Influence of construction interfaces on dynamic characteristics of

J. Cent. South Univ. (2015) 22: 1521−1535
DOI: 10.1007/s11771-015-2669-5
Influence of construction interfaces on dynamic characteristics of
roller compacted concrete dams
GU Chong-shi(顾冲时)1, 2, 3, WANG Shao-wei(王少伟)1, 2, 3, BAO Teng-fei(包腾飞)1, 2, 3
1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,
Hohai University, Nanjing 210098, China;
2. National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety,
Hohai University, Nanjing 210098, China;
3. College of Water-Conservancy and Hydropower, Hohai University, Nanjing 210098, China
© Central South University Press and Springer-Verlag Berlin Heidelberg 2015
Abstract: To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams (RCCDs),
mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring artificial boundary (VSAB) is adopted
to simulate the radiation damping of their infinite foundations, and based on the Marc software, a simplified seismic motion input
method is presented by the equivalent nodal loads. Finally, based on the practical engineering of a RCC gravity dam, effects of
radiation damping and construction interfaces on the dynamic characteristics of dams are investigated in detail. Analysis results show
that dynamic response of the RCC gravity dam significantly reduces about 25% when the radiation damping of infinite foundation is
considered. Hot interfaces and the normal cold interfaces have little influence on the dynamic response of the RCC gravity dam.
However, nonlinear fracture along the cold interfaces at the dam heel will occur under the designed earthquake if the cold interfaces
are combined poorly. Therefore, to avoid the fractures along the construction interfaces under the potential super earthquakes,
combination quality of the RCC layers should be significantly ensured.
Key words: roller compacted concrete dam; construction interface; nonlinear fracture; radiation damping; viscous-spring artificial
boundary; dynamic response
1 Introduction
The construction technique of roller compacted
concrete dam (RCCD) has been rapidly developed in the
last 30 years. It is widely applied for its rapidness. With
the implementation of the National West to East Power
Transmission Project, a large number of high dams are
constructed or under construction in western China.
During this process, RCCD is more frequently adopted
by designers to shorten the construction period,
especially the RCC gravity dams. There are 49 RCCDs
in China with the dam height more than 100 m, and 36 of
them are gravity dams [1]. While all these RCCDs are
gravity dams if the dam height exceeds 150 m, such as
Longtan (Hmax=217 m, the highest RCCD in the world at
present), Huangdeng (Hmax=202 m), Guangzhao
(Hmax=201 m) and Guanyinyan RCC gravity dam
(Hmax=168 m). The special mountain valleys in western
China provide advantageous topographic conditions for
the construction of these high dams. However, dam
safety becomes an important issue in the western area
due to the complicated geological conditions as well as
strong earthquakes of high frequency. The recent
immense earthquake in Wenchuan of the Sichuan
province on May 12, 2008 in China, its huge destructive
force reminds us that more attention should be paid to
the seismic safety of dams.
A large number of construction interfaces exist in
dam bodies due to the construction technology of thin
roller compaction layers of the RCCDs. Under the effects
of material property, local weather condition,
construction machinery and management, and some
other construction influencing factors, these construction
interfaces perform as effect zones with actual thickness
and gradually changed mechanical properties [2−3].
What’s more, the disappearance or poor quality of
embedment between two adjacent concreting lifts always
results in a reduced bond strength of construction
interfaces, and the bigger maximum size of concrete
Foundation item: Projects(20120094110005, 20120094130003) supported by the Research Fund for the Doctoral Program of Higher Education of China;
Projects(51379068, 51139001, 51279052, 51209077, 51179066) supported by the National Natural Science Foundation of China;
Project(NCET-11-0628) supported by the Program for New Century Excellent Talents in University, China; Projects(201201038,
201101013) supported by the Public Welfare Industry Research Special Fund Project of Ministry of Water Resources of China
Received date: 2013−12−09; Accepted date: 2014−04−10
Corresponding author: WANG Shao-wei, PhD; Tel: +86−25−83786957; E-mail: [email protected]
J. Cent. South Univ. (2015) 22: 1521−1535
1522
aggregates, the lower bond strength [4]. Therefore,
nonlinear fracture may occur along these interfaces under
strong earthquakes.
However,
seismic
failure
mechanisms are more frequently focused on normal
concrete dams [5−7], and RCCDs are similarly treated in
which effects of the construction interfaces are ignored
[8−10]. So, it is more useful to study the mechanical
property of construction interface and its influence on the
seismic failure mechanism of RCCDs.
The key problem in studying the seismic failure
mechanism of the RCCDs under the influence of
construction interfaces by the finite element method
(FEM) is the acquisition of real dynamic responses of
dams. Dam seismic response analysis is actually a
simulation of seismic waves propagating in the open
system composed by dam body and its infinite
foundation. Under the effects of seismic waves, dam
vibration occurs, at the same time dam body will serve as
a scattering source to radiate energies to external
foundation during earthquakes, namely the radiation
damping of infinite foundations. Research results [11]
show that compared with the massless foundation input
model which does not consider the radiation damping,
seismic response of dam bodies in displacement and
stress are significantly reduced when using the
viscous-spring artificial boundary (VSAB) to model the
influence of radiation damping of infinite foundations.
The reduction amplitude ranges between 10% and 65%,
and the higher the foundation flexibility, the bigger the
reduction amplitude. The commonly used seismic input
model at present is the massless foundation model
proposed by CLOUGH [12] who just took the elasticity
of dam foundation into account, while the inertia effects
are ignored. Meanwhile, the massless foundation input
model is established on the finite foundation, so the
radiation of seismic energies to the external infinite
foundations cannot be simulated. Based on the numerical
simulation technology of FEM, wave differential
equations and physical boundary conditions are
dispersed in temporal and spatial domain, and virtual
artificial boundaries are established on the periphery of
the computational domain to insure that the scattered
waves caused by dam body can successfully propagate
out of the finite domain without reflection. These
artificial boundaries are viscous boundary [13], VSAB
[14−17], and artificial transmission boundary [18].
Especially the VSAB, which not only overcomes the
problem of instability at low frequency and the inability
of simulating the elastic recovery of infinite foundations
in the viscous boundary, but also there is no need to
increase a large number of boundary elements. In
addition, the seismic waves in VSAB can be translated
into equivalent nodal loads at the intercepted boundaries,
which can be easily realized in FEM.
In this work, to study the influence of construction
interfaces on the dynamic characteristics of the RCCDs,
mechanical properties of the RCC construction interfaces
are firstly analyzed. Then, according to the convention of
dam FE mesh in dynamic analyses, the equivalent nodal
loads of seismic waves at the intercepted boundaries of
the VSAB input model are respectively deduced, and a
simplified seismic motion input method is presented on
the basis of the Marc software. Based on the combination
of these two, a dynamic nonlinear fracture analysis
model for the RCCDs is established, in which the
radiation damping of infinite foundations and the
construction interfaces are both considered. Finally,
based on the practical engineering of a RCC gravity dam,
effects of radiation damping and construction interfaces
on the dynamic response are investigated in detail, and
some conclusions are drawn.
2
Mechanical
properties
construction interfaces
of
RCC
The biggest difference between the RCCDs and the
normal concrete dams is that the former are made up of
super-stiff concretes. Thin roller compaction layers by
large rolling equipments are conducted during the dam
filling, so a large number of slightly smooth construction
interfaces are formed in this process. Combination
quality of the compacted layers is affected by these
interfaces more or less; especially, the poor combination
quality will threaten the integrity of the RCCDs. From
the construction process of the RCCDs, these
construction interfaces can be divided into two types,
namely hot construction interfaces and cold construction
interfaces, which are determined by the interval time of
two adjacent RCC layers. Figure 1 shows the typical
structure model of RCC layers, in which B represents the
thickness of RCC layers and ba denotes the thickness of
effect zones.
Fig. 1 Structure model of RCC layers
2.1 Hot construction interface
RCCDs are commonly constructed by the
technology of thin roller compaction layers, and the
completed layer thickness is defined as 30 cm in Chinese
J. Cent. South Univ. (2015) 22: 1521−1535
1523
design specification. Research results show that
combinations between RCC layers are in good quality if
the upper RCC layers are poured in normal conditions
before the initial setting of the lower RCC layers, and the
mechanical properties of the interface effect zones
change slightly, so these interfaces are defined as the hot
construction interfaces [19]. Meanwhile, effect zones of
hot interfaces can be regarded the same as the RCC
noumena as isotropic medium due to their thin thickness.
However, back analysis results of mechanical parameters
of the RCCDs show that elastic modulus of the interface
effect zones is a little smaller than that of the RCC
noumena [20], so RCCs are layered structures consisting
of two isotropic mediums. Compared with the
aftermentioned so-called cold construction interface, hot
interfaces have a higher bond strength so that the
potential interface fracture under strong earthquakes may
firstly occur along the cold construction interfaces.
Therefore, to reduce the total number of FE meshes and
also take the mechanical properties of hot interfaces into
account, these hot interfaces are equivalently reflected by
the relevant RCC noumena, and the layered structures
are converted into the transversely isotropic bodies [21].
In the global coordinate system, the transversely
isotropic surface is assumed parallel to the xOy
coordinate surface, and z axis is perpendicular to the
interface. According to the theories of composite
material mechanics, and based on the limit conditions of
static equilibrium and deformation compatibility, the
layered structures can be converted into the transversely
isotropic body. Calculation models of series structure and
parallel structure used for determining the equivalent
elastic parameters of RCCs are shown in Fig. 2. For
example, as for the elastic modulus of E1 (in the direction
perpendicular to the interface), the series structure model
in Fig. 2(a) should be used, and the limit conditions
are:  z   az  (1   ) cz and  z   az   cz . The five
used equivalent elastic parameters for RCCs in the model
of transversely isotropic body are deduced as follows:
E1  Ec (1   )  Ea 
(1)
Ea Ec
Ea (1   )  Ec 
(2)
E2 
u1 
Ec c (1   )  Ea a 
Ec (1   )  Ea 
(3)
u2 
Ea Ec [ c (1   )  a  ]
[ Ea (1   )  Ec  ][ Ec (1   )  Ea  ]
(4)
G2 
Ga Gc
Ga (1   )  Gc 
(5)
where E1, μ1 and E2, μ2 are elastic modulus and Poisson
ratio in directions of parallel and perpendicular to the
interface, respectively; G2 is the plane shear modulus
perpendicular to the interface; β=(k−1)ba/[kbc+(k−1)ba] (k
is the number of roller compaction layers).
Then, the elasticity matrix D corresponding to the
stress−strain relationship of RCCs is expressed as
follows:
C1
C
 2
C
D 3
0
0

0
C3
C3
0
0
0
0
C3
0
0
0
C4
0
0
0
0
C5
0
0
0
0
C6
0
C1  E1
where
C3  E1
C2
C1
2
m
;
(1  n 2 2 )
;
(1  1 )m
C4  E2
0 
0 
0 

0 
0 

C6 
(6)
C2  E1
1  n2 2
;
(1  1 )m
1  1
E1
; C5 
; C6=G2;
m
2(1  1 )
n=E1/ E2; m  1  1  2n 22 .
Fig. 2 Equivalent calculation models of RCC layers: (a) Series
model; (b) Parallel model
2.2 Cold construction interface
RCCDs are compacted by the intermittent
construction technology. Long time interval between the
continuous concreting lifts (usually 3.0 m every placing
lift) is designed to satisfy the temperature control and
some other field operations. The interval time is usually
a few days, which exceeds the initial setting time of RCC,
so the cold construction interfaces are formed in this
period. Layer face treatments, such as interface
roughening and laying mortar cushion, are implemented
before the next concreting lift. However, bond strength
of the cold construction interfaces is obviously reduced
due to the disappearance or poor quality of embedment
between two adjacent concreting lifts, so that the
adjacent concreting lifts cannot be completely combined.
Therefore, dam safety is seriously threatened by the
reciprocating phenomenon of cracking, closing and
sliding along the cold construction interfaces under
strong earthquakes.
Nonlinear fracture may occur along these interfaces
under strong earthquakes if the cold construction
interfaces are treated badly, so both the plastic
deformation and the fracture along the cold construction
interfaces should be considered when studying the
influence of the RCC interfaces on the seismic failure
1524
mechanism of the RCCDs, namely, yield criterion and
failure criterion are both needed in the dynamic response
analyses of the RCCDs.
Instead of assuming the development of cracks’
location and direction, the actual concrete cracks are
converted to the relevant elements in FEM simulation by
the smeared crack model [22]. In this model, the
damaged concretes are regarded as anisotropic materials
if the maximum principal stress at the integral points
exceeds the concrete tensile strength, and the constitutive
relationships are adjusted to reflect the degradation of
mechanical properties caused by cracking. Hence, the
smeared crack model is adopted in this work to represent
the nonlinear fracture along the cold construction
interfaces. The stress−strain relationship is shown in
Fig. 3. Tensile softening property is presented when the
maximum principal stress comes up to the concrete
tensile strength. Linear softening is adopted in this work,
the softening modulus is determined to be about 1/10 of
the original elastic modulus, and the transfer coefficient
of the residual shear force after cracking is defined as 0.1.
The reloading rigidity under cyclic loads keeps the same
as the original, and the closed cracks are assumed to have
the complete compressive bearing capacity during the
reciprocating process of opening and closing.
Fig. 3 Stress-strain diagram of concrete
J. Cent. South Univ. (2015) 22: 1521−1535
Drucker-Prager yield criterion is commonly used for
concretes and rock materials as it can yield a smooth
failure surface and is determined corresponding to the
hydrostatic stress. Therefore, the Drucker-Prager yield
criterion is combined with the smeared crack model to
represent the nonlinear deformation of RCCs, especially
the nonlinear fracture along the cold construction
interfaces.
3 Mechanism and realization of seismic
motion input by VSAB
3.1 Foundation of VSAB
In order to simulate the scattered waves propagating
out of the finite domain without reflection, shunt-wound
spring−damper components are set in the intercepted
finite domain to absorb the seismic energies carried by
the scattered waves in the VSAB. Figure 4 shows the
sketch of transverse section of gravity dam−foundation
system with the concentrated VSAB.
According to the different realization methods,
VSAB can be divided into two forms, namely, the
consistent VSAB [14] and the concentrated VSAB [15].
The former VSAB is more complex due to its realization
method of adding anisotropic viscous-spring boundary
elements at the intercepted boundaries, and it is more
difficult to deal with the stiffness matrix and the damping
matrix for boundary elements; while the concentrated
VSAB is widely used for its clear mechanical concepts.
Sketch of the isolated body of spring−damper
components used in the concentrated VSAB is shown in
Fig. 5. Three pairs of spring−damper components are
added to every node of the artificial boundaries, in which
two pairs work in the tangential direction and one is in
the normal direction. One end of the spring−damper
components is connected with the artificial boundary
nodes, and the other one is fixed in three directions. In
Fig. 4 Sketch map of transverse section of gravity dam−foundation system with concentrated viscous−spring artificial boundary
J. Cent. South Univ. (2015) 22: 1521−1535
1525
addition, seismic motion input in the concentrated VSAB
can be accurately realized by translating the earthquake
motion into the equivalent nodal loads acting on the
artificial boundaries, in which displacement field and
stress field at the intercepted boundaries should be
precisely kept as the same as the seismic free-field.
Fig. 5 Sketch map of isolated body of spring−damper
components
The key problem of establishing the concentrated
VSAB is the determination of the spring stiffness and the
damping coefficient. Published research results show that
it is more consistent in the damping coefficient. However,
due to different type assumptions of the scattered waves
(plane wave or spherical wave), large differences exist in
the equivalent calculation of the spring stiffness. As for
the hydraulic dams, the spherical wave assumption is
more in accordance with the actual situation due to the
anisotropy of dam foundations as well as the uneven
slope surfaces. Based on the theory of spherical elastic
wave, LIU et al [15] deduced the spring stiffness
coefficients and the damping coefficients of the
concentrated VSAB in three-dimensional space.
Tangential direction:
K BT 
n
2G n
Ai , CBT   cs  Ai

R i 1
i 1
(7)
Normal direction:
K BN 
n
4G n
Ai , CBN   cp  Ai

R i 1
i 1
(8)
where KBN and KBT are the normal and tangential
stiffness coefficients, respectively; CBN and CBT are the
normal and tangential damping coefficients, respectively;
G and ρ are the medium’s shear modulus and mass
density, respectively; R is the distance from the scattered
wave source to the artificial boundary point. However,
due to the uneven slope surfaces, the scattered waves are
not conducted by a point source during the propagation
of seismic waves in the dam-foundation system. Here,
the scattered wave source is assumed to be located at the
center of the interface between dam and foundation for
simplicity, and R for all points on the same straight
boundary surface is similarly determined as the shortest
distance from the assumed scattered wave source to the
boundary surface. cs and cp are wave velocities of the S
wave and P wave, respectively.
The dam-foundation system is isolated from the
infinite rock domain by the VSABs, and energies of the
out-going scattered waves caused by dam body and
slopes are absorbed by the boundary located springs and
dampers. To satisfy the original seismic free-field, the
mechanism of seismic motion input is determined by the
conditions of displacement continuity and internal force
equilibrium at the interface of artificial boundaries. The
simulated seismic motion is inputted at the bottom of the
near-field foundation in the VSABs. While in the seismic
risk evaluation of the practical engineering project areas,
the proposed seismic motion represented by the peak
acceleration is the maximum horizontal ground motion
on the flat free surface of the half-space isotropic rock
foundations [23]. Due to the inertia effects caused by the
mass of the simulated rock foundations, seismic motions
are enlarged during the propagation from deep bedrock
to land surface. Therefore, the designed free-surface
seismic motion should be converted into the incident
wave propagated from deep bedrocks. Taking the
reflection of the free-surface into account, the commonly
used method by researchers at present is that the
amplitude of the free-field incident wave is determined
to be half of the peak value of the designed free surface
seismic motion.
3.2 Equivalent nodal loads of seismic motion in VSAB
input model
The free-field stress and displacement are denoted
as σ Bff ( x, y, z , t )
and
U Bff ( x, y, z , t )  [u ( x, y, z , t )
v( x, y, z , t ) w( x, y, z , t )], respectively; where w is the
normal displacement, and u and v are tangential
displacements. Hence, in order to accurately simulate the
seismic motion, the stress field and displacement field
created by the equivalent nodal loads should satisfy the
following conditions:
σ  σ Bff ( x, y, z, t )
U  U Bff ( x, y, z , t )
(9)
(10)
According to the mechanical model of the
spring−damper components in the VSAB, to satisfy the
conditions of Eqs. (9) and (10), equivalent nodal loads
applied to the artificial boundaries are composed of three
parts [16]. The first two parts are used in removing the
effects that the spring-damper components work on the
seismic motion input, namely, to offset the spring force
and damping force caused by the motion of boundary
nodes accompanied with the ground seismic motion. The
third one is the free-field stress on the boundary surface
J. Cent. South Univ. (2015) 22: 1521−1535
1526
created by the free-field motion. Therefore, the
equivalent nodal loads exerted on the boundary node i
can be expressed as
FBi  K BU Bff  C BU Bff  σ Bff nABi
(11)
where U Bff and U Bff are the free-field displacement
and velocity at the boundary node i, respectively; ABi is
the influence area of node i; n=[l m n]T is the outward
normal direction cosine of the selected artificial
boundary; KB and CB are 3×3 diagonal matrixes
consisting of the spring and damping coefficients,
respectively; σ Bff is the free-field stress tensor at node i.
KB, CB and σ Bff are represented as follows:
0
0 
 K BT

KB   0
K BT
0 
 0
0
K BN 
0
0 
CBT

C B   0 CBT
0 
 0
0 CBN 
σ Bff
 xx

  xy

 xz
analyses, the incident seismic wave at the bottom of the
near-field foundation can be represented by three
components, namely, seismic waves at the stream,
cross-stream and vertical directions, respectively. In the
global coordinate system, the aforementioned directions
are respectively denoted as the x, y and z axes. The
corresponding time histories of displacement of the input
seismic waves are denoted as u0(t), v0(t) and w0(t), in
which u0(t), v0(t) are transverse waves and w0(t) is the
longitudinal wave. Based on the wave theory, the seismic
free-field at node i is stacked by the incident wave and
the reflected wave as follows:
U Bff

l
2L  l 
)
 u0 (t  )  u0 (t 
cs
cs


u
  
l
2L  l 
)
  v    v0 (t  )  v0 (t 
cs
cs


 w 
2L  l 
l
 w0 (t  )  w0 (t 
)
cp
c p 

(12)
U Bff

l
2L  l 
)
 u0 (t  )  u0 (t 
cs
cs


 u  
2L  l 
l


  v    v0 (t  )  v0 (t 
)
cs
cs

 w  
l
2L  l 
 w 0 (t  )  w 0 (t 
)
cp
cp 

(13)
 yx  zx 
 yy
 yz

 zy 

 zz 
As for the half-space problems, the free-field
consists of two parts, namely, the seismic incident wave
and the reflected wave caused by the free surface of
homogeneous elastic semi-infinite space. Therefore, the
free-field in half-space should be firstly determined
before calculating the boundary equivalent nodal loads of
the seismic motion. Reflection sketch of the seismic
wave is shown in Fig. 6. The free-field at node i at any
time t is stacked by the bottom incident wave and the top
reflected wave. As for arch dams, obvious differences of
elevation are shown on the valley surfaces. Here, to
simplify the auxiliary pre-treatment, the free surface can
be simply defined at a reasonable elevation between the
maximum and the minimum elevation of dams.
According to the commonly used component
representation method of seismic wave in hydrodynamic
Fig. 6 Reflection sketch of seismic wave
Components of the free-field stress on the surface of
the bottom artificial boundary are the normal stress (  zz )
caused by the longitudinal wave, and the shear stresses
(  zx and  zy ) caused by the transverse waves in the
stream and cross-stream directions, respectively.

w
w
  c 2p
 zz  (  2G )

z
z

u

u

  cs2
 zx  G

x
x


v

2 v
 zy  G y   cs y

(14)
where λ and G are the medium’s Lame constants, which
also determine the wave velocity of S wave and P wave.
According to the wave theory, the differential equation
can be deduced as p( x, t ) x  (1 c) (p( x, t ) t ),
where p(x, t) is the wave displacement equation and c is
the wave velocity. As for the free-field, the incident wave
and the reflected wave propagate in the opposite
direction, namely (cs, cp) and (−cs, −cp), respectively.
Substituting Eqs. (7), (8) and (12) to (14) into
Eq. (11), and taking the outward normal direction of the
bottom artificial boundary n=[0 0 −1] and l=0 into
account, the equivalent nodal loads at the bottom
artificial boundary are expressed as follows:
J. Cent. South Univ. (2015) 22: 1521−1535


2L 
 FBx  K BT u0 (t )  u0 (t  )   2CBT u0 (t )
cs 




2L 

 FBy  K BT v0 (t )  v0 (t  )   2CBT v0 (t )
cs 



 F  K  w (t )  w (t  2 L )   2C w (t )
BN
0
0
BN 0
 Bz
c p 


1527
(15)
Mechanism of calculating the equivalent nodal
loads at the lateral artificial boundaries (four intercepted
surfaces) is similar to that of the bottom. Differences are
mainly focused on the varied distance from the lateral
boundary nodes to the bottom surface, so different time
intervals between the incident wave and the reflected
wave appear in the lateral artificial boundaries. In
addition, directions of the spring-damper components in
the global coordinate system should be carefully dealt
with due to their different coefficients in the normal and
tangential directions, and also the directions of the
free-field stress.
3.3 Realization of VSAB based on Marc software
The realization of the VSAB contains two steps.
Firstly, the normal and tangential spring−damper
components should be set at the boundaries of the
intercepted finite domain. Then, the seismic motion is
simulated by exerting the equivalent nodal loads at the
artificial boundaries.
To establish the spring−damper components, one
end of the spring−damper components is fixed on the
discrete boundary nodes of the FE mesh, and the other
one is fixed on the external constrained nodes one to one
corresponding to the discrete boundary nodes and added
in advance. According to the node number of the
spring−damper components and the FE mesh, the
spring−damper components addition subroutine (based
on the FORTRAN platform) for the VSAB has been
created, and the spring stiffness coefficients and the
damping coefficients are calculated according to Eqs. (7)
and (8). Finally, based on the commonly used FEM Marc
software, the spring-damper components are added in the
Marc input file by the key word “Springs”.
According to the relationship between the global
coordinate system and the surface direction of the
artificial boundaries, equivalent nodal loads at the
bottom and lateral artificial boundaries are respectively
calculated and exerted by Marc’s user subroutine of
Forcdt [24]. Thus, the concentrated VSAB and its
relevant equivalent nodal load input model has been fully
realized.
4 Dynamic response analyses of a RCC
gravity dam
A RCC gravity dam is located in the west of China
with the maximum dam height of 85.0 m. The width at
the crest is 8.0 m, all dam sections are designed with a
vertical upstream dam surface, and the downstream dam
surface is at a gradient of 1:0.75. The designed ground
motion is determined by the exceeding probability of
10%, and the corresponding horizontal peak acceleration
represented at the land surface is 0.154 g.
The typical No. 7 water retaining dam section with
the maximum dam height is dynamically analyzed as an
example. The FEM model and the sketch of the VSAB
are shown in Fig. 7, in which every symbol of the screw
between the external fixed node and the interrupted
boundary contains three pairs of spring−damper
components: two pairs work in the tangential direction
and one pair in the normal direction. The range of the
FEM model is about two times the maximum dam height
in the upstream, downstream and downward directions
according to the dam heel and dam toe. The damfoundation system is discretized into eight-node and
six-node solid elements with 17740 elements and 23070
nodes, in which 936 fixed nodes are added around the
bottom and lateral artificial boundaries as the fixed ends
of the spring−damper components. According to the
current Chinese specifications for seismic design of
hydraulic structures DL5073−2000 [25], the cross-stream
seismic can be ignored in the dynamic analysis of single
gravity dam section, so normal constraints are applied to
the cross-stream lateral boundaries.
Static material properties of the dam−foundation
system are listed in Table 1. The dynamic modulus and
strength of concretes are taken as 1.3 times the
corresponding static parameters, respectively. A normal
concrete cushion with the thickness of 1.0 m is poured
above the foundation plane. For seepage control, normal
concretes and the second grade RCCs are consecutively
poured on the dam upstream surface, and the thickness of
these impermeable concretes are 1.0 m and 4.0 m,
respectively. Other parts are mainly constructed by the
three grade RCCs. Thicknesses of the compacted layer
and its effect zone are 30.0 cm and 2.0 cm, respectively,
and the concreting lifts are about 3.0 m in height.
To better analyze the influence of the construction
interfaces and the radiation damping of infinite
foundations on the dynamic response of the RCC gravity
dam, only the seismic load is considered in this work.
Time histories of displacement, velocity and acceleration
of the input horizontal seismic wave at the ground
surface are shown in Fig. 8. The vertical peak
acceleration is 2/3 of the horizontal value, and the
cross-stream seismic is not considered. The dynamic
dam−water interaction is modeled by the added mass
assumption [26] as follows:
pw ( h ) 
7
ah  w H 0 h
8
(16)
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Fig. 7 Dam-foundation FEM model: (a) FEM model; (b) Sketch of VSAB
Table 1 Static material properties of RCC gravity dam
Strength/MPa
Material
Modulus/GPa
Poisson ratio
Mass density/
(kN·m−3)
Tensile
Compressive
Normal concrete
19.6
0.167
24.0
1.60
18.5
Noumenon of RCC I (three grade)
17.9
0.163
24.0
1.32
14.3
Noumenon of RCC II (second grade)
19.6
0.163
24.0
1.60
18.5
Interface of RCC I (three grade)
13.0
0.3
24.0
1.0
14.3
Interface of RCC II (second grade)
15.0
0.3
24.0
1.2
18.5
Dam foundation
9.0
0.24
26.2
—
—
Notes: Strengths of the hot construction interfaces are the same as the RCC noumena; the bond strength parameters of cohesion force (c) and friction angle (φ)
used in the Drucker-Prager yield criterion are equivalently calculated by ft and fc as c=0.5(fc·ft)1/2, φ=arcsin[(fc−ft)/ (fc+ft)]; the cohesion force and the friction
angle of the foundation rocks are 1.3 MPa and 48 °, respectively.
Fig. 8 Time histories of input seismic
wave: (a) Acceleration; (b) Velocity;
(c) Displacement
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where pw(h) is the hydrodynamic pressure acting on the
dam upstream surface at the water depth of h; ah is the
designed seismic peek ground acceleration in the
horizontal direction; ρw is the water density; H0 is the
water depth related to the normal reservoir water level.
4.1 Influence of radiation damping on dynamic
response of RCC gravity dam
To study the influence of the radiation damping of
infinite foundations on the dynamic response of the RCC
gravity dam, dynamic analyses are performed by input
models of the massless foundation and the VSAB,
respectively. Here, the RCC construction interface and
the nonlinear deformation are both not considered. In the
massless foundation input model, the mass density of the
foundation rocks is defined as zero, and the damping
ratio of the dam-foundation system is determined as 5%
according to the hydraulic specification of DL5073−
2000 [25]. The Rayleigh damping is adopted in this work,
in which the damping matrix is expressed as follows
[27]:
[C ]   [ M ]   [ K ]
(17)
where [M] and [K] are the mass matrix and the stiffness
matrix, respectively; α and β are damping parameters.
According to the Rayleigh damping, α and β are
determined by ξ=0.5α/ωi+0.5βωi. Hence, α and β are
gradually changed with the circular frequency ωi under a
constant damping ratio ξ. However, α and β are
commonly assumed to be constant in the sensitive
frequency domain of dams, and these two parameters are
cooperatively calculated by the upper and lower limits of
the sensitive frequency domain [28]. In this work, the
sensitive domain is determined from the first to the tenth
frequency, namely 2.023 Hz to 24.066 Hz for the
selected RCC gravity dam section. Corresponding to a
5% damping ratio, α=1.1725 and β=6.1×10−4.
For comparison analyses, the stream displacement
at dam crest in this work is denoted by the relative
displacement corresponding to dam heel, and the positive
value represents the downstream direction displacement;
otherwise, it is towards the upstream direction.
Figures 9 and 10 show the time histories of
displacement along river at the dam crest and the
maximum principal stress at the dam heel, respectively.
The envelope diagrams of the maximum principal stress
are shown in Fig. 11. It can be seen that dynamic
response of the dam body reduces obviously in the
VSAB input model. The peak displacements along river
at the dam crest are 28.24 mm and 21.21 mm for the
massless foundation model and the VSAB input model,
respectively. The peak maximum principal stresses at
dam heel are 4.85 MPa and 3.99 MPa. It can be seen that
both of the peak values are reduced by about 25% in the
VSAB input model. As for the envelope value of the
maximum principal stress of dam body, it reduces
obviously on the upstream dam surface when the
radiation damping is considered, especially for the region
of dam heel commonly considered the tensile stress
control area. The reduction of the dynamic response in
the VSAB input model can better reflect the radiation of
seismic energies to the infinite foundations, which is
modeled by the energy absorption action of the
spring-damper components.
Fig. 9 Time history of displacement along river at dam crest
Fig. 10 Time history of maximum principal stress at dam heel
4.2 Influence of construction interfaces on dynamic
response of RCC gravity dam
4.2.1 Influence of hot construction interfaces
Based on the mechanical property analyses of the
hot construction interfaces of the RCCDs in section 2.1,
two FEM models are established to study the influence
of the hot interfaces on the dynamic response of the RCC
gravity dam, in which no interface is considered in
model 1, while the hot interfaces are represented by the
transversely isotropic dam materials in model 2.
Radiation damping of the infinite foundation is modeled
by the VSAB in two models.
Natural frequencies of the RCC gravity dam are
shown in Table 2, and Fig. 12 shows the comparison of
time histories of displacement along river at the dam
crest. It can be seen that natural frequencies are slightly
reduced when the hot construction interfaces are
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Fig. 11 Envelope diagrams of maximum principal stress of dam body: (a) Massless foundation model; (b) VSAB input model
Table 2 Natural frequency of RCC gravity dam
Model
Natural frequency/Hz
1
2.023
4.002
5.352
8.971
13.436
16.105
18.337
20.893
22.752
24.066
2
2.016
3.996
5.319
8.917
13.338
15.945
18.191
20.678
22.554
23.869
Fig. 12 Time history of displacement along river at dam crest
represented by the transversely isotropic dam materials
in model 2. Dynamic responses of dam body at any time
are almost the same in both models, and the peak
displacements at dam crest in the stream direction are
21.21 mm and 21.56 mm, respectively. Therefore, it can
be concluded that the hot construction interfaces have
little influence on the seismic response of the RCC
gravity dam, so the hot interfaces can be ignored for
simplification.
4.2.2 Influence of cold construction interfaces
The poor bond strength of the cold construction
interfaces is mainly caused by the disappearance or poor
quality of the embedment between two adjacent
concreting lifts. Nonlinear fracture along these cold
construction interfaces maybe occurs under strong
earthquakes, and is also accompanied with reciprocating
phenomenon of cracking, closing and sliding, which
makes the dynamic response of the RCCDs more
complicate than that of the normal concrete dams.
Therefore, the cold construction interfaces should be
seriously considered in the seismic safety evaluation of
the RCCDs.
Aiming at the property of the lower bond strength,
dynamic nonlinear fracture analysis model for the
RCCDs is established with the thickness cold
construction interfaces, and different reduction ratios for
the bond strength of the cold interfaces are adopted to
reflect the combination quality of the compacted layers.
Therefore, to study the influence of the bond strength of
the cold construction interfaces on the dynamic response
of the RCC gravity dam, five computation cases are
performed based on the VSAB model and its equivalent
nodal load input method. The aforementioned smeared
crack model in section 2.2 is used for all dam concretes,
and the nonlinear deformation of foundation rocks is
determined by the Drucker-Prager yield criterion.
Performance of the cold construction interfaces and the
peak dynamic response of each case are shown in Table 3.
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Without considering the construction interfaces,
time histories of displacement along river at the dam
crest in the linear elastic model and the smeared crack
model are comparatively shown in Fig. 13. It can be seen
that dynamic response of dam body obviously reduces
when the nonlinear deformation is considered in
the smeared crack model. The peak displacement along
river at the dam crest reduces from 21.21 mm (−25.97
mm) to 16.15 mm (−17.98 mm), with a reduction
amplitude of about 25%. The envelope diagrams of the
maximum principal stress in these two constitutive
models also comparatively show a obvious reduction
amplitude. The reduced dynamic response is mainly
caused by the seismic energy consumption in the
development of plastic deformation and fracture, so the
nonlinear deformation should be considered to obtain the
real dynamic response of the RCCDs.
Dynamic responses of case 1 and case 2 are
comparatively shown in Figs. 14−16. It can be seen that
although the bond strength of the normal cold interfaces
is reduced at certain amplitude compared with the RCC
noumena, normal cold construction interfaces have little
influence on the dynamic response of the RCC gravity
dam. Envelope values of the maximum and minimum
Fig. 13 Time history of displacement along river at dam crest
without construction interfaces
Fig. 14 Time history of displacement along river at dam crest
with construction interfaces or not
Table 3 Computation cases and peak dynamic response
Tensile strength
Maximum
Displacement
reduction ratio
principal
Case Interface
along river at
of cold
stress at dam
dam crest/mm
interface
heel/MPa
Case 1
×
/
16.15 (−17.98)
1.26
Case 2
√
1.0
15.87 (−18.12)
1.14
Case 3
√
0.8
14.95 (−18.86)
1.05
Case 4
√
0.7
14.61 (−22.01)
1.01
Case 5
√
0.6
Non-convergence
Notes: “×” means no cold interfaces; “√” means that cold interfaces are
considered in this case.
Fig. 15 Envelope diagrams of the maximum principal stress of dam body with construction interfaces or not: (a) Case 1; (b) Case 2
1532
J. Cent. South Univ. (2015) 22: 1521−1535
Fig. 16 Envelope diagrams of the minimum principal stress of dam body with construction interfaces or not: (a) Case 1; (b) Case 2
principal stress are only slightly changed on the
downstream surface of the dam body. As for the tensile
stress control area of the dam heel, there is almost no
difference. Under the designed earthquake, no cracking
appears in case 1, and smaller cracking areas appear at
the dam heel when the normal cold construction
interfaces are considered in case 2. However, dam safety
is not likely to be seriously threatened by these cracks
due to their shallow depth.
Under different tensile strengths of the cold
interfaces, time histories of displacement along river at
the dam crest and the equivalent cracking strain at the
first RCC layer of the dam heel are shown in Figs.17 and
18, respectively. It can be seen that dynamic responses of
the RCC gravity dam in cases 2, 3 and 4 are almost the
same at the early stage of earthquake, which indicates
that dam deformation is mainly in the stage of linear
Fig. 17 Time history of displacement along river at dam crest
under different tensile strengths of cold construction interfaces
Fig. 18 Time history of equivalent cracking strain at first RCC
layer of dam heel under different tensile strengths of cold
construction interfaces
elasticity. With the intensification of the seismic motion,
plastic yielding and fracture appear successively, and a
slightly reduced peak displacement is represented.
Smeared cracks begin to appear when the maximum
principal stress exceeds the tensile strength of the
concrete, resulting in a decline of the integral rigidity of
the RCC dam body, especially under a large reduction
ratio of the tensile strength of the cold construction
interfaces. The enlarged cracking areas at the dam heel
promote the development of residual deformation
towards the upstream direction. Figure 18 also shows the
reciprocating opening and closing process of the smeared
cracks at the dam heel, so the dynamic nonlinear fracture
of concrete can be perfectly simulated by the smeared
crack model.
Plastic yielding and cracking firstly appear at the
dam heel and on downstream dam surface where the
J. Cent. South Univ. (2015) 22: 1521−1535
envelop values of the principal stress are higher, and the
nonlinear deformation areas gradually extend to inside
dam body. Therefore, with the reduction of the tensile
strength of the RCC interfaces, it can be seen from Figs.
15 and 19 that envelope values of the maximum principal
stress reduce on the dam surface and increase inside dam
body.
The envelope diagrams of the minimum principal
stress of dam under different tensile strengths of cold
1533
construction interfaces are shown in Fig. 20. Cracking
processes are shown in Fig. 21. It can be seen that the
lower tensile strength of the RCC interfaces is, the earlier
the cracking occurs and the bigger the cracking areas are;
the cracking areas are all at the dam heel and the
foundation gallery. Meanwhile, the enlarged cracking
areas also result in an increased envelop value of the
compressive stress at the dam toe which can be
concluded from Figs. 16 to 20.
Fig. 19 Envelope diagrams of the maximum principal stress of dam under different tensile strengths of cold construction interfaces:
(a) Case 3; (b) Case 4
Fig. 20 Envelope diagrams of the minimum principal stress of dam under different tensile strengths of cold construction interfaces:
(a) Case 3; (b) Case 4
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Fig. 21 Sketch map of equivalent cracking strain of RCC dam body: (a) Case 2 (t=9.52 s); (b) Case 2 (the last); (c) Case 3 (t=9.48 s);
(d) Case 3 (t=9.52 s); (e) Case 3 (t=17.30 s); (f) Case 4 (t=5.86 s); (g) Case 4 (t=9.56 s); (h) Case 4 (t=17.32 s)
5 Conclusions
1) To study the influence of construction interfaces
on the dynamic characteristics of the RCCDs,
mechanical properties of construction interfaces are
firstly analyzed, and according to their causes of
formation, these interfaces are divided into two
categories, namely, hot interface and cold interface,
which are respectively represented by the transversely
isotropic body and the smeared crack model in the
dynamic analysis.
2) The VSAB seismic input model is adopted to
simulate the radiation damping of dam infinite
foundations. The equivalent nodal loads of seismic
waves at the intercepted boundaries of the VSAB input
model are respectively deduced, and a simplified seismic
motion input method is presented on the basis of the
Marc software.
3) The effects of radiation damping and
construction interfaces on the dynamic characteristics of
a RCC gravity dam are investigated at last. Research
results show that the dynamic responses of the RCC
gravity dam both reduce by about 25% when the
radiation damping of infinite foundation and the
nonlinear deformation of dam body are respectively
considered. Under the designed earthquake, no cracking
occurs in the assumed RCC gravity dam model without
interfaces. As for the interfaces model, almost no
influence is conducted by the hot construction interfaces,
and the normal cold interfaces show a little influence on
the dynamic response of the RCC gravity dam and a
smaller cracking area at the dam heel. While the cracking
area develops rapidly with the reduction of the bond
strength of the cold RCC interfaces. Therefore, in order
to avoid the fractures along the construction interfaces
under the potential super earthquakes, combination
quality of the compacted layers of the RCCDs should be
significantly ensured.
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