Theoretical model of the equivalent elastic modulus of a cobblestone-soil matrix for TBM tunneling

Cobblestone-soil mixed ground is a composite comprising cobblestones surrounded by soil. It is typical mixed-face ground encountered during tunnel boring machine (TBM) tunneling, and it may result in cutter wear, jamming of the roller cutterhead, poor TBM performance and cost overruns. The present paper investigates the deformation problem of cobblestone-soil mixed-face ground during TBM excavation. The ground under study is composed of two components (soil matrix and cobblestones) usually firmly bonded together at the interface, and can be regarded as a continuum. Previous studies have proposed many theoretical models for a composite material with two components. Representative models include the parallel model, series model, and effective medium theory model. Nonetheless, these models are limited by their assumptions and preconditions. In the present study, under an assumption of uniform strain, analytical solutions were derived for the equivalent elastic modulus while the cobblestone is assumed to be perfectly spherical or ellipsoidal. Triaxial compression tests were carried out to validate the analytical solutions. The equivalent elastic modulus derived from the triaxial experiments and theoretical models matched rather closely. The analytical solutions are helpful in clarifying the deformation of such ground and enhancing TBM performance.