Seismic Safety Assessment of “Tsankov Kamak” Arch Dam
Part II –Ultimate Capacity
A. Andonov, K. Apostolov, A. Iliev
Risk Engineering LTD, Sofia, Bulgaria
M. Kostov, D. Stefanov, G. Varbanov, A. Kaneva & N. Koleva
CLSMEE,BAS, Sofia, Bulgaria
ABSTRACT:
The large dam systems are high-cost infrastructural projects with significant economical importance. Many of
the large dams are built in earthquake prone countries which form additional demands on their structural safety.
Inadequate seismic behaviour of such dam could lead to severe consequences for the local communities.
Therefore the seismic safety assessment of large dams systems is important engineering task. The current paper
is focused on the structural assessment of “Tsankov Kamak” dam subjected to seismic loadings above the design
ones as well as the assessment of the dam’s ultimate seismic capacity. For the purpose a series of non-linear
dynamic analyses, as well as two Push Over analyses are performed. The obtained results are used for
assessment of the dam seismic safety.
Keywords: Double Arch Dam, Non-linear Analysis, Ultimate Capacity, Failure Mode, Seismic Safety
1. INTRODUCTION
The large dam reservoirs are infrastructural systems from vital importance for the economic of the
surrounding regions, sometimes even for the economic of entire countries. Therefore, any eventual
structural failures can lead to enormous direct and indirect economic losses, as well as to human
causalities. From other side, many of the existing large dams are built in seismic prone zones, which
provide additional demand on assuring of their structural safety. The seismic safety importance of the
large dams is widely recognised from the dam owners, the regulatory comities and the engineering
community, and several engineering guidelines were produced from ICOLD, FERC and the U.S.
Army Corpus of Engineers. According to the current concepts in the seismic design of large dams, two
seismic levels should be considered: Operational Basis Earthquake and Maximum Credible
Earthquake. The acceptance criteria for the dam response to both seismic events are different. The
requirements for OBE are generally to have an elastic response. Regarding the MCE, damages over
the structure are admissible until they do not provoke uncontrolled release of water from the reservoir.
Therefore, one of the most controversial parts in the MCE assessment procedure is the evaluation of
the significance of the observed damages for the dam structural safety. For this reason, it is very useful
to evaluate the dam response to seismic levels above the one considered for MCE. In this way
knowing the structural response to more severe seismic conditions and the remaining load bearing
capacity more realistic assessment of the dam response to MCE can be made. The current paper
presents the results from such analyses of the “Tzankov Kamak” arch dam subjected to seismic
loadings with peak ground acceleration exceeding with 50% and 100% the MCE peak ground
acceleration of 0,42g. Additionally two Push Over analyses are performed for assessment of the dam
failure modes in upstream and downstream direction.
2. DESCRIPTION OF TSANKOV KAMAK ARCH DAM
Tsankov Kamak dam is a double-arch concrete dam. The dam is consisted of 17 separately erected 20-
meter-wide cantilever blocks and abutments blocks, tangential to the crest’s axis, connecting the dam
in both banks. The contraction joints between the vertical blocks are formed with series of 10-cm-thick
shear key locks on both surfaces of each cantilever block, ensuring uniformly distributed shear force
transmission between the blocks. A spillway with four divisions is situated in the middle part of the
crest. A total of five galleries are situated in the dam’s body: one injection gallery following the base
line and four horizontal inspection galleries on different levels of the dam.
The general geometrical properties of the dam are: total crest length – 459.4m; crest length (curved
part) – 340.0m; maximum height – 130.5m; maximum width of crest – 8.8m; maximum width of base
– 26.36m; total volume of mass concrete – around 400000m3. View of the dam under construction is
shown in Fig.1
Figure 1. “Tzankov Kamak” dam under construction.
3. STRUCTURAL MODEL AND ANALYSIS
The spatial structural model of “Tzankov Kamak” dam includes the dam wall, the base rock and the
water reservoir. Special attention is paid on the modelling of the contraction joints behaviour, the dam
to rock interface and the rock geology immediately beneath the dam. Non-linear material models are
used for modelling the behaviour of the mass concrete, the first layers of the base rock, the base and
the contraction joints. The structural model is presented in Fig.2.
3.1. FE mesh
The entire structural model is built up from solid finite elements. However, the FE mesh accuracy
varies in the different parts of the model. The average size of the solid elements modelling the wall is
about 3m in vertical and arch directions. In direction of the dam’s width the element size varies from
1m at the top to 3m at the base. Totally, eight layers of solid elements are used in the dam’s width
direction. The spillway and the galleries are included in the model too. The contraction joints are
modelled by thin layer of solid finite elements between the blocks. The same material constitutive law
as for the concrete in the main dam body is used, but with reduced tensile strength. In this way the
arch tensile strains are concentrated in the inter-blocks space (in the gaps) and thus the propagation of
arch tensile stresses that exceed the “gap” cracking strength is restricted. The modelled contraction
joints keep their shear stress transfer capabilities, even after cracking occurs, by using a shear stiffness
parameter implemented in the material model. The dam-to-base rock interface is modelled with solid
finite elements also. The elements' dimensions are similar to these of the elements in the base of the
dam. Similar approach as for the contraction joint modelling is used for the base gap. The base gap is
modelled as a layer of solid elements with decreased tensile strength. In this way the unrealistic
concentration of vertical tensile stresses and strains at the dam base is avoided. The base rock FE mesh
is with similar accuracy for the base rock in the vicinity of the dam base and with smoothly growing
element size with the increasing of the distance from the dam base. The base rock FE model includes
all typical rock types based on the geological surveys, as well as the concrete plugs substituting the
weakened and weathered zones (Fig.2 - b). The dimensions of base rock model are in function of the
dam height, respectively half dam’s height in direction perpendicular to the stream; one dam’s height
in direction parallel to the stream; one dam’s height in vertical direction. Velocity based fluid FE are
also used for cross check calculations by Fluid Structure Interaction analyses (Figure 2 – a). The FSI
analyses are used mainly for adjustment of the added masses. The main non-linear analyses are
decoupled and the hydrodynamic pressure is taken into account by added masses. The boundary
conditions are in the form of translational restraints applied on all nodes belonging to the lateral sides
of the base rock model. Totally the structural model consists of 83000 solid elements.
Figure 2. 3D view of the FE model of “Tzankov Kamak” dam.
3.2. Material models and parameters
Non-linear models of the materials are used; in this way the stiffness of the elements is being
continuously modified during of the computation process, depending on the deformations accumulated
in the structure and the constitutive stress-strain laws of the materials used. The mass concrete, the
base joint and the contraction joints are modelled by CONCRETE material model (SOLVIA, 2003),
corresponding basically to the Ottosen model. However, different strength parameters are used for
each distinguish part. The material constitutive laws are shown in Fig. 3
Figure 3. Constitutive laws for the CONCRETE material model.
The material parameters for the concrete, the concrete-rock interface, the contraction joints and the
base rock are derived based on in situ and laboratory tests. In Table 1 the dynamic material parameters
for the concrete, the dam to rock interface and the grouting joints are presented.
Table 1. Dynamic Material Properties
Abbreviation
[Units]
Concrete / Dam
Body
34000
45.6
Dam to Base Rock
Interface / Base
Joint
34000
45.6
Block Joints
Interface /
Contraction Joints
34000
45.6
Elastic Modulus
Maximum
Compressive
Strength
Ultimate
Compressive
Strength
E [MPa]
 c [MPa]
σu [MPa]
41.0
41.0
41.0
Tensile Strength
5.5
3.5
2.2
Poisson’s ratio
Density
 t [MPa]

 [kg/m3]
Damping
ξ [%]
0.2
2380
4-7
0.2
0
7-10
0.2
2380
4-7
3.3. Loads
The loading sequence used for the analyses is presented on Fig.4. The earthquake loading is applied on
initially stressed structure under self weight, hydrostatic pressure and temperature loading.
Figure 4. Loading sequence
The hydrodynamic pressure is taken into account by means of added masses using modified
Westergaard approach. The input earthquake excitation is applied by accelerograms for the dynamic
analyses and as lateral concentrated forces for the static analyses. For the dynamic analyses, three
statistically independent time histories, are generated for each of the investigated seismic levels. The
accelereograms are generated to be compatible with the corresponding response spectra for each
seismic level. For the static analyses, the lateral loading is presented by concentrated forces at each
structural node, computed proportionally to the displacement pattern of the dam obtained through
response spectrum analysis based on the first ten modes.
3.4. Analytical procedure
The dynamic analyses are performed using direct time integration analysis, with Hilber-Hughes
integration method. The BFGS method is used for performing of the equilibrium iterations during the
solution. The system damping is modelled as Rayleigh damping. Different damping curves are
assigned for each material model. The basic time step used is 0,01s for most of the analyses. However,
in some cases smaller time step is used, when convergence problems are encountered. The Push Over
analysis also is performed applying dynamic analysis method with smooth loading curve and high
damping (99%) to simulate the static response of the structure. This type of solution was found to be
much more numerically stable than the classical non-linear static analysis which encounter serious
convergence problems after the first structural damages occur.
4. STRUCTURAL RESPONSE AND DAMAGE LEVEL
A series of non-linear dynamic analyses with increased loading intensity up to PGA=0,8g. are
performed to study the seismic safety of “Tzankov Kamak” dam. Additionally, two Push Over
analyses, in upstream and downstream directions until failure of the structure, are carried out. The
combination of these types of analyses, allows better understanding of the structural response.
4.1. Capacity curves
One convenient approach to represent of the results from non-linear seismic analyses (Push Over or
dynamic) with incremental loading is by so called “Capacity Curve”. The capacity curve is usually
represented as plot of the base shear vs. the top displacement. The capacity curve generally contains
important information for the structural response under severe seismic loadings. The initial slope
marks the elastic stiffness of the structure. The change in the slope of the capacity curve is a mark for
structural softening, i.e. damage accumulation. Horizontal or decreasing fragments from the curve
mark the approaching of the structural limit capacity. The relative distance of the curve fragment with
the reduced slope (stiffness) compared with the curve fragment with the initial slope (stiffness) marks
the structural ductility and demarcates the structural failure mode: brittle or ductile. On Fig.5 the
capacity curves in upstream (Fig.5-a) and downstream (Fig.5-b) directions are presented. The blue
lines represent the capacity curves obtained by non-linear static analyses. The red dots and the black
lines represent the results from the dynamic analyses with increasing loading intensity with PGA from
0,2g to 0,8g. The base shear and the top displacements are relative to the initial. The base shear on the
vertical axis is scaled to the self weight of the structure. The displacement plotted on the horizontal
axis is the “system displacement” of the structure, calculated according to Eqn. 4.1, where dsys denotes
the “system displacement”, the mi denotes the mass of block “i” and di denotes the crest displacement
of block “i”.
d sys 
i
2
i
i
i
 m .d
 m .d
(4.1)
The necessity of using the “system displacement” instead of the displacement of existing physical
location from the structure is due to the non-uniform crest displacement (See Fig.6).
Figure 5. Capacity curves obtained through Push Over and Incremental Dynamic Analyses: a) in upstream
direction and b) in downstream direction.
Good coincidence between the “static” and the “dynamic” results in downstream direction is observed,
while in upstream direction the Push Over analysis underestimates the response. One of the possible
reasons for this could be that the idealised horizontal loading in upstream direction produces
“opening” of the wall and disconnection of the arch action. The arch dam is transformed into a system
of separate cantilevers, which has significantly lower lateral stiffness than the arch dam. During the
dynamic analysis, the loading is in the form of continuously changing its principal direction in the 3D
space acceleration vector, and such idealised upstream lateral loading can not be produced. However,
both approaches predict higher elastic capacity and brittle failure in downstream direction (the length
of the initial curve slope). Another conclusion is that the deformation capacity of the structure exceeds
the deformations produced by the dynamic loadings. Therefore, according to the obtained results,
structural failure even for the loading of 0,8g is not expected.
4.2. Deformed shapes at different seismic levels
The envelopes of the maximal radial crest displacements obtained by dynamic analyses with
PGA=0,4g, PGA=0,6g and PGA=0,8g are plotted on Fig.6. The deformed shapes of the crest at
failure, obtained applying Push Over analyses are also plotted (thick red lines). The deformed shapes
are relative, i.e. the initial displacements due to the non-seismic loadings are extracted. Again, better
consistence of the results in downstream direction is observed. The maximal crest displacements are
generally concentrated in the quarters of the crest. This is observed in all analyses, except the Push
Over in upstream direction, where the maximal displacements are concentrated in the central section
of the crest. The main reason for that is again the idealised unidirectional loading used during the Push
Over analysis and leading to early disconnection of the arch action in the dam.
Radial Crest Displacement Envelope (m)
-0.34
-0.35
-0.34
-0.32
-0.32
-0.30
-0.32
-0.28
-0.31
-0.21
-0.26
-0.14
-0.19
0.19 0.16
-0.06
0.14
0.16
0.19
0.24
-0.01
0.04
0.26
0.27
0.12
0.21
-0.09
0.23
0.24
0.26
0.17
0.09
-0.01
0.03
ZERO LINE
UPSTREAM_ULTIMATE_CAPACITY
DYNAMIC_PGA=0.8g_DOENSTREAM
DYNAMIC_PGA=0.8g_UPSTREAM
DOWNSTREAM_ULTIMATE_cAPACITY
DYNAMIC_PGA=0.4G_UPSTREAM
DYNAMIC_PGA=0.4g_DOWNSTREAM
DYNAMIC_PGA=0.6g_UPSTREAM
DYNAMIC_PGA=0.6g_DOWNSTREAM
Figure 6. Radial crest displacement envelopes
Similarly to the capacity curves on Fig.5, the deformed shapes presented on Fig.6 predict that the
deformation capacity of the structure (the red lines) exceeds the deformations produced by the
investigated seismic loadings up to PGA of 0,8g, i.e. structural failure for loadings up to this level is
not expected.
4.3. Damage intensities at different seismic levels
Generally, the response to seismic loadings up to PGA of 0,2g is practically elastic. The non-linear
response begins at higher levels, initially through cracking at the base joint and the contraction joints.
A more prominent non-linear response and cracking in the main dam body is observed at seismic
loading with PGA of 0,4g. The damages accumulated over the structure during the investigated
seismic levels are presented on Fig.7. The results from three seismic levels are presented, respectively
with PGA=0,4g (Fig.7-a), 0,6g (Fig.7-b) and 0,8g (Fig.7-c).
Figure 7. Damage distribution over the structure obtained through dynamic analyses: a) PGA=0,4g; b)
PGA=0,6g and c) PGA=0,8g.
At the 0,4g PGA level, the cracking is rather superficial in the form of horizontal cracks on the
downstream surface. Slightly deeper horizontal cracks are concentrated beneath the spillway. At
PGA=0,6g the cracking is already on both surfaces of the wall and the cracks from the downstream
side propagate up to the service galleries. The cracking is still concentrated in the upper portion of the
wall. At PGA of 0,8g extensive cracking on both surfaces is observed, with horizontal cracks
propagating up to the upper two service galleries. At such seismic levels, water filtration into the
galleries through the cracks should be expected.
4.4. Ultimate capacity, failure mode and critical zones
Fig.8 presents, the failure modes of the structure in upstream and downstream directions obtained as a
result of the non-linear static analyses with monotonically increasing unidirectional lateral loading.
The failure modes in the two directions are with similar failure mechanisms, but are distinguish as
location and effect on the structural safety. The failure mode in both directions generally is exceeding
of the shear capacity along a horizontal failure plane. With increasing of the lateral loading direction
the intensity of cracking on the opposite to the loading direction surface of the wall increases too. The
depth of the cracking zone increases too, and thus the compressed zone of the cross sections is
continuously reduced. The stress redistribution leads to increasing of the compressive and the shear
stresses in the compressed zone. The failure will be formed when this stress redistribution provokes
compressive or shear stresses above the respective limit strength. Regarding the obtained from the
Push Over results, the failure mode in both directions is formed due to the exceeding of the shear
strength.
Figure 8. Failure modes in a) upstream and b) downstream directions obtained through non-linear static analysis
For the failure mode in upstream direction, the failure plane is formed on a horizontal plane through
the service gallery immediately under the spillway in the three central blocks of the dam. For the
failure mode in downstream direction the failure plane is formed in the middle height of blocks R3 to
R5 and L3to L5.
5. CONCLUSIONS
The seismic safety of “Tsankov Kamak” arch dam is assessed through a series of non-linear dynamic
and non-linear static analyses with increasing loading intensity. Thus the structural response and
damage levels, corresponding to different seismic intensities are evaluated, as well the ultimate
structural capacity and the structural failure mode. Based on the obtained results, the following
conclusions can be drawn:
- The expected dam response to seismic loadings with peak ground acceleration up to 0.2g
(Operational Basis Earthquake) is entirely elastic for the main dam body, i.e. no structural
damages are expected. However, slight cracking of the grouting joints in the upper quarter
of the blocks neighbouring to the spillway is expected to occur. A light cracking of the
upstream side of the base joint, mostly concentrated in the middles of the left and the right
half parts of the dam is probable too.
- The first structural cracks/damages occur for seismic loadings with PGA above 0.35g. The
cracking is initially in the form of superficial horizontal cracks concentrated in the central
zone of the downstream face of the dam, immediately bellow the spillway.
- At seismic loadings with PGA of 0,4g corresponding to MCE superficial cracking on both
faces of the wall is observed in the form of shallow horizontal cracks. The cracking on the
downstream face is much more widespread than on the upstream face. The contraction
joints opening are in the range of 1cm, which is much bellow the shear keys thickness of
10cm. The observed compressive and shear stresses over the structure is much bellow the
corresponding strengths. The deformations over the structure are sufficiently less the
deformation capacity obtained by the Push Over analysis. It could be concluded that the
dam will respond to MCE with limited damages, expressed as superficial cracking on both
surfaces, and with adequate reserve of structural load bearing capacity.
-
-
-
-
At seismic loading with PGA of 0,6g the cracking spreads over the entire upper half of
both faces and the cracks propagates approximately ¼ from both side of the cross section.
In the central part of the dam, the cracks penetrate up to the service gallery. However, the
comparison of the compressive and the shear stresses, and the deformations over the
structure are bellow the corresponding limit values, therefore exhausting of the structural
capacity is not expected.
At seismic loading with PGA of 0,8g the structure is already heavily cracked on both
surfaces, including propagating through the whole cross section cracks in the upper
portion of the wall. The cracks from the upstream face propagates up to the two upper
service galleries, therefore infiltration of water into the galleries is expected after such
seismic loading. The structural failure is still not reached.
The structural failure modes in upstream and downstream directions are analysed through
non-linear static analyses with monotonically increasing lateral loading. The main failure
modes in the both directions occur as a result of the exceeding of the shear capacity of the
most stressed cross section over horizontal plane. The main reason for this overstressing is
the stress redistribution in the cross section produced by the continuously reduced
compressive zone due to the increasing of the cracked zone from the opposite side of the
cross section. This together with the increasing lateral loading produces overstressing and
exceeding of the shear capacity and lead to structural failure.
The failure plane for the upstream failure mode, propagates through the service gallery
beneath the spillway and cover the central 1/3 part of the dam. The failure planes for the
failure mode in downstream direction, are located in the middles of the two half parts of
the dam and propagate approximately through the middle height of the dam.
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U.S.A.C.E. (2007). Earthquake Design and Evaluation of Concrete Hydraulic Structures - EM 1110-2-6053.
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