Utilizing the Modified Popovics Model in study of effect of water to cement ratio, size and shape of aggregate in concrete behavior

Document Type : Original Article


1 Department of civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Engineering Technology Department, South Carolina State University, SC, USA


Three parameters, size, shape of aggregate, and water to cement ratio, play important role on concrete behavior. To study the effect of these parameters, two types of aggregates were used, rounded (river) and sharped corners (broken). The maximum sizes of aggregates were chosen to be 9.5, 12.5, 19 and 25 mm for water to cement ratio were 0.35, 0.42, 0.54 and 0.76. In this investigation, the total of 32 mixed designs were made. The stress-strain tests were performed on the entire samples, and the results were compared with the Popovics model. To further evaluate the analysis, three criteria, correlation coefficient, variation coefficient, and percentage of change in energy absorption were demonstarted. Analysis showed that there is significant differences between the Popovics model and our experimental results. The Modified Popovics model was introduced for better understanding the concrete behavior in compression. The proposed model covered a wide range of the parameters concerned in this investigation. The Modified Popovics model was comapred with several models such as the Popovics, Hognestad, Thorenfeldt, and Tsai and the results showed that modified approach has a better clarification for behavior of concrete in compression. Moreover, the results indicated that these models were more accurate for prediction of concrete behavior with rounded aggregates in comparison to sharped aggregates.


1.     Kaplan, M., "Flexural and compressive strength of concrete as affected by the properties of coarse aggregates", Journal Proceedings, Vol. 55, No. 5, (1959), 1193–1208.
2.     Walker, S., and Bloem, D., "Effects of aggregate size on properties of concrete", Journal Proceedings, Vol. 57, No. 9, (1960), 283–298.
3.     Bloem, D., and Gaynor, R., "Effects of aggregate properties on strength of concrete", Journal Proceedings, Vol. 60, No. 10, (1963), 1429–1456.
4.     Cordon, W., and Gillespie, H., "Variables in concrete aggregates and Portland cement paste which influence the strength of concrete", Journal Proceedings, Vol. 60, No. 8, (1963), 1029–1052.
5.     Ruiz, W. ., Effect of volume of aggregate on the elastic and inelastic properties of concrete, M.S. Thesis, Cornell University, (1966).
6.     Brzezicki, J. M., and Kasperkiewicz, J., "Automatic Image Analysis in Evaluation of Aggregate Shape", Journal of Computing in Civil Engineering, Vol. 13, No. 2, (1999), 123–128. doi:10.1061/(asce)0887-3801(1999)13:2(123)
7.     Mehta, P., and Monteiro, P., Concrete: Microstructure, Properties, and Materials, McGraw-Hill Education, (2014).
8.     Li, Z., Advanced Concrete Technology, John Wiley & Sons, (2011).
9.     ASTM C125., Standard Terminology Relating to Concrete and Concrete Aggregates. West Conshohocken, PA: ASTM, (2019).
10.   Ede, A. N., Olofinnade, O. M., Bamigboye, G. O., Shittu, K. K., and Ugwu, E. I., "Prediction of fresh and hardened properties of normal concrete via choice of aggregate sizes, concrete mix-ratios and cement", International Journal of Civil Engineering and Technology (IJCIET), Vol. 8, No. 10, (2017), 288–301 http://eprints.covenantuniversity.edu.ng/id/eprint/9581
11.   Neetu, N., and Rabbani, A., "Influence of size of aggregates on the Compressive strength of concrete", International Journal of Engineering Development and Research, Vol. 5, (2017), 27–30.
12.   Ogundipe, O. M., Olanike, A. O., Nnochiri, E. S., and Ale, P. O., "Development of Soil Distribution and Liquefaction Potential Maps for Downtown Area in Yangon, Myanmar", Civil Engineering Journal, Vol. 4, No. 4, (2018), 836. doi:10.28991/cej-0309137
13.   Yu, F., Sun, D., Wang, J., and Hu, M., "Influence of aggregate size on compressive strength of pervious concrete", Construction and Building Materials, Vol. 209, (2019), 463–475. doi:10.1016/j.conbuildmat.2019.03.140
14.   Mehta, P. K., "Studies on blended Portland cements containing Santorin earth", Cement and Concrete Research, Vol. 11, No. 4, (1981), 507–518. doi:10.1016/0008-8846(81)90080-6
15.   Hognestad, E., Study of Combined Bending and Axial Load in Reinforced Concrete Members, University of Illinois, Urbana, (1951).
16.   Smith, G., and Young, L., "Ultimate flexural analysis based on stress-strain curves of cylinders", Journal Proceedings, Vol. 53, No. 12, (1956), 597–609.
17.   Desayi, P., and Krishnan, S., "Equation for the stress-strain curve of concrete", Journal Proceedings, Vol. 61, No. 3, (1964), 345–350.
18.   Kent, D., and Park, R., "Flexural members with confined concrete", Journal of the Structural Division, Vol. 97, No. 7, (1971), 1969–1990.
19.   Sargin, M., Ghosh, S. K., and Handa, V. K., "Effects of lateral reinforcement upon the strength and deformation properties of concrete", Magazine of Concrete Research, Vol. 23, Nos. 75–76, (1971), 99–110. doi:10.1680/macr.1971.23.76.99
20.   Popovics, S., "A numerical approach to the complete stress-strain curve of concrete", Cement and Concrete Research, Vol. 3, No. 5, (1973), 583–599. doi:10.1016/0008-8846(73)90096-3
21.   Wang, P., Shah, S., and Naaman, A., "Stress-strain curves of normal and lightweight concrete in compression", Journal Proceedings, Vol. 75, No. 11, (1978), 603–611.
22.   Carreira, D. J., and Chu, K.-H., "Stress-Strain Relationship for Plain Concrete in Compression", Journal Proceedings, Vol. 82, No. 6, (1985), 797–804.
23.   Thorenfeldt, E., "Mechanical properties of high-strength concrete and applications in design", Symposium Proceedings, Utilization of High-Strength Concrete, Norway, (1987).
24.   Tsai, W. T., "Uniaxial Compressional Stressā€Strain Relation of Concrete", Journal of Structural Engineering, Vol. 114, No. 9, (1988), 2133–2136. doi:10.1061/(asce)0733-9445(1988)114:9(2133)
25.   Hsu, L. S., and Hsu, C.-T. T., "Complete stress — strain behaviour of high-strength concrete under compression", Magazine of Concrete Research, Vol. 46, No. 169, (1994), 301–312. doi:10.1680/macr.1994.46.169.301
26.   Almusallam, T. H., and Alsayed, S. H., "Stress–strain relationship of normal, high-strength and lightweight concrete", Magazine of Concrete Research, Vol. 47, No. 170, (1995), 39–44. doi:10.1680/macr.1995.47.170.39
27.   Attard, M., and Setunge, S., "Stress-strain relationship of confined and unconfined concrete", Materials Journal, Vol. 93, No. 5, (1996), 432–442.
28.   Kumar, P., "A compact analytical material model for unconfined concrete under uni-axial compression", Materials and Structures, Vol. 37, No. 9, (2004), 585–590. doi:10.1007/bf02483287
29.   Lokuge, W. P., Sanjayan, J. G., and Setunge, S., "Constitutive Model for Confined High Strength Concrete Subjected to Cyclic Loading", Journal of Materials in Civil Engineering, Vol. 16, No. 4, (2004), 297–305. doi:10.1061/(asce)0899-1561(2004)16:4(297)
30.   Tasnimi, A. A., "Mathematical model for complete stress–strain curve prediction of normal, light-weight and high-strength concretes", Magazine of Concrete Research, Vol. 56, No. 1, (2004), 23–34. doi:10.1680/macr.2004.56.1.23
31.   Lokuge, W. P., Sanjayan, J. G., and Setunge, S., "Stress–Strain Model for Laterally Confined Concrete", Journal of Materials in Civil Engineering, Vol. 17, No. 6, (2005), 607–616. doi:10.1061/(asce)0899-1561(2005)17:6(607)
32.   Nematzadeh, M., and Hasan-Nattaj, F., "Compressive Stress-Strain Model for High-Strength Concrete Reinforced with Forta-Ferro and Steel Fibers", Journal of Materials in Civil Engineering, Vol. 29, No. 10, (2017), 04017152. doi:10.1061/(asce)mt.1943-5533.0001990
33.   Al-Tikrite, A., and Hadi, M. N. S., "Stress–Strain Relationship of Unconfined RPC Reinforced with Steel Fibers under Compression", Journal of Materials in Civil Engineering, Vol. 30, No. 10, (2018), 04018234. doi:10.1061/(asce)mt.1943-5533.0002445
34.   Peng, J.-L., Du, T., Zhao, T.-S., Song, X., and Tang, J.-J., "Stress–Strain Relationship Model of Recycled Concrete Based on Strength and Replacement Rate of Recycled Coarse Aggregate", Journal of Materials in Civil Engineering, Vol. 31, No. 9, (2019), 04019189. doi:10.1061/(asce)mt.1943-5533.0002847
35.   ASTM C150. Standard Specification for Portland Cement, West Conshohocken, PA: ASTM, (2005).
36.   ASTM C33. Standard Specification for Concrete Aggregates, West Conshohocken, PA: ASTM, (2018).
37.   ASTM C494. Standard specification for chemical admixtures for concrete, West Conshohocken, PA: ASTM, (2005).
38.   Kim, B. S., Park, S. G., You, Y. K., and Jung, S. I., Probability & Statistics for Engineers & Scientists, Pearson education-Korea Inc, (2011).
39.   MATLAB, The MathWorks Inc. Natick, MA, USA, (2017).