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UNIVERSITI PUTRA MALAYSIA
MOHD NORDIN BIN MOHD PILUS
FK 2007 97
THE STRUCTURAL RESPONSE OF A BUNKER SUBJECTED TO BLAST LOADING
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THE STRUCTURAL RESPONSE OF A BUNKER
SUBJECTED TO BLAST LOADING
By
MOHD NORDIN BIN MOHD PILUS
GS 15617
A Project Report Submitted in Partial Fulfillment
Of the Requirements for the Degree of
Master of Science in Structural Engineering and Construction
In the Faculty of Engineering
University Putra Malaysia
2007
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APPROVAL SHEET
This project attached here, entitled “THE STRUCTURAL RESPONSE OF A
BUNKER SUBJECTED TO BLAST LOADING” prepared and submitted by
MOHD NORDIN BIN MOHD PILUS ( GS 15617 ) in partial fulfillment of
the requirements for the Degree in Master of Science in Structural
Engineering and Construction is hereby approved.
…………………………………………………….. Date: ……………….
Supervisor
( ASSOC PROF IR DR JAMALODIN NOORZAEI )
Department of Civil Engineering, UPM
…………………………………………………….. Date: ………………
Panel Examiner
( ASSOC PROF IR DR MOHD SALEH BIN JAAFAR )
Department of Civil Engineering, UPM
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DECLARATION
I hereby declare that the thesis is based on my original work except for
quotations and citations which have been duly acknowledged. I also declare
that it has not been previously or concurrently submitted for any other
degree at UPM or other institutions.
.................................................................
MOHD NORDIN BIN MOHD PILUS
Date :
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ACKNOWLEDGEMENT
All praise for the almighty ALLAH S.W.T the most Benevolent and the most
Merciful, for giving me the strength and spirit to have this project completed
successfully.
I would like to take this opportunity to express my sincere thanks and
deepest gratitude to my supervisor, Associate Professor Ir Dr Jamaloddin
Noorzaei for his deep insight and guidance in the preparation of this work
and during the course of my studies at University Putra Malaysia. I also
would like to thank Associate Professor Ir Dr Mohd Saleh Jaafar for his
advices and assistance.
I sincerely express my appreciation to my beloved family; my wife Yusfida,
my children Rizal, Syahirah and Syakir Haziq for their companionship,
patience, understanding and continuous encouragement throughout this
challenging endeavor. Finally, I dedicate this work to my beloved parents,
without whom my achievements would have been impossible.
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ABSTRACT
In recent years there is an increasing incidence of bomb attacks on civil
engineering structures which frequently caused substantial damage or
even collapse of structures. Such incidence always results in economic loss
and more seriously loss if life. This clearly indicates that it is timely for
structural engineers to consider blast loads in their design.
There are substantial costs incurred in designing structures against blast
loads. Therefore there are only a certain category of structures which
require such design in accordance to the level of protection required. In
this paper a reinforced concrete bunker was used to represent such
structure, whereby its structural response to an external explosion of a
surface charge was investigated.
The blast load was theoretically generated based on the explosion of 300
kg of TNT at a distance of 50 meters from the structure. Both linear and
non-linear analyses were conducted using a computer program
considering the dead load alone as well as the combination of dead and
blast loads. The program utilizes the finite element method which provides
results in the form of nodal displacements and stress resultants.
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As expected, the linear analysis gave lower results than the non-linear
analysis. Linear analysis is only applicable in the linear elastic range and is
unreliable when extreme loadings are involved. Since the blast loads
caused severe effect on structures, non-linear analysis is more appropriate
for the purpose.
Blast load causes a tremendous increase of stress levels in structures,
indicating the severity of the loading. This is due to the fact that such load
acts as moving pulses loading only a small part of the structure at a time.
Therefore the structure must be design to resist the high stress levels.
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TABLE OF CONTENTS
ACKNOWLEDGEMENT
ABSTRACT
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
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CHAPTER 1 – INTRODUCTION
1.0 Introductory Remarks
1.1 Blast Loads
1.2 Nature of the Problem
1.3 Objectives of Study
1.4 Scope of Study
1.5 Organization of Report
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CHAPTER 2 – LITERATURE VIEW
2.0 Introduction
2.1 Surface Explosion
2.2 Surface Blast Parameters
2.3 Ground Shock Wave from Surface Explosions
2.4 Time Lag Between Ground Shock and Blast Pressure Arrival
2.5 External Blast Loads on Aboveground Structures
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2.5.1 Reflection from a Rigid Wall
2.5.2 Pressure Distribution Along a Rigid Wall
2.5.3 Blast Pressure on Roof, Side and Rear Wall
2.6 Blast Load on Arches
2.7 Concluding Remarks
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CHAPTER 3 - METHODOLOGY
3.0 Introduction
3.1 Research Methodology
3.2 The Structure
3.3 Load Configuration
3.3.1 Dead Load
3.3.2 Blast Load
3.3.3 Overpressure on Structure
3.3.3.1 Front Face
3.3.3.2 Rear Face
3.4 Classical Approach
3.4.1 Thin Shell Theory
3.4.2 Internal Force System in a Shell
3.4.3 Membrane Theory of Cylindrical Shells
3.4.4 Cylindrical Shell Behavior
3.4.5 Beam-Arch Analysis
3.4.5.1 Beam Analysis
3.4.5.2 Arch Analysis
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3.5 Numerical Approach
3.5.1 Virtual Work Method
3.5.2 Finite Element Formulation
3.5.2.1 Shape Functions
3.5.2.2 Strain-displacement Relationship
3.5.2.3 Stress-strain Relationship
3.6 Computer Program
3.7 Concluding Remarks
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CHAPTER 4 – ANALYSIS AND RESULTS
4.0 Introduction
4.1 Load Computation
4.2.1 Dead Load
4.2.2 Blast Load
4.3 Classical Approach
4.4 Numerical Approach
4.4.1 Input Data
4.4.2 Result
4.5 Discussion of Result
4.5.1 Linear vs Non-linear Analysis
4.5.2 Diffraction and Drag Loadings
4.5.3 Positive Phase Duration
4.5.4 Stress Distribution
4.5.5 Moment Distribution
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4.5.6 Mode Shape
4.6 Concluding Remarks
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CHAPTER 5 - CONCLUSIONS AND RECOMMENDATIONS
5.0 Conclusion
5.1 Design Recommendations
5.2 Design Philosophy
References
Appendices:
Appendix A: Drawings of Reinforced Concrete Bunker
Appendix B: Blast Load Computation
Appendix C: Manual Calculation
Appendix D: Nodal Coordinates and Element Connectivity
Appendix E: Tabulation of Displacement Values
Appendix F: Tabulation of Stress Resultant Values
Appendix G: 3-D Representation of Displacement
Appendix H: Stress Distribution
Appendix I: Moment Distribution
Appendix J: Design Calculation
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A-1 to A-3
B-1
C-1 to C-8
D-1 to D-4
E-1 to E-4
F-1 to F-4
G-1 to G-6
H-1 to H-2
I-1 to I-3
J-1 to J-2
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LIST OF TABLES
CHAPTER 2 – LITERATURE VIEW
Table 2.1: Peak Dynamic Pressure vs Drag Coefficient
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APPENDIX B – Blast Load Computation
Table B1: Blast load parameters due to a charge of 300 kg TNT
at a distance of 50 m Table B2: Blast load parameters due to a charge of 500 000 kg
TNT at a distance of 250 m.
B-1
B-1
APPENDIX C – Manual Calculation
Table C1: First moment of area for each section
Table C2: Longitudinal stress and in-plane shear stress
Table C3: Vertical and horizontal force components
Table C4: Summary of numerical calculations
Table C5: Transverse moments
Table C6: Transverse stresses
Table C7: Stress resultants summary
Table C8: Displacements from manual calculation
Table C9: Displacements from numerical approach
C-2
C-2
C-3
C-5
C-6
C-7
C-7
C-8
C-8
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LIST OF FIGURES
CHAPTER 2 – LITERATURE VIEW
Figure 2.1: Blast load categories
Figure 2.2: Comparison of peak pressure attenuation against
scaled distance
Figure 2.3: Arrival time vs scaled distance
Figure 2.4: Typical free-air pressure-time history
Figure 2.5: Duration of pressure rise to peak value
Figure 2.6: Duration of pressure decay to ambient pressure
Figure 2.7: Positive phase duration for 1000 kg of TNT
Figure 2.8: Comparison of simulated and predicted air blast
pressure
Figure 2.9: Simulated acceleration time history on rock surface at
10 m distance from charge.
Figure 2.10: Simulated PPA attenuation on rock surface vs scaled
distance.
Figure 2.11: The envelope function for simulated acceleration time
history on rock surface at 10 m distance with a 2 ton
charge
Figure 2.12: Definition of stress wave duration.
Figure 2.13: Definition of principal frequency (PF)
Figure 2.14: Principal frequency of shock wave on rock surface
under different charge weight
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Figure 2.15: Predicted and simulated power spectrum of an
acceleration time history
Figure 2.16: Ratio of horizontal peak reflected pressure to peak
free air pressure
Figure 2.17: Reflected pressure distribution along a rigid wall
Figure 2.18: Shock wave on a surface due to a surface burst
Figure 2.19: Blast load on arch structure
Figure 2.20: Variation of reflected coefficient with
reflection/incident angle.
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CHAPTER 3 - METHODOLOGY
Figure 3.1 Research Methodology Flow Chart
Figure 3.2: Side-on blast wave parameters for spherical charges
of TNT in free air
Figure 3.3: Structure profile in relation to blast source
Figure 3.4: Front face loading
Figure 3.5: Reflected pressure coefficient (Cr) vs angle of
incidence (α)
Figure 3.6: Internal force resultants in a shell element
Figure 3.7: Membrane and bending resultant force fields
Figure 3.8: Cylindrical shell geometry
Figure 3.9: Free body diagram of a cylindrical membrane
Figure 3.10: Beam action of long cylindrical vaults
Figure 3.11: Shear force mechanism of applied forces to the end
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arches
Figure 3.12: Shear force mechanism of load transfer to
longitudinal edge beam.
Figure 3.13: Typical cross-section of a hemispherical shell.
Figure 3.14: Free-body diagram of a transverse arch of a shell
Figure 3.15: Convergence of FEM Model
Figure 3.16: Eighteen-node and nine-node element
Figure 3.17: Nine-node isoparametric element
Figure 3.18: Model of the structure
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CHAPTER 4 – ANALYSIS AND RESULT
Figure 4.1: Transverse profile of a structure
Figure 4.2: Blast load on structure
Figure 4.3: Equivalent static load as input to computer program
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CHAPTER 1
INTRODUCTION
1.0 Introductory Remarks
There is growing interest nowadays in designing civil engineering
structures to withstand dynamic loads. Dynamic loads refer to any load
whose magnitude, direction and position vary with time. Similarly, the
responses of a structure (the resulting displacements and stresses) to
such loads are also time-varying. Examples of dynamic loads are
impact, explosion, earthquake, wind, waves and loads due to
unbalanced mass in a rotating machine. All loads in nature are time-
dependent, but in most cases the variation is slow compared to the
natural period of vibration of the structure which implies that static
conditions can be assumed. Thus, whether a load varies slowly or fast
is only in relation to the time required for the structure to complete a
full cycle of vibration.
Dynamic loads can be further categorized as periodic or non-periodic
loadings. Periodic loadings are repetitive loads which exhibit the same
time-variation successively for a large number of cycles. Non-periodic
loadings may be either short-duration (impulsive) or long-duration
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general forms of loads. A blast or explosion is a typical source of
impulsive load. For such short-duration loads, special simplified forms
of analysis may be employed. For long-duration load such as
earthquake, it can be treated only by general dynamic analysis
procedure.
Dynamic analyses essentially focus on evaluation of time dependent
displacements, from which the stress state of the structure under
consideration can be computed. In these analyses the dynamic
properties of the structure are required, primarily the natural period of
vibration which is a function of the structure’s mass and stiffness and
the amount of damping.
In modeling of structures for structural dynamic problems, the
structures are regarded as distributed or continuous mass or discrete
or lumped mass. The distributed mass concept is realistic but difficult
and involves lengthy process. The lumped-mass concept provides a
simple means of limiting the number of degrees of freedom that must
be considered and leads to an approximate solution to the problem. It
is most effective in treating systems in which a large proportion of the
total mass is concentrated at a few discrete points such as frame
structures.
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1.1 Blast Loads
The need to consider blast load in the design of certain important
structures has increased significantly in the recent years, due to the
enhanced use of explosives for security as well as terrorist attacks. The
origin of the blast can either be within or outside the structure, thus
giving rise to the terms internal and external blasts. This paper
attempts to analyze the structural response of a reinforced concrete
bunker which is an arch structure when subjected to an external blast
of a charge placed on the ground (surface burst).
The basic difference between blast loads and other dynamic loads is
that the blast loads are moving pulse loads, loading different part of
the structure at different times, with varying magnitudes and
durations, depending on the distance and angle of incidence. The
shock front due to a surface burst is hemispherical in shape with its
parameters such as side-on overpressure (pso), positive phase duration
(Ts) and arrival time (t) being functions of the stand-off distance
(radial distance) of the target.
The pressure pulses generated by detonations on the ground are
transmitted through the air and soil. When a shock front reaches an
obstacle such as a building, there is an abrupt pressure rise to a
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maximum (shock-like) followed by decay to below atmospheric
pressure which is generally neglected except when a rebound analysis
of a roof is required.
The transient, impulsive dynamic loading of external blasts may act
locally over building parts or over the entire structure, depending on
the duration of loading. When the blast loading is of short duration (or
blast source is very near to the structure) only the closest structural
parts to the detonation source will be acted on by the blast loading. On
the contrary, if the blast duration is long such as large nuclear
weapons or other extremely large explosions, it can be considered to
act over the entire building at the same time with the same time
history.
The blast loads on arch surfaces are functions of time as well as space,
since the incident angle which fixes the reflection coefficient
continuously changes with the traverse of the shock front. Dynamic
analysis using the lumped mass concept is very complicated since the
mass is continuous over the structure. A simplified method of
evaluating the blast response is to represent the blast load as an
equivalent static load. A more rigorous approach is to treat the blast
pressure as a moving triangular pulse traversing the curved surface. In
this paper the equivalent static load method is adopted.
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1.2 Nature of the Problem
In the last decade, there has been an increasing incidence of bomb
attack on modern societies. Therefore it is becoming more evident that
structural engineers need to consider blast loadings in their design in
order to protect the societies from such attacks.
An explosion generates extreme loads which in most cases result in
severe damage or even collapse of structures. As a consequence, it
always causes economic loss and usually loss of life and unavoidable
psychological impact on societies. In order to reduce the consequences
of such threat, a clear understanding of structural response and
damage characteristics due to explosive loads is essential.
The requirement for protection against blast loadings depend on the
likelihood of a particular building will be subjected to such loadings,
established by means of a threat analysis. This indicates that only
certain critical and important buildings require such protection.
Furthermore there is a cost associated with each level of protection
provided. In this study, a reinforced concrete bunker is used to
represent such buildings for the purpose to demonstrate the effect of
blast loading on structures. Furthermore the arch structure is among
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the leading structural forms employed for protection from weapon
effects.
1.3 Objectives of Study
The primary objectives of this study are:
(a) To propose a computational model to simulate geometry and
constitutive non-linearity.
(b) To investigate the structural response of a reinforced concrete
bunker when subjected to the explosion of a surface charge.
(c) To suggest procedures and factors to be considered for design
purposes.
1.4 Scope of Study
In the investigation of the structural response of a reinforced concrete
bunker subjected to a blast load, the study was conducted within the
following scope:
(a) Reviewing the literature to establish the current state of
knowledge on the nature and characteristics of loads generated by
detonation of high explosives.
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(b) Establishing the loads to be applied to the structure which
comprise of the dead load of materials and the blast loads generated
by detonation of a surface charge.
(c) Using the Finite Element Method through shell elements with
the features of material non-linearity and crack analysis capability.
1.5 Organization of Report
In order to achieve the objectives of the study, this report was written
and organized in the following manner:
(a) Chapter 1 - Introduce the subject matter and provides general
description of the problem of interest.
(b) Chapter 2 - Presents a general view of blast loads with the aim
to keep abreast with the current state of knowledge with regards to
the nature and characteristics of blast loads.
(c) Chapter 3 - This chapter presents in detail the methodology
adopted in the study. The problem was approached through the
classical method as well as the numerical method which involved the
finite element formulation of the problem. This chapter also provides
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the detail procedure in calculating the blast loads which serve as data
for the analyses.
(d) Chapter 4 - In this chapter the analyses both linear and non-
linear were carried out and the results presented, compared and
discussed.
(e) Chapter 5 - The last chapter provides conclusions drawn from
the study. Recommendations for future studies and research are also
provided.
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REFERENCES
1. Blast Effects on Buildings, Edited by G.C. Mays and P.D. Smith,
Thomas Telford, London, 1995.
2. Blast and Ballistic Loading of Structures, P.D. Smith and J.G.
Hetherington, Butterworth Heinemann, Oxford, 1994.
3. Explosive Loading of Engineering Structures, P.S. Bulson, E & FN
SPON, London, 1997.
4. Design of Buildings to withstand abnormal loading, Béla Goschy,
Butterworths, 1990.
5. Abnormal Loading on Structures - Experimental and Numerical
Modelling, Edited by K.S. Virdi, R.S. Matthews, J.L. Clarke and F.K. Garas, E &
FN Spon, London, 2000.
6. Shock and Impact on Structures, Edited by C.A. Brebbia and V.
Sánchez-Gálvez, Computational Mechanics Publications, Southampton, 1994.
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7. Design and Analysis of Shell Structures, M. Farshad, Kluwer Academic
Publishers, Netherlands, 1992.
8. Thin Shell Concrete Structures, David P. Billington, McGraw-Hill Book
Company, 1982.
9. Design of Reinforced Concrete Structures, Henry J. Cowan, Prentice-
Hall Inc., New Jersey, 1982.
10. Fundamentals of Reinforced Concrete, John N. Cernica, Addison-
Wesley Publishing Company Inc., 1964.
11. Impact and Explosion – Analysis and Design, M.Y.H. Bangash,
Blackwell Scientific Publications, 1993.
12. The Dynamics of Explosion and Its Use, Josef Henrych, Publishing
House of the Czechoslovak Academy of Sciences, Prague, 1979.
13. Dynamic Loading and Design of Structures (Chapter 6), Edited by A.J.
Kappos, Spon Press, London, 2002.
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14. Technical Manual (TM-5-855-1), Fundamentals of Protective Design for
Conventional Weapons, Headquarters, Washington DC: Department of the
United States Army; 1990.
15. A.K. Pandley, Ram Kumar, D.K. Paul and D.N. Trikha, 2005, “ Non-
linear Response of Reinforced Concrete Containment Structure Under Blast
Loading”, Journal of Nuclear Engineering and Design 236 (2006), pp 993-
1002.
16. Chengqing Wu and Hong Hao, 2006, “Numerical Simulation of
Structural Response and Damage to Simultaneous Ground Shock and Air Blast
Loads”, International Journal of Impact Engineering 34 (2007), pp 556-572.
17. Chengqing Wu and Hong Hao, 2004, “Modelling of Simultaneous
Ground Shock and Air Blast Pressure on Nearby Structures from Surface
Explosions”, International Journal of Impact Engineering 31 (2005), pp 699-
717.
18. Q.M. Li and Norman Jones, 1993, “Blast Loading of a Short Cylindrical
Shell with Transverse Shear Effects”, International Journal of Impact
Engineering 16 (1995), pp 331-353.
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19. M.V. Dharaneepathy, M.N. Keshava Rao and A.R. Santhakumar, 1993,
“Critical Distance for Blast-resistant Design”, Journal of Computers and
Structures 54 (1995), pp 587-595.
20. F.B.A. Beshara 1992, “Modelling of Blast Loading on Aboveground
Structures – General Phenomenon and External Blast”, Journal of Computers
and Structures 51 (1994), pp 585-596.
21. M.V. Dharaneepathy, M.N. Keshava Rao and A.R. Santhakumar 1991,
“The Influence of Geometry on the Blast Response of Circular Arches”,
Journal of Computers and Structures 45 (1992), pp 755-763.
22. J. Jiang and M.D. Olson 1990, “Non-linear Dynamic Analysis of Blast
Loaded Cylindrical Shell Structures”, Journal of Computers and Structures 41
(1991), pp 41-52.
