Institutional Repository
Technical University of Crete
EN  |  EL



My Space

Influence of nonlinearity and double elasticity on flexure of rock beams-II. Characterization of Dionysos marble

Exadaktylos Georgios, Vardoulákīs, Iōánnīs, Kourkoulis, Stavros K

Full record

Year 2001
Type of Item Peer-Reviewed Journal Publication
Bibliographic Citation G. E. Exadaktylosa, I. Vardoulakisb and S. K. Kourkoulis, "Influence of nonlinearity and double elasticity on flexure of rock beams - II. Characterization of Dionysos marble," Int. J. Solids Struct., vol. 38, no. 22-23, pp. 4119-4145, May-Jun. 2001. doi:10.1016/S0020-7683(00)00252-3
Appears in Collections


A technical bending theory of beams accounting for nonlinearity due to damage and bimodularity of brittle rocks was proposed in Part I. In order to check the validity of the above theory, a series of three-point bending (3PB) tests has been carried out using Dionysos marble beams that have been sampled from the same extracted block. Although the modeling of the 3PB test is considerably more complicated than that of the four-point bending test, the experimental procedure in the former test is simpler than in the later test and most importantly, the location of the fracture is better controlled in the 3PB test. Herein, it is demonstrated that the test results have very good repeatability and they support the above technical theory. The bending tests also indicate that Dionysos marble is characterized by different elastic modulus in compression (Ec) and in tension (Et) at small loads, such that the relation m=Ec/Et≅0.8 holds true. This relationship of elastic moduli for this type of marble is also supported independently by uniaxial compression and direct tension tests on test specimens cored from the same marble block. A plausible physical explanation for this type of marble anisotropy has yet to be made. This observed difference cannot be explained by considering the rock simply as a material with cracks. It may be attributed to pure micromechanical reasons such as the complex microstructure of this type of rock, characterized by a complex previous loading history (metamorphism). Until such an explanation is available, the apparent behavior can be used in analyzing the stress–strain behavior of rocks. Further, the 3PB experiments indicate that fracture of marble starts always at the bottom fiber of the middle cross-section of the beam and the failure extension strain is the same with that occurring in the direct tension test. This last result is due to the fact that the central section of marble beam is almost under extensional strain, which in turn is caused by the combination of the concentrated load and Poisson’s effects. The damage parameter that enters the direct tension stress–strain law was obtained independently from longitudinal strain measurements at the outermost compression and extension fibers, as well as, from bending curvature and deflection measurements. This value of the damage factor is in accordance with the damage measured from the direct tension tests. It is also demonstrated that a linear Timoshenko-type theory containing an intrinsic length scale is able to approximate the nonlinear deflection behavior of Dionysos marble beams. Finally, based on a suggestion by Ludwig Prandtl, the stress–strain relationships in unconfined compression and direct tension, as well as Poisson’s ratio, of Dionysos marble were derived from bending tests.