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TECHNICAL PAPER

Figure 3: Specimen and output required for the toughness test prescribed in IS: 17161.

of Nayar and Gettu [18, 19] , which influenced the IRC guidelines to assess the plastic shrinkage mitigation potential of a wide
[20]
for FRC pavements and the ICI guidelines for floor slabs (ICI range of fibres in concretes prone to early-age cracking, such as
[21]
TC/09 ). This design methodology has also been translated those with supplementary cementitious materials [28-31] .
[22]
and published in a Spanish book on FRC applications . The
basic design requirement is summarized in Equation (2): The application of the R-curve method for assessing the
toughening of concrete due to fibre incorporation was
[4]
6p f ctk illustrated by Stephen et al. (2018) , where it was shown that
f e,nkrequired = � 2 f (c/1) – A + f Δt + f sh � γ c (2)
h γ c
the toughening phenomenon can be captured as seen in
where f e,nkrequired is the required characteristic equivalent flexural Figure 4, where the fracture toughness K IR is determined as
strength to provide sufficient moment rotation capacity at the a function of the crack extension Δa for a M40 concrete with
yield lines, P, h, c, l and A are the applied load, slab thickness, hooked-ended cold drawn steel fibres at dosages ranging from
contact radius of load, radius of relative stiffness and a 0 to 45 kg/m (the last number on the curve label denotes the
3
constant that depends on the type of load and expected dosage. However, though it represents the direct application of
failure pattern, f(c/l) is the limiting moment function obtained fracture mechanics principles, the R-curve approach has limited
from inelastic analyses, f Δt , f sh and γ c are the stresses due to applicability in structural analysis and is, at best, indicative of
temperature effects, stresses due to restrained shrinkage trends in material response.
[18]
and the material safety factor . A software SPADIF has been
developed with simple application of this methodology to
slab design, and is being used by some designers mainly for
[23]
warehouse flooring .
Toughness based on the load-crack width
response of notched beams

In line with international practices, notched specimens have
also been used for the characterization of FRC toughness
through first-crack strength and residual flexural strengths,
[5]
following EN 14651 . Since floors are being designed on the
basis of this standard, extensive work has been done at IIT
Madras to develop a database for concretes with different types
and dosages of fibres in order to facilitate the development
of rational design [15, 24, 25] . Structural design with the residual
flexural strength, following the fib methodology has been
[26]
Figure 4: R-curves obtained for steel fibre reinforced concretes
illustrated [14, 27] to promote the application of this approach. It (note: CMOD = crack mouth opening displacement) showing the
should be noted that notched specimens have also been used increase in fracture toughness with crack extension

44 THE INDIAN CONCRETE JOURNAL | FEBRUARY 2026