Effect of strength theory in elastic-plastic analysis of a circular tunnel

A reasonable strength criterion is very critical in elastic-plastic analysis of rock tunnel. Under the plane strain condition, a unified linear equation is first established inductively for eight commonly used strength criteria in geotechnical engineering. Then, with considerations of dilatancy and different elastic strains in the plastic zone, new solutions for stress and displacement of elastic-perfectly plastic rock are deduced. Furthermore, the feasibility analysis of the obtained solutions is carried out. Finally, both the effect of strength theory and parametric studies about the plastic displacement of tunnel are investigated. It is found that the unified linear equation is concise and flexible, which is convenient to discuss the effect of strength theory. The new solutions of elastic-perfectly plastic rock can be degraded into many existing solutions and have broad applicability. The effect of strength theory in elastic-plastic analysis of a circular rock tunnel is remarkable, therefore the generalized Matsuoka-Nakai criterion, the unified strength theory with parameter b=1/2, the Mogi-Coulomb criterion and the generalized Lade-Duncan criterion are recommended to be adopted. The application of the unified strength theory with parameter b=1 and the circumscribed Drucker-Prager criterion should be adopted cautiously. The inscribed Drucker-Prager criterion and the Mohr-Coulomb criterion are not encouraged. The dilatancy and the elastic strains in the plastic zone affect the plastic displacement of tunnel significantly, and the influencing extent of these two factors obviously varies with different strength criteria. The effects of the dilatancy, elastic strains in the plastic zone and strength theory should be comprehensively considered.