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Simulation of Crack Propagation in Concrete Hydropower Dam StructuresRichard Malm1,2, Manouchehr Hassanzadeh1,3 Tobias Gasch2, Daniel Eriksson2
1 KTH Royal Institute of Technology / Concrete Structures
2 Vattenfall Research and Development / Civil Engineering
3 Lund University / Building Materials
Crack Propagation in Concrete Hydropower
Dam Structures
• Ongoing extensive program to upgrade the Swedish hydropower plants
- Generator foundation
- Influence of cracks on the dam safety
Insulating wall
Water level
Buttress wall
Inspection gangway
Upstream side
Downstream side
Front-plate
Storfinnforsen hydropower dam
• Storfinnforsen concrete buttress dam
- Total length of 1200 m (800 m concrete)
- 100 concrete monoliths
• Several different types of cracks found in-situ
Insulating wall
Water level
Buttress wall
Inspection gangway
Upstream side
Downstream side
Front-plate
2.5 m
c400 mm
c4
00
mm
c400 mm
c1
50
mm
c400 mm
c3
00
mm
c400
mm
Two layers of
rebars φ19 mm
Each 50 mm
below the
concrete
surface
Numerical simulations
• One monolith is modeled with 3D shell elements
- Reinforced concrete
• Nonlinear material model CDP (Concrete Damaged Plasticity) in ABAQUS v 6.10
• Thermal analyses
- Winter air temperature – 15 °C
- Summer air temperature +25 °C
• Simulation steps
- Static loads (gravity, water pressure)
- Cycle winter and summer temperatures for the initial
design of the monolith
- Cycle winter and summer temperatures after the
insulating wall was installed
Steady State Thermal Calculations
• Cyclic steady state thermal calculations were performed
- Summer – winter (without an insulating wall)
- Summer – winter (with an insulating wall)
• Coupled thermo-stress analysis
- Importing the steady state temperatures into a model that
calculate resulting stresses and predict cracking
Winter conditions Summer conditions
Simulation - Seasonal temperature variation
Before the insulating wall
After the insulating wall
Inclined cracks in the buttress
Horizontal cracks in the front-plate
Inclined crack in the buttress
Cyclic seasonal temperature variation (summer/winter)
Deformation scale factor 400
Animation of the crack propagation
Probabilistic analyses
• Study the influence of material properties and material distribution on the crack trajectory
- Starts from an analysis where the inclined crack is initiated
and simulate further crack propagation
• Monte Carlo Simulation - 1000 analyses
- Sub-model of the area of interest with a significantly refined
mesh
Sub-model
Stochastic material properties
• Generated 1000 random material properties with log-normal distribution
• Assuming a high correlation between the material properties, above 95%
0 1 2 3 4 5 6 70
0.05
0.10
0.15
0.20
0.25
Tensile strength (MPa)
50 100 150 200 250 3000
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Fracture energy (Nm/m )210 15 20 25 30 35 40 45
Elastic modulus (GPa)
Pro
bab
ility
N = 1000µ = 2.53 MPaσ = 0.78 MPaCOV = 0.31
Statistics of randomgenerated properties
Statistics of randomgenerated properties
2
Statistics of randomgenerated properties
N = 1000µ = 120.9 Nm/mσ = 35.8 Nm/mCOV = 0.30
N = 1000µ = 25.2 GPaσ = 3.8 GPaCOV = 0.15
2
Pro
bab
ility
Pro
bab
ility
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
50 100 150 200 250 3000
2
4
6
8
Fracture energy (Nm/m2)
Tensile
str
ength
(M
Pa)
10 20 30 40 500
2
4
6
8
Elastic modulus (MPa)
Tensile
str
en
gth
(M
Pa)
10 20 30 40 5050
100
150
200
250
300
Elastic modulus (MPa)
Fra
ctu
re e
nerg
y (
nm
/m2)
Material distribution
• Randomly assigning a set of material properties (ft, Ec, Gf) for each element in the sub-model and simulating the crack propagation
Mean ft = 2.54 MPa
Tensile Strength [MPa]
1
2
3
4
5
6
Regions With Low Tensile Strength [MPa]
Min
2.5
Max
Area subjected to cracking
• Based on all simulations
- All cracked elements summarized in one plot
- Calculated probability of crackingCrack Pattern Calculated probability of cracking
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Cracked element from the all simulations
Cracked element in the original
analysis (with mean values)
Conclusions
• Several, more or less cracked dams in Sweden.
- In many cases due to the new pattern of generator operation
- Extensive ongoing program to upgrade the dams
• In this project, the non-linear finite element method have been used to
- Explain the cause of cracks in a concrete buttress dam
- Study the influence of distribution in material properties on the
crack trajectory
- Preliminary results shows a difference in crack trajectory obtained
from a deterministic analysis with mean values compared to the
most probable crack trajectory obtained from probabilistic
analyses
Thanks for your attention!
Richard Malm, PhD
KTH Royal Institute of TechnologyConcrete Structures ([email protected])
Vattenfall Research and Development Civil Engineering ([email protected])