18 CHAPTER 3 CONCRETE CORE DRILLING TECHNIQUE 3.1 INTRODUCTION An experimental method known as the concrete core-drilling technique for the determination of in-situ stresses in reinforced/prestressed concrete structures under uniaxial stress condition is developed. The concrete core-drilling technique is formulated by a special arrangement of four electrical resistance strain gages suitably placed around the indented core and connected through a Wheatstone bridge circuit in a full bridge configuration to magnify the strain response. Numerical analysis was carried out to evaluate the efficacy of the method. The reliability of this technique was established in the laboratory, by conducting experimental investigations on concrete specimens with known stress/strain conditions. The development of this technique is discussed here in detail. 3.2 THROUGH-HOLE ANALYSIS The introduction of a hole into a stressed body relaxes the stresses at that location. This occurs because every perpendicular to a free surface (hole surface in this case) is necessarily a principal axis on which the shear and normal stresses are zero. The elimination of these stresses on the hole surface
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CHAPTER 3
CONCRETE CORE DRILLING TECHNIQUE
3.1 INTRODUCTION
An experimental method known as the concrete core-drilling
technique for the determination of in-situ stresses in reinforced/prestressed
concrete structures under uniaxial stress condition is developed. The concrete
core-drilling technique is formulated by a special arrangement of four
electrical resistance strain gages suitably placed around the indented core and
connected through a Wheatstone bridge circuit in a full bridge configuration to
magnify the strain response. Numerical analysis was carried out to evaluate
the efficacy of the method. The reliability of this technique was established in
the laboratory, by conducting experimental investigations on concrete
specimens with known stress/strain conditions. The development of this
technique is discussed here in detail.
3.2 THROUGH-HOLE ANALYSIS
The introduction of a hole into a stressed body relaxes the stresses at
that location. This occurs because every perpendicular to a free surface (hole
surface in this case) is necessarily a principal axis on which the shear and
normal stresses are zero. The elimination of these stresses on the hole surface
19
changes the stress in the immediately surrounding region, causing the local
strains on the surface of the stressed body to change correspondingly. Based
on this principle the concrete core-drilling technique is developed.
In practical applications of the method, the drilled hole depth is small
compared to the thickness of the test specimen/structure. This problem is
complex since no closed-form solution is available from the theory of
elasticity for direct calculation of the existing stresses from the measured
strains. However, the simpler case of a hole drilled completely through a plate
in which the stress is uniformly distributed through the plate thickness can be
used with acceptable approximation.
Consider a thin plate Figure 3.1a, which is subject to a uniform stress,
x in one direction.
a) plate without hole b) plate with hole
Figure 3.1 Stress states in stressed body at point A(r, )
Y
XX
X
r
rA
Y
XX
X
r
arA
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The stress state at any point A (r, ), in polar coordinate system is
defined by, ra, a, r
a. These stresses are given by,
2cos12
xar (3.1)
2cos12
xa (3.2)
2sin2
xar (3.3)
The same plate after a small hole is drilled through it at the centre
(Figure 3.1b): the stresses in the vicinity of the hole are now quite different,
since r and r must be zero everywhere on the hole surface, and the stress
state at any point A (r, ) in polar coordinates is rb, b, r
b and given by
(Timoshenko and Goodier (1970)),
2cos4312
12 2
2
4
4
2
2
ra
ra
ra xxb
r (3.4)
2cos312
12 4
4
2
2
ra
ra xxb (3.5)
2sin2312 2
2
4
4
ra
raxb
r (3.6)
Subtracting the initial stresses (Equations (3.1), (3.2), (3.3)) from the
final (after drilling) stresses (Equations (3.4), (3.5), (3.6)) gives the change in
stress, or released stress at point A (r, ) due to hole drilling. The released
stresses rR, R, r
R at point A (r, ) can be evaluated from the following
equations.
2cos432 2
2
4
4
2
2
ra
ra
raxR
r (3.7)
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2cos32 4
4
2
2
ra
raxR
(3.8)
2sin222
443
2 ra
raxR
r (3.9)
where, a= hole radius and r = arbitrary radius from hole center
Based on Equations (3.7), (3.8), (3.9) the variations of released stresses
along the principal axes for a unit compressive stress ( x = -1N/mm2) were
evaluated. Figures 3.2 and 3.3 show the variation of released radial and
tangential stresses along the loading direction ( =0 ) and along perpendicular
to the loading direction ( =90 ) with distance from the center of the drilled
hole respectively. Figure 3.4 shows the variation of released radial stress along
loading direction ( =0 ) and tangential stress along perpendicular to the
loading direction ( =90 ).
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.0 2.0 3.0 4.0 5.0r/a
RadialTangential
Figure 3.2 Released radial and tangential stresses along the
loading direction ( =0 )
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-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0 2.0 3.0 4.0 5.0r/a
RadialTangential
Figure 3.3 Released radial and tangential stresses perpendicular
to the loading direction ( =90 )
-2.0
-1.0
0.0
1.0
2.0
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0r/a
Radial (along x axis)Tangential (along y axis)
Figure 3.4 Released radial( =0 ) and tangential( =90 ) stresses
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It is seen from Figure 3.4, the released radial stress along loading
direction (x-axis) is tensile in nature. This released stress is opposite to that of
the applied (existing) stress. The released tangential stress perpendicular to
the loading direction (y-axis) is compressive. This stress state is similar to
that of the applied stress state. It is also noted here that the released radial
stress along x-axis and tangential stress along y-axis are of opposite polarity.
This behavior forms the basis to the development of concrete core drilling
technique. The development of concrete core drilling technique is explained
in the following para.
3.3 CONCRETE CORE-DRILLING TECHNIQUE
Concrete core-drilling technique was developed by considering the
practical aspects of the strain gage instrumentation using a special
arrangement of electrical resistance strain gages suitably placed around the
core for assessment of in-situ stress. The configuration and the gage length
used in the core drilling technique are shown in Figure 3.5.
Figure 3.5 Strain gage arrangement for concrete core drilling technique
Concrete
50
SG2
Depthof cut
SG1
Sec- A A
All dimensions are in mm
SG1
d=50
A
Plan
SG3 SG4
SG2
x
30
Ax
3535
100
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This consists of two radial gages (SG1 and SG2) and two tangential
gages (SG3 and SG4) of 30mm gage length aligned around the indented core.
All four gages are connected through a Wheatstone bridge circuit in full
bridge configuration as shown in Figure 3.6. This will magnify the response
of measured strain. The temperature effect during measurement is also
minimised/cancelled.
Figure 3.6 Wheatstone bridge circuit
On drilling a circular core of 50 mm diameter, the strain gages measure the
change in strain due to core drilling. A standard concrete core cutting
machine, with diamond tipped cutting tool as shown in Figure 3.7 was used to
drill the core in this method.
Vin
x
Voutx
SG3
SG1
SG4
SG2
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Figure 3.7 Standard concrete core cutting machine
Strain gage data logger was used to measure the strain response
(Figure 3.8). Data logger used was capable of accepting four types of inputs
from quarter-, half-, and full-bridge strain-gage circuits, including strain-gage-
based transducers with a measurement resolution of 1 micro-strain.
Figure 3.8 Strain gage data logger used to measure the strain response
3.4 NUMERICAL ANALYSIS
Numerical analysis was carried out to check the efficacy and suitability
of the method and to evaluate the calibration constant (Cf), for the chosen
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configuration. The calibration constant is the ratio of the total released
(measured) strain from the four gages to the existing (applied) strain in the
structure due to the applied load. Finite element model of dimensions
500mm×500mm×100mm with core diameter of 50mm was created using
ANSYS. Since the core was drilled at the increments of 10mm (up to a
maximum depth of 50mm), five models with depth of 10mm, 20mm, 30mm,
40mm and 50mm were created. Apart from this, a model of dimensions
500×500×100mm without core also was created. A model with 50mm
diameter through hole also created. This model was used to check the
numerical model by comparing the results with closed form solution of
through-hole analysis results. SOLID95 element was used in modeling the
geometry. The element is defined by 20 nodes having three degrees of
freedom per node: translations in the nodal x, y, and z directions. For the
analysis, assuming that the existing stress (compressive) state corresponds to
x = -1 N/mm2, the same stress state was considered in the analysis. The
stress was applied as pressure on the elements lying on the surface. It may be
noted that this stress state was assumed to be uniform over the thickness.
Translations along the loading direction not allowed at the other end of the
model was given as the boundary conditions. Concrete of M40 grade with
modulus of elasticity (EC) of 31623 N/mm2 and Poisson’s ratio ( ) of 0.17 was
used in the analysis. Loading and boundary conditions were applied on the
models as shown in Figure 3.9.
The results of the model with through hole was compared with the
closed from solution of plate with hole. Comparison of radial and tangential
stresses along loading and perpendicular to the loading direction is shown in
Figure 3.10. The stresses are matching closely. This ensures that the
numerical model can be used for further study.
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Figure 3.9 Typical model showing the boundary condition and loading
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0r/a
Radial (along x axis) Close form solutionTangential (along y axis) Close form solutionRadial (along x axis) NumericalTangential (along y axis) Numerical
Figure 3.10 Comparison of released stresses from close
form and numerical solution
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Further from the analysis, strain distribution on the surface of the
model was obtained. Figures 3.11 to 3.15 show the strain Contours for
different core depths of 10mm, 20mm, 30mm, 40mm and 50mm respectively.
Figure 3.11 Strain Contours for core depth of 10mm
Figure 3.12 Strain Contours for core depth of 20mm
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Figure 3.13 Strain Contours for core depth of 30mm
Figure 3.14 Strain Contours for core depth of 40mm
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Figure 3.15 Strain Contours for core depth of 50mm
From the analysis, the released strains along the gage orientations were
calculated for the four gages by deducting the strain from the model with and
without core.
The variation of released strain along the gage orientation was plotted
and shown in Figures 3.16 and 3.17. From these plots, it is observed that the
released strain is less for smaller depth of cut, and as the depth of cut increases
the magnitude of released strain also increases. Further, as expected the strain
release is higher near the vicinity of the core and beyond 150mm away from
the core the released strain is negligible.
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0
10
20
30
40
0 50 100 150 200 250Distance in mm
10mm20mm30mm40mm50mm
Figure 3.16 Variation of released strain along radial gage
-20
-10
0
-40 -20 0 20 40Distance in mm
10mm20mm30mm40mm50mm
Figure 3.17 Variation of released strain along tangential gage
From the released strain variations, strain response for radial and
tangential gages SG1, SG2, SG3 and SG4 were obtained by averaging the
strain variation for the gage length of 30mm. The total released strain value
was calculated by adding algebraically the strains from the four gages as the
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output of the Wheatstone bridge. Cf was computed by calculating the ratio of
total released strain to the applied strain. This procedure was repeated for
various core depths of 10mm, 20mm, 30mm, 40mm, and 50mm.
The strain response from radial and tangential gages and calibration
constants are given in Table 3.1 for different core depths. Figure 3.18 shows
the variation of calibration constants for various core depths. It is seen that
the calibration constant for depth of 10mm is less. As the depth increases the
calibration constant also increases. Calibration constants are increasing at
higher rate up to 30 mm and after 30 mm the change is less.