Unified elasto-plastic solution for deep-buried circular tunnels considering the swelling characteristics of surrounding rock

SHEN Yingnan; XU Yongtao

doi:10.11860/j.issn.1673-0291.20230089

Abstract：Addressing the challenge of quantifying variations in stress and displacement fields induced by surrounding rock swelling due to water absorption in tunnels and underground engineering, this study develops a unified elastic-plastic solution for deep-buried circular tunnels. The solution considers the intermediate principal stress effect and swelling characteristics of the surrounding rock, employing elastic-plastic theory and humidity stress field theory. Firstly, stress and displacement solutions under elastic conditions of the surrounding rock are derived by integrating equilibrium and constitutive equa-tions considering humidity changes. Secondly, a method for determining the elastic-plastic state of sur-rounding rock is proposed, and an analytical solution under plastic conditions is then obtained based on the unified strength theory and non-correlated flow rule. Finally, the accuracy of the proposed unified solution is verified by the example comparison and analysis. Further, the study investigates the influ-ence of intermediate principal stress, humidity swelling coefficient, and water content changes on sur-rounding rock stress fields and plastic zone radius. Results indicate that comparative analysis with lit-erature demonstrates a negligible 0.136％ deviation in the plastic zone radius, validating the rationale of the proposed unified solution. Incorporating swelling characteristics increases the plastic zone radius and hoop stress at the elastic-plastic interface by 1.06 times under equivalent support resistance condi-tions. Increasing the unified strength theoretical parameter from 0.0 to 1.0 results in a 6.6％ increase in hoop stress, a 13.9％ decrease in plastic zone radius, and a 16.0％ reduction in tunnel wall displace-ment. Moreover, varying the humidity swelling coefficient from 0.0 to 0.1 leads to 17.98％ and 27.4％ increases in hoop stress and plastic zone radius, respectively. Similarly, increasing the maximum wa-ter content from 0.0 to 0.06 results in a 16.9％ increase in hoop stress, a 23.1％ expansion in plastic zone radius, and a 100％ increase in tunnel wall displacement. These findings provide theoretical in-sights for the design of swelling rock tunnel structures.