The butterfly plastic zone theory based on Mohr Coulomb criterion has been widely used in coal mine production. In order to verify the universality of the theory, it is necessary to compare the distribution of plastic zone under different strength criteria. Based on the elastic-plastic mechanics, the principal stress distribution function around the circular tunnel is deduced in the paper, and the boundary and radius of the plastic zone under different strength criteria are calculated. The results show that the change laws of the plastic zone around the circular tunnel under different strength criteria has the following commonness: firstly, with the increase of the lateral pressure coefficient, the shape of the plastic zone presents the change laws of “circle ellipse butterfly”; Secondly, with the increase of the lateral pressure coefficient, the radius of the plastic zone is exponential distribution, while the characteristic value is different when the radius of the plastic zone is infinite. At same time, it shows that the butterfly plastic zone has a low sensitivity dependence on the strength criterion, no matter which strength criterion is adopted, and the butterfly plastic zone will inevitably appear in the surrounding rock mass of circular tunnel in the high deviator stress environment; The plastic zone with butterfly shape is highly sensitive to the stress change, and the small stress change may promote the expansion of the plastic zone. This result is significant for us to understand and prevent rock engineering disasters and accidents.

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In order to study the mechanical properties of defect-free thin walled elbows (TWE), and evaluate impacts of the intermediate principal stress effect, tension/compression ratio, and strain-hardening of materials into logical consideration, this research, in the framework of finite deformation theory, derived the computational formula of burst pressure for defect-free TWE according to unified strength theory (UST). In addition, influences of various factors on burst pressure were analyzed, which include strength disparity (SD) effect of materials, intermediate principal stress, curvature influence coefficient, strain-hardening exponent, yield to tensile (Y/T) and thickness/radius ratio. The results show that the greater the tension/compression ratio is, the higher the burst pressure is. The influence of the SD effect of materials is more obvious with the increase of elbow curvature and intermediate principal stress. The intermediate principal stress effect can bring the self-bearing capacities and strength potential of materials into a full play, which can achieve certain economic benefits for projects. Moreover, the burst pressure of defect-free TWE increases with the growth of yield ratio and thickness/radius ratio, while decreases with the rise of curvature influence coefficient and strain-hardening exponent. It is also concluded that the Tresca-based and Mohr–Coulomb-based solutions of TWE are the lower bounds of the burst pressure, the twin shear stress (TSS)-based solution is the upper bound of the burst pressure, and the solutions based on the other yield criteria are between the above two. The unified solution in this paper is suitable for all kinds of isotropous materials which have the SD effect and intermediate principal stress effect. As the deduced formula has unified various burst pressure expressions proposed on the basis of different yield criteria for elbows of any curvature (including straight pipelines), and has established the quantitative relationships among them, its applicability is broader. Therefore, the unified solution is of great significance in security design and integrity assessment of defect-free TWE.