An analytical solution for the arching effect induced by ground loss of tunneling in sand

Because the earth pressure above tunnel crown was assumed uniform and the effect of particle flow of sand and ground loss were not considered, Terzaghi method generally produces discrepancies from model tests and field observations. To overcome this deficiency, the flow of sand particles above a tunnel was investigated firstly to define the shape and size of loosening zone by following the gravity flow principles. Then, by assuming non-uniform distribution of earth pressure and incorporating the factor of ground loss, a modified Terzaghi method has been developed. It can not only determine the loosening pressure on tunnel, but also the shape and size of loosening zone corresponding to ground loss and properties of sand particles. The research results reveal that the shape of loosening zone is ellipsoidal or a part of ellipsoid affected by the eccentricity and loosening factor of sand. The height of loosening zone increases with ground loss of tunneling, resulting in the propagation of loosening zone from deep in ground to ground surface. For most shield tunnels, with ground loss ratio less than 4.0%, the loosening zone is formed only at the upper tip of the ellipse and its shape resembles to a curved arch. According to the proposed method, the height of the loosening zone for shield tunnels in sandy ground is approximately 0.1D-0.7D (D, tunnel diameter) and the earth pressure is about 35-90% of the total overburden earth pressure for typical ground loss within the range of 0.5-4.0%. Via detailed comparison with model tests and Terzaghi method, the proposed method is proved to be closer to the model tests than the Terzaghi method. For the sake of convenience in application, simplified design curves for the height of loosening zone and earth pressure were plotted against ground loss, which is of great importance for engineers to set reasonable goal of ground loss in tunneling practice.