Model uncertainties and partial safety factors of strain-based approaches for structural concrete: Example of punching shear

The development of mechanical models relating the state of strains and the resistance of reinforced concrete structures has become a trend in the last decades. These types of models are referred to as strain-based approaches. Since strain-based approaches usually involve multiple sub-models and take implicit forms, their model uncertainties tend to be more complex than those of the explicit design equations commonly used in design codes. The characteristics of the model uncertainties of strain-based approaches is investigated using the Critical Shear Crack Theory (CSCT) for the punching shear resistance of structural concrete members as example. Both by performing theoretical parametric analyses and by evaluating relevant experimental data, it is shown that the model uncertainty of global resistance solution of strain-based approach can be viewed as resultant of the model uncertainties of the sub-models. In addition, it is also shown that the model uncertainty of the global resistance solution can be lower than those of the sub-models, depending on their sensitivity relationship. The model uncertainties of different Levels-of-Approximation (LoA) of the CSCT for punching are also compared. The LoA approach intends to provide consistent and progressively refined model for different design tasks in practice. The model uncertainty quantification result confirms that the model uncertainty of higher LoA of CSCT has lower variability and also less conservative bias than lower LoA. Finally, based on the obtained model uncertainties, different types of partial safety formats for strain-based approaches are compared and discussed. Using the CSCT punching shear model as an example, it is shown that the partial factors applied to the sub-models are more suitable for higher LoAs since they can effectively account for the change of model uncertainty associated to the change of failure mode. Based on the assumptions described in this work, the relationship between the partial factors of the punching shear provisions in the 2nd generation of Eurocode 2 for the design of new structures and the assessment of existing critical ones is established.