Experimental Study of Three Direct Tensile Strength of Fly Ash Concrete by menez

Civil Engineering and Technology March 2015, Volume 4, Issue 1, PP.1-8

Experimental Study of Three Direct Tensile Strength of Fly Ash Concrete X.X. He, Y.H. Zhang # School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China #

Email: zhangyanhe900@126.com

Abstract This paper studies the effects of the different strength grade of concrete under the condition of constant total cementitious material change of fly ash replacement rate to the direct tensile strength of concrete. Compareded the direct tensile of concrete by three methods of direct tention, as well as the corresponding splitting tensile strength ,bending flexural strength of the trabecular midpoint. Propose the conversion relationship formulas between the direct tensile strength and compressive strength and other tensile strength, explore the mechanism of action of fly ash concrete. Keywords: Fly Ash Concrete; Direct Tensile Strength; Splitting Strength; Flexural Strength

1 INTRODUCTION At present, the development of the global construction industry is rapid, accompany with the consumption of cement greatly. This is a huge consumption of energy and resources to make serious environmental load[1]. Using grinding fly ash to replace partial cement mixing into concrete to improve the work-ability of concrete, improve the durability of concrete, save cement, and reduce carbon dioxide emissions. Because of its morphological effect, active effect and micro aggregate effect of fly ash[2], the micro-structure of concrete becomes density, the mechanical performance deserves further exploration. At present, there are some experimental research about the compressive strength of fly ash concrete[3][4][5], but the research about direct tensile properties of fly ash concrete is less. As a result of splitting strength, flexural strength belongs to the indirect tensile strength, splitting specimen is not a pure axial tensile[6] and bending specimen has the problem of stress gradient[7]. These two kinds of strength is not the true tensile strength, so it is also increasingly important to find the conversion relationship between direct tensile strength and indirect tensile strength of concrete[8].

2 TEST OF RAW MATERIALS AND SCHEME Cement used the Zuan Pai P.O42.5# ordinary portland cement from Hebei Yanxin Building Materials Company; fine aggregate used natural river sand; coarse aggregate using crushed limestone, 5mm~10mm and 10mm~20mm two kinds of gradation; two-grade fly ash; admixtures used KSM-830 polycarboxylate superplasticizer with water reducing rate of 38%; mixing water used in Beijing city tap water. TABLE 1. THE MIX PROPORTION OF CONCRETE

The strength grade number 1

W/ (kg/m3) 160

B=C+FA (kg/m3) 311

165

140

W/B

FA/ B/ (kg/m3) G/ (kg/m3)

S/ (kg/m3)

Î˛s

0.51

0,0.2,0.4,0.6

1169

780

0.41

437

0.37

0,0.2,0.4,0.6

1100

734

0.4

560

0.25

0,0.2,0.4,0.6

1051

645

0.38

Notice: W/B-Water-binder ratio, Î˛s-Sand coarse aggregate ratio, W-Water, C-Cement, FA-Fly ash, S-Sand, G-Gravel.

Select the mix proportion of three kinds of strength grades in the test (see Table 1 in 1, 2, 3), design referring to -1http://www.ivypub.org/cet

‘Specification for mix proportion design of ordinary concrete’ [9] and on this basis determine the mix ratio. Then according to the principle of constant total amount of cementing material B and other components, the concrete was replaced by fly ash cement at ratio of 0%, 20%, 40%, 60% in the preparation of concrete. Stirring method is mechanical mixing; templates are steel mold; vibration mode is artificial; curing way adopts indoor natural maintenance with 28- day test age. In this paper, the test methods include direct tensile test, splitting test and flexural test. The cross-section of the specimen size is standard size of 150mm×150mm and the fly ash replacement rates are 0%, 20%, 40%, 60%. Test methods for total are shown in the following table. Use three kinds of direct tensile method to test concrete axial tensile strength ( Figure 1), such as the direct tension of middle embedded rebar (DTM, steel exposed length 75mm), the direct tension of I shape (DTE) and the direct tension of four embedded bar (DTF). Adopt soft cable tensile machine to ensure the specimen in the state of direct tensile. Indirect test methods are cube splitting and central point bending. The specimen cross section is 150mm×150mm and tensile length is 150mm. The test scheme is shown in Table 1.

FIG.1 DIMENSION SCHEMATIC OF THREE KINDS OF TENSILE SPCIMEN TABLE 2. TEST METHOD FOR TOTAL TABLE

Method Code

Method

Direct tension strength of middle embedded rebar Direct tension strength of I shape Direct tension strength of four embedded bar Splitting strength

Flexural strength

DTM DTE DTF

Strength Code

Section size a/mm

Eends configuiration Length b/mm

Tensile section Length c/mm

Rebar exsert length e/mm

Radius r/mm

Rebar diamater d/mm

ftm

150

fte

150

190

150

ftf

150

260

fts

150

450

3 THE MAIN TEST RESULTS Each set of three specimens, the average strength test results, as shown in table 3.

3.1 Direct Tensile Failure Mode Figure 2 is the three kinds of tensile mode when the typical failure pattern, among these, the DTM cracks randomly distribute in the middle(Fig 2a ), the DTE cracks tend to occur at the ends (Fig 2b),the DTF cracks appear more at the ends. -2http://www.ivypub.org/cet

TABLE 3 THE AVERAGE RESULTS (F /MPA) AND COEFFICIENT OF DISPERSION (CV)

Strength category

FA/B 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6

Direct tension Direct tension Cube compressive strength of middle strength of I strength embedded rebar shape fcu/MPa Cv ftm/MPa Cv fte/MPa Cv 36.0 0.03 2.28 0.03 3.01 0.02 31.3 0.08 2.04 0.08 2.40 0.01 24.9 0.01 1.82 0.01 1.97 0.04 16.9 0.05 1.40 0.05 1.44 0.08 53.8 0.06 2.87 0.06 3.15 0.06 47.2 0.12 2.77 0.12 3.46 0.05 45.3 0.04 2.49 0.04 2.59 0.01 37.5 0.06 2.07 0.06 2.01 0.02 63.0 0.02 3.04 0.02 3.81 0.04 56.9 0.11 2.50 0.11 0.07 52.5 0.12 2.87 0.12 3.20 0.03 41.1 0.18 2.14 0.18 2.25 0.07

(a) the direct tension of middle embedded rebar

Direct tension strength of four embedded rebar ftf/MPa Cv 1.55 0.20 1.19 0.10 1.60 0.10 1.16 0.10 3.35 0.06 2.30 0.06 2.67 0.06 1.64 0.18 3.22 0.06 2.60 2.93 0.10 1.46 0.07

(b) the direct tension of I shape

Flexural strength ff/MPa 5.74 5.21 3.88 2.55 6.52 7.17 6.50 4.97 8.41 6.25 4.81 4.76

Cv 0.17 0.07 0.15 0.06 0.03 0.04 0.10 0.10 0.04 0.19 0.27 0.12

Splitting strength fst/MPa 2.25 2.26 2.18 1.60 3.40 4.36 3.66 2.90 5.14 4.26 4.19 3.86

Cv 0.21 0.31 0.20 0.08 0.15 0.11 0.10 0.11 0.06 0.14 0.12

FIG.2 THE TYPICAL FAILURE PATTERN OF CONCRETE IN DIRECT TENSION DT F- 0-150 DT F-0.2-150 DT F-0.4-150 DT F-0.6-150

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

C30

C50

C70

(a) the direct tension of middle embedded rebar

1.2

DT E- 0-150 DT E-0.2-150 DT E-0.4-150 DT E-0.6-150

L/b

1.4

L/b

1.4

DT M- 0-150 DT M-0.2-150 DT M-0.4-150 DT M-0.6-150

0.0 C30

C50

(b) the direct tension of I shape

C70

C30

C50

C70

FIG.3 THREE KINDS OF DIRECT TENSILE CRACKS LOCATION L/B

Firgure 3 is the ratio L/b of direct tensile cracks with the end of specimen distance of L and the length b of the ends configuration of the specimen. As can be seen, L/b of DTF is 1.0 in average value, failure usual occurs in the area of steel buried anchoring ends, which may be related to mutations in the section stiffness; L/b of DTE is 0.80 in average value, cracks randomly distribute in the area of ends configuiration in the tensile segment, cracks in which crosssectional area larger than the central section; L/b of DTM is 1.13 in average value. The strength level and fly ash replacement rate had no significant effect on damage location. The average coefficient of dispersion of the tensile strength: DTM 0.04,DTE 0.1,DTF 0.16,ST 0.13,FT 0.12.The direct tension of middle embedded bar strength shows stable, with the small coefficient of dispersion and ideal fracture morphology. In summary, form the point of abnormal failure position of the I shape and four embedded bar tension mothod, the resulting situation of these tensile strength is not ideal, the direct tension method of middle embedded bar is relatively simple and accurate. -3http://www.ivypub.org/cet

3.2 Influence of the Method of Direct Tension to Strength Fig 4 is the comparison of three direct tensile strength. As can be seen, the strength of DTM is medium of three strength. The strength of DTE is the highest strength, that and failure location go deep into the the area of ends configuiration which’s sectional area larger than the size of the middle tensile secition size are related. The strength of DTF is the lowest in three strength, since the failure location of the specimens reinforced anchor positon substantially in the end, this section of concrete goes weaken which turn to the lower tensile strength on account of reinforced.

3.3 The Relationship between Direct Tensile Strength and Compression Strength Figures 5,6,7 are the relationship between direct tensile strength and compression strength which for grouped statistics on fly ash replacement rate statistic, the curves are the power function test regession curve, solid and dashed lines represent the fly ash replacement rate of zero and non-zero regression test results.

4.0 3.0

y = 0.2849x0.5677 R2 = 0.9184 y = 0.2108x0.6846

2.0

4.0

f tm/MPa

f tm,f te,f tf/MPa

DT M-0~0.6 DT E-0~0.60 DT150 F-0~0.6 乘幂 (DT M-0~0.6) 乘幂 (DT E-0~0.60) 乘幂 (DT F-0~0.6)

3.0

0.5256

y = 0.3483x 2

R = 0.9936 0.4039

y = 0.5258x

2.0

R2 = 0.7998 1.0 f cube/MPa 0.0 10

y = 0.0818x0.8692 R2 = 0.7032

1.0 0.0 10

f te/MPa

4.0 3.0

4.0 y = 0.807x0.3609

2.0 1.0 0.0 10

FIG.5 THE CHANGE OF FDTM WITH FCU

f tf/MPa

FIG.4 COMPARISON OF THREE TENSILE STRENGTH

R2 = 0.6913

3.0

y = 0.1091x0.897

2.0

DT E-0-150 R2 = 1 DT E-0.2-150 DT E-0.4-150 y = 0.2852x0.5967 DT E-0.6-150 2 乘幂 (DT E-0.2-150) R = 0.9349 f cube(DT /MPa 乘幂 E-0.6-150) y = 0.3814x0.469 乘幂 (DT E-0.4-150) 乘幂 (DT E-0-150) 2 50 70

R = 0.9764

FIG.6 THE CHANGE OF FDTE WITH FCU

R = 0.6411 DT M-0-150 DT M-0.2-150 0.5867 y = 0.2739x DT M-0.4-150 DT M-0.6-150 2 R = 0.9864 乘幂 (DTfM-0.2-150) cube/MPa 0.4814 (DT M-0.6-150) 乘幂 y = 0.3597x 乘幂 (DT M-0.4-150) 2 50M-0-150) 70 R = 0.9994 乘幂 (DT

DT E- 0-150 DT E-0.2-150 DT E-0.4-150 DT E-0.6-150 乘幂 (DT E-0.6-150) 乘幂 (DT E-0.4-150) 乘幂 (DT E-0.2-150) 乘幂 (DT E- 0-150)

y = 0.0097x1.4282 R2 = 0.8992 y = 0.0112x1.3605 R2 = 0.9734 y = 0.1166x0.8167

1.0 f cube/MPa

R2 = 0.998

0.0 10

y = 0.4672x0.3252 R2 = 0.8339

FIG.7 THE CHANGE OF FDTF WITH FCU

As can be seen,(1) The direct tensile strength of concrete increases with the compression strength;(2)For DTM and DTE, with the increase of the fly ash replacement rate, the compression strength and direct tensile strength are reduced. As the compression strength constant, the larger replacement rate get , the lower tensile strength reduce, wherein the tensle strength of I shape in Figure 4 to reduce the most obvious;(3)From the point of the test result by three kins of tensile methods, fly ash has no obvious influence to the slope of the regression curve and values, the power function index average value of the regression curve of DTM is 0.5,the coefficient is 0.38,which is lower than the standard 0.55 and 0.395; the power function index average value of the regression curve of DTE is 0.58,the coefficient is 0.4 ,which is similar with the standard; the value of DTF is discrete, the power function index average value of the regression curve is 0.98, the coefficient is 0.15. Somsak[10], Kristiwan[11] and other studies had indicated that fly ash has stronger influence for the tensile direct strength of low-strength concrete to high-strength concrete, this test has a similar conclusion(Fig 8).Fig 8 is three kinds of concrete strength level change with fly ash replacement rate (FA/B),vertical axis represents the ratio the strength of concrete to the strength which fly ash replacement rate is zero, among these,(a)~(d) correspondence to the -4http://www.ivypub.org/cet

tensile strength ratio of DTM, DTE, ST, FT, (e)correspondence to the compression strength ratio. The solid line is the regression curve of the three groups corresponding to the strength of the lowest group, this solid line has the largest decrease in the slope of the regression test in the three levels of the curve.

1.0

DT M-1-150 DT M-2-150 DT M-3-150 线性 (DT M-3-150) R2 = (DT 0.9768 线性 M-2-150) 2 线性 M-1-150) R = (DT 0.5713

0.8

R2 = 0.9324

1.2

f /f FA=0

0.6

DT E-1-150 DT E-2-150 DT E-3-150 2 (DT E-3-150) R线性 = 0.9957 线性 (DT E-2-150) 2 R = 0.7467 线性 (DT E-1-150) 2 R = 0.9017

1.0 0.8 0.6

FA /B(%)

0.4 0.0

0.2

0.4

0.6

0.0

0.2

(a)

1.2

f /f FA=0

1.0

R2 = 0.8721

0.8

(b)

1.0

0.6

0.4

0.4 0.2

R2 = 0.8503

0.8

0.6

0.0

CUBE-1-150 CUBE-2-150 CUBE-3-150 线性 (CUBE-1-150) 2 R线性 = 0.9868 (CUBE-2-150) 2 线性 (CUBE-3-150) R = 0.9541

0.8

R2 = 0.956

0.6 FA /B(%)

0.0

0.4 0.6 FA /B(%)

0.6

ST -1-150 1.2 ST -2-150 ST -3-150 线性 (ST -3-150) 2 R线性 = 0.6868 (ST -2-150) 1.0 2 R线性 = 0.2178 (ST -1-150)

1.2

f /f FA=0

FT -1-150 FT -2-150 FT -3-150 线性 (FT -3-150) R2 =(FT 0.9691 线性 -2-150) 2 (FT -1-150) 线性 R = 0.54

0.4

f /f FA=0

1.2

0.2

(c)

0.4

0.4 0.6 FA /B(%)

0.0

0.2

(d)

0.4

0.6

(e)

FIG.8 THE CHANGE OF THE STRENGTH OF THE CONCRETE IN DIFFERENT STRENGTH LEVEL WITH FA/B

3.4 The Ratio of Tensile Strength to Compression Strength

f tm,f te/f cu

0.08 0.07 0.06 0.05 0.04 10

DT E-0 DT E-0.2 DT E-0.4 DT E-0.6 DT M-0 DT M-0.2 DT M-0.4 DT M-0.6 乘幂 (DT E-0.2) 乘幂 (DT E-0.4) 乘幂 (DT E-0.6) 乘幂 (DT E-0) 乘幂 (DT M-0.2) f cu /MPa 乘幂 (DT M-0.4) 乘幂 (DT M-0.6) 乘幂 (DT M-0)

FIG.9 THE CHANGE OF FDTM/FCU, FDTE/FCU WITH FCU

ST -0 R2 = 0.6471 ST -0.2 ST -0.4 2 ST -0.6 R = 0.5558 FT -0 FT -0.2 R2 = 0.7475 FT -0.4 FT -0.6 R2 = 0.5737 乘幂 (ST -0.2) 乘幂 (ST -0.4) 2 = 0.1109 乘幂 (ST R -0.6) 乘幂 (ST -0) 2 乘幂 (FTR -0.2) = 0.9965 乘幂 (FT -0.4) 2 -0.6) = 0.8172 f cu /MPa乘幂 (FTR 乘幂 (FT -0)

f r,f ts /f cu

0.09

0.16 0.12

0.08 0.04 10

R2 = 0.2166

FIG.10 THE CHANGE OF FST/FCU, FFT/FCU WITH FCU

Fig 9 is the change of the ratio of the tensile strength of DTM and DTE whih compression strength. As can be seen, fdt / fcu decrease with the improve of fcu. As compressive strength is near, the more fly ash replacement rate, the more fdt / fcu decrease obvious. Fig 10 is the change of fst/fcu, fft/fcu, fdt/fcu with fcu. Among these, fft decreases with the increase of fcu, the descendant slope has no obvious change with the change of fly ash replacement rate. With the increase of fcu, two groups of fts / fcu increase, and the other two decrease. Figure 11 for different reference strength ft/fcu of concrete changes with the fly ash replacement rate of FA/B. The rule of the graph is not single. on the strength of 1 group (C30 group), apart from figure 9 (E), almost all ft/fcu increases with the increase of FA/B , explain the rate of tensile strength decrease with increasing rate of fly ash is lower than the rate of compressive strength decrease. The reference strength of 2 group (C50 group), apart from figure 11 (c), the ft/fcu of FA/B 20% is greater than FA/B 0%, but with FA/B more than 20%, the ft/fcu decrease with the increase of FA/B. The reference strength of 3 group (group C70), the ft/fcu of FA/B 20% group less than FA/B 0% -5http://www.ivypub.org/cet

group , 40% group of FA/B almost greater than 20% groups, FA/B 60% group was increased or decreased, that is, with the increase of FA/B while the emergence of the wave changes. DT E-2

f te/f cu

0.10

0.08

DT F-1

DT E-3

f tf/f cu

0.10 f tm/f cu

DT E-1

DT M-1 DT M-2 DT M-3

0.08

0.06

0.04 0.02 0.2

0.4

0.6

0.0

0.2

(a)

0.4

0.06

0.02 0.0

0.6

0.2

(b)

0.10

0.18

0.08

0.16 0.14

ST -1

0.06

ST -2

0.6

FT -1 FT -2 FT -3

0.12 0.10 0.08

ST -3

0.04

0.4 (c)

f r/f cu

f ts /f cu

DT F-3

FA /B(%)

0.02 0.0

DT F-2

0.08

0.04

FA /B(%)

0.10

FA /B(%)

0.06

0.02 0.0

0.2

0.4

0.0

0.6

0.2

(d)

0.4

0.6

(e)

FIG.11 THE CHANGE OF FT/FCU IN DIFFERENT STRENGTH LEVEL WITH FA/B

Studies have pointed out that the change of fly ash CH crystal shape and growth orientation of concrete; The activity of fly ash[12] effects can promote some CH crystal and its active ingredient have secondary hydration reaction to generate C-S-H gel. Part surface of fly ash is covered by C-S-H gel, improve the density of concrete structure, the increase of gel materials can reduce the stress concentration of the crack tip[13], these are advantageous to improve the tensile strength. But when fly ash replacement rate is too high, further reduce the consumption of cement, fly ash and hydration products of cement CH crystal reaction decreases, the lack of the generated C-S-H gel, and because of its high specific surface of the fly ash particles, reduce the compactness and homogeneous degree of the concrete, eventually lead to ft/fcu reduce, brittleness improvement effect weakened. As can be seen, the change of ft/fcu with fly ash replace rate is not monotonous. The existing test results can not give conclusions on the brittleness of conrete of fly ash.

3.5 Comparison of Tensile Strength and Currently National Code 4.0 3.0 2.0

y = 0.2791x 0.5694 R2 = 0.9446

1.0

0.5397

f cube/MPa 0.0 10

y = 0.4016x R2 = 0.7882

y = 0.2684x 0.5939 R2 = 0.8687

FIG.12 CHANGES IN FTM AND FTE WITH FCU

ft=0.395*fcu^0.55 fts=0.19fcu^2/3 FT -0~0.2 FT -0.4~0.6 ST -0~0.2 ST -0.4~0.6 DT M-0~0.2 DT M-0.4~0.6 乘幂 (FT -0~0.2) 乘幂 (ST -0.4~0.6) 乘幂 (FT -0.4~0.6) 乘幂 (ST -0~0.2) 乘幂 (DT M-0~0.2) 乘幂 (DT M-0.4~0.6)

f r,f tse,f tm/MPa

f tm,f te,f tf/MPa

0.395fcu^0.55 DT M-0~0.2 DT M-0.4~06 DT150 E-0~0.2 DT E-0.4~0.6 0.3fcu^0.55 乘幂 (DT M-0~0.2) 乘幂 (DT M-0.4~06) 乘幂 (DT E-0~0.2) 乘幂 (DT E-0.4~0.6) y = 0.3915x 0.4889 R2 = 0.7955

10.0 8.0 6.0 4.0

y = 0.0381x1.1722 R2 = 0.8356 y = 0.1363x0.8678 R2 = 0.9684 y = 0.914x0.5095 R2 = 0.6872 y = 0.4292x0.6606 R2 = 0.8011 y = 0.3915x0.4889

2.0 f cu /MPa

R2 = 0.7955 y = 0.2791x0.5694

0.0 10

R2 = 0.9446

FIG.13 CHANGES IN FTM, FST AND FFT WITH FCU

Figure 12 to according to the low dosage of fly ash content (0, 20%), and the high dosage (40% and 60%) group, obtained the power function model of regression curve of f tm and f te . It can be seen that the fly ash replacement test value is lower than the low dosage group, and test gap is bigger, and the font center embedded bar close to two -6http://www.ivypub.org/cet

groups of data. Among these, the two groups of test value and the high dosage group were lower than standard values ( f t  0.395 fcu0.55 ),indicating that the current specification does not apply to direct tensile test results, and also does not apply to the tensile strength of fly ash concrete. Figure 13 as a center point bending strength and splitting tensile strength test value according to the grouping of high and low dosage of fly ash regression results, it can be seen that the center point bending strength decrease more with the increasing dosage of fly ash, but split strength was no significant difference. Thick solid line in the figure to specification for ‘Design of concrete structures’GB50010-2010 edition recommended formula[14], the thick dashed line for related research suggests splitting strength and cubic compressive strength equation [15]. As can be seen, splitting strength test value is lower than the relevant suggestions of formula, but the recommended formula is almost consistent with the current specification, due to the splitting strength higher than the direct tensile strength of concrete, it shows that the current specifications of concrete tensile strength value is not used in the current concrete, and overestimate the direct tensile strength of concrete. Central point flexural strength is much higher than normative formula, and with increasing strength, flexural strength growth rate increased, it may be the bending state, trabecular section stress zone, and ultimately depends strength not only on the tension zone of the concrete, but related to the concrete flexural capacity.

4 CONCLUSIONS (1) Between three kind of tensile methods, it’s more simple to make the specimen of the direct tension of middle embedded rebar, discrete of tensile strength is small, fracture morphology is reasonable. this method is better than the others. (2) With the increase of fly ash replacement, fcu ,fdt ,fft, fst all have a decreasing trend, among these, fly ash has a greater impact on low strength level concrete. (3) fdt / fcu decrease with the improve of fcu, the brittleness of specimens increase. With the increase of fly ash replacement, fdt / fcu show a trend of increase in low strength concrete, but fly ash is no significant trend influence to fdt / fcu in high strength concrete. (4) It shows that the current specifications of concrete tensile strength value is not used in the fly ash concrete, and overestimate the direct tensile strength of concrete. According to the result of the method of DTM, proposal conversion formula is described as f t  0.3 fcu0.55 .

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Materials, 2012, 237-238 [14] GB50010-2010.Design of concrete structures[S]. China Architecture & Building Press, 2010 [15] Zhang Jianjing. Concrete structure engineering [M]. China Architecture & Building Press, 1998.11

AUTHORS 1

nationality, Masterâ&#x20AC;&#x2122;s degree, Professor,

degree, postgraduate, the research field: Research on fly ash

The research field: Concreted and high

concrete tensile properties and size effect.

performance

Email: zhagnyanhe900@126.com

X.X. He (Born-1961), Famale, Han

concrete

mechanical

Y.H. Zhang (Born-1990), Male, Han nationality, Masterâ&#x20AC;&#x2122;s

properties and damage mechanism, the concrete structure. Email: 68322510@sina.com

-8http://www.ivypub.org/cet