African Design Magazine ADM #42 July 2018 | Page 53

TECHNOLOGY
discrete beam elements and are
connected to the matrix elements with
interface beams [21, 23], as shown in
Figure 2. The network constructed by the
matrix beams and nodes represents the
matrix of UHPFRC. Since the matrix of
UHPFRC is very homogenous, the lattice
nodes are generated to at the centre
of the square grids so that a uniform
network can be constructed. With a given
volume fraction, fibre beams with a given
diameter and length are generated and
randomly distributed within the matrix.
Along with the fibre beam, extra nodes
were generated at the location where the
fibre beam intersects the square grid. In
order to represent the fibre-matrix bond,
interface beams were generated between
the extra nodes and lattice nodes.
More details on the lattice network
construction for fibre-reinforced concrete
can be found in [23].
Figure 2: Schematic 2D representation of fibre-
lattice construction.
material properties of the matrix and
fibre beam can be obtained directly
with experiments, and the properties
of interface beam normally can be
determined by fitting the experimental
results of the single fibrepullout test
[21, 24].
The lattice fracture model could simulate
a series of mechanical tests in the lab,
such as compressive test [6], tensile test
[13], and flexural test. With different
boundary condition settings on the lattice
network, different mechanical tests can
be simulated.
The fracture process simulation is
described in detail in [13, 23, 25].
In summary, the fracture process is
simulated step by step. At every step,
a prescribed force or displacement is
applied on the lattice network, and the
stresses in the beams can be calculated.
The beam with the highest stress/
strength ratio is removed from the
lattice network, representing the crack
growth process. After the simulation,
the stress-strain response diagram, the
crack pattern, and the crack propagation
process can be obtained.
Simulation of Flexural Response
of UHPFRC
After the lattice network construction, the
mechanical properties of all the beams
have to be assigned. According to the
previous studies [21], the matrix and
fibre beams are set to be brittle and will
fail under tension at their corresponding
tensile strength, and the interface
beams are set to be ductile and can fail
either in tension or compression. The
Proportion and Properties of UHPFRC
The flexural response of a typical UHPFRC
with 2% steel fibres was simulated in the
paper. The proportion of the UHPFRC is
shown in Table 1. Cement, fly ash, and
silica fume were used as binders. River
sand had a maximum particle size of
2.36 mm. The superplasticiser was a type
of liquid agent with a solid content of
28%. The length, diameter, and tensile
AFRICAN DESIGN MAGAZINE © | JULY 2018
53