• KSCE Journal of Civil and Environmental Engineering Research
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• v.38 no.2
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• pp.193-202
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• 2018

This paper proposed a crack spacing calculation formulation which is an important parameter for calculating the crack width, that is the main factor for verification of serviceability limit states and durability performance evaluation of reinforced concrete members. The basic equation of average crack spacing is derived by considering the bond characteristics which is the governing equation for the analysis of cracking behavior in reinforced concrete members. In order to consider the effect of the cover thickness and concrete compressive strength, the crack spacing measured in 124 direct tensile tests performed by several researchers was analyzed and each coefficient was proposed. And, correlation analysis was performed from 80 specimen data where the maximum and average crack spacing were simultaneously measured, and a correlation coefficient that can easily predict the maximum crack spacing from the average crack spacing was proposed. The results of the proposed average crack spacing equation and maximum crack spacing correlation were compared with those current design code specification. The comparisons of proposed equations and the Korean design codes show that the proposed formulation for the average crack spacing and the maximum crack spacing improves the accuracy and reliability of prediction compared to the corresponding provisions of the Korean Concrete Structural Design Code and Korean Highway Bridge Design Code (Limit States Design).

• Journal of the Korea Concrete Institute
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• v.26 no.4
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• pp.475-482
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• 2014

This paper presents the experimental results concentrically reinforced concrete tension members and compares cracking behavior of amorphous steel fiber and normal steel fiber reinforced concrete members. Two kind of steel fibers were included as a major experimental parameter together with the six cover thickness to bar diameter ratio ($c/d_b$). The presence of amorphous steel fibers effectively controlled the splitting cracks initation and propagation. In the amorphous steel fiber reinforced specimens, no splitting cracks were observed that becomes higher with cover thickness to bar diameter ratio is 2.0. Crack spacing of the each specimens reinforced with amorphous steel fibers and normal steel fibers becomes larger with the increase in cover thickness, and also measured maximum and average crack spacing are significantly smaller than current design code provision. Based on the measured crack spacings, a relationships for predicting the crack spacing is proposed using the measured average crack spacing in amorphous steel fiber reinforced concrete tension members.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.87-98
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• 2011

Crack formations are inevitable in reinforced concrete structures. To estimate crack widths, empirical formulae are used widely and indirect crack controling methods of limiting bar spacing and bar diameter are also used due to their simplicity. In EC2, the characteristic crack width is calculated by multiplying maximum crack spacing and average strain. In this study, limit values of maximum bar spacing and bar diameter are examined as the material characteristics are varied. Two models of tension stiffening effect and maximum crack spacing and their effects are evaluated. The obtained results are compared with the values obtained using KCI method. The results showed that a significant difference is found when two tension stiffening effect are employed, and an under-estimation is found when 2nd order tension stiffening effect and maximum crack spacing limit from Part II were implemented. Therefore, a rational indirect crack control method attained using the tension stiffening effect of 2nd order form is needed. Also, a consistency in serviceabiliy analysis in flexural members needs to be secured. In order to achieve these goals, two crack controling models are suggested.

• Magazine of the Korea Concrete Institute
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• v.9 no.4
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• pp.207-214
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• 1997

This study was performed to verify the effect of axial force due to restraint on the mechanical behavior and the average crack spacing of the reinforced concrett. ilexural menlbers. For. this purpose, the flexural sttvngt.h and rigidity werc experimentally investigated undcl. axially rcstmined and unr.est.rainrd conditions. Furthermore , the average crack spacing was also checkcd for the axilly restrained contlit.ion. Thc test results showd that the flexual strength and rigidity of t,he restrained beam were higher. than those of the unrestrained beam. The major. factors affecting on the average crack spacing were steeel stress, axial force, cicumference of reinforcing bar and effective tension arm of concrete. However. the concrete compressive strength was minor effect. Including thesc factors, a prediction equation for the average crack spacing of the restrained member was proposed.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.67-68
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• 2010

The bond stress and crack spacing are effected the calculated crackwidth. EC2 and MC90 suggest crackwidth function that maximum crack spacing and difference average strain. This study is predict crackwidth, according to each design standard than comprison and analyis test data. The result, each design standard ways are predict well to test data.

• The Journal of the Petrological Society of Korea
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• v.26 no.2
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• pp.127-141
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• 2017

Jurassic granite from Geochang was analysed with respect to the characteristics of the rock cleavage. The multicriteria evaluation for the six directions of rock cleavages was performed using the microcrack spacing-related parameters derived from the enlarged photomicrographs (${\times}6.7$) of the thin section and the spacing-cumulative frequency diagrams. The results of analysis for the representative values of these spacing parameters with respect to the rock cleavage are summarized as follows. First, the analysis for deriving the main parameter indicating the order of arrangement among six diagrams was performed. The values of five parameters with respect to six directions of the rock cleavages were arranged in increasing or decreasing order for the above analysis. The decreasing order of the values of main parameter(mean spacing-median spacing, $S_{mean}-S_{median}$) and mean spacing are consistent with the order of H1, H2, G1, G2, R1 and R2 directions. These sequential arrangements of six directions of the rock cleavages can provide a basis for those of the six diagrams related to spacing. Second, the nine correlation charts between the above main parameter and various parameters were arranged in decreasing order of correlation coefficient ($R^2$). These related charts shows a high correlation of power-law function in common. The values of mean spacing, density (${\rho}$) and length of line oa are directly proportional to the value of main parameter, while the values of constant (a), exponent (${\lambda}$), spacing frequency (N), length of line oa', slope of exponential straight line (${\theta}$) and total length ($1mm{\geq}$) are inverse proportional. Third, the results of correlation analysis between the values of parameters for three planes and those for three rock cleavages are as follows. The values of frequency, total spacing, constant, exponent, slope and length of line oa' for three planes and three rock cleavages show an order of R' < G' < H' and H < G < R, respectively. On the other hand, the values of mean spacing, (mean spacing-median spacing), density and length of line oa show an order of H' < G' < R' and R < G < H, respectively. The correlation of the mutually reverse order of the values of parameters between three planes and three rock cleavages can be drawn. This type of correlation analysis is useful for discriminating three quarrying planes.

• The Journal of the Petrological Society of Korea
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• v.25 no.1
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• pp.13-27
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• 2016

The characteristics of the rock cleavage inherent in Jurassic granite from Geochang were analysed. The phases of distribution of microcrack spacings were derived from the enlarged photomicrographs(${\times}6.7$) of the thin section. The evaluation for the six directions of rock cleavages was performed using nine parameters such as (1) frequency of microcrack spacing(N), (2) frequency ratio(${\leq}1mm$ and 4 mm >) to total spacing frequency(N:191), (3) spacing ratio(${\leq}1mm$) to total spacing(118.49 mm), (4) mean spacing($S_{mean}$), (5) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$), (6) density of spacing, (7) median spacing, (8) reduction ratio of spacing frequency to length frequency and (9) magnitude of exponent(${\lambda}$ and b) related to the distribution type of diagram. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of (I) parameters(1, 2 and 3), (II) parameters(4, 5 and 6), (III) parameter(7), (IV) parameter(8) and (V) parameter(9) show the various orders of H(hardway, H1+H2) < G(grain, G1+G2) < R(rift, R1+R2), R < G < H, R < H < G, G < H < R and H < G < R, respectively. On the contrary, the values of the above four groups(I~IV) of parameters for three planes show reverse orders. This type of correlation analysis is useful for discriminating three quarrying planes. Six spacing-cumulative frequency diagrams were arranged in increasing order on the value of main parameter($S_{mean}-S_{median}$). These diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, the above six diagrams can be summarized in order of rift(R1+R2) < grain(G1+G2) < hardway(H1+H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, the above main parameter could provide advanced information for prediction the order of arrangement among the diagrams.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.805-812
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• 2002

The number of old concrete structure which needs to be strengthened has been increased. The repair and strengthening methods have to be determined based on the current status of the structure. Consequently the estimation method for the damage status of the structure has been desperately needed, but no studies have been tried to use the crack and deflection characteristics to estimate the damage status. In this study, the crack characteristics depending on load level were measured and analysed. The crack characteristics observed from 11 samples were compared with damage status, and load level, The crack characteristics examined in this study include crack number, crack length, crack range, crack interval, maximum crack length, crack area, and average crack length. The deflections were normalized based on yield deflection, and the relationship between the relative deflection and the standardized crack characteristics were compared. Among the crack characteristics, crack interval, crack area, crack range, and maximum crack length, have been showed a close relationship to the relative deflection. Therefore, if such crack characteristics are evaluated, the maximum load applied to the structure is believed to be estimated. if additional parameters such as size of specimen, strength of concrete and steel, and steel ratio are studied, the damage status of structure can be estimated more accurately.

• Korean Journal of Mineralogy and Petrology
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• v.34 no.1
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• pp.41-56
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• 2021

The characteristics of the six rock cleavages(R1~H2) in Jurassic Hapcheon granite were analyzed using the distribution of ① microcrack lengths(N=230), ② microcrack spacings(N=150) and ③ Brazilian tensile strengths(N=30). The 18 cumulative graphs for these three factors measured in the directions parallel to the six rock cleavages were mutually contrasted. The main results of the analysis are summarized as follows. First, the frequency ratio(%) of Brazilian tensile strength values(kg/㎠) divided into nine class intervals increases in the order of 60~70(3.3) < 140~150(6.7) < 100~110·110~120(10.0) < 90~100(13.3) < 80~90(16.7) < 120~130·130~140(20.0). The distribution curve of strength according to the frequency of each class interval shows a bimodal distribution. Second, the graphs for the length, spacing and tensile strength were arranged in the order of H2 < H1 < G2 < G1 < R2 < R1. Exponent difference(λS-λL, Δλ) between the two graphs for the spacing and length increases in the order of H2(-1.59) < H1(-0.02) < G2(0.25) < G1(0.63) < R2(1.59) < R1(1.96)(2 < 1). From the related chart, the six graphs for the tensile strength move gradually to the left direction with the increase of the above exponent difference. The negative slope(a) of the graphs for the tensile strength, suggesting a degree of uniformity of the texture, increases in the order of H((H1+H2)/2, 0.116) < G((G1+G2)/2, 0.125) < R((R1+R2)/2, 0.191). Third, the order of arrangement between the two graphs for the two directions that make up each rock cleavage(R1·R2(R), G1·G2(G), H1·H2(H)) were compared. The order of arrangement of the two graphs for the length and spacing is reverse order with each other. The two graphs for the spacing and tensile strength is mutually consistent in the order of arrangement. The exponent differences(ΔλL and ΔλS) for the length and spacing increase in the order of rift(R, -0.08) < grain(G, 0.14) < hardway(H, 0.75) and hardway(H, 0.16) < grain(G, 0.23) < rift(R, 0.45), respectively. Fourth, the general chart for the six graphs showing the distribution characteristics of the microcrack lengths, microcrack spacings and Brazilian tensile strengths were made. According to the range of length, the six graphs show orders of G2 < H2 < H1 < R2 < G1 < R1(< 7 mm) and G2 < H1 < H2 < R2 < G1 < R1(≦2.38 mm). The six graphs for the spacing intersect each other by forming a bottleneck near the point corresponding to the cumulative frequency of 12 and the spacing of 0.53 mm. Fifth, the six values of each parameter representing the six rock cleavages were arranged in the order of increasing and decreasing. Among the 8 parameters related to the length, the total length(Lt) and the graph(≦2.38 mm) are mutually congruent in order of arrangement. Among the 7 parameters related to the spacing, the frequency of spacing(N), the mean spacing(Sm) and the graph (≦5 mm) are mutually consistent in order of arrangement. In terms of order of arrangement, the values of the above three parameters for the spacing are consistent with the maximum tensile strengths belonging to group E. As shown in Table 8, the order of arrangement of these parameter values is useful for prior recognition of the six rock cleavages and the three quarrying planes.

• Journal of the Korea institute for structural maintenance and inspection
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• v.21 no.5
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• pp.134-140
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• 2017

In this study, the flexural behavior of high strength concrete members with different curing condition of 90 MPa of compressive strength was investigated. Experimental parameters included normal and low temperature curing conditions, tensile steel amount and concrete compressive strength. 8 beam members were fabricated and flexural tests were carried out. Crack spacing, load-deflection relation, load-strain relation and ductility index were determined. Experimental results show that as the amount of rebar increases, the number of cracks increases and the crack spacing decreases. The higher the concrete strength, the smaller the number of cracks, but the effect is significantly smaller than the amount of rebar. As a result of comparison with the proposed average crack spacing in the design criteria, the experimental results are slightly larger than the results of the proposed formula, but the proposed formula does not reflect the concrete strength and curing conditions. The ductility index of normal temperature cured members was 3.36~6.74 and the ductility index of low temperature cured members was 1.51~2.82. The behavior of low temperature cured members was found to be lower than that of normal temperature cured members. As a result of comparing the ductility index with the existing studies similar to the experimental members, the ductility index of the high strength concrete member was larger than the ductility index of the ordinary strength concrete of the previous study. Further research is needed to understand more specific results.