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Analysis and Design of Blast Resistant Underground Shelters Supervisor: Prof. T.K. Datta Abhinav Agrawal

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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.

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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.

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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.

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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.

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Characterization of Ground Shock R Waves (Rayleigh) S Waves (Shear) Groundshock Waves Surface Waves P Waves (Compression) Body Waves

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Quantification of Groundshock The propagation velocity of P-Waves where K is the bulk modulus and is given by The term seismic velocity c is defined as

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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.

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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.

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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.

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The concrete material of the structure is harder than the soil medium, the elastic model without damping has been considered.

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Load Variation with time

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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.

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Propagation of Stress Waves through soil media

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Time Histories of Pressure at Critical Locations Pressure variation at point 1Pressure variation at point 2

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Time History Plots of Total and Strain Energies Total Energy of the system Strain Energy of the system

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The modified model with an extended boundary Pressure variation at point 1 Pressure variation at point 2

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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 2 Pressure variation at point 1 Pressure variation at point 2

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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.

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Stresses with variation in depth of burial Depth of burial below surface = 12 m

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Depth of burial below surface = 10 m

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Depth of burial below surface = 7.5 m

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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

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Stresses at the critical points Shelter Size = 5m x 5mShelter Size = 10m x 10m

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Shelter Size = 5m x 5mShelter Size = 10m x 10m

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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

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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.

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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.

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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

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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

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