Analysis of additional stress for a curved shield tunnel

Abstract

This paper focuses on analytical solutions of additional stresses for a curved shield tunnel. General equations of additional stress caused by construction loadings were deduced by rewritten Mindlin solutions, and additional thrust and friction force were considered. In addition, theoretical formulae of additional stress caused by soil loss were deduced based on the three-dimensional image theory, and the actual processes of synchronous grouting and over-excavation were considered. Then, by using a curved tunnel in Zhuhai City, China as a case study, the distribution laws of additional stress along the directions of advancement and circumference were investigated. Under the coaction of construction loadings and soil loss, it was found that the distributions of σx and σy along the advancement direction for curved tunnels are similar to those for straight-line tunnels. However, the soil around a curved tunnel is more likely to yield because the difference between the normal stresses in two directions is greater than that for soil around a straight-line tunnel. Additional stresses caused by soil loss along the circumferential direction for a curved tunnel were found to no longer have the characteristics of strictly axial symmetry. The values of compressive stress σx and σy at the outer side of the curved tunnel were found to be greater and smaller than those at the inner side, respectively. As the curvature radius decreases, the maximum tensile stresses σx and σy for curved tunnels were found to decrease and increase, respectively. Furthermore, an insufficient quantity of injection grouting will trigger detrimental effects to nearby structures during the approaching excavation.