Analytic Solutions for Diametral Point Load Strength Tests
Publication: Journal of Engineering Mechanics
Volume 124, Issue 8
Abstract
This paper investigates the tensile stress distribution within a solid circular cylinder of diameter D and length 2L subjected to double diametral indentors or diametral point load strength test (PLST). The contact problem between the indentors and the cylinder is solved analytically, and exact solution for stress distribution is obtained through the use of displacement functions and double Fourier expansion in θ- and z-coordinates. Numerical results show that the tensile stress at the center of the cylinders, in general, decreases with Poisson's ratio ν and increases with 2L/D for 2L/D< 1, but remains roughly constant for 2L/D> 1. This prediction agrees exactly with the shape effect observed experimentally for the PLST for marbles, granite, and tuff found in Hong Kong and with previous published results for other rocks. The magnitude of tensile stress at the center is about three times the prediction obtained by using Wijk's formula, but seems more comparable with experimental results. The size effect of the point load strength index observed experimentally is also predicted by our theory.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abramowitz, M., and Stegun, I. A., eds. (1965). Handbook of mathematical functions. Dover Publications, Inc., New York, N.Y.
2.
Bieniawski, Z. T.(1974). “Estimating the strength of rock materials.”J. South Afr. Inst. Min. Metall., 74, 312–320.
3.
Bieniawski, Z. T.(1975). “The point test in geotechnical practice.”Engrg. Geol., 9, 1–11.
4.
Boisen, B. P. (1977). “A hand-portable point load tester for field measurements.”Energy resources and excavation technology, 18th U.S. Symp. on Rock Mech., F. D. Wang and G. B. Clark, eds., 5C2-1–5C2-4.
5.
Broch, E., and Franklin, J. A.(1972). “The point-load strength test.”Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 9, 669–697.
6.
Brown, J. W., and Churchill, R. (1993). Fourier series and boundary value problems, 5th Ed., McGraw-Hill International Editions, New York, N.Y.
7.
Chau, K. T.(1992). “Normality and bifurcation in a compressible pressure-sensitive circular cylinder under axisymmetric tension and compression.”Int. J. Solids and Struct., 29(7), 801–824.
8.
Chau, K. T.(1993). “Anti-symmetric bifurcation in a compressible pressure-sensitive circular cylinder under axisymmetric tension and compression.”J. Appl. Mech., ASME, 60(2), 282–289.
9.
Chau, K. T.(1995). “Buckling, barrelling, and surface instabilities of a finite transversely isotropic circular cylinder.”Quart. Appl. Math., 53(2), 225–244.
10.
Chau, K. T., and Wong, R. H. C.(1996). “Uniaxial compressive strength and point load strength of rocks.”Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 33(2), 183–188.
11.
Chau, K. T., and Wong, R. H. C.(1997). “Effective moduli of microcracked-rocks: Theories and experiments.”Int. J. Damage Mech., 6(3), 258–277.
12.
Costin, S. L.(1986). “Damage mechanics in the post-failure regime.”Mech. Mat., 4, 149–160.
13.
Goodman, R. E. (1989). Introduction to rock mechanics, 2nd Ed., John Wiley & Sons, Inc., New York, N.Y.
14.
Gradshteyn, I. S., and Ryzhik, I. M. (1980). Table of integrals, series, and products, Corrected and Enlarged Ed., Academic Press, Inc., New York, N.Y.
15.
Guidicini, G., Nieble, C. M., and de Cornides, A. T.(1973). “Analysis of point load test as a method for preliminary geotechnical classification of rocks.”Int. Assoc. Eng. Geol., 7, 37–52.
16.
Hassani, F. P., Scoble, M. J., and Whittaker, B. N. (1980). “Application of the point load index test to strength determination of rock and proposals for a new size-correction chart.”The state of the art in rock mechanics, Proc., 21st U.S. Symp. on Rock Mech., 543–553.
17.
Hiramatsu, Y., and Oka, Y.(1966). “Determination of the tensile strength of rock by a compression test of an irregular test piece.”Int. J. Rock Mech. Min. Sci., 3, 89–99.
18.
International Society for Rock Mechanics (ISRM).(1985). “Suggested method for determining point load strength.”Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 22, 53–60.
19.
Kulhawy, F. H.(1978). “Geomechanical model for rock foundation settlement.”J. Geotech. Engrg. Div., ASCE, 104(2), 211–227.
20.
Malvern, L. E. (1969). Introduction to the mechanics of a continuous medium. Prentice-Hall, Inc., Englewood Cliffs, N.J.
21.
Peng, S. S.(1976). “Stress analysis of cylindrical rock discs subjected to axial double point load.”Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 13, 97–101.
22.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1992). Numerical recipes: The art of scientific computing, 2nd Ed., Cambridge Univ. Press, New York, N.Y.
23.
Robins, P. J.(1980). “The point-load strength test for concrete cores.”Mag. of Concrete Res., 32(111), 101–111.
24.
Rudnicki, J. W. (1977). “The effect of stress-induced anisotropy on a model of brittle rock failure as localization of deformation.”Energy resources and excavation technology, Proc., 18th U.S. Symp. on Rock Mech., 3B4-1–3B4-8.
25.
Rudnicki, J. W., and Chau, K. T. (1996). “Multiaxial response of a microcrack constitutive model for brittle rock.”Rock mechanics, tools and techniques, Proc., 2nd North Am. Rock Mech. Symp.: NARM'96, M. Aubertin, F. Hassani, and H. Mitri, eds., 1707–1714.
26.
Shah, K. R., and Wong, T.-F. (1996). “Grain fracturing and comminution in porous materials.”Rock mechanics, tools and techniques, Proc., 2nd North Am. Rock Mech. Symp.: NARM'96, M. Aubertin, F. Hassani, and H. Mitri, eds., 859–866.
27.
Sternberg, E., and Rosenthal, F.(1952). “The elastic sphere under contracted loads.”J. Appl. Mech., ASME, 19, 413–421.
28.
Timoshenko, S. P., and Goodier, J. N. (1982). Theory of elasticity, 3rd Ed., McGraw-Hill Inc., New York, N.Y.
29.
Watson, G. N. (1944). A treatise on the theory of Bessel functions, 2nd Ed., Cambridge Univ. Press, Cambridge, England.
30.
Wijk, G.(1978). “Some new theoretical aspects of indirect measurements of the tensile strength of rocks.”Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 15, 149–160.
31.
Wijk, G. (1979a). “The tensile stress in a cylinder subject to the point load test.”Rep. DS 1979:4, Swedish Detonic Res. Found., Stockholm, Sweden.
32.
Wijk, G. (1979b). “The effect of the sample shape on the point load test strength index.”Rep. DS 1979:16, Swedish Detonic Res. Found., Stockholm, Sweden.
33.
Wijk, G.(1980). “The point load test for the tensile strength of rock.”Geotech. Test. J., 3(2), 49–54.
34.
Wijk, G., Rehbinder, G., and Logdstrom, G.(1978). “The relation between the uniaxial tensile strength and the sample size for Bohus granite.”Rock Mech., 10, 201–219.
35.
Zhang, J., Wong, T. F., and Davis, D. M.(1990). “Micromechanics of pressure-induced grain crushing in porous rocks.”J. Geophys. Res., 95, 341–352.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 8 • August 1998
Pages: 875 - 883
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Aug 1, 1998
Published in print: Aug 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.