For underground excavations in sand and blocky rock masses with low cohesive strength

the loosening pressure above a shallow tunnel varies with the developing ground deformation due to evolutions of ground arching. However

the normal ground arching method fails in determining the existence of the ground arch

resulting in critical deformation when the ground arch reaches the ground surface and the variation of the loosening pressure as a function of the developed arching effect. This paper presents a modified method by introducing a continuously developed ground arching mechanism. Rotations of the principal stress and the correlation between orientations of the principal stress and the shear surface are used to determine the stress state within the arch. Previous methods determining the rotation of the shear surface as a function of the ground deformation was also modified to better reflect the test results. On the basis of the above three steps

a modified method is proposed. Comparisons of the results among the previous methods

the proposed method and the experiments examined the validity of the proposed method. Parametric analysis studied the initial loosening pressure

the evolution of the loosening pressure and the critical deformation. A case study by the proposed method indicates its practical use. Some important conclusions are: (1) the initial loosening pressure comes from the weight of the ground within the arch. The area of the initial-loosening zone is independent on the cover-depth ratios. Instead

the area is controlled by the friction angle of the ground. Grounds with low friction angles tend to have large initial-loosening zone with a high initial loosening pressure; (2) the loosening pressure increases with the developing ground deformation

and a lower raising rate is found for a deeper

smaller tunnel ( ); (3) the critical deformation increases with the raising cover-depth ratio and the increasing friction angle

indicating that a stronger arching effect is expected in such grounds; (4) for Xiabeishan tunnel

the arching effect exists

the initial loosening pressure is 0.37

the critical value is 0.41

the ultimate is 0.54

and the critical relative deformation is 5.7%.