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 (malm@byv.kth.se)

Vattenfall Research and Development Civil Engineering (richard.malm2@vattenfall.com)