NON-LINEAR TRANSIENT AND QUASI-STATIC ANALYSES

OF THE DYNAMIC RESPONSE OF BUILDINGS TO BLAST LOADING
Philip Esper
BSc (Hons), MSc, MBGS
Consultant, Griffiths Cleator & Associates, London, UK
Lecturer, University of Westminster, London, UK



ABSTRACT

On Saturday 24th April 1993, a bombing incident took place at approximately 10:25 a.m. within the Bishopsgate area of the city of London. As a result, one person was killed and 34 people were injured. Damage to building structures, fabric and contents, within a radius of about 500 m of the device ranged from total devastation to minor damage. As a consequence of this incident, the author was involved, as a consultant to Griffiths Cleator and Associates (GCA), in the reinstatement of over ten commercial buildings of various sizes, construction and degrees of damage. Finite Element Analysis was carried out on two of these buildings using ANSYS. A non-linear transient dynamic analysis was performed on a 3-D model of a typical floor of the first building, and a quasi-static analysis was performed on a full 3-D model of the second building. This paper presents a brief overview of the bombing incident and its damaging effects on building structures, outlines the investigation and testing techniques used, discusses both types of FE analyses employed, presents the dynamic response of the two buildings as predicted by FEA, correlates the analysis results with the investigation and testing that was carried out on site, and discusses the reliability of using FEA in highlighting problematic zones in the structure.

INTRODUCTION

At approximately 10:25 on Saturday morning, 24th April 1993, a terrorist bomb exploded in city of London. The device which was made of unknown quantity of home-made explosives was carried in the back of a vehicle that was parked on the Bishopsgate southbound carriageway in the position shown in Fig.1. One person was killed and approximately 34 people were injured. Building structures, fabric and contents, within approximately 500 m radius of the device exhibited different degrees of damage with the maximum being close to the bomb.



Location plan of the source of detonation and the two buildings; Building A93 marked in red; Building B93 marked in green.
FIGURE 1
LOCATION PLAN OF THE SOURCE OF DETONATION AND THE TWO BUILDINGS; BUILDING A93 MARKED IN RED; BUILDING B93 MARKED IN GREEN.

The 14th century St Ethelburga's Church, which was only about 7 m away from the bomb, was practically levelled to the ground. The size of the bomb was estimated to be approximately 850 kg TNT equivalent. This estimation was based on specialist forensic evidence and study of the crater measurements and the soil properties.

As a consultant to Griffiths Cleator and Associates (GCA) at the time, the author was involved in the investigation and reinstatement of over ten commercial multi-storey buildings with the closest being 11 m from the bomb.



For the purpose of this paper the number of buildings discussed shall be limited to the ones modelled and analysed by FEA using ANSYS and they will be referred to as A93 (marked in red in Fig.1) and B93 (marked in green in Fig.1). The proximity of these two buildings to the source of detonation is 11 m and 75 m respectively.

Typical Explosion Wave Pressure - Time Graph.
FIGURE 2
TYPICAL EXPLOSION WAVE PRESSURE - TIME GRAPH.

Royal Ordnance, being a division of British Aerospace Defence Limited, was appointed to provide information on the magnitudes of the blast pressures experienced by the two buildings, externally and internally, in the form of time-history graphs at specific points of each structure using 3-D simulation packages named 'INBLAST' and 'CHAMBER'. This paper investigates the dynamic response of the two buildings as observed on site on one hand and as predicted by FEA on the other hand. It correlates the analysis results with the investigation and testing findings, and discusses the reliability of FEA as a tool not only for predicting the response but also in highlighting problematic zones that may not be easy to observe on site without major opening up and breakage of the structure.


2. CHARACTERISTICS OF BOMB BLAST

An explosion is an instantaneous conversion of a small volume of solid, or liquid, into a large and highly pressurised volume of very hot gases that undergo violent expansion. As a result, a blast wave is formed by the rapidly moving compressed air which is characterised by an instantaneous rise in pressure. This is followed by a decay over a period called the positive phase duration (see Fig.2). As the energy of the expanding gases becomes dissipated, their momentum falls and they begin to contract, creating a suction phase known as the negative phase. At this phase, the blast wave pressure is below ambient (atmospheric) pressure.
If the explosion is contained by soil at a considerable depth from the ground surface, the energy will be converted into vibrations that propagate through the ground as seismic waves. At lesser depths, as is the case here, smaller proportions of the energy will be transmitted as seismic waves and much of the explosive force will be absorbed by the earth close to the surface displacing it and forming a crater (see Plate-1).

Crater formed by the explosion of the bomb.  (Diameter=9M; Depth=2.5M)
PLATE 1
CRATER FORMED BY THE EXPLOSION OF THE BOMB (DIAMETER = 9M; DEPTH = 2.5M).



As the blast waves radiate out within the confined city streets they will be reflected and refracted by adjacent buildings. The blast waves will travel over the tops of buildings and down light wells thus totally enveloping these buildings and subjecting them to large unbalanced transient blast loads such as pressure pulses, gas filling and linear windage all of which have different times of arrivals. The geometry of the individual buildings, and in particular their elevations, can further magnify the incident transient blast loads.

Building A 93.  (Note the damage indicated by the red arrow.
PLATE 2
BUILDING A 93. (NOTE THE DAMAGE INDICATED BY THE RED ARROW).

The blast loads, although being transient in nature, would nevertheless have been many orders of magnitude greater than the original structural design loads for the buildings within the affected zone. Due to the random nature of blast loads, damage to building structures is notoriously unpredictable. Depending on the location of the explosive device, the configuration of the surroundings and the quantity of free space into which the gas may expand, the effects of a given explosive device on a structure are notoriously unpredictable.


3. DESCRIPTION OF THE TWO BUILDINGS

3.1 Building A93

This was a grade II listed steel framed building, 7 storey high constructed in 1928 (see Plate-2). Its architectural form can be described as stone classical facade. Above 5th floor, the elevation steps inwards and extends up the 7th floor where it was crowned with a cornice. Above this was a steep slated mansard roof with dormer windows. The structural frame was made up of plated mild steel R.S.J's (Beams and columns) or made up plated beams secured with rivets and either riveted or bolted end connections. The floors plates were generally insitu reinforced ribbed slabs with permanent hollow tile liners used as shuttering. Part of the 3rd floor slab which was a later adaption was infilled using a timber joist floor supported on steel beams.
The internal columns were encased with 100 mm terracotta hollow blocks, the external columns were buried within the masonry and the internal downstand beams were concrete cased. At 1st and 2nd floors vertical continuity of some columns was interrupted and these were supported off substantial plated transfer beams which spanned 10 meters and were approximately 1 meter deep. The column point loads on these beams were approximately 1500 kN each. Transfer beams also occurred at 6th floor to cater for the step back in the elevation.
The basement and lower ground floor extended out under the Bishopsgate pavement and at the north west corner of the building the reinforced concrete basement retaining wall bounded the perimeter of the bomb crater. It was established from preliminary site investigations and inspection of archival details that the entire basement had an external asphalt membrane applied prior to casting the sub-structure concrete.

3.2 Building B93

This property was constructed sometime between the late 1950's and early 1960's. The building had a basement, ground and five upper floors (see Plate-3).



Building B 93
PLATE 3
BUILDING B 93

Its construction consisted of a concrete cases structural steel frame supporting hollow tiles reinforced concrete floor slabs. At 5th floor the elevation stepped back and the perimeter cavity brickwork wall provided support to the high level 5th floor roof.
The enclosure to the basement was a combination of reinforced concrete retaining walls and a solid masonry party wall. The infill apron panels were faced with slate which were faced fixed to backing brickwork and downstand concrete beams. The parapet walls and staircase enclosures had stone panels similarly fixed. The beam column connections consisted of riveted seating cleats and site bolting of the beams to the cleats. Only in some locations were the top flange restrained with a cleat. Vertical stability was achieved through lift/staircase and flank walls.

4. DAMAGE INVESTIGATION AND TESTING

Immediately following the city bombing all efforts were naturally directed at damage limitation measures. The general condition of the fabric was recorded, photographed and videoed prior to it being removed, as this may give important clues on both the blast wave pressures and the manner in which they propagated through the structure. The preliminary bomb damage assessment report included a program of recommendations for further detailed inspections, opening up works and testing required to assess fully the effects of the blast on the structure.


Where visual evidence of distortions, deflections, and cracking to the structure and its finishes existed, selective local opening up of these elements were undertaken to establish if failure have occurred.
Having identified the areas of structure for detailed investigation, a regime of site and laboratory testing was prepared, starting from locations of greatest visible blast damage. Analytical methods proved very valuable here in terms of indicating areas of possible serious overstressing of the structure. Given the unpredictability of blast effects on buildings, it was found to be more cost and time effective to implement methods, such as finite element analysis that may highlight areas of damage prior to undertaking extensive opening of the structure.
Static proof load testswere carried out on floor panels which sustained maximum physical damage to compare actual deflections with analysis predictions. These results were compared with the results from a control area selected on the basis of least visual damage and similarly for all other materials tested. Also, plumb line surveys were carried out on the external elevations of both buildings, and FE analysis results were compared with recorded lateral displacements of the elevations of building B93.

5. BLAST OVERPRESSURE EXPERIENCED BY THE TWO BUILDINGS

What needs to be estimated first, is the magnitude of the blast pressures that the building may have experienced so that, FE technique, for example, can be used to obtain an indication of the dynamic response of the structure prior to it coming to rest. The consequences of this response on the structural integrity of the building can hence be evaluated. Royal Ordnance (a division of British Aerospace Defence Limited) were appointed to provide information on the magnitudes of the blast pressures experienced by the two buildings both on their external elevations and inside each structure through gas filling. Two distinct elements of calculations were carried out. The first, was to perform detailed external shock reflection modelling using INBLAST. For this analysis, 82 external test points on the elevations of building A93, and 88 external test points on the elevations of building B93 were selected by the author.




The second element of the calculation, was the analysis of the blast wave ingress into the structure and loads on internal slabs. This assessment used a program named CHAMBER which assesses the internal reflection and diffraction of blast waves entering through openings. For this analysis, 6 internal test points on a typical floor of building A93, and 5 internal test points on a typical floor of building B93 were selected.

5.1 Building A93

Bomb blast pressures are transient in nature and frequently of short duration. On this building, this duration did not exceed 350 ms. The maximum peak positive pressures ranged from 1,365 kN/m2 on the north corner of the building (close to the bomb), to 91 kN/m2 on the south corner (away from the bomb). The arrival times of these pressures were 12 m.sec and 138 m.sec respectively. In order to appreciate the magnitudes of these pressures, it is worth pointing out that buildings in the London region, including this one, are designed usually for a maximum wind pressure of 1.5 kN/m2.
With regard to the internal pressures, their arrival times were similar to the external pressures and their peak positive pressures ranged from 490 kN/m2 north to 126 kN/m2 south of the building. Careful examination of these pressures at various time intervals concluded that these pressures subjected the floor plates to highly complex transient behaviour in both upward and downward direction occurring simultaneously on individual floor panels and far exceeded the original design loads of 10 kN/m2.


5.2 Building B93

All points on the rounded corner of the building between Bishopsgate and Wormwood Street have seen very high blast pressures that reached a maximum value of 131 kN/m2 at first floor level. The reason being that this corner was approximately normal to the shock waves. This is also 87 times the wind load that the building was designed for in the laterally. At ground floor level, however, these pressures were less than those at 1st floor level. This can be attributed to the frictional effects of the ground on the shock waves.
The internal pressures on the test points at ground floor level were significantly higher than those on the corresponding test points at 1st floor level. This is attributed in this case to the large vent sizes of the shop windows at ground floor level. The values of the internal pressures on the ground floor ranged between 118 kN/m2 and 167 kN/m2. This can be appreciated again when compared with the original design load on floors of 4-5 kN/m2. The internal pressures duration was approximately 200 m.sec.
It is important to note the difference in the arrival time of the blast pressures to the two building from the time of explosion of the bomb (15 m.sec to the external elevation of building A93, compared to 140 m.sec when it hit the external elevation of building B93; a time lag of 125 m.sec).



6. FINITE ELEMENT MODELLING AND ANALYSIS

6.1 General

In the analysis of the dynamic response of a building structure to bomb blast, the following procedures must be followed [Esper & Keane, 1995]:

  1. The characteristics of the blast wave must be determined (as explained above).
  2. The natural period of response of the structure (or the structural element) must be determined.
  3. The positive phase duration of the blast wave is then compared with the natural period of response of the structure.
Based on (3) above, the response of the structure is then defined as follows:
  • If the positive phase duration of the pulse is shorter than the natural period of vibration of the structure, the response is described as impulsive. In this case, most of the deformation of the structure will occur after the blast loading has diminished.
  • If the positive phase duration of the pulse is longer than the natural period of vibration of the structure, the response is defined as quasi-static. In this case, the blast will cause the structure to deform whilst the loading is still being applied.
  • If the positive phase duration of the pulse is close to the natural period of vibration of the structure, then the response of the structure is referred to as being dynamic. In this case, the deformation of the structure is a function of time and the response is determined by solving the equation of motion of the structural system.

6.2 Building A93

The fifth floor slab of this building was modelled using ANSYS. Two element types were used; shell element (shell 63) for the reinforced concrete slab, and beam element (beam 4) for the steel beams. The total number of elements in the model was 945, and the total number of nodes was 627. Each node had 6 DOF; three translations Ux, Uy, Uz, and three rotations qx, qy, qz. The column locations were considered as support points for the slab. Material properties of concrete and steel were incorporated based on actual testing of the concrete cores and examinations of the steel materials of the beams. The values used in the analysis were as follows:
For steel:
Ex= 205 kN/mm2
n = 0.3
Dens = 7800 kg/m3

and for concrete:
Ex= 25 kN/mm2
n = 0.2
Dens = 2400 kg/m3
By carrying out a modal analysis first, using ANSYS, the natural frequencies for the first three modes of the floor plate of building A93 were given as follows:
f1= 12.495 Hz
f2= 13.459 Hz
f3= 13.490 Hz



The fundamental period of the plate was hence calculated and found to be equal to:
T1 = 1 / f1 = 0.080 sec = 80 msec
The positive phase duration was found on the internal pressures-time history graphs to be ranging between 20-45 m.sec. Since this was shorter than the fundamental period of the floor plate, a 3-D non-linear transient dynamic analysis was, then carried out in order to determine the response of the floor slab to the internal pressures.
The blast pressures were applied on the top and bottom faces of the concrete floor as pressure-time history graphs as produced by Royal Ordnance. Consequently, two graphs for every node of the model were obtained, one representing the deflections due to the pressures acting on the bottom face of the slab, and the other representing the deflection of the floor slab due to pressures acting on the top face of the slab. The two graphs were superimposed over each other so that the actual net deflection at any time can be estimated. As an example node 124 is considered and located near the middle of the bay next to the North stairs. It can be seen that the floor slab, at this point, was lifted upward by 16 mm before the pressures acting at the top of the slab were able to start pushing it downward.


It has been demonstrated by the FE analysis that when the soffit of the floor plate saw a positive peak pressure, it took 10 msec on average to develop its maximum deflection which ranged between 16 mm and 24 mm. It was observed that a 5 msec time lag in the pressures hitting the top surface of the slab was sufficient to result in a net upward deflection of approximately 16 mm above the horizontal. This momentary uplift of the plates will result in tension cracks to the top surface of the structural topping. This is combined with the subsequent rebound of the plate will cause crack aggravation over the supports, thus impairing the performance of the bond between the concrete and its reinforcement. This would result in failures similar to those that were recorded on the 5th floor load test, i.e. slippage of the reinforcement over the supports.
Further corroboration of these pressures, is the damage observed to the slab soffits which included cracking along the joints between the asbestos pots, hairline cracking of the concrete between the structural topping and the ribs. This cracking was reported in the petrographic tests of the cores that were taken from the structural slab.


6.3 Building B93

A full 3-D FE model of this building was generated using ANSYS. Two element types were used here too; shell element (shell 63) for the reinforced concrete slabs, and beam element (beam 4) for the steel beams and columns. The total number of elements in the model was 5232, and the total number of nodes was 3912. Each node had 6 DOF; three translations Ux, Uy, Uz, and three rotations qx, qy, qz. From Plate-3, it can be seen that this building has a large window area in each floor all the way around except on the west elevation (flank wall). Taking also into account the fact that it was reported by various sources [Royal Ordnance, 1993 and later by Mayes & Smith, 1995] that normal glass, as a brittle material, takes only 5-8 msec to break, it was found obviously sensible not to include the glass panels in the FE analysis. This is true as long as the glass panels are weak enough not to transfer any load to the structural elements (such as frame members).
Material properties of concrete and steel were incorporated based on actual testing of the concrete cores and examinations of the steel materials of the beams. The values used in the analysis were as follows:
For steel: For concrete:
Ex = 205 kN/mm2
n = 0.3
Dens = 7800 kg/m3
Ex= 24 kN/mm2
n = 0.2
Dens = 2400 kg/m3



By carrying out a modal analysis first, using ANSYS, the natural frequencies for the building were given as follows:
f1= 1.899 Hz
f2= 1.961 Hz
f3= 2.586 Hz
The fundamental period of the plate was hence calculated and found to be equal to:
T1 = 1 / f1 = 0.527 sec = 527 msec
The positive phase duration was found on the internal pressures-time history graphs to be ranging between 50-80 m.sec. Since this was shorter than the fundamental period of the floor plate, the response of the building was impulsive, and the proper analysis that would be used is a non-linear transient dynamic one. Since the main concern was concentrated on the actual stability of the building, a quasi-static analysis was carried out as follows: The blast pressures were applied at different time intervals as a static load that has a variable value throughout all the elements forming the facades of the building. These values were extracted from the pressure-time history graphs produced by Royal Ordnance at each specific time interval considered in the analysis. This has allowed one to look at the maximum deflection that could have been experienced by the building with considerable saving of computer time and analysis efforts (such as feeding all the pressure-time history graphs to all the locations of the selected external 80 test points on all the elevations of the building).


7. CORRELATION BETWEEN DAMAGE AND FEA RESULTS

Tremendous damage was observed in the Bishopsgate incident. In buildings close to the explosion, floor slabs were momentarily lifted, load bearing walls moved and became out of plumb, and hidden damage resulted. Hidden damage in building structures due to dynamic loading became of more concern to engineers particularly after the investigation of damaged buildings following the Northridge earthquake [NCE, 1994] and the Kobe earthquake [Esper & Tachibana, 1995] where the same types of damage described above were found.
In the case of this explosion, building A93 exhibited damage in the form of cracking, high speed spalling and scabbing of concrete cover, shear and/or tensile failure of columns, upward failure of floors, snapping of rods and prying of frame connections. The main feature of this damage was the cracking in the concrete floors and failure under load testing. This was predicted also in the FE analysis. Location of cracking zones were highlighted in the FE analysis and these fine cracks were found as predicted by the FEA when the preliminary inspection / investigation did not report them. This was particularly important when these cracks were discovered in the mezzanine floor (2nd floor) where timber joists exhibited longitudinal fine cracks that were difficult to observe in the preliminary investigation.


In the case of Building B93, less damage was observed to the floor slabs because it was located much further than building A93 relative to the bomb. However, what was of a major concern in this building is the effect of the blast on the stability of the building and its residual strength to carry the original design load. This urged the need to look at the global behaviour of the structure and the magnitudes of permanent deflections in all three direction that may have resulted in the structure. Plumb survey was carried on the structure, along with all the other specified regular tests. Finite Element results from the 3-D quasi-static analysis over different time steps of the load showed good correlation with both the deformed shape and displacement magnitudes of the structure at corresponding points. Maximum deflection of 25 mm that was observed in the plumb survey on line V7, for instance, had a displacement value in the same direction of 22 mm in the FE analysis. Although these magnitudes may not seem particularly significant, design check calculations were carried out in order to predict the additional forces and moments values induced, in the structural frame, by the new displacements, and the adequacy of the frame to carry these forces and moments. Additional bracing was needed in this case for the structure to carry on functioning in the manner it was originally designed for.


8. CONCLUSIONS

Given the unpredictability of blast effects on buildings, it was found to be more cost and time effective to implement methods, such as finite element analysis that may highlight areas of damage prior to undertaking extensive opening of the structure.
This was the case in both building A93 and building B93. In the former, the scope of testing was greatly reduced in terms of opening up of beam-column connections and directed the next investigation / testing stage in a manner that was more efficient and economic. Decisions made later regarding future use of different parts of the structure (e.g. floor slabs, steel frame, etc.) carried great confidence particularly that they were backed up by site testing results.
Although the response of building B93 was transient, but considering the type of concern encountered here (i.e. stability of the structure and the magnitudes of the displacements associated with it), it proved to be very cost effective to carry out a quasi-static analysis particularly when taking into account the size of the structure modelled here, and the efforts involved in terms of feeding all the necessary information to carry a non-linear transient dynamic analysis. The other advantage is obviously the saving in computer time necessary to carry out the non-linear transient analysis. Once more, and being more important here, the combined analysis and testing carried out hand in hand proved to be very efficient in reducing the scope of carrying either of them separately, and having at the same time more confidence in the results, in addition to achieving the best economic solution.


ACKNOWLEDGEMENTS

The author gratefully acknowledges the valuable contribution made by William Keane of Griffiths Cleator & Associates. The author also wishes to express his appreciation for the support provided by Griffiths Cleator and Associates, University of Westminster, and Taylor Woodrow Construction Holdings Limited. Finally, the support provided by the help desk and other members of the STRUCOM company on ANSYS is greatly appreciated.

REFERENCES

Esper, P., and Keane, W., The St Mary Axe / Bishopsgate Experiences on the Dynamic Response of Buildings to Bomb Blast, A paper presented and discussed at the Institution of Structural Engineers, Thames Valley Branch, on Wednesday 4th October 1995 at 6 p.m., London, UK.
Esper, P., and Tachibana, E., The lesson of Kobe Earthquake, Geohazards and Engineering Geology Conference, Coventry, 1995.
Mayes, G. C., and P. D. Smith, Blast Effects on Buildings, London, 1995.
New Civil Engineer (NCE), 29th September 1994 edition, London, UK.
Royal Ordnance, Report on the Analysis of the Effects of the Bishopsgate Bombing on Hasilwood House, Swindon, 1993.


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