Blast mitigation using cementitious foams: Experimental investigation and theoretical development

Blast vulnerability of buildings in an urban environment has motivated the Structural Engineering community to develop and implement blast mitigation strategies for existing structures. The work presented in this dissertation is aimed at researching the concept of a protective system for structural elements consisting of compressible, low-strength, cementitious foam. A cladding made of cement foam is intended for use as a sacrificial protective material, which would reduce the stress amplitude transmitted to the structural element from an applied blast pressure loading. The attenuation of the applied pressure loading is produced by the irreversible compaction of the material. Brittle shattering or spalling of structural elements, primarily made of reinforced concrete or brick masonry, can be prevented or suppressed in cement foam cladded structures.Experiments were conducted to investigate the quasi-static and dynamic response of cement foam. Instrumentation for accurately measuring the applied blast pressure and the stress pulse transmitted through the foam to the structural element were developed. Specimens made of cement foams of different densities and lengths were evaluated for different blast pressure loadings. The cementitious foams exhibit a concave stress-strain relationship associated with crushing of cells, which leads to densification of the material. Under blast loading, a compaction front which exhibits shock-type characteristics, forms and propagates in the foam. The compaction front creates an interface which separates the densified material consisting of crushed cells from the uncrushed cells. Experimental results identified a critical length, Lcr, which depends on the stress-strain response of the foam, required for completely attenuating an applied blast pressure loading. When foam of length larger than Lcr is used, there is a clear beneficial effect in reducing the amplitude of the transmitted stress. The blast pressure loading applied at one end of foam specimen is transmitted to the substrate as a rectangular shaped pulse. The stress amplitude of the rectangular pulse is close, but slightly higher than the crushing strength of cement foam. When a length smaller than Lcr , is used, there is an increase in the stress following the initial rectangular stress pulse. The stress enhancement can exceed the applied blast pressure amplitude when the length of foam is significantly smaller than L cr.Two approaches based on different representations of the bulk deformation of the cement foam were developed to predict the dynamic compaction of the cement foam under transient loadings. The first approach considers a rigid-plastic-plastic-locking (RPPL) idealization of the quasi-static stress-strain curve and results in a simplified one-dimensional 'shock' model. Closed form solutions for calculating Lcr and the transmitted stress when the length of foam exceeds Lcr were also obtained analytically for typical blast loadings. The second approach considers the actual stress-strain behavior of the foam, which, when combined with the conservation laws, results in a set of non-linear hyperbolic equations. A finite volume implementation of the hyperbolic conservation equations in a Lagrangian framework was developed. A Second-Order TVD version of WAF scheme based on the exact solution of the local Riemann problem successfully predicted the wave structure consisting of the elastic wave and compaction fronts propagating in foam materials undergoing dynamic compression. The transmitted stress predicted by the exact Riemann based finite volume method compares favorably with the experimental measurement when the length of the foam is both larger and smaller than Lcr. The finite volume simulation provides an insight into the wave structure in the foam following blast wave incidence and leads to an understanding of the stress enhancement phenomenon. There is a steady attenuation of the compaction front, which results in diminishing its amplitude as it travels in the material. A completely diminished compaction front results in a reduce level of transmitted when the length of foam exceeds Lcr. The reflection of a partially attenuated compaction front leads to the stress enhancement when the length of the foam is less than Lcr.A design guideline for using foam cladding to protect the structural elements made of quasi-brittle material, such as reinforced, un-reinforced concrete or masonry, for a prescribed level of projected threat from a blast is presented. The proposed design approach includes a two step process and considers damage mechanisms in two time scales associated with stress wave propagation and structural motion.