Geotechnical News March 2011
31
GEOTECHNICAL INSTRUMENTATION NEWS
structure undergoes loading immedi-
ately after casting (see Collotta
et al
[2010]).
In the following, the proposed con-
version procedure is described, based
on the following assumptions:
• There is perfect bonding of the steel
bars to surrounding concrete;
• The strain distribution is linear
within the monitored section (ac-
cording to traditional beam theory);
• The concrete is linear elastic, but
with a tension cut-off (at the aver-
age concrete tensile strength);
• The variation of Young’s modulus
with time, the creep coefficients
and the development of shrinkage
strain follows the rules proposed
in the CEB-FIB Model Code 1990
(Comité Euro-International du Bé-
ton [CEB], 1991);
• The monitored cross-section under-
goes axial force and bending mo-
ment around an axis orthogonal to
the virtual line passing through the
two strain gauges.
Procedure
In the following formulas, subscript “
i
”
means that the quantity is computed at
the time of measurement
t
i
. At all times,
correcting for the gauge thermal error,
the total strain at time
t
i
is
ε
tot,i
, being the
difference between the measured strain
at the gauge and the initial measurement.
On the basis of the assumption of a
linear strain distribution, the total strain
at any given point along the cross-
section is derived from the total strain
at the two measuring points within
the monitored cross-section. Thus the
strain can be computed at the extreme
fibres of the concrete section as well
as at the positions of the reinforcing
bars. Assuming perfect bonding, the
corrected measured strain is assumed to
apply both to the concrete and the steel.
The stress in the steel bars can then
be easily derived in each measuring
instant by the computed total strain
(
ε
s
tot,i
), taking into account the thermal
contribution:
where T
i
and T
0
are respectively the
measured temperature at instant t
0
and instant t
i
,
E
s
is the steel Young’s
modulus (210 GPa) and
α
s
is the steel
thermal coefficient.
As for the computation of concrete
stress in any given point in the cross-
section, a step-by-step procedure
has been adopted (see Ghali A.
et al
[2002]), so as to properly take into ac-
count the contribution of shrinkage and
creep strains and the effects of Young’s
modulus variations over time. Know-
ing the corrected total strain at a cer-
tain point on the section, from t
0
to t
i
,
the concrete stress at the same point
in each interval between consecutive
measurements is obtained using the
following formula, as a function of the
total strain at all the previous measur-
ing instants:
where
ε
cs,i
is the shrinkage strain at
instant t
i
,
ϕ
i,j
is the creep coefficient
between instants t
j
and t
i
and
E
c,i
is the
concrete Young’s modulus at instant t
i
and A
i-1
is a function of the previous
load steps as follows:
The curves of such quantities versus
time can be obtained from National
codes, Eurocodes or other relevant
codes. In this case, we have adopted the
suggestions given by CEB-FIP Model
Code 1990 (Comité Euro-International
du Béton [CEB], 1991).
Having derived the stresses in the
reinforcement and in the concrete sec-
tion borders for each time of measure-
ment, it is possible to verify whether
the concrete section cracks. If it does
not, i.e. if it is completely compressed
or if the maximum computed stress in
the concrete is lower than its tensile
resistance, the whole concrete section
has to be considered in the calcula-
tions. Otherwise, the effective concrete
section has to be calculated at each in-
stant by computing at what height the
concrete stress reaches its mean tensile
resistance. Then, by integrating the
forces over the effective section, in-
ternal actions (axial force and bending
moment), can be derived.
Application to Real Structures
The proposed procedure is applicable
in every case where performance
monitoring of concrete structures is
required. In the following section, the
results obtained from two different
applications are presented: first, a
concrete ring beam support for a shaft
excavation; second, the permanent
lining of a highway tunnel. Both
examples are derived from a large
construction site for the development of
a new highway route between Bologna
and Florence in the central part of Italy.
In the first case, the reinforced con-
crete ring beam was cast after excavat-
ing down to the ring beam location.
Further excavation of the shaft transfers
the force to the ring beam. To counter-
balance the radial thrust acting all over
its circumference, a compressive axial
force develops; gauges have been in-
stalled to compare the actual values of
the axial force to the design assump-
tions and to check for unexpected
bending moments due to unsymmetri-
cal thrusts or geometric imperfections.
The ring beam is thus loaded just one
or two days after casting, when harden-
ing is still taking place.
In the second case (the Buttoli tun-
nel), the permanent lining is cast all
around the tunnel boundary, usually in
two or more pours (first, the invert and,
then, the crown) in order to sustain part
of the soil pressure in the short-term
and all of it in the long-term. Moreover
it is designed to protect the tunnel inner
space from humidity and possible wa-
ter ingress. The gauges have been in-
stalled to measure the actual values of
axial force and bending moments act-
ing on the lining both in the short and
in the long term. During tunnelling, the
excavation continues immediately after
the casting of the concrete and there-
fore the initial loading of the concrete
occurs just after the casting.
In order to estimate the axial force
and possible bending moments in the
annular beam, four instrumented sec-
tions are provided, each formed by a
two strain gauges, located one at the
