The existing stress measurement of the PC bridges by slit stress relief
techniques using the optical full-field measurement method
Kenichi HIDA1, Yukihiro ITO2, Katsuya MITA2,
Akira DEMIZU3, Takuji OKAMOTO4, Masaki YONEMOTO4
1

K&T Consultant Co. Ltd; Tokyo, Japan,
Phone: +81-4-7141-0115, Fax: +81-4-7141-0116; e-mail: k-hida@kt-c.co.jp
2
Saga University; Saga, Japan, e-mail: itoy@cc.saga-u.ac.jp, mita@cc.saga-u.ac.jp
3
Nagasaki University; Nagasaki, Japan, e-mail: demizu@nagasaki-u.ac.jp
4
Keisoku Research Consultant Co. Ltd; Hiroshima, Japan,
e-mail: okamoto@krcnet.co.jp,yonemoto@krcnet.co.jp
Abstract
Tendon of pre-stressed concrete bridge corrodes for damage from chloride attack, and pre-stress decreases. And abridge falls by corrosion of PC-tendon. It is necessary to grasp the stress which acts on concrete of PC
bridges.Therefore authors have developed the existing stress measurement method by slit stress relief techniques
using the optical full-field measurement method.This report introduces a measurement method of pre-stress by theexisting stress measurement method by slit stress relief techniques using the optical full-field measurement
method.The following measured case of pre-stress of PC bridges will be reported.
1) Cause investigation in the central hinge bridge where I transformed abnormally2) Confirmation of safety of the PC bridge damaged by chloride attack.
3) Decision of the strengthening amount of the PC bridge damaged by chloride attack
Keywords: optical full-field measurement method, slit stress relief technique, existing stress measurement

1. Introduction
Concrete structures are believed to be durable permanent structures. However, in recent years,
remarkable changes in condition have been observed in some concrete structures. Thesechanges include cracks and corrosion of reinforcing steel due to deterioration caused bychloride attack, carbonation, alkali-aggregate reaction, etc.
In post-tensioned prestressed concrete (hereinafter, PC) girders, cases of severe cracking or
bridge collapse as a result of corrosion and rupture of PC tendons occurred due to chloride
attack or hydrogen embrittlement fracture at points where grout filling was incomplete havebeen reported. There have also been cases in which prestress was reduced by unexpected

creep/shrinkage, and deflection exceeding the design value occurred. Since a decrease in theprestress of a PC structure has a large effect on its load bearing capacity and leads to reduced
safety, an accurate grasp of existing stress is necessary for proper maintenance of PC structures.
However, the amount of existing prestress is not controlled; only the tensioning force of the PC
tendons in the initial stage is controlled. The current methods for measuring the existing stressof PC structures include an estimation method in which strain gauges are placed on 3 axes andcore stress is relieved, and a slot stress method developed in France, among others. [1] Because
techniques for PC structures have same problems and have not been applied practically very
much, a technique that enables accurate estimation is demanded. In order to improve accuracy

in comparison with the conventional existing stress measurement methods, in this research, theauthors developed an existing stress measurement method for PC structures by the stress relief
method which is an existing stress measurement method, and the digital image correlation
method. This method has features of highly accurate, noncontact and full-field measurement.

2. Existing stress measurement by slit stress relief technique using opticalfull-field measurement method
2.1 Overview
If a slit is cut perpendicular to the direction of stress in a concrete member on which uniform
compressive stress acts, liberating strain will be generated in the area surrounding the slit. The
analytical model of this technique is shown in Fig. 1. Figure 2 shows the relationship between
the liberating strain and the distance from the slit center when the slit cutting depth in the model
is changed from 10 mm to 20 and 30 mm.
As a feature of the existing stress measurement method by the slit relief technique developedin this research (hereafter, slit stress relief technique), the optical full-field measurement method
is used in order to improve accuracy in comparison with the conventional method whenmeasuring the liberating strain caused by slit-cutting.
In the slit stress relief technique, the area around the slit is measured with a full-field strain
measurement device before and after cutting the slit, and the distribution of liberating strain is
obtained from the measured images by the digital image correlation method, which is one
optical full-field measurement method.
By using the optical full-field measurement method, strain measurements can be performed
with high accuracy extending to micro areas in the vicinity of the slit. The existing stress of theconcrete member is calculated based on the measured liberating stress distribution by inverse
analysis by FEM analysis.
2.2 Optical full-field measurement method
The specifications of the optical full-field strain measurement device are shown in Table 1,
and the appearance of the device is shown in Fig. 3. A mechanism that enables highly accurate
travel was realized by fixing the drive device for sub-scanning on a high-rigidity frame toimprove travel accuracy in the sub-scanning direction, and adopting two moveable linear guiderails for the line sensor and using a stepping motor in a precision ball screw in this part. A linear
encoder with resolution of 0.1 μm is used to control the movement distance in the sub-scanning
direction. A jig is attached so that the device can be attached easily and firmly to the object ofmeasurement.

400

6.00E-04

10N/mm10ｍｍ

25.00E-04

20ｍｍ
30ｍｍ

400

Slit
10,20,30mm

Releasing strain

4.00E-04
3.00E-04
2.00E-04
1.00E-04

400

Ec=
25000 N/mm2

liberating Strain
0.00E+00
0

50

100

150

Distance from slit (mm)Figure 2. Distribution of liberating strain by slitFigure 1. Analytical model

cutting200

Table 1. Specifications

Main-

Vice scanning

2.3 Existing stress measurement by slit stress relief
technique
The released strain distribution and change ratio
distribution of the distance between the optical marks
is obtained by applying the digital image correlation
method to the photographed images. The digital image
correlation method, as shown in Fig. 4, is an image
Sensor type
Greatest manuscript size
Optics resolution(mainscanning × vice-scanning)
Source of light
Power supply
Electricity consumption
Size (width × depth × height)
WeightN(pixels)

Figure 3. Optical full-field measurement
deviceanalysis technique in which theamount of movement from theposition before slit-cutting is
obtained based on digital informationof the pixel clusters in the initial
image, by locating pixel clusters forthe same digital information from theimage after slit-cutting.
The change ratio distribution of theDistance from slit center（ｍｍ）

Digital informationin subset

0

10

20

30

40

50

60

70

80

90

100

0

N
(pixels)-1,000The strain or the object
point(μ)

Subset (N x N pixels)

CIS
210×210mm
1200dpi×1200dpi(About0.021mm/pixel)
LED
DC15V
15W
387mm×262mm
×90mm
About 8000g

Line sensor-2,000

Before deformation
Displacement
amountChange ratio distribution of
distance of optical marksε=⊿L/L

Analytica-3,000Measurement-4,000

Displacement
direction-5,000After deformation-6,000Figure 4. Digital image correlation

Figure 5. The object point

Figure 6. Example of the strain

methoddistance rate of change

distribution of object point

distance between the optical marks is obtained from the measured images by the digital image
correlation method, and existing stress is then estimated by obtaining a change ratio distribution
between optical marks that approximates the measured change ratio distribution by inverse
analysis by FEM analysis.
The change ratio distribution between optical marks, as shown in Fig. 5, is the ratio of thechange in distance between two points, assuming the slit is the center of that distance. Existing
stress is estimated from the analysis values obtained by inverse analysis by FEM analysis whichcoincide with the measured values by using the analytical model shown in Fig. 7 and the meshdiagrams shown in Fig. 8. Figure 6 shows an example of the change ratio distribution of the
optical marks of the analytical values and the measured values at the center of a span. Figure 9shows the work procedure.

T

Slit depth

Before cutting
Figure 7. Analytical model

After cutting

Figure 8. Mesh diagrams

1. Rebar probe
Using a reinforcing bar
probe, the PC tendon
position is confirmed
and the measurement
position is decided.

4. Initial image
The initial image isphotographed with aflat scanner.

2. Surface treatment
The surface is smoothed
to enable photographyof focused images.

5. Slit-cutting
slit-cutting is
performed with adedicated cutter.

3. Surface condition
before stress relief
A random black andwhite pattern is
attached.

6. Photography after
stress relief
The image after slitcutting isphotographed with theflat scanner.

Figure 9. Work procedure

3. Cause investigation of abnormal deformation of central hinge bridge
3.1 Overview
This bridge is a 3-span hinge PC box girder rigid frame bridge which was constructed in a
mountainous area in 1989. Abnormal deflection occurred in the central hinge part. The
maximum deflection, as shown in Fig. 10, is approximately 140 mm. Focusing on inadequate
prestress and creep deformation in the pier capital section, a study of stress (strain) in the central
hinge bridge was carried out to determine the cause of this abnormal deformation. [2] In thisstress investigation, the existing strain of the reinforcing steel was measured by the slit stressrelief technique and the rebar cutting method. The investigation positions are shown in Fig. 11.
Cross sections of pier capitals P1 and P2 were taken.

Slit stressrelief techniqueFigure 10. Transition of deflection

Rebar cutting
methodFigure 11. Investigation positions

Table 2. Measurement results
Slit stress relief technique
Measurement position

P1
piercapitalP2
piercapital

Upper
slab
Lower
slab
Upper
slab
Lower
slab

Rebar cutting method

Existing stressσC

Strain of concreteεC

Strain of rebar
εr

3.89±0.38 N/mm2

177×10-6

1334×10-65.10±0.59 N/mm2

232×10-6

1378×10-6

1.73±0.44 N/mm2

79×10-6

916×10-66.33±0.63 N/mm2

288×10-6

1328×10-6

3.2 Measurement results
The measurement results are shown in Table 2. From the results of sample core tests, theelastic modulus of the concrete was assumed to be EC=22 kN/mm2. Creep/Shrinkage and elasticstrain, which were the existing strain at those positions, had occurred in the reinforcing steel
arranged in the PC bridge. That is, the liberating strain which was measured by the rebar cutting
method included elastic strain and creep/shrinkage. Therefore, if the existing stress of theconcrete can be measured, creep/ shrinkage strain can be separated from the liberating strain
obtained by the rebar cutting method by using Eq. (1).
εr=εl+εφs=σc／EC+εφs(1)

where, εr: rebar strain, εl: elastic strain of rebar (εl=σc ／EC), εφs: creep/shrinkage strain of
concrete, σc: concrete stress (N/mm2), Ec: elastic modulus of concrete (N/mm2).
3.3 Estimation of cause of abnormal deflection of center hinge
Figure 12 shows the strain distribution diagram of the P1 pier capital for rebar strain (εr),
which includes concrete strain (εc), i.e., a type of elastic strain, and drying shrinkage. εr and εcshow substantially the same slopes. Assuming that drying shrinkage strain (εsh) andElastic strain εc

Creep/Shrinkage strain

Rebar strain

εφs

εr

Figure 12. Strain distribution (measured) of P1

Figure 13. Deflection distribution by estimatedpier headcreep coefficient

Table 3. Estimated creep coefficients and shrinkage
Measurement
position

P1
pier capitalP2
pier capitalGirderheight
(m)
4.300
4.050
0.700
0.000
Average
4.300
4.050
0.700
0.000
Average

εr×10-6

εc×10-6εφs×10-6nεsh×10-6

1330.71334.01378.01387.2

172.7
176.8
231.8
243.3

1158.01157.21146.21143.9

2.3
2.3
1.9
1.9

885.3
916.0
1328.01414.1

63.0
78.6
287.7
331.4

822.2
837.4
1040.31082.7

2.7
2.5
1.5
1.4

469.2
462.3
385.9
372.8
422.6
535.4
501.9
301.9
283.6
405.7

φ
3.99
3.93
3.28
3.17
3.59
4.55
4.27
2.57
2.41
3.45

* Average creep coefficient of P1 and P2 pier capitals: φ=3.52

creep strain (εφ) are proportional to the design shrinkage strain and the design creep coefficient,
the shrinkage and creep coefficient of the P1 and P2 pier capital parts can be obtained by Eq.
(2).
εφs =εsh +εφ=n・(εsh0+εc・φ0) (2)εsh= n・εsh0, εφ= n・εc・φ0, φ= n・φ0
where, εsh: shrinkage strain, εφ: creep strain, φ: estimated creep coefficient, εsh0: design
shrinkage (200×10-6), φ0: design concrete creep coefficient (1.7).
Table 3 shows the estimated creep coefficients and shrinkage. As these values areapproximately the same, they are considered to express the creep coefficient and drying
shrinkage of the actual bridge. Figure 13 shows the calculated deflection values calculated using
the average estimated creep coefficient (φ=3.52) and the results of longitudinal leveling.
Because the calculated values of deflection using the estimated creep coefficients are in good
agreement with the results of longitudinal leveling, it is thought that the main cause of theabnormal deflection in this bridge is creep deformation.

4. Confirmation of safety of PC bridge damaged by chloride attack
4.1 Overview
This bridge is a post-tensioned PCT girder bridge which passes over a sea area and had been
in service for approximately 40 years since construction. The bridge, as shown in Fig. 14, hadsuffered progressive deterioration in the forms of loose and peeling scale and corrosion of thereinforcing steel, and a reduction of load bearing performance was feared as a result of progressof corrosion of the members due to chloride attack and corrosion of the PC tendons. Therefore,
a stress investigation, etc. was carried out to confirm the load bearing capacity of the bridge. [3]In the stress investigation, generated strain was measured by the slit stress relief technique anda dynamic load test assuming the service load. The measurement positions are shown in Fig.
15.
4.2 Measurement results
Table 4 shows the results of measurements by the slit stress relief technique, and Table 5shows the results of the dynamic load test. As the elastic modulus, the design elastic modules
at the time of construction, Ec=35 kN/mm2 was assumed. In the dynamic load test, a dump truck
with a gross weight of 20 t and a 50 t class rafter crane with a gross weight of approximately
40 t were assumed as the load vehicles. One lane was closed to traffic, the load vehicles were
stopped in the center of the span on the closed lane, and the vehicles were allowed to travel on
the open land when no general vehicles were passing. Measurements were performed under thefollowing three load vehicle patterns.
Pattern 1: Dump truck stops on closed lane, dump truck travels on open lane.
Pattern 2: Dump truck stops on closed lane, rafter crane travels on open lane.
Pattern 3: Rafter crane stops on closed lane, dump truck travels on open lane.

G1

G2

Strain measurement

G3

G4

★

★

Slit stress relief techniqueFigure 15. Measurement positions (span center)

Figure 14. Deterioration of main girder

Table 4. Results of measurement by slit stress relief technique
Measurement
position
G3
G4

Existing stress (N/mm2)
3.46
3.21

±
±

0.15
0.25

3.31
2.96

-

Error
3.61
3.46

4.3%
7.7%

Table 5. Results of dynamic load test

Pattern 1

Pattern 2

Pattern 3

Max. tensilestress(A) Dump truck load(B) Dump truck load (traveling)(A)＋(B)(A) Dump truck load(B) Crane load (traveling)(A) + (B)(A) Crane load(B) Dump truck load (traveling)(A)＋(B)
Dump truck single load
Crane single load
Dump tuck + dump truck
parallel load
Dump tuck + crane parallel load

G1
-0.2
-1.1
-1.3
-0.3
-1.6
-1.9
-0.5
-1.0
-1.5

G2
-0.5
-0.9
-1.4
-0.5
-1.4
-1.9
-0.9
-0.9
-1.8

G3
-0.8
-0.6
-1.4
-0.8
-0.9
-1.7
-1.3
-0.6
-1.9

G4
-0.8
-0.3
-1.1
-0.9
-0.5
-1.4
-1.3
-0.4
-1.7

-1.1
-1.6
-1.4
-1.9
2

Unit: N/mm

Compressive (+), tensile (-)

4.3 Evaluation of load bearing performance
In the PC girder of this bridge, from Table 4, the existing stress, which was stress on theresistance side, has become compressive stress of approximately 3.0 N/mm2 or more. On theother hand, from Table 5, the maximum tensile stress due to single loading by a dump truck,
which seems to have a high possibility of being the actual loading mode, is on the order of 1.0
N/mm2. The maximum tensile stress due to single loading by a dump truck and parallel loading
by dump trucks, which appear to have a small possibility, is about 1.5 N/mm2, and the maximum
tensile stress due to parallel loading by a dump truck and a rafter crane, which seems to havean extremely small possibility, is about 2.0 N/mm2. Accordingly, the PC girder of this bridge isconsidered to be safe at the present point in time.

5. Design of Strengthening for PC bridge damaged by chloride attack
5.1 Overview
This structure is a pre-tensioned PCT girder comprising the superstructure of a rock shedwhich is in contact with the sea coast. It had been in service for approximately 30 years. In the
structure, as shown in Fig. 16, deterioration in the forms of loose and peeling scale andcorrosion of steel materials has progressed, and a reduction of load bearing performance wasfeared as a result progressive corrosion of the steel materials due to chloride attack andcorrosion of the PC tendons. Therefore, an investigation by the slit stress relief technique was
performed to confirm the loading bearing performance of the structure. The investigation
positions were the six main girders on the lower side of the structure.
5.2 Measurement Results
The measurement results are shown in Table 6. As the elastic modulus of the concrete, thedesign elastic modulus at the time of construction, EC=35 kN/mm2 was assumed.

Table 6. Results of measurement byslit stress relief technique
Measurement
position

Figure 16. Damage of main girder

Existing

Error

stressStandard
deviation(N/mm2)(N/mm2)(%)

No. 14 Sea

2.27

1.67

71.3

No. 15 Mountain

-0.62

0.05

7.1

No. 16 Mountain

1.18

0.51

40.8

No. 20 Sea

0.95

0.64

63.1

No. 25 Mountain

0.11

0.04

35.5

No. 29 Sea

0.8

0.46

54.3

Existing stress : Compressive (+), tensile (-)

Table 7. Reduction of prestressMeasurement
position

Existing stress2

Prestress2

Tensioning force

Reduction(N/mm )

(N/mm )

(kN)

(%)

σcl'

σcp'=σcl'-σdl-σsl

Pt'=σcp'(1/Ac+yep/Zl)

Pt'/Pt

No 14 Sea

2.27

5.16

405.4

119.60%No. 15 Mountain

-0.62

2.27

178.2

52.60%

No. 16 Mountain

1.18

4.07

319.7

94.30%

No. 20 Sea

0.95

3.84

301.6

89.00%

No. 25 Mountain

0.11

3.00

235.6

69.50%

No. 29 Sea

0.80

3.69

289.8

85.50%

Section areaAc=

2.93E+05(mm2)

Average85.10%

Section modulus

Zl=-3.29E+07(mm3)Standard deviation

20.80%

Steel eccentricity

yep=-305.5(mm)

Lower limit

64.30%

Effective tensioning force

Pt=

Pt0*η= 338.9(kN)

Upper limit

105.90%5.3 Evaluation of load bearing performance
The estimated results of the decrease of prestress are shown in Table 7. The amount ofdecrease of the prestress of the PC girders of this rock shed was 85.1% ±20.8% of the designprestress. Therefore, for the amount of prestress of the PC girders of the rock shed, the amountof strengthening was set assuming 60% of the design prestress, which was the lower limit of
the estimated reduction of prestress.
5.4 Design of Strengthening
Bending strengthening of the PC girders of the PC rock shed, assuming 60% of the designprestress, was carried out by using 1 layer of high modulus carbon fiber sheet by the carbon
fiber sheet adhesive method. In addition, 2 layers of middle modulus type carbon fiber sheet
were used for shear strengthening. The cross section of the strengthening of the rock shed isshown in Fig. 17.

Figure 17. Sectional view of reinforcement

6. Conclusions
1) It is possible to separate creep/drying shrinkage strain from concrete stress (strain), which isa type of elastic stress, and estimate the creep coefficient of existing structures by using a
combination of the slit stress relief technique and strain measurement of reinforcing steel by
the rebar cutting method.
2) The load bearing capacity of existing PCT girder bridges, in which a reduction of prestressdue to deterioration caused by chloride attack is an issue, can be evaluated by a comparative
study of the resistance stress obtained by the slit stress relief technique, and the acting stressobtained by strain measurements in the dynamic load test supposing the service load.
3) The amount of reduction of prestress can be estimated from the results of the slit stress relief
technique, and the proper load bearing performance can be evaluated. The proper amount ofstrengthening can then be set based on the amount of prestress (existing prestress) in the current
condition.
References
1. Akira Demizu, Kenichi Hida, Yukihiro Ito, Masakazu Uchino, Takuji Okamoto, Hiroshi
Matsuda: Measurement of existing stress of post-tensioned girders by optical technique andstress release method, Proceedings of the Annual Conference on Experimental Mechanics,
Japanese Society for Experimental Mechanics, No. 10 GS5-5, pp281-286, 2010
2. Kenichi Hida, Yukihiro Ito, Mitsuaki Tsukihara, Haruyuki Koitabashi: “Report ofinvestigation of central hinge bridge in which abnormal deformation occurred after
approximately 30 years in service,” Proceedings of the 22nd Symposium, pp345-348, 2013.10
3. Kenichi Hida, Yukihiro Ito, Akira Demizu, Masakazu Omachi: “Report on investigation ofload bearing capacity of post-tensioned PCT girder bridge with damage by chloride attack,”
Proceedings of the 23rd Symposium, pp649-652, 2014.10