Three-Dimensional Analysis Model of Surrounding Rock Deformation and Support Stiffness for Tunnel Construction

In the field of analyzing 3D tunnel construction mechanics, the current mechanical models have many difficulties, including low computing accuracy, high computing resource requirements, and low computing efficiency, which can't meet the practical requirements; thus, a new analysis model of a deep-buried circular tunnel was proposed with considering the equivalent force acting on the wall and the face to simulate the excavation effect. To evaluate two cases of a tunnel face near the entrance and far from it, the integral formulae of the deformation field of the surrounding rock were derived based on the Mindlin and Kelvin solutions, respectively. The paper treated the excavation medium as support mass and developed the formulae of surrounding rock deformation through introducing the support force into the analysis model. According to the above formulae, the deformation field of surrounding rock and the quantitative values of its demand for the support structures might be calculated. The results show that: under the two cases, the deformation distribution of the surrounding rock is basically consistent; while the face is near to the entrance, the maximum calculation and numerical results of the axial displacement of the lengthwise section are 6.1 mm and 5.5 mm, and the radial displacements at the face are 2.4 mm and 2.6 mm, and the errors are 9.8% and 8.3%, respectively. When the face is far from the entrance, the maximum calculation and numerical results of the axial displacement of the lengthwise section are 6.0 mm and 5.7 mm, respectively and the error is 5.0%; for an arbitrary set of calculation parameters of surrounding rock and supporting structures, the results of advanced displacement at the face are 3.6 mm and 3.0 mm and the results of final displacement are 9.1 mm and 8.5 mm, and the errors are 16.7% and 6.6%, respectively, showing that the calculation results of longitudinal deformation are not consistent with the numerical results; and for the penstock 2# deformation of Dagangshan Hydropower Station, its calculation and mortoring results of advanced displacement are 0.4 mm and 0.4 mm and their results of final displacement are 1.0 mm and 1.1 mm, and their errors are 0 and 10%, respectively. Therefore, the stiffness requirement of the surrounding rock could be determined quantitatively by combining the deformation control standard and the proposed model; the finding can guide the design parameters of the supporting structures.