A consistent safety format and design approach for brittle systems and application to textile reinforced concrete structures

Design and verification of structures in modern codes of practice account for a safety format, ensuring that the probability of failure does not exceed a given threshold. Although specific safety formats are proposed in some cases for special types of structures or analyses, most designs and verifications are currently performed on the basis of the Partial Safety Factor Format (PSFF). This format is applied to cover different materials and structural responses, allowing for a uniform methodology to account for reliability. Such consideration greatly simplifies the design process, but raises concerns on its consistency when different structural responses are observed. In the PSFF as considered in fib Model Code and Eurocodes, no explicit distinction is made on the value of the partial safety factors (for actions or materials) depending on whether a structural system has a brittle or a ductile response. This can be potentially inconsistent, as brittle systems have limited or no redistribution capacity of internal forces (which can give rise to premature failures if action effects are poorly estimated), while ductile systems have large potentials to redistribute internal forces and are thus little sensitive to this issue. In this paper, to investigate on the suitability of PSFF for brittle structures, the most suitable manner to determine internal forces for brittle elements failing in bending and the corresponding model uncertainties of action effects are investigated in detail. The concepts are derived from a theoretical perspective and applied to the case of Textile Reinforced Concrete (TRC). This material is a promising development to reduce the footprint of concrete construction and to build lightweight structures, but exhibits a very brittle response in bending (contrary to ordinary reinforced concrete with usual reinforcement ratios). In this paper, by means of an experimental and theoretical investigation, it is shown that following a suitable approach to estimate internal forces for brittle systems as TRC leads to a low level of model uncertainty of action effects. This leads to the conclusion that, compared to standard design of ductile systems, no additional correction is required for safety issues. Following this outcome, the partial factors for TRC structures are calibrated. In addition, due to the significance of geometrical uncertainties, a method for designing TRC on the basis of a design value of the effective depth (a reduced value accounting for construction tolerances instead of its nominal dimension) is eventually discussed, showing that it allows for a more uniform level of safety.