Effect of AlkaliSilica Reactivity Damage to TipOver Impact Performance of Dry Cask Storage Structures
Abstract
This paper investigates the effect of concrete degradation due to alkalisilica reactivity (ASR) and its effect on the performance of vertical concrete casks in the case of a hypothetical tipover event. ASR is one of the major problems in certain concrete structures exposed to high relative humidity and temperature. Using the first order kinetic model, the mechanical and environmental effects of degradation are modeled for a drycask storage structure under the conditions that ASR is completely extended. Following the degradation, a tipover impact simulation was performed and compared with that of an intact cask in terms of failure modes, damage patterns, stresses, and accelerations. It was seen that concrete crushing and shear banding are major failure modes in the cask with intact concrete, but in the case of the ASR affected cask, the concrete is fully damaged and a longitudinal crack which separates the cask into two parts propagates through the outerpack.
Keywords
impact analysis alkalisilica reaction dry cask storage structures concrete degradation failure analysis1 Introduction
Degradation of concrete limits the service life of structures. Creep and shrinkage due to moisture transfer in the early age of concrete and expansion due to thermal effects and alkalisilica reaction (ASR) may degrade the concrete properties. Dry cask storage structures in the form of thickwalled cylinders are widely used for storage of spent nuclear fuel. The US Nuclear Regulatory Commission provides regulations to investigate their performance under hypothetical events (Dilger et al. 2012; Halstead and Dilger 2006). A dry cask structure needs to be designed to safeguard the internals under a tipover impact scenario. Expansion of ASR gel between aggregate and cement paste reduces the stiffness and strength of concrete and may cause cracking (Champiri et al. 2012). Substantial experimental work was performed by Larive (1998) to evaluate the ASR expansion in concrete. Similarly, work has been done to evaluate the tipover impact performance of dry cask storage structures.
Many researchers worked on hypothetical events including tipover, drop test and free drop test of concrete cylinders with different geometries. Gupta (1997) proposed a mathematical approach for tipover simulation. He assumed a rigid pad and a single degreeoffreedom massspring system. Other researchers used finite element (FE) method which is now extensively applied for crash simulations. Since implicit time integration is not capable of simulating this contact–impact problem due to the convergence issues with regard to the large deformations and rotations and high nonlinearity, explicit time integration is generally used. Teng et al. (2003) used a dynamic explicit FEA code, named DYNTRAN (2008) for impact analysis of a cask. Elfahal (2003) performed an experimental and numerical study to investigate the size effect in normal and high strength concrete cylinders subjected to static and dynamic axial compressive loads. Lee et al. (2005) simulated the drop impact of a cask using LSDYNA (Hallquist 2006) and ABAQUS (Hibbitt, Karlsson and Sorensen, Incorporated 2002). Kim et al. (2007) studied shockabsorption characteristics of concrete pads for casks using ABAQUS explicit (Hibbitt, Karlsson and Sorensen, Incorporated 2002). Champiri et al. (2015a, b, 2016) investigated the behavior of a degraded concrete dry cask storage structure under drop test and tipover event using LSDYNA (Hallquist 2006). However, the performance of a dry cask structure affected by ASR expansion under tipover event has not been studied in detail to our knowledge.
In the following sections, the ASR swelling model is briefly reviewed. Then, the behavior of a concrete model in LSDYNA (Hallquist 2006) is evaluated for the purposes of this study. Later, the modeling of the dry cask storage structure is introduced and tipover event is simulated for the intact and degraded concrete outerpacks. The paper concludes with a discussion of the results and possible future studies.
2 Finite Element Modeling
2.1 Material Models
2.1.1 AlkaliSilica Reaction (ASR) Swelling Model
This paper uses the first order kinetic approach to calculate degradation due to ASR for concrete outerpack which is based on Ulm et al. (2000) and Saouma and Perotti (2006) and the experimental work by Larive (1998). A brief summary of this method is provided in this section. Further details are available in Champiri et al. (2018).
These functions for elastic modulus and tensile strength are calculated for a fully developed ASR extension where ξ = 1, and implemented to the dry cask storage structures for tipover contact–impact scenario as described in the following sections.
2.1.2 Continuous Cap Surface Model for Concrete
The CSCM material parameters calibrated based on experimental data (Mousavi et al. 2016).
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} MPa^{2} 
The results of Figs. 3, 4 and 5 show that the model has a realistic behavior. However, it is clearly seen that the lateral strains are too large relative to the experimental data (Mousavi et al. 2016) since this material model uses an associate flow rule. It is expected to observe a higher value of lateral expansion in this material model compared to the experimental data (Mousavi et al. 2016) which was confirmed from the analysis results. The value of 100 was selected for parameter B for further analysis which matches with the experimental data.
2.2 Geometry, Boundary Conditions and Meshing
Dimensions of 1/3scale cask used in tipover impact simulations.
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 
Lidtop  –  –  –  –  431.8  6.4 
Lidbottom  –  –  –  –  352.4  3.2 
Lidrib  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 
Steel properties for tipover simulation.
Properties  Values 

Density  7850 kg/m^{3} 
Young’s modulus  206 × 10^{3} MPa 
Poisson’s ratio  0.26 
Initial yield stress  250 MPa 
Concrete properties for tipover simulation.
Properties  Values 

Density  2450 kg/m^{3} 
Young’s modulus  31 × 10^{3} MPa 
Poisson’s ratio  0.15 
Uniaxial tensile strength  4.3 MPa 
Uniaxial compressive strength  41.4 MPa 
Biaxial compressive strength  55 MPa 
Friction phenomena exist whenever contacts occur. Friction may play an important role. Classical friction laws (linear dry friction) and nonclassical friction laws (e.g., elastoplastic friction) exist for modeling friction. Classical friction law has physical deficiencies since it allows small relative motion of two contacting bodies even if the friction force is less than μ_{s}N, where μ_{s} is the coefficient of static friction, and N is the normal force. The classical friction law ignores the dependence of friction coefficient on the relative sliding velocity. This dependency is significant when the relative sliding velocity is large. The actual coefficient of friction μ_{c} = μ_{d} + (μ_{s} − μ_{d})e^{−dc.v} is assumed to depend on μ_{s}, μ_{d}, and dc, where μ_{d} is the coefficient of dynamic friction, dc is the exponential decay coefficient and considered to be 0 in this paper, and v is the relative velocity of the surface in contact and equal to \( {\text{v}} = \frac{{{\text{C}}_{1} {\text{C}}_{0} }}{{\Delta {\text{t}}}} \) where C_{1}, C_{0} are the coordinates of slave node and contact point on the master segment. If exponential decay dc = 0 then μ_{c} = μ_{s} and f = μ_{s}N.
Internal and external forces are summed at each nodal point, and a nodal acceleration is computed by dividing by nodal mass. The solution is advanced by integrating this acceleration in time. The maximum time step is limited by the Courant condition, producing an algorithm which typically requires many relatively inexpensive time steps.
A fine mesh was used for tipover simulation. Eighty elements were specified along the length of the concrete outerpack. As a result, each element had a size of 25 by 25 by 25 mm. The whole model had 266,830 elements and 304,329 nodes.
2.3 Solution Techniques and Assessment Metrics
Hourglass mode was considered using the Belytschko–Bindeman (1993) formulation of assumed strain corotational stiffness form for 2D and 3D solid elements with one integration point. This form is available for explicit problems in LSDYNA (Hallquist 2006). Hourglass energy, which is the work done by the forces calculated to resist the hourglass modes, was removed from the physical energy of the system. Hourglass energy was taken acceptable when it is less than 10% of the total energy (www.LSDYNAonline.com). Sliding interface energy or contact energy is another important issue in this problem. This energy should not be less than zero to satisfy the definition of the contact. In addition, it is recommended that this number should be less that 10% of the total energy (www.LSDYNAonline.com). Rate effects should also be considered in impact–contact type problems. Therefore, the rate sensitivity of concrete was considered here for the CSCM (Murray 2007).
Failure criteria in literature for concrete in LSDYNA (Hallquist 2006).
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) 
A mesh size of 25 × 25 × 25 mm was used here, which is reasonable based on the literature review. Activating the element erosion algorithm makes the model run faster since some elements were deleted while performing the tipover simulations.
It was discovered that using only the maximum compressive strength as an erosion criterion is not acceptable because the stiffness of the structure is highly decreased when the element is deleted, in other words, the stiffness of elements in the softening part is neglected. Then, a damage based criterion was tried. A damage parameter of 0.99 was used. However, it was seen that this criterion cannot capture the shear band and shear cracks correctly. Therefore, a combination of damage and maximum shear strain was used. Selecting a value for maximum shear strain is not straightforward and it is highly dependent on the material model. A value between 0.1 and 0.9 was reported in the literature (Coughlin et al. 2010; Morris et al. 2013; Wang et al. 2010; Xu and Lu 2006). It was concluded that a value of 0.1 can better describe this criterion for CSCM during this contact–impact problem.
3 Results and Discussion
3.1 TipOver Analysis of Dry Cask Structure with Intact Concrete
3.2 Failure Analysis of TipOver Analysis of 1:3 Model Dry Cask Structures
In this section, failure modes of the dry cask structure are investigated. The same geometry, boundary and initial conditions, and material properties as for the previous sections were used. The failure criteria described in Sect. 2.3 was adopted.
3.3 TipOver Simulation of Model Dry Cask Using the ASR Affected Concrete
The first order swelling model (Saouma and Perotti 2006; Ulm et al. 2000), which was described briefly in Sect. 2.1, was implemented to determine the level of degradation for a fully extended ASR state in the dry cask structure. COMSOL Multiphysics (2015) was used to model the ASR behavior of dry cask structure. For this purpose, only the concrete outerpack and the steel liner were considered. A 2D axisymmetric model was developed. The stress and strain components were calculated in all directions including axial (z), radial (r), and tangential (θ) directions. Friction was applied between these two parts and the same coefficient of friction with the same value of 0.45 as in the tipover impact case was used.
For fully extended ASR, E was obtained to be 15,500 MPa, where it was originally 31,000 MPa. Using the ACI formulation (2008), Here, the uniaxial compressive strength was calculated as \( {\text{f}}_{\text{c}}^{\prime} \) = 12.5 MPa, where it was originally 41.1 MPa. Additionally, the reduced the tensile strength was obtained as \( {\text{f}}_{\text{t}}^{ \prime} = 2.15\;{\text{MPa}} \)
ASR strain was computed in three orthogonal directions based on the first order kinetic model. It was shown that ε_{r} = ε_{θ} =0.0087, and ε_{ z } =0.0076. This initial strain was translated into LSDYNA (Hallquist 2006) model as initial strains in form of the temperature gradient using different values for the thermal coefficient (α) in each direction.
Concrete properties for tipover simulation.
Properties  Values 

Density  2450 kg/m^{3} 
Young’s modulus  15.5 × 10^{3} MPa 
Poisson’s ratio  0.15 
Uniaxial tensile strength  2.15 MPa 
Uniaxial compressive strength  12.5 MPa 
The internal time step of this analysis was 4.44E−07 s. This simulation took longer than the intact model since strain states were introduced to all the elements of the concrete outerpack. Contact happened at time equal to 1.2078 s (corresponding to the maximum acceleration at tip of the cask) after starting the tipover simulation from the initial condition.
Concrete crushing was observed as the dominant failure mode in this case and it was seen that most regions of the concrete outerpack are fully damaged in both ductile and brittle damage (red regions). Since the concrete is damaged due to ASR, shear banding does not occur at the same extent as for the intact cask. Additionally, it was seen that during this impact, concrete outerpack is divided into two parts through a large crack (see Fig. 24). The vonMises stresses were reduced in the ASR damaged cask which is an indication that the elements are in the softening regime and they are destressed.
4 Conclusions

It was shown the intact dry cask is locally damaged under this tipover 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 LSDYNA (Hallquist 2006) in the form of temperature gradient before tipover 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.
Notes
Acknowledgements
The financial support for this project was provided by the United States Department of Energy through the Nuclear Energy University Program under the Contract No. 00128931. The findings presented herein are those of the authors and do not necessarily reflect the views of the sponsor.
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