Investigation, validation and implementation of the p-alpha equation of state for concrete media simulation

Abstract

Concrete is the most common material in the construction industry and almost the only material used for building security and protective structures. Such structures are intended to withstand extremely high blast and impact loading. One of the key mechanical properties of materials subjected to such extreme loading is the relationship between the hydrostatic pressure and the volumetric strain, which is known as the equation of state (EOS). In porous materials, this relationship is substantially inelastic due to the closure and collapse of pores. Commonly the EOS is obtained experimentally. Implementation of the experimental EOS curves in analytical and numerical solutions for different applications requires approximate simplified expressions for these curves. One of the most common approximations for describing the nonlinear compression of porous media is the p-alpha EOS. The present paper reviews the p-alpha EOS approximations appearing in the literature and discusses controversial issues concerning the full compaction pressure. New p-alpha EOS approximations are presented for a variety of experimental hydrostatic test results conducted by the authors for different concrete compositions with equal uniaxial compressive strength. An extended investigation is dedicated to the formulation of the p-alpha approximation in the case of limited available data, and a “blind prediction” of the pi-alpha EOS is proposed.

To demonstrate the implementation of the derived p-alpha EOS, an extended example is presented, where the quasi-static cavity expansion problem in a concrete medium that is characterized by the p-alpha EOS is worked out.