## 1 Introduction  
With the rapid development of urban construction, a series of problems has been caused because of heavy transportation systems and a lack of public space in the metropolises [1; 2]. Currently, metro transportation has become the main way to solve traffic congestion. It can effectively reduce the heavy transportation problem, but it also adversely affects the surrounding environments, such as ground surface settlement and stress redistribution of soil [3; 4; 5]. The ground surface settlement induced by tunnel construction has been widely investigated, and estimation of the settlement trough has been a key factor in related studies [6; 7; 8; 9; 10; 11; 12]. Meanwhile, several analytical methods have been adopted to predict ground surface settlement caused by the tunnel excavation [13; 14]. On one hand, it is very important to understand the mechanics of the development of stress and deformation by applying analytical approaches. On the other hand, these are generally complicated and inconvenient to directly evaluate the settlement. In engineering projects, empirical formulas have been widely adopted to estimate ground surface settlement, especially some simple expressions. The Peck formula [15] is one of the most widely used empirical equations according to field measurements. To improve the practicality of the formula to general cases, the formula was modified and developed in other studies [16; 17; 18; 19; 20]. According to above references, most studies are devoted to ground surface settlement caused by single-line tunnels in clay and soft layer, and few investigations have focused on double-O-tube tunnels in a sand layer. Compared to single-line tunnels, there are more factors that induce ground surface settlement, such as interactions between left and right tunnels, especially urban tunnels, which usually have a larger size. Therefore, the predication formula of the ground surface settlement caused by double-O-tube tunnels in a sand layer is investigated in this paper. Due to the limitations of geological conditions and construction technology, and although shield construction technology has made great progress in recent years, it inevitably disturbs the soil and causes ground surface settlement or uplift, which has been investigated by some scholars [21; 22; 23; 24; 25; 26]. There are few analyses of the additional stresses in surrounding soil caused by construction. Previous studies generally only consider the effect of frontal additional thrust and friction between the shield shell and the soil on additional stress [27; 28; 29; 30; 24]. The influence of ground loss on additional loads is not considered in the sand stratum. Additionally, most soil layers of the additional stresses during shield construction are located in the clay soil and lack some studies on sandy soil. Moreover, for the current studies of [PERSON]'s solution, frontal additional thrust of tunnel is usually defined as 20 kPa. Friction between the shield shell and the soil is assumed as uniform distribution along a radial direction of the shield. The vertical pressure of the center of the tunnel is defined as the mean pressure. For the aforementioned studies, it is a lager gap with the actual condition. Finally, few investigations have focused on the cut-off function predicted shape of the surface settlement curve. In this research, theoretical calculations of the additional stress caused by shield construction, the modified Peck formula, and the shape of the ground surface settlement curve are studied based on data from line 4 of the Xian metro under construction by two tunnel boring machines (TBMs).