## 1 Introduction  
In densely built urban areas, there is an increasing demand for further development of underground transit systems due to the lack of surface space, which promotes the excavation of shallowly buried tunnel crossing beneath existing buildings. Shallow tunneling in soft ground inevitably entails the generation of stress relief and ground settlement around the tunnel [1, 2, 3]. The critical factors affecting ground settlement around the tunnel are essentially the physical and mechanical parameters of the soil and tunnel. The excessive ground settlement eventually transfers to the building foundation, and is responsible for the potential deformation or even damage of the existing buildings [4, 5, 6]. To ensure the safety and serviceability of the existing buildings, reliable assessment of the influences of shallow tunneling on the existing buildings is necessary for engineers, and is always a serious concern.  
Considerable efforts have been made to investigate the response of strip foundation buildings to tunnel excavation. The methods used for analyzing this problem can be broadly classified as theoretical analysis, numerical simulation, model testing, and field monitoring. In theoretical analysis, researchers developed a two-stage method to rapidly predict the building deformation [7, 8, 9, 10, 11] or damage [12, 13, 14, 15] induced by shallow tunneling. The existing building is commonly considered as an equivalent elastic thick beam, Euler-Bernoulli beam, or Timoshenko beam. The ground is usually presented by the Winkler model or the Pasternak model. Numerical simulation provides insights into the building response with different characteristics subjected to the tunneling-induced ground settlement. Refined numerical models were established using the finite element method [16; 17; 18; 19; 20], finite difference method [21], and discrete element method [22], while the tunnel, soil, and building are computed as a whole. Model testing is capable of creating similar conditions in a small-scale model to those of the full-scale prototype. The centrifuge model tests [23; 24; 25] and the 1 g model tests [26; 27; 28] can both serve as effective tools to study the interaction between the shallow buried tunnel and the existing building. Field monitoring is the most straightforward method for analyzing the displacements and cracks of the building strip foundation that result from tunneling, and has been widely employed by researchers in practice [29; 30; 31; 32; 33].  
Current studies using theoretical analysis mainly focus on the case of the building axis perpendicular to the tunnel axis under plane strain condition without considering the effects of the tunneling process. To gain a better mechanical understanding of the strip foundation building response arising from tunnel excavation, a new analytical method taking into account the tunneling process is proposed in this paper. The proposed method can be applied to the condition that the angle between the building axis and the tunnel axis is arbitrary. The building response obtained from the proposed method is verified by comparing with results from the finite element and finite difference methods. Based on the verified analytical solutions, a parametric analysis is performed to systematically explore the effects of different factors on the building deformation and internal forces.