Compression field modelling of fibre reinforced concrete shear critical deep beams: a numerical study

Numerical analyses represent an important way to study the behaviour of both reinforced concrete and fibre reinforced concrete (FRC) structural elements under different loading conditions. Even though advanced computer codes able to model concrete fracture phenomena were developed in the past decades, numerical and analytical tools still require improvements and verifications against new experimental evidences, especially with respects to non-standard or quite critical structures. The present paper focuses on the numerical modelling of the shear behaviour of deep beams whether with fibres (FRC) or no shear reinforcement (PC), by means of a suitable implementation of the modified compression field theory (MCFT) and the disturbed stress field model (DSFM). After a numerical validation against some new available experimental results, specific numerical analyses were performed in order to study the size effect influence on the shear behaviour of FRC elements. These analyses were conducted considering a broad variety of beams, from 250 to 1500 mm high and with different amount of fibres. In the modelling, particular attention was devoted to the nonlinear behaviour of materials, especially with regard to the tension softening of FRC. The latter was modelled through inverse analysis on 3PBTs (EN14651) and by using the recently published Model Code 2010 linear model (MC2010). Refined nonlinear constitutive models and relationships for describing crack spacing and crack width, both in case of PC and FRC, were utilized as well. The numerical results show the reliability of the MCFT and DSFM in modelling both PC and FRC deep beams critical in shear. Moreover, the positive influence of fibres in reducing and significant altering the size effect trend is clearly confirmed by a broad parametric study herein reported.