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Symposium “Management for Safe Dams” - 91st Annual ICOLD Meeting – Gothenburg 13-14 June 2023
Realistic numerical simulations of concrete dam failures
J. Enzell
KTH Royal Institute of Technology, Stockholm, Sweden
R. Hellgren
Svenska kraftnät, Norrköping, Sweden
R. Malm
FOI Swedish Defence Research Agency, Stockholm, Sweden
E. Nordström
KTH Royal Institute of Technology, Stockholm, Sweden
A. Sjölander
KTH Royal Institute of Technology, Stockholm, Sweden
A. Ansell
KTH Royal Institute of Technology, Stockholm, Sweden
ABSTRACT:
Dam failures
may
have catastrophic consequences, including the release of large
amounts of water, significant property damage, and loss of life. However, safety assessments of
concrete gravity and buttress dams often rely on simplified methods that do not consider the in-
teraction between monoliths, the shape of the foundation or the presence of stiff abutments. Nu-
merical modeling can be a valuable tool for analyzing the stability of these dams, but it can be
difficult to validate these models due to a lack of documented dam failures. This paper presents
the results of a numerical study examining the ability of dynamic finite element analyses to sim-
ulate dam failures. The study used the results from a series of physical model tests as a case study
for validation. It was found that the numerical model was able to accurately reproduce the failure
mode and breach development observed in the physical model tests and capture the effect of the
loading rate on the failure mode and time for the failure to develop. Simulations were also per-
formed in prototype scale to verify that the model tests were representative of a real dam failure.
Further research is needed to determine the reliability of the numerical models under different
loading conditions and in realistic geological settings. However, these findings suggest that nu-
merical modeling can be a valuable tool for analyzing the stability of concrete gravity and buttress
dams and predicting the development of failures.
1 INTRODUCTION
Dam failures may have catastrophic consequences, including the release of large amounts of wa-
ter, significant property damage, and loss of life. Knowledge about the failure process is important
for emergency preparedness and the dam's safety evaluation. An increased understanding of fail-
ure events in concrete dams also allows for establishing better alarm limits for the instrumentation
installed in many concrete dams. Safety assessments of concrete gravity and buttress dams often
rely on simplified analytical stability analysis, considering sliding and overturning failure modes
of a simplified geometry (USACE 1995, FERC 2016, Ridas 2017). However, the failure of a
concrete dam is a complex process, impacted by irregular geometries, nonlinear material behav-
ior, dynamic effects from water release, and rock and soil erosion. In the stability analyses, single
monoliths are considered, and potential interaction between monoliths is not considered. The
foundation is commonly also simplified to a flat surface. The development of a breach is typically
based on simplified assumptions for concrete dams (ICOLD 1998). Contrarily, methods have
been developed for embankment dams to calculate the size of a breach (ICOLD 1998, Zagonjolli
2007).
Models can be used to evaluate concrete gravity dams' stability and failure process, particularly
for complex geometries or when nonlinear behavior is expected. Before the introduction of com-
mercial finite element software, physical model tests were the standard tool for analyzing complex
structures within civil and structural engineering (Fumagalli 1973). In physical model tests, a
scale model is created by scaling a prototype, e.g., a dam, to a manageable scale for the specific
structure. Similitude requirements must be met for the scale to retain a valid representation of the
actual structure. These are based on Buckingham's theorem (Buckingham 1914) and are presented
by, e.g., Fumagalli (1973) and Harris and Sabnis (1999). However, producing accurate physical
models is difficult, especially when material properties require scaling.
As an alternative to physical models, numerical analysis can be used to simulate the behavior
of the structure. In such analysis, a numerical model of the full-size structure is used, removing
the issues associated with the similitude requirement. Numerical analysis can be used to evaluate
the stability of concrete gravity dams, particularly for complex geometries or when nonlinear
material behavior is expected (Mirzabozorg et al. 2014, Hellgren and Malm 2017, Hellgren et al.
2020). However, it can be challenging to validate numerical models, especially in the case of dam
failures where no sufficiently documented cases exist. An approach to overcome this problem is
to use physical model tests and experiments to validate the numerical models. The validated nu-
merical model can then be used for further studies. This approach has been used to validate nu-
merical analyses of concrete dams (Oliveira and Fariab 2006, Hofstetter and Valentini 2013,
Enzell et al. 2021).
In this study, physical model tests performed by Enzell et al. (2023) are utilized to examine the
ability of dynamic finite element simulations to simulate dam failure. The physical model consists
of five scale-model monoliths loaded to failure using hydrostatic pressure. The physical model
test is replicated using a finite element model consisting of the five model monoliths, the founda-
tion, and two side supports. All simulations were load-controlled and performed using nonlinear
geometry. The model tests were also simulated at full scale to validate whether the results from
the physical model test were representative of an actual dam.
2 CASE STUDY
2.1 Physical model tests
The results from the physical model tests performed by Enzell et al. (2023) were used to validate
the numerical simulations performed in this study. In the model tests, a concrete buttress dam was
loaded to failure using hydrostatic pressure. The dam failed in a sliding mode, and the water was
allowed to act on the dam throughout the failure, see Figure 1. The model was created in the scale
1:15 and consisted of five monoliths. It was 1.2 m high and 4.0 m wide. The foundation of the
dam was a flat concrete slab. Since a sliding failure mode is close to a rigid body motion and no
cracking or crushing was expected, the model was created from regular strength concrete, i.e., the
properties material were not scaled.
Symposium “Management for Safe Dams” - 91st Annual ICOLD Meeting – Gothenburg 13-14 June 2023
a)
b)
Figure 1. Presentation of the physical model a) setup of the physical model and b) an example of a dam
failure (Enzell et al. 2023).
The model was built with modular shear keys and side supports. The side supports added a stiff
boundary condition, which controlled the failure mode. The test series used in this study are pre-
sented in Table 1. The failure load is given in mm of hydraulic head.
The foundation was built with a flat concrete slab for a foundation. The tests did not consider
cohesion in the foundation-dam interface. The friction angle between the monoliths and the foun-
dation and the monoliths and the side supports was 29.2°, representing a friction coefficient of
0.56.
Table 1. Test series in this study.
Test series Acronym Number
of tests Avg. failure
load [mm] Std. Dev.
[mm]
Failure of a single Monolith
SM
3
1083
81
Full dam, Side Supports, no shear keys
SP
6
1309
94
Full dam, Side Supports and shear keys
SP+SK
6
1586
56
2.2 Finite Element Models
The physical model tests presented in Table 1 were first simulated in the model scale. Thereafter,
the dam failure was simulated in the prototype scale, and the results were compared between the
two scales. A nonlinear material model was added for the concrete to analyze the impact of the
material behavior on the failure mode in the prototype scale. The nonlinear material behavior
turned out to have a significant impact on the results in the case SP+SK. Reinforcement was
therefore added to the monoliths in a separate analysis.
The finite element model consisted of the five model monoliths, the foundation slab, the two
side supports, and the stop bar. The geometry and mesh of the model are shown in Figure 2. The
foundation slab was defined as a 1 mm thick shell fixed in all degrees of freedom (DOF). Abaqus
2019 was used for all simulations. Linear hexahedral elements, denoted C3D8R, were used for
the monoliths, side supports and stop bar. The foundation and the reinforcement in the nonlinear
simulations were defined using 4-node shell elements, denoted S4R in Abaqus. The number of
elements and nodes is presented in Table 2. The shear keys are small, so these models require
more elements.
Table 2. Summary of mesh for the presented numerical models.
Model
Scale
Elements
Nodes
Single monolith
Model scale
4210
5352
Single monolith
Prototype scale
5380
6478
Full dam, supports
Model scale
12
,
532
17
,
654
Full dam, supports
Prototype scale
14
,
720
20
,
240
Full dam, SP+SK
Model scale
15
,
297
21
,
568
Full dam, SP+SK
Prototype scale
17
,
400
23
,
600
Full dam, SP+SK, reinforced
Prototype scale
59
,
026
70
,
982
The material properties are presented in Table 3. The concrete density was modified in the nu-
merical model so that the total weight matched the monolith's measured weight in the physical
model tests. In the nonlinear simulations, all parts except the dam and the reinforcement were
linear elastic. For the nonlinear behavior of the concrete, a coupled damage and plasticity material
model (Lubliner et al. 1989, Lee and Fenves 1998) was used, denoted Concrete Damaged Plas-
ticity in Abaqus. The nonlinear compressive behavior was defined according to the uniaxial curve
given in Eurocode 2 (2013). The exponential crack opening curve defined by Reinhardt et al.
(1986) was used for the tensile behavior. A dilation angle of 35° was used, and the remaining
parameters in the material model were assigned default values for concrete according to Dassault
Systèmes (2014). See Malm (2016) for further information.
The reinforcement for the dam was not known. Therefore, a reinforcement grid of 20 mm bars
at a 200 mm distance was assumed, which is a typical reinforcement amount in buttress dams. All
surfaces were reinforced except for the joints, the top and the foundation surface. The nonlinear
behavior for the reinforcement was defined according to Eurocode 2 (2013). The failure strain
was 4.5 %, and the quote between the ultimate stress and the yield stress was
/
= 1.08. The
built-in function Rebar in Abaqus was used to define the correct direction and stiffness of the
reinforcement.
Table 3. Material properties for numerical simulations.
Concrete
Steel
Young's
m
odulus [GPa]
E
33
210
Poisson's
r
atio
ν
0.2
0.3
Density [kg/m
3
]
ρ
2432
7750
Tensile strength
[MPa]
f
t
2.9
500
Compressive strength
[MPa]
f
c
38
500
Strain at fc [‰]
ε
c1
2.5
Fracture
e
nergy
[
Nm/m
2
]
G
f
200
The side supports, foundation slab, and stop bar were fixed using boundary conditions. All parts
were connected using interactions, defined to transmit compressive forces in the normal direction
but not carry tensile forces, resulting in a joint opening. Coulomb friction was defined for the
tangential behavior, with a friction coefficient of 0.56, see Section 2.1. The reinforcement was
restrained to the surrounding concrete in all DOF.
All simulations were load-controlled and performed using nonlinear geometry. An implicit dy-
namic solver was used for all simulations except for the nonlinear case with shear keys and sup-
ports (SP+SK), where an explicit dynamic solver was used. The water load was applied using
pressure loads. To match the loading in the model tests, the water pressure up to the crest level
was applied as linearly increasing, and the added pressure from the overtopping was uniformly
distributed. The joints were sealed in the model tests. Therefore, the uplift pressure was assumed
to be small and not considered in the simulations.
a)
b)
Figure 2. Geometry and mesh of the numerical model a) single monolith and b) full dam.
3 RESULTS
A comparison between the simulations and each test series is presented in Figure 3. In the case of
the single monolith (SM), the failure corresponded well between the analytical calculation, the
Symposium “Management for Safe Dams” - 91st Annual ICOLD Meeting – Gothenburg 13-14 June 2023
numerical simulation and the model tests. In the numerical simulation, some elastic displacements
occur, which are not present in the model tests.
The average failure load was accurately predicted in the numerical simulation in the case with
supports (SP) and the case with supports and shear keys (SP+SK). However, the pre-failure dis-
placement was not captured well, likely due to the difficulty in accurately representing the imper-
fect geometry of the physical model numerically. An initial displacement was observed in the
numerical simulation but was smaller and had a more even distribution than in the physical model
tests.
The comparison between the model-scale simulations and the full-scale prototype simulations
is presented in Figure 3d. In the figure, the displacement and hydrostatic pressure are divided by
the dam height (18 m in the prototype scale and 1.2 m in the model scale). The agreement between
the two simulations is good. Because of the difference in inertia, comparing the time signals for
the simulations in prototype and model scale becomes difficult. The difference in inertia is re-
flected in the similitude requirements, where the time is scaled1: √15 for a linear elastic, dynamic
model (Harris and Sabnis 1999). The time must therefore be multiplied by √15, while the com-
pared unit, e.g., displacement, is multiplied by 15.
The stress was high in both models using side supports, see Figure 4. The stress increased as
the monoliths had some initial displacements and peaked before the failure of the dam. The peak
tensile stress was 4.4 MPa for SP and 153 MPa for SP+SK. The peak compressive stress was 8.0
MPa for SP and 282 MPa for SP+SK. The stress values for SP indicate that some concrete crack-
ing will occur. However, the stress values for SP+SK are unrealistic, and large-scale cracking and
crushing of the concrete would have occurred before this point.
a)
b)
c)
d)
Figure 3. Comparison between model tests and numerical simulations a) single monolith (SM), b) supports,
no shear keys (SP), c) supports and shear keys (SP+SK) and d) comparison between the simulations in
model scale and prototype scale.
a)
b)
Figure 4. Presentation of the stress distribution in the linear elastic numerical simulation of SP+SK in the
prototype scale a) compressive stress and b) tensile stress.
A nonlinear material model was defined for the concrete to assess the impact of the stress on the
failure load. The nonlinear simulations were performed in the prototype scale to ensure correct
material behavior. The single monolith failure was not simulated using the nonlinear material
model since the linear elastic simulations did not indicate cracking. The model without shear keys
(SP) experienced some cracking in the joints, as indicated by the linear elastic simulation, see
Figure 5. There was large-scale cracking in the model with shear keys (SP+SK). The edge mon-
oliths cracked severely in both the front plate and the support buttress, resulting in large defor-
mations. The three central monoliths had severe cracking in the front plate and some cracking in
the buttress. For the case with supports but no shear keys (SP), the failure load was similar for the
linear elastic and nonlinear simulations. This means that friction was the governing material prop-
erty and the material strength had a limited impact on the results. However, when the nonlinear
material model was used in the case with shear keys (SP+SK), the failure load decreased by 15 %,
see Figure 6. The failure mode also changes from a pure sliding failure to a combined material and
sliding failure. Because of the large nonlinear deformation of the monoliths, reinforcement was
added to the simulation. The dam still had a combined material and sliding failure with the rein-
forcement, but the failure load was slightly larger. The failure load was 6 % lower than the linear
elastic case.
4 DISCUSSION
In this numerical study, the physical model tests performed by Enzell et al. (2023) were recreated
using load-controlled finite element simulations. The load-controlled simulation gave failure at a
correct load level. However, the simulations failed to show the pre-failure displacements obtained
in the model tests. The difference is likely due to imperfections in the geometry of the model test.
The lack of pre-failure displacement in the numerical simulations might make predicting potential
pre-failure displacements challenging in real concrete dams.
The simulations in the prototype scale agreed well with the model-scale simulations. The agree-
ment confirms that the model tests were correctly scaled and representative of the prototype scale.
However, the difference in inertia made the comparison difficult. The simulations in the prototype
Symposium “Management for Safe Dams” - 91st Annual ICOLD Meeting – Gothenburg 13-14 June 2023
scale required a longer total time with a slower load application. If the load were applied too
quickly, the dam would not have time to displace, and the failure load would appear higher than
the actual failure load. A step time of 15 seconds seemed sufficient for the simulations in the
prototype scale. The issue of inertia in load-controlled simulations was previously discussed by
Enzell et al. (2021).
a)
b)
c)
d)
Figure 5. The extent of cracking in the numerical simulation using the nonlinear material model a) cracking
in SP simulation, b) crushing in SP+SK simulation using reinforcement, c) cracking in SP+SK simulation
using reinforcement and d) cracking in SP+SK simulation using reinforcement.
Figure 6. Comparison of failure behavior between the linear elastic and nonlinear simulation.
In the prototype-scale simulations, stresses indicative of crushing and cracking of the concrete
was detected. The cracking and crushing were confirmed in the nonlinear simulations. In the case
without shear keys (SP), the cracking was limited to the joints, and the failure occurred at the
same load level. However, the cracking was extensive in the case with supports and shear keys
(SP+SK). A new failure mode was also introduced due to the nonlinear material, and the failure
occurred at a failure load 6 % lower. Therefore, the assumption of rigid body motions in the model
tests was reasonable except for the case with supports and shear keys (SP+SK). In that case, the
material should have been scaled to achieve more accurate results. In traditional dam design and
analysis of existing dams, the dam is often assumed to be rigid during the stability analysis. The
simulation results indicate that this might be a non-conservative assumption under certain circum-
stances.
The physical model tests helped to validate the load-controlled simulations. However, in the
simple load-controlled simulations, the discharging water and the secondary effects from the
flowing water cannot be assessed. A step in developing the numerical routine would be adding
fluid-structure interaction (FSI) to the simulations. The water could be simulated by, e.g., Coupled
Euler-Lagrange (CEL) or Smoothed Particle Hydrodynamics (SPH) simulations.
The model tests are limited to a specific setup and geometry. As a further study, more numerical
simulations should be performed with real dams as case studies. More realistic boundary condi-
tions should also be studied to give a more reasonable range of impact from different types of
boundaries, such as rock abutments, embankment dams or massive concrete intake buildings.
5 CONCLUSIONS
This paper presents the results of a numerical study examining the ability of dynamic finite ele-
ment simulations to replicate dam failures. The results from the physical model tests performed
by Enzell et al. (2023) were used as a case study to validate the numerical results. It was found
that the numerical model was able to accurately reproduce the failure mode and breach develop-
ment observed in the physical model tests. However, the pre-failure displacement was not simu-
lated accurately. It could also be confirmed using the numerical simulation that the tests were
representative of the dam on the prototype scale. However, the model test with the highest degree
of restraint had a lower load-bearing capacity and collapsed in a different failure mode when a
nonlinear material model was used. This means that the assumption of rigid bodies was invalid in
this model test. The assumption of rigid bodies might also be non-conservative in real dams under
certain circumstances.
Load-controlled finite element simulations were sufficient for simulating the behavior of the
physical model tests. However, the water discharge and potential effects on adjacent structures
could not be simulated. The possibility of implementing FSI methods in the simulation of dam
failures should be studied further.
Further research is needed to determine the reliability of numerical models for predicting dam
failures under different loading conditions and in more realistic geological settings. However,
these findings suggest that load-controlled FE models can be a valuable tool for analyzing the
stability of concrete gravity dams. The simulations can also help predict the development of fail-
ures for an entire dam, including the interaction between the monoliths and connecting structures,
such as abutments.
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