# Multi-Field Models of Fiber Reinforced Concrete for Structural Applications
## 5 Hygro-Mechanical Analyses of Plastic Settlement  
### Background  
Cemetitious materials exhibit semi-fluid behavior during the initial several hours after casting, prior to significant degrees of cement hydration. Sizable volumetric reduction, termed generalized plastic shrinkage, is caused by two sequential processes: plastic settlement and capillary shrinkage. The former process is driven by the gravitational consolidation of cementitious particles and aggregate, accompanied with upward drainage of free water to the top surface of the member, which is usually called bleeding [74]. The latter process is a consequence of the rise of capillary pressure within the interstices between particles [75; 76]. Pore water menisci are formed among solid particles near the top surface after the surface layer of bleed water is consumed by evaporation, as well as by the early stages of hydration. This produces capillary pressure and the associated shrinkage, which may result in cracking of the exposed surface. The extent of plastic shrinkage is highly dependent on mixture composition and evaporation rate [77; 78]. Composition of the mixture mainly affects the mechanical and moisture transport properties of concrete, which govern the maximum deformation. Evaporation rate generally determines duration of the plastic settlement period together with the composition-determined bleeding rate and the magnitude of capillary shrinkage. Thus, the problems caused by plastic shrinkage could be mitigated by controlling those factors. However, concrete mixture design is often governed by various other performance requirements. Rate of evaporation is also difficult to control in some circumstances, particularly for drying environments. The addition of fibers has thus been proposed as a means for controlling plastic shrinkage without compromising mechanical performance of concrete [2; 79; 80; 81; 82; 83]. While the concrete is in a plastic state, fibers contribute to consistency of the mixture and provide stiffness against contractive deformation. In addition, fibers may significantly modify the transport properties of the matrix. Fibers are believed to work as bleeding channels that assist the transport of pore water to the concrete top surface, replenishing bleed water that has been consumed by evaporation [80; 81; 82; 84; 85]. These bleeding channels may result from greater permeability of the fiber-matrix interface, particularly for the case of hydrophobic fiber materials. Through fiber additions, the occurrence of capillary shrinkage can therefore be significantly postponed, which provides additional time for strength development of the matrix. Other research suggests that fibers may increase tortuosity of the flow paths, thus decreasing the bleeding rate and the settlement rate [79; 80]. Synthetic fibers, such as polypropylene, polyvinyl alcohol, and glass fibers, have been preferred in controlling plastic shrinkage cracking due to their large interfacial surface area as well as, in some cases, faster development of bonding strength. Neglecting early-age hydration reactions, plastic settlement of cementitious material is analogous to the consolidation of soil. [PERSON] [86] proposed a one-dimensional small-strain consolidation model for soil, which was refined and extended to three dimensions by [PERSON] [87]. The correctness and capabilities of the Biot model were confirmed using dual-field (displacement and pore pressure) coupled equations considering mass conservation of water [88]. [PERSON] et al. [89] modeled settlement along gravitational direction specially for plastic concrete. The model was later modified by [PERSON] and [PERSON] [90; 91] featuring thermal coupling and evaporation calculation to determine the initial time of capillary shrinkage. This dual-field approach was later implemented within 2D finite element models [92], which were validated through comparisons with experimental data. [PERSON] [77] introduced fracture to the planar model using the same dual-field finite element method.