Empirical relationships for Mohr-Coulomb parameters in concrete & mortar: application in mix design

The Mohr-Coulomb theory is widely accepted to describe the failure behaviour of brittle materials such as concrete. However, limited relationships exist between the failure envelope parameters ( ) and the characteristic compressive strength i.e., the grade of concrete. This paper investigates the variation of c − ɸ parameters for both concrete and mortar cubes in relation to the uniaxial unconfined compressive strength, utilizing extensive testing across a range of M30 to M90 grades. Conventional tests for determining the average values of cohesion ( c ) and internal angle of friction ( ɸ ) have limitations and require specific setups or special methods. Alternatively, recent developments made in our other research progress which is reported elsewhere suggest that a single uniaxial unconfined compression test-based method can be employed to ascertain the failure envelope of the Mohr-Coulomb theory. Such a procedure is free from specimen-to-specimen variability while constructing the sample space for parameter estimation. In this paper, the same test procedure is utilized, and the following empirical relationships are developed: a) the relationship between compressive strength and cohesion of concrete and mortar cubes; b) the relationship between compressive strength and cohesive strength (the strength at which cohesion is lost) of concrete and mortar cubes; and c) the relationship between the cohesive strength of concrete and cohesive strength of its mortar phase. The results indicate that the internal angle of friction does not show any specific trend against the compressive strength but remains bounded between 10~30°. Hence, a modal estimate may be used for all practical purposes. However, the other relationships exhibit a positive linear correlation. Overall, this paper addresses the existing gap in c ɸ relationships for concrete and mortar and explore their potential application to the mix design of concrete. A possible flowchart for the c ɸ based mix design framework is also included. − − c −ɸ.