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Least-square fitting of the linear Mohr envelope

Lisle, Richard John and Strom, C. S. 1982. Least-square fitting of the linear Mohr envelope. Quarterly Journal of Engineering Geology 15 (1) , pp. 55-56. 10.1144/GSL.QJEG.1982.015.01.07

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Introduction Mohr's hypothesis proposes that when shear failure along a plane takes place, the normal stress and the shear stress acting on that plane have a characteristic functional relationship. This function relating and , it is proposed, depends on the material and can be represented on the plane by a line defining the critical values of and for shear failure. In practice this critical line is constructed tangen-tially to Mohr circles representing different combinations of principal stresses applied to specimens of a particular material and is therefore referred to as the Mohr envelope. For some materials a straight Mohr envelope with the equation = c + µ appears from the results of triaxial testing. Furthermore in the routine testing of some materials (e.g. soils) a straight line envelope is sometimes assumed a priori. In such tests small deviations of the Mohr circles from the envelope are attributed to errors and a best-fitting straight line is used to obtain the parameters (µ, c) necessary to characterize the properties of the material. We describe here a procedure for calculating a best-fitting straight Mohr envelope from data consisting of the applied principal stresses (i.e. from the Mohr circles). The concept of best-fit used The criterion used for selecting the envelope of best fit is illustrated in Fig. 1. By means of a least-squares fit we represent the Mohr envelope by a straight line = c + µ- subject to the condition that S

Item Type: Article
Date Type: Publication
Status: Published
Schools: Earth and Ocean Sciences
Subjects: Q Science > QE Geology
Publisher: Geological Society
ISSN: 1470-9236
Last Modified: 04 Jun 2017 02:11

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