一般財団法人 大成学術財団
2020 年度 助成研究梗概書

確率論に基づくコンクリート構造物の塩化物浸透及び補修最適化システムの構築

東京大学
宮崎大学
埼玉大学
東京大学
Structural reliability analysis
Corrosion progression

Chloride diffusion
Surface treatment○王 眺 1*

李 春鶴 2**
欒 堯 3***
石田 哲也 4*

Concrete crack
Repair mortar

1. Purpose of researchexpensive, and chloride-induced corrosion is one of the mostserious threats to their integrity. Accordingly, this study develops
a Monte Carlo simulation-based system for assessing thecorrosion-related degradation of RC structures. A rapid numericalapproach for measuring the chloride diffusion in cracked concrete

60

Relative frequency (%)

Maintaining reinforced concrete (RC) structures is veryis used to incorporate the coupled degradation effect of crack

50403020100development and corrosion progression into a system for2030

estimating the probable corrosion failure of RC beams over time.

40 50 60 70 80 90
Concrete cover depth (mm)Fig. 1 Statistics data of concrete cover depth
40

2.1 Field investigation

35

A filed investigation of RC bridge was conducted to collectstatistics data for the reliability analysis. Several parameters weremeasured, including concrete cover depth, crack width andcompression

strength.

Theseparameters

follow

normaldistribution (Fig.1 ~ Fig. 3). It shows that these statistics data canRelative frequency (%)

2. Research contents

30252015105

be used for Monte-Carlo simulation.

0

2.2 Analysis system

0.0

0.1
0.2
0.3
Crack width (mm)0.4

Fig. 2 Statistics data of crack width

combination of chloride ingress and loading actions. A reliability

40

assessment system was developed to estimate the failure time of35

RC structures under the coupled degradation effects of crackdevelopment and corrosion progression (Fig. 4). The required
inputs are the water-binder ratio, temperature, the rebar properties,
concrete strength, pH of a pore solution, geometry of an RC beamand the boundary conditions to which the concrete beam will be
exposed during its life cycle. These parameters are assigned
probabilistic distributions in Monte Carlo simulations (Fig. 4a),in each of which the chloride diffusion profile of cracked concrete
is first represented as a rapid two-layer diffusion model (Fig. 4b).

Relative frequency (%)

RC structures undergo continuous deterioration due to a0.530252015105020253035404550
Compression strength (MPa)Fig. 3 Statistics data of compression strengthThen, based on the chloride content of rebar, the corrosion rate
and pitting corrosion area are determined using corrosion rate andequilibrium analyses of the corroded rebar (Fig. 4d), and these

pitting corrosion propagation models (Fig. 4c). Next, the widths

crack geometry data are used as the input for the estimation ofand thicknesses of the cracks are determined through mechanicalchloride ingress next step. The above steps are repeated until theReliability analysis and life-cycle cost optimization of repairing
strategy of cracked concrete structures exposed to chloride attack

WANG Tiao１, LI Chunhe 2
LUAN Yao 3, ISHIDA Tetsuya 4

stress on the rebar is higher than its yield strength (Fig. 4e), i.e.,

Conclusions
This study develops a reliability analysis system that incorporates

Finally, all of the Monte Carlo simulation enables the CFP of thethe coupled degradation effects of crack development andRC to be determined (Fig. 4f). As flexural cracks are the mostcorrosion progression into the assessment of the CFP of RC

common cracks in RC structures, we simplify the reliabilitystructures.

analysis system by considering an RC beam subjected to flexural
moment.
2.3 Analysis results
Parmeter analyses were conducted to study various effect on
corrosion failure probability (CFP) of RC beam. The results showthat (1) the CFP of RC structures is significantly underestimated
if the coupled degradation effect of crack development andcorrosion progression is not considered (Fig. 5); (2) surface
treatments efficiently improve the durability of RC structures
Corrosion failure probability (%)

with crack development
without crack development

10060

Dcr /1.00
Dcr /1.33
Dcr /2.00
Dcr /4.00
Dcr /8.00

8060

40 Failure probability
200of 10%

020

4060
Time (year)

80

100

Future study
It should be noted that only flexural cracks are addressed in thisstudy, which means that future research should examine othertypes of mechanical degradation cracks, such as shear cracks,
fatigue cracks and corrosion expansion cracks.

40% (100 kN)
50% (125 kN)
60% (150 kN)
70% (175 kN)
80% (200 kN)

80

100 Dcr (54.8 mm2/day), OPC 60% (150 kN)

Fig. 6 Effect of surface treatment on corrosion failure probability

subjected to heavy loads (Fig. 6).
120

Corrosion failure probability (%)

until it fails, and the time to failure for the simulation is recorded.

40 Failure probabilityof 10%

2000204060Time (year)

80

100Fig. 5 Effect of loading on corrosion failure probability

Acknowledgment
The authors are grateful for financial support from The Taisei
Foundation (2020) and the Yoshida Award’s ‘Encouraging Prize’
from the Japanese Civil Engineering Society.

Fig. 4 Reliability assessment system for RC structures under chloride ingression* 東京大学 大学院工学系研究科** 宮崎大学 工学教育研究部*** 埼玉大学 理工学研究科* The University of Tokyo** The University of Miyazaki*** Saitama University