Assessment of the Influence of Breakage Strength Rocks by Cox Method
Abstract
Analyzed according to the theory of continuous mechanics, medium rock massif is a natural environment difficult to know, so the forecasts referring to its behaviour are approximate and uncertain. Such an assertion becomes a certitude, even resulting from reality; consequences of the four fundamental features of massif are multiple and involve really difficult issues in mining field and generally, in the constructions field. The concept and the way to assess the stability of underground construction involves understanding its phenomenological evolution and doubtless the character of rocks behaviour in massif. Based on the principle scheme of rocks behaviour way to failure, we propose a statistical analysis method of results obtained by laboratory tests using Cox regression. This method offers the possibility to provide quantitatively and qualitatively the time when the breakage occurs. The method enables us to establish the link between a certain factor through which can forecast rock breakage and the ability to resist; the method can be developed and applied on a massif scale and also in the stability analysis of underground works.
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References
[2]. Armitage P., Berry G., Statistical Methods in Medical Research (3rd Edition), Blackwell, 1994.
[3]. Barlow W. E., Robust variance estimation for the case-cohort design. Biometrics., 50, p. 1064-1072, 1994.
[4]. Barlow W. E., Ichikawa L., Rosner D., Izumi S., Analysis of case-cohort designs, Journal of Clinical Epidemiology, 12, p. 1165-1172, 1999.
[5]. Bieniavski Z. T., Mechanism of brittle fracture of rock, Int. J. of Rock Mech. and Min. Sci., no. 4, 1967.
[6]. Cox D. R., Partial Likelihood, Biometrika, vol. 62, p. 269-276, 1975.
[7]. Dennis E. Hinkle, William Wiersma, Stephen G. Jurs, Applied Statistics for the Behavioural Sciences, Boston, Published by Houghton Mifflin (Academic), 3rd Edition, p. 706, ISBN 10: 0395675553, 1994.
[8]. Gorunescu F., Gorunescu M., Analiza exploratorie şi procesarea datelor cu simulări în Matlab, Editura Albastra.
[9]. Gorunescu F., Gorunescu M., Modele regresive, math.ucv.ro/~gorunescu/courses/EDA/curs2EDA.pdf.
[10]. Hinkle D. E., Wiersma W., Jurs S. G., Applied statistics for the behavioral sciences (3rd), Boston, USA, Houghton Mifflin Company, 1994.
[11]. Lin D. Y., Cox Regression Analysis of Multivariate Failure Time Data: The Marginal Approach, Statistics in Medicine, vol. 13, p. 2233-2247, 1994.
[12]. Keppel G., Design and analysis: a researcher’s handbook (3rd ed.), Englewood Cliffs, USA: Prentice-Hall Inc, 1991.
[13]. Kleinbaum D. G. et al., Applied Regression Analysis and Other Multivariable Methods (3rd Edition), Duxbury Press, 1998.
[14]. Radu I., Miclea M., Albu M., Nemeş S., Moldovan O., Szamoskozi Ş., Metodologie psihologică şi analiza datelor, ClujNapoca: Editura Sincron, 1993.
[15]. Schoenfeld D., Partial Residuals for The Proportionnal Hazards Regression Model, Biometrika, vol. 69, p. 239-241, 1982.
[16]. Spiekerman C. F., Lin D. Y., Marginal Regression Models for Multivariate Failure Time Data, Journal of the American Statistical Association, vol. 93, p. 1164-1175, 1998.
[17]. Toderas M., Mecanica rocilor, pământurilor şi construcţii subterane, Editura Universitas, Petroşani, ISBN 978-973-741-381-9, 1167 p., vol. I, ISBN 978-973-741-382-6, vol. II, ISBN 978-973-741-383-3, 2014.
[18]. Toderas M., Cercetări şi rezultate în stabilitatea lucrărilor miniere subterane, Editura Universitas, Petroşani, ISBN 978-973-741-486-1, 343 pages, 2016.
[19]. Toderaş M., Danciu C., Analysis Possibilities of Rocks Breakage by Means of Proportional Hazard Regression, 7th International Multidisciplinary Symposium „Sustainable Development through Quality and Innovation in Engineering and Research” SIMPRO 2016, Universitatea din Petroşani, p. 299-302. ISSN–L 1842-4449; ISSN 2344-4754, 2016.
[20]. Ying Z., Wei L. J., The Kaplan-Meier Estimate for Dependent Failure Time Observations, Journal of Multivariate Analysis, vol. 50, p. 17-29, 1994.