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Influence of nonlinearity and double elasticity on flexure of rock beams-I. Technical theory

Exadaktylos Georgios, Vardoulákīs, Iōánnīs, Kourkoulis, Stavros K

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Περίληψη

As a rule, solids display nonlinearity during loading in the relation between strains and stresses. Deviations from Hooke’s linear constitutive law were also registered in the range of initial, small loads both in uniaxial compression and tension of crystalline rocks. Nonlinearity of strain in rocks is manifested primarily in the stress dependency of tangent or secant elasticity modulus and Poisson’s ratio and is caused by closure, initiation, propagation and linkup of pre-existing and new microcracks, frictional sliding along cracks, growth of dislocations, etc. Many experimenters and standardization procedures assume that the dependence of the strain on the applied stress is linear and for practical calculations only two elasticity constants are used: the tangent or secant elasticity modulus at 50% of the failure load in compression and Poisson’s ratio at the same stress level. Apart from nonlinearity many rock types and concretes have quite different stress–strain relations in tension and compression. Yet direct tensile testing is seldom performed because of its many inherent difficulties. Such unrecognized double elasticity and nonlinearity of rocks can invalidate a stress analysis, and in addition, produce a meaningless overestimate (or underestimate) of tensile strength based upon the modulus of rupture derived from a bending test. In Part I of the present study, it is shown that both double elasticity and nonlinearity have a profound effect on flexural strength of rocks as predicted by application of fundamental continuum damage mechanics relations and an appropriate technical theory. The proposed theory is validated in Part II of this work, in which an appropriate back-analysis procedure is suggested for the characterization of the mechanical properties of Dionysos marble in the uniaxial tension and compression regime from properly designed three-point bending tests.

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