Experimental poromechanics of trabecular bone strength: role of Terzaghi's effective stress and of tissue level stress fluctuations

Abstract

In the 1920s and 1930s, Terzaghi and coworkers realized that the failure of various porous geomaterials under internal pore pressure is given through evaluating the failure function for the same materials at zero pressure, with 'total stress plus pore pressure' instead of 'total stress alone' as argument. As to check, probably for the first time, the relevance of this ('Terzaghi's') failure criterion for trabecular bone, a series of poromechanical and ultrasonic tests was conducted on bovine and human trabecular bone samples. Evaluation of respective experimental results within the theoretical framework of microporomechanics showed that (i) Terzaghi's effective stress indeed governs trabecular bone failure, (ii) deviatoric stress states at the level of the solid bone matrix (also called tissue level) are primary candidates for initiating bone failure, and (iii) the high heterogeneity of these deviatoric tissue stresses, which increases with increasing intertrabecular porosity, governs the overall failure of trabecular bone. Result (i) lets us use the widely documented experimental results for strength values of bone samples without pore pressure, as to predict failure of the same bone samples under internal pore pressure. Result (ii) suggests a favorable mode for strength modeling of solid bone matrix. Finally, result (iii) underlines the suitability of microfinite element simulations for trabecular bone microstructures.