Simulation of Crack Propagation in Concrete Hydropower Dam ...

Simulation of Crack Propagation inConcrete Hydropower DamStructuresRichard Malm 1,2 , Manouchehr Hassanzadeh 1,3 Tobias Gasch 2 ,Daniel Eriksson 21 KTH Royal Institute of Technology / Concrete Structures2 Vattenfall Research and Development / Civil Engineering3 Lund University / Building MaterialsCrack Propagation in Concrete HydropowerDam Structures• Ongoing extensive program to upgrade the Swedishhydropower plants- Generator foundation- Influence of cracks on the dam safetyWater levelUpstream sideFront-plateButtress wallDownstream sideInspection gangwayInsulating wall

2.5 mStorfinnforsen hydropower dam• Storfinnforsen concrete buttress dam- Total length of 1200 m (800 m concrete)- 100 concrete monoliths• Several different types of cracks found in-situWater levelUpstream sideFront-plateButtress wallDownstream sideInspection gangwayInsulating wallNumerical simulations• One monolith is modeled with 3D shell elements- Reinforced concrete• Nonlinear material model CDP (Concrete DamagedPlasticity) 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 initialdesign of the monolith- Cycle winter and summer temperatures after theinsulating wall was installedc150 mmTwo layers ofrebars φ19 mmEach 50 mmbelow theconcretesurfacec400 mmc400 mmc400 mmc400 mmc300 mmc400 mm

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 thatcalculate resulting stresses and predict crackingWinter conditionsSummer conditionsSimulation - Seasonal temperature variationBefore the insulating wallInclined cracks in the buttressHorizontal cracks in the front-plateAfter the insulating wallInclined crack in the buttress

Animation of the crack propagationCyclic seasonal temperature variation (summer/winter)Deformation scale factor 400Probabilistic analyses• Study the influence of material properties and materialdistribution on the crack trajectory- Starts from an analysis where the inclined crack is initiatedand simulate further crack propagation• Monte Carlo Simulation - 1000 analyses- Sub-model of the area of interest with a significantly refinedmeshSub-model

Stochastic material propertiesProbability• Generated 1000 random material properties with log-normaldistribution0.250.200.150.100.05Statistics of randomgenerated propertiesN = 1000µ = 2.53 MPaσ = 0.78 MPaCOV = 0.3100 1 2 3 4 5 6 7Tensile strength (MPa)Probability0.200.180.160.140.120.100.080.060.040.02Statistics of randomgenerated propertiesN = 1000µ = 120.9 Nm/m22σ = 35.8 Nm/mCOV = 0.30050 100 150 200 250 3002Fracture energy (Nm/m )010 15 20 25 30 35 40 45Elastic modulus (GPa)• Assuming a high correlation between the material properties,above 95%88300Probability0.200.180.160.140.120.100.080.060.040.02Statistics of randomgenerated propertiesN = 1000µ = 25.2 GPaσ = 3.8 GPaCOV = 0.15Tensile strength (MPa)642Tensile strength (MPa)642Fracture energy (nm/m 2 )250200150100050 100 150 200 250 300Fracture energy (Nm/m 2 )010 20 30 40 50Elastic modulus (MPa)5010 20 30 40 50Elastic modulus (MPa)Material distribution• Randomly assigning a set of material properties (f t , E c , G f ) foreach element in the sub-model and simulating the crackpropagationTensile Strength [MPa]Regions With Low Tensile Strength [MPa]Max6542.532Mean f t= 2.54 MPa1Min

Area subjected to cracking• Based on all simulations- All cracked elements summarized in one plot- Calculated probability of crackingCrack PatternCalculated probability of cracking0.50.450.40.350.30.250.20.15Cracked element fromthe all simulationsCracked element in the originalanalysis (with mean values)0.10.05Conclusions• 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 beenused to- Explain the cause of cracks in a concrete buttress dam- Study the influence of distribution in material properties on thecrack trajectory- Preliminary results shows a difference in crack trajectory obtainedfrom a deterministic analysis with mean values compared to themost probable crack trajectory obtained from probabilisticanalyses

Thanks for your attention!Richard Malm, PhDKTH Royal Institute of TechnologyConcrete Structures (malm@byv.kth.se)Vattenfall Research and DevelopmentCivil Engineering (richard.malm2@vattenfall.com)