The missile-target interaction method is used to perform simulations of the impact of a commercial B767 aircraft on a shield building made of steel-concrete-steel sandwich panels to study impact damage characteristics. Refined finite element models of a shield building and two large commercial B767 aircraft are developed. The aircraft impact force is given and assessed with the Riera function to verify the B767 aircraft model, and a simulation analysis of tests is performed to verify the concrete model. The peak impact forces of the fuselage, engine, wing, and entire aircraft are approximately linearly proportional to the square of each impact velocity. The shield building subjected to the aircraft impact exhibits no perforation, and the damage range of the shield building expands with increasing impact velocity. The influences of impact velocity, aircraft mass, impact angle, and tie bar diameter on the deformation of the shield building are significant. The thickness of the steel plate plays an important part in the deformation of the shield building, whereas the compressive strength of concrete and the water in circular tank have only a slight effect on the deformation of the shield building.
A nuclear power plant (NPP) contains a significant amount of radioactive material; once radiation leaks occur, the consequences are extremely serious. Historically, the Three-Mile Island accident, the Chernobyl accident, and the accident in Fukushima have resulted in serious disasters. An aircraft crashing into a NPP is considered to be extremely hazardous and could cause extensive damage to the NPP. In the 1960s, the U.S. Nuclear Regulatory Commission requested that the safety of the Three-Mile Island NPP station against accidental aircraft impact be evaluated [
In the 1960s, Riera [
Experimental studies were performed at University Karlsruhe to study the load-time curves induced by a soft missile with a mass and stiffness distribution along its axis similar to those of a commercial aircraft (neglecting the wing geometry and turbines) impacting a rigid target. Load-time curves under different conditions were obtained by changing the mass of the material in the tank, the impact velocity, and the impact angle [
Numerical simulations can also be used to study NPP containment subjected to aircraft impacts. Rebora et al. [
NPP safety assessment and design against large commercial aircraft crashes have attracted increasing attention. The damage characteristics of nuclear containment against a large commercial aircraft crash are different from those of a small aircraft crash; studies on nuclear containment against a large commercial aircraft crash must be conducted. As seen from the above research methods, the impact force of aircraft normally impacting the rigid wall can be proposed using simplified theoretical models. Experimental research is available for the impact effect of full-scale or scaled aircraft; these results can be compared with numerical simulation results to enhance the credibility of the numerical simulation of full-scale aircraft impacts. Numerical simulations can be divided into three categories: (1) perform simulations of a scaled aircraft impact test to conduct comparative analyses of numerical simulation results with test results to validate the numerical simulation, thus providing credible support for full-scale aircraft impact analyses; (2) load the impact force time-history curve by the Riera model or the aircraft normally impacting the rigid wall on a containment to study the impact damage effects on structure, and (3) develop numerical models of aircraft and nuclear containment to simulate the impact interaction process. The second numerical simulation has its own restriction; that is, it does not consider the interaction between the aircraft and structure. The load area is difficult to determine, and the damage effects of the impact area are not sufficiently simple to assess, but the third numerical simulation can overcome the aforementioned restriction. Thus, the third numerical simulation is employed to study the impact damage characteristics of a shield building subjected to a large commercial aircraft impact in this paper. First, the refined models of a commercial aircraft and shield building are developed; comparative verification of the total impact force is obtained from an aircraft normally impacting the rigid wall versus from the Riera function. The constitutive models are validated by simulating scaled tests in the existing literature, and the impact force time-history curves of each part of the aircraft are proposed. Finally, the impact responses of the shield building in different impact scenarios are discussed.
In general, the selection of commercial aircraft requires accurate representation, including aircraft takeoff weight, aircraft flight hours per year, and aircraft ownership in one region. The Boeing 767-200ER is widely used worldwide and is selected in this impact study as a typical large commercial aircraft. Many related studies have been conducted using this aircraft, and substantial data are available in the literature. One of the two aircraft that impacted the World Trade Center on September 11, 2001, was a Boeing 767-200ER aircraft. The Boeing 767-200ER can accommodate 224 passengers; the maximum takeoff weight is approximately 179 tons. The total length is 48.5 m, the wingspan is 47.6 m, and the fuselage diameter is 5 m, as shown in Figure
Boeing 767-200ER size.
In this paper, the Boeing 767-200ER is simplified as follows to develop a finite element model (FEM): (a) the geometry is matched to the actual aircraft; (b) the main structures are considered, including aircraft skin, wing ribs, empennage ribs, fuselage frames and strings, and floor beams; the sizes of structures are selected according to actual sizes; and (c) the mass distribution is matched to the actual aircraft, as shown in Table
Mass distribution of a Boeing 767-200ER.
Type | Part | Fuselage | Wing | Engine | Empennage | Fuel | Cargo | Total |
---|---|---|---|---|---|---|---|---|
Aircraft A | Mass (ton) | 53.97 | 16.78 | 8.75 | 2.7 | 31.3 | — | 113.5 |
Aircraft B | Mass (ton) | 53.97 | 16.78 | 8.75 | 2.7 | 73.36 | 23.63 | 179.19 |
Liu et al. [
Boeing 767-200ER finite element meshing.
Currently, international nuclear power construction has entered the third-generation development period. The containment of NPP is composed of an inner steel containment and outer shield building. The main function of the shield building is to keep the internal steel containment and reactor cooling system from damage by external events. A rational simplified model of the shield building is developed by referring to Westinghouse Electric Corporation [
Shield building size.
Finite element meshing of the shield building.
The fuselage, wing, and empennage of a Boeing 767-200ER are made of aluminium alloy, and the engine is made of steel. The Johnson-Cook model is used for the impact simulation of shell elements. The equation of the Johnson-Cook model [
Johnson and Cook [
MAT015 parameters.
Parameter | | | | | | | | | | |
---|---|---|---|---|---|---|---|---|---|---|
Aluminium alloy | 369 | 684 | 0.0083 | 1.7 | 0.73 | 0.13 | 0.13 | −1.5 | 0.011 | 0 |
Steel | 350 | 275 | 0.022 | 1.0 | 0.36 | 0.05 | 3.44 | −2.12 | 0.002 | 0.61 |
MAT03 parameters.
Parameter | Density (ton/mm3) | Elastic modulus (MPa) | Shear modulus (MPa) | Poisson’s ratio | Tangent modulus (MPa) | | | | FS |
---|---|---|---|---|---|---|---|---|---|
Aluminium alloy | 2.8 × 10−9 | 7.19 × 104 | 2.78 × 104 | 0.33 | 690 | 490 | 6500 | 4 | 0.3 |
Steel | 7.8 × 10−9 | 2.0 × 105 | 7.7 × 104 | 0.3 | 1050 | 400 | 40 | 5 | 0.3 |
Aircraft A impacting the rigid wall target (
Comparison of the total impact force of aircraft A (
Riera [
As shown in (
A comparison of the total impact force calculated by the Riera method with the numerical simulation result is shown in Figure
Comparison of the total impulse of aircraft A (
Details of the experimental study of 1/7.5-scale models of aircraft and different thicknesses of SCS panels were provided in a previous study [
The impact scenarios of the full SCS panel subjected to a scaled aircraft model are simulated to verify the material model of concrete because the cylindrical wall of the shield building is a SCS structure in this paper. The full SCS panels are FSC-60 and FSC-80 in the aforementioned impact experiments.
LS-DYNA is widely applied in studying structural responses to shock and impact loads among the readily available FE software [
A comparison of the FEM analysis results with both the experimental and analytical results (DEM) [
Comparison of the test and numerical results.
Case | Impact velocity (m/s) | Results | Residual velocity of engine (m/s) | Velocity of debris of back face (m/s) | Size of crater (mm) | |
---|---|---|---|---|---|---|
Front face | Back face | |||||
FSC-60 | 152 | Test [ | 22 | 58 | 340 | 550 |
DEM [ | 40 | 65 | 410 | 520 | ||
Mat072R3 | 30 | 68 | 287 | 540 | ||
Mat084 | 34 | 59 | 280 | 465 | ||
| ||||||
FSC-80 | 146 | Test [ | — | — | 450 | — |
DEM [ | — | — | 430 | — | ||
Mat072R3 | — | — | 463 | — | ||
Mat084 | — | — | 398 | — |
Velocity time-history curves of engine impacting FSC-60.
Velocity time-history curves of fuselage impacting FSC-60.
Velocity time-history curves of engine impacting FSC-80.
Velocity time-history curves of fuselage impacting FSC-80.
In the case of FSC-60, the change in the velocity of the engine until 5 ms in the FEM results is approximately the same as in the test and DEM results. The residual velocity of the engine after 8 ms is 30 m/s in Mat072R3 compared to 34 m/s in Mat084 and 22 m/s in the test after approximately 12 ms and 40 m/s in DEM after approximately 8 ms, as shown in Figure
In the case of FSC-80, the crater diameter on the front face of the panel in Mat072R3 is 463 mm, which corresponds closely with the 450 mm crater size in the test, as shown in Table
Damage results to steel plates of FSC-60.
Front face (test) [
Back face (test) [
Front face (MAT072R3)
Back face (MAT072R3)
Front face (MAT084)
Back face (MAT084)
Damage results to steel plates of FSC-80.
Front face (test) [
Back face (test) [
Front face (MAT072R3)
Back face (MAT072R3)
Front face (MAT084)
Back face (MAT084)
The comparison of the results illustrates that the results of MAT072R3 correspond better with experimental and DEM results [
Five impact velocities—100 m/s, 125 m/s, 150 m/s, 175 m/s, and 200 m/s—are selected to simulate an entire aircraft impacting a rigid wall to investigate the influence of the Boeing 767-200ER impact velocity on the impact force. The impact forces of the fuselage, engine, and wing extracted at different aircraft impact velocities are compared in Figures
Comparison of impact force of fuselage of aircraft A.
Comparison of impact force of two engines of aircraft A.
Comparison of impact force of wing of aircraft A.
Comparison of total impact force of aircraft A.
As shown in Figure
The total impact force is the combination of the crushing force and the inertial force, which is related to the square of the velocity against the rigid target, according to (
The peak impact force ratio versus the square of the impact velocity ratio of aircraft A.
Impact velocities of 100, 125, and 150 m/s are considered to study the influences of impact velocity on the impact displacement of the shield building. The FE model of the aircraft is aircraft A, the thickness of the plate in the SCS panel of the shield building is 20 mm, the compressive strength of concrete is 46 MPa, Poisson’s ratio of concrete is 0.2, the density of concrete is 2.3 × 103 kg/m3, and the diameter of the tie bar is 20 mm. There is no perforation in the impact area of the shield building at the three impact velocities mentioned above. The displacement time-history curves of the impact center are shown in Figure
Comparison of displacement of impact center at different impact velocities of aircraft A.
Aircraft A impacts the shield building.
Side view
Bottom view
Plastic strain of concrete in the outer face of the shield building according to the impact velocity of aircraft A.
The maximum impact force peak will appear when the aircraft impacts the shield building normally; the peak impact force and damage to the shield building will be reduced if the aircraft impacts the shield building at a certain angle. Thus, the normal impact of the aircraft is typically discussed instead of the impact at other impact angles. However, the damage to the shield building subjected to aircraft impact at a certain angle must be analysed because a normal aircraft impact is rare. The four impact angles, 0°, 15°, 30°, and 45°, considered for comparative analysis with the other parameters are mentioned in Section
The relationship curves of displacement of impact center versus impact angle are shown in Figure
Comparison of displacement of impact center at different impact degrees.
There are many types of commercial aircraft used worldwide, and the masses of commercial aircraft differ from each other. Even a representative aircraft selected to impact the shield building also has a difference in mass. To study the influence of aircraft mass on impact displacement, two FE models with different masses, aircraft A and aircraft B, are developed; the mass of aircraft A is 113 tons, and the mass of aircraft B is 179 tons. Their impact velocities are both 100 m/s, the parameters of the shield building are the same as Section
The displacement time-history curves of the impact center of the shield building subjected to two aircraft are shown in Figure
Comparison of displacement of impact center in case of different aircraft.
The analyses of the aforementioned parameters are based on parameter variations with respect to aircraft. The interaction of the aircraft impacting the shield building must be investigated; the parameters of the aircraft and shield building should be considered. The parameters related to the SCS shield building are considered in this paper, including the tie bar diameter, steel plate thickness, concrete compressive strength, and water in the circular tank. The impact velocity equals 100 m/s, the aircraft model is aircraft A, the thickness of the plate in the SCS panel of the benchmark shield building is 20 mm, the compressive strength of concrete is 46 MPa, and the diameter of the tie bar is 20 mm.
The SCS structure is an effective composite structure because the tie bars are welded to the steel faceplates to form the interaction with concrete and develop the composite behaviour of the steel faceplates and concrete. Three diameters—
The comparison of impact center displacement in cases of different tie bar diameters is shown in Figure
Comparison of displacement of impact center in case of different tie bar diameter.
The influence of steel plate thickness on the impact displacement is shown in Figure
Comparison of displacement of impact center in case of different steel plate thickness.
Three concrete compressive strengths—28, 37, and 46 MPa—are considered to analyse the influence of concrete compressive strength on the ability of the SCS shield building to withstand impact. As shown in Figure
Comparison of displacement of impact center in different concrete cases.
The studies above on the shield building subjected to aircraft A or aircraft B did not consider the water in the circular tank at the top of the shield building. But the water in the circular tank of the shield building will vibrate because of impact of aircraft. When a tank containing liquid vibrates, the liquid exerts impulsive and convective hydrodynamic pressure in addition to the hydrostatic pressure; the water can be divided into two parts: the impulsive water moving synchronously along with the tank and the convective water oscillating itself and producing pressures on the walls and the base of the tank [
Comparison of displacement of impact center considering water or not.
This study developed refined FE models of a shield building and two large commercial B767-200ER aircraft with different masses. The missile-target interaction method was used to perform simulations of a commercial B767-200ER aircraft impacting an SCS shield building. A comparison of the aircraft impact force resulting from an aircraft vertically impacting the rigid wall and an assessment with the Riera function were performed to verify the B767-200ER aircraft model. Then, simulation analyses of SCS panels subjected to scaled aircraft were carried out using FE code LS-DYNA with two constitutive models of concrete to verify and select the more reasonable one. The results in terms of residual velocities, velocity time histories, and crater sizes correlated well with the test and DEM analytical results. The simulation analysis demonstrated that MAT072R3 can simulate the nonlinear response of concrete in the SCS structure in the case of large deformation and a higher strain rate.
Impact force time-history curves of the engine, fuselage, wing, and their resultant impact force time-history curves were proposed by an entire Boeing 767-200ER impacting the rigid wall at different velocities. The peak impact forces of each part and their resultant increase with increasing impact velocity. The peak impact forces of the fuselage, engine, wing, and entire aircraft were approximately linearly proportional to the square of each impact velocity.
A parametric study was performed to investigate the influences of the related parameters on the damage to the shield building subjected to a Boeing 767-200ER. The influences of impact velocity, aircraft mass, impact angle, and tie bar diameter on the deformation of the shield building were significant in the impact scenarios and parametric analyses. The peak impact displacement increased 1.9 times when the impact velocity increased from 100 to 150 m/s, decreased sharply with increased in the impact angle, and increased approximately 4 times when the tie bar diameter increased from 0.5
The authors declare that they have no conflicts of interest regarding the publication of this paper.
This study was supported by the National Science and Technology Major Project of China (Grant no. 2011ZX06002-10).