Failure waves in a prestressed layer of porous material

Abstract

Unlike the traditional modelling of the reaction of high buildings to dynamic actions using standard software packages, which encounters fundamental difficulties due to the large number of structural components and the complex geometry of the joints, an alternative description of the collapse of a building is proposed in which the building is considered as a brittle continuum with a high initial porosity. To describe the accumulation of dispersed failures and the collapse of a building, an energy model of the damage of a brittle material with an initial porosity, which enables one to describe a number of qualitative features of its behaviour, is used. The most important of these features is the existence of a threshold deformation at which a damage accumulation begins, leading, in the final analysis, to the occurrence of rheological instability, which characterizes the tensile, shear and compressive strength of a porous medium. These limit states depend both on the parameters of the material as well as on the strain history. The propagation of stress waves caused by a pulsed compressive load applied to the upper boundary of a plane layer is investigated. It is shown that a relatively weak action can be transformed into a failure wave on account of the initial stresses in the material in a gravitational field. It is established that moderate compressive actions lead to shear fractures and that the stresses can both increase and decrease during the propagation of the head wave, depending on the level of the action. It is shown that intense actions lead to bulk failure which, due to strong damping, only occurs in the initial stage of the motion. The equation of a macrofailure wave is obtained. The conditions under which it is formed and the collapse retardation time for a dynamic action are investigated. It is shown that an increase in the shear modulus and in the absorption coefficient of the energy released increases the resistance of a building. A decrease in the parameters of the porous medium, which characterize the release of energy as a consequence of the damage evolution, will lead to the same thing. A new effect is revealed which is related to the weak dependence of a macrofailure wave on the applied stress.