progressive failure analysis on a nuclear power plant shield ......an external impactor is a...

Progressive failure analysis on a nuclear power plant shield building

subjected to impact loads

*Shuang Li1), Zhan Shu2), Yiting He3) and Miaoying Zhou4)

1),3),4)Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education

(Harbin Institute of Technology), Harbin 150090, China; 1),3),4)

Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin

150090, China 2)

Department of Structural Engineering, Tongji University, Shanghai, 200092, China 1)

[email protected]

ABSTRACT

Evaluation on the impact resistant capability of nuclear reactor containment under an external impactor is a realistic issue in the design consideration. The shield buildings are commonly designed to protect the internal containment vessel of nuclear power plants. In this study, finite element model of a reinforced concrete shield building and the missile-like cylindrical impactor are developed incorporating ANSYS/LS-DYNA. Numerical simulations of the dynamic behaviors of the shield building subjected to impacts on different locations and different impact angles along its elevation are conducted. The structural responses have been monitored in the impact regions to describe the damage levels of the shield building. Consequently, four failure modes are defined according to the observed response characteristics and the damage levels. It is shown that when under such type of impactor, the local failure phenomena are dominant for the shield building and the disproportionate collapse of the structure will not happen. Finally, parametric study on the mass and impact velocity of the impactor is performed to quantify the conversion between the four failure modes. 1. INTRODUCTION In recent years, there has been a resurgence of interest to construct the nuclear power plants (NPPs) in both developed and developing counties because nuclear power could make a significant contribution towards reducing greenhouse gas emissions (Adamantiades and Kessides 2009). Several types of NPPs are designed

1)

Associate Professor 2)

Post-Doc 3),4)

Graduate Student

mailto:[email protected]

with double-layer nuclear reactor containments, i.e., the outside shield building and the inside containment vessel, for achieving a more safety and functional considerations. For example, the generation III+ reactor of AP1000, its shield building is designed to protect the internal steel containment vessel and it is also a part of the passive containment cooling system, which employs the natural circulation, gravity, convection and compressed gas, to operate cool task on inside containment vessel in accident events (Winters et al. 2004; Zhao et al. 2014). If the shield building is destroyed by an impact force in an accident event, may lead to damage in both the structural and functional aspects, and finally lead to catastrophic results since it could prevent achieving or maintaining safe shutdown of the NPPs.

Many work has been done relevant to the impact response of the NPPs on the structural safety issues. It is worth to emphasize some studies that considering high speed aircraft impacts into the various shield buildings in the past decade, where the shield building and the impactors are simulated with the refined finite element methods (e.g., Arros and Doumbalski 2007; Jeon et al. 2012; Siefert and Henkel 2014). These researches stem from that, after the September 11 attacks, the importance of aircraft impacts on critical infrastructures such as NPPs was recognized again. Moreover, the safety assessment for impact of an aircraft on NPPs were seemed as a beyond design basis event by the U.S. Nuclear Regulatory Commission (NEI 2011). Thereafter, new shield buildings design requires a design-specific assessment of the effects of an aircraft impact on the facilities through realistic analyses, which usually termed as missile-target interaction analysis method (Lee et al. 2013). On the other hand, the Riera method (Riera 1968; 1980) using the force-time history function as impact load was also used in aircraft impact analyses (e.g., Abbas et al. 1996; Kukreja 2005; Petrangeli 2010; Frano and Forasassi 2011; Iqbal et al. 2012; Sadique et al. 2013). Despite the convenient adoption of the force-time history data, it provides indirect and approximate evaluation, and the dynamic analysis using a pre-defined force-time history implies some uncertainties of the target location, the impact angle, and the influences of mass and velocity of the impactors. A review on the aircraft impact analysis on nuclear safety-related concrete structures was provided by Jiang and Chorzepa (2014), in which the methods available for and aircraft impact analysis are summarized with an emphasis on the building damage analysis. However, the missile-like impactors may also be generated by many other events beside aircrafts, e.g., tornado missiles, turbine missiles, missiles induced by explosion nearby the NPP site (blasting induced flying objects), and other missiles by deliberate or accidental attacks. The missiles generated by above events are generally featured with different masses and impact velocities in a wide range, which still need to be explored. In addition, few researches focus on the potential risk for further damage on the functions of NPPs by the impacts.

In this study, the finite element model of an NPP shield building designed with passive containment cooling system and the cylindrical impactor were firstly developed. Then analysis of the behavior of the NPP shield building under impact was conducted, and four failure modes were presented to define the progressive damage levels. The relationship between the failure modes and the mass and velocity of the impactor were addressed.

2. SHIELD BUILDING DETAILS AND FINITE ELEMENT MODEL

The studied NPP shield building is a reinforced concrete structure with a water storage tank at the upper part of the structure (shown in Fig. 1). Total height of the shield building is 83.4 m. The geometric parameters of the shield building include the diameter (44.2 m), height (65.6 m), and thickness (0.9 m) of the cylinder part of the building, as well as the external diameter (27.1 m), inner diameter (8.8 m), height (11.7 m), and thickness (0.6 m) of the water storage tank. Considering the dimensions of the aircraft head and missiles induced by the abovementioned other events, the used impactor is a cylinder rigid-body object having a semispherical head with the diameter of 3.0 m. The procedures including modeling, meshing and analyzing were carried out using finite element package ANSYS/LS-DYNA (2009).

The assemble model, smeared model and discrete model are the three kinds of finite element models generally used for reinforced concrete structures. In the discrete model, concrete and reinforcing bars are modelled individually and then merged together. Advantages of the discrete model are simulation of the two materials, i.e., concrete and reinforcing bars, in a more accurate way. Therefore, the discrete model of the reinforced concrete is often adopted to model the complex reinforced concrete structures. The discrete model was used in this study to investigate the impact response of the shield building. The concrete and the impactor are meshed by the solid element of Solid164, while reinforcing bars are simulated by the beam element of Beam161. The water in the storage tank is modelled in a simplified way, used the mass element of Mass166, and attached them on the nodes of solid elements for modelling of the water storage tank.

Previous researches show that strain rate plays an important role on the behavior of structures under impact loads (Karagiozova and Marcılio 2004). The behavior of concrete in the numerical simulations was incorporated using Johnson-Holmquist model (Holmquist et al. 1993). Such model is suitable for concrete subjected to large strains, high strain rates, and high pressures. Piecewise linear isotropic plasticity model including the strain rate effects was used to simulate the behavior of the reinforcement material. In the analyses, failure elements were deleted from the structural model according to the excursion criteria of limits of principle strain for the concrete and plastic strain for the reinforcement, respectively. In the meantime, the material model of the impactor was assumed rigid. The contact technique of surface to surface (ESTS) was used to simulate the collision between the impactor and concrete, and node to surface (ENTS) was used to simulate the collision between the impactor and reinforcement, respectively.

Four locations are selected along the elevation of the NPP shield building to subject the impact loads. In order to achieve a more accurate result, the concrete and reinforcing bar element meshes are refined in the impact regions. Fig. 1 shows the finite element models corresponding to the four different impact locations, i.e., (a) Model L1: 1/2 height of the cylinder surface; (b) Model L2: 2/3 height of the cylinder surface; (c) Model L3: 1/2 height of the conical surface; and (d) Model L4: 1/2 height of the water storage tank. Fig. 2 shows the refined meshes of concrete and reinforcing bar of the impact region with node tags. The responses of these tagged nodes are used in the subsequent study to illustrate the failure modes of the shield building.

Impact

region

(a) Model L1 (b) Model L2 (c) Model L3 (d) Model L4

Fig. 1 Finite element models of the shield building for the four impact locations (concrete and reinforcing bar meshes are shown in the upper and

lower parts, respectively).

N1N2

N3N4

N5N6

N7N8

N9

Impact

region

Concrete

N10N11

N12N13

N14N15

N16N17

N18

Impact

region

Reinforcing bar

Fig. 2 Diagram of concrete and reinforcing bar meshes of impact

region. 3. IMPACT FAILURE MODES OF THE SHIED BUILDING

Utilizing the above developed finite element model, analysis of the behavior of the shield building under impact loads is performed, in which change of mass and initial velocity of the impactor. The change of mass is achieved by adjusting the density in order to avoid influencing the result due change of the impactor shape. Four failure modes of the shield building for this type of NPP shield building are identified according to the damage levels, corresponding to repair consideration and potential risk after the damage. The Model L1 (i.e., impact location is at the 1/2 height of the cylinder surface) is used to illustrate the four failure modes in this section, and Model L2 to Model L4

also suffer from the four failure modes but their results are not presented here due to limited space.

Failure Mode 1: local depression. The surface concrete of the shield building is slightly damaged. The depression can be observed but the concrete layer is not damaged. This failure mode corresponds to the concrete damage up to the level that the stress nearly approaches its maximum compressive strength. Because the concrete and reinforcing bars are not broken, reparation is not needed from the operation view of the NPP. An example of this type of impact case with mass and initial velocity of the impactor is shown in Fig. 3. Fig. 3(d) shows the damage situation of the impact region and Fig. 3(e) and (f) show the node (N1-N9, N10-N18) responses of concrete and reinforcing bar as given in Fig. 2. The figures illustrate that the depression deformation occurs while the concrete and reinforcing bar elements in the finite element model are not damaged.

(a) t=0.072s (b) t=0.144s (c) t=3s

(d) Damage of impact

region

0 1 2 3

-0.2

-0.1

0.0

N1

N2

N3

N4

N5

N6

N7

N8

N9

Time (s)

Dis

pla

cem

en

t (m

)

(e) Displacement response of concrete in impact region

0 1 2 3-0.15

-0.10

-0.05

0.00

N10

N11

N12

N13

N14

N15

N16

N17

N18

Time (s)

Dis

pla

cem

ent

(m)

(f) Displacement response of reinforcing bar in impact

region Fig. 3 Illustration of failure mode 1: local depression (case with kgm 4102 and

smv /50 ).

Failure Mode 2: concrete spalling. The concrete of the shield building is damaged.

Spalling of the concrete can be observed and the concrete layer is totally broken. This failure mode corresponds to the concrete damage up to the level that the strain approaches its ultimate strain. Partial concrete at the impact region falls out, which leads to a hole in the shield building (the reinforcing bars in the impact region don’t fracture). This damage may disturb the function of cool task on inside containment vessel in accident events. Therefore, reparation is needed from the operation view. Because only partial concrete is damaged and the impactor is rebound after the

collision on the shield building, the possibility of further damage after the collision, caused by such as blasting, corrosion and oil burning on the internal steel vessel, is low. An example of this type of impact case with mass and initial velocity of the impactor is shown in Fig. 4. In the example case, the mass remains same as the example case in failure mode 1, but the initial velocity increased. Fig. 4(d) shows the damage situation of the impact region and Fig. 4(e) and (f) show the node (N1-N9, N10-N18) responses of concrete and reinforcing bar. The figures illustrate that the concrete is damage while the reinforcing bars are not fractured. The failure concrete elements in the finite element model are deleted, therefore the response time-histories are discontinuous in the figures, which are different compared with the case in Fig. 3(e) and (f).

(a) t=0.040s (b) t=0.102s (c) t=3s

(d) Damage of impact region

0 1 2 3-0.4

-0.2

0.0

N1

N2

N3

N4

N5

N6

N7

N8

N9

Time (s)

Dis

pla

cem

ent

(m)

(e) Displacement response

of concrete in impact region

0 1 2 3-0.4

-0.3

-0.2

-0.1

0.0

N10

N11

N12

N13

N14

N15

N16

N17

N18

Time (s)

Dis

pla

cem

ent

(m)

(f) Displacement response of

reinforcing bar in impact region

Fig. 4 Illustration of failure mode 2: concrete spalling (case with kgm 4102 and

80 /v m s ).

Failure Mode 3: reinforcing bar fracture. More concrete around the impact region

is damaged and partial reinforcing bars are fractured. This failure mode corresponds to the steel damage up to the case that the strain approached its ultimate strain. Similar as in the failure mode 2, this damage may disturb the function of cool task on inside containment vessel in accident events, therefore reparation is needed from the operation view. Although the impactor is finally rebound after the collision on the shield building, part of the impactor penetrates into the shield building during the impact process. In this case, the possibility of further damage after collision, caused by such as blasting, corrosion and oil burning on the internal steel vessel, is higher than that in failure mode 2. The example impact case with mass and initial velocity of the impactor is shown in Fig. 5. In the case, the initial velocity increased to 180 m/s. Fig. 5(d) shows

the damage situation of the impact region and Fig. 5(e) and (f) show the node (N1-N9, N10-N18) responses of concrete and reinforcing bar. The figures illustrate that both the concrete and reinforcing bars are damaged. Note that the response time-history of reinforcing bars shown in Fig. 5(f) are continuous, but the reinforcing bars fractured as shown in Fig. 5(d). The tagged nodes (shown in Fig. 2) are not deleted in this case but their surrounding parts damaged and therefore are deleted.

(a) t=0.038s (b) t=0.106s (c) t=3s


region

0.0 0.5 1.0

-0.4

-0.2

0.0

N1

N2

N3

N4

N5

N6

N7

N8

N9

Time (s)

Dis

pla

cem

ent

(m)

(e) Displacement response of concrete in impact region

0.0 0.5 1.0

-1.2

-0.8

-0.4

0.0

N10

N11

N12

N13

N14

N15

N16

N17

N18

Time (s)

Dis

pla

cem

ent

(m)

(f) Displacement response of reinforcing bar in impact

region Fig. 5 Illustration of failure mode 3: reinforcing bar fracture (case with kgm 4102

and 180 /v m s ).

Failure Mode 4: penetration. The concrete and reinforcing bars at the impact

region are damaged. This failure mode corresponds to the penetration damage of the shield building. Similar as in the failure modes 2 and 3, this damage may influence the function of cool task on inside containment vessel in accident events, therefore reparation is needed from the operation view. In this case, the impactor penetrates into the shield building and will impact on the internal steel vessel later. Thereafter, the possibility of further damage after collision, caused by such as blasting, corrosion and oil burning on the internal steel vessel or internal equipment, is very high. The example impact case with mass and initial velocity of the impactor is shown in Fig. 6. Fig. 6(d) shows the damage situation of the impact region and Fig. 6(e) and (f) show the node (N1-N9, N10-N18) responses of concrete and reinforcing bar. The figures illustrate that both the concrete and reinforcing bars are damaged and the damage region is larger than that in failure mode 3.

(a) t=0.012s (b) t=0.022s (c) t=3s


region

0.0 0.1 0.2-0.8

-0.6

-0.4

-0.2

0.0

N1

N2

N3

N4

N5

N6

N7

N8

N9

Time (s)

Dis

pla

cem

ent

(m)

(e) Displacement response

of concrete in impact region

0.0 0.1 0.2-0.4

-0.2

0.0

N10

N11

N12

N13

N14

N15

N16

N17

N18

Time (s)

Dis

pla

cem

ent

(m)

(f) Displacement response of

reinforcing bar in impact region

Fig. 6 Illustration of failure mode 4: penetration (case with kgm 4102 and

300 /v m s ).

4. RELATIONSHIP BETWEEN FAILURE MODES AND IMPACTOR PARAMETERS

As previously mentioned, several events may lead to the impact loads, such as airplanes with masses of hundred tons, turbine and explosion induced missiles with medium mass, or tornado induced missiles with relative smaller masses but higher velocity, which all might potentially damage to the shield buildings. Therefore, the possible variation range of parameters of the impactor is wide. In this research, impactors with mass from 0.1×103kg to 100×103kg and velocity from 5m/s to 400m/s are analyzed. The parameters are listed in Table 1, which contains a total of 9×17=153 cases for each of the four impact locations. These parameter variation range could cover most flying objects which have possibilities of impact on the shied buildings.

4.1 Conversion of the failure modes

Tab. 1 Parameter variations of the impactor.

Range of mass (×103kg)

0.1, 1, 5, 10, 20, 40, 60, 80, 100

Range of velocity (m/s)

5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200, 250,

300, 350, 400

The 153 cases for each finite element model are analyzed and the statistical results of the failure diagrams of the shield building are presented. Fig. 7 shows the diagrams of the four failure modes, which illustrate that the combination of mass and velocity parameters could greatly influence the failure modes of the shield building. From the figure, one could notice that when an impactor mass and velocity are low, there would be no damage to the shield building. With the increase of mass and velocity, the four failure modes occurred successively. Over the considered parameter variation range, the local depression failure mode has largest the occurrence possibility, followed by the concrete spalling mode and penetration failure mode, and the reinforcing bar fracture failure mode has the smallest occurrence possibility.

v m × 103kg v m × 103kg v m × 103kg v m × 103kg

(a) Model L1 (b) Model L2 (c) Model L3 (d) Model L4

Fig. 7 Diagram of failure modes with respect to impactor mass and velocity

( Undamaged Local depression Concrete spalling Reinforcing bar

fracture Penetration).

Pen

etra

tion

Rei

nfo

rcin

g

bar

fra

cture

Concrete spalling

400337.554E

k ( 103KJ)

0.08

Loca

l dep

ress

ion

(a) Model L1

Pen

etra

tion

Rei

nfo

rcin

g

bar

fra

cture

Concrete spalling

400337.554E

k ( 103KJ)

0.05

Loca

l dep

ress

ion

(b) Model L2

Pen

etra

tion

Reinforcing

bar fractureConcrete spalling

1000562.5100E

k ( 103KJ)

0.05

Loca

l dep

ress

ion

(c) Model L3

Penetration

Rei

nfo

rcin

g

bar

fra

cture

Concrete

spalling

312.518025

Ek ( 103KJ)

0.08

Loca

l dep

ress

ion

(d) Model L4

Fig. 8 Diagram of failure modes with respect to impactor kinetic energy.

Fig. 8 presents kinetic energy (EK) distribution corresponding to the four failure modes, respectively. This figure clearly divides the four damage sections based on the energy distribution. The differences between failure mode sections of local depression and concrete spalling are small for Model L1 and Model L2, which means that only marginal influences on failure modes due to the variation of impact location along on the cylinder part of the shield building. The areas of reinforcing bar fracture and penetration failure modes for Model L3 are smallest compared with the other three models; meanwhile, the kinetic energy demand corresponding to each failure mode is larger than those in the other three models. Therefore, it can be concluded that the conical surface of the shield building is the safer location under impact loads. For Model L4, the kinetic energy demands corresponding to each failure mode are smaller than those in the other three models. Similarly, it can be concluded that the water tank of the shield building is the comparatively dangerous location under impact loads.

4.2 Influence of the impact angles The above sections focus on the impact behavior when the impact is normal to

the surface of the shield building. However, in most cases, the impact angle of the impactor is undetermined. In this section, the impact behaviors with the impact angles of 30° and -30° are discussed, which corresponds to the impact cases with oblique incidence angles.

The diagrams of the failure modes with mass and velocity parameters of the Model L1 with incidence angles of -30° and 30° are shown in Fig. 9. The case with incidence angle of -30°, compared with the results obtained in the case with incidence

angle of 0°, has larger areas of failure modes of local depression and concrete spalling,

and smaller areas of failure modes of reinforcing bar fracture and penetration. On the other hand, the case with incidence angle of 30°, compared with the results obtained in the case with incidence angle of 0°, has larger area of failure mode of local depression, and smaller areas of failure modes of concrete spalling, reinforcing bar fracture and

penetration. Fig. 10 presents the threshold values of the impactor kinetic energy for

conversion to each failure mode. For the impactor with incidence angle of -30°, the values are 0.02×103KJ, 64×103KJ, 400×103KJ, and 450×103KJ; for the impactor with incidence angle of 30°, the values are 0.13×103KJ, 64×103KJ, 405×103KJ, and 450×103KJ. Observations are made when compared with the incidence angle of 0° (0.08×103KJ, 54×103KJ, 337.5×103KJ, 400×103KJ), only the threshold value of local depression failure mode for -30° case is a little smaller than that of the 0° case; else, the threshold values of all the four failure modes are larger than those of the 0° case. Therefore, for Model L1, the adverse incidence angle is 0°, and 30° is relative safer.

Similar figures as Fig. 9 and Fig. 10 are plotted for the Model L2, Model L3, and Model L4, which are presented from Fig. 11 to Fig. 16. For Model L2, Model L3 and Model L4, the threshold values of impactor kinetic energy for conversion to each failure mode are different for normal impact or oblique incident impacts, however, similar conclusion to the Model L1, the adverse incidence angle is 0°, and 30° is relative safer. The differences between -30° and 30° are caused by the gravity and are insignificant.

v m × 103kg v m × 103kg

(a) -30° case (b) 30° case

Fig. 9 Failure modes of Model L1 with oblique incidence angles (

Undamaged Local depression Concrete spalling Reinforcing bar


Pen

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Rei

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g

bar

fra

cture

Concrete spalling

400 45064E

k ( 103KJ)

0.02

Loca

l dep

ress

ion

(a) -30° case

Pen

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Rei

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g

bar

fra

cture

Concrete spalling

405 45064E

k ( 103KJ)

0.13

Loca

l dep

ress

ion

(b) 30° case

Fig. 10 Failure modes and impactor kinetic energy of Model L1 with oblique

incidence angles.

v m × 103kgv m × 103kg

(a) -30° case (b) 30° case




Pen

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Rei

nfo

rcin

g

bar

fra

cture

Concrete spalling

400 45064E

k ( 103KJ)

0.02

Loca

l dep

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ion

(a) -30° case

Pen

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g

bar

fra

cture

Concrete spalling

405 45064E

k ( 103KJ)

0.05

Loca

l dep

ress

ion

(b) 30° case

Fig. 12 Failure modes and impactor kinetic energy of Model L2 with

oblique incidence angles.

v m × 103kgv m × 103kg

(a) -30° case (c) 30° case




Pen

etra

tion

Reinforcing bar fractureConcrete

spalling

1400562.596E

k ( 103KJ)

0.05

Loca

l dep

ress

ion

(a) -30° case

Pen

etra

tion

Reinforcing

bar fracture

Concrete

spalling

1400600112.5E

k ( 103KJ)

0.06

Loca

l dep

ress

ion

(b) 30° case



v m × 103kgv m × 103kg

(a) -30° case (c) 30° case




Pen

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Concrete spalling

400 67572E

k ( 103KJ)

0.08

Loca

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(a) -30° case

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Concrete spalling

400 67564E

k ( 103KJ)

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(b) 30° case



5. CONCLUSIONS

The study analyzed the impact damage phenomena of a nuclear power plant shield building. Impacts are considered at four typical locations along the elevation of the building. A progressive failure criterion is proposed to quantify the damage levels of the shield building under impact loads. The criteria, is based on the damage level at the impact region, the repair consideration, and the potential risk after damage. Specifically, the criteria include four failure modes, i.e., local depression mode, concrete spalling mode, reinforcing bar fracture mode, and penetration mode. The diagram of failure modes regarding impactor mass and velocity is a useful tool to represent the results on failure modes by potential impactors. In addition, for the studied type of NPP shield building, specific conclusions are obtained:

1. Parametric analysis results show that impactors with diameter up to 3.0 m, mass ranges from 0.1×103kg to 100×103kg and velocity ranges from 5m/s to 400m/s, only leads to local damage to different levels of the shield building, rather than the

disproportionate collapse to initial damage which usually occurred in the ordinary buildings.

2. The surface of water storage tank has relatively smaller impact resistant capability, while the conical surface has relatively larger impact resistant capability; the impact resistant capabilities along the cylinder surface are almost same. The normal incidence impact is more unfavorable than impacts with other incidence angles. ACKNOWLEDGMENT

This research project was partially supported by the National Natural Science Foundation of China (Grant No. 51238012). The financial support offered by the research fund is greatly appreciated by the authors. REFERENCES Abbas H, Paul DK, Codbole PN, Nayak GC. (1996), “Aircraft crash upon outer

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progressive failure analysis on a nuclear power plant shield ......an external impactor is a...

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