Crushing failure in hollow cylinders made of quasi-brittle materials

Several engineering problems, such as the collapse of borehole in rocks, can be investigated by means of multiaxial compression tests. However, the brittle failure that occurs during the excavation of circular tunnels in rock masses cannot be completely reproduced by laboratory tests on hollow cylinders having a diameter of few centimetres. Thus, referring to these specimens subjected to hydrostatic pressure, and made of concrete or other quasi-brittle materials, a numerical model capable of predicting their structural response at different scales is here presented. Due to the absence of confinement, strain localization and crushing failure appear around the inner surface of the cylinders, which behave nonlinearly even in the case of low pressures. Similarly to cement-based beams in bending, this phenomenon can be modelled by adopting a suitable stress–inelastic displacement relationship for the post-peak response under compression. With regard to hollow cylinders subjected to multiaxial compression, it is possible to predict the size effect on fracture strength, which needs to be taken into account when laboratory tests are used to analyze the borehole failures. The effectiveness of the proposed approach is checked by comparing the computed results with the test data measured by Elkadi and van Mier [Elkadi AS, van Mier JGM. Experimental investigation of size effect in concrete fracture under multiaxial compression. Int J Fract 2006;140(1–4):55–71] on concrete specimens.