Size effect and design safety in concrete structures under shear

Safe design requires a valid mechanical model and correct probabilistic analysis. Concrete, which is an archetypical quasibrittle material, typically exhibits stable crack propagation in many types of failure. Therefore, a scientific approach requires analyzing concrete failure on the basis of fracture mechanics. One of the simplest ways to incorporate fracture mechanics into design practice is through the size effect. Statistical analysis reveals that an unevenly sampled database cannot be used to extract the size effect formula for shear failure of concrete beams purely empirically. Therefore the basic form of this size effect formula should be selected first. Simple dimensional analysis of the shear capacity of reinforced concrete beams yields the asymptotic properties of size effect, which are characterized by a plastic strength limit for sufficiently small sizes and an asymptotic LEFM (Linear Elastic Fracture Mechanics) trend for very large sizes. Together with the established small- and large-size second-order asymptotic properties of the cohesive crack model, the analysis unambiguously demonstrates that the energetic size effect law is a correct choice as the basic form of the design formula for concrete beams under shear. Then the new proposed shear design formula is verified and calibrated by a large number of experimental test data. Its validity for practical situations that are not fully covered by the current experimental database is supported by computer simulations based on microplane model. For correct fracture analysis to be made, the fracture energy values need to be measured. For this purpose an improved version of Guinea et al.'s method is presented, to reduce the statistical problem to linear regression by exploiting the systematic trend of size effect. Another obstacle to safe design is the misleading use of understrength factors in the current code provisions. The current design codes for concrete structures contain covert understrength factors. This prevents distinguishing between different combinations of separate risks due to statistical scatter of material properties, the error of the design formula and the degree of brittleness of failure mode, and also makes any prediction of structural reliability impossible. As a remedy, it is shown how the covert understrength factor of the design formula could be made overt. Its coefficient of variation can be based on the supporting test data and on the specified type of probability distribution, which then also implies the failure probability cutoff.