## 1 Introduction  
With the acceleration of urbanization in China, the growth rate of urban land use is much lower than the urban population growth rate. The limited number of urban surface land resources can no longer meet people's needs for living space. The development direction of urban space is gradually changing from the horizontal direction of extension to the vertical direction of intension, which has resulted in many underground structures [1; 2; 3; 4]. Although the development of urban underground space has detailed plans and arrangements before construction, it still has some unpredictability in the long term. Therefore, the negative conditions that new underground structures create near the existing ones happen from time to time. As the main artery of underground traffic in modern cities, this phenomenon of metro tunnels is particularly prominent. Among many construction methods of metro tunnel, shield tunneling is becoming the preferred construction scheme because of its advantages of fast construction and small disturbance to stratum [5; 6; 7; 8; 9]. Although shield tunneling has many advantages as mentioned above, and the construction technology has made great progress in many years, due to the defects of geological conditions and construction technology, the advance of shield tunneling will inevitably create a disturbance, change the stress state of soil and cause stratum displacement. Therefore, how to evaluate and control the stratum displacement has always been a concern for engineers [10; 11; 12]. The important of this problem has prompted researchers to study many methods for predicting stratum displacement induced by shield tunneling. Based on the factors affecting stratum displacement, the methods can be divided into two categories. The first category concerns the ground loss factors during shield excavation, and the second addresses the mechanical effect factors. In terms of ground loss factors, empirical solution is one of the most commonly used methods. [PERSON] assumed that the curve of land settlement trough satisfies the conditions of Gauss distribution and invariant stratum volume, as was deduced [PERSON]'s empirical formula based on field monitoring data [13]. [PERSON] et al. [14] and many other researchers [15; 16; 17; 18; 19] noted that [PERSON]'s empirical formula cannot accurately describe soil settlement trough in many cases and proposed improved empirical formulas under different geologic conditions. Besides empirical solution, there are also many researchers who contribute significantly through analytical solution [20; 21; 22; 23], numerical simulation [24; 25; 26] and model testing [27; 28]. In terms of mechanical effect factors, [PERSON]'s solution is one of the well-known solutions to calculate the stress and displacement caused by a point load at an embedment depth in an elastic half-space [29]. Based on [PERSON]'s solution, many modified analytical solutions are proposed [30; 31; 32; 33]. For instance, [PERSON] et al. derived a theoretical solution for the deformations of an elastic half-plane with a circular cavity, which is often used in tunnel excavation. [34; 35]. However, most previous studies only consider the stratum displacement caused by ground loss factors, ignoring the influence of mechanical factors without clear theoretical basis [7; 8; 17; 21]. A few studies containing mechanical factors are not thorough enough, and they are usually shown in the form of total displacement without the quantitative analysis of the proportion of stratum displacement caused by each factor [6; 9; 10]. In this paper, based on the engineering project of an interval tunnel between Shizishan Station and Chuanshi Station in Chengdu Metro Line 7, China, combining Loganathan empirical formula and mirror source-sink method, the stratum displacement caused by ground loss factors is calculated. The mechanical effect factors are divided into four parts and calculated based on the Mindlin solution.