Model uncertainty in discrete and smeared crack prediction in RC beams under flexural loads

Abstract

Advanced non-linear finite element models are currently available to perform the design of concrete structures. The development and calibration of the safety factors for the next generation of design guidelines will require a deep understanding of the uncertainty associated with such models. This paper presents a first study focusing on the assessment of the uncertainty of discrete and smeared crack models applied to the simulation of the behavior of RC beams under flexural loads. The discrete strong discontinuity approach (DSDA) and the smeared crack model available in ATENA were chosen for this purpose. Experimental data for mean and maximum crack widths, and average crack spacing for four beams were used as reference. The mesh size dependency and its relation with the uncertainty in the prediction of deflections, crack openings and spacing was investigated. The model uncertainty of mean and maximum crack widths was evaluated for progressive load stages of serviceability conditions for the two crack models considering subsets of data based on the reinforcement ratios and concrete cover.

An extended finite element method with polygonal enrichment shape functions for crack propagation and stiff interfaceproblems

“…The solution also agrees well with the result obtained with the DSDA retrieved from a previous publication devoted to the simulation of strengthened slabs. 84 Even though the polygonal enrichment formulation compares slightly better than XFEM with the experimental data and DSDA, it is worth mentioning that the performance of both formulations is not very different in this example. This is related to the fact of the problem consisting of nonlinear fracture propagation, in which standard XFEM has already proven its adequacy.…”

Numerical Modeling and Analysis of Concrete Slabs in Interaction with Subsoil

“…The localization of the deformation in the crack band is close to a real discrete crack. Refs [69][70][71] describe the basic idea of the crack band approach, which reduces the sensitivities of the numerical model depending on the size of the finite element mesh [68]. Figure 1.…”

A specialised finite element for simulating self-healing quasi-brittle materials

“…potential, with an associated healing surface [5], to modelling the healing as a chemical reaction such as curing of the healing agent [7] or further hydration in the autogenous healing of cementitious materials [6]. The treatment of cracks in the above methods may be categorised as, (i) discrete crack methods that simulate the separation between elements directly, (ii) strong-discontinuity approaches that maintain the background mesh but add enhanced fields to represent cracks and, (iii) smeared crack approaches that 'smear' the crack displacement jumps over elements [21][22][23][24]. Smeared approaches are convenient to implement and can represent bands of diffuse cracks that are found in materials such as concrete prior to the formation of dominant cracks but cannot directly simulate localised failure and can suffer from stress-locking.…”

“…Discrete approaches provide accurate descriptions of cracks but are not computationally convenient, particularly when multiple cracks occur, as in reinforced concrete members. Strong-discontinuity methods provide a good compromise between the two approaches because they are -in general-computationally convenient yet still provide an explicit representation of cracks; including the location, geometry and crack opening [22][23][24][25][26][27][28]. This is particularly important for modelling self-healing systems, as this information is required for the simulation of the transport of healing agents in discrete cracks.…”

“…(2020) 7:32in which M w = M I 3 −K e −1 K +K h and M h =K e −1Kh . Since an increment of healing takes place under a zero change in stress, it may be assumed that;δ −K e −1 K +K h δw and δε ϑ = M w δw The virtual work equation for the damage-healing is obtained by using Eqs (22)(23)(24). in Eq (14),.…”