chapter 3 concrete core drilling technique 3.1...

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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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Page 1: CHAPTER 3 CONCRETE CORE DRILLING TECHNIQUE 3.1 …shodhganga.inflibnet.ac.in/bitstream/10603/15821/8/08_chapter 3.pdf21 cos2 3 2 4 4 2 2 r R x a a (3.8) sin2 2 2 2 4 3 4 2 r a r R

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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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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21

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.

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

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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.