Journal of Engineering and Applied Sciences

Year: 2018
Volume: 13
Issue: 12 SI
Page No. 9431 - 9437

Fuzzy Logic Application to Coaxial and Non-Coaxial Components of Shear Strength of Soils

Authors : J. Rajaraman, K. Thiruvenkatasamy and S. Narasimha Rao

Abstract: Fuzziness is explored as an alternative to randomness for describing uncertainty. The new sets as points geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hyper cube and a non-fuzzy set with a vertex of the cube. In fuzzy logic a crisp set is a set in which all members match the class concept and the class boundaries are sharp. The degree to which an individual observation z is a member of the set is expressed by the membership function F which can take the value of 0 or 1 for Boolean sets. In fuzzy logic the membership function is a number in the range of 0.1 with 0 representing non-membership of the set and 1 representing full membership of the set. In fuzzy sets, the grade of membership is reflected in terms of a scale that can fluctuate continuously between 0 and 1. Normally, we can visualize the membership function by having x axis with the element of the fuzzy set and y axis with the value of the membership function. There are better ways of visualization. AKosko cube@ is the starting point. Kosko uses the term@ fit@ values to designate the value of the membership function. This is to contrast the term Abit@ which is used for binary values the f stands for Afuzzy@. To achieve better results the fuzzy power set F(2x) is examined. Thus, the 2x is the set of all sub-sets of x and x is our universe of discourse. The set of all sub-sets equals the unit hyper cube In = [0.1]n. A two dimensional version of Kosko cube is considered. In Geology/sediments/soil samples usually consists of clay and sand in ideal conditions. If p is percentage of clay then (1-p) is % of sand. Clay properties relate to pure shear or cohesion or coaxial shear component of the sample. Similarly the sand % represents simple shear or friction or non-coaxial shear component. Fuzzy logic suits this problem when % are expressed in the range 0, 0.1, 0.2, etc., up to 1.0. The membership functions in the combination of coaxial and non-coaxial shear component is represented in kosko cube. Taking Skempton's experimental data (clay+sand) points distributed in quadrants 1-4 inside the cube as points in are interpreted through simple geological processes.

How to cite this article:

J. Rajaraman, K. Thiruvenkatasamy and S. Narasimha Rao, 2018. Fuzzy Logic Application to Coaxial and Non-Coaxial Components of Shear Strength of Soils. Journal of Engineering and Applied Sciences, 13: 9431-9437.

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