1 Introduction
2 Finite Element Modeling
2.1 Material Models
2.1.1 Alkali-Silica Reaction (ASR) Swelling Model
2.1.2 Continuous Cap Surface Model for Concrete
Parameters | Symbols | Values |
---|---|---|
Shear surface constant term under compression |
α
| 14.2 MPa |
Shear surface exponent under compression |
β
0
| 0.01929 MPa−1 |
Shear surface nonlinear term under compression |
λ
| 10.51 MPa |
Shear surface linear term under compression |
θ
| 0.2965 |
Shear surface constant term under tension |
α
1
| 0.7473 |
Shear surface exponent under tension |
β
1
| 7.25 × 10−2 MPa−1 |
Shear surface nonlinear term under tension |
λ
1
| 0.17 |
Shear surface linear term under torsion |
θ
1
| 1.204 × 10−3 MPa−1 |
Shear surface constant term under extension |
α
2
| 0.66 |
Shear surface exponent under extension |
β
2
| 7.25 × 10−2 MPa−1 |
Shear surface nonlinear term under extension |
λ
2
| 0.16 |
Shear surface linear term under extension |
θ
2
| 1.45 × 10−3 MPa−1 |
Fracture energy under compression |
G
c
| 10 KPa.cm |
Fracture energy under tension |
G
T
| 0.1 KPa.cm |
Fracture energy under shear |
G
s
| 0.1 KPa.cm |
Maximum plastic volume compaction | W | 0.05 |
Maximum aggregate size | Agg. size | 16 mm |
Cap aspect ratio | R | 5 |
Softening parameter under compression | B | 10–500 |
Softening parameter under tension | D | 0.05–10 |
Hardening initiation |
N
H
| 0.7 |
Hardening rate parameter |
C
H
| 999 |
Initial cap location |
X
0
| 90 MPa |
Cap linear shape parameter |
D
1
| 2.5 × 10−4 MPa |
Cap quadratic shape parameter |
D
2
| 3.5 × 10−7 MPa2 |
2.2 Geometry, Boundary Conditions and Meshing
Part | Height (mm) | Length (mm) | Width (mm) | Internal radius (mm) | External radius (mm) | Thickness (mm) |
---|---|---|---|---|---|---|
Rectangular concrete pad | 381.0 | 3810.0 | 3810.0 | – | – | – |
Subgrade soil | 2540.0 | 5080.0 | 5080.0 | – | – | – |
Steel liner | 1962.2 | – | – | 355.6 | 371.5 | 15.9 |
Outerpack concrete cask | 1962.2 | – | – | 371.5 | 609.6 | 238.1 |
Lid-top | – | – | – | – | 431.8 | 6.4 |
Lid-bottom | – | – | – | – | 352.4 | 3.2 |
Lid-rib | 50.8 | – | – | 349.3 | 352.4 | 3.2 |
Concrete lid | 50.8 | – | – | – | 349.3 | 349.3 |
Base plate | – | – | – | – | 609.6 | 63.5 |
Canister | 1905.5 | – | – | 349.3 | 352.4 | 3.2 |
Properties | Values |
---|---|
Density | 7850 kg/m3 |
Young’s modulus | 206 × 103 MPa |
Poisson’s ratio | 0.26 |
Initial yield stress | 250 MPa |
Properties | Values |
---|---|
Density | 2450 kg/m3 |
Young’s modulus | 31 × 103 MPa |
Poisson’s ratio | 0.15 |
Uniaxial tensile strength | 4.3 MPa |
Uniaxial compressive strength | 41.4 MPa |
Biaxial compressive strength | 55 MPa |
2.3 Solution Techniques and Assessment Metrics
Problems | Materials | Criteria | Limits | Mesh sizes (mm) | References |
---|---|---|---|---|---|
Impact | Concrete 27.5 MPa | Principal strain | 0.003 | 80 × 80 × 60 | Huang and Wu (2009) |
Blast | Concrete 40 MPa | Principal strain | 0.01 | 18.75 × 18.75 × 25 | Xu and Lu (2006) |
Blast | Concrete 24 MPa | Principal strain | 0.15 | 50 | Shi et al. (2010) |
Blast | Concrete 24 MPa | Shear strain | 0.9 | 50 | Shi et al. (2010) |
Blast | Concrete 60 MPa | Tensile strain | 5 MPa | 6.25–100 | Tang and Hao (2010) |
Blast | Concrete 60 MPa | Principal strain | 0.1 | 6.25–100 | Tang and Hao (2010) |
Blast | Concrete 40 MPa | Maximum strain | 0.1 | 50 | Wu et al. (2011) |
Blast | FRC 1% 28 MPa | Shear strain | 0.4 | Wang et al. (2009) | |
Blast | FRC 1% 28 MPa | Tensile stress | 5.4 MPa | Wang et al. (2009) | |
Blast | FRC 1.5% 30 MPa | Shear strain | 0.4 | Wang et al. (2010) | |
Blast | FRC 1.5% 30 MPa | Tensile stress | 6 MPa | Wang et al. (2010) | |
Blast | FRC 2% 32 MPa | Shear strain | 0.4 | Wang et al. (2010) | |
Blast | FRC 2% 32 MPa | Tensile stress | 7.5 MPa | Wang et al. (2010) | |
Blast | FRC 45 MPa | Damage | 0.99 | 25 × 25 | Coughlin et al. (2010) |
Dynamic | Concrete 35 MPa | Principal strain | 0.002 | 6–8 | Tu and Lu (2010) |
Impact | Concrete 40 MPa | Strain limit | 1.5 | Tu and Lu (2010) | |
Impact | Concrete 48–140 MPa | Strain failure | −1 (Comp) 0.5 (Tens) | 2 | Islam et al. (2011) |
Impact | FRC 28–32 MPa | Tension stress failure | 5.4 MPa | 1.25 | Teng et al. (2003) |
Impact | FRC 28–32 MPa | Shear strain | 0.4 | 1.25 | Teng et al. (2003) |
Impact | HPFRC | Ultimate shear strain | 0.012 | 6 × 8 | Farnam et al. (2010) |
3 Results and Discussion
3.1 Tip-Over Analysis of Dry Cask Structure with Intact Concrete
3.2 Failure Analysis of Tip-Over Analysis of 1:3 Model Dry Cask Structures
3.3 Tip-Over Simulation of Model Dry Cask Using the ASR Affected Concrete
Properties | Values |
---|---|
Density | 2450 kg/m3 |
Young’s modulus | 15.5 × 103 MPa |
Poisson’s ratio | 0.15 |
Uniaxial tensile strength | 2.15 MPa |
Uniaxial compressive strength | 12.5 MPa |
4 Conclusions
-
It was shown the intact dry cask is locally damaged under this tip-over scenario, where the edge of concrete in the contact zone crushes, and the other edge is exposed to the shear banding. Several cracks were observed also observed.
-
When the ASR is fully developed in the concrete outerpack, a reduction of approximately 50% was observed for the modulus of elasticity and tensile strength.
-
Environmental degradation due to ASR was calculated in the form of strain tensor and implemented in LS-DYNA (Hallquist 2006) in the form of temperature gradient before tip-over starts.
-
Maximum acceleration at outer edge of concrete reaches to 150 g which reduces to 100 g when the stiffness is reduced due to ASR damage.
-
Concrete crushing is the dominant failure mode in the case of fully expanded ASR where damage parameter reaches to 0.99 in the form of brittle damage and ductile damage in the entire structure.
-
It was shown that a large crack divides the cask into two parts when the effect of ASR is considered in this hypothetical event.