# Multi-Field Models of Fiber Reinforced Concrete for Structural Applications
## 5 Hygro-Mechanical Analyses of Plastic Settlement
### Influences of Short-Fiber Reinforcement: Parametric Study  
The effects of straight, short fibers on the mechanical and transport properties of plastic cementitious material are assessed independently and in combination. The fibers are assumed to be 12 mm in length and 0.04 mm in diameter, and homogeneously distributed within the computational domain using coordinates and angles supplied by a uniform random number generator. The fibers are assumed to be hydrophobic, leading to enhanced porosity of the fiber-matrix interface. The effect of this enhanced porosity is lumped into the transport properties of the fibers, as described later. The elastic modulus of the fibers is chosen to be 40 GPa. It is further assumed that no relative movement (i.e., slip) occurs between the fibers and surrounding matrix. Fiber dosages up to 2% are considered. The stiffening effect of fibers on plastic settlement is investigated first. Figure 15a shows the influence of fiber dosage on controlling plastic settlement. By increasing fiber dosage, the stiffness contributions of the fibers increase. As expected, higher volume fractions of fibers lead to less plastic settlement. Allowance for slip along the fiber matrix interface would reduce the magnitude of this trend. The cases of high fiber dosage also exhibit larger dispersion in the values of plastic settlement for any given nodal point  
Figure 14: Nodal values of vertical displacement and pore pressure at differing times after casting. Figure 13: Comparison of top layer settlement with time among multi-dimensional VCLM meshes and original planar FE model of [PERSON] et al. (2010). elevation, as shown in Figure 16. This is reasonable considering the local stiffening effects of individual fibers, which is a source of heterogeneity. The potential influence of enhanced transport, due to porosity of the fiber-matrix interface, on plastic settlement is investigated next. As noted above, the effective transport properties of the interface are considered by modifying the transport properties of the fibers. For this case, the Voronoi cell sizes are large relative to the fiber length. Accordingly, to account for the local influences of each fiber on the flow field, effective conductivity of the fiber depends on the location of the facet intersection point along the fiber length [98,99]. Conductivity grows from the fiber ends, similar to the shear lag effect present in the mechanical representations of the fibers [21]. In an average sense, the conductivity of the fibers was assumed to be greater than that of the matrix by a factor of about 10 (i.e., \(\sigma_{f}/\sigma_{m}\approx 10\)). The results shown in Figure 15b support some of the experimental observations that fiber additions may increase plastic settlement, along with concurrent increases in the amount of bleed water. Figures 17 and 18 show how the distribution of pore  
Figure 16: Effect of stiffening fiber dosage on the vertical displacement of all nodal points at \(t=150\) min. Figure 15: Influence of fiber dosage on surface layer settlement considering: (**a**) stiffness contributions of fibers; (**b**) conductivity contributions of fibers; and (**c**) combined stiffness and conductivity effects of fibers. pressure over the specimen height is potentially affected by conductivity of the fiber-matrix interface. Within increasing solution time, pore pressure diminishes over the specimen height. With the addition of fibers, however, the rate of pore pressure decrease is higher and the shape of the pore pressure profile also differs. Here, too, the introduction of locally enhanced transport properties, due to the presence of fibers, causes greater dispersion of the pore pressure values at any given nodal elevation. Figure 17: Influence of fiber dosage on the development of pore pressure distribution over time. Figure 18: Pore pressure distribution and nodal value profile at \(t=90\)  min for: (**a**) \(V_{f}=0\%\); and (**b**) \(V_{f}=0.2\%\).