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2. A transfer coefficient method for rock slope toppling.
- Author
-
Liu, C.H., Jaksa, M.B., and Meyers, A.G.
- Subjects
FORCING (Model theory) ,MODEL theory ,WEIGHTS & measures ,MATHEMATICS ,ARITHMETIC ,MANAGEMENT information systems ,ROCK slopes - Abstract
A common block toppling mode is adopted for analysing toppling stability of rock slopes. A transfer coefficient method is developed based on Goodman and Bray’s kinematic model, by introducing two parameters: the transfer coefficient and equivalent toppling weight, which, given the geometrical and geotechnical parameters of the slope, can be determined as functions of the relative position of the block to the slope crest. Accounting for the case that the block base is not normal to the dominant discontinuities, the arithmetic is extended. The method describes a concise relationship between the normal force of the blocks and their weight represented by their equivalent toppling weight. The analysis process is formulated and easily implemented. A spreadsheet procedure is presented and a typical case is illustrated. It is demonstrated that the transfer coefficient method provides a considerably straightforward means for analysing block toppling of rock slopes and is computationally very efficient. On a adopté un mode courant de basculement de bloc pour analyser la stabilité par basculement des pentes rocheuses. Une méthode de coefficient de transfert est développée sur la base du modèle cinématique de Goodman et Bray, en introduisant deux paramètres: le coefficient de transfert et le poids équivalent de basculement qui, étant donné les paramètres géométriques et géotechniques de la pente, peuvent être déterminés comme des fonctions de la position relative du bloc par rapport à la crête de la pente. Tenant compte du cas où la base du bloc n’est pas normale aux discontinuités dominantes, l’arithmétique est élargie. La méthode décrit une relation concise entre la force normale des blocs et leur poids représenté par leur poids équivalent de basculement. Le processus de l’analyse est formulé et facilement mis en application. Une procédure de chiffrier est présentée et un cas typique est illustré. On démontre que la méthode du coefficient de transfert fournit un moyen considérablement simple pour analyser le basculement de blocs des pentes rocheuses et est très efficace du point de vue calcul. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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3. On the Definition of Lens Distortion Reference Data with Odd-Power Polynomials
- Author
-
Hartmut Ziemann and Sabry F. El-Hakim
- Subjects
Degree (graph theory) ,Aerial survey ,Photography ,Reference data (financial markets) ,General Engineering ,General Earth and Planetary Sciences ,Arithmetic ,General Environmental Science ,Mathematics ,Power (physics) - Abstract
Odd-power polynomials were determined for all lens distortion reference data ever included in the various editions of the Canadian Specification for Aerial Survey Photography. The degree of polynomials as well as the number of valid digits of the polynomial coefficients were varied in an attempt to best fit the given data. For 15 of the 19 lens types included in the investigation, the maximum deviation between best-fitting polynomial and given data was smaller than or equal to the resolution with which the original data were given. The values for the other four lens types were 1.1, 1.4, 1.3 and 1.7 times that resolution; the last two values apply to lenses no longer in service in Canada. Appended to the paper is Appendix I of the latest edition of the Specification for Aerial Survey Photography listing the polynomials which define lens distortion reference data.
- Published
- 1983
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