Improving the shear design of steel-bar reinforced ultra high performance fibre reinforced concrete beams using mesoscale modelling

Understanding the failure mechanisms of steel-bar reinforced ultra high performance fibre reinforced concrete (UHPFRC) beams is crucial to improving their design but challenging because of the contrast between beam size and fibre size. We develop a 2D mesoscale finite element model with the fibres explicitly resolved to bridge this gap by simulating the damaging and fracturing processes of the beams. To make fibre distribution in the model mechanically representative, we propose a method to project the fibres from 3D to 2D. The continuum damaged plasticity model is used as the constitutive law for the UHPC matrix, and the zero-thickness cohesive elements with softening constitutive law are used to model the nonlinear bond-slip behaviour of the fibre- and bar-matrix interfaces. The models are validated against experimental data obtained from 3 and 4-point loading tests by comparing the simulated and measured fracturing processes, crack patterns and the load-displacement curves. The validated models are then used to analyse the sensitivity of the shear strength of the beams to fibre content, shear span-to-depth ratio, as well as shear and longitudinal reinforcement ratios in the beam, from which a shear strength equation is proposed to improve the design of reinforced UHPFRC beams. The improvement of the new equation over the AFGC equation is demonstrated against experimental data measured from 32 beams with various material properties.