Open Access
Hasan Dilbas
- Faculty Department of Civil Engineering, Van Yuzuncu Yil University Van Turkey
Abstract
Falling behavior is generally studied by mathematicians. The first study is conducted by Comte de Buffon with name “Falling needles experiment” and is widely known. Buffon researched the falling needle behavior finding the fall of needles in relation with Pi. However, although aggregates are fallen to the mould in cement paste, falling behaviour of concrete is rarely studied considering the statistical parameters of the fall. Accordingly, an experimental study is conducted to research the falling behavior of the aggregate and its distribution in cementitious composite “concrete”. A conventional concrete design according to TS 802 is considered, and many cylindrical concrete specimens are produced in the laboratory. Then, a method is improved to determine the aggregate location on a surface of sliced concrete face and coordinates of the maximum size aggregates are determined. As a result, the falling behavior of the aggregates in concrete is found in relation with Pi as similar as falling needles. Pi is calculated as “3.139534884…” with a very small error while Pi is “3.141592654…”. In addition, it is found that mould edges cause a wall effect decreasing aggregate concentration near the edges. When gone from the edge to “a region” of concrete -it is named as concrete core in this paper-, the aggregate concentration increases.
Keywords: Falling behavior, distribution of aggregate, concrete core, wall effect.
[This article belongs to International Journal of Concrete Technology(ijct)]
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References
1. Badger, L.: Lazzarini’s lucky approximation of Pi. Mathematics Magazine 67, 83-91, 1994.
2. McCreary, J., Allen, M.: Various estimations of π as demonstrations of the monte Carlo method. Department of Mathematics Technical Report No. 2001-4. Tennessee Technological University, Cookeville, TN 38505, 2001.
3. Solomon, H.: Geometric Probability – Buffon Needle Problem, Extensions, and Estimation of Pi, pp. 1-24, SIAM, Philadelphia, 1978.
4. Diaconis, P.: Buffon’s Needle Problem with a Long Needle. J. Appl. Prob. 13, 614-618, 1976.
5. Dörrie, H.: 100 Great Problems of Elementary Mathematics: Their History and Solutions-Buffon’s Needle Problem. pp. 73-77. New York, Dover 1965.
6. Mantel, L.: An Extension of the Buffon Needle Problem. Ann. Math. Stat. 24, 674-677, 1953.
7. Schuster, E. F.: Buffon’s Needle Experiment. Amer. Math. Monthly 81, 26-29, 1974.
8. Kraitchik, M.: Mathematical Recreations-The Needle Problem, New York, W. W. Norton, pp:132-140, 1942.
9. Wegert, E., Trefethen, L. N.: From the Buffon Needle Problem to the Kreiss Matrix Theorem. Amer. Math. Monthly 101, 132-139, 1994.
10. Abed, M., Nemes, R., Tayeh, B.A.: Properties of self-compacting high-strength concrete containing multiple use of recycled aggregate. J. King Saud Univ.-Eng. Sci. 32, 108-114, 2018.
11. Zheng, J.J., Li, C.Q., Jones, M.R.: Aggregate distribution in concrete with wall effect. Magazine of Concrete Research 55, 257-265, 2003.
12. TS EN 197-1. Cement-Part 1: Composition, specifications and conformity criteria for common cements. Turkish Institute of Standards, Yucetepe, Ankara, Turkey, 2012.
13. TS 706 EN 12620. Aggregates for concrete. Turkish Institute of Standards, Yucetepe, Ankara, Turkey, 2003.
14. TS EN 206-1. Concrete-Part 1: Specification, performance, production and conformity. Turkish Institute of Standards, Yucetepe, Ankara, Turkey, 2002.
15. Erdoğan, T.Y., Beton, METU Press, Ankara, Turkey, 2007.
16. Kocatürk, A.N., Haberveren, S., Altıntepe, A., Bayramov, F., Ağar, A.Ş., Taşdemir, M.A.: Agrega konsantrasyonunun betonun aşınma direncine etkisi. In: 5. Ulusal Beton Kongresi, pp.535-544, Istanbul, Turkey, 2003.
International Journal of Concrete Technology
| Volume | 7 |
| Issue | 2 |
| Received | September 21, 2021 |
| Accepted | October 10, 2021 |
| Published | January 10, 2023 |