CALCULATION MODEL AND RELIABILITY ANALYSIS FOR FLEXURAL CAPACITY OF NORMAL SECTION OF RECYCLED CONCRETE BEAM

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1 CALCULATION MODEL AND RELIABILITY ANALYSIS FOR FLEXURAL CAPACITY OF NORMAL SECTION OF RECYCLED CONCRETE BEAM Jiachuan YAN (1), Chaoying ZOU (1), and Qiong HU (1) (1) School of Civil Engineering, Harbin Institute of Technology, China Abstract The application of recycled concrete in civil engineering was an effective method to resolve the problem of dealing with a large amount of construction waste. The recycled concrete beams were investigated in this paper. The RC beam flexural capacity calculation formula dependent on the replacement ratio of recycled aggregate was founded, which was based on the theoretical analysis according to the design code of concrete structures. And the M-ϕ relation curves of the RC beams were calculated by the numerical method. The results showed that the results of theoretical calculation accorded well with the existed experimental results of recycled concrete beams at home and abroad. Variance Analysis proved that the theoretical analysis method and numerical analysis method were both applicable. The reliability analysis of flexural capacities of RCA beams was given. The influence of different factors on the reliability index was studied. This research provided much valuable references for the design of recycled concrete beam. Keywords: recycled concrete; replacement ratio; flexural capacity; numerical method; reliability 1. INTRODUCTION Concrete is the largest used building material which is used in various construction projects. In China, more than 20 billion tons of concrete is used every year, and the content of aggregates accounts for approximately 70%. Over the years, because the sand and crushed stone aggregate is easy to get, low price, and it was considered that the aggregates are of inexhaustible supply. The present situation of excessive exploitation and waste is created. China is consuming massive natural resources annually. Meanwhile, as an example, according to estimates, 10 million tons of waste was produced in the construction industry in Shenzhen in Most of the construction waste were stacked outdoor or buried without any waste disposal. This situation not only occupies massive farming land, and consumes construction 586

2 expenses such as the clean and transport of waste, but also has created a huge consumption to the nature resources. The engineering application of the recycled concrete can resolve this contradiction of the abandoning of the construction waste and the shortage of the resources of sand and crushed stone [1]. Recycled concrete (RCA) refers to replacing of the natural aggregates partially or completely by the recycled aggregates (produced from concrete waste after the process of crushing, cleaning, classifying and mixing according to a certain proportion) [2]. A large number of experiments of recycled concrete have been carried out in China and worldwide, and many achievements in research have been obtained. The results show that the performance of RCA after the reasonable design can achieve the requirement of the concrete reference, and the application of RC in the civil engineering is feasible. In order to promote RCA to be applied in structures in engineering projects, further research of the structure performance and the design method of RCA needs to be conducted. The proportion of flexural members to the structure members is the largest, therefore studying the performance of the RCA beam is of quite importance. The experiments of RC beams at home and abroad have specific object respectively, and based on the specific experiments the researchers propose the theoretical formula correspondingly. But these formulas are not the theoretical formula based on the stress-strain relation of RCA, and corresponding numerical method is not taken as the analysis verification. Meanwhile, the corresponding safety evaluation for RCA is not considered. The RCA beams are investigated in this paper. Based on the stress-strain curve, the RC beam flexural capacity calculation formula and related parameters with the recycled aggregate replacement rate r was founded according to the Code for design of concrete structures (GB ) [3]. The M-ϕ relation curves and the flexural capacities of the RCA beams were calculated by numerical method. Based on the RC beam experiments at home and abroad, the validity of the calculation formula and numerical method is verified. The reliability analysis of flexural capacities of RC beams was given. The influence of different factors on the reliability index was studied. 2. ANALYSIS FOR FLEXURAL CAPACITY OF NORMAL SECTION OF THE RC BEAM 2.1 The constitutive relation of RC The compression strength is the most important mechanics property of the RCA. Concerning the compressive strength of RC, many experiments were carried out. References [4] and [5] proposes that because of the influence of the diversity of the source for the original concrete, the recycled aggregates replacement rate, the preparation condition of basal concrete and RC, and the experiment condition and method on the compressive strength, the results from various experiments vary a lot. The conclusion accepted widely is that the compressive strength of RCA approach that of normal concrete. The normalized stress-strain relationship of RC is [4] : ax+ ax + a x x y = x x 1 2 bx ( 1) + x 2 3 (3 2 ) ( 2) 0 1 (1) 587

3 In equation (1), the value of parameter a and b is in the Table 1. The parameter a is the initial tangential modulus, and the smaller a is, the initial modulus is smaller. The parameter b is related to the integral area of the normalized stress-strain curve, and the larger b is, the descent of the curve is more abrupt and the ductility of the material is worse. From Table 1, it can be concluded that with the increase of the recycled aggregate replacement rate, the degree of brittleness will increase. Table 1: The value of parameter a and b [6] r 0% 30% 50% 70% 100% a b As normal concrete, the prism compression strength and the cube compression strength relate well. Taking the results of reference [5] and [6] into consideration, this paper proposes f c /f cu =0.8. (f c is the prism compression strength and f cu is the cube compression strength.) Reference [7] considers that based on the comparison of the crush index, the strength of recycled aggregates is slightly lower than that of the natural aggregates. This difference can influence the peak value of the strain of RC, so the peak value of the strain of RC is larger than that of the normal concrete. With the increase of the recycled aggregates replacement rate, the peak value of the strain of RCA increases. According to these results above, this paper puts forward that the peak value of the strain of RCA ε 0 = The result of experiment from reference [4] shows that the ultimate compressive strain of RCA is larger than that of normal concrete. Based on this conclusion above, this paper suggests that the ultimate compressive strain of RC ε cu = Method based on the current code Reference [5] proves that in the bending process of the RCA beam, the section strains of the normal section remain a plane. According to the calculation method [8-9] for flexural capacity of normal section of concrete beam which is adopted in the present code, the calculation formula for flexural capacity of normal section of the RCA beam is: α1 fbx c = fyas M Mu = α1fbx c h0 x α1 = r ( 2) In the formula above: r recycled aggregate replacement rate; M design value of moment; M u design value of flexural capacity; b section width of the beam; h section height of the beam; f y design value of tensile strength of steel; x height of conversion compressive region. The application condition of equation (2) is: (2) 588

4 (1) In order to prevent the over reinforced damage of the beam, it should be satisfied that ξ ξ b, and the value of ξ b is in Table 2; (2) In order to prevent the shortage reinforced damage of the beam, it should be satisfied that A s ρ min bh. From the result of the experiment of the tensile strength for RC [7], the value of tensile strength of RC is less, and the influence of recycled aggregate replacement rate on that is not noticeable. So according to the present code, the minimal ratio of reinforcement is: f ρmin = max 0.002,0.45 t f y (3) Table 2: Value of ξ b Steel bar class ξ b r=0% r=30% r=50% r=70% r=100% HPB HRB HRB The ρ-m u relationship curves of RC beams of different recycled aggregate replacement rates resulted from equation (3) is shown in Fig.1 and the comparison of these curves with the results of related experiments in China and worldwide is also shown in Fig.1. The number of experiments compared is 9 and totally 52 beams are included [10-17] (under reinforced beams, over reinforced beams, and high-strength concrete beams are excluded) M u fbh c r=0% r=30% r=50% r=70% r=100% 0.15 Andrej HUANG Qing F.Yagishita SONG Xinwei 0.10 Ippei GAO Ce 0.05 Mukai LIN Jun LAN Yang f y ρ f Fig. 1: ρ-m u relationships curves From Fig. 1, it can be concluded that in the case of ratio of reinforcement of the RCA beam is little, with the increase of the recycled aggregate replacement rate, the flexural capacity of normal section of the RCa beam decreases slightly. In the case of ratio of reinforcement of the RCA beam is large, the influence of recycled aggregates replacement rate on the flexural capacity of normal section of the RCA beam is noticeable. That is with the increase of the recycled aggregate replacement rate, the flexural capacity of normal section of the RCA beam decreases greatly. c 589

5 2.3 Numerical method Calculation beginning of M-ϕ relationship Information of the material and section of the member Initial curvature ϕ=0 ϕ=ϕ+ ϕ Assuming the strain of concrete at the rim of compression region ε c Calcualting the strain of each strip of concrete ε ci and steel bar ε si Calcualting the stress of each strip of concrete σ ci and steel bar σ si Collecting the axial force of strips and steel bar N=N c +N s No Whether N satisfies the balance condition Yes Calculating bending moment of the section under the current curvature Whether bending moment decreases to 85% of the critical moment or the strain of concrete achieve the ultimate No Yes Calculation finish Fig. 2: Flow chart for calculation of curvature-moment relationship 590

6 The whole process of bending of concrete beam can be obtained by the nonlinear analysis method. In the nonlinear analysis method, the basic analysis is the nonlinear analysis of the section of each structural member, and the relationship curve of the moment-curvature (M-1/ρ) can be acquired by the nonlinear analysis of section. The flow chart for calculation of moment-curvature relationship of the normal section of the RCA beam is Fig. 2 [9]. According to Figure 2, this paper compiles a program by FORTRAN for calculating the moment-curvature curve and curvature-depth of compression region curve of the normal section of the RCA beam. Meanwhile, moment-curvature curves and curvature-depth of compression region curves of each beam from the experiments at home and abroad are obtained. The related calculation data of each beam are shown in reference [18]. The moment-curvature curves of the beams from of the experiment of Andrej are illustrated in Figure 3. In Figure 3, G1 and O1 are normal concrete beams M (KN m) O1 O2 O3 G1 G2 G ϕ (1/m) Fig. 3: Experiment of Andrej From Figure 3, it can be seen that the shape and the variation law of the M-ϕ curve of the RCA beam is similar to that of the normal beam. The M-ϕ curve conforms to the three stages of the bending process in the experiment of the RCA beam, i.e. the elastic stage, the stage of working with the cracks, and damage stage. From the M-ϕ curve, it also can be concluded that the flexural capacity of the RCA beam is slightly smaller than that of the normal concrete beam. Meanwhile, the gradient of the M-ϕ curve represents the flexural rigidity of section of the RCA beam. With the increase of the recycled aggregate replacement rate, the flexural rigidity of section of the RCA beam decreases. And the more the recycled aggregate replacement rate rises, the more the flexural rigidity reduces. 2.4 Contrastive analysis of the experiments For the RCA beams from the experiments in China and worldwide, this paper assumes that the flexural capacities obtained from the experiments are M u t, the flexural capacities resulting from the method based on the current code are M u c, and the flexural capacities rising from the numerical method are M u a. The ratio of M u t /M u c and M u t /M u a is shown in Figure 4 and Figure 5 respectively. 591

7 M t u /Mc u Andrej 试验 F.Yagishita 试验 Ippei 试验 Mukai 试验兰阳试验 黄清试验宋新伟试验高策试验李俊试验 f c Fig. 4: The value of M u t /M u c M t u /Ma u Andrej 试验 F.Yagishita 试验 Ippei 试验 Mukai 试验兰阳试验 Fig. 5: The value of M u t /M u a f c 黄清试验宋新伟试验高策试验李俊试验 The testing hypothesis is used for analyzing the ratio of M u t /M u c and M u t /M u a. The results calculated from the kolmogorov test [19] are presented in Table 3. Table 3: Statistical analysis of M u t /M u c and M u t /M u a M t c u /M u M t a u /M u max min µ σ δ probability distribution % normal distribution % normal distribution The mean value of is M u t /M u c , and the mean value of M u t /M u a is The discreteness of the results calculated from the method based on the current code and the numerical method are little. The results calculated from these two methods accord well with the results of the experiments. 3 RELIABILITY ANALYSIS FOR FLEXURAL CAPACITY OF NORMAL SECTION OF RECYCLED CONCRETE BEAM In the practical application of RC, because the water cement ratio, service life, carbonation degree, mineral content, admixture content, service environment and damage degree of the recycled aggregate may have many differences, the material properties may have larger differences. The differences of material properties will increase the variability of structural resistance of the RCA structure. This section will conduct the reliability analysis for flexural capacity of normal section of the RCA beam which is designed by the method introduced in Limit state equation of flexural capacity The limit state equation of flexural capacity of normal section of the RCA beam is: Z = R γ S (4) 0 For the building which the security level is the second level, γ 0 =1.0. From the related formula in the current code, it can be deduced that [3]: ( c, y) (, ) Z = R f f S GQ (5) Af s y R= kpaf s y h0 2α1 fb c (6) 592

8 k p is the uncertainty factor for the calculation mode, and it reflects the inaccuracy of the calculation formula. When designing the section of the RCA beam, the design value of load effect is equal to the design value of resistance. So the design value of load effect can be obtained by the design value of resistance: Af s y S( GQ, ) = Af s y h0 2α1 fb c Supposing the ratio of load effect is q=s Qk /S Gk. According to the maximal value of the load effect combination, the standard value of the load effect is: S S Gk Qk G (, ) S GQ = γ + q γ G Q (, ) q S GQ = γ + q γ Q 3.2 Probability distribution model and statistical parameter of the random variable Based on the reference [20], the probability distribution models and statistical parameters of each random variable in the limit state equation are shown in Table 4. Table 4: Probability distributed models and statistical parameters of random variables random variable probability distribution model deviation coefficient of factor k variation δ width of section b (mm) normal distribution useful height of section h 0 (mm) normal distribution diameter of bar d (mm) normal distribution dead load (N) normal distribution live load (office building) (N) typeⅠ extreme value distribution formula approximate coefficient k p normal distribution (7) (8) (9) The deviation factor is defined as k= the mean value/ standard value. According to the result of the method based on the current code, the mean value of formula approximate coefficient µ kp =1.0, and the coefficient of variation δ kp =0.07 (in the Unified standard for design of building structures, δ kp =0.04). Table 5: Statistics of reinforcement strength strength class µ fc δ fc HPB HRB HRB f y 593

9 The statistics of reinforcement strength is shown in Table 5. Because the statistical data of the compression strength of the RCA concrete are deficient, this paper assumes that the probability distributed model and statistical parameter of random variable of the compression strength of the RCA concrete is identical with the normal concrete (µ fc =26.1MPa, δ fc =0.14). 3.3 Result of reliability index The FORM [21] is adopted for calculating the reliability index, and the law of variation of the reliability index with the variation of each parameter is mastered. The results are shown in Figure r=0% r=30% r=50% r=70% r=100% r=0% r=30% r=50% r=70% r=100% β 5.6 β (a) load effect ratio q h (b) width of section β r=0% r=30% r=50% r=70% r=100% HPB235 HRB335 HRB400 钢筋类别 (c) class of steel bar β r=0% r=30% r=50% r=70% r=100% (d) reinforcement ratio Fig. 6: Reliability index β From Figure 6, it can be seen that if the discreteness of RCA can achieve the level of the normal concrete, the recycled aggregate replacement rate r ranging from 0 to 100% (Fig. 6(a)- Fig. 6(d)) and the reinforcement ratio ρ ranging from ρ min to ρ max (Fig. 6(d)), the reliability index β is larger than the target reliability index [β] =3.2 which is the limit of ductility damage of secondary level structure. 4. CONCLUSIONS (1) The RCA beam flexural capacity calculation formula and related parameters with the recycled aggregates replacement rate r is found to be in accordance with the requirements of the Code for design of concrete structures (GB ). The results ρ 594

10 calculated from this method accord well with the results of the experiments. The mean value of the ratio of the results calculated from this method to the results of the experiments is 1.081, and the coefficient of variation is (1) The M-ϕ relation curves and the flexural capacities of the RCA beams are calculated by numerical method. The results calculated from this method accord well with the results of the experiments. The mean value of the ratio of the results calculated from this method to the results of the experiments is 1.087, and the coefficient of variation is (2) If the discreteness of RCA can achieve the level of the normal concrete, the reliability index β can meet the request of target reliability index. REFERENCES [1] YAO Wu. 'Green concrete'. Chemical Industry Press. 2006:27~45 (in Chinese) [2] D.I.F. Proposed Amendment to the Danish Concrete Code[S]: Use of Recycled Demolition Rubble, 2001, (4):25~26 [3] The Ministry of Construction of the People's Republic of China. Code for design of concrete structures (GB ) [S]. China Architecture & Building Press. 2002:41~48 (in Chinese) [4] HUANG Qing. 'Experiment research and finite element analysis of the recycled concrete beam'. Dissertation for Master degree, Harbin: Harbin industrial university, 2005:15~17 (in Chinese) [5] Song Can, Zou Chaoying, Xu Wei. 'Experiment Analysis on Basic Mechanic Property of Recycled Concrete'. Low Temperature Architecture Technology. 2007, (3):15~16 (in Chinese) [6] LI Jiabin. 'Research on basic mechanical properties of recycled concrete'. Dissertation for Master degree, Tongji University, 2005:19~21(in Chinese) [7] HUANG Wenfeng. 'Experimental research on the influence of recycled aggregate and admixture on mechanical properties of recycled concrete'. Dissertation for Master degree, Harbin: Harbin industrial university, 2007:46~52 (in Chinese) [8] Southeast University, Tianjin University, Tongji University. Design principle of concrete structure. China Architecture & Building Press. 2002:61~65 (in Chinese) [9] GUO Zhenhai, SHI Xudong. Principle and analysis of concrete structure. Tsinghua University Press. 2003:102~114 (in Chinese) [10] F.Yagishita, M.Sano, M.Yamada. 'Behaviour of Reinforced Concrete Beams Containing Recycled Aggregate' [C], Demolition and Reuse of Concrete and Masonry Proceedings of the Third International RILEM Symposium, Ed. Erik K.Lauritzen, 1993:331~343 [11] Mukai T, Kikuchi M. 'Properties of Reinforced Concrete Beams Containing Recycled Aggregate' [C]. Proceedings, 2nd International Symposium RILEM Demolition and Reuse of Concrete and Masonry, Tokyo, Nov, 1988; Chapman and Hall, London-New York, V :670~679 [12] Andrzej B. Ajdukiewicz, Alina T. Kliszczewicz. Behavior of RC Beams from Recycled Aggregate Concrete[C]. Proceedings of the American Concrete Institute 2002: 10~13 [13] Ippei Maruyama, Masaru Sogo, Takahisa Sogabe et al. Flexural Properties of Reinforced Recycled Concrete Beams[C]. Conference on the Use of Recycled Materials in Building and Structures. 2004:19~21 [14] XIAO Jianzhuang, LAN Yang. Experimental research on the flexural property of recycled concrete beam. Special structure. 2006, (3) 9~12 (in Chinese) [15] SONG Xinwei. Experimental Research on Recycled Concrete Beams Bending Performance. Dissertation for Master degree, Zhengzhou University. 2006:65~67 (in Chinese) [16] GAO,Ce. Study on the Flexural Behavior of Recycled Coarse Aggregates Concrete Beam. Dissertation for Master degree, Southwest Jiaotong University. 2007:61~63 (in Chinese) 595

11 [17] LIN Jun. Experiment Research on Compressive Strength Of recycled Concrete and Performance of Recycled reinforced Concrete Beam. Dissertation for Master degree, Guangxi University. 2007:34~36 (in Chinese) [18] YAN Jiachuan. Research on calculation model and reliability of flexural capacity of normal section of the recycled concrete beam. Dissertation for Master degree, Harbin: Harbin industrial university, 2008:37~47 (in Chinese) [19] YANG Hu, ZHONG Bo, LIU Jingsun. Applied Mathematical Statistics. Tsinghua University Press. 2006:142~156 (in Chinese) [20] China Academy of Building Research. Unified standard for design of building structures (GBJ68-84). China Architecture & Building Press. 1984:12~15 (in Chinese) [21] ZHAO Guofan. Structural Reliability Theory. China Architecture & Building Press. 2000:21~34 (in Chinese) 596