CHAPTER 3 CONCRETE CORE DRILLING TECHNIQUE 3.1...
Transcript of CHAPTER 3 CONCRETE CORE DRILLING TECHNIQUE 3.1...
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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
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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
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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.
Table 3.1 Calibration constants evaluated numerically
Released strainDepth ofcut SG1, SG2
( RR)
SG3, SG4( T
R)Total strainrelease ( M)
Calibrationconstant
(mm) Micro-strain Cf
10 10.2 -4.9 30.2 0.96
20 16.2 -8.2 48.8 1.54
30 18.3 -10.6 57.8 1.83
40 18.8 -12.3 62.2 1.97
50 18.7 -14.2 65.8 2.08
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0
10
20
30
40
50
0 0.5 1 1.5 2 2.5 3Calibration constant
Figure 3.18 Calibration constants evaluated numerically
3.5 EXPERIMENTAL STUDIES
The reliability of this technique for in-situ stress evaluation was
established in the laboratory, by conducting experimental investigations on
concrete specimens with known stress / strain. Six concrete specimens of
dimension of 500×500×100mm were used for this study.
3.5.1 Preparation of Specimens
Test specimens of size 500×500×100mm were cast using concrete of
mix proportion 1: 1.514: 2.233 with water-cement ratio 0.5. Ordinary Portland
cement (OPC) 43 grade, natural river sand confirming to zone I (IS:383-1999)
and angular shaped crushed granite of 10 - 12.5mm nominal size coarse
aggregate were used as the concrete ingredients. The mean strength of
concrete used for specimens were 40 N/mm2.
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Steel moulds were used for casting the specimens. Mild steel bars of
8mm diameter with yield stress of 250 N/mm2 were used as the reinforcement.
The reinforcement cage was placed inside the mould and to maintain the cover
at the bottom cover blocks were placed as shown in Figure 3.19. A tilting
type drum mixer machine was used for preparing the concrete. The moulds
were filled with concrete in three layers and each layer was compacted well
using 25mm needle type immersion vibrator. The top surface of the specimen
was leveled with hand trowel (Figure 3.19). The specimens were demoulded
after 24 hours and cured by immersing them in water for 28 days.
Figure 3.19 Preparation of the test specimen
3.5.2 Instrumentation and Testing
Experiments were conducted on 500×500×100mm size concrete
specimens. Six specimens were studied for this purpose. On each specimen,
at the centre, 30mm length, 120 ohm resistance strain gages were bonded as
per the configuration described in the Figure 3.5. All the gages were with 1m
length pre attached lead wire. Additionally one more gage also bonded at the
middle of the intended core to measure the applied strain. Figure 3.20 shows
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the specimen instrumented with strain gages. Standard procedures were
followed for bonding the strain gages. Before bonding the strain gages the
surface of the specimen was cleaned with emery sheets. A pre-coat of two
component epoxy was applied on the surface as moisture protection. All the
gages were bonded to the specimen using cynoacyralic based quick setting
cement. After bonding, the gages were protected with a layer of M-coat and
wax protection. Additionally, silicon rubber coating was provided as water is
used as a coolant during drilling the core.
Figure 3.20 Strain gage instrumented specimen for testing
A special test set-up was designed and fabricated to apply axial
compression to the specimen, by means of pedestal and a hydraulic jack. The
schematic diagram of test setup is shown in Figure 3.21. The load was
measured using a calibrated load cell. The pedestals were fixed to the heavy
duty test floor at structural testing laboratory, CSIR- SERC.
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Figure 3.21 Schematic diagram of experimental setup
Axial compression was applied to the instrumented specimen, by using
300kN capacity hydraulic jack as shown in Figure 3.22. The applied load was
measured through a 300 kN load cell. This load cell was specially fabricated
for this purpose. A strain gage data logger was used to measure the strain
response. All the strain gages were connected to the strain gage data logger
individually in a quarter bridge configuration. During loading, the load and
strain responses were measured in order to have the real applied strain to the
specimens.
PLAN
PedestalJack
Load cell
Concretespecimen
ELEVATION
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Figure 3.22 Experimental setup for concrete core drilling technique
After the application of load, the four strain gages were connected in
the full bridge configuration as shown in Figure 3.6 and the bridge circuit was
initialized. Now in the stressed specimen, a circular core of 50 mm diameter
was formed by core drilling equipment with diamond tip drill bit. Drilling was
carried out in steps of 10mm to 50mm depth with the increments of 10mm. At
each depth of cut the released strain was measured. Totally six specimens
were tested. The specimens were identified as U1, U2, U3, U4, U5 and U6.
The results of each specimen are given below:
3.5.3 Results on Concrete Core Drilling Technique
3.5.3.1 Test results of Specimen U1
Specimen U1 was stressed to a load of 195kN. The corresponding
strain developed in the specimen was -121micro-strain. Released strain was
measured by drilling the core in the stressed specimen in incremental depth of
10mm up to 50mm. The calibration constant calculated from the released
strain and applied strain is given in Table 3.2. Calibration constant Cf is the
ratio of total released strain to the applied strain. Figure 3.23 shows the
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released strain vs. depth of cut for specimen U1. The calibration constant vs.
depth of cut for specimen U1 is given in Figure 3.24. Maximum strain of
221micro-strain was released at the depth of 30mm. The corresponding
calibration constant is 1.83. Calibration constant varies from 0.48 to 1.80. The
strain release up to 30mm depth increases and beyond this depth the strain
release stabilises.
Table 3.2 Released strain and calibration constant for the Specimen U1
Depth of cut inmm
Released strain ( m)inmicro-strain
Calibrationconstant (Cf)
10 58 0.4820 169 1.4030 221 1.8340 216 1.7950 218 1.80
0
10
20
30
40
50
60
0 50 100 150 200 250
Micro-strain
Figure 3.23 Released strain vs. depth for Specimen U1
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0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Figure 3.24 Calibration constant vs. depth for Specimen U1
3.5.3.2 Test results of Specimen U2
A compressive load of 173kN was applied to the specimen U2. The
strain developed in the specimen due to the applied load was -120micro-strain.
Concrete core drilling technique was applied to the loaded specimen.
Released strain was measured at different core depths by drilling the core
incrementally and is given in Table 3.3.
Table 3.3 Released strain and calibration constant for the Specimen U2
Depth of cut inmm
Released strain( m) inmicro-strain
Calibrationconstant (Cf)
10 77 0.6420 128 1.0730 190 1.5840 203 1.6950 214 1.78
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Figure 3.25 shows the released strain vs. depth of cut for Specimen U2.
The calibration constant was calculated from the released strain and applied
strain and are given in Table 3.3. Figure 3.26 shows the calibration constant
vs. depth of cut for Specimen U2.
0
10
20
30
40
50
60
0 50 100 150 200 250
Micro-strain
Figure 3.25 Released strain vs. depth for Specimen U2
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Figure 3.26 Calibration constant vs. depth for Specimen U2
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For Specimen U2, the maximum strain of 214 micro-strain was measured at
the depth of 50mm and the corresponding calibration constant is 1.78. In this
specimen, released strain rate is higher up to 30mm and beyond this depth the
rate of change is less. More than 85% of strain release occurred at the depth
of 30mm.
3.5.3.3 Test results of specimen U3
The Specimen U3 was stressed to a load of 237kN. The corresponding
strain developed in the specimen was -80micro-strain. Released strain was
measured in the stressed specimen by drilling the core incrementally. The
released strain for different depth of cut is given in Table 3.4.
Table 3.4 Released strain and calibration constant for the Specimen U3
Depth of cut inmm
Released strain ( m)inmicro-strain
Calibrationconstant (Cf)
10 46 0.5820 114 1.4330 130 1.6340 141 1.7650 154 1.93
The calibration constant calculated from the released strain and applied
strain for different core depths are given in Table 3.4. Figure 3.27 shows the
released strain vs. depth of cut for Specimen U3. Maximum strain release of
154micro-strain measured at 50mm depth. Corresponding calibration constant
is 1.93. Figure 3.28 shows the calibration constant vs. depth of cut for
Specimen U3. It is seen that almost 85% of the strain released at 30mm depth.
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0
10
20
30
40
50
60
0 50 100 150 200Micro-strain
Figure 3.27 Released strain vs. depth for Specimen U3
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Figure 3.28 Calibration constant vs. depth for Specimen U3
3.5.3.4 Test results of Specimen U4
The Specimen U4 was loaded with 158kN and the corresponding strain
developed was -105micro-strain. Released strain was measured by using
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core-drilling technique in the stressed specimen. During drilling, released
strain was measured for different depths of cut from 10mm to 50mm and is
given in Table 3.5. Figure 3.29 shows the released strain vs. depth of cut for
Specimen U4. The calibration constant calculated from the released strain and
applied strain is given in Table 3.5.
Table 3.5 Released strain and calibration constant for the Specimen U4
Depth of cut inmm
Released strain ( m)inmicro-strain
Calibrationconstant (Cf)
10 68 0.6520 138 1.3130 165 1.5740 197 1.8850 192 1.83
0
10
20
30
40
50
60
0 50 100 150 200 250
Micro-strain
Figure 3.29 Released strain vs. depth for Specimen U4
Figure 3.30 shows the calibration constant vs. depth of cut for
Specimen U4. It is seen that the maximum of 197micro-strain was measured
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for the applied strain of -105micro-strain during core drilling at the depth of
40mm and the corresponding calibration constant is 1.88.
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Figure 3.30 Calibration constant vs. depth for Specimen U4
3.5.3.5 Test results of Specimen U5
The load of 222kN was applied to the Specimen U5 and the
corresponding strain developed was -163micro-strain. By concrete core-
drilling technique released strain was measured in the stressed specimen.
Released strain measured and the calibration constant calculated for different
core depth is given in Table 3.6. The released strain vs. depth of cut for
Specimen U5 is given in Figure 3.31. The maximum strain release measured
at a depth of 50mm with 321micro-strain and the corresponding calibration
constant is 1.97.
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Table 3.6 Released strain and calibration constant for the Specimen U5
Depth of cut inmm
Released strain ( m)inmicro-strain
Calibrationconstant (Cf)
10 94 0.5820 225 1.3830 304 1.8740 314 1.9350 321 1.97
Figure 3.32 shows the calibration constant vs. depth of cut for
Specimen U5. It is seen that around 95% o f strain released at the depth of
30mm.
0
10
20
30
40
50
60
0 50 100 150 200 250 300 350
Micro-strain
Figure 3.31 Released strain vs. depth for Specimen U5
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0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Figure 3.32 Calibration constant vs. depth for Specimen U5
3.5.3.6 Test results of Specimen U6
Specimen U6 was applied with a load of 229kN. The corresponding
strain developed in the specimen was -125micro-strain. Released strain was
measured in the stressed specimen for different depth of cut during drilling
and is given in Table 3.7.
Table 3.7 Released strain and calibration constant for the Specimen U6
Depth of cut inmm
Released strain ( m)inmicro-strain
Calibrationconstant (Cf)
10 55 0.4420 123 0.9830 180 1.4440 221 1.7750 230 1.84
Calibration constant was calculated from the released strain and applied
strain and are given in Table 3.7. Figure 3.33 shows the released strain vs.
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depth of cut for Specimen U6. Maximum of 230micro-strain released at a
depth of 50mm and the corresponding calibration constant is 1.84. Figure 3.34
shows the calibration constant vs. depth of cut for Specimen U6. Around 80%
of maximum strain released at the depth of 30mm.
0
10
20
30
40
50
60
0 50 100 150 200 250Micro-strain
Figure 3.33 Released strain vs. depth for Specimen U6
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Figure 3.34 Calibration constant vs. depth for Specimen U6
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3.6 DISCUSSIONS
Concrete core-drilling technique was carried out on six specimens U1
to U6 stressed with different load levels. The strain release for different
depths of cut for the tested specimens is given in Tables 3.2 to 3.7.
Figure 3.35 shows the released strain vs. depth for the tested specimens. The
pattern of the strain release is similar for all specimens. It is seen that there is
an enhancement of released strain compared to the applied strain. Out of six
specimen tested, maximum strain release occurred at a depth of 50mm for four
specimens. It is also noted here that the released strain rate is more up to
30mm and beyond this depth the strain released rate is less.
0
10
20
30
40
50
60
0 50 100 150 200 250 300 350
Micro-strain
U1U2U3U4U5U6
Figure 3.35 Released strain vs. depth for specimens U1 to U6
The calibration constants calculated from the released strain and
applied strain for the tested specimens are given in Table 3.8. Figure 3.36
shows the calibration constants vs. depth for the tested specimens. Calibration
constants for 10mm depth of cut vary between 0.44 and 0.65 with an average
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of 0.56. The variation of calibration constant is 0.98 and 1.43 with an average
of 1.26 and 1.44 to 1.87 with an average of 1.65 for depths 20mm and 30mm
respectively. For 40mm and 50mm depths, the variations of constants are
1.69 to 1.93 with an average of 1.8 and 1.78 to 1.97 with an average of 1.86
respectively. As the depth increases the calibration constants also increases.
The rate of increase of constant is higher up to 30mm and beyond 30mm the
variation is less. At 30mm depth, more than 85% of maximum release
occurred.
Table 3.8 Calibration constants for the tested specimen
Depthin mm U1 U2 U3 U4 U5 U6 Avg
0 0 0 0 0 0 0 010 0.48 0.64 0.58 0.65 0.58 0.44 0.5620 1.40 1.07 1.43 1.31 1.38 0.98 1.2630 1.83 1.58 1.63 1.57 1.87 1.44 1.6540 1.79 1.69 1.76 1.88 1.93 1.77 1.8050 1.80 1.78 1.93 1.83 1.97 1.84 1.86
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
U1
U2
U3
U4
U5
U6
Avg
Figure 3.36 Calibration constants vs. depth for uniaxial stress condition
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From the calibration constants evaluated experimentally for the tested
specimen, the average constants at different depth of cut were calculated.
Table 3.9 gives the calibration constants evaluated experimentally and
numerically. The comparison of calibration constants evaluated
experimentally and numerically is shown in Figure 3.37. It is noted here that
the experimental values is less than the numerical constants. This may be due
to that the strain average effect of the sensor. Also cutting operation such as
abrasion of drill bit, drilling speed etc., can also be attributed to this. The
percentage of variation between numerical and experimental for 10mm depth
is around 40% and for 20mm depth is around 20%. This may be due to the
fact that the cutting tool comes and contact for the first time influences this
error. The manufacturing stress (Owens, 1993) in concrete which is balance
between stresses of different sign in the matrix and aggregate may also
contribute to this variation. Further the numerical analysis carried out in an
ideal condition of the stress distribution along the depth is uniform. But in the
experiments there may be slight eccentricity in the applied load and hence the
stress distribution was not uniform across the depth. Concrete is a
heterogeneous material but in the numerical analysis concrete was considered
as homogenous material. These factors may influence the difference between
experimental and numerical constants. The percentage of variation between
numerical and experimental constants varies between 10.7% and 8.5% for
30mm to 50mm depth of cut.
Table 3.9 Comparison of Calibration constants
Calibration co-efficient(Cf)Depth of cut in mm Experimental Numerical% of
variation10 0.56 0.96 41.720 1.26 1.54 18.130 1.65 1.83 9.740 1.80 1.97 8.550 1.86 2.08 10.7
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0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3
Calibration constant
Experimental
Numerical
Figure 3.37 Comparison of Calibration constants
From the experimental studies, calibration constants were evaluated for
different depths. By using the concrete core-drilling technique, the in-situ
stress or existing stress ( E) can be evaluated from the equation given below.
E=f
mc
CE (3.10)
Here, m is the total measured strain through the Wheatstone bridge, Cf
is the calibration co-efficient for the used gage size and configuration and Ec is
the modulus of elasticity of concrete.
3.7 SUMMARY
For assessing the existing stress in distressed reinforced
concrete/prestressed concrete structures the concrete core-drilling technique
can be used. This core drilling technique is a stress measurement technique in
which a small core is drilled in the structure and the strain perturbations
52
around the core are measured by instrumenting a special arrangement of
electrical resistance strain gages suitably placed around the core for
assessment of in-situ stress under uniaxial stress condition. This consists of
two radial gages (SG1 and SG2) and two tangential gages (SG3 and SG4)
aligned around the indented core. All the four gages were connected through a
Wheatstone bridge circuit in full bridge configuration. Laboratory studies
were conducted to evaluate the reliability of this concrete core drilling
technique. Calibration constants were evaluated experimentally for the used
gage length, location and configuration. Comparison was also made with
constants evaluated numerically. This concrete core drilling technique can be
used to determine the in-situ stress with enhanced sensitivity in "in-service"
prestressed concrete structures.