Derivation and verification of multilevel particle packing model for Ultra-High Performance Concrete (UHPC): Modelling and experiments

This paper aims to address the conflict between gap gradation and continuous particle packing for the precise design of ultra-high performance concrete (UHPC). More exactly, a new multilevel particle packing model is proposed by deriving the modified Anderson and Andreasen (MAA) equation. The key parameters of the model are determined by Box-Behnken design method. On this basis, the dense packing states of powder and aggregate segments are achieved, and the accurate ratio of two segments are confirmed. Thus, the optimal mix proportion of UHPC matrix can be calculated. Moreover, some novel viewpoints on the development of dense particle packing theory are presented in this study, including the derivation of multilevel particle packing model with n times of gap gradation and the discussion of general mix design procedure that unifies gap gradation and continuous packing, which could further improve the design theory of UHPC composites.