Response of Reinforced Concrete Structures 

to Aircraft Crash Impact 

Prepared for 

U.S. Nuclear Regulatory Commission 

Contract NRC−02−07−006 

Prepared by 

T. Wilt 

A. Chowdhury 

Center for Nuclear Waste Regulatory Analyses 

San Antonio, Texas 

P.A. Cox 

SouthWest Research Institute 

San Antonio, Texas 

September 2011
ii 

CONTENTS 

Section Page 

FIGURES ..................................................................................................................................... iv 

TABLES ........................................................................................................................................ iii 

EXECUTIVE SUMMARY .............................................................................................................vii 

ACKNOWLEDGMENTS .............................................................................................................. ix 

1 INTRODUCTION .................................................................................................................. 1-1 

 1.1 Background ................................................................................................................. 1-1 

 1.2 Current Need for Aircraft Crash Simulation Capabilities ............................................. 1-2 

 1.3 Objective and Scope ................................................................................................... 1-3 

 1.4 Organization of the Report .......................................................................................... 1-3 

2 MATERIAL MODELING OF CONCRETE ............................................................................ 2-1 

 2.1 LS-DYNA Concrete Damage Model ............................................................................ 2-1 

 2.2 Application of LS-DYNA Concrete Damage Model for Impact Simulations ................. 2-5 

 2.3 Refinement of LS-DYNA Concrete Damage Model Material Parameters ................... 2-9 

3 EVALUATION OF AIRCRAFT IMPACT LOADS .................................................................. 3-1 

 3.1 Introduction ................................................................................................................. 3-1 

 3.2 The Riera Method ....................................................................................................... 3-1 

 3.3 Comparison of Riera-Calculated Impact Forces With Measured Impact 

 Forces From a Full-Scale F-4 Crash Test ................................................................... 3-2 

 3.4 Evaluation of the Full-Scale F-4 Impact Test Target Response .................................. 3-7 

 3.4.1 Finite Element Modeling of the Concrete Block Target ................................... 3-7 

 3.4.2 Concrete Block Target Response Using Measured and Calculated 

 Load Histories .................................................................................................. 3-8 

4 NUMERICAL MODELING OF THE F-15E AIRCRAFT ........................................................ 4-1 

 4.1 Introduction ................................................................................................................. 4-1 

 4.2 A Smoothed Particle Hydrodynamics Model of the F-15E .......................................... 4-1 

 4.3 Materials and Parameters ........................................................................................... 4-4 

5 RIGID WALL IMPACT ANALYSIS ....................................................................................... 5-1 

 5.1 Introduction ................................................................................................................. 5-1 

 5.2 Impact Forces Using the Riera Method ....................................................................... 5-1 

 5.3 Impact Forces Using the SPH Method ........................................................................ 5-3 

 5.3.1 Mesh Sensitivity ............................................................................................... 5-6 

 5.3.2 Contact Modeling ........................................................................................... 5-12 

6 FULL-SCALE IMPACT SIMULATION .................................................................................. 6-1 

 6.1 Introduction ................................................................................................................. 6-1 

 6.2 Finite Element Modeling of a Reinforced Concrete Wall ............................................. 6-1 

 6.3 Simulation of the F-15E SPH Model Impacting a Reinforced Concrete Wall .............. 6-2 

7 SUMMARY AND CONCLUSIONS ....................................................................................... 7-1 

 7.1 Summary ..................................................................................................................... 7-1 

 7.2 Conclusions ................................................................................................................. 7-3 

8 REFERENCES ..................................................................................................................... 8-1 
iii 

FIGURES 

Figure Page 

2-1 Idealized Engine Model of GE J79 Engine Used in Finite Element Simulation of 

Full-Scale Test ............................................................................................................... 2-5 

2-2 LS-DYNA Finite Element Model of Full-Scale GE J79 Engine Simulant ........................ 2-7 

2-3 Results of LS-DYNA Simulations Showing Different Damage Models for an 

Idealized Engine Striking Reinforced Concrete Panels .................................................. 2-8 

2-4 Displacement Versus Time Comparison for Full-Scale Engine Test ............................ 2-10 

2-5 Displacement Versus Time Results for Full-Scale Panel Test ..................................... 2-10 

2-6 LS-DYNA Finite Element Results Showing Crater Depth Due to Impact of 

Engine Simulant ........................................................................................................... 2-11 

3-1 Mass Per Unit Length, μ, for the F-4 Aircraft With and Without Skids and Rockets ....... 3-2 

3-2 Measured Crush Force, Pc, for the F-4 Aircraft Including Skids and Rockets ................ 3-3 

3-3 Calculated Impact Force on a Rigid Surface Using Riera Method ................................. 3-3 

3-4 Comparison of Measured (Sugano, et al., 1993) and Calculated Impact Forces for the F4 Aircraft Including Skids and Rockets ........................................................................... 3-4 

3-5 Comparison of Measured (Sugano, et al., 1993) and Calculated Impulses for the 

F-4 Aircraft Including Skids and Rockets ....................................................................... 3-5 

3-6 Proposed Nonlinear Mass Adjustment Factor Used in Calculation of Impulse Force .... 3-5 

3-7 Comparison of Calculated Impulse Using Mass Adjustment Factor to Measured 

Impulse (Sugano, et al., 1993) for the F-4 Aircraft Including Skids and Rockets ........... 3-6 

3-8 Comparison of Calculated Impact Force Using Mass Adjustment Factor to the 

Measured Force (Sugano, et al., 1993) for the F-4 Aircraft with Skids and Rockets ..... 3-6 

3-9 Comparison of LS-DYNA Calculated Target Block Velocity to Test Data Target 

Block Velocity ................................................................................................................. 3-8 

3-10 Comparison of LS-DYNA Calculated Displacement (Back Face of Target) Time 

History to Measured Test Data ...................................................................................... 3-9 

3-11 Calculated Load-Time History of the Full-Scale F-4 Aircraft Test Using the 

Riera Method ................................................................................................................ 3-10 

3-12 Comparison of Test Data (Sugano, et al., 1993) With Simulation Results Using the Riera 

Calculated Loading ...................................................................................................... 3-10 

4-1 Finite Element Surface Model of the F-15 Aircraft ......................................................... 4-2 

4-2 Grouping of SPH Particles in 1-m [3.3-ft] Increments Along the F-15E With 

Positions Indicated for Various Parts of the Aircraft ....................................................... 4-3 

4-3 Full SPH Model of the F-15E (Top) and SPH Model with Aircraft Skin 

Removed (Bottom) ......................................................................................................... 4-5 

4-4 Fuselage and Component Mass Distribution as Compiled in 1-m [3.3-ft] 

Increments from the SPH Model .................................................................................... 4-6 

4-5 Fuel Mass Distribution as Compiled in 1-m [3.3-ft] Increments From the 

SPH Model ..................................................................................................................... 4-6 

4-6 Total Aircraft Mass Distribution as Compiled in 1-m [3.3-ft] Increments from the 

SPH Model ..................................................................................................................... 4-7 

5-1 Crush Force for the F-4 (Sugano, et al., 1993) and Crush Force for the F-4 Scaled to the 

Length of the F-15E ....................................................................................................... 5-1

5-2 Crush Force for the F-15E Scaled from the F-4 Aircraft Using Distributed Mass ........... 5-2 
iv 

FIGURES (continued) 

Figure Page 

5-3 Impact Force Computed by the Riera Method (Riera, 1968) for the F-15E 

Impacting a Rigid Surface at 112 m/s [367 ft/s] ............................................................. 5-3 

5-4 Impact Force Computed by the Riera Method (Riera, 1968) for the F-15E 

Impacting a Rigid Surface at 190 m/s [623 ft/s] ............................................................. 5-4 

5-5 Impact Force Computed by the Riera Method (Riera, 1968) for the F-15E 

Impacting a Rigid Surface at 215 m/s [705 ft/s] ............................................................. 5-4 

5-6 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

for an Impact Velocity of 112 m/s [367 ft/s] into a Rigid Surface .................................... 5-5 

5-7 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

for an Impact Velocity of 190 m/s [623 ft/s] Into a Rigid Surface ................................... 5-5 

5-8 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

for an Impact Velocity of 112 m/s [367 ft/s] Into a Rigid Surface ................................... 5-7 

5-9 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

for an Impact Velocity of 190 m/s [623 ft/s] Into a Rigid Surface ................................... 5-7 

5-10 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

for an Impact Velocity of 215 m/s [705 ft/s] Into a Rigid Surface ................................... 5-8 

5-11 Mass Distribution from the Original SPH Model Obtained by Summing the Masses 

Over 0.4-m [1.3-ft] Increments ....................................................................................... 5-9 

5-12 Mass Distribution From the Modified SPH Model Obtained by Summing the 

Masses Over 0.4-m [1.3-ft] Increments .......................................................................... 5-9 

5-13 F-15E Crush Force Computed from the F-4 Crush Force Using the Mass 

Distribution of Figure 5-12 ............................................................................................ 5-10 

5-14 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

Using LS-DYNA Version 971 for an Impact Velocity of 112 m/s [367 ft/s] ................... 5-11 

5-15 Comparison of Impact Forces Calculated by the Riera Method and the SPH Model 

Using LS-DYNA Version 971 for an Impact Velocity of 215 m/s [705 ft/s] ................... 5-11 

5-16 The Effect of SPH Model Mesh Refinement on Impact Force Calculated with 

LS-DYNA Version 971 for an Impact Velocity of 112 m/s [367 ft/s] ............................. 5-12 

5-17 Comparison of Impact Forces Calculated with LS-DYNA Versions 970 and 971 for 

an Impact Velocity of 112 m/s [367 ft/s] ....................................................................... 5-13 

5-18 Impact Simulation Showing Contact Problem that Allowed SPH Particles of the 

F-15 Model To Pass Through the Wall ........................................................................ 5-13 

6-1 Dimensions of the Reinforced Concrete Wall and Buttresses ....................................... 6-1 

6-2 Finite Element Model of the Reinforced Concrete Wall and Buttresses ......................... 6-2 

6-3 Reinforced Concrete Wall and Position of the F-15E SPH Model Just 

Before Impact ................................................................................................................. 6-3 

6-4 Response of the Wall Backside Showing Surface Damage and Contours of 

Effective Plastic Strain for the F-15E Impact at 190 m/s [623 ft] .................................... 6-4 

6-5 Front Face Wall Damage and Contours of Effective Plastic Strain After the F-15E 

Impact at 190 m/s [623 ft] ............................................................................................... 6-4 

6-6 Section Through the Wall and F-15E When First External Fuel Tank Reaches the 

Wall (Left) and When the Engines Contact the Wall (Right) at an Impact Velocity of 

190 m/s [623 ft] .............................................................................................................. 6-5 

6-7 Sequence Showing the Wall Back Surface Damage and Contours of Effective 

Plastic Strain for the F-15E Impact at 112 m/s [367 ft/s] ................................................ 6-5 
v 

FIGURES (continued) 

Figure Page 

6-8 Front Face Wall Damage and Contours of Effective Plastic Strain After the F-15E 

Impact at 112 m/s [367 ft] ............................................................................................... 6-6 

6-9 Time History of the Wall Back Surface Displacement Located at the Center for 

Impact of the F-15E at 112 m/s [367 ft] .......................................................................... 6-6 
vi 

TABLES 

Table Page 

2-1 List of Concrete Model Input Parameters ....................................................................... 2-3 

2-2 Damage Function Values ............................................................................................... 2-3 

2-3 Volumetric Strain Versus Pressure ................................................................................ 2-4 

2-4 LS-DYNA Results and Comparison with Experiments: Small-Scale (1/7.5 Scale) 

Idealized GE-J79 Engine ............................................................................................... 2-6 

2-5 LS-DYNA Results and Comparison with Experiments: Intermediate-Scale 

(1/2.5 Scale) Idealized GE-J79 Engine .......................................................................... 2-6 

2-6 LS-DYNA Results and Comparison with Experiments: Full-Scale Idealized 

GE-J79 Engine ............................................................................................................... 2-6 

4-1 F-15E Weights ............................................................................................................... 4-2 

4-2 Mass of F-15E Components in the SPH Model ............................................................. 4-5 

4-3 Metal Material Properties Used in the SPH Model ......................................................... 4-7 

4-4 Properties for Fluids Used in the SPH Model ................................................................. 4-7 

5-1 Data for the F-4 and F-15E Aircraft ................................................................................ 5-2 

5-2 Final Parameters for Aluminum and Fuel Used in the SPH Model ................................ 5-6 
vii 

EXECUTIVE SUMMARY 

In preparation for reviewing a license application for the proposed repository at Yucca Mountain, 

the U.S. Nuclear Regulatory Commission (NRC) independently analyzed the performance of 

important to safety (ITS) structures in the geologic repository operations area that were to be 

relied on to limit or prevent potential event sequences, as required in 10 CFR 63.112(e)(8). One 

area of importance was the performance evaluation of ITS surface structures when subject to 

an impact of an aircraft crash. The surface structures of the proposed repository at 

Yucca Mountain were to be constructed of reinforced concrete. Therefore, NRC directed the 

Center for Nuclear Waste Regulatory Analyses to develop the computational capability to 

predict damage to reinforced concrete structures caused by an aircraft crash impact. 

An aircraft crash impact is a short duration dynamic load that could involve very large 

deformations and damage to both the reinforced concrete structure and the aircraft itself. 

Therefore, simulation of aircrash impact is computationally challenging. Because of this, the 

selection of an appropriate concrete material model and robust finite element software that is 

specialized for this type of analysis was the first step. 

The computer code LS-DYNA was selected as the finite element code for this numerical 

analysis. LS-DYNA is a general purpose finite element code that is designed for large 

deformation, short duration dynamic (i.e., impact) analysis. LS-DYNA has several concrete 

material models built into the code (e.g., the pseudotensor model, soil/concrete model, Winfrith 

concrete model, and concrete damage model). For the analyses described in this report, the 

selected concrete damage model is essentially an improved version of the pseudotensor model. 

Each model has its specific applications and, in general, requires a different set of input 

parameters, some of which may not be easily obtainable from literature. The selection of the 

associated material parameters were partly based upon LS-DYNA recommendations. In 

addition, the parameters were correlated with experimental data from an explosion against a 

reinforced concrete wall, missiles impacting reinforced concrete panels, and a full-scale test of 

an F-4 aircraft striking a concrete block. 

The goal of the numerical simulations and the correlation with experimental results was to show 

that LS-DYNA, using the appropriate concrete constitutive model and material parameters, can 

accurately predict the structural response of reinforced concrete walls when subject to intense 

blast and impact loads up to and including failure. The good correlations with experimental data 

indicated that the selected methodology, including how the concrete material was characterized, 

was able to appropriately model the impact events and increased confidence that the selected 

modeling approach was robust. 

Two methods have been used in this report to evaluate the impact loads produced by an aircraft 

crashing into reinforced concrete buildings: the Riera method (Riera, 1968) and a finite element 

model of the aircraft. The Riera method is an analytical method of calculating impact and 

impulse forces on a structure due to an aircraft crash. This method uses the mass distribution, 

crush force, and velocity of an aircraft to compute an equivalent impact load resulting from an 

aircraft crashing into a structure. The results obtained demonstrated that the Riera total impulse 

was higher than the measured impulse, making the Riera method a conservative approach. 

The second approach studied used a finite element model of the F-15E aircraft. The F-15E 

aircraft model mesh was developed using the smooth particle hydrodynamics (SPH) approach. 

An SPH mesh can undergo very large deformations while maintaining stability. Therefore, SPH 
viii 

is an attractive option to utilize when modeling problems where large deformations and 

complete destruction is expected, and the primary mode of loading is due to mass/momentum. 

LS-DYNA simulations of the F-15E aircraft impacting rigid surfaces and reinforced concrete 

walls were performed. For impacts into rigid surfaces, the forces the LS-DYNA simulations of 

the F-15E produced were compared to those the Riera method (Riera, 1968) predicted. At low 

impact velocities {112 m/s [367 ft/s]}, the forces LS-DYNA predicted were 33 percent lower than 

the Riera forces. The difference was due to the approximate crush force used in the Riera 

calculations. At higher impact velocities {215 m/s [705 ft/s]}, the impact forces LS-DYNA 

predicted were 4 percent lower than the Riera forces, inertial forces dominate, and the 

differences in crush force becomes less significant. 

After the F-15E aircraft model rigid wall impact calculations were completed and good results 

obtained, impact analyses of the aircraft striking a reinforced concrete wall representative of a 

nuclear surface facility was conducted. For the impact analyses, two impact speeds were 

selected based on what was used for the rigid surface impact analyses 112 and 190 m/s 

[367 and 623 ft/s]. The aircraft impacted normal to the wall, with the nose directly in the center. 

At an impact speed of 112 m/s [367 ft/s], the wall was not breached by the aircraft; however, 

substantial damage was evident from eroded elements and the effective plastic strain. Some 

evidence of possible cracking was indicated by the large plastic strains at the intersection with 

the buttresses and other areas of the wall. At this point the aircraft model had disintegrated and 

transferred all energy to the wall. At an impact speed of 190 m/s [623 ft/s], the results of the 

analysis showed that the wall was breached by the aircraft. During the impact, the wall began 

to fail as tensile forces caused the rear face rebar to break and concrete elements were deleted 

due to excessive plastic strain. When the simulation was stopped at this point in time, there 

was still significant motion of the wall; therefore, it was expected that large pieces of the wall 

would break off, yielding a larger breach area. 

REFERENCE 

Riera, J.D. “On the Stress Analysis of Structures Subjected to Aircraft Crash on Building 

Structures.” Nuclear Engineering and Design. Vol. 8. pp. 415–426. 1968. 
ix 

ACKNOWLEDGMENTS 

This knowledge capture report was prepared under Contract No. NRC–02–07–006 to 

document a detailed overview of the work performed by the Center for Nuclear Waste 

Regulatory Analyses (CNWRA®) for the U.S. Nuclear Regulatory Commission (USNRC) under 

Contract No. NRC–02–02–012. The activities reported here were performed on behalf of the 

USNRC Office of Nuclear Material Safety and Safeguards, Division of High-Level Waste 

Repository Safety. The report is an independent product of CNWRA and does not necessarily 

reflect the views or regulatory position of USNRC. The authors would like to thank B. Dasgupta 

for the technical review and B. Sagar for the programmatic review. The authors also appreciate 

A. Ramos for providing word processing support and L. Mulverhill for editorial support in 

preparation of this document. 

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT 

DATA: All CNWRA-generated original data contained in this report meet the quality assurance 

requirements described in the Quality Assurance Manual. Data used in this report are primarily 

experimental observations obtained from other publicly available sources. Each data source is 

cited in this report and should be consulted for determining the level of quality for those cited 

data. The work presented in this report is documented in Scientific Notebooks 702 and 776 

(Ghosh, et al., 2008; Wilt, et al., 2009). 

ANALYSES AND CODES: The finite element analyses presented in this report were 

conducted using ANSYS LS-DYNA, Version 10.0 (ANSYS, Inc., 2005). The version of 

LS-DYNA included with this software is Mpp970 (Livermore Software Technology 

Corporation, 2003). This version of the software is suitable for parallel processing and has 

been brought under CNWRA configuration control under Technical Operating Procedure–018, 

Development and Control of Scientific and Engineering Software. To date the software has 

been used only for configuration management and for the development of analysis 

capabilities. Spreadsheet calculations were accomplished using Microsoft® Excel®

(Microsoft® Corporation, 2002). 

REFERENCES 

ANSYS, Inc. “ANSYS LS-DYNA.” Version 10.0. Canonsburg, Pennsylvania: 

ANSYS, Inc. 2005. 

Ghosh, A., J. Mathis, and P.A. Cox. “Impact Analyses of Aircraft Crashing into the Proposed 

Facilities at the Potential Repository at Yucca Mountain.” Scientific Notebook No. 702. 

San Antonio, Texas: Center for Nuclear Waste Regulatory Analyses. 2008. 

Livermore Software Technology Corporation. “LS-DYNA Keyword Users Manual.” Version 970. 

Livermore, California: Livermore Software Technology Corporation. April 2003. 

Microsoft® Corporation. “MicrosoftExcel 2002.5P3.” Redmond, Washington: 

Microsoft Corporation. 2002. 

Wilt, T., J. Mathis, and P.A. Cox. “Impact Analyses of Aircraft Crashing into Structures Using 

ANSYS/LS-DYNA Computer Code Package in 8-Node Cluster.” Scientific Notebook No. 776. 

San Antonio, Texas: Center for Nuclear Waste Regulatory Analyses. 2009. 
1-1 

1 INTRODUCTION 

This report was prepared as part of the knowledge management activities for the U.S. Nuclear 

Regulatory Commission (NRC) high-level waste repository safety program. This report 

summarizes the work performed in developing the computational capabilities to simulate aircraft 

crash into reinforced concrete structures. The report is based on existing reports developed 

during prelicensing activities (Cox, et al., 2007, 2006, 2005). In addition, the report incorporates 

some additional aircraft crash simulations using input data and an LS-DYNA aircraft model 

documented in previous reports (i.e., Cox, et al., 2007, 2006, 2005). 

1.1 Background 

The Center for Nuclear Waste Regulatory Analyses (CNWRA®) staff began the process of 

developing the computational capabilities to simulate aircraft crashing into reinforced 

concrete structures in 2005. A report by Cox, et al. (2005) documented progress made in 

selecting appropriate material damage models for reinforced concrete under impact loads. 

Additionally, the report compared experimental observations of high explosive detonation 

and impact by simulated missiles on concrete walls with the numerical simulation results. 

The analysis resulted in the selection of a concrete damage model available in the finite 

element code LS-DYNA with appropriate erosion capabilities for modeling aircraft impacting 

a concrete structure. 

The numerical simulation results were compared with published results, and the comparisons 

showed good correlation between measurements and calculated results. The good correlation 

indicated that the methodology, including how the material is characterized, was able to 

appropriately model aircraft crash events. 

A second report by Cox, et al. (2006) continued to develop the CNWRA’s computational 

capabilities, which involved (i) refinements of the concrete damage model characterization, 

(ii) structural modeling of an engine simulant representing a GE J79 aircraft engine, and 

(iii) evaluation of the Riera method (Riera, 1968) for calculating impact forces. The results of 

this study determined (i) the adequacy of the engine simulant finite element model and (ii) the 

appropriate selection of material parameters to characterize the response of reinforced concrete 

structures under impact loading. Again, correlation of numerical simulation results with 

experimental observations allowed refinements in the values of the concrete damage model 

parameters. Finally, the Riera method was used to compute impact loads on a structure by an 

aircraft crash. It was determined that the Riera method is conservative. 

The main objective of a final report by Cox, et al. (2007) was to determine the impact forces as 

a result of an F-15 aircraft striking a rigid wall. In this report, two approaches were used: 

(i) equivalent impact loads were calculated using the Riera method (Riera, 1968) and (ii) a finite 

element and a smoothed particle hydrodynamics model of the F-15 aircraft was developed. 

This report found that the overall impact force results for both methods showed reasonable 

agreement. Also, the impulse force the Riera method calculated and that produced from the 

LS-DYNA model of the F-15 aircraft analysis compared well overall. It was concluded that the 

preliminary full-scale impact simulation using the aircraft smoothed particle hydrodynamics and 

finite element model showed a promising path forward for the study of aircraft impact scenarios. 
1-2 

1.2 Current Need for Aircraft Crash Simulation Capabilities 

The assessment of both commercial and military aircraft crash hazards and their impact on 

nuclear and other critical facilities continues to be important to the owners of these facilities and 

many federal government agencies. 

In preparation for reviewing a license application for the proposed repository at Yucca Mountain, 

NRC conducted independent analyses of the performance of important to safety (ITS) structures 

in the geologic repository operations area that were to be relied on to limit or prevent potential 

event sequence, as required in 10 CFR 63.112(e)(8). One area of importance was the 

performance evaluation of ITS surface structures when subject to an impact of an aircraft crash. 

The surface structures of the proposed repository at Yucca Mountain were to be 

constructed of reinforced concrete. Therefore, NRC directed the CNWRA to develop the 

computational capability to predict damage to reinforced concrete structures caused by an 

aircraft crash impact. 

On September 11, 2001, terrorists simultaneously attacked the World Trade Center in 

New York City, New York, and the Pentagon in Washington, DC, utilizing large commercial 

aircraft as weapons, which caused widespread loss of life and destruction of property. 

These incidents have drawn special attention from the public, industry groups such as the 

Nuclear Energy Institute (NEI), and federal government agencies such as the National Institute 

of Standards and Technology (NIST) and NRC. 

NRC has determined that it is prudent for nuclear power plant designers to rigorously account 

for the potential effects of an impact of a large, commercial aircraft. In the Federal Register 

(74 FR 28111; June 12, 2009), effective July 13, 2009, NRC issued a final rule that will require 

applicants for new nuclear power reactors to perform an assessment of the effects of the impact 

of a large commercial aircraft. As stated in the Federal Register (74 FR 28111; June 12, 2009), 

the technical issues related to aircraft impact assessment should include the following damage 

mechanisms: (i) structural response, (ii) shock and vibration effects, and (iii) fire effects of the 

aircraft impact. The structural analysis should evaluate both local and global plantwide 

response. Also specified in the Federal Register (74 FR 28111; June 12, 2009), “the structural 

assessment is to be based on a detailed model of the plant accounting for nonlinear material 

and geometric behavior.” 

As a result of the ruling, regulations in 10 CFR Part 50 were amended to include section 

10 CFR 50.150, Aircraft Impact Assessment. In particular, 10 CFR 50.150(a) specifies that 

“the applicant shall identify and incorporate into the design those design features and functional 

capabilities to show that, with reduced use of operator actions: (i) The reactor core remains 

cooled, or the containment remains intact; and (ii) spent fuel cooling or spent fuel pool integrity 

is maintained.” 

Subsequently, NRC issued Draft Regulatory Guide DG–1176 (NRC, 2009). The guide sets 

forth a method that NRC considers acceptable for satisfying the regulations in 10 CFR 50.150. 

Specifically, this draft guide endorses the aircraft impact assessment methodologies described 

in the NEI’s report 07-13 (NEI, 2009). It is the NRC position that conformance with guidance 

described in NEI 07-13 is an acceptable method for satisfying the regulatory requirements in 

10 CFR 50.150(a), which pertains to the assessment of aircraft impacts for new nuclear power 

reactors (NRC, 2009). 
1-3 

NEI 07-13 (NEI, 2009) states that for containment structures and spent fuel pools, two structural 

failure modes need to be evaluated: (i) local failure characterized by scabbing and perforation 

due to impact of the aircraft engines and (ii) global failure in the form of plastic collapse due to 

impact of the entire aircraft. One approach for determining both local and global structural 

failure is the explicit modeling of the aircraft, the target (e.g., a building), and the simulation of 

the aircraft crashing into the structure. As discussed in Section 1.1, the CNWRA has developed 

the computational capabilities to perform this type of analysis. 

The analyses reported in this report were performed for application to surface structures 

handling high-level waste and spent-fuel of a repository site. The analyses were generic in 

nature and no effort was made to relate those to nuclear power plants or spent fuel pools. 

In addition to performing a local and global structural analysis, it is also necessary to evaluate 

the effects of fire and shock that can cause damage to important systems utilized for fuel 

cooling. For fire and shock damage, important considerations are (i) effects of a large fire 

outside the containment and effects of fire inside any adjacent buildings below the point of 

impact and (ii) shock damage to fragile structures, systems, and components directly attached 

to the containment wall. If the structural analyses indicate perforation of the containment 

boundary, then fire and physical damage inside the containment must be considered. 

1.3 Objective and Scope 

The objective of this report is to present a detailed overview of the work the CNWRA performed 

(Cox, et al., 2007, 2006, 2005) to develop the ability to computationally simulate and analyze 

the effects of an aircraft crashing into reinforced concrete structures. The particular finite 

element software chosen for this work was LS-DYNA (Livermore Scientific Technology 

Corporation, 2003a,b). The CNWRA has used LS-DYNA in past programs for NRC to solve 

problems that involve high rate loading and material failure. The code has undergone 

verification and validation testing by the CNWRA. 

1.4 Organization of the Report 

Chapter 2 discusses the characterization of the selected LS-DYNA concrete model using 

experimental data and the results of impact experiments using both rigid and deformable 

missiles against reinforced concrete walls. Chapter 3 details the Riera method (Riera, 1968) 

and evaluates its accuracy for predicting impact loads. Chapter 4 discusses the development of 

a smoothed particle hydrodynamics model of an F-15E aircraft. Chapter 5 compares the impact 

forces on a rigid surface produced by the Riera method and the F-15E smooth particle 

hydrodynamics (SPH) model. Chapter 6 details a full-scale impact simulation of the F-15E SPH 

model striking a reinforced concrete wall. Finally, Chapter 7 provides a summary and 

conclusions for the report. 
2-1 

2 MATERIAL MODELING OF CONCRETE 

2.1 LS-DYNA Concrete Damage Model 

The LS-DYNA explicit finite element program has several concrete material models available 

(e.g., the pseudotensor model, soil/concrete model, Winfrith concrete model, and a concrete 

damage model) (Livermore Software Technology Corporation, 2003b). Each model was 

developed for a specific application and requires a different set of input parameters. In general, 

the values of the necessary material parameters cannot always be found in the literature. The 

aircraft crash impact analyses presented in this report utilized the LS-DYNA concrete damage 

model (keyword *MAT_CONCRETE_DAMAGE) Malvar, et al. (1997) formulated, which is an 

improved version of the pseudotensor model. 

The concrete damage model Malvar, et al. (1997) developed is a three-invariant plasticity 

model that accounts for changes in yield stress as a function of plastic strain. The specific 

forms of the invariants used in the model are ܫଵ ൌ ሺߪଵ ൅ ߪଶ ൅ ߪଷሻ, which is the first invariant of 

the total stress tensor; ܬଶ ൌ ሾሺݏଵ

ଶ ൅ ݏଶଶ ൅ ݏଷଶሻ/2ሿ, which is the second invariant of the deviatoric 

stress tensor where ݏଵ, ݏଶ, ݏଷ are principal deviatoric stresses; and ܬଷ ൌ ݏଵݏଶݏଷ, which is the 

third invariant of the deviatoric stress tensor. Note that including ܫଵ accounts for pressure 

dependence. As with conventional ܬଶ-plasticity, ܬଶ enters the yield function and the specific form 

of the yield function defines the yield surface. The third invariant, ܬଷ, is used to calculate the 

Lode angle (Chen, 2007), which modifies the shape of the failure surface in the deviatoric plane. 

Including ܬଷ is commonly used for materials such as concrete, which have a triangular-shaped 

failure surface. 

The deviatoric stress used in the second and third invariants is limited by the function 

∆ߪሺݕ, ݉, ݎሻ defined by linear relationships of three failure surfaces that are functions of pressure: 

(i) yield surface, ∆ߪ௬; (ii) maximum failure surface, ∆ߪ ;௠and (iii) residual failure surface, ∆ߪ௥, 

∆ߪ௬ ൌ ܽ଴௒ ൅

ܲ

ܽଵ௒ ൅ ܽଶ௒ܲ

(2-1) 

 

൅ ଴ܽ ൌ௠ ߪ∆

ܲ

ܽଵ ൅ ܽଶܲ

(2-2) 

 

ܲ ൌ௥ ߪ∆

ܽଵ௙ ൅ ܽଶ௙ܲ

(2-3) 

 

in which P (pressure) is defined by ܫଵ/3. As normally defined in standard plasticity, the yield 

surface determines the stress state at which plasticity first occurs. The yield surface then 

increases until it reaches the maximum failure surface, which defines the upper limit on the 

stress. Once the stress passes the upper limit, the concrete material begins to soften until the 

residual failure surface is reached. Thus, these surfaces are defined by eight material 

parameters: ܽ଴௒, ܽଵ௒, ܽଶ௒, ܽ଴, ܽଵ, ܽଶ, ܽଵ௙, ܽଶ௙. 

The parameter ܽ଴ represents the maximum failure strength when the pressure, ܲ, is zero and ܽ଴

is defined by ݂௖

ᇱ

⁄4 where ݂௖

ᇱ

 is the compressive strength of the concrete. The parameter ܽଵ has 

been assigned a value of 1/3, and ܽଶ is defined as 1 ݂௖

ᇱ ⁄ . All of these parameter values were 
2-2 

taken from the *MAT_PSEUDO_TENSOR model given in the LS-DYNA Keyword User’s Manual 

(Livermore Software Technology Corporation, 2003a). 

In addition, the initial yield strength ∆ߪ௬ is estimated by the following equation: 

∆ߪ௬ ൌ 0.45∆ߪ ௠ൌ 0.45 ൬ܽ଴ ൅

ܲ

ܽଵ ൅ ܽଶܲ

൰ (2-4) 

Recall that the parameters ܽ଴, ܽଵ, ܽଶ were previously determined. The parameters ܽ଴௒, ܽଵ௒, ܽଶ௒

are then obtained from a graphical fit to the initial yield surface, which is determined from triaxial 

compression tests of plain concrete. Malvar, et al. (1997) detail the procedure for determining 

these parameters. 

For the residual failure surface parameters, ܽଵ௙, ܽଶ௙, the parameter ܽଵ௙ was assigned a value 

of 0.385 as suggested in the *MAT_PSEUDO_TENSOR model given in the LS-DYNA Keyword 

User’s Manual (Livermore Software Technology Corporation, 2003a). The term ܽଶ௙ is obtained 

from an experimentally determined failure surface. Again, Malvar, et al. (1997) detail the 

procedure for determining this parameter. 

In addition, damage accumulation is defined by the parameters ܾଵ, ܾଶ, ܾଷ. The concrete model’s 

damage is separated into shear (deviatoric) and volumetric components. The parameters ܾଵ, ܾଶ

are associated with shear damage accumulation, and the parameter ܾଷ is associated with 

volumetric damage. For brevity, the lengthy equations used to calculate ܾଵ, ܾଶ, ܾଷ are not 

presented here; however, all details for obtaining these parameters are given in Malvar, et al. 

(1997). All required material parameters and their values used in the analyses presented in this 

report are summarized in Table 2-1. 

Additional details of the selection of the material parameters listed in Table 2-1 are given in 

Cox, et al. (2005). 

The current failure surface is defined using linear interpolation between the two active failure 

surfaces. After reaching the initial yield surface, yet below the maximum surface, the active 

failure surface is defined as 

 (2-5) ௬ߪ∆ ൅ ௬൯ߪ∆ െ௠ ߪ∆൫ߟ ൌ ߪ∆

After the maximum failure surface has been reached, the concrete material begins to soften. 

The active failure surface is then determined by linearly interpolating between the maximum 

failure surface and the residual failure surface; that is, 

 (2-6) ௥ߪ∆ ൅ ሻ௥ߪ∆ െ௠ ߪ∆ሺߟ ൌ ߪ∆

The material parameter ߟ in Eqs (2-5) and (2-6) is defined as the damage function, which is 

expressed in terms of user-defined pairs ሺߟ, ߣሻ where the term ߣ is the accumulated effective 

plastic strain. 

The damage function increases to a value of one, which corresponds to the concrete’s 

maximum strength, and then decreases (i.e., softens) to a value of zero, which corresponds to 

the concrete’s residual strength. The damage function, ߟሺߣሻ, is given in Table 2-2. The values 
2-3 

Table 2-1. List of Concrete Model Input Parameters 

Material Parameter Value 

ρ, kg/m3 [lb/ft3] Mass Density 2,300 [144]* 

ν, Poisson’s Ratio 0.19† 

fୡ

ᇱ

, Pa [psi] Compressive Strength of Concrete 2.35 × 107 [3,408]* 

a0, Pa [psi] Cohesion 5.88 × 106 [853]‡ 

a1, Pressure Hardening Coefficient 0.333‡ 

a2, Pressure Hardening Coefficient 1.42 × 10−8‡ 

a0Y, Pa [psi] Cohesion for Yield 2.64 × 106 [383]§ 

a1Y, Pressure Hardening Coefficient for Yield Limit 0.75§ 

a2Y, Pressure Hardening Coefficient for Yield Limit 3.10 × 10−8§ 

a1F, Pressure Hardening Coefficient for Failure 0.39§ 

a2F, Pressure Hardening Coefficient for Failure 1.39 × 10−8§ 

b1, Damage Scaling Factor 1.250‡ 

b2, Damage Scaling Factor for Uniaxial Tension 4.0§ 

b3, Damage Scaling Factor for Triaxial Tension 10.0§ 

*Wang, C.K. and C.G. Salmon. Reinforced Concrete Design. 5th Edition. New York City, New York: 

Harper-Collins. 1992. 

†MacGregor, J.G. and H.K. Wright. Reinforced Concrete Mechanics and Design. 4th Edition. Upper Saddle 

River, New Jersey: Prentice Hall. 2005. 

‡Livermore Software Technology Corporation. “LS-DYNA Keyword User’s Manual.” Version 970. 

Livermore, California: Livermore Software Technology Corporation. April 2003. 

§Malvar, L.J., J. Crawford, J. Wesevich, and D. Simons. “A Plasticity Concrete Material Model for DYNA3D.” 

International Journal of Impact Engineering. Vol. 19, Nos. 9–10. pp. 847–873. 1997. 

Table 2-2. Damage Function Values 

Effective Plastic Strain Damage Scale Factor 

λ η(λ) 

0 0.309 

8.62 × 10−6 0.543 

2.15 × 10−5 0.840 

3.14 × 10−5 0.975 

3.95 × 10−4 1.0 

5.17 × 10−4 0.79 

6.38 × 10−4 0.63 

7.98 × 10−4 0.469 

9.67 × 10−4 0.383 

1.41 × 10−3 0.247 

1.97 × 10−3 0.173 

2.59 × 10−3 0.136 

0.909 0 

listed in Table 2-2 are those suggested from the *MAT_PSEUDO_TENSOR model described in 

the LS-DYNA Keyword User’s Manual (Livermore Software Technology Corporation, 2003a). 

In addition to the material parameters for the concrete damage model, an equation of state is 

needed to describe the pressure-compaction curve representing the volumetric response 

behavior of the concrete. The tabulated compaction model was chosen, and values for the 

model were determined from a procedure found in the Winfrith concrete material model 

(*MAT_WINFRITH_CONCRETE) description in the LS-DYNA Keyword User’s Manual 
2-4 

(Livermore Software Technology Corporation, 2003a). If a pressure-compaction response 

curve specific to the concrete being modeled cannot be obtained from experimental data, the 

*MAT_WINFRITH_CONCRETE model description in the LS-DYNA Keyword User’s Manual 

suggests a method for developing a compaction curve. 

First, pressure is defined as positive in compression, and volumetric strain is defined as the 

natural log of the relative volume, which is negative in compression. The compaction curve data 

are input in a tabular format and given in order of increasing compression with no initial zero 

point (Livermore Software Technology Corporation, 2003a). The LS-DYNA recommended 

values of the pressure-compaction response curve are shown in Table 2-3. 

In Table 2-3, the parameters p1 and K are defined by the following expressions. p1, the 

pressure at uniaxial compressive failure, is given as 

݌ଵ ൌ ݂௖

ᇱ

3

(2-7) 

where ݂௖

ᇱ

 is the concrete’s unconfined compressive strength. The bulk modulus K is given as 

ൌ ܭ

௦ܧ

3ሺ1 െ 2ߥሻ

(2-8) 

where Es is one-half the tangent modulus for the concrete and ߥ is Poisson’s ratio for 

the concrete. 

In addition to the concrete damage model, element erosion was used to simulate concrete 

breakup. Erosion was used to simulate, in a qualitative sense, representation of concrete 

scabbing and spalling effects. Element erosion was activated by using the 

*MAT_ADD_EROSION option as described in the LS-DYNA Keyword User’s Manual 

(Livermore Software Technology Corporation, 2003a). Elements that reach a user-specified 

failure strain are deleted from the analysis. A parametric study was performed, which consisted 

of running numerical simulations with different erosion strain values and observing overall 

damage. Based on this study, an erosion failure strain parameter of 0.5 was selected. 

Table 2-3. Volumetric Strain Versus Pressure 

Volumetric Strain Pressure (MPa) 

−p1/K 1.00 × p1

−0.002 1.50 × p1

−0.004 3.00 × p1

−0.010 4.80 × p1

−0.020 6.00 × p1

−0.030 7.50 × p1

−0.041 9.45 × p1

−0.051 11.55 × p1

−0.062 14.25 × p1

−0.094 25.05 × p1
2-5 

2.2 Application of LS-DYNA Concrete Damage Model for 

 Impact Simulations 

As discussed in Section 2.1, the selection of some of the material parameters was based upon 

values taken from different references. Cox, et al. (2005) presented details of using LS-DYNA 

to simulate impact loading on reinforced concrete panels using small-, intermediate-, and 

full-scale idealized aircraft engine models. The results of the LS-DYNA simulations were 

compared with experiments Muto, et al. (1989a,b) and Esashi, et al. (1989) conducted. 

The impact tests of Muto, et al. (1989a,b) and Esashi, et al. (1989) were based on the GE J79 

engine used in the F-4 Phantom fighter aircraft. Dimensions of the GE J79 engine and the 

simplified models used in the tests are given in Muto, et al. (1989a,b) and Esashi, et al. (1989). 

As an example, Figure 2-1 shows the actual GE J79 engine and its corresponding simulant 

used in the full-scale tests of Muto, et al. (1989b). 

These GE J79 engine simulants were used in impact experiments involving reinforced concrete 

panels of different thicknesses supported at the corners with steel backup plates. Additional 

details of the reinforced concrete panel, such as width, height, and reinforcement steel 

placement, are given in Cox, et al. (2005); Muto, et al. (1989a,b); and Esashi, et al. (1989). 

Depending on the scale of the idealized engine, the experiments were performed at impact 

speeds of 215, 150 m/s, and 100 m/s [705, 492, and 328 ft/s]. The experimental results of 

Muto, et al. (1989a,b) and Esashi, et al. (1989) described the physical damage to the concrete 

wall produced by the engine impacts. Additional details of the panel thickness, engine weight, 

and the velocities used in the different tests are shown in Tables 2-4, 2-5, and 2-6. 

Figure 2-1. Idealized Engine Model of GE J79 Engine Used in Finite Element Simulation 

of Full-Scale Test (Muto, et al., 1989b) 

(All Dimensions Are Given in mm; 25.4 mm = 1 in) 
2-6 

Table 2-4. LS-DYNA Results and Comparison With Experiments:* 

Small-Scale (1/7.5 Scale) Idealized GE-J79 Engine 

Wall 

Thickness Engine Weight 

Engine 

Velocity 

Observed 

Damage Mode 

LS-DYNA 

Results 

12 cm 

[4.72 in] 3.5 kg [7.72 lb] 

215 m/s 

[705 ft/s] Perforation Perforation 

150 m/s 

[492ft/s] Scabbing Scabbing 

100 m/s 

[328ft/s] Penetration Penetration 

*Muto, K., H. Tachikawa, T. Sugano, H. Tsubota, H. Kobayashi, Y. Kasai, N. Koshika, and T. Tsujimoto. 

“Experimental Studies on Local Damage of Reinforced Concrete Structures by the Impact of Deformable 

Missiles, Part 1: Outline of the Test Program and Small-Scale Tests.” Transaction of the 10th International 

Conference on Structural Mechanics in Reactor Technology (SMiRT 10), Anaheim, California, August 14–19, 

1989. Los Angeles, California: American Association for Structural Mechanics in Nuclear Reactors. 1989. 

Table 2-5. LS-DYNA Results and Comparison With Experiments:* 

Intermediate-Scale (1/2.5 Scale) Idealized GE-J79 Engine 

Wall 

Thickness Engine Weight Engine Velocity 

Observed 

Damage Mode 

LS-DYNA 

Results 

35 cm 

[14 in] 

100 kg 

[221 lb] 

215 m/s 

[705 ft/s] Perforation Perforation 

45 cm 

[18 in] 

215 m/s 

[705 ft/s] Scabbing No Scabbing† 

45 cm 

[18 in] 

250 m/s 

[820 ft/s] 

Just 

Perforation Just Perforation 

*Esashi, Y., H. Ohnuma, C. Ito, and K. Shirai. “Experimental Studies on Local Damage of Reinforced Concrete 

Structures by the Impact of Deformable Missiles, Part 2: Intermediate-Scale Tests.” Transaction of the 

10th International Conference on Structural Mechanics in Reactor Technology (SMiRT 10), Anaheim, California, 

August 14–19, 1989. Los Angeles, California: American Association for Structural Mechanics in Nuclear 

Reactors. 1989. 

†However, there was significant penetration. 

Table 2-6. LS-DYNA Results and Comparison With Experiments:* 

Full-Scale Idealized GE-J79 Engine

Wall 

Thickness Engine Weight 

Engine 

Velocity 

Observed 

Damage Mode 

LS-DYNA 

Results 

160 cm 

[63 in] 

1,463 kg 

[3,225 lb] 

215 m/s 

705 [ft/s] Penetration Penetration 

*Muto, K., H. Tachikawa, T. Sugano, H. Tsubota, N. Nagamatsu, N. Koshika, M. Okano, K. Suzuki, and 

S. Ohrui. “Experimental Studies on Local Damage of Reinforced Concrete Structures by the Impact of 

Deformable Missiles, Part 3: Full-Scale Tests.” Transaction of the 10th International Conference on Structural 

Mechanics in Reactor Technology (SMiRT 10), Anaheim, California, August 14–19, 1989b. Los Angeles, 

California: American Association for Structural Mechanics in Nuclear Reactors. 1989.

Figure 2-2 shows a representative example of an LS-DYNA finite element model of the GE J79 

engine simulant. 
2-7 

Figure 2-2. LS-DYNA Finite Element Model of Full-Scale GE J79 Engine Simulant 

(Cox, et al., 2006) 

The GE J79 engine simulant used in the experiments of Muto, et al. (1989b) was constructed of 

steel. Therefore, the LS-DYNA finite element model used elastic-plastic material parameters to 

model the steel. Full details of the elastic-plastic material parameters used for the steel can be 

found in Cox, et al. (2006). 

Muto, et al. (1989c) performed a displacement-controlled crush test of the full-scale engine 

simulant. Similarly, an LS-DYNA analysis was performed to simulate the crush test. The 

LS-DYNA simulation results, documented in Cox, et al. (2006), showed good agreement overall 

with the experimental test data of Muto, et al. (1989c). These results demonstrated that the 

LS-DYNA engine simulant finite element model’s structural behavior was similar to that of the 

actual engine simulant. 

The damage modes observed in the tests were classified according to Muto, et al. (1989a) in 

the following terms: 

 Perforation mode: the engine passed through the panel completely 

 Just perforation mode: perforation is just barely prevented—the engine did not pass 

through the panel but stuck in the panel creating a large opening with breakage of 

reinforcement bars 

 Scabbing mode: considerable concrete debris is ejected off the back surface of the 

panel and may include the severe case where a small opening is created on the rear 

surface; and (iv) penetration mode: a crater is formed on the front face of the panel, 

but no damage occurs on the rear face 

The LS-DYNA impact simulation results and the experimental observations of Muto, et al. 

(1989a,b) and Esashi, et al. (1989) are compared in Tables 2-4, 2-5, and 2-6 and Figure 2-3. 

The damage modes from the LS-DYNA impact simulations agree with the actual damage 

observed in the experiments of Muto, et al. (1989a,b) and Esashi, et al. (1989). 

In addition to matching the damage modes, a quantitative comparison was made for penetration 

depth for the full-scale engine simulant impacting the 160-cm [63-in]-thick panel at a velocity of 

215 m/s [705 ft/s]. The experimentally measured crater depth was approximately 21 cm [8.3 in] 

with no observed scabbing of the back surface (Muto, et al., 1989b). The approximate average 

depth of penetration observed in the LS-DYNA numerical simulation was 22 cm [8.7 in], and 

there was no back surface scabbing, which compares well with the experimental results. The 

crater predicted in the LS-DYNA numerical simulation is shown in Figure 2-3(d). 
2-8 

Figure 2-3. Results of LS-DYNA Simulations Showing Different Damage Modes for an 

Idealized Engine Striking Reinforced Concrete Panels. (a) Small-Scale Engine Impacting 

12 cm [4.7-in] Thick Panel at 215 m/s [705 ft/s]: Perforation of Panel. (b) Small-Scale 

Engine Impacting 12-cm [4.7-in] Thick Panel at 150 m/s [492 ft/s]: Scabbing Damage at 

Rear of Panel. (c) Intermediate-Scale Engine Impacting 45-cm [17.7-in] Thick Panel at 

215 m/s [705 ft/s] Strike (Left) and Rear (Right) Faces: Penetration Occurred at the Strike 

Face. (d) Full-Scale Engine Impacting 160 cm [63 in] Thick Panel at 215 m/s [705 ft/s] 

Strike Face: Penetration in Form of a Crater. 

(a) (b) 

(c) 

(d) 
2-9 

Backside surface displacements, located at the center of the panel, were compared using those 

obtained from the LS-DYNA simulation and the experiments of Muto, et al. (1989b) as shown in 

Figure 2-4. 

Note that the LS-DYNA simulation matched measured maximum displacements in magnitude 

(Figure 2-4) but not in the character of the displacement history. Specifically, the LS-DYNA 

simulation results failed to capture the experimentally measured feature of “bounce back” where 

after reaching the peak displacement, the displacement rate decreases, as shown in the curve 

labeled “Test Data” in Figure 2-4. Therefore, the concrete damage material parameters were 

further refined in an attempt to improve correlation with the experimentally observed 

displacement history of Muto, et al. (1989b). 

2.3 Refinement of LS-DYNA Concrete Damage Model Material Parameters 

To refine the material parameters used in the LS-DYNA concrete damage model, additional 

LS-DYNA simulations were run for the case of the full-scale engine simulant impacting a 

160-cm [63-in]-thick reinforced concrete panel with a velocity of 215 m/s [705 ft/s]. A sensitivity 

study of the concrete damage material parameters b2 and b3 (Table 2-1) was performed to 

improve the match with the experimentally measured back surface displacements. Selected 

results from the sensitivity study are shown in Figure 2-5. 

The analysis with the concrete damage material parameters b2 = 15 and b3 = 5 was considered 

the best fit to the measured data. This selection was based upon the LS-DYNA simulation back 

surface displacement matching the peak magnitude of the displacement and because the 

simulation results now capture the experimentally observed bounce-back effect. All other 

concrete damage model parameters listed in Table 2-1 remain the same. 

The maximum penetration depth from the LS-DYNA simulation also was compared with 

experimental results to investigate the effect of changes in b2 and b3. As discussed in 

Section 2.2, experimental data indicated 21 cm [8.25 in] of penetration into the front face of the 

concrete panel. The LS-DYNA simulation now results in a crater depth of approximately 20 cm 

[7.8 in], which is comparable to the test data. A cross-sectional view of the panel with the crater 

is shown in Figure 2-6. 

Note, however, there is an offset in the LS-DYNA calculated displacement time history that 

begins at approximately 4 milliseconds, which is not evident in the measured displacements 

of Muto, et al. (1989b). Further investigation to determine the cause of this behavior 

was performed. 

To investigate a possible cause of the offset in the calculated displacement, the tangent 

(hardening) modulus and the failure strain material parameters for steel, used in the LS-DYNA 

engine simulant model, were varied to see their effect on the calculated displacements. Based 

on a sensitivity study, it became apparent that the offset in the displacement time history was 

caused by the collapse of the front cylinder of the LS-DYNA engine simulant model. This 

produced a decrease in the displacement rate (i.e., penetration slowed) between approximately 

4 and 8 milliseconds, after which the displacement rate resumed as the engine simulant’s 

intermediate bulkhead impacted the panel. 
2-10 

Figure 2-4. Displacement Versus Time Comparison for Full-Scale Engine Test 

(Muto, et al., 1989b). Displacement Measured on Backside of Test Plan [1 cm = 0.39 in]. 

Figure 2-5. Displacement Versus Time Results for Full-Scale Panel Test 

(Muto, et al., 1989b). Trial Runs with Various Values of Concrete Damage Parameters 

b2 and b3 [1 cm = 0.39 in]. 
2-11 

Figure 2-6. LS-DYNA Finite Element Results Showing Crater Depth Due to Impact of 

Engine Simulant [1 cm = 0.39 in] 

Based on these results, there appeared to be a coupling between the concrete material 

parameters and the crush behavior of the LS-DYNA engine stimulant, which directly affects the 

structural response of the panel. At this time, additional numerical studies would be needed to 

further investigate the cause of the temporary decrease in the displacement rate that is 

now present. 
3-1 

3 EVALUATION OF AIRCRAFT IMPACT LOADS 

3.1 Introduction 

When a facility (e.g., a high-level waste repository surface facility, a spent fuel facility, etc.) is 

subject to impact by an aircraft (missile), the global damage is evaluated in terms of excessive 

deformation (i.e., displacement, or collapse of the structure). 

For a global response evaluation, the target’s deformation due to missile impact depends on the 

characteristics of the missile and the target. The important parameters for the missile are 

mass, stiffness, strength, size, and velocity. The important parameters for the target are 

geometry, support conditions, stiffness, and strength. 

As given in Hossain, et al. (1997), there are three analytically based methods that can be used 

to evaluate global damage: (i) energy balance method, (ii) force time history analysis method, 

and (iii) missile target interaction analysis method. 

This chapter , the focuses will be on the force time history analysis method, which is typically 

associated with Riera (1968). The Riera method uses the aircraft’s mass, strength properties, 

and its velocity to determine the impact force time history. The Riera method makes two 

assumptions: (i) the target is rigid and (ii) the impact orientation is normal to the target so the 

aircraft fuselage will progressively crush/buckle axially. Hossain, et al. (1997) state that the 

impact orientation assumption results in the highest missile stiffness making the Riera method 

conservative. Thus, the damage potential of a crashing aircraft depends on the combination of 

the mass of the aircraft (or any hard components, such as engine or landing gear) and the 

speed of the impact. The critical impact speed is different for each aircraft type due to 

differences in the distribution of mass. 

Section 3.2 will discuss the Riera method that can calculate the equivalent impact force for 

different types of aircraft. Section 3.3 will use results from a full-scale impact test using an 

F-4 aircraft to evaluate the accuracy of the Riera method for calculating the impact force. 

Finally, Section 3.4 will present LS-DYNA finite element analyses using experimentally 

measured and Riera-calculated load-time histories to evaluate the response of the concrete 

block target used in the full-scale F-4 aircraft impact tests. 

3.2 The Riera Method 

For a crashing aircraft striking a target, normal to the impact surface at time t, the impact force 

ܨሺݐሻ is given by 

ܨሺݐሻ ൌ ܲ௖ሾݔሺݐሻሿ ൅ ߤሾݔሺݐሻሿݒଶሺݐሻ (3-1) 

where ݔሺݐሻ is the distance measured from the nose of the aircraft to the current location, ܲ௖ሾݔሺݐሻሿ

is the load necessary to crush or deform the aircraft fuselage, ߤሾݔሺݐሻሿ is the mass per unit length 

of the aircraft, and ݒሺݐሻ is the velocity of the uncrushed portion. Both ܲ௖ሾݔሺݐሻሿ and ߤሾݔሺݐሻሿ are 

functions of the position along the aircraft, which is usually measured from the nose. 

Given known distributions for both ܲ௖ሾݔሺݐሻሿ and ߤሾݔሺݐሻሿ, and the initial impact velocity, Eq. (3-1) 

is solved stepwise in time starting at the instant of impact to provide the impact force on a rigid 
3-2 

surface. For the results presented next, a Microsoft® Excel® (Microsoft Corporation, 2002) 

spreadsheet program was written to calculate the impact forces as a function of time. 

3.3 Comparison of Riera-Calculated Impact Forces With Measured Impact 

 Forces From a Full-Scale F-4 Crash Test 

Sugano, et al. (1993) performed experiments consisting of an actual full-scale F-4 aircraft 

crashing into a massive concrete block. Sugano, et al. (1993) included the mass distribution 

and crushing force for the F-4 aircraft, which are required input for the Riera method 

(Riera, 1968). The test result data also included the measured impact forces generated by the 

F-4 aircraft striking the concrete block. To demonstrate the Riera method, the experimentally 

measured impact forces were compared to numerical calculations of impact forces using the 

Riera method. 

The mass per unit length ߤ and crush force ܲ௖ of the F-4 aircraft were obtained directly from 

data Sugano, et al. (1993) reported. Both quantities, which are a function of position along the 

length of the aircraft, were measured from nose to tail. The mass per unit length ߤ and crush 

force ܲ௖ are shown in Figures 3-1 and 3-2, respectively. Note that the distribution of ߤ in 

Figure 3-1 is given for both the F-4 aircraft only and the F-4 aircraft in its test configuration, 

which included skids and rockets. Figure 3-2 shows the crush force ܲ௖ as a function of position 

along the aircraft, which was measured during the test. Using this experimental data, an Excel 

(Microsoft Corporation, 2002) spreadsheet program was written to calculate the impact forces 

shown in Figure 3-3 for the F-4 aircraft. 

Because the experimental F-4 test of Sugano, et al. (1993) was performed at 215 m/s [705 ft/s], 

this same velocity was used for the comparison between measured impact forces Sugano, et al. 

(1993) reported and those calculated using the Riera method (Riera, 1968) discussed 

previously. The results of this comparison are shown in Figure 3-4. 

Figure 3-1. Mass Per Unit Length, ࣆ, for the F-4 Aircraft With and Without Skids and 

Rockets Using Digitized Data From Sugano, et al. (1993) 

[1 kg = 2.2 lb; 1 m = 3.28 ft] 
3-3 

Figure 3-2. Measured Crush Force, ࢉࡼ, for the F-4 Aircraft Including 

Skids and Rockets Using Digitized Data (Sugano, et al., 1993) 

[1 N = 0.225 Lbf; 1 m = 3.28 ft]

Figure 3-3. Calculated Impact Force on a Rigid Surface Using Riera Method 

(Riera, 1968) at a Speed of 215 m/s [1 N = 0.225 Lbf] 
3-4 

Figure 3-4. Comparison of Measured (Sugano, et al., 1993) and Calculated Impact Forces 

for the F-4 Aircraft Including Skids and Rockets [1 N = 0.225 Lbf] 

Notice that except for a slight time shift, the impact forces are in excellent agreement, with the 

calculated maximum impact force being only 2.6 percent higher than the maximum measured 

impact force. The reason for the slight time shift in Figure 3-4 can be determined by examining 

the experimental data shown in Figures 3-1 and 3-2, as Sugano, et al. (1993) reported. From 

Figures 3-1 and 3-2, because the mass per unit length and impact forces are essentially zero for 

a distance of 1.6 m [4.8 ft] from the nose of the aircraft, the calculated impact forces using the 

Riera method (Riera, 1968) will be essentially zero in this region. 

As an additional comparison between the experimental data and the calculations the 

Riera method (Riera, 1968) produced, the impact forces in Figure 3-4 were integrated to obtain 

the total impulse delivered to the rigid surface. As shown in Figure 3-5, the total impulse the 

Riera method calculated is overestimated by 22.2 percent, thus making the Riera method 

considered conservative. 

To improve the correlation between the impulse force calculated using the Riera method 

(Riera, 1968) and the experimental data, Sugano, et al. (1993) showed that uniformly reducing 

the aircraft mass per unit length μ by a factor of 0.9 produced the best fit to measured data. 

However, based on Figure 3-5, the data match very well until approximately 0.05 seconds into 

the impact event. Therefore, Cox, et al. (2006) suggested that rather than reducing the mass 

uniformly along the length of the aircraft, a mass adjustment factor that reduces the mass near 

the tail of the aircraft appears more suitable. The reasoning behind this approach is that, as 

debris from the crash builds up on the rigid surface, the debris spreads and strikes the rigid 

surface obliquely, reducing its effect. This effect is greatest near the tail of the aircraft. 
3-5 

Figure 3-5. Comparison of Measured (Sugano, et al., 1993) and Calculated Impulse for 

the F-4 Aircraft Including Skids and Rockets [1 N = 0.225 Lbf]

The mass adjustment factor, specific to this case, is shown versus the nondimensional length 

(x/L) of the aircraft in Figure 3-6. Applying this mass adjustment factor to the calculations 

Figure 3-6. Proposed Nonlinear Mass Adjustment Factor Used in Calculation 

of Impulse Force (Cox, et al., 2005) 
3-6 

using the Riera method (Riera, 1968), the impulse force is reduced to within 10 percent of the 

measured value as shown in Figure 3-7. Using the same mass adjustment factor on the 

calculated impact force produces a slightly lower peak in magnitude than the measured impact 

force as shown in Figure 3-8. 

Figure 3-7. Comparison of Calculated Impulse Using Mass Adjustment Factor to 

Measured Impulse (Sugano, et al., 1993) for the F-4 Aircraft Including Skids and Rockets 

[1 N = 0.225 Lbf] 

Figure 3-8. Comparison of Calculated Impact Force Using Mass Adjustment Factor to the 

Measured Force (Sugano, et al., 1993) for the F-4 Aircraft with Skids and Rockets 

[1 m = 3.28 ft] 
3-7 

3.4 Evaluation of the Full-Scale F-4 Impact Test Target Response 

This section evaluates the global response of the large concrete block target used in the 

full-scale F-4 aircraft impact testing presented in Sugano, et al. (1993). An additional 

component of the experimental testing in Sugano, et al. (1993) was to evaluate the overall 

force-time history resulting from the F-4 crashing into the concrete block target (essentially 

a rigid wall) at a velocity of 215 m/s [705.4 ft/s]. As described in Sugano, et al. (1993), the 

concrete block rested on a concrete platform that incorporated air bearings to support the 

weight of the block and platform. 

The numerical simulations of the test consisted of creating a finite element model representing 

the large 7.0 × 7.0 × 3.66-m [22.9 × 22.9 × 12.0-ft] concrete block. Force-time loads taken 

from the experiment of Sugano, et al. (1993) and calculated force-time loads using the 

Riera method (Riera, 1968) are applied to the concrete block target. The concrete block’s 

global response is compared to test results of Sugano, et al. (1993). 

3.4.1 Finite Element Modeling of the Concrete Block Target 

An LS-DYNA finite element model representing the concrete block target was constructed using 

a mesh of 75,505 solid elements. The solid elements’ hourglass control was specified to use 

the Flanagan-Belytschko viscous form with exact volume integration. The concrete block used 

the same concrete damage constitutive model described in Chapter 2, and the associated 

material parameters are those previously listed in Table 2-1. 

The finite element concrete block model, having the same dimensions as the block used in the 

test, had a calculated mass of 468,960 kg [1,033,880 lb] as compared to the actual concrete 

block’s mass of 469,000 kg [1,033,968 lb]. Sugano, et al. (1993) described the concrete block 

as having reinforcement steel; however, no details were provided. Therefore, no reinforcement 

steel was included in the finite element concrete block model and the concrete density was 

adjusted to more closely match the actual mass. Modeling the concrete block without 

reinforcement steel was deemed adequate for predicting back surface motions because flexure 

and shear of the block will not occur due to the block thickness {3.66 m [12.01 ft]}. Also, 

Sugano, et al. (1993) reported that damage to the concrete block produced by the impact of the 

F-4 aircraft was limited to front face erosion. 

Sugano, et al. (1993) stated that air bearings were used to provide for an essentially frictionless 

contact between the bottom of the platform and the surface that it rested on; however, the air 

bearings and platform were not modeled in the finite element analysis. Instead, the contact 

condition between the base of the finite element concrete block and the ground plane was 

specified to be frictionless to simulate the effect of the air bearings. 

The loading of the finite element concrete block model was defined by specifying a force-time 

history distributed over the impact area. The full-scale test results determined the estimated 

impact area was 10 m2

 [107.6 ft2]. For modeling purposes, the shape of the loading area used 

in the finite element model was idealized as a circle with its center at the center of the block. 

The force-time history was applied evenly over the circular area to each of the 647 nodes 

encompassed by the area. The results of the finite element analysis were compared with the 

available test data of Sugano, et al. (1993), which measured the displacement and velocity at 

the center of the backside of the concrete block. 
3-8 

3.4.2 Concrete Block Target Response Using Measured and Calculated 

Load Histories 

This subsection contains an evaluation of the concrete block target response that was made by 

performing two LS-DYNA analyses. The first used the load history obtained directly from the 

full-scale F-4 impact test, and the second used a load history calculated using the Riera method 

(Riera, 1968). The load histories were used as input to an LS-DYNA analysis of the concrete 

block target finite element model. The response was measured in terms of the concrete 

block’s velocity. 

The first LS-DYNA analysis used the experimentally measured load obtained directly from the 

full-scale F-4 impact test that included the sled and the rockets, which were used to accelerate 

the aircraft. The force-time history used in this analysis is that shown in Figure 3-8 labeled as 

the “measured” data. 

The concrete block velocity-time history predicted by the LS-DYNA analysis and that of the 

measured test data is shown in Figure 3-9. Good agreement in the maximum velocity is 

observed between the measured data from the F-4 test and the LS-DYNA results. Figure 3-10 

shows a comparison of the displacements, measured on the back face of the concrete block 

target, for the test data and the LS-DYNA results. In terms of the actual damage to the concrete 

block from the test, Sugano, et al. (1993) observed a maximum penetration depth of 60 mm 

[2.36 in] on the front face of the block—partly a result of the engines impacting the block. 

The penetration depth due to the fuselage was a maximum of 20 mm [0.79 in]. Thus, 

Sugano, et al. (1993) considered the damage caused by the fuselage insignificant as compared 

to the damage caused by the engines. The overall damage to the concrete block was 

characterized as superficial scarring over the impact region (Sugano, et al., 1993). The most 

significant amount of damage, in the form of concrete spalling, was due to the impact of the 

carriage sled and rockets (Sugano, et al., 1993). 

Figure 3-9. Comparison of LS-DYNA Calculated Target Block Velocity to Test Data Target 

Block Velocity (Using the Measured Load in Figure 3-8) of Sugano, et al. (1993) 

[1 m = 3.28 ft] 
3-9 

Figure 3-10. Comparison of LS-DYNA Calculated Displacement (Back Face of Target) 

Time History to Measured Test Data of Sugano, et al. (1993) [1 m = 3.28 ft] 

The LS-DYNA results did not show any penetration into the target. This was most likely due to 

the load being uniformly applied over an idealized circular area. In addition, the finite element 

mesh used was considered to be relatively coarse. A finer mesh was not used, because the 

object of the analysis was not to capture the details of the penetration into the block, but rather 

to determine the overall global response of an essentially rigid structure. Also, because aircraft 

and sled loads were lumped together and applied over the same circular area, no local 

penetrations could be captured. 

The second LS-DYNA analysis used the input load history calculated using the Riera method 

(Riera, 1968) to represent the F-4, the carriage sled, and rockets. The calculated load history 

using the Riera method, shown in Figure 3-11, was applied uniformly over a circular area of the 

concrete block finite element model. 

A comparison of the velocity-time history from the LS-DYNA analysis versus the test data is 

shown in Figure 3-12. The LS-DYNA results show good overall agreement; however, the final 

velocity from LS-DYNA using the Riera method is approximately 7 percent higher than the test 

data velocity. These results tend to confirm the findings in Section 3.2 that the Riera method 

(Riera, 1968) predicts loads that are conservative. 
3-10 

Figure 3-11. Calculated Load-Time History of the Full-Scale F-4 Aircraft Test Using the 

Riera Method (Riera, 1968) [1 N = 0.225 Lbf] 

Figure 3-12. Comparison of Test Data (Sugano, et al., 1993) With Simulation Results 

Using the Riera Calculated Loading [1 m = 3.28 ft] 
4-1 

4 NUMERICAL MODELING OF THE F-15E AIRCRAFT 

4.1 Introduction 

In Chapter 3, the Riera method (Riera, 1968) (force-time history analysis) was used to calculate 

the impact force. The Riera method was evaluated to access its accuracy for calculating the 

impact force as compared to measured data from a full-scale F-4 impact test. The conclusion 

made in Chapter 3 was that the Riera method is considered conservative. 

Another method to evaluate global damage is the missile target interaction analysis 

method (Hossain, et al., 1997). This method has an advantage over the force-time history 

analysis method because it can more realistically represent the impact behavior of the 

aircraft and the target response. A missile target interaction analysis is typically performed 

using three-dimensional finite element analysis. The finite element method can accurately 

model the material and geometric nonlinearity of the aircraft and the target unlike the Riera 

method (Riera, 1968), which is based on the assumption of a rigid target. 

In conventional finite element models, elements are directly connected to each other via nodes 

forming a mesh. The finite element method can have difficulties solving very large deformation 

problems where significant mesh (element) distortion occurs. Robust element formulation to 

account for large strains and large rotations in addition to adaptive mesh refinement are typical 

solutions to handle large deformations. An alternative to conventional finite elements is the 

mesh-free approach. One such mesh-free approach is known as the smoothed particle 

hydrodynamics (SPH) method. Because the particles are not directly connected, an SPH mesh 

can undergo very large deformations while maintaining stability. Therefore, the SPH method is 

an effective alternative to the conventional finite element approach when performing an analysis 

in which large deformations leading to complete destruction are expected and the primary mode 

of loading is due to mass/momentum. 

LS-DYNA has the capability to construct SPH models. The LS-DYNA Theory Manual 

(Livermore Software Technology Corporation, 2003b) provides theoretical details of the SPH 

method and how it is implemented in LS-DYNA. The LS-DYNA Theory Manual provides 

guidance on coupling conventional finite element models with SPH models through the use of 

contact conditions. It also notes that proper SPH meshes should be as uniform as possible 

(Livermore Software Technology Corporation, 2003b). 

The following sections detail developing an SPH model for simulating aircraft crash impact into 

a reinforced concrete structure. 

4.2 A Smoothed Particle Hydrodynamics Model of the F-15E 

This section details constructing the F-15E aircraft model using the SPH method. Initially, a 

surface mesh of an F-15 was constructed using TrueGrid (XYZ Scientific Applications, Inc., 

2006). The external geometry of the aircraft was imported into TrueGrid from a computer-aided 

design (CAD) surface file, in initial graphics exchange specification (IGES) format, of the 

F-15 aircraft. Images of the surface mesh for the F-15, created from the IGES file, are shown 

in Figure 4-1. Additional details of the initial F-15 model are given Cox, et al. (2007). The 

F-15E model used in this report has a more refined and evenly spaced mesh. 
4-2 

Figure 4-1. Finite Element Surface Model of the F-15 Aircraft 

After the initial surface mesh was created, it was converted into SPH particles using the 

LS-DYNA preprocessing software LS-PrePost (Livermore Software Technology Corporation, 

2003c). The geometry file for the F-15E provided no details on the internal structural 

components (e.g., stringers, frames, bulkheads), as it only represented the external skin of the 

aircraft. Therefore, it was necessary to include the mass of the internal structures in the 

aircraft’s external skin. Table 4-1 lists the major aircraft components and their weights. 

Table 4-1. F-15E Weights* 

Components Weights 

Structure 8,936 kg [19,700 lb]

 Fuselage 4,672 kg [10,300 lb] 

 Landing Gear 1,179 kg [2,600 lb] 

 Tail 499 ka [1,100 lb] 

 Wing 2,585 kg [5,700 lb] 

Power Plant 4,354 kg [9,600 lb]

 Engines 3,357 kg [7,400 lb] 

 Nacelles 998 kg [2,200 lb] 

Equipment 1,225 kg [2,700 lb]

 Fixed 771 kg [1,700 lb] 

 Mission 454 kg [1,000 lb] 

Useful Load 19,232 kg [42,400 lb]

 Fuel 15,604 kg [34,400 lb] 

 Payload 3,629 kg [8,000 lb] 

Takeoff Weight 33,747 kg [74,400 lb]

*Hossain, Q.A., R.P. Kennedy, R.C. Murray, K. Mutreja, and B.P. Tripathi. “Structures, Systems, and 

Components Evaluation Technical Support Document. DOE Standard, Accident Analysis for Aircraft Crash 

into Hazardous Facilities.” UCRL–ID–123577. Livermore, California: Lawrence Livermore National 

Laboratory, United States Department of Energy. 1997. 
4-3 

Because mass distribution data were not available for the F-15E, various available resources 

were used to make assumptions on the location of major components. 

NRC furnished an isometric drawing of the F-15, which provided visual information on the 

location of various internal components; however, the drawing was not dimensioned. The 

isometric drawing and overall aircraft dimensions from the external surface file were used to 

estimate the location of internal and external fuel tanks, landing gear, equipment, payload, and 

engines for the aircraft. 

To represent the aircraft’s internal structure, a known mass distribution of the F-4 Phantom 

fuselage (Sugano, et al., 1993) was scaled to the length of the F-15. This distribution was then 

used as the fuselage mass distribution for the F-15E. 

The fuselage mass plus the mass of other components (landing gear, tail, wing, equipment, and 

payload) were all placed in the external skin of the aircraft. The mass contributions from each 

component were added at their respective positions along the length of the aircraft. Figure 4-2 

shows a plan view of the aircraft skin mesh, divided into 1-m [3.3-ft] segments along its length. 

The locations of the aircraft component weights are also shown. The component labels shown 

in Figure 4-2, except for the fuselage, have their total weights (from Table 4-1) distributed 

evenly across the number of segments shown. 

Each colored segment contains a collection of SPH particles. The particles in a given segment 

all have the same mass. The mass of each particle is therefore based on the total mass of the 

segment divided by the number of particles in the segment. In LS-DYNA, the user explicitly 

Figure 4-2. Grouping of SPH Particles in 1-m [3.3-ft] Increments Along the F-15E With 

Positions Indicated for Various Parts of the Aircraft 
4-4 

defines the particle masses. To automate this process, a program was written in FORTRAN, 

which steps along the length of the model at predefined spatial increments and assigns the 

appropriate mass to each particle contained within a segment. 

The aircraft fuel was modeled separately from the skin. Three major fuel loads were 

considered: internal fuel, external tanks, and the conformal fuel tanks. Fuel distribution for the 

F-15E was obtained from Aerospaceweb.org (2011), which indicated an internal fuel capacity 

(fuselage and wings) of 5,953 kg [13,125 lb] and an external capacity of 9,818 kg [21,645 lb]. 

Thus, the total fuel load is slightly higher than that given in Table 4-1. External capacity was 

approximately equal for each of the three external tanks and the two conformal fuel tanks. 

Location of the external tanks was determined from the CAD model. The location of the internal 

fuel was estimated by scaling its position from the isometric drawing. All fuel was meshed with 

SPH particles. 

The engines and nacelles also were modeled separately from the fuselage. The F100-PW-229 

engine and nacelle weights are given in Table 4-1. The overall length and diameter of the 

engines were obtained from Pratt and Whitney (2011) and by scaling the isometric drawing. 

Based on the isometric drawing, the total engine package has two components: the engine 

(consisting of shafts, compressor, turbine, and combustor) and the nacelles (consisting of the 

afterburner section, nozzles, and general engine containment). The main engine component 

has a length of 3 m [118 in], and the nacelle section aft of the engines has a length of 2.3 m 

[90 in]. The average diameter of the engine is 1 m [40 in]. Therefore, each engine model 

consisted of a forward section, with a total weight of 1,678 kg [3,700 lb] evenly distributed along 

the length, and an aft section, with a total weight of 544 kg [1,200 lb] evenly distributed along its 

length. The engines were also meshed with SPH particles. 

The entire aircraft mesh including all internals is shown in Figure 4-3. Also shown is the 

aircraft with the skin removed, exposing the fuel and engine components. The model has a total 

of 135,049 SPH particles. 

The model represented a total weight of 33,472 kg [73,793 lb]. The actual weight breakdown is 

shown in Table 4-2. The total weight is just under the takeoff weight provided in Table 4-1 due 

to roundoff when calculating the fuselage weight. 

After construction of the SPH model, its mass distribution was evaluated to ensure it reasonably 

represented the true mass distribution of the F-15E, which was not known other than the details 

provided in Table 4-1. The initial mass distribution calculations were performed in Excel at 1-m 

[3.3-ft] increments because the model is based on all SPH particles having equal mass within 

each 1-m [3.3-ft] segment along the aircraft. Three calculations were performed: (i) mass 

distribution of the fuselage including all added components in Figure 4-4, (ii) mass distribution of 

the fuel in Figure 4-5, and (iii) mass distribution of the entire aircraft including components, fuel, 

and engines in Figure 4-6. 

4.3 Materials and Parameters 

The skin of the aircraft was modeled using aluminum as the material. The engines were 

modeled using steel. Both the aluminum and steel were modeled with the LS-DYNA 
4-5 

Figure 4-3. Full SPH Model of the F-15E (Top) and SPH Model With 

Aircraft Skin Removed (Bottom) 

Table 4-2. Mass of F-15E Components in the SPH Model 

Component Mass 

Engines 4,326 kg [9,537 lb] 

Fuel 15,773 kg [34,774 lb] 

 Internal 5,954 kg [13,126 lb] 

 External 5,356 kg [11,808 lb] 

 CFT 4,465 kg [9,844 lb] 

Fuselage (Includes All Major Components) 13,371 kg [29,477 lb] 

Total 33,472 kg [73,793 lb] 
4-6 

Figure 4-4. Fuselage and Component Mass Distribution as Compiled in 1-m [3.3-ft] 

Increments From the SPH Model 

Figure 4-5. Fuel Mass Distribution as Compiled in 1-m [3.3-ft] Increments 

From the SPH Model 

F15-E SPH Fuselage Mass Distribution

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 2 4 6 8 10 12 14 16 18 20

Position (m)

Mass Distribution (kg/m)

Total Fuselage

Wing

Gear

Equipment

Payload

Tail

Fuselage

F15-E SPH Fuel Mass Distribution

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16 18 20

Position (m)

Mass Distribution (kg/m)

Total Fuel

External Fuel

CFT

Internal Fuel
4-7 

Figure 4-6. Total Aircraft Mass Distribution as Compiled in 1-m [3.3-ft] 

Increments From the SPH Model 

*MAT_PLASTIC_KINEMATIC material model (Livermore Software Technology Corporation, 

2003a). Table 4-3 lists the values used in the initial analysis. 

The fuel was modeled as a liquid using the LS-DYNA keyword *MAT_NULL, which defines a 

material with no yield strength and behaves with fluidlike characteristics. The use of 

*MAT_NULL requires an equation of state that determines the hydrostatic, or bulk, behavior of 

the material. The LS-DYNA keyword *EOS_GRUNEISEN is used to define the equation of 

state (Livermore Software Technology Corporation, 2003a). Table 4-4 lists the fluid parameters 

used in LS-DYNA. Note that the density of the fuel has been adjusted to that of aluminum. This 

was required for computational stability. LS-DYNA, and the SPH method in general, does not 

handle situations where vastly different densities (or masses) are found between closely 

neighboring particles. It is important to note that this does not affect the weight of the fuel, as 

the mass is explicitly defined at each node. 

Table 4-3. Metal Material Properties Used in the SPH Model 

Aluminum Steel 

Density 2,770 kg/m3 [173 lb/ft3] 7,830 kg/m3 [489 lb/ft3] 

Young’s Modulus 69.0 × 109 Pa [10,008 ksi] 2.01 × 1011 Pa [29,152 ksi] 

Yield Stress 95.0 × 106 Pa [13.8 ksi] 3.49 × 107 Pa [5.06 ksi] 

Poisson Ratio .33 .3 

Failure Strain 0.4 0.05 

Table 4-4. Properties for Fluids Used in the SPH Model 

*MAT_NULL

Density 2,770 kg/m3 [173 lb/ft3] 

Pressure Cutoff −1.0 Pa [−1.45 × 10−7 ksi] 

Dynamic Viscosity 100 Pa-s [1.45 × 10−5 ksi-s] 

Gruneisen Constants

C 1,560 m/s [1,560 ft/s] 

S1 2.0 

Gamma 1.1 

F15-E SPH Model Mass Distribution

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 2 4 6 8 10 12 14 16 18 20

Position (m)

Mass Distribution (kg/m)

Total Fuselage

Total Fuel

Engines

Total Aircraft
5-1 

5 RIGID WALL IMPACT ANALYSIS 

5.1 Introduction 

As discussed in Section 3.1, the Riera method (Riera, 1968) makes the assumption that the 

target is rigid. Thus, in this chapter, impact forces based on a rigid wall were calculated. The 

impact forces were calculated by two methods: the Riera method (Riera, 1968) and using the 

smooth particle hydrodynamic (SPH) aircraft model described in Chapter 4. Impact forces 

computed by the Riera method are presented in Section 5.2, and Section 5.3 presents the 

impact forces using the SPH aircraft model. 

5.2 Impact Forces Using the Riera Method 

As was discussed in Chapter 3, the Riera method (Riera, 1968) requires that the mass 

distribution and the crush force along the aircraft’s length are known. Because the F-15E mass 

distribution was not available for this project, values from the SPH model (Figure 4-6) described 

in Chapter 4 were used. To obtain a crush force, values Sugano, et al. (1993) reported for the 

F-4 aircraft (Figure 5-1) were scaled to obtain the F-15E values. This approach is believed to 

be suitable because the F-15E is similar in size and weight to the F-4 aircraft as shown in 

Table 5-1. 

Figure 5-1. Crush Force for the F-4 (Sugano, et al., 1993) and Crush Force for the F-4 

Scaled to the Length of the F-15E [1 m = 3.28 ft; 1 N = 0.22 lbf] 

Crush Force

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

0 2 4 6 8 10 12 14 16

Position (m)

Force (N)

F-4

F-4 Scaled to F-15 Length
5-2 

Table 5-1. Data for the F-4 and F-15E Aircraft 

Aircraft Component F-4 F-15E 

Overall Length 17.8 m [58.4 ft] 19.43 m [63.75 ft] 

Wing Span 11.8 m [38.7 ft] 13.05 m [42.82 ft] 

Weight Empty 12,776 kg [28,171 lb] 14,376 kg [31,700 lb] 

Maximum Ordinance Load 8,480 kg [18,698 lb] 11,111 kg [24,500 lb] 

Maximum Takeoff Weight 27,900 kg [61,519 lb] 33,560 kg [74,000 lb] 

Internal Fuel 4,735 kg [10,440 lb] 5,953 kg [13,126 lb] 

Number of Engines 2 2 

Engine Type GE J79 F100-PW-229 

Engine Weight, Each 1,791 kg [3,949 lb] 1,678 kg [3,700 lb] 

Scaling was performed in two steps: (i) data for the F-4 were scaled by length to obtain the 

modified values for the F-4 also given in Figure 5-1 and (ii) the values were scaled linearly by 

the unit masses of the two aircraft (higher unit mass produced higher crush force) to obtain the 

F-15E values in Figure 5-2. When scaling by length, the total area under the curve (force times 

distance) was unchanged. When scaling by the unit mass, the crush force for the F-15E was 

found to be higher than for the F-4 because its unit mass was higher than that of the F-4 at 

some locations along the length of the aircraft. 

The Excel spreadsheet program, previously described in Section 3.3, calculated the impact 

forces using the Riera method for the F-15E aircraft impacting a rigid surface at 112 m/s 

[367 ft/s] (Figure 5-3). These calculations used adjustment factors for mass and crush force 

that were previously shown in Section 3.3 (Figure 3-7) to provide good correlation to measured 

Figure 5-2. Crush Force for the F-15E Scaled from the F-4 Aircraft Using Distributed 

Mass in Figure 4-6 {190 m/s [623 ft/s]; 1 N = 0.22 lbf} 
5-3 

Figure 5-3. Impact Force Computed by the Riera Method (Riera, 1968) for the F-15E 

Impacting a Rigid Surface at 112 m/s [367 ft/s]. Riera Calculations Used the Mass 

Distribution from Figure 4-6 and Crush Force from Figure 5-2 {1 N = [0.22 lbf]}. 

impulse force for the F-4 aircraft. A constant adjustment factor (constant over the full length of 

the aircraft) of 0.75 was applied to the crush force, and the nonuniform adjustment factor 

(Figure 3-7) was used for the distributed mass. 

Similar calculations at different impact velocities yielded the impact forces in Figures 5-4 and 

5-5. Subsequently, revisions were made to the mass distribution of the F-15E by summing 

particle masses from the SPH model over different increments along the length of the aircraft. 

Smaller increments produce more variation in the unit mass along the aircraft’s length. 

However, if the increments are too small, no SPH particles may lie in the interval and a zero 

mass value is obtained. Such values are artificial and are avoided by increasing the interval 

over which the particle masses are summed. Therefore, an increment of 0.4 m [1.3 ft] was used 

in the final calculations. 

5.3 Impact Forces Using the SPH Model 

LS-DYNA analyses were performed using the SPH aircraft model discussed in Chapter 4 to 

simulate an F-15E impacting a rigid wall. The simulations used the LS-DYNA 

RIGID_WALL_FORCES option (Livermore Software Technology Corporation, 2003a), which 

places a rigid wall at a defined location and calculates the equivalent reaction force on the wall 

due to the aircraft impact. The simulations were performed for aircraft speeds of 112 and 

190 m/s [367 and 623 ft/s]. Figures 5-6 and 5-7 show the results of the SPH model simulation 

along with a comparison to the Riera-calculated impact forces, previously shown in Figures 5-3 

and 5-4. 

Figure 5-7 indicates that the SPH model shows better agreement with the Riera calculation at 

the higher impact speed of 190 m/s [623 ft/s]. However, Figure 5-6 shows that at the lower 

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Time (sec)

Force (N)
5-4 

Figure 5-4. Impact Force Computed by the Riera Method (Riera, 1968) for the F-15E 

Impacting a Rigid Surface at 190 m/s [623 ft/s]. Riera Calculations Used the Mass 

Distribution from Figure 4-6 and Crush Force from Figure 5-2 {1 N = [0.22 lbf]}. 

Figure 5-5. Impact Force Computed by the Riera Method (Riera, 1968) for the F-15E 

Impacting a Rigid Surface at 215 m/s [705 ft/s]. Riera Calculations Used the Mass 

Distribution from Figure 4-6 and Crush Force from Figure 5-2 {1 N = [0.22 lbf]}. 

0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.20E+08

1.40E+08

1.60E+08

0 0.02 0.04 0.06 0.08 0.1 0.12

Time (sec)

Force (N)

0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.20E+08

1.40E+08

1.60E+08

1.80E+08

2.00E+08

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Time (sec)

Force (N)
5-5 

Figure 5-6. Comparison of Impact Forces Calculated by the Riera Method (Riera, 1968) 

and the SPH Model for an Impact Velocity of 112 m/s [367 ft/s] into a Rigid Surface 

Figure 5-7. Comparison of Impact Forces Calculated by the Riera Method (Riera, 1968) 

and the SPH Model for an Impact Velocity of 190 m/s [623 ft/s] into a Rigid Surface 

F-15E Crush Force @ 112 m/s (367 fps)

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Time (sec)

Force (lb)

Riera

SP H Simulation 112 m/s

F-15E C rush Force @ 190 m/s (623 fps)

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

4.00E+07

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

T ime (sec)

Force (lb)

Riera

SPH sim ulation 190 m /s
5-6 

impact speed of 112 m/s [367 ft/s] the peak impact force is lower and has an overall impulse 

that is much lower than the Riera method (Riera, 1968). This can be attributed to the higher 

speed impact force being dominated by momentum, where material crush strength has less of 

an effect. The SPH method and the particular mesh used for the skin are not particularly well 

suited for accurate modeling of bending or crushing. In addition, some of the missing structural 

components that were lumped in with the skin may have more of an effect on impact forces at 

the lower speed. 

To better match the Riera calculations, some of the material properties of the skin strength 

and stiffness and the dynamic viscosity of the aircraft fuel were modified through several 

iterations until better agreement was obtained. The modified parameters included are shown in 

Table 5-2. 

The Young’s modulus required a drop of two orders of magnitude before better agreement was 

established for the lower speed case. Some justification for doing this comes from the 

methodology used to model the aircraft structure and components. Because all of the internal 

structure and other major components were lumped in with the weight of the skin, the effective 

thickness/volume of the skin is much greater than reality. Lowering the skin stiffness is one way 

to offset this. The dynamic viscosity of the fuel was also increased to obtain better agreement 

with the Riera method. The results of the rigid wall impact case with the modified parameters 

are shown in Figures 5-8, 5-9, and 5-10. The additional simulation performed at an impact 

speed of 215 m/s [705 ft/s] is the same impact speed that was used in the original test of 

Sugano, et al. (1993). As, noted previously the Riera-calculated impact forces are shown in 

Figures 5-3 and 5-4. 

On the basis of Figures 5-8, 5-9, and 5-10, better agreement is observed using the modified 

parameters for both speeds. This further emphasizes that the SPH method is better suited for 

high speed impacts where momentum governs the loading on the wall. 

5.3.1 Mesh Sensitivity 

A mesh sensitivity study was conducted to determine whether any significant differences in the 

impact forces on the rigid wall would be observed. Mesh refinement was done on the internal 

fuel and conformal fuel tanks, and the external fuel tanks were remeshed to improve uniformity, 

which actually decreased the number of SPH particles in the external tanks by 12,108 SPH 

particles. Separate models were created with (i) remeshed external tanks and the original mesh 

for the internal fuel tanks and conformal fuel tanks and (ii) remeshed external tanks and internal 

and conformal fuel tanks. For both cases, the original mesh for the fuselage was used. 

Mesh refinement to the internal and conformal fuel tanks increased the number of fuel SPH 

particles in the internal tanks by 33,416 particles and number of fuel particles in the conformal 

fuel tank by 42,480 particles. The fuselage skin was not remeshed, because significant effort 

was required for its remeshing. However, if major differences were observed by the remeshing 

of the fuel, a mesh convergence study would be undertaken for the fuselage as well. Also, it 

was important to keep the total number of SPH particles low enough. 

Table 5-2. Final Parameters for Aluminum and Fuel Used in the SPH Model 

Aluminum 

Young’s Modulus (Pa) 69.0 × 107

Yield Stress (Pa) 40.0 × 106

Fuel 

Dynamic Viscosity (Pa-s) 1.0 × 105
5-7 

Figure 5-8. Comparison of Impact Forces Calculated by the Riera Method (Riera 1968) 

and the Revised SPH Model for an Impact Velocity of 112 m/s [367 ft/s] Into a 

Rigid Surface 

Figure 5-9. Comparison of Impact Forces Calculated by the Riera Method (Riera 1968) 

and the Revised SPH Model for an Impact Velocity of 190 m/s [623 ft/s] into a 

Rigid Surface

F-15E Crush Force @ 112 m/s (367 fps)

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Time (sec)

Force (lb)

Riera

SPH 112m/s Stiffness Mod

F-15E C rush Force @ 190 m/s (623 fps)

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

4.00E+07

0 0.02 0.04 0.06 0.08 0.1 0.12

Time (sec)

Force (lb)

Riera

190mps Stiffness Mod
5-8 

Figure 5-10. Comparison of Impact Forces Calculated by the Riera Method 

(Riera, 1968) and the Revised SPH Model for an Impact Velocity of 215 m/s [705 ft/s] 

Into a Rigid Surface 

SPH impact simulations could be conducted in a reasonable amount of time and the memory 

capacity of the computer system would not be exceeded while still achieving accurate results 

(Figue 5-10). 

The SPH model’s mass distribution was also refined The mass distribution presented earlier 

(Figure 4-4) was calculated for 1-m [3.3-ft] increments along the length of the fuselage. 

However, smaller increments lead to greater variability in the unit mass, even though the total 

mass and mass distribution of the SPH model has not changed. By varying the increment size, 

a value of 0.4 m [1.3 ft] gave a similar variability in mass as the F-4 aircraft, as shown by 

Sugano, et al. (1993). 

Figures 5-11 and 5-12 show the distributed mass for the F-15E computed with a 0.4-m [1.3-ft] 

increment. Figure 5-11 shows the mass distribution for the unrefined SPH mesh, and 

Figure 5-12 shows the mass distribution using the refined SPH mesh. Comparing Figures 5-11 

and 5-12, relatively small differences are apparent. The overall mass of the SPH model has not 

changed for any of these cases. 

For completeness, the crush force for the F-15E aircraft was recomputed using the mass 

distribution of Figure 5-12 to obtain the values shown in Figure 5-13. Recall that the crush force 

for the F-15E was scaled from the crush force measured for the F-4 by first scaling by length 

and then by unit mass. When compared to the initial calculation of the crush force shown in 

Figure 5-2, determined using the mass distribution in Figure 4-6, the crush force in Figure 5-13 

has more variability and a slightly higher peak value. These changes are consistent with the 

changes in mass distribution between Figures 4-6 {computed for a 1-m [3.3-ft] increment along 

F-15E Crush Force @ 215 m/s (705 fps)

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0 0.02 0.04 0.06 0.08 0.1

Time (sec)

Force (lb)

Riera

SPH 215m/s Stiffness Mod
5-9 

Figure 5-11. Mass Distribution From the Original SPH Model Obtained by Summing the 

Masses Over 0.4-m [1.3-ft] Increments 

Figure 5-12. Mass Distribution From the Modified SPH Model Obtained by Summing the 

Masses Over 0.4-m [1.3-ft] Increments 

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12 14 16 18 20

Position (m)

Unit weight (kg/m)

Fuselage

Internal fuel

Engine, front

Engine, rear

External Fuel

Confromal fuel

Total

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12 14 16 18 20

Position (m)

Unit weight (kg/m)

Fuselage

Internal fuel

Engine, front

Engine, rear

External Fuel

Confromal fuel

Total
5-10 

Figure 5-13. F-15E Crush Force Computed from the F-4 Crush Force Using 

the Mass Distribution of Figure 5-12 

the aircraft’s length} and Figure 5-12 {computed for a 0.4-m [1.3-ft] increment along the 

aircraft’s length}. 

New impact simulations, using the SPH model with the modified fuel mesh, were performed and 

compared with Riera calculations made using the mass distribution and crush force for the 

refined mesh computed with a 0.4-m [1.3-ft] increment. Figures 5-14 and 5-15 show the impact 

forces, computed by the Riera and SPH methods, for impact velocities of 112 and 215 m/s 

[367 and 705 ft/s], respectively. 

Consistent with previous results discussed in Section 5.3, the simulation at the higher impact 

speed (Figure 5-15) shows the best overall agreement between the SPH model and the 

Riera method. Figure 5-16 shows a comparison of impact force histories on the rigid wall 

computed with the SPH model with different meshes. The calculations were performed with the 

original mesh, the modified fuel mesh, and the modified external tank mesh. The mesh study 

concluded that no significant differences were observed between the original mesh and 

modified meshes. 

For example, the peak impact forces are higher at some points and lower in others, but overall 

they are very similar. The small differences are believed to be the result of the refined fuel 

mesh and how LS-DYNA computes particle interaction (i.e., particle-to-particle contact between 

different parts). When more fuel particles are included due to mesh refinement, their presence 

partially slows down the particles used in the rear of the aircraft as it approaches the wall. 
5-11 

Figure 5-14. Comparison of Impact Forces Calculated by the Riera Method (Riera, 1968) 

and the SPH Model Using LS-DYNA Version 971 for an Impact Velocity of 

112 m/s [367 ft/s] 

Figure 5-15. Comparison of Impact Forces Calculated by the Riera Method (Riera, 1968) 

and the SPH Model Using LS-DYNA Version 971 for an Impact Velocity of 

215 m/s [705 ft/s] 

F-15E C rush Force @ 112 m/s (367 fps)

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

2.00E+07

0 0.05 0.1 0.15 0.2 0.25

Time (sec)

Force (lb)

Riera

SPH Sim ulations 112 m /s

F-15E C rush Force @ 215 m/s (705 fps)

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0 0.02 0.04 0.06 0.08 0.1 0.12

Time (sec)

Force (lb)

Riera

SPH Sim ulation 215 m /s
5-12 

Figure 5-16. The Effect of SPH Model Mesh Refinement on Impact Force Calculated With 

LS-DYNA Version 971 for an Impact Velocity of 112 m/s [367 ft/s] 

Results for higher speed impact cases gave similar results. Note that the simulations used to 

investigate the fuel mesh refinements were run using LS-DYNA Version 971 due to its release 

during the course of this work. However, a simulation of the revised external tank mesh was run 

using both LS-DYNA Versions 970 and 971 to check for any differences and the results are 

shown in Figure 5-17. Figure 5-17 shows that differences between LS-DYNA Versions 970 

and 971 are considered insignificant. 

5.3.2 Contact Modeling 

One issue that occurred during the impact modeling using the SPH model involved particle 

contact with solid elements not working properly. It was observed that particles were passing 

through a wall made of solid elements without interaction as shown in Figure 5-18. If a 

significant number of particles pass through the wall, not all of the impact energy will be 

transferred to the structure. 

By investigating the different contact options available in LS-DYNA, it was determined that using 

the SOFT=1 (soft constraint formulation) option worked best for the impact cases being 

simulated. This option is effective for contact between materials of different stiffness or 

dissimilar mesh densities (Livermore Scientific Technology Corporation, 2003a). 

Another LS-DYNA option used was to invoke a solid element thickness (SLDTHK) for the 

purpose of contact. This is equivalent to covering the brick elements with null shell elements. 

To improve computation speed, only the elements with the potential for contact were defined in 

the segment sets for contact. This can dramatically decrease the computation time required 

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

1.4E+07

0.00 0.05 0.10 0.15 0.20 0.25

time (s)

Force (lb)

112 m/s-Fuel Mesh

Ref ined

112 m/s-Original

mesh

112 m/s-External tank

mesh coarsened
5-13 

Figure 5-17. Comparison of Impact Forces Calculated with LS-DYNA Versions 970 and 

971 for an Impact Velocity of 112 m/s [367 ft/s] 

Figure 5-18. Impact Simulation Showing Contact Problem That Allowed 

SPH Particles of the F-15 Model To Pass Through the Wall 

during the contact search algorithms in LS-DYNA. These settings considerably improved the 

contact situation and minimized the number of particles passing through the solid elements 

without interaction. 

112 m/s Impact Force C omparision of R esults from 

Ls-Dyna v970 and v971

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

1.4E+07

0.00 0.05 0.10 0.15 0.20 0.25

tim e (s)

Force (lb)

112 m /s v971

112 m /s v970
6-1 

6 FULL-SCALE IMPACT SIMULATION 

6.1 Introduction 

Chapter 4 discussed the details of constructing the smooth particle hydrodynamic (SPH) model 

of the F-15E aircraft. Chapter 5 utilized the SPH model to determine the impact forces 

produced when striking a rigid wall, and comparisons were also made with the impact forces the 

Riera method (Riera, 1968) calculated. The SPH model underwent a number of refinements to 

the mesh used for the fuel-related components to improve the match with the Riera-calculated 

impact forces. Overall, the SPH aircraft model produced good results. 

This chapter discusses an impact analysis of the SPH aircraft model striking a reinforced 

concrete wall. 

6.2 Finite Element Modeling of a Reinforced Concrete Wall 

The reinforced concrete wall to be modeled consisted of a 76-m [250-ft]-long section with 

two buttresses spaced equally along its length. Due to the size of the wall, and to allow for a 

reasonable computation time, only a portion of the wall was modeled. This portion included the 

two buttresses and the wall between them. An isometric view of the wall and its dimensions are 

shown in Figure 6-1. 

The section of the wall that was modeled was 26.5 m [87 ft] long and 12.2 m [40 ft] high, with a 

buttress at each end. Specific dimensions of the buttress are shown in Figure 6-1. The wall is 

1.2 m [4 ft] thick and has #11 reinforcement steel (rebar) spaced at 30.5 cm [12 in] in both 

directions with 15.2 cm [6 in] of concrete cover. 

The reinforced concrete wall finite element model had a total of 769,904 elements: 

704,016 solid elements for the concrete and 65,888 beam elements for the rebar. The rebar 

beam elements were explicitly defined within the solid elements and shared co-incident nodes. 

Figure 6-1. Dimensions of the Reinforced Concrete Wall and Buttresses 
6-2 

There were 18 solid elements through the total thickness of the wall, with 3 solid elements to 

model the thickness of the concrete cover over the rebar. Note that the finite element mesh 

shown in Figure 6-2 is not uniform and is refined in the area where the aircraft impact will occur. 

The elements in this area had a discretization interval of approximately 7.6 cm [3 in]. 

The finite element model of the wall had boundary conditions applied to the top and bottom to 

account for the contribution due to the intersection of a floor and roof with the wall. Thus the 

boundary conditions consisted of fixing the translational degrees of freedom along the wall 

boundary but with free rotation about an axis parallel with the length of the wall. 

The concrete material properties used are those given in Section 2. The reinforcement steel 

(rebar) was modeled using the LS-DYNA *MAT_PLASTIC_KINEMATIC material model, and the 

properties were consistent for rebar having a yield strength of 414 MPa [60 ksi]. Both the 

concrete and steel materials used a model for failure based on the effective plastic strain. Once 

the specified plastic strain value was reached, the element was eroded and no longer included 

in the calculations. 

6.3 Simulation of the F-15E SPH Model Impacting a Reinforced 

 Concrete Wall 

This section will discuss the results of the LS-DYNA simulation of the F-15E SPH model 

impacting the reinforced concrete wall given in Section 6.2. 

Figure 6-2. Finite Element Model of the Reinforced Concrete Wall and Buttresses 
6-3 

For the following impact simulations, 2 impact speeds were selected based on what was used 

for the rigid surface impact analysis: 112 and 190 m/s [367 and 623 ft/s]. The aircraft impacted 

normal to the wall, with the nose directly in the center. The SPH aircraft model used the 

modified external tank mesh as discussed in Section 5.3.1. Figure 6-3 shows the complete 

finite element model of the reinforced concrete wall and the SPH aircraft model prior to impact. 

Figure 6-4 shows progressive snapshots of the simulation of the aircraft striking the wall at 

190 m/s [623 ft/s]. The view of the wall shows the response of the backside of the wall. 

The colored contours shown in Figure 6-4 are the effective plastic strain in the concrete 

elements and are representative of large-scale tensile or shear cracking taking place. 

Figure 6-5 shows a view from the front of the wall near the end of the simulation. The aircraft 

has been removed to show the details of the wall. As indicated by the rear and front views, the 

aircraft has breached the wall. When the simulation was stopped at this point, there still was 

significant wall motion; therefore, it was expected that large pieces of the wall would continue to 

break off yielding a larger breach area than shown. During the impact simulation, the wall 

began to fail as tensile forces caused the rear face rebar to break and concrete elements were 

deleted due to excessive plastic strain. A major portion of the damage occurred due to the 

impact of the conformal and internal fuel load, and the wall was breached when the engines 

struck the wall. Figure 6-6 shows a cut plane view vertically through the center of the wall, 

when the internal fuel load and engines struck the wall. 

A second impact analysis was also performed at an impact speed of 112 m/s [367 ft/s]. 

Figure 6-7 shows progressive snapshots of the backside of the wall during simulation of the 

aircraft striking the wall. 

Figure 6-3. Reinforced Concrete Wall and Position of the F-15E 

SPH Model Just Before Impact 
6-4 

Figure 6-4. Response of the Wall Backside Showing Surface Damage and Contours of 

Effective Plastic Strain for the F-15E Impact at 190 m/s [623 ft/s] 

Figure 6-5. Front Face Wall Damage and Contours of Effective Plastic Strain After the 

F-15E Impact at 190 m/s [623 ft/s] 
6-5 

Figure 6-6. Section Through the Wall and F-15E When First External Fuel Tank Reaches 

the Wall (Left) and When the Engines Contact the Wall (Right) at an Impact 

Velocity of 190 m/s [623 ft/s] 

Figure 6-7. Sequence Showing Wall Back Surface Damage and Contours of Effective 

Plastic Strain for the F-15E Impact at 112 m/s [367 ft/s] 
6-6 

Figure 6-8 shows the final deformed shape of the wall from the front of the wall. For this impact 

velocity, the wall had not been breached by the aircraft; however, substantial damage was 

evident from the eroded elements and the distribution of effective plastic strain. Some evidence 

of possible cracking was indicated by the large plastic strains at the intersection with the 

buttresses and in the area where the aircraft struck the wall. A displacement time history of a 

node located at the center of the backside of the wall is shown in Figure 6-9. This time history 

indicated that the maximum displacement of the wall occurred at 0.2 seconds and had a 

magnitude of 0.44 m [17 in]. Subsequently, the wall began to spring back and the simulation 

was stopped because at this point the aircraft model had disintegrated and transferred all of its 

energy to the wall. 

Figure 6-8. Front Face Wall Damage and Contours of Effective Plastic Strain After the 

F-15E Impact at 112 m/s [367 ft/s] 

Figure 6-9. Time History of the Wall Back Surface Displacement Located at the Center of 

Impact of the F-15E at 112 m/s [367 ft/s] 
7-1 

7 SUMMARY AND CONCLUSIONS 

7.1 Summary 

NRC issued a final rule (74 FR 28111; June 12, 2009) that will require applicants for new 

power reactors to perform an assessment of the effects on the reactors of the impact of a 

large, commercial aircraft. As a result, NRC amended 10 CFR Part 50 to include Section 

10 CFR 50.150, Aircraft Impact Assessment. Subsequently, NRC issued Draft Regulatory 

Guide DG–1176 (NRC, 2009), which sets forth a method that NRC considers acceptable for 

satisfying the regulations in 10 CFR 50.150. NRC has endorsed (NRC, 2009) the use of 

guidance described in NEI 07-13 (NEI, 2009) as an acceptable methodology for the assessment 

of aircraft impacts for new nuclear power reactors. 

NEI 07-13 (NEI, 2009) states that two structural failure modes need to be evaluated: (i) local 

failure characterized by scabbing and perforation due to impact of the aircraft engines and 

(ii) global failure in the form of plastic collapse due to impact of the entire aircraft. One 

approach for determining both local and global structural failure is the explicit modeling of the 

aircraft, the target (e.g., a building), and the simulation of the aircraft crashing into the structure. 

The CNWRA has developed the computational capabilities to perform this type of analysis. 

The objective of this report was to present a detailed overview of the work the CNWRA 

performed as reported by Cox, et al. (2007, 2006, 2005). This CNWRA work was 

performed under the NRC high-level waste repository safety program. The overall objective 

of this work was to develop the ability to computationally simulate and analyze the effects of 

an aircraft crashing into reinforced concrete structures. The structural analysis should evaluate 

both local and global structurewide responses (NEI, 2009). Thus, two structural failure modes 

need to be evaluated: (i) local failure characterized by scabbing and perforation due to impact 

of the aircraft engines and (ii) global failure in the form of plastic collapse due to impact of the 

entire aircraft. 

To achieve this objective, a methodology needed to be developed, which included: 

(i) selection of the appropriate concrete damage model that was readily available in 

LS-DYNA, (ii) an accurate characterization of the concrete damage model’s material 

parameters, (iii) a comparison of analytical and numerical methods for calculating the 

impact force, and (iv) development of an accurate representation of the F-15E aircraft 

using LS-DYNA. 

Chapter 2 discussed the material modeling of concrete. In particular, Section 2.1 presented the 

LS-DYNA concrete damage model that was used in this study. Among the concrete material 

models available in LS-DYNA, the concrete damage model based on the formulation of 

Malvar, et al. (1997) was chosen. The concrete damage model’s formulation was thoroughly 

discussed. The selection of the numerical values for the model’s material parameters was 

based on recommendations given in the LS-DYNA Keyword User’s Manual (Livermore Software 

Technology Corporation, 2003a) and in Malvar, et al. (1997). 

To investigate the accuracy of modeling local failure of a reinforced concrete structure, 

Section 2.2 presented the experimental work of Muto, et al. (1989a,b,c) and Esashi, et al. 

(1989). These experiments involved impact of small-, intermediate-, and full-scale engine 

simulants impacting reinforced concrete panels. The engine simulants were based on the 

GE J79 engine used in the F-4 Phantom fighter aircraft. The experimental results described 
7-2 

the damage to the reinforced concrete panels and the panel’s back surface displacement due 

to the impact. 

LS-DYNA simulations were performed using finite element models of the different engine 

simulants impacting reinforced concrete panels. The results in terms of predicted damage 

showed very good agreement with the experimental results of Muto, et al. (1989a,b,c) and 

Esashi, et al. (1989). The agreement between the LS-DYNA numerical simulations and 

experimental results gave confidence that the initial selection of the material parameters needed 

for the concrete damage model was appropriate. The displacement time history of the back 

surface displacement from the LS-DYNA simulation using the full-scale engine simulant 

matched the measured experimental results in terms of peak displacement. However, it 

was noted that the bounce back of the reinforced concrete panel was not observed in the 

LS-DYNA simulation. 

Therefore, Section 2.3 presented a sensitivity study to determine specific values of the damage 

parameters such that the LS-DYNA simulation would also predict the bounce back of the back 

surface displacement. The results of the study determined values of the damage parameters so 

that the LS-DYNA simulation results exhibited the bounce back. 

However, now the LS-DYNA back surface displacement time history had an unexpected 

decrease in the displacement rate between approximately 4 and 8 milliseconds . The 

conclusion was that there appeared to be a coupling between the concrete material parameters 

and the crush behavior of the LS-DYNA engine simulant and that this required further 

numerical studies. 

Evaluating the accuracy of modeling global structural failure, the force time history analysis 

method and the missile target interaction analysis method were investigated. 

Chapter 3 introduced the force-time history analysis method of Riera. The objective was to 

study the Riera method (Riera, 1968), which computes the loads imparted to a rigid surface by 

an aircraft crash. Riera, calculated impact and impulse forces were compared to the 

experimental data of Sugano, et al. (1993). The results compared favorably to experimentally 

measured loads of Sugano, et al. (1993). In general, it was found the Riera method would 

overestimate the impact and impulse forces making the Riera method conservative. 

Chapter 4 presented details of the numerical modeling of the F-15E aircraft. Modeling of impact 

simulations involves large deformations. It is known that the finite element method can have 

difficulties solving very large deformation problems where significant mesh (element) distortion 

occurs. Therefore in this report, a mesh-free approach using the SPH method, available in 

LS-DYNA, was used. 

Because limited data were available for the F-15E, the external geometry of the aircraft was 

constructed from available CAD files. An NRC furnished isometric drawing of the F-15, was 

used to determine approximate locations of internal components because the drawing was not 

dimensioned. Using the known weights and location of the aircraft’s components, their mass 

contributions were placed in the external skin of the aircraft. Fuel distribution and information on 

the aircraft’s engines were obtained from various sources. Based upon all of this information, 

an SPH model of the F-15E aircraft was developed. 

In Chapter 5, the impact forces calculated using the Riera method (Riera, 1968) were compared 

to those produced by the LS-DYNA impact simulation using the SPH model of the F-15E 
7-3 

aircraft. Velocities of 112 and 190 m/s [367 and 623 ft/s] were used in the comparisons. 

The first comparison indicates that at the lower impact speed of 112 m/s [367 ft/s], the LS-DYNA 

simulation produces a peak impact force that is 33 percent lower than the impact force the 

Riera method calculated. This may be due the crush force (i.e., structural stiffness) of the 

aircraft having a significant effect on the impact force. The second comparison shows that 

for the impact speed of 190 m/s [623 ft/s], the impact force from the LS-DYNA simulation is 

4 percent lower than the impact force the Riera method (Riera, 1968) calculated. The better 

agreement with the Riera calculation at the higher impact velocity may be due to the dominance 

of the inertial force with the differences in crush force becoming less significant. 

Finally, Chapter 6 used the missile target interaction analysis method to model the global failure 

of a reinforced concrete wall. The impact into a reinforced concrete wall was simulated using 

the LS-DYNA SPH model of the F-15E aircraft. At an impact velocity of 112 m/s [367 ft/s], 

considered as low, the wall withstands the impact but suffers damage. At a 190-m/s [623-ft/s] 

impact velocity, the model predicts significant damage with the wall being breached. 

7.2 Conclusions 

The assessment of commercial and military aircraft crash hazards and their impact on nuclear 

and other critical facilities are important to the owners of these facilities and many federal 

government agencies. Based on the results summarized previously on the work the CNWRA 

performed for NRC high-level waste repository program, some conclusions have been made 

regarding the effectiveness of the methodology developed for simulation of the response of 

reinforced concrete structures due to aircraft crash impact. 

Application of the concrete damage model for impact simulations using idealized aircraft engine 

models striking reinforced concrete panels matched experimentally observed damage modes. 

However, the panel’s back surface displacements did not capture the observed bounce-back 

behavior. Attempts were made to adjust the concrete damage material parameters to capture 

the bounce-back behavior. By performing a sensitivity study, the bounce-back behavior was 

captured; however, these adjustments to the concrete material parameters resulted in an offset 

in the LS-DYNA calculated displacement time history. 

A second sensitivity study to further investigate the displacement offset was performed, in which 

material parameters used in the LS-DYNA engine simulant model were varied. Based on the 

results of the sensitivity study, it was determined that the offset in the displacement time history 

was also affected by the collapse of the front cylinder of the LS-DYNA engine simulant model. 

The conclusion is that there appears to be a coupling between the concrete material parameters 

and the crush behavior of the LS-DYNA engine simulant. This conclusion is important because 

it demonstrates that the global response of the concrete structure is affected not only by the 

concrete material behavior, but also by the crush behavior of the engine. Therefore, it is 

recommended that additional numerical studies be performed to further investigate this 

apparent coupling and its effect on the structure’s displacement time history. 

Lack of data affects the use of the force-time history (i.e., Riera) method because it requires the 

mass distribution and the crush force along the length of the aircraft. In this current study, when 

the Riera (Riera, 1968) method was used to calculate the impact force for the F-15E aircraft, the 

required crush force was scaled from the F-4 aircraft crush force Sugano, et al. (1993) provided. 

This was considered acceptable because the F-15E is similar in size and weight to the F-4 

aircraft. Therefore, a possible limitation using the Riera method is the availability of mass 
7-4 

distribution and fuselage crush strength data. Hossain, et al. (1997) also noted this limitation. 

The development of the F-15E SPH model was also difficult due to lack of data. An isometric 

drawing of the F-15 provided only an approximate location of the internal components, and the 

F-15E’s mass distribution had to be scaled from the known mass distribution of the F-4. 

Therefore, using either the force-time history or missile target interaction method to perform a 

realistic aircraft impact assessment using a commercial aircraft would require sufficiently 

detailed data. However, obtaining this data from an aircraft manufacturer may be difficult, as it 

is usually proprietary information. 

The use of the SPH method to model the aircraft can be considered a somewhat novel 

approach. In this report, the SPH method was shown to provide an alternative to the finite 

element method for performing impact crash analysis. However, its use may only be 

appropriate when the inertial force is dominant (i.e., high velocity impact where the crush 

strength has less of an effect). As shown in Figure 5-7, at an impact velocity of 112 m/s 

[367 ft/s] the SPH model produced a significantly lower peak impact force as compared to the 

Riera method (Riera, 1968). Thus it was concluded that at low velocities, the bending, buckling, 

or crushing of the fuselage may become significant. 

Although this report focused on reinforced concrete structures, the same methodology can be 

applied to other structures that may be constructed of steel only or a combination of both steel 

and reinforced concrete. Accurately modeling the behavior of steel would be straightforward 

because constitutive models for metals that include high strain rate effects, temperature 

dependence, and failure criteria are well established. 

Additional technical issues not covered in this report that are important to address are (i) shock 

and vibration analysis of the complete structure and (ii) the evaluation of fire effects to 

determine the extent of structural damage due to possible spread of aviation fuel. For example, 

as the NIST study of the WTC terrorist attack determined, fire caused steel trusses to fail, which 

played a significant part in the structural collapse of the towers. 

As documented in this report, a significant amount of work has been accomplished in 

establishing a methodology for the simulation of the response of reinforced concrete structures 

due to aircraft crash impact. 

The experience gained from these studies will be useful for performing aircraft impact 

assessments for reinforced concrete structures of geologic repositories and other 

critical facilities.
8-1 

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