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The small strain assumption routinely made in tunnel analyses remains sufficient from an engineering point of view as long as wall convergences do not exceed 10. Although convergences are indeed less than 10 in the great majority of tunnelling projects very large deformations may take place when crossing weak rocks under a high overburden (so called squeezing conditions). In such cases where the undeformed and the deformed tunnel geometry differ significantly small strain theory overestimates rock deformations considerably. Motivated by the practical importance of squeezing in tunnelling the inability of small strain theory to describe large deformation problems correctly and the lack of relevant rigorous studies in the area of finite strain elasto plasticity this doctoral thesis presents: (i) an exact finite strain closed form solution for the ground response curve in dry or completely drained grounds obeying the linear Mohr Coulomb yield criterion; (ii) rigorous semi analytical finite strain solutions for the ground response curve in dry or completely drained grounds obeying arbitrary non linear Mohr type failure criteria; (iii) exact finite strain analytical solutions for the ground response curve under undrained conditions using the Mohr Coulomb model and the modified Cam clay model; (iv) a very simple theoretically well founded sufficiently accurate and widely applicable relationship e xpressing the convergences obtained from finite strain elasto plastic analyses of tunnels with large deformations as a function solely of the corresponding convergences obtained from small strain analyses; (v) a finite strain theoretical analysis of the ground response round highly deformed circular tunnel cross sections that are subjected to re profiling in order to re establish the desired clearance (using the Mohr Coulomb model); and (vi) a finite strain numerical study of the rock support interaction in tunnelling through squeezing ground. In order to obtain a better insight into the effects of geometric non linearity in the analysis of geotechnical problems the cavity expansion problem was also analysed leading to: (vii) a rigorous semi analytical solution for the problem of undrained cylindrical cavity expansion in critical state soils; and (viii) a relationship between small and finite strain solutions for general cavity expansion problems in elasto plastic soils. vi Therefore the contribution f the present doctoral thesis consists in the rigorous theoretical analysis of some rock and soil mechanics problems in the framework of finite strain elasto plasticity using rate type constitutive equations and in providing simple and practical tools for the nalysis and design of tunnels crossing heavily squeezing ground. |
