TECHNOLOGY
experiments will consume time , money , natural resources , energy , and so on . Therefore , numerical simulation has become popular to predict the properties of materials and could assist in the material design [ 7 ]. As for UHPFRC , its fracture process under the flexural load is very important when UHPFRC is applied for structures as large-span bridges and thin-wall shields . Many models have been proposed to simulate the fracture process of concrete under loads , such as discrete crack model [ 8 , 9 ], smeared crack model [ 10 , 11 ], damage model [ 12 ], and lattice fracture model [ 13 ]. Among them , the lattice fracture model is more suitable for the simulation of the flexural response of UHPFRC .
The lattice fracture model was firstly developed by Schlangen and van Mier in 1990s [ 14 ]. Over the last few decades , it has been successfully used for the simulation of the fracture process in concrete . Based on the lattice fracture model , Arslanet al . simulated the strainsoftening behaviour of concrete under tension [ 15 ]; Vervuurt studied the interface fracture behaviour of concrete [ 16 ]; Van Vliet investigated the size effect in tensile fracture of concrete and rock [ 17 ]; Man revealed the effect of aggregate shape on the compressive strength of concrete [ 18 ]; Caduff and van Mier analysed the compressive fracture behaviour of normal concrete , high-performance concrete , and foam concrete [ 19 ]; Grassl and Davies simulated the corrosion-induced cracking in reinforced concrete [ 20 ]; Montero and Schlangen modelled the fracture process of engineered cementitious composites ( ECC ) under uniaxial tension [ 21 ]; and Qian et al . simulated the fracture process
of concrete considering the structural information of concrete at different scales [ 13 ]. Nevertheless , the application of the lattice fracture model for simulating the fracture process of fibre-reinforced concrete , especially UHPFRC , under the flexural load is rarely seen . In order to aid the material design , in this study , the flexural response of UHPFRC was simulated with the lattice fracture model ; moreover , the effects of fibre content and orientation were studied and discussed .
Description of the Lattice Fracture Model for UHPFRC The main idea of the lattice fracture model is to replace the composite by a network of beam elements [ 21 ]. The different phases are represented by beams with different materials properties . The procedures to perform lattice fracture simulation are shown in Figure 1 .
Figure 1 : Procedures of lattice fracture simulation .
The first step is to construct the lattice network . UHPFRC is considered to be composed of two phases , that is , the matrix and fibres [ 22 ]. Discrete fibres are embedded in the matrix . Correspondingly , in the lattice fracture model , fibres are implemented as
52 AFRICAN DESIGN MAGAZINE © | JULY 2018