Safety Assessment of Airtight Protective Doors of Nuclear Power Plants Subjected to Wind-Borne Missile Impact

Abstract

This paper aims to study the dynamic response and damage of airtight protective doors of nuclear power plants subjected to tornado and wind-borne missile impact. Firstly, a safety performance evaluation method is proposed, considering the structural characteristics of the airtight protective door and relying on support rotation and airtightness. Then, the commercial finite element (FE) program LS-DYNA is utilized to perform the numerical simulations of airtight protective doors in nuclear power plants exposed to tornadoes and wind-borne missile impacts. Subsequently, the parameter analysis method is employed to investigate the impact of keel quantity, size and arrangement, door panel thickness, door core material, and boundary conditions on the dynamic response, airtightness, and failure mode of the airtight protective door. The results show that tornado wind pressure has little effect on the resistance of airtight protective doors and that the impact load of wind-borne missiles plays a leading role. The number and thickness of the keel have significant effects on the force transfer mode and failure mode of airtight protective doors. The thickness of the door panel has a great influence on the damage mode and airtightness of airtight protective doors. The door core improves the local resistance of the airtight protective door to a certain extent, and foam aluminum material has a better energy absorption effect. The change in boundary conditions has little influence on the resistance of airtight protective doors.

1. Introduction

In the wake of war and global climate impact, the energy crisis is escalating, emphasizing the growing significance of nuclear power projects. Simultaneously, the safety performance of nuclear power plants, deemed crucial lifeline projects, has emerged as the most pressing concern in public discourse. The design of safety-related structures, systems, and components in nuclear power plants must consider the impacts of severe meteorological events [1], including tornadoes and wind-borne missile impact loadings. Wind-borne missiles have the potential to impact the structure of nuclear power plants, potentially penetrating the roof and other protective structure components. This could result in the loss of protective function, posing a direct threat to the safety of equipment and personnel inside the structure. Furthermore, it may lead to the leakage of radioactive materials, triggering more significant environmental disasters. Serving as a crucial protective component in nuclear power engineering, steel airtight protective doors play a pivotal role in enhancing the overall safety performance of the structure. In consideration of the catastrophic consequences, regulations stipulate that the airtight protective door of nuclear power plants must be designed to withstand potential tornado loads and the impact of wind-borne missiles.

Over the past decades, many experimental, theoretical, and numerical studies have been conducted to explore the mechanism of wind-borne missile impact. Stephenson et al. [2] conducted the first full-scale impact test on concrete slabs under common tornado missile impact and studied the failure mode of concrete slabs subjected to tornado missile impact. Kar et al. [3,4] investigated tornado-induced missiles based on full-scale results and introduced a method to predict the contact pressure at the interface between the missile and the target, along with the velocity and deceleration time histories of the missile. Terranova et al. [5,6] conducted numerical simulation research on full-scale tests, studied the calculation method of concrete penetration thickness under wind-borne missile impact, and gave the design thickness of a concrete structure against a tornado. Zamanian et al. [7] further conducted a sensitivity analysis on the performance of concrete slabs under wind-borne missile impact. Kulkarni et al. [8] carried out a numerical study on the performance of high-performance concrete slabs against wind-borne missiles. The research on other structures under wind-borne missile impact has also attracted the attention of scholars. Heribin et al. [9] systematically analyzed the vulnerability of building envelope components under wind-borne missiles. Chen et al. [10,11,12] conducted experimental and numerical simulation studies on building composite thermal insulation materials, thermal insulation boards, and corrugated cardboard under wind-borne missile impact.

On the other hand, the performance of steel structures subjected to wind-borne missile impact has been also investigated. Li et al. and Wang et al. [13] conducted a study on the safety of a nuclear power plant considering the steel ducts/pipes used in construction against the impact of a tornado. This study introduced a simplified, lumped parameter nonlinear analysis methodology using a single degree of freedom model. It was applied to the coupled commodity support system subjected to tornado impulse loading. An experimental study of metal roof decking systems subjected to tornado-borne missile impact has been conducted by Cui et al. [14]. The results showed that the deformation of the metal roof deck increases proportionally with the impact velocity, and larger deformations occur at impact locations farther away from the support. A drop weight impact test and numerical simulation on the dynamic response of a steel plate subjected to tornado-induced missile impact have been conducted at the Sakamoto lab of the Central Research Institute of Electric Power Industry [15]. The applicability of the Ballistics Research Lab formula and the limiting of the triaxial strain principle for a steel plate was also discussed. In addition, they proposed a simplified method for calculating the impact force of the steel plate subjected to pipe impact. Jaffe et al. [16] performed the wind speed estimates for garage door failures in tornadoes and found the resulting range of expected failure wind speeds obtained to be 130–265 km/h. Schmitt et al. [17] investigated the qualification of a water-filled tank subjected to the tornado-induced missile impact using numerical simulations. The results indicated that the water-filled cylindrical tank ensured the availability of water inventory in the tank to mitigate the post-impact effects. Zou et al. [18] conducted impact tests and a numerical analysis on the large-scale steel LNG storage tanks under wind-borne missile impact.

In the study of airtight protective doors, the focus is on the structural dynamic response under blast conditions. He et al. [19] predicted the blast responses of composite fluted-core sandwich protective door panels by using anisotropic dynamic theory. Thimmesh et al. [20] conducted a numerical investigation on the blast resistance of door panels. Al-Rifaie et al. [21] studied the blast-induced response of lightweight gates with a uniaxial graded auxetic damper. Chen et al. [22] conducted numerical research on a new multi-arch, double-layered blast resistance door panel. The results showed that this new structural form of panel can withstand higher explosive loads. Research on the force characteristics and structural optimization of mine anti-outburst doors under the influence of coal and gas outburst impact airflow has been carried out by Dai et al. [23]. The research results provide a theoretical basis and technical support for optimizing the antishock performance of underground anti-outburst doors in coal mines. However, to date, there have been limited studies focusing on the performance of the airtight protective doors of a nuclear power plant subjected to tornado and wind-borne missile impact. Furthermore, there is a lack of applicable design standards for tornado-resistant airtight protective doors. Therefore, it is necessary to address these issues to guide the tornado-resistant design of airtight protective doors in the nuclear power plant. The damage pattern and dynamic response of steel airtight protective doors subjected to tornado load and wind-borne missiles are still unclear and require in-depth studies.

This paper aims to assess the impact resistance and dynamic behaviors of airtight steel protective doors in nuclear power plants using the commercial finite element program LS-DYNA [24]. Firstly, the verification of the utilized numerical algorithm, constitutive models, and the corresponding parameters was conducted based on an impact test of the steel plate. This was achieved by comparing the test data. Subsequently, based on the validated finite element analysis approach, the dynamic response and damage level of the airtight protective door were further assessed numerically.

2. Validation of Numerical Model

The current research on the dynamic response of airtight protective doors heavily relies on plate theory. In the case of airtight protective doors subjected to the impact of tornado-induced missiles, the penetration of the steel plate becomes a critical issue. In the study of metal penetration, a series of experimental and numerical simulation studies have been conducted [25,26,27]. In this section, the impact tests of a steel plate subjected to tornado-induced missile impact conducted by Sakamoto [15] were simulated using the commercial finite element program LS-DYNA to verify the accuracy of the numerical simulation method and the material model of steel under wind-borne missile impact.

Figure 1 and Figure 2 display the dimensions of the test steel plate, the bolt positions, and images of the assembled equipment. The material of the test plate was SS400, and the dimensions of the plate were 2140 mm wide, 1400 mm deep, and 9 mm thick. In the impact tests, a drop weight was employed to simulate the tornado-induced missile. The drop weight possesses the same impact energy as a tornado-induced missile composed of a steel pipe with the dimensions of 4.2 m length, 0.3 m width, and 0.2 m depth, featuring an impact velocity of 51 m/s and a mass of 135 kg. The mass part was a rigid body, and BCR295 was utilized as the material for the pipe part. The total mass of the drop weight amounted to 1114.3 kg. The actual equipment and drop weight utilized in the experiment are depicted in Figure 2.

Table 1. Summary of the drop weight impact tests.

Test	Falling Height (m)	Impact Velocity (m/s)	Impact Energy (KJ)	Plate Damage
SS-1	17.0	18.3	186	The pipe penetrated the plate
SS-2	12.5	15.7	137	The pipe penetrated the plate
SS-3	9.5	13.7	104	Local large deformation
SS-4	11.0	14.7	120	Local large deformation

provides a summary of the test number, falling height, impact velocity, impact energy, and observed local damage.

In the finite element model, the test plate, pipe, and connecting part were modeled with 10 × 10 mm shell elements. The mass component and load cells were represented using solid elements, with the maximum size of the solid elements being 20 mm. In the analytical models, the test plate, supporting frames A and B, and two load cells were integrated into a unified structure instead of being individually assembled with bolts and stoppers. The supporting frames were modeled with shell elements. The load cells were modeled with solid and beam elements. The models were fixed completely at the bottom of the load cells. The finite model is shown in Figure 3. MAT_24 (piecewise linear plasticity) is a commonly used elastic–plastic material model, and it is capable of characterizing the strain rate effect of materials using stress–strain curves or a function reflecting the influence of strain rate. The MAT_24 model was employed to simulate both the pipe and the test plate. The primary emphasis is on the deformation of the steel plate. Therefore, the mass part was modeled by the rigid material model. The supporting frames and the four load cells were modeled by the elastic material model. The Cowper–Symonds model was used to consider the strain rate effect of the steel. The material parameters of steel are presented in

Table 2. Parameters of steel material.

Material	Density (kg/m3)	Yield Stress (MPa)	Tensile Stress (MPa)	Poisson’s Ratio	Elastic Modulus (GPa)	Ultimate Uniform Elongation	Strain Rate Parameters
							C	P
BCR295	7860	400.2	436.7	0.3	214.6	0.0770	1458	4
SS400	7860	322.3	474.4	0.3	209.7	0.1624	391	4

.

As shown in Figure 4, the perforation of the test plate occurred in the simulation and experiment results of both SS-1 and SS-2. Moreover, the test steel plate experienced significant deformation in the impact area without penetration in both the results of the SS-3 and SS-4 tests. Consequently, the predicted permanent deformations of the steel plate consistently matched the experimental observations. Figure 5 shows the impact force curves measured by the reaction force of the simulations and experiments. It was noted that the reaction force curves in the simulation results by Sakamoto exhibited higher frequency vibrations than those in the experiments. This could be attributed to the fixed boundary condition between the test plate and the supporting frame assumed in their model rather than the real situation in the experiments. Furthermore, the simulation results in this study demonstrated much better alignment with the experimental results than the analytical results of Sakamoto. The displacement curves of simulations and experiments are shown in Figure 6. In SS-1 and SS-2, the penetration of the test plate occurred in the impact area. It was observed that the simulation results were close to the experimental results. Moreover, the displacement curves in this study agreed better with the experimental results compared with the simulation results of Sakamoto.

Table 3. Comparison of results from simulations and tests.

Test	Maximum Reaction Force (KN)		Maximum Deformation (mm)		Impact Time (ms)
	Experiment	Analysis (Error%)	Experiment	Analysis (Error%)	Experiment	Analysis (Error%)
SS-1	2714	2645 (2.5%)	163	168 (3.1%)	15.6	14.7 (5.8%)
SS-2	2258	2447 (8.4%)	161	158 (1.9%)	19.6	19.4 (1.0%)
SS-3	2011	1917 (4.7%)	168	142 (15.5%)	25.2	23.8 (5.6%)
SS-4	2027	2220 (9.5%)	172	150 (11.6%)	25.1	23.3 (7.2%)

compares the maximum reaction force, maximum displacement, and impact time of simulation with the experimental data. The maximum error of peak impact force, maximum displacement, and impact duration were 9.5%, 15.5%, and 7.2%, respectively. Based on these discussions, the reliability of the modeling techniques, material model, and failure criterion was confirmed. The difference between the airtight protective door and the tested plate may introduce uncertainty in fully guaranteeing the validation of the airtight protective door. However, both of them belong to the category of low-velocity impact problems. Maintaining consistency in mesh size and constitutive parameters during the numerical simulation process ensures that the accuracy meets the requirements of airtight protective door engineering.

3. Performance Study on Airtight Protective Doors

3.1. Safety Performance Assessment Method

For the performance assessment of airtight protective doors subjected to tornado and wind-borne missile impact, three aspects should be considered: airtightness, global and local deformation, and the bearing capacity of airtight protective doors against tornado-induced missile impact. In this study, the global deformation of airtight protective doors was assessed through the rotational deformation at the support. According to UFC 3-340-02 [28], the airtight protective door is permitted to deform with a rotational deformation of 2° at the support and can be repairable after impact. The deformation of the airtight protective door under impact load is illustrated in Figure 7. The support rotation angle is determined as follows:

$$\tan \left({\theta }_{\max }\right)=2w_{\max }/\left(B-L\right)$$

(1)

where ${\theta }_{\max }$ is the maximum support rotations deformation, w_max is the maximum displacement of the steel plate at the stiffener, B is the span of the airtight protective door, and L is the span of the airtight protective door keel beam. Due to the influence of the skeleton beam, the overall displacement and corner of the steel plate will be reduced.

The local response to the airtight protective door was assessed using the damage state, which included local large deformation, outer door panel penetration, and inner door panel penetration. The airtightness of the airtight protective door should be considered from two aspects, i.e., the penetration of the inner door panel and the support rotations deformation. When the support rotations deformation exceeds 2° or the inner door panel is penetrated, it is assumed that the airtightness of the airtight protection door cannot meet the requirements.

In this section, the numerical simulation analysis of an airtight protective door in nuclear power plants subjected to tornado and wind-borne missile impact was performed using LS-DYNA. The airtight protective door was 1080 mm wide, 2160 mm deep, and 180 mm thick, in which the cover plate had a thickness of 10 mm. The airtight protective door consisted of three parts: outer and inner door panels, a door keel, and a door core. The door keel consisted of six transverse beams and four vertical beams. The keel beams were welded by the square tubes with a section with the dimensions of 160 × 80 × 5 mm. The framework area was filled with an expanded perlite door core. The airtight protective door was clamped on the metal doorframe with two heavy-duty hinges on the left side and three sets of compression buckles on the right side. The material of the door panel and door keel was Q235B steel. The structural layout of the airtight protective door is shown in Figure 8.

In an area with a nuclear power plant site, the Fujita F4 tornado may occur, with a maximum wind speed of 116 m/s, a rotation radius of 138 m, and a maximum atmospheric pressure of 10.1 kPa. In this scenario, the structural design for tornado resistance should consider various combinations of wind pressure loads and missile impacts [29]. Therefore, the load combination type considered both the tornado wind pressure and impact load together. The wind pressure load is given as follows [30]:

$$W_w=K{W}_0$$

(2)

where K = 0.7 is the shape coefficient; the wind reference pressure is given by the equation of $W_0=k\rho v^2/2$, k = 1.22 is the air density correction factor, ρ = 1.226 kg/m³ is the air density, and v is the velocity of the tornado.

Regulatory Guide 1.76 specifies three types of tornado missiles, including the Schedule 40 pipe, automobile, and solid steel sphere to be used for the design of the exterior structure [31]. The Schedule 40 pipe was used as a penetrating missile, and the automobile was used as a massive, high-kinetic energy missile. The solid steel sphere could also pass through the openings in the protective barriers. The primary focus among these missiles is the Schedule 40 pipe due to its higher likelihood of penetrating the door panel. The impact velocity of the missiles was determined based on the maximum wind speed of the tornado. Figure 9 shows the schematic diagram of the Schedule 40 pipe. The mass of the Schedule 40 steel pipe was 130 kg. With a maximum wind speed of 116 m/s for the F4 tornado and assuming the plant is located in region I, the impact velocity of the Schedule 40 pipe, according to Regulatory Guide 1.76, is 41 m/s.

3.2. Finite Element Model of the Airtight Protective Door

In the numerical model, shell elements were employed for the door panel and door keel. Eight-node solid elements were used to model the door core and the pipe. The maximum size of the elements for the door model was 10 mm, and the element size of the pipe did not exceed 23 mm. The FE model of the airtight protective door comprised 39,058 shell elements, 15,472 solid elements, and 43,487 nodes. The pipe was modeled with 8000 solid elements and 16,080 nodes. The FE model of the airtight protective door is shown in Figure 10.

The MAT_24 (piecewise linear plasticity) model was used to model the door panel and door keel. The properties of Q235 steel were obtained from the quasi-static and dynamic tensile tests of Q235 steel by Chen [32]. In this case, the effective plastic strain was used as the failure criterion for Q235 steel, and elements were deleted once the damage parameter reached a value of 0.1. The strain-rate parameters of steel follow the Cowper–Symonds formulation. In this study, the parameters (C = 305.8 and P = 2.7515) were obtained by fitting the strain–stress curve of Q235 steel with different strain rates. The MAT_03 (PLASTIC_KINEMATIC) steel model was used for the Schedule 40 pipe missile, with a yield strength of 413 MPa. The other parameters of the Schedule 40 pipe are presented in

Table 4. Material parameters of the Schedule 40 pipe.

Density (kg/m3)	Elastic Modulus (MPa)	Poisson’s Ratio	Tangent Modulus (MPa)	Yield Strength (MPa)
7850	2.06 × 105	0.32	2.0 × 103	413

. The SOIL_AND_FOAM material model was used to model the expanded perlite of the door core. Stevens et al. [33] assumed that a relationship exists between the pressure and strain of the expanded perlite, as shown in Figure 11. Based on the verified model, the failure criterion was added to the expanded perlite material.

Table 5. Material parameters of perlite.

Density (kg/m3)	Shear Modulus (Pa)	Yield Constant (Pa2)	Pressure Cutoff (Pa)
99.56	2.6 × 105	3.59 × 107	−1304

presents the density, shear modulus, yield modulus, and pressure cutoff of the expanded perlite.

In the numerical model of the airtight protective door, the translational degrees of freedom in the x, y, and z directions and rotational degrees of freedom in the x and y directions of the two heavy-duty hinges on the left side were constrained. Furthermore, the translational degrees of freedom in the y direction of the three sets of compression buckles on the right side were constrained. The keyword named *CONTACT_AUTOMATIC_SURFACE_TO_ SURFACE was used to simulate the contact between the Schedule 40 pipe and the airtight protective door. The interaction between the door core and the pipe was modeled by the keyword *CONTACT_ERODING_SURFACE_TO_SURFACE.

3.3. Safety Performance Assessment

3.3.1. Results of Airtight Protective Door Subjected to Tornado Wind Pressure

Figure 12 illustrates the displacement of the airtight protective door subjected to a tornado pressure load. It was observed that the maximum displacement of the airtight protective door was 0.044 mm, which occurred at the center of the outer door panel and the door core. The stress on the airtight protective door subjected to tornado wind pressure load is shown in Figure 13. No stress concentration was observed on the airtight protective door under the wind pressure load. The maximum stress appeared in the element near the hinge, which was 8.2 MPa. Thus, when the airtight protective door was subjected to the tornado pressure load, it was in the elastic stage. Based on the simulation results, it was inferred that the tornado wind pressure load had little effect on the airtight protective door and did not affect the normal use and resistance of the airtight protective door.

3.3.2. Airtight Protective Doors Subjected to Tornado Pressure and Wind-Borne Missile Impact

This section entails the numerical simulation of the airtight protective door under tornado pressure load and the impact of a Schedule 40 pipe. Subsequently, the performance of the airtight protective door was assessed. The effective plastic strain contours and damage on the door panels, door keel, and door core after impact were plotted in Figure 14. It was observed that the penetration occurred in the impact area of the outer door panel and door core. The plastic zone of the door keel predominantly existed at the impact and hinge positions, with a maximum effective plastic strain value of 0.11. Consequently, no fracture damage occurred at the door keel post-impact. The effective plastic strain of the inner door panel was concentrated in the impact area, with a maximum value of 0.09, significantly below the failure strain limit. Thus, the inner door panel had a certain degree of safety. These observations suggested that the tornado missiles could not penetrate the airtight protective door, thereby ensuring the safety of indoor personnel and equipment.

Figure 15 shows the energy histories of the airtight protective door and the Schedule 40 pipe. The kinetic and internal energies, the eroded energy activated by the removal of the failed elements, and the hourglass energy are plotted in this figure. It was observed that the energy consumption of the system mainly depended on the deformation of the door panel, door keel, and Schedule 40 pipe. Additionally, the expanded perlite comprising the door core made a negligible contribution to the energy consumption of the airtight protective door. The initial energy in the system is the kinetic energy of the Schedule 40 pipe that was calculated using Equation (3), where m = 130 kg is the mass and v = 42 m/s is the initial velocity of the Schedule 40 pipe. The simulation values of energy at time t = 20 ms are shown in Figure 15 and presented in

Table 6. Summary of energies.

	Energy (KJ)		Energy (KJ)		Energy (KJ)
$I{E}_{pipe,i}$	114.66	$I{E}_{frame}$	31.38	$E{E}_{KE}$	0.93
$I{E}_{plate,in}$	7.82	$K{E}_{frame}$	0.91	$E{E}_{IE}$	11.69
$K{E}_{plate,in}$	0.72	$I{E}_{core}$	0.65	$E_{HG}$	0.66
$I{E}_{plate,out}$	35.55	$K{E}_{core}$	0.01	$K{E}_{pipe,f}$	0.93
$K{E}_{plate,out}$	0.83	$I{E}_{pipe}$	22.39	$E_t$	113.73

.

$$K{E}_{pipe,i}=\frac{1}{2}m{v}^2$$

(3)

$$\begin{array}{l}K{E}_{pipe,i}=I{E}_{plate,in}+K{E}_{plate,in}+I{E}_{plate,out}+K{E}_{plate,out}+I{E}_{pipe}+I{E}_{frame}+\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}K{E}_{frame}+I{E}_{core}+K{E}_{core}+E{E}_{KE}+E{E}_{IE}+E_{HG}+K{E}_{pipe,f}=E_t\end{array}$$

(4)

where $I{E}_{plate,in}$ and $K{E}_{plate,in}$, $I{E}_{plate,out}$ and $K{E}_{plate,out}$, $I{E}_{frame}$ and $K{E}_{frame}$, and $I{E}_{core}$ are the internal and kinetic energies of the inner door panel, outer door panel, door keel, and door core, respectively. $K{E}_{\mathit{pipe}}$ is the internal energy of the pipe, EE_IE and EE_KE are the eroded internal and kinetic energy, respectively, EE_HG is the hourglass energy of the system, $K{E}_{pipe,f}$ is the residual kinetic energy of the pipe, and E_t is the total residual energy of the system. E_t is calculated using Equation (4).

In accordance with the law of conservation of energy, the total energy should be equal to the initial kinetic energy of the pipe. Inferred from the results in Table 6, the total residual energy of the system is very close to the initial kinetic energy of the Schedule 40 pipe, indicating that the energy of the system was conserved during the impact process.

The eroded energy of the airtight protective door accounted for 11% of the total energy, and the proportion of the internal energy of the airtight protective door was as high as 66%. It indicated that the airtight protective door mainly relied on the deformation of the door to consume energy. Hourglass energy served as an effective indicator for verifying the accuracy of the numerical simulation. According to the results presented in Table 6, the ratio of the hourglass energy to the total energy was about 0.2%, which implied that the hourglass energy of the simulation model was very well controlled. This observation showed that the numerical simulation results were reliable.

Figure 16 shows the impact force and pipe velocity histories of the simulation results. Two distinct triangular pulses were observed in the impact force history. In the first triangular pulse, two force peaks were observed. The initial collision of the pipe with the outer door resulted in the appearance of the first peak in the force, which exhibited a brief, rapid decay. This occurred because the deformation rate of the door panel exceeded the velocity of the pipe, leading to the brief separation of the pipe and the outer panel. Additionally, under the influence of inertia, the pipe collided with the outer door panel once more, generating the second peak of 1763 KN. Moreover, during the unloading phase, perforation occurred in the outer door panel, and the eroded elements moved along with the pipe until the two were separated. The velocity of the pipe exhibited a rapid drop during the first triangular pulse. This happened because the kinetic energy of the pipe was rapidly consumed by the deformation of the airtight protective door. The second triangular pulse represented the contact force between the pipe and the inner door panel. The pipe penetrated the outer panel and door core before hitting the inner panel. Simultaneously, the kinetic energy of the pipe was transferred to the deformation energy of the airtight protective door. Consequently, the velocity of the pipe was reduced to zero, and it moved in the opposite direction.

Figure 17 shows the deformation contours on the airtight protective door after impact at time t = 20 ms. Additionally, the evolution of door panel displacement is shown in Figure 18. It is observed that the response of the door is mainly a local response, near the point of impact, and the overall response is relatively small. From Figure 18, a slight shift in the top and bottom of the door panel was observed. This is because in the numerical simulation process, only the behavior of the hinge is simulated, and the effect of the contact between the door and the door frame is ignored. The boundary effect of the airtight protective door will be discussed in detail later. The maximum deflection at the stiffened position w_max is 9.7 mm, and ${\theta }_{\max }=1.1$ is obtained from the Equation (1). Thus, the rotational deformations at the hinged support are within the limited criteria. Consequently, concerning overall deformation and airtightness, these results indicate that the presented door structures can meet the essential requirements for protection, ensuring the door remains in repairable and operable states after impact.

These results indicated that the tornado pressure load had little influence on the airtight protective door’s resistance, while the wind-borne missile impact played a dominant role. Perforation resulting from the impact of the Schedule 40 pipe occurred in both the outer door panel and door core. Additionally, the airtight protective door remained functional after the impact. Nevertheless, the inner panel effectively prevented pipe penetration, ensuring the safety of both equipment and personnel within the building.

3.4. Parametric Analysis

Building upon the aforementioned results and discussions, parametric studies were undertaken to investigate the impact of various door configurations (number and dimensions of the skeleton beam, panel thickness, and boundary conditions) on the structural response to tornado missile impacts. The mass of the pipe and the impact velocity employed in all simulations remained consistent with those utilized in Section 3.2. Additionally, the parameters of the airtight protective door that remained constant throughout all simulations were identical to those employed in Section 3.2. The analyzed response quantities encompassed peak displacement, permanent displacement, maximum support rotational deformation, door penetration, and hinge fracture damage.

3.4.1. Effects of the Configuration of Keel Beam

The design of an airtight protective door is significantly influenced by the number and arrangement of keel beams. Additionally, it is crucial to investigate the impact of the keel beams’ quantity and arrangement on the resistance of the airtight protective door. This section compares three types of airtight protective doors: one without a keel beam, another with 2 × 2 keel beams, and a third with 4 × 2 keel beams. Figure 19 illustrates the distribution of keel beams in the three types of airtight protective doors.

Table 7. Comparison between displacement, support rotations deformation, and damage for airtight protective doors with different arrangements of keel beams.

Keel Beam	Max Displacement of Panel (mm)				Penetration of Panel		Damage of Hinges	Rotational Deformation (Degree)	Damage of Airtightness
	Peak		Permanent		Inner	Outer
	Inner	Outer	Inner	Outer
None	61.6	146.0	21.9	127.7	None	None	Fracture	4.3	Occurs
2 × 2	38.5	65.2	30.6	-	None	Occurs	None	1.4	None
4 × 2	29.1	53.8	24.2	-	None	Occurs	None	1.1	None

presents the numerical results of the airtight protective door with different keel beam arrangements. The effective plastic strain contours and damage on the door panels, door keel, and door core with different arrangements of keel beam were plotted in Figure 20. It was observed that as the number of keel beams increased, the peak displacements of the inner and outer panels gradually decreased. Using the door without a keel beam as the benchmark, the peak displacements of the other two inner and outer door panels decreased by 37.5% and 52.8%; and 55.3% and 83.4%, respectively. Nevertheless, the permanent displacement of the other two inner door panels increased by 39.7% and 10.5%, respectively. These results indicated that the door keel had a great influence on the resistance of the airtight protective door. It was also observed that perforation did not occur in the outer panel for the door without the keel beam, while it did occur in the outer panel for the airtight protective doors with 2 × 2 and 4 × 2 keel beams. This is because the keel beam divided the door panel into small squares with four sides fixed, which changed the force transmission mode and deformation ability of the airtight protective door. The rotational deformation of the door without the keel beam reached 4.3°, exceeding the limit of 2°. Consequently, the airtightness was compromised, and the door structure failed due to the larger overall deformation. Furthermore, the door without keel beams fractured near the hinges. However, the rotational deformations of the other two airtight protective doors are 1.4° and 1.1°, respectively. Thus, it can be concluded that the existence of the door keel beam changed the force characteristics of the airtight protective door and improved its resistance against tornado and wind-borne missile impact. Therefore, the airtight protective door should be equipped with an appropriate number of keel beams.

3.4.2. Effect of the Section of Keel Beam

To investigate the impact of keel beam dimensions on the resistance of an airtight protective door, section heights of 140, 150, 160, and 170 mm; section widths of 60, 70, 80, and 90 mm; and section thicknesses of 4, 5, 6, and 8 mm, respectively, were examined. The cross-section of the keel beam is shown in Figure 21.

Figure 22 shows the effective plastic strain contours and damage on the airtight protective door with different section heights of the keel beam. The calculation results of the airtight protective door with different section heights of the keel beam subjected to tornado and pipe impact are presented in

Table 8. Comparison between displacement, support rotations deformation, and damage for airtight protective doors with different section heights of keel beams.

Height (mm)	Max Displacement of Panel (mm)				Penetration of Panel		Damage of Hinges	Rotational Deformation (Degree)	Damage of Airtightness
	Peak		Permanent		Inner	Outer
	Inner	Outer	Inner	Outer
140	31.6	49.7	25.3	-	None	Occurs	None	1.2	None
150	31.6	51.5	24.0	-	None	Occurs	None	1.1	None
160	29.1	53.8	24.2	-	None	Occurs	None	1.1	None
170	29.2	53.3	23.0	-	None	Occurs	None	1.1	None

. It was observed that the results of the displacement, support rotations deformation, airtightness, and damage of the airtight protective door with different section heights of keel beams were close. This suggests that altering the section height of keel beams has minimal impact on impact resistance. Therefore, in designing an airtight protective door, the height of the keel beam can be reduced to enhance cost-effectiveness.

Figure 23 shows the effective plastic strain contours and damage on the airtight protective door with different section widths of the keel beam. As presented in

Table 9. Comparison between displacement, support rotations deformation, and damage for airtight protective doors with different section widths of keel beams.

Width (mm)	Max Displacement of Panel (mm)				Penetration of Panel		Damage of Hinges	Rotational Deformation (Degree)	Damage of Airtightness
	Peak		Permanent		Inner	Outer
	Inner	Outer	Inner	Outer
60	31.4	54.4	25.4	-	None	Occurs	None	1.0	None
70	31.1	53.1	26.2	-	None	Occurs	None	1.0	None
80	29.1	53.8	24.2	-	None	Occurs	None	1.1	None
90	31.7	54.8	20.8	-	None	Occurs	None	1.2	None

, the width of the keel beam has little effect on the deformation and damage of the airtight protective door. The rotation displacement increased with the increase in section width, and both were within 2°. Furthermore, it was observed that penetration did not occur at the inner door panel; thus, the airtightness of the airtight protective door was not destroyed. Based on these results, it was inferred that the width of the keel beam had little effect on the resistance of the airtight protective door. Thus, in the design, the variation in the width of the skeleton beam can be ignored, and only the local stability of keel beams is considered.

Figure 24 shows the effective plastic strain contours and damage on the airtight protective door with different section thicknesses of the keel beam. In

Table 10. Comparison between deformation, support rotations deformation, and damage for airtight protective doors with different thicknesses of keel beams.

Thickness (mm)	Max Displacement of Panel (mm)				Penetration of Panel		Damage of Hinges	Rotational Deformation (Degree)	Damage of Airtightness
	Peak		Permanent		Inner	Outer
	Inner	Outer	Inner	Outer
4	32.0	73.4	25.4	63.6	None	Occurs	Fracture	1.5	None
5	29.1	53.8	24.2	-	None	Occurs	None	1.1	None
6	35.6	55.6	28.9	-	None	Occurs	None	0.8	None
8	38.8	54.5	33.8	-	Fracture	Occurs	None	0.7	Occurs

, the results of the airtight protective door with different thicknesses of keel beam when subjected to tornado and missile impact are compared. With the increase in the thickness of the keel beam, the maximum displacements of the four inner door panels were 32.0, 29.1, 35.6, and 38.8 mm, respectively, thereby indicating that the local deformation of the inner door panel increased proportionally with the thickness of the keel beam. With the thicknesses of 4, 5, 6, and 8 mm, the maximum displacements of the outer panel were 73.4, 53.8, 55.6, and 54.5 mm. It was observed that, when the thickness of the keel beam was 4 mm, the displacement was much larger than the other three door panels. This was because the thickness of the keel beam changed the failure mode of the airtight protective door when subjected to missile impact. The perforation of the inner panel occurred in the thickness of 8 mm; however, it did not occur in the other three airtight protective doors. It was inferred that, as the thickness of the keel beam increased, the airtight protective door became more susceptible to penetration. There are two reasons for this phenomenon. The increase in the thickness of the keel beam enhances the stiffness of the door and reduces the deformation; thus, most of the energy was consumed by the deformation of the door panel. Furthermore, the thicker keel beam reinforces the boundary condition of the small square panel, thereby causing the door panel to be more susceptible to penetration. As the thickness of the keel beam increases, the overall deformation of the airtight protective door increases gradually along with the rotation deformation; however, all were within 2°.

Based on these results, the thickness of the keel beams significantly influences the resistance of the airtight protective door. A thicker keel beam increases the likelihood of partial penetration in the airtight protective door panel. Nevertheless, with a decrease in the thickness of the keel beam, the overall deformation of the airtight protective door increases, and the hinge becomes more susceptible to failure. Therefore, under the condition of ensuring the overall stiffness of the airtight protective door, the thickness of the keel beam should be appropriately reduced to minimize the possibility of penetration.

3.4.3. Effect of the Thickness of Door Panel

To study the effect of different thicknesses of door panels, four airtight protective doors with door panel thicknesses of 6, 8, 10, and 12 mm are considered herein.

Table 11. Comparison between displacement, support rotations deformation, and damage for airtight protective doors with different thicknesses of the door panel.

Thickness of Panel (mm)	Max Displacement of Panel (mm)				Penetration of Panel		Damage of Hinges	Rotational Deformation (Degree)	Damage of Airtightness
	Peak		Permanent		Inner	Outer
	Inner	Outer	Inner	Outer
6	56.4	56.8	-	-	Occurs	Occurs	None	1.0	Occurs
8	55.3	52.9	-	-	Occurs	Occurs	None	1.2	Occurs
10	29.1	53.8	24.2	-	None	Occurs	None	1.1	None
12	24.5	55.7	16.9	45.5	None	None	None	1.1	None

shows the results of the airtight protective door with different thicknesses of door panels subjected to tornado and missile impact. Effective plastic strain contours and damage on the airtight protective door with different thicknesses of the door panel are shown in Figure 25. It is evident that, as the door panel thickness increases, the maximum displacements of the inner door are 56.4, 55.3, 29.1, and 24.5 mm, respectively. As the thickness of the door panel increases, the maximum displacement and residual displacement of the inner door panel decrease gradually. Moreover, with the increase in the door panel thickness, the maximum displacements of the outer panels were very close to each other. From the results of the penetration for the panel, it is inferred that the smaller the thickness of the door panel, the more likely it is for penetration to occur at the door panel, and the airtightness is more likely to be destroyed. As the thickness of the door panel increases, the rotation angle changes slightly, and they all are within 2°. Hence, the design thickness of the door panel should be maintained within a specific range.

3.4.4. Effect of Boundary Condition

To study the influence of boundary conditions on the dynamic response of the airtight protective door subjected to the tornado missile, five airtight protective doors with different boundary conditions are considered in this section. Figure 26 shows the effective plastic strain contours and damage on the airtight protective door with different boundary conditions. The comparison of the results of displacement, support rotations deformation, airtightness of the door, and damage to the airtight protective door with different boundary conditions are presented in

Table 12. Comparison between displacement, support rotations deformation, and damage for airtight protective doors with different boundary conditions.

Boundary Condition	Max Displacement of Panel (mm)				Penetration of Panel		Damage of Hinges	Rotational Deformation (Degree)	Damage of Airtightness
	Peak		Permanent
	Inner	Outer	Inner	Outer	Inner	Outer
Four sides fixed	29.7	53.9	24.9	-	None	Occurs	None	0.9	None
Four edges simply	30.2	53.1	26.3	-	None	Occurs	None	1.0	None
Three edges simply	30.0	52.9	26.6	-	None	Occurs	None	1.1	None
Two edges simple	31.3	52.9	25.7	-	None	Occurs	None	1.2	None
Two hinges	29.1	53.8	24.2	-	None	Occurs	None	1.1	None

. It is observed that the results of the displacement and penetration of the door panel do not change with different boundary conditions. Thus, the boundary condition had little effect on the local response of the airtight protective door. Under the boundary condition of four sides fixed, four sides simply supported, three sides simply supported, and two opposite sides simply supported, the rotational deformations of the airtight protective door were 0.9°, 1.0°, 1.1°, and 1.2°, respectively. The variation in boundary conditions had a discernible impact on rotational deformation, affecting the overall deformation of the airtight protective door. The observations suggest that, as the number of constraints increases, the overall displacement of the airtight protection door decreases.

4. Summary and Conclusions

In this study, the performance of airtight protective doors of nuclear power plants subjected to F4 tornado and wind-borne missile impact has been investigated by using LS-DYNA. Four free drop impact steel panel tests were simulated to validate the accuracy and reliability of the numerical method for the impact problem. Subsequently, the safety performance of the airtight protective door subjected to tornado and wind-borne missile impact was evaluated. Furthermore, the effects of door structure parameters on the dynamic response of the airtight protective door were investigated. The main findings are summarized as follows:

(1) Under the influence of F4 tornado and wind-borne missile impact, the airtight protective door effectively prevented the perforation caused by the tornado missile, and it met the specified criteria for both overall deformation and airtightness. The primary mechanism for the airtight protective door to dissipate the impact’s kinetic energy was through the deformation of the door panel and keel, with the expanded perlite door core contributing minimal energy consumption.

(2) The structural layout had a substantial impact on the resistance of the airtight protective door. The resistance of the airtight protective door increased in proportion to the density of the keel beam distribution. The resistance of the airtight protective door was minimally affected by the section height and width of the keel beams. Nevertheless, enhancing the section thickness of the keel beam significantly enhances the resistance of the airtight protective door.

(3) The door panel with thinner keel beams was less prone to breaking through; nevertheless, the airtightness of the airtight protective door was more susceptible to failure. The resistance of the airtight protective door grew proportionally with the thickness of the door panel, and alterations in the boundary conditions minimally affected the resistance of the airtight protective door.