.6 27.0
Poisson’s ratio 0.17 0.13 0.16 0.12
Unit weight (kN/m3) 24.027 24.027 24.027 24.027
Tensile strength (MPa) 3.66 5.50 3.00 4.50
* Orthotropic properties presented here are in vertical direction. Properties for other directions are
same as isotropic material.
Fig. 7. Components of the Manjil earthquake on 20 June1990: (a) US/DS component; (b) cross-
stream component; (c) vertical component.
a
c
b
Figure 7 shows three components of the ground motion recorded at the
Ab-Bar station during Manjil earthquake at 20 June 1990, which was chosen for
the analyses. It’s noteworthy that record has been obtained based on probabilistic
seismic hazard analysis of dam site and normalized/filtered for the Karadj dam site.
The horizontal and vertical PGAs at maximum credible level (MCL) are 0.43 and
0.33 g at the dam site, respectively.
4. Results. This section provides the results of linear and nonlinear analysis of
dam–reservoir–foundation system in seismic condition. Figure 8 shows the
comparison of displacement time-history at mid-point of the crest in the stream
direction for isotropic and orthotropic materials resulted from linear analysis. As
can be seen, both models experience crest displacement about 39 mm in the DS
direction due to self-weight and hydrostatic pressure. There is great consistency
between the two models under seismic loads. The maximum crest displacement in
the downstream direction for isotropic material is 111.8 mm while this value for
the model with orthotropic material reaches 113.5 mm. The same consistency
between the provided two models can be found in the vertical and cross-stream
directions so that the maximum crest displacements in vertical and cross stream
directions for the case with isotropic material are 34.3 and 46 mm, respectively.
These values for the case with orthotropic material reach to 35.1 and 45.4 mm.
For the case with isotropic material, both maximum tensile arch and cantilever
stresses occur at time 7.050 s. Figure 9 shows the contours of arch and cantilever
stresses at the time of maximum stresses occurrence. As can be seen, high arch
stresses occur on the US face in vicinity of the crest and also on the DS face near
the abutments and at the bottom of the dam body. In addition, due to cantilever
action of the blocks, high cantilever stresses are observed on the US face in
vicinity of the crest and also at upper parts of the DS face near the crest and
abutments.
Utilizing orthotropic material in the model leads to generation of maximum
tensile arch and cantilever stresses at different times. Based on the results, the
maximum tensile arch stress occurs at time 7.050 s, while the maximum tensile
cantilever stress occurs at time 7.475 s. Figure 10 shows contours of arch and
cantilever stresses at the time of maximum stresses occurrence. Looking at the
figures, the location of high tensile arch stresses on the US and DS faces are very
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 35
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
Fig. 8. Time-history of crest displacement in the stream direction using linear analysis for isotropic
and orthotropic materials.
similar in the cases with isotropic and orthotropic materials. On the other hand,
location of high tensile cantilever stresses resulted from the two provided modes
are different, especially on the DS face.
Figure 11 represents time-history of the crest displacement in the stream
direction when tensile cracking is permitted within the dam body. As in linear
analyses, the two nonlinear analyses are conducted so that at the first analysis, the
initial material defined for the intact mass concrete is isotropic and for the second
one, the intact material is orthotropic so that the initial elastic modulus and tensile
strength in vertical direction is different from the two other directions. Clearly,
after cracking initiation at each Gaussian point, the behavior at the cracked point is
anisotropic as defined in the proposed damage mechanics model.
As the previous analyses with linear models, there is good consistency
between the two models while using nonlinear models lead to higher displacements.
The maximum displacement for isotropic-based material is 117.4 mm in the
downstream direction while due to utilizing orthotropic material the crest
experiences 128.7 mm movement in the downstream direction. In addition based
on the isotropic material used model, the dam has displacements about 48.3 and
36.02 mm in the cross-stream and vertical directions, respectively. The values of
corresponding displacements using orthotropic material are 50.4 and 40.21 mm.
36 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
a c
b d
Fig. 9. Arch and cantilever stress contours at the time of maximum stresses based on linear analysis and
isotropic material using mass-less foundation: (a) arch stress in US; (b) arch stress in DS; (c) cantilever
stress in US; (d) cantilever stress in DS.
Figure 12 shows crack profiles within the dam body at the end of the
nonlinear analysis. As can be seen, in the model using isotropic-based material,
there is just one cracked element under seismic loads while using orthotropic-
based material leads to more severe damage within the dam body. The cracked
areas are concentrated in bottom of the dam and also upper parts of the body near
the crest.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 37
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
Fig. 10. Arch and cantilever stress contours at the time of maximum stresses based on linear analysis
and orthotropic material using mass-less foundation: (a) arch stress in US; (b) arch stress in DS;
(c) cantilever stress in US; (d) cantilever stress in DS.
a c
b d
Fig. 11. Time-history of crest displacement in stream direction using nonlinear analysis for isotropic
and orthotropic materials.
6. Discussion. In the previous section the linear and nonlinear response of
arch dam–reservoir–foundation system was studied using isotropic-based and
orthotropic-based material. Foundation medium was assumed to be mass-less and
just its stiffness matrix was considered in overall coupled equations. Table 2
summarizes the values of crest displacement in three orthogonal directions. As can
be seen, almost in all cases using orthotropic-based material leads to higher
displacement. Also damage analysis of the system leads to more displacement due
to cracking of elements and softening of the dam body.
Figure 13 shows the contours of arch and cantilever tensile stresses at the time
of maximum stresses for linear analysis of the dam body on rigid foundation for
isotropic-based materials. Maximum tensile arch stresses are at t � 8.135 s while
the maximum of tensile cantilever stresses occurs at t � 7.515 s. The location of
high arch stresses are the same with those obtained from mass-less foundation
while the area with high cantilever stresses are relocated from upper parts of the
dam in mass-less model to the interface of the dam-foundation and also middle part
of the dam body in the rigid foundation model. The values of arch stresses have
increased in the case with rigid foundation while the values of cantilever stresses
have reduced. Figure 14 represents the same plots for orthotropic-based materials
in linear analysis of the system on the rigid foundation. Using rigid foundation
decreases both arch and cantilever stresses for orthotropic materials.
38 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
a b
Fig. 12. Crack profile under nonlinear seismic analysis using mass-less foundation in isotropic- (a)
and orthotropic-based (b) material.
T a b l e 2
Maximum Displacement Values (mm) in Crest Points Using Mass-Less Foundation
Model Position Isotropic-based material Orthotropic-based material
Stream Cross-stream Vertical Stream Cross-stream Vertical
Linear Mid-point
Left-quarter
Right-quarter
111.8
70.1
69.1
46.0
44.9
31.9
34.3
13.7
15.2
113.5
78.1
66.8
45.4
46.6
36.6
35.1
15.3
16.0
Nonlinear Mid-point
Left-quarter
Right-quarter
117.4
73.6
72.5
48.3
47.1
33.5
36.0
14.4
15.9
128.7
80.0
80.4
50.4
49.5
39.1
40.2
17.6
19.2
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 39
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
Fig. 13. Arch and cantilever stress contours at the time of maximum stresses based on linear analysis
and isotropic material using rigid foundation: (a) arch stress in US; (b) arch stress in DS; (c) cantilever
stress in US; (d) cantilever stress in DS.
Fig. 14. Arch and cantilever stress contours at the time of maximum stresses based on linear
analysis and orthotropic material using rigid foundation: (a) arch stress in US; (b) arch stress in DS;
(c) cantilever stress in US; (d) cantilever stress in DS.
a c
b d
a c
b d
Table 3 summarizes the values of crest displacement in three directions using
the system with rigid foundation. Like as mass-less foundation model using
orthotropic-based material leads to higher displacement for most cases. In
addition, comparing the two models, it can be found that we have lower values
of displacements for the model with rigid foundation, which is logical and
expected.
Figure 15 shows crack profile in the dam body at the end of the nonlinear
analysis when the system is on the rigid foundation. Like the previous model,
orthotropic-based material leads to more damage. For the isotropic-based material
the number of cracked elements is same in mass-less and rigid foundations (one
cracked elements) while its location differs. For the orthotropic-based material the
crack profiles are completely different, in a way that the cracked elements are
distributed in lower and upper parts of the body.
One of the main shortcomings of the conducted analyses is neglecting the
effect of vertical joints due to scope limit of the study. Obviously, vertical
contraction joints can affect the seismic response of the body significantly. However,
the main object of the current study is considering the lift joint effects on the
seismic response. Taking into account the vertical joint effects is in future work of
the authors.
40 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
T a b l e 3
Maximum Displacement Values (mm) in Crest Points Using Rigid Foundation
Model Position Isotropic-based material Orthotropic-based material
Stream Cross-stream Vertical Stream Cross-stream Vertical
Linear Mid-point
Left-quarter
Right-quarter
101.0
49.6
56.8
30.6
22.8
22.2
36.4
8.9
10.1
103.0
51.1
62.5
34.0
32.4
24.2
37.2
9.8
11.6
Nonlinear Mid-point
Left-quarter
Right-quarter
107.3
61.2
61.2
33.8
23.6
23.7
39.5
10.8
13.9
117.0
55.9
65.8
37.9
29.0
25.5
42.8
11.8
15.2
a b
Fig. 15. Crack profile under nonlinear seismic analysis using mass-less foundation in isotropic- (a)
and orthotropic-based (b) material.
Conclusions. In the present paper, an anisotropic damage mechanics approach
was introduced and its application for seismic assessment of concrete arch
dam–reservoir–foundation system was investigated. Due to main object of the
study and considering that the effects of contraction joints have been investigated
by many researchers simulation of contraction joints was neglected in the present
case and only lift joints were taken into account. Two different characteristics were
assumed for mass concrete in which in the first model, the dam body was modeled
using isotropic material and in the second one orthotropic material was used in a
direction perpendicular to the lift surfaces in order to considering weak horizontal
planes. Reservoir was modeled by Eulerian fluid elements and foundation medium
assumed to be both rigid and mass-less. The dynamic equilibrium equation of the
coupled system was solved using the staggered displacement method.
Results show that generally, using orthotropic-based material lead to higher
values of displacements in benchmark points in comparison with the model with
isotropic-based material in both linear and nonlinear analyses; however their
differences are significant for nonlinear case (using anisotropic damage mechanics).
In addition, using mass-less foundation leads to higher displacement than rigid one.
Due to arrangement of material properties, in both isotropic- and orthotropic-based
materials and also mass-less and rigid foundations, the pattern of arch stresses at
the time of maximum arch stress are close to each other and concentrated in
vicinity of the crest on the upstream face and near the abutments on the downstream
face. Because of different properties of orthotropic-based material in vertical
direction, the pattern of cantilever stresses has some differences especially on the
downstream face. Mass-less foundation leads to relocation of the area with high
cantilever stresses from upper parts of the dam to the dam-foundation interface and
also middle part of the body. Moreover, using orthotropic-based materials in
conjunction with anisotropic damage mechanics approach generates more damages
in the dam body than to isotropic-based materials for both mass-less and rigid
foundations; however the crack profile changes by foundation condition.
Ð å ç þ ì å
Íà â³äì³íó â³ä ìîäåëþâàííÿ óñàäêîâèõ øâ³â, ïðè ÷èñåëüíîìó àíàë³ç³ áåòîí-
íèõ àðî÷íèõ ãðåáåëü ðîáîòà ³ âïëèâ áóä³âåëüíèõ øâ³â çàçâè÷àé íå âðàõîâó-
þòüñÿ. Äîñë³äæóºòüñÿ ñåéñì³÷íà íåë³í³éíà ðåàêö³ÿ ñèñòåìè (áåòîííà) àðî÷íà
ãðåáëÿ–ðåçåðâóàð–îñíîâà ç óðàõóâàííÿì 䳿 áóä³âåëüíèõ øâ³â íà îñíîâ³ îðòî-
òðîïíîãî ìàòåð³àëó. Ïðåäñòàâëåíèé àí³çîòðîïíèé ï³äõ³ä äî ìåõàí³êè ðóéíó-
âàííÿ çì³íåíî äëÿ óðàõóâàííÿ ñëàáêèõ ãîðèçîíòàëüíèõ ïëîùèí ì³æ øàðàìè
áåòîíó â ïðîöåñ³ áóä³âíèöòâà. Öÿ ìîäåëü äîïóñêຠóðàõóâàííÿ õàðàêòåðèñòè-
êè ïîïåðåäíüîãî ðîçì’ÿêøåííÿ, êðèòåð³þ âèíèêíåííÿ ðîçì’ÿêøåííÿ ³ õàðàê-
òåðèñòèêè àí³çîòðîïíîãî ðîçòð³ñêóâàííÿ. Çà äîïîìîãîþ ìåòîäó ñõ³ä÷àñòèõ
ïåðåì³ùåíü, ïðèïóñêàþ÷è, ùî ñêåëüîâó îñíîâó ñêëàäàþòü íåâàãîì³ æîðñòê³
ò³ëà, ðîçâ’ÿçàíî ñèñòåìó çâ’ÿçàíèõ ð³âíÿíü ðóõó â ñèñòåì³ ãðåáëÿ–ðåçåðâóàð.
Ðóõ ´ðóíòó çà òðèêîìïîíåíòíîþ òåõíîëî㳺þ çáóäæóº äàíó ñèñòåìó íà ìàêñè-
ìàëüíî ³ìîâ³ðíîìó ð³âí³. Óñòàíîâëåíî, ùî âèêîðèñòàííÿ îðòîòðîïíîãî ìàòå-
ð³àëó çá³ëüøóº çì³ùåííÿ ãðåáåíÿ ãðåáë³ ³, ÿê íàñë³äîê, ïîøêîäæåííÿ ò³ëà
ãðåáë³ â á³ëüø³é ì³ð³ ïîð³âíÿíî ç âèêîðèñòàííÿì ðîçïîâñþäæåíîãî ³çîòðîï-
íîãî ìàòåð³àëó.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 41
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
1. J. R. Hess, “RCC lift-joint strength,” Concrete Int., 24, No. 1, 50–56 (2002).
2. H. Arabshahi and V. Lotfi, “Nonlinear dynamic analysis of arch dams with
joint sliding mechanism,” Eng. Comput., 26, No. 5, 464–482 (2009).
3. L. Fronteddu, P. Leger, and R. Tinawi, “Static and dynamic behavior of
concrete lift joint interfaces,” J. Struct. Eng., 124, No. 12, 1418–1430 (1998).
4. E. Puntel, G. Bolzon, and V. E. Saouma, “An experimental and numerical
investigation of concrete dam joints,” in: Proc. 11th Int. Conf. on Fracture
(ICF XI), Turin, Italy (2005), p. 396.
5. S. Mojtahedi and G. Fenves, Effects of Contraction Joint Opening on Pacoima
Dam in 1994 Northridge Earthquake, Report CSMIP/00-05, University of
California, Berkeley, USA (2000).
6. S. Malla and M. Wieland, “Analysis of an arch-gravity dam with a horizontal
crack,” Comput. Struct., 72, 267–278 (1999).
7. M. Wieland and S. Malla, “Earthquake safety of an arch-gravity dam with a
horizontal crack in the upper portion of the dam,” in: Proc. 12th World Conf.
on Earthquake Engineering, Auckland, New Zealand (2000).
8. N. R. Hansen and H. L. Schreyer, “A thermodynamically consistent framework
for theories of elasto-plasticity coupled with damage,” Int. J. Solids Struct.,
31, No. 3, 359–389 (1994).
9. I. Doghri and L. Tinel, “Micromechanical modeling and computation of
elasto-plastic materials reinforced with distributed orientation fibers,” Int. J.
Plasticity, 21, No. 10, 1919–1940 (2005).
10. A. Menzel, M. Ekh, K. Runesson, and P. Steinmann, “A framework for
multiplicative elastoplasticity with kinematic hardening coupled to anisotropic
damage,” Int. J. Plasticity, 21, 397–434 (2005).
11. G. Z. Voyiadjis, Z. N. Taqieddin, and P. I. Kattan, “Theoretical formulation of
a coupled elastic-plastic anisotropic damage model for concrete using the
strain energy equivalence concept,” Int. J. Damage Mech., 18, No. 7, 603–638
(2009).
12. J. Lee and G. L. Fenves, “A plastic-damage model for cyclic loading of
concrete structures,” J. Eng. Mech., 124, No. 8, 892–900 (1998).
13. L. Jason, G. Pijaudier-Cabot, A. Huerta, et al., “An elastic plastic damage
formulation for the behavior of concrete,” in: V. Li, C. K. Y. Leung, K. J.
William, and S. L. Billington,, (Eds.), Fracture Mechanics of Concrete
Structures (2004), p. 549–556.
14. N. Bonora, D. Gentile, A. Pirondi, and G. Newaz, “Ductile damage evolution
under triaxial state of stress: theory and experiments,” Int. J. Plasticity, 21,
981–1007 (2005).
15. L. Jason, A. Huerta, G. Pijaudier-Cabot, and S. Ghavamian, “An elastic plastic
damage formulation for concrete: application to elementary tests and comparison
with an isotropic damage model,” Comput. Meth. Appl. Mech. Eng., 195,
7077–7092 (2006).
16. A. Pirondi, N. Bonora, D. Steglich, et al., “Simulation of failure under cyclic
plastic loading by damage models,” Int. J. Plasticity, 22, 2146–2170 (2006).
42 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
17. J. U. Wu, J. Li, and R. Faria, “An energy release rate-based plastic-damage
model for concrete,” Int. J. Solids Struct., 43, 583–612 (2006).
18. D. J. Celentano and J. L. Chaboche, “Experimental and numerical
characterization of damage evolution in steels,” Int. J. Plasticity, 23, 1739–
1762 (2007).
19. J. L. Chaboche, “Development of continuum damage mechanic for elastic
solids sustaining anisotroic and unilateral damage,” Int. J. Damage Mech., 2,
311–329 (1993).
20. G. Z. Voyiadjis and T. M. Abu-Lebdeh, “Plasticity model for concrete using
the bounding surface concept,” Int. J. Plasticity, 10, 1–21 (1994).
21. S. Govindjee, G. J. Kay, and J. C. Simo, “Anisotropic modelling and
numerical simulation of brittle damage in concrete,” Int. J. Num. Meth. Eng.,
38, 3611–3633 (1995).
22. D. Halm and A., Dragon, “A model of anisotropic damage by mesocrack
growth: unilateral effect,” Int. J. Damage Mech., 5, 384–402 (1996).
23. I. Carol, E. Rizzi, and K. J. William, “On the formulation of anisotropic elastic
degradation. II: Generalized pseudo-Rankine model for tensile damage,” Int. J.
Solids Struct., 38, 519–546 (2001).
24. E. Hansen, K. William, and I. Carol, “A two-surface anisotropic damage/
plasticity model for plain concrete,” in: R. de Borst, J. Mazars, G. Pijaudier-
Cabot, and J. G. M. van Mier (Eds.), Fracture Mechanics of Concrete
Structures, Lisse, Balkema (2001), pp. 549–556.
25. F. Gatuingt and G. Pijaudier-Cabot, “Coupled damage and plasticity modeling
in transient dynamic analysis of concrete,” Int. J. Num. Anal. Meth. Geomech.,
26, 1–24 (2002).
26. M. Brunig, “An anisotropic ductile damage model based on irreversible
thermodynamics,” Int. J. Plasticity, 19, 1679–1713 (2003).
27. U. Cicekli, G. Z. Voyiadjis, and R. K. Abu Al-Rub, “A plasticity and
anisotropic damage model for plain concrete,” Int. J. Plasticity, 23, 1874–
1900 (2007).
28. Y. Hammi and M. F. Horstemeyer, “A physically motivated anisotropic
tensorial representation of damage with separate functions for void nucleation,
growth, and coalescence,” Int. J. Plasticity, 23, 1641–1678 (2007).
29. F. Ghrib and R. Tinawi, “Nonlinear behavior of concrete dams using damage
mechanics,” J. Eng. Mech., 121, No. 4, 513–526 (1995).
30. F. Ghrib and R. Tinawi, “An application of damage mechanics for seismic
analysis of concrete gravity dams,” Earthquake Eng. Struct. Dynamics, 24,
157–173 (1995).
31. H. Mirzabozorg, M. Ghaemian, and M. R. Kianoush, “Damage mechanics
approach in seismic analysis of concrete gravity dams including dam-reservoir
interaction,” Eur. Earthquake Eng., XVIII, No. 3, 17–24 (2004).
32. R. M. Gunn, “Non-linear design and safety analysis of arch dams using damage
mechanics. Pt. 1: Formulation,” Hydropowers & Dams, 2, 67–74 (2001).
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6 43
Orthotropic Material and Anisotropic Damage Mechanics Approach ...
33. R. M. Gunn, “Non-linear design and safety analysis of arch dams using damage
mechanics. Pt. 2: Applications,” Hydropowers & Dams, 3, 74–80 (2001).
34. H. Horii and S. C. Chen, “Computational fracture analysis of concrete gravity
dams by crack-embedded elements-toward an engineering evaluation of seismic
safety,” Eng. Fract. Mech., 70, 1029–1045 (2003).
35. J. Oliver, A. Huespe, M. D. G. Pulido, and S. Blanco, “Computational
modeling of cracking of concrete in strong discontinuity settings,” Comput.
Struct., 1, No. 1, 61–76 (2004).
36. O. A. Pekau and C. Yuzhu, “Failure analysis of fractured dams during
Earthquake by DEM,” Eng. Struct., 26, 1483–1502 (2004).
37. Y. Calayir and M. Karaton, “A continuum damage concrete model for
earthquake analysis of concrete gravity dam–reservoir systems,” Soil Dyn.
Earthquake Eng., 25, 857–869 (2005).
38. M. Ardakanian, M. Ghaemian, and H. Mirzabozorg, “Nonlinear behavior of
mass concrete in three-dimensional problems using damage mechanics
approach,” Eur. Earthquake Eng., 2, 65–89 (2006).
39. S. Oliveira and R. Faria, “Numerical simulation of collapse scenarios in
reduced scale tests of arch dams,” Eng. Struct., 28, 1430–1439 (2006).
40. H. Mirzabozorg, 3D Nonlinear Seismic Analysis of Concrete Dams Considering
Dam–Reservoir Interaction Effects, Ph.D. Thesis, Sharif University of
Technology, Tehran, Iran (2003).
41 H. Mirzabozorg, A. R. Khaloo, and M. Ghaemian, “Staggered solution
scheme for three dimensional analysis of dam reservoir interaction,” Dam
Eng., 14, No. 3, 147–179 (2003).
Received 30. 07. 2013
44 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2013, ¹ 6
M. A. Hariri-Ardebili and H. Mirzabozorg
<<
/ASCII85EncodePages false
/AllowTransparency false
/AutoPositionEPSFiles true
/AutoRotatePages /All
/Binding /Left
/CalGrayProfile (Dot Gain 20%)
/CalRGBProfile (sRGB IEC61966-2.1)
/CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2)
/sRGBProfile (sRGB IEC61966-2.1)
/CannotEmbedFontPolicy /Warning
/CompatibilityLevel 1.4
/CompressObjects /Tags
/CompressPages true
/ConvertImagesToIndexed true
/PassThroughJPEGImages true
/CreateJDFFile false
/CreateJobTicket false
/DefaultRenderingIntent /Default
/DetectBlends true
/DetectCurves 0.0000
/ColorConversionStrategy /LeaveColorUnchanged
/DoThumbnails false
/EmbedAllFonts true
/EmbedOpenType false
/ParseICCProfilesInComments true
/EmbedJobOptions true
/DSCReportingLevel 0
/EmitDSCWarnings false
/EndPage -1
/ImageMemory 1048576
/LockDistillerParams false
/MaxSubsetPct 100
/Optimize true
/OPM 1
/ParseDSCComments true
/ParseDSCCommentsForDocInfo true
/PreserveCopyPage true
/PreserveDICMYKValues true
/PreserveEPSInfo true
/PreserveFlatness true
/PreserveHalftoneInfo false
/PreserveOPIComments false
/PreserveOverprintSettings true
/StartPage 1
/SubsetFonts true
/TransferFunctionInfo /Apply
/UCRandBGInfo /Preserve
/UsePrologue false
/ColorSettingsFile ()
/AlwaysEmbed [ true
]
/NeverEmbed [ true
]
/AntiAliasColorImages false
/CropColorImages true
/ColorImageMinResolution 300
/ColorImageMinResolutionPolicy /OK
/DownsampleColorImages true
/ColorImageDownsampleType /Bicubic
/ColorImageResolution 300
/ColorImageDepth -1
/ColorImageMinDownsampleDepth 1
/ColorImageDownsampleThreshold 1.50000
/EncodeColorImages true
/ColorImageFilter /DCTEncode
/AutoFilterColorImages true
/ColorImageAutoFilterStrategy /JPEG
/ColorACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/ColorImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000ColorACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000ColorImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasGrayImages false
/CropGrayImages true
/GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK
/DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic
/GrayImageResolution 300
/GrayImageDepth -1
/GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000
/EncodeGrayImages true
/GrayImageFilter /DCTEncode
/AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG
/GrayACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/GrayImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000GrayACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000GrayImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasMonoImages false
/CropMonoImages true
/MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK
/DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic
/MonoImageResolution 1200
/MonoImageDepth -1
/MonoImageDownsampleThreshold 1.50000
/EncodeMonoImages true
/MonoImageFilter /CCITTFaxEncode
/MonoImageDict <<
/K -1
>>
/AllowPSXObjects false
/CheckCompliance [
/None
]
/PDFX1aCheck false
/PDFX3Check false
/PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true
/PDFXTrimBoxToMediaBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXOutputIntentProfile ()
/PDFXOutputConditionIdentifier ()
/PDFXOutputCondition ()
/PDFXRegistryName ()
/PDFXTrapped /False
/Description <<
/CHS <FEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000500044004600206587686353ef901a8fc7684c976262535370673a548c002000700072006f006f00660065007200208fdb884c9ad88d2891cf62535370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002>
/CHT <FEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef653ef5728684c9762537088686a5f548c002000700072006f006f00660065007200204e0a73725f979ad854c18cea7684521753706548679c300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002>
/DAN <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>
/DEU <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>
/ESP <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>
/FRA <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>
/ITA <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>
/JPN <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>
/KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020b370c2a4d06cd0d10020d504b9b0d1300020bc0f0020ad50c815ae30c5d0c11c0020ace0d488c9c8b85c0020c778c1c4d560002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken voor kwaliteitsafdrukken op desktopprinters en proofers. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
/NOR <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>
/PTB <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>
/SUO <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>
/SVE <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>
/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|