If the booths / towers are anything vaguely 'beam like' you could treat like a cantilever and work out the foundation forces from this, in the normal way.(ie, get natural frequency work out DAF for the pulse shape from say Biggs then design load is DAF x blast pressure etc etc) Depending on the natural frequency of the cantilever beam there may or may not be much dynamic amplification of the blast,

If you need software you could look at
www.electronic-calculus.com.

Good luck.

LalyaZ,

The Army Corps of Engineers in Vicksburg, MS, has done a lot of blast mitigation research.  You might try getting hold of some non-secure analysis programs through them.

David

You really need a geotechnical engineer to help you with this one...do you need a reference?  I know a really good one in the Ohio/Kentucky area.  (His first name is Ron.)  This sounds like a good project for him.  If you want his name, let me know -

It sounds like you are working on a program that requires security clearance for your firm and personnel.  I would expect that the NRC could (should) smooth the way for access to secure information or personnel -

Please see FAQ731-376  by VPL for tips on how to make the best use of Eng-Tips Fora.

LaylaZ,

This is a good challenge!

Looking at it from an idiot point of view (meaning self as an outsider) the blast pressure is equivalent to over 1038ft or 310m of water pressure in 7 ms.  Most highway bridges are designed for less than equivalent of 5 to 6ft of water when the length is fully loaded.  The magnitude is therefore about 200 times except it happens in a split second.

The foundation is this case may have to fail in the normal sense by having large displacement unacceptable for a normal permanent structure.  If one is prepared to rebuild the booth every time someone throw a bomb at it then the problem becomes somewhat manageable.  

Soil’s dynamic modulus is easily twice the static value for analysis of vibratory plant and I could imagine a much bigger increase in the case of a short blast.  Soil takes time to react to external load.  Although I haven’t done one before I believe some dynamic E-values of the soil were the stress and strain measurements originated from a blast.  A higher E-value means the soil can accept a much a high load if it is applied dynamically.

The booth is likely to be separated from the host structure and has its own foundation that can be designed differently as long as the soil movement/disturbance from the blast does not materially affect the host structure.

In a blast it may be easy to have the booth fly away due to a above-ground shear failure of the booth’s superstructure but in compression or passive pressure the soil could possibly just dig deeper or spread wider to dissipate the blasting energy, by mobilising a larger soil mass to participate in the resistance.  Indeed soil participation factor has been used in the design of the vibratory foundations to reduce the foundation weight.

The 450psi pressure is about 8 times the soil is currently taking for a heavy lorry wheel.  A solution therefore should not be too difficult to find.  

LaylaZ,
You could clearly be sent on a big research exercise on this...
How about posting a few more details so we can have a better shot at the problem. Like what sort of shape and  dimensions do these booths have, also the 7 millisecs, is this the rise time or the pressure pulse duration? What shape is the pulse etc - normally it would be triangular with the rise time and duration given.
Even more good luck.

Guys,
thank you so much for the valuable info each of you has provided.
JWB46, the pulse is triangular and its duration is 7ms.
As to the shape of the booth it's a square, 8'x10'x 8' high. The bomb is assumed to be placed at a certain distance X (safetyguard info! sorry :)), to produce about 450 psi.

For the ones that are elevated, I understand that I have to beef up the bracings of the tower, due to the excessive shear. Any special techniques?

Also, since I am new to this, any tips for good foundation reinforcements against shear forces?

Thanks a lot.

Layla.

Not in my field, but

MIL-HDBK-297 INTRODUCTION TO WEAPON EFFECTS FOR SHIPS

might be somewhat interesting reading.

TTFN

LaylaZ,
On the assumption that the pressure and pulse refer to drag load (this would make sense - small building ,small time duration of the blast)I think you have to go for flexibility in the supports to reduce the natural frequency of the system. This will result in a small dynamic load factor even if the peak pressure is high.
For example, thinking about the tower mounted booths, if you designed them like a box on a pedestal you can easily design the system to have a longish natural period of say 0.5s, which for the given pulse duration will give DLF<<1. So the design lateral force will be small.
You can apply the same principle to the ground booths by use of flexible bearings.
(Alternatively, if the towers are not too high you could use the same design for the ground booths just by putting the pedestal and its base in a hole in the ground! This would obviously be a daft idea if the towers are tall.)

I did a couple of simple analyses for a pedestal mounted booth with your data using EC-DYABLO and it seems to work, the pedestal moments are relatively low compared with very large peak forces on the booth.

I take it that the basic design data you are using comes from a reliable source. The pressure looks very high, but I can believe the pulse duration.
Hope this helps.
Good luck again

LaylaZ,
   I agree with the "soft" foundation approach by JWB46.  This is similar to good siesmic resistance design.  There are grade level foundation seismic supports that could be used for the grade level pillboxes.  

   However, please verify the 450 psi overpressure!! Should this not be 450 psf?  If your ~50 kip? bulletproof pillbox on a soft foundation is slammed with 450 psi, everything mounted rigid inside would probably see large and destructive forces ~ 100g's?.  Maybe one could isolate an inner structure for equipment/occupancy from the outer structure with further compliant supports, Cheyenne Mountain style.  

Is the load considered the Reflected overpressure (Pr)or is it Pso+q?

What is the height of the tower, and what is the frequency of the tower?

  

It seems to me that there are two fundamental approaches to the problem. For the sake of argument say that the structure is very stiff. Then the applied impulse will cause an acceleration in the whole structure and you can calculate the final velocity and how the support has to flex to bring the velocity back to zero before it is damaged. This doesn't make sense because it assumes that the wall paneling (which is where the impulse is applied) is stiffer than the structural members.

The only practical approach is to use an energy aborbing material on the outside of the structure to minimize the amount of force transfered to the structural frame. The explosive shock wave contains a finite amount of energy which must be dissapated in some way. The energy is in the gas pressure which is moving through the air as a pressure wave at sonic velocity. Reflection occurs when the wave hits a rigid surface, like concrete. Maximum force is applied if the concrete does not move and no energy is absorbed. If the concrete moves, some energy was transfered to it. Now you have to figure out what to do with the energy in the concrete.

To go another, step lets say you have a 1 pound brick one foot in front of a one ton block. The 450 psi over presure will not damage the brick or the block. But the brick will be sent flying into the block which doesn't move. When the brick hits the block it will be shattered. Interestingly if the brick is in contact with the block it will not be damaged. Ultimately all energy will end up as heat. The trick is to convert the energy to heat before it reaches the structure.

If you put a foam material on the out side of the building with , say, a 10 psi compression strength then the load transfered to the building cannot exceed 10 psi until the foam is completely compressed. The energy absorbed by the foam is force times distance or 10 psi times foam thickness. This assumes the foam crushes rather than deforms elastically.

There are many types of foams specifically designed for energy absorption and they are great thermal insulation as well. Urethane, styrofoam, and glass foam would appear to be good choices.

Damn, Compositepro beat me to the punch.  THE trick is energy dissipation to reduce the overall pressure load on the building frame, and hence foundation.  I have little experience personally on this.  However, my uncle runs a firm that has as one of its specialties, blast absorbtion/mitigation retrofitting. Mainly he works on vehicles, particularly for peace keeping forces and mine clearly vehicles.  He has talked to me many times about incorporating his system into structures.  This sounds like the perfect oportunity for both him and you.  The scale of your structure would be perfect for his system.

If you are interested, please email me at

structuresguy@yahoo.ca

I will give you his name and contact info.  His company does lots of work for federal, law enforcement and military organizations.  I am sure he would love to discuss the matter with you.  BTW, he led me to believe that the overpressure from blast can be reduced down to the order of 1-10 psi, from several hundred psi.  His company also designs and manufactures a variety of other site security and access control devices.