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38

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concrete

FIBRES

of a lining with increasing deformation

due to ground movements. Further, the

beam test set-up is statically determinate,

whereas a fibre-reinforced sprayed concrete

lining is internally and externally statically

indeterminate. Such hyperstatic structures

allow for moment or stress redistribution,

which provides redundant structural capacity,

whereas in a beam test, only one single crack

will develop and eventually lead to failure.

The failure mode of a linear structure such as

a simply supported beam is a cross-sectional

failure, which is in complete contrast to the

multiple cracking and system redundancy of

a sprayed concrete lining, and thus does not

represent the biaxial bending occurring in

ground support.

Beam tests produce very conservative

results compared to in-situ behaviour of

fibre-reinforced sprayed concrete in linings

because in-plane compression almost always

coexists with bending moments and these

stresses act to enhance ductility compared to

what is observed in simply supported beams.

It is for this reason that strain-hardening

behaviour is not required in a beam test even

EN14651 only tests toCMOD3.5mm (3mmdeflection),

which is not representative of a sprayed concrete lining.

EFNARC panel test on continuously

supported base.

The cross-sectional failure mode of a typical beam test

with a single crack does not reflect the behaviour in a

sprayed concrete lining.

if deflection-hardening behaviour is desired

in a tunnel lining.

The beam test yields a stress–strain

relationship for a small deformation range

and provides data for service considerations.

However, ground deformation and crack

development can make it very difficult to

predict the exact stresses in a sprayed concrete

lining. Performance data from panel tests

at larger displacements could be the safer

option. A beam test is a low deformation

test (up to 4mm central displacement)

and thus does not provide information for

larger displacements that can be found in

underground environments.Due to the

geometry of the specimens, a beam test

focuses only on small crack widths in a very

short crack length (125–150mm, depending

on the specimen width).

These limitations make it unrepresentative

for sprayed concrete linings, where stress

redistribution is possible and larger

deformations occur.One should be careful

of extrapolating the results of standard beam

tests – where there is limited opportunity for

load redistribution – to tunnel linings, which,

in static terms, are highly redundant shells

that can redistribute loads very effectively (see

Picket and Thomas

(6)

).

The difficulty in determining net

deflections and using the required closed-

loop, servo-controlled testing machines and

the inherent variability of beam flexural

testing are further disadvantages of beam

tests. They have a high variability due to the

limitation in measuring only a single crack in

a statically determinate system. Coefficients

of variation (COV) of up to 35% are not

uncommon in post-crack beam results. This

makes it very difficult to manage on-site QA