Numerical simulations of SFRC precast tunnel segments

Table 1. Concrete composition (quantities refer to 1 m 3 ).
2 MATERIALS
Weight [Kg] Volume [l]
Cement Portland 52,5R 425 134,92
Water 142 142
Superplasticiser – 3,20
Aggregates 1885 699,88
Air assumed – 20,00
Water/cement ratio 0,33 –
Table 2. Geometrical characteristic of the fibers.
Fiber L f � f L f/� f
code [mm] [mm] [-] Fiber shape
Wirand 50.0 1.00 50.0
FF1
Wirand 50.0 0.75 67.0
FF3
The concrete matrix was made with cement CEM I
52.5R (UNI-ENV 197) and a natural river gravel with
a rounded shape and a maximum diameter of 15 mm;
its composition is summarized in Table 1. The grain
size distribution of aggregates was chosen very close
to the Bolomey curve by using nine classes of aggregates.
An acrylic based super-plasticizer was used.
The two different types of fibers that were considered
in this research are reported in Table 2 where
the fiber length (L f), the fiber diameter (� f) and the
aspect ratio (L f/� f) are shown. All the fibers are cold
drawn, have a hooked shape, a rounded shaft and a
tensile strength higher than 1100 MPa.
Fibers with an aspect ratio equal to 50 (FF1) were
used with two different volume fractions (V f), equal
to 0.45% (35 kg/m 3 ) and to 0.58% (45 kg/m 3 ). Fibers
with a higher aspect ratio (FF3) were used with a
lower dosage, equal to 25 kg/m 3 (V f � 0.32%) and to
35 kg/m 3 (V f � 0.45%).
Eight beam specimens were made for each type of
SFRC; in addition, 8 beams of plain concrete were
used as reference specimens.
The slump(s) of the fresh concrete was always
greater than 150 mm.
Specimens were stored in a fog room (R.H. � 95%;
T � 20 � 2°C) until 24 hours before testing.
Table 3 reports the mechanical properties of concrete
(average values), as determined after about
60 days of curing; in particular, tensile strength (f ct)
from cylinders (� �80 mm, L � 240 mm), compressive
strength from cubes (f c,cube) having 150 mm side
and Young’s modulus (E c) from compression tests on
cylinders (� �80 mm, L � 240 mm), are reported.
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Table 3. Mechanical properties of concrete (average values).
f c,cube [MPa] f ct [MPa] E c [GPa]
FF1 64.7 64.1 4.11 4.07 38.8 38.1
FF3 63.5 4.04 37,4
Figure 2. Geometry (a) and instrumentation (b) of the
notched specimen for the beam tests.
Fracture properties were determined from notched
beams (150 � 150 � 600 mm) tested under four point
bending according to the Italian Standard (UNI, 2003;
Fig. 2a). The tests were carried out with a closed-loop
hydraulic testing machine by using the Crack Mouth
Opening Displacement (CMOD) as a control parameter,
which was measured by means of a clip gauge
positioned astride a notch in the mid-span, having a
depth of 45 mm (Fig. 2a). Additional Linear Variable
Differential Transformers (LVDTs) were used to
measure the Crack Tip Opening Displacement (CTOD)
and the vertical displacement at the beam mid span
and under the load points (Fig. 2b).
Figure 3 shows typical experimental results from
bending tests on beams with fibers FF1.
Inverse analyses of the bending tests, based on
NLFM, allowed to determine the best-fitting softening
law for the SFRCs adopted in the present research
(Roelfstra & Wittmann, 1986). The Young’s modulus
(E c) was the one experimentally measured from the