Abstract
Prior to excavation, any point in a rock mass is subjected to stress, which has to be considered in the overall stress distribution after the excavation work is completed. Over the past three decades, empirical, analytical, and field studies have shown that the ratio of average horizontal stress to vertical stress plays a dominant role in engineering structure design. Notationally, this ratio is referred to as the coefficient of lateral stress K, which is a dimensionless positive quantity. The intent of this paper was to bring out the intrinsic characteristic of K with the use of probabilistic and statistical techniques, which have not been considered extensively in any previous context.
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REFERENCES
Aitchison, J., and Brown, J. A. C., 1957, The lognormal distribution: Cambridge University Press, London, 375 p.
Brown, E. T., and Hoek, E., 1978, Trends in relationships between measured in-situ stresses and depth: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 15, p. 211–215.
Gay, N. C., 1975, In-situ stress measurements in southern Africa: Tecnophysics, v. 29, p. 447–459.
Haimson, B. C., 1978, The hydro fracturing stress measuring method and recent field results: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 15, p. 167–178.
Hoek, E., 1999, Putting numbers to geology-An engineer's viewpoint: Quaternary J. Eng. Geol., v. 32, p. 1–19.
Hoek, E., and Brown, E. T., 1980, Underground Exavations in Rock: Institution of Mining and Metallurgy, London, 527 p.
Koch, S., and Link, R. F., 1971, Statistical Analysis of Geological Data: Dover Publications, New York, 375 p.
Lame, G., 1986, Leçons sur la Théorie Mathématique de l'Elasticité des Corps Solidés: Gauthier-Vollars, Paris, p. 211–224.
McCutchen, W. R., 1982, Some elements of a theory for in-situ stress: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 19, p. 210–213.
Sheory, P. R., 1994, A theory for in situ stresses in isotropic and transversely isotropic rock: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 31, p. 23–34.
Worothicki, G., and Denham, A. M., 1970, The state of stress in the upper part of earth's crust in Australia according to measurements in tunnels and mines and from seismicobservations: Investigation of stress in Rock-Advances in Stress Measurement, p. 71-82.
Zoback, M. L., 1992, First-and second-order patterns of stress in the litosphere; The World Stress Map Project: J. Geophys. Res., B. v. 97, no. 8, p. 11703–11728.
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Şen, Z., Sadagah, B.H. Probabilistic Horizontal Stress Ratios in Rock. Mathematical Geology 34, 845–855 (2002). https://doi.org/10.1023/A:1020928727867
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DOI: https://doi.org/10.1023/A:1020928727867