## 1 Introduction  
With the increasing demand for underground space in cities, the construction of rail transportation and comprehensive pipeline corridors is developing rapidly. The pipe jacking method has a low environmental impact and is usually used to construct underground passages with shallow buried depths and short lengths. Rectangular pipe jacking has the advantages of a shallower buried depth and higher space utilization than circular pipe jacking and represents the development trend in urban short tunnel construction technology [1]. Environmental impact control must be considered in pipe-jacking construction, especially when crossing existing roads, railroads, and other surface or underground infrastructures [2]. The empirical method, stochastic medium theory, and elastic mechanics theory can be used to address the ground settlement prediction problem of shallow buried tunnel excavation. For a shallow buried circular tunnel excavation, the Peck empirical formula method is widely used in circular tunnel excavation impact prediction [3, 4] and has been continuously supplemented and improved. [PERSON] et al. [5] proposed a modified three-dimensional Peck formula for the calculation of the ground settlement of double parallel shield tunnel construction. [PERSON] et al. [6] counted the ground deformation data of several tunnel constructions to obtain the corrected parameters of the stratum loss rate and the sinkhole width coefficient in [PERSON]'s formula. Using the stochastic medium theory method [7; 8], [PERSON] et al. [9] proposed a ground settlement calculation formula for the non-uniform convergence of an elevation arch without augmentation for circular, elliptical, rectangular, and horseshoe tunnel sections and analyzed the relationship with the empirical formula of [PERSON]. [PERSON] et al. [10] proposed a ground settlement calculation formula for large-section header tunnels and used field measurement data to show the maximum impact of ground loss. Using elastic mechanics and [PERSON]'s solution [11; 12] to express the effect of pipe-jacking (shield) thrust, [PERSON] et al. [13] proposed a ground settlement calculation formula for multi-tube pipe-jacking construction. Based on the theory of elastic mechanics, [PERSON] [14] deduced the calculation formula for ground settlement using the virtual mirror method. Then, [PERSON] [15] and others considered the deformation of tunnel ovalization, [PERSON] et al. [16] suggested that the ground loss suffers from the influence of over-excavation, soil deformation, and construction error, and [PERSON] et al. [17] found that the non-uniform convergence mode of the circular shield tunnel is closer to the actual situation. Based on the complex function method of elastic mechanics theory [18; 19], [PERSON] [20] derived an analytical solution of the ground stress and displacement generated by the convergent deformation of a shallow circular tunnel. Then, [PERSON] et al. [21] derived the analytical solution of the ground stress and displacement generated by the elliptical deformation of a shallow circular tunnel, and [PERSON] et al. [22] obtained the ground stresses of a shallow circular tunnel in the conditions of zero stress at the excavation boundary and the surface boundary under stress. For the prediction of ground settlement in a shallow non-circular tunnel excavation, [PERSON] et al. [23] converted a rectangular tunnel excavated with the mining method into a circular tunnel according to the principle of area equivalence and corrected the width coefficient of the surface subsidence slot in [PERSON]'s formula. For a proposed rectangular shield tunnel, [PERSON] et al. [24] discretized the excavation boundary as a series of sets of rectilinear units. Using the analytical solution of the virtual mirror method and considering the effect of the dislocation of all linear units, they calculated the ground displacement generated by the top subsidence and the convergence of the two sides of the excavation boundary. [PERSON] et al.