Transcript Analysis and Design of Blast Resistant Underground Shelters Abhinav Agrawal

Analysis and Design of Blast Resistant
Underground Shelters
Abhinav Agrawal
Supervisor: Prof. T.K. Datta
Introduction to the problem

Civil defense shelters are typically built to provide protection to
personnel and equipment against the effects of weapon
detonation.

Apart from the basic objective of preventing failure of the
structure itself, a major concern is the dynamic response of the
structure.

A rapid movement of the shelter may cause injury to its human
occupants and cause damage to built-in equipment such as
generators and electrical fittings.

However, the relevant information appears to be scarce
because of the confidential nature of the subject.

The present study tries to analyze the response of an
underground shelter under the influence of blast waves
impinging upon it.
Description of Groundshock

Buried structures can be vulnerable to transient stresses
propagated through the soil and rock in which they have been
constructed.

Sensitive equipment may suffer damage from transmitted
groundshock.

The isotropic component of the transient stress pulse causes
compression of the soil with particle motions parallel to the
direction of propagation of the wave. These are known as
compression or ‘P’-waves.

The component of the stress pulse causing shearing of the soil
with a particle velocity perpendicular to the direction
propagation of the waves are known as shear or ‘S’ waves.

Near the ground surface particles adopt a circular motion.
These are known as Rayleigh or ‘R’ waves.

P and S waves are attenuated more rapidly than R waves and
so R waves tend to dominate at large range.
Characterization of Ground Shock
Groundshock
Waves
Body Waves
P Waves
(Compression)
Surface Waves
S Waves
(Shear)
R Waves
(Rayleigh)
Quantification of Groundshock

The propagation velocity of P-Waves
cp 

K

where K is the bulk modulus and is given by
2 1 
c
3 1  2

The term seismic velocity c is defined as
c
E

Objectives of the work

Modeling the underground shelter surrounded by rock and soil
strata and subject the system to a short duration, high intensity
load, simulating a blast.

Carry out the finite element analysis of the system using
ABAQUS.

Study the response in form of stresses, strains, energies, etc. of
the system.

Use the obtained response in designing the structural system
resistant to the balst waves.
Precise objectives of the work done

Modeling the soil strata as a semi-infinite medium, minimizing
the disturbances created by the presence of boundary
conditions in the simulations.

Analyzing the system by varying depth of burial, size of the
shelter and energy imparted by the blast, etc.

Studying the differences in the structural response in the above
scenarios.
Material model used in the simulations

Under blast loading, the initial response is important.

Beyond a certain distance, the response will not involve plastic
deformation.

The design stand-off distances are not short enough to cause
plastic deformation very near the shelter.
  1800 kg m 3
E  1.0  108 N / mm2
  0.3

The concrete material of the structure is harder than the soil
medium, the elastic model without damping has been
considered.
  2400 kg m 3
E  5000 f ck  25000 N / mm2
f ck  20 N / mm2
  0 .2
Load Variation with time
Load Amplitude with time
1.2
Relative Amplitude
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
Time (seconds)
1
1.2
Modeling the soil as a semi-infinite medium

In dynamic analysis, a fictitious boundary would reflect waves
originating from the vibrating structure back into the discretizied soil
region instead of letting them propagate towards infinity.

It is set at a sufficient distance where either the reflective waves are
not produced or the effect of reflection on the response is not
significant.
Propagation of Stress Waves through soil media
Time Histories of Pressure at Critical Locations
Pressure variation at point 1
Pressure variation at point 2
Time History Plots of Total and Strain Energies
Total Energy of the system
Strain Energy of the system
The modified model with an extended boundary
Pressure variation at point 1
Pressure variation at point 2
Comparison of the extended model with a further
extension of the boundary to a larger distance
Pressure variation at point 1
Pressure variation at point 1
Pressure variation at point 2
Pressure variation at point 2
Modifying the depth of burial
There is a possibility that the stresses and strains generated in the
shelter can be different at different depths of burial of the structure.
This can help in reduction of the vibrations which occur in response to
an explosive blast action.
The effect of varying the depth of burial has been studied at 3 different
depths 7.5 m, 10 m and 12 m.
Stresses with variation in depth of burial
Depth of burial below surface = 12 m
Depth of burial below surface = 10 m
Depth of burial below surface = 7.5 m
Observations

The plots indicate sharper and more prominent peaks in the
shelters with a lesser soil overburden.

The closer distance of the shelters to the center of detonation
which causes larger vibrations in the structure

Also, the overburden stresses reduce the vibrations occurring in
response to the striking blast waves
Stresses at the critical points
Shelter Size = 5m x 5m
Shelter Size = 10m x 10m
Shelter Size = 5m x 5m
Shelter Size = 10m x 10m
Observations

The pressure levels generated in the smaller size shelters are
lower in comparison to those in the larger one.

An analysis of the time history of stresses also highlights lower
stress levels in smaller shelter.

The peaks are significantly more prominent in simulation with a
smaller shelter size.

Prominence of peaks in the time histories plots in the smaller
shelters due to their lower mass, makes them undergo vigorous
vibrations
Conclusions

An elaborate and extensive analysis of shelter response was
carried out using ABAQUS.

In the work, an elastic soil model was adopted based on which
a 3-D stress analysis was performed.

The problem of modeling of soil as a semi-infinite medium was
solved.

The influence of the boundary of the soil medium on the model
was eliminated by gradually extending the medium farther away
from the center of detonation of the explosive charge.

Different cases of buried shelters subjected to detonations were
studied
(a)
Different depths of burial indicated the stability of structures buried
at a larger depth below the ground surface with respect to the
structural vibrations induced in them.
(b)
Varying the size on the shelter response observed to indicate that
shelters with a smaller size undergoes more serious vibrations
when impacted by blast.
Future work on the project

Study the system response with a charge exploding within the
soil strata, by extending the system boundary either side of it.

Study of the effects of variation parameters like input energy,
stand-off distance and shelter properties, etc. on the stresses at
critical points on the structure.

Adoption of more complicated non-linear soil models with the
objective of obtaining a more realistic representation and more
accurate analysis.

3-D modeling of the system to study the stresses generated
and hence designing the structural system
References

Yang Zhengwen, “Finite element simulation of response of buried
shelters to blast loadings”, Finite Elements in Analysis and
Design 1997; 24:113-132

Smith P, Hetherington J, “Blast and Ballistic Loading of
Structures”, Oxford: Butterworth and Heinemann; 1994.

Lu Yong, “Underground blast induced ground shock and its
modeling using artificial neural networks”, Computers and
Geotechnics 2005; 32:164-78