Considerations on the partial safety factor format for reinforced concrete structures accounting for multiple failure modes

The increasing usage of nonlinear analyses for the design of reinforced concrete structures and the necessity of codes of practice to provide a consistent safety format for them is one of the challenges that new generations of codes of practice are facing. Suitable safety formats shall thus account for the peculiarities of nonlinear analysis, such as the possibility of having multiple potential failure modes. In this paper, the applicability of the classical Partial Safety Factor Format (PSFF) for the resistance of reinforced concrete structures (composed of two safety factors: gamma C for concrete compressive strength and gamma S for reinforcement yield strength) is investigated accounting for the possibility of multiple failure modes in nonlinear analysis. In addition, the similarities between nonlinear analysis and typical simple cases in the design of structural concrete are shown. Reliability analysis is performed for the design resistance of concrete structures according to PSFF under different design situations (crosssectional resistance or load-bearing capacity of structural elements and of simple structural systems). The results show that the PSFF applied to material strength variables leads to a satisfactory level of reliability, independently of the development of different failure modes induced by material uncertainties in nonlinear analysis. In addition, it is also observed that the simplification of integrating geometrical and model uncertainties into the partial safety factors for material strength variables can potentially underestimate their influence on the structural reliability in some cases. The case studies shows that occurrence of multiple failure modes can result into significantly different distribution characteristics between the tail and most probable region of the resistance of concrete structures. Attention should also be paid to a proper tail approximation of the probability distribution of the resistance when calibrating safety formats for concrete structures.

Development of a consistent approach for design and assessment of structural concrete members using stress fields and strut-and-tie models

Filip Niketic

Designing new concrete members and assessing the strength of existing elements subjected to in-plane stress state conditions is often conducted by means of Stress Fields (SF) and Strut-and-Tie Models (STM). These methods are usually accounting for identical load-carrying mechanisms for design and assessment, even if the goals for these two tasks are not the same. When designing new elements, the aim is to obtain solutions that are in equilibrium with external actions, with simple reinforcement layouts while ensuring satisfactory behaviour at serviceability limit state. When assessing the ultimate strength of existing elements, the goal is to avoid an unnecessary strengthening and limit the amount of retrofitting. The required complexity of assessment models depends on the strength requirements, and need to be gradually refined if the results from current models prove to be insufficient. This refinement process ultimately leads to increasingly more exact solutions that eventually correspond to the largest possible strength according to the limit analysis. This thesis presents various strategies which can be employed to develop SF and STM suitable for the design and assessment of structural concrete members. The idea of a gradual model refinement (both for design and assessment) is introduced through practical examples, while potential challenges related to each solution are indicated and discussed. Moreover, the accuracy and the generality of exact solutions obtained using Elastic-Plastic Stress Fields (EPSF) are investigated. To do this, ultimate loads estimated with EPSF are compared to test results found in the literature. To facilitate further studies by other researchers, they are available online. The analysis of structural members with insufficient anchorage and indirectly supported concrete elements with EPSF are presented and discussed. Furthermore, this thesis focuses on a sensitivity analysis of the EPSF, to investigate the stability of the results as a function the size, shape and orientation of the finite elements. The influence of the number of iteration steps on the accuracy of EPSF models is evaluated, and clear recommendations are provided. Stress fields based on exact solutions of the theory of plasticity simulate the physical behaviour of structural concrete members more accurately than current code provisions. On this basis, a procedure for tailoring partial safety factors for steel and concrete is presented and discussed. Reduced PSF could potentially be used when assessing the strength of existing reinforced and prestressed concrete elements, which would (could?) lead to significant cost reductions in the field of structural maintenance. To better understand the mechanical origins of concrete compression softening (important for an accurate application of stress fields), a mechanical model for estimating the effective concrete compressive strength is developed and discussed. Concrete cover spalling, concrete crushing and crack sliding are taken into account. Special attention is given to the dowel action of the reinforcement and its effects on the surrounding concrete matrix. The model is validated using experimental results found in literature. Finally, the pertinence of existing semi-empirical approaches for determining the effective concrete compressive strength is evaluated and discussed.

EPFL2017

On the compressive and bond strength of reinforced concrete as structural properties

Francesco Rafael Alberto Moccia

Traditionally, the concrete strength is measured on cubes or cylinders having normalized dimensions, suitable vibration and curing conditions and their strength is assessed in laboratory under fast loading rates. However, the in-situ strength of structural elements can considerably differ from that of a small and homogenous control specimen due to a number of issues. Notably, phenomena taking place during the consolidation process of fresh concrete may affect the compressive resistance of tall members as well as the bond strength of reinforcing bars located in top layers. During concrete consolidation, water migrates in the direction of the free surface while concrete settles downwards, phenomena referred as concrete bleeding and plastic settlement respectively. Under these circumstances, a decrease in the concrete properties near the upper surface is observed as well as a development of cracks and voids surrounding horizontal reinforcing bars, causing potential disturbances on the compressive stresses and affecting the mechanical engagement between bars and concrete. In addition, the response of structural concrete may differ from that of material samples due to non-uniform stress states, the material brittleness, the cracking induced by imposed strains, the rheological response of concrete and the presence of embedded disturbances. As a result, the strength measured in material samples needs to be corrected with strength reduction factors to ensure suitable structural analysis. In this thesis, an in-depth investigation is performed on the different phenomena affecting the compressive and bond strength of structural members. These aspects are assessed by means of several testing programmes instrumented with refined measurements techniques such as tomography and Digital Image Correlation. An extensive experimental programme comprising 76 column and prism tests was carried out to evaluate the influence of casting position, loading direction and bar disturbances on the compressive resistance of structural elements. The detailed measurements performed at the fresh and hardened state resulted in the proposal of consistent design rules accounting for the investigated phenomena. Focus was also given on the influence of material brittleness and the implications of internal stress redistributions on the structural response of reinforced concrete columns and compression zones of members in bending. The pertinence of the investigations were validated based on more than 400 column tests collected from the literature. The implications of casting conditions on pull-out and spalling failures were also assessed by means of 137 pull-out tests on reinforcing bars presenting variable diameter, concrete cover, casting height and embedded length. The investigations resulted in the proposal for a physically-consistent approach, evaluating the pull-out resistance as function of casting conditions and reinforcement characteristics. Finally, the phenomenon of cover spalling was examined with respect to the action of a radial inner pressure, as originated by bond engagement or associated to the volumetric expansion of corroded reinforcement. The mechanisms inducing spalling were analysed by means of a comprehensive experimental programme comprising 56 specimens instrumented with Digital Image Correlation. A mechanical model is eventually proposed to evaluate bond-related cases of cover spalling.

EPFL2021

Partial safety factor format for the resistance of structural concrete considering multiple failure modes

Miguel Fernández Ruiz, Aurelio Muttoni, Qianhui Yu

In this paper, the applicability of the Partial Safety Factor Format (PSFF) of EN1992-1-1:2004 (Eurocode 2 for Concrete Structures) to the reliability verification of structural concrete resistance involving multiple failure modes is investigated. This is performed by means of an example dealing with the bending resistance of reinforced concrete sections and accounting for different failure regimes. The results show that the PSFF yields to a satisfactory reliability level independently of the regime governing failure. In addition, compared to global safety factor approaches, PSFF has the advantage of achieving better tail approximation of the probability distribution of resistance random variable. Finally, some potential improvements on the assumption of lumping geometric and material uncertainties currently adopted EN1992-1-1:2004 are discussed.