Aiming at the problems of the existing calculation methods for the support pressures of shallow tunnels in layered jointed rock strata, by using OAT (orthogonal array testing strategy) and DEM (distinct element method), 12 influencing factors including the thickness of the weathered overburden, and the states of the rock joints were considered. Then, the classification of the loosening zone was analysized. On this basis, by using the DEA (data envelopment analysis) theory, quantitative analysis on the influencing factors was conducted. By analyzing the influence of the key factors, a prediction formula of the boundary of the ringent trumpet-shaped loosening zone was established. According to principles of stress transformation, the formula of support pressures of the loosening zone which could considering the key factors were deduced. Finally, a practical case was introduced and studied to verify the proposed method.


In recent years, various urban subway tunnels are increasingly carried out through jointed rock strata in many cities. Rock masses are discontinuous mediums with fissures, fractures, joints, bedding planes, and faults. The frequency of joints, their orientation with respect to the engineering structures, and the roughness of the joint have a significant importance from the stability point of view. However, there is a lack of understanding about the influence of the joints on the stability of tunnels. Therefore, how to measure the degree of the joints' influence is a problem that needs to be solved.

For the calculation of the support pressures, until now, many research results were focused on soil ground (Bierbäumer 1913; Terzaghi, 1943; Peck, 1969; Sabatini et al., 1999). In terms of site tests and model indoor tests, by measuring strut loads and calculating earth pressure based on strut spacing, the results proposed by Peck (1969) and Tschebotarioff (1973) have been widely used in practice for designing excavation support systems under sand (drained) and clay (undrained) soil conditions. Note that, it is unclear whether these findings could be extended to rock strata. For numerical simulations, how to simulate the states of the rock joints is a key problem that needs to be solved.

Some studies including those by Yoo & Kim (2000) have been conducted for the earth pressures measured in multilayered ground including rock, but they did not consider the effects of rock and joint conditions on the earth pressure. Wang et al. (2014) have examined the influencing factors including the joint conditions of the loosening zone and deduced calculation formulae of support pressures of shallow tunnels in layered jointed rock strata by using upper bound limit analysis method. However, the long calculation procedure of the proposed method is more complicated compared with classical methods.

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