| Popis: |
A new, elasto-plastic, analytical-numerical solution, considering the axial-symmetry condition, for a circular tunnel excavated in a strain-softening and Hoek–Brown rock mass is proposed. To examine the effect of initial stress variations, and also the boundary conditions at the ground surface, the formulations are derived for different directions around the tunnel. Furthermore, the effect of the weight of the plastic zone is taken into account in this regard. As the derived differential equations have no explicit analytical solutions for the plastic zone, the finite-difference method (FDM) is used in this study. On the other hand, analytical expressions are derived for the elastic zone. Several illustrative examples are given to demonstrate the performance of the proposed solution, and to examine the effect of various boundary conditions. It is concluded that the classic solutions, based on the hydrostatic far-field stress, and neglecting the effect of the boundary conditions at the ground surface, give applicable results for a wide range of practical problems. However, ignoring the weight of the plastic zone in the analyses can lead to large errors in the calculations. Članek predstavlja novo analitično-numerično rešitev za krožni tunel v deformacijsko popuščajoči in Hoek-Brownovi hribini, ob upoštevanju pogojev osne simetrije. Izpeljani so izrazi za določitev sprememb začetne napetosti in robnih pogojev površine tal v različnih smereh okrog tunela. Pri tem so upoštevani tudi vplivi teže v plastični coni. Ker izpeljane diferencialne enačbe ne predstavljajo eksplicitne analitične rešitve za plastično cono, se v študiji uporablja metoda končnih razlik (MKR). Izpeljani pa so analitični izrazi za elastično cono. Učinkovitost predlagane rešitve in učinek različnih robnih pogojev sta ponazorjena z več pojasnjevalnimi primeri. Ugotovljeno je, da dajejo klasične rešitve, ki temeljijo na oddaljeni hidrostatični talni napetosti in zanemarjajo vpliv robnih pogojev na površini tal, uporabne rezultate za veliko praktičnih problemov. Vendar pa lahko neupoštevanje teže v plastični coni v analizah privede do velikih napak v izračunih. |
