# Influence of Cracking on Oxygen Transport in UHPFRC Using Stainless Steel Sensors
## 1 Introduction  
Model Code 2010 defines fiber reinforced concrete (FRC) as a composite material that is characterized by cement matrix (concrete or mortar) and discontinuous discrete fibers, which can be made of steel, polymers, carbon, glass, or natural materials [1]. Cracks in reinforced concrete structures are the main entrance point for aggressive agents that could initiate the degradation processes in the structure. The incorporation of fibers into the cementitious matrix can improve its durability behavior due to the reduction of crack width and the spacing of the cracks produced by the internal redistribution of stresses. The dosage, type, and geometry of the fibers will modify the crack pattern and, in general, high fiber content will lead to multiple micro-cracking with reduced spacing between cracks, instead of localized macro-cracks spaced apart several centimeters. Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC) is a type of FRC with compressive strength between 140-200 MPa and tensile strength between 7-15 MPa [2]. This type of concrete has very low maximum particle size (1-2 mm) and well graded aggregates, high content of fibers, usually steelfibers, and it displays high ductility, producing very thin cracks under load (\(<\)60 \(\upmu\)m). The durability performance of UHPFRC is excellent, due to its high matrix density and its multi-cracking behavior that is provided by the fibers [3]. Other FRC families, such as Strain Hardening Cementitious Composites (SHCC), Engineered Cementitious Composites (ECC), or some deflection hardening cementitious composites (DHCC), also exhibit similar behavior in terms of multi-cracking with very thin cracks [4; 5; 6]. The multi-cracking response of these materials comes as a consequence of the strain or pseudo strain hardening responses, similarly to what occurs with reinforced concrete elements with a very high reinforcement ratio [4]. Some studies indicate that plain concrete specimens have microcracks inside their matrix, even in their initial stage before applying any load. These cracks are bond cracks (in the interface paste-aggregate), but also matrix microcracks that are produced by shrinkage, with sizes of around 2-3 microns [7]. When a load is applied, these cracks increase their size two or five times, even at a load level of 15% of concrete compressive strength [7]. Increasing the load level further produces widening and propagation of the cracks until they bridge to other microcracks [7; 8; 9]. The RILEM TC-122-MLC on \"Micro-cracking and Lifetime Performance of Concrete\" defined micro-cracks as those with a crack width below 10 microns. Cracks around this size allow for the interchange of fluids and dissolved solids with the environment [10]. RILEM TC-122-MLC also differentiates the potential relevance of transport, depending on the state of the material being transported (values at atmospheric pressure):  
* Gaseous materials, such as CO\({}_{2}\), water and acid vapor, may take part in transport in cracks up to a few tenths of micrometer (i.e., 0.1, 0.2 microns). * Liquid materials, such as water, solutions of acids, might be of minor importance in microcracks below 1 micron. Generally, the allowable surface cracks widths indicated in the codes for reinforced concrete assume that cracks up to 100 microns are allowable, even in highly aggressive environments. However, as the TC-122-MLC explains [10], these codes assume V-shaped cracks with the most open area in the surface of the element and decreasing crack width going towards the interior of the element. The codes assume that those sizes, combined with the recommended covers, ensure that the crack does not reach the rebar or does it at a very low size (around 10 microns). In the case of FRC, it has been reported [11] that the internal crack pattern greatly changes when fibers are added to concrete (as compared to cracks in reinforced concrete), increasing crack branching and crack tortuosity, despite having a similar total crack width when compared to reinforced concrete without fibers.