Abstract
The collapse mechanism of a circular unlined tunnel roof subjected to the pore water pressure under plane strain conditions is investigated in this article. First, the model of calculating the function expression of the detaching surface for the collapsing block is formed in the framework of the upper bound theorem of limit analysis and the extremum principle. The analytical solution of the pore water pressure around the tunnel in a two-dimensional steady seepage field is employed in the equations of the model. Then, the numerical approach based on the Runge–Kutta algorithm and traversal search method is proposed to solve the complex equations. The obtained expression of the detaching surface for the collapsing block provides the shape of the collapsing block and a theoretical basis for designing the support force for tunnels. The proposed limit analysis method and numerical approach are verified by comparing with existing theoretical solutions and the numerical simulation result, and they are suitable for deep, shallow tunnels and layered strata. Moreover, the effects of different parameters on the collapse mechanism are investigated, and qualitative results are provided.
Highlights
Academic Editor: Hui Yao e collapse mechanism of a circular unlined tunnel roof subjected to the pore water pressure under plane strain conditions is investigated in this article
En, the numerical approach based on the Runge–Kutta algorithm and traversal search method is proposed to solve the complex equations. e obtained expression of the detaching surface for the collapsing block provides the shape of the collapsing block and a theoretical basis for designing the support force for tunnels. e proposed limit analysis method and numerical approach are verified by comparing with existing theoretical solutions and the numerical simulation result, and they are suitable for deep, shallow tunnels and layered strata
Different from the existing upper bound analysis, Fraldi and Guarracino obtained the two-dimensional shape of the collapsing block for tunnel roofs directly by combining the upper bound theorem and the extremum principle, and the collapse load of tunnels is further obtained by integrating the area between the detaching surface of the collapsing block and the tunnel boundary, which provides the theoretical basis for designing the support force for tunnels [20]. us, the predefined collapse mechanism is Advances in Civil Engineering not required in the calculation process for this method, and any shape of the detaching surface in the final result is possible [21]
Summary
Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach. E study of Fraldi and Guarracino [20] is extended in this article, the upper bound theorem and extremum principle are combined to form the model of calculating the function expression of the detaching surface for the collapsing block, and the analytical solution of the pore water pressure distribution around the tunnel in twodimensional steady seepage field is employed in the equations of the model. To calculate the detaching surface of the collapsing block of the tunnel subjected to pore water pressure, the first condition is the work equation derived from the upper bound theorem in limit analysis In this case, an unlined tunnel with a circular crosssection in the steady seepage field is analyzed in the limit analysis. As stated in the upper bound theorem, for any assumed collapse mechanism, if the external rate of work exceeds the internal rate of dissipation, it means the rock masses are
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
