On the Stochastic Approach to the Three-dimensional Problems of Strata Mechanics

• Autorzy: Szczepiński W.
• Języki publikacji: EN

Abstrakty

EN

A numerical procedure for determining three-dimensional terrain subsidence caused by underground cavities is proposed. The Litwiniszyn's idea, according to which the movement of cavities upwards is treated as a random process, constitutes the basis of the procedure. The proposed algorithm is based on the assumption of an imagined three-dimensional device analogous to the so called Galton's two-dimensional board. Small balls falling down in the device are randomly directed into particular cells below with the probability equal to 1/4. Complex three-dimensional problems are solved.

Słowa kluczowe

EN

terrain subsidence; random walk of cavities

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2003
• Tom: Vol. 51, nr 4
• Strony: 336--345
• Opis fizyczny: 13 rys., bibliogr. 8 poz.

Twórcy

autor

Szczepiński W.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, PL-00-049 Warsaw (Instytut Podstawowych Problemów Techniki PAN)

Bibliografia

• [1] J. Litwiniszyn, Application of the equation of stochastic processes to mechanics of loose bodies, Arch. Mech. Stos., 8 (1956) 393-411.
• [2] J. Litwiniszyn, On application of the random walk argument to the mechanics of granular media, Proc. IUTAM Symp. on Rheology and Soil mechanics, Grenoble (April 1964) Springer Verlag, 1966.
• [3] J. Litwiniszyn, Stochastic methods in mechanics of granular bodies, CISM Courses and Lectures, No. 93, Springer Verlag, Udine 1974.
• [4] V. V. Sokolovsky, Statics of granular media, Pergamon Press, New York 1965.
• [5] W. Szczepiński, Limit states and kinematics of granular materials (in Polish), PWN, 1974.
• [6] W. Szczepiński, Z. Kotulski, Error analysis - with applications in engineering, Lastran Co., Rochester, N.Y. 2000.
• [7] W. Szczepiński, On the movement of granular materials in bins, Part II -Three-dimensional problems, Engng Trans., to be published.
• [8] A. Z. Smolarski, On some applications of linear mathematical models of the strata mechanics, Prace Komisji Nauk Technicznych PAN w Krakowie, Seria Mechanika (3) 1967.