Lin Yu

The calculation of conformal mapping for irregular domains is a crucial step in deriving analytical and semi-analytical solutions for irregularly shaped tunnels in rock masses using complex theory. The optimization methods, iteration methods, and the extended Melentiev’s method have been developed and adopted to calculate the conformal mapping function in tunnel engineering. According to the strict definition and theorems of conformal mapping, it is proven that these three methods only map boundaries and do not guarantee the mapping’s conformal properties due to inherent limitations. Notably, there are other challenges in applying conformal mapping to tunnel engineering. To tackle these issues, a practical procedure is proposed for the conformal mapping of common tunnels in rock masses. The procedure is based on the extended SC transformation formulas and corresponding numerical methods. The discretization codes for polygonal, multi-arc, smooth curve, and mixed boundaries are programmed and embedded into the procedure, catering to both simply and multiply connected domains. Six cases of conformal mapping for typical tunnel cross sections, including rectangular tunnels, multi-arc tunnels, horseshoe-shaped tunnels, and symmetric and asymmetric multiple tunnels at depth, are performed and illustrated. Furthermore, this article also illustrates the use of the conformal mapping method for shallow tunnels, which aligns with the symmetry principle of conformal mapping. Finally, the discussion highlights the use of an explicit power function as an approximation method for symmetric tunnels, outlining its key points.

Huanghuai area is rich in coal resources, but due to the increasingly complex geological environment faced by coal mining, the complexity of structural stress is one of the main problems. In order to find out the distribution law of deep in situ stress in the Huanghuai area, the in situ stress measurement data of 81 effective measuring points in 24 mines with depths ranging from −100 m to −1200 m are analyzed in the present study base on the in situ stress measurement data. Furthermore, numerical simulation and field observation are used to analyze the deformation and failure characteristics of the surrounding rock. The research results show that the deep mining area of Huanghuai exhibited a high stress level, and the vertical and horizontal principal stress increases with increasing depth. The ratio of the lateral pressure coefficient ranges from 0.90 to 2.70, and the in situ stress field presented a trend of transition to the quasihydrostatic pressure field type as the depth extended, in which 80.23% of the measuring points are distributed between 1.20 and 2.10, belonging to the typical tectonic stress field type in which tectonic stress is absolutely dominant. The observation results of the surrounding rock and numerical simulation reveal that when the layout axis of the roadway is approximately perpendicular to the direction of the maximum horizontal principal stress, a high stress concentration area is present on the roof and floor of the roadway, the deformation increases sharply, and the support pressure of the roof and floor increases.

This paper presents an analytical method to predict the response of a strip foundation building to shallow tunneling based on the two-stage method. The existing building is simplified as a Euler–Bernoulli beam resting on the Pasternak model. The tunneling process and different relative positions between the tunnel and the existing building can be considered in the proposed method. The accuracy of the proposed method is verified through comparisons with results from the finite element and finite difference methods. The results indicate that the differential settlement of the building reaches a maximum and the rotation angles are symmetric with respect to the building centerline when the tunnel face arrives at the middle of the building. The maximum bending moments occur at the middle of the building, while the maximum shear forces occur at about one-fifth and four-fifths of the building length when the tunnel face is located at the two ends of the building. According to the parametric analysis, the alignment angle, elastic modulus and Poisson’s ratio of the soil, bending stiffness, and gap parameter greatly affect the building response.

Due to the lack of historical subsidence data on goaf sites alongside expressways, it is difficult to comprehensively evaluate the stability of goaf sites and accurately identify potential risk points. An investigation to study the stability of goaf sites in the Huaibei section of the Xu Huaifu Expressway is conducted through SBAS-InSAR technology and field investigation. Initially, the stability of the goaf site around the route is anticipated through field investigation. Afterwards, based on the extraction of Sentinel-1 satellite images, subsidence data of the goaf sites from 2017 to 2021 were extracted. Finally, the stability of risk points is analysed. Results demonstrate that although mining in the area stopped more than five years ago, the goaf site has continued to slowly sink. According to four years of goaf site subsidence data extracted by SBAS-InSAR technology, two subsidence risk areas, namely, Y1-05 and Y1-09, were discovered, and the subsidence areas displayed an obvious inverted “convex” shape. Of these two areas, Y1-05 is a potential risk point that was not found during the field investigation. The subsidence basin in the Y1-05 area has developed gradually, and the residual subsidence is expected to be close to 475 millimetres within the next 15 years. Although it can be considered a stable area, the subsidence value is quite large and may pose risks to route safety. Therefore, a flexible reinforced mesh can be adopted for the route. The subsidence basin of Y1-09 is the largest, but the expected residual subsidence is only 50 millimetres and will have insignificant influence on the route. Engineering practice shows that SBAS-InSAR technology can effectively analyse the surface deformation of goaf sites and has important practical significance in optimising the selection of special geological routes in expressways.