# Analysis on Response of a Single Pile Subjected to Tension Load Considering Excavation Effects
## 1 Introduction  
With the development of urbanization around the world, the demand for extensive underground space utilization has increased dramatically in recent years. To meet these demands, deep excavations are widely used for the construction of geotechnical infrastructures such as tunnels [1], basements [2], bridge foundations [3], and launch shafts for piping [4]. Piles are often installed beneath these infrastructures to bear the uplift or compression loads. As excavation results in stress relief, principal stress rotation, and disturbance to soil [5; 6; 7; 8], the shaft resistance of the piles will decrease [9; 6; 10]. Therefore, it is crucial to investigate the load-displacement behavior of piles subjected to uplift load in order to check the safety of the pile design. In engineering applications, piles are often installed before basement and tunnel excavation, especially when using the bottom-up excavation method. Conventionally, the pile load-displacement behavior is evaluated by means of a load test conducted at the ground surface before excavation. Although the shaft resistance within the excavation depth is eliminated by the sleeve, the load test still overestimates the pile capacity due to the stress relief and excavation disturbance. Additionally, excavation beneath a pile-supported building to add basement space has become popular [11]. The bearing features of the pile after a new excavation are different from those before a new excavation [12]. The reasonsfor the change in pile load-displacement behavior after excavation are stress relief and heave-induced tension. Stress relief decreases the pile capacity and stiffness. [PERSON] and [PERSON] [13] reported that the base resistance of a pile after excavation decreased by 20%, with a vertical effective stress reduction of 50%. [PERSON] et al. [14] found that the reduction in the pile capacity could be up to 45% with increasing excavation depth normalized by pile length. For piles under uplift load, [PERSON] et al. [15] found that the uplift capacity of the pile decreased by 9.84% with an excavation of 13 m. Tension force develops in a pile after excavation due to soil heave [16]. As the tension force develops, the shaft resistance is mobilized, and the shear stiffness at the interface decreases. Thus, the pile stiffness decreases due to the initial pile-soil slip. Existing studies have mainly investigated the change in pile load-displacement behavior after excavation through model tests and numerical simulations. The change in pile capacity under compression and tension conditions has been investigated. However, there is still a lack of a method to evaluate the change in pile capacity due to excavation. Numerous methods have been proposed to evaluate the pile capacity [17; 18; 19; 20]. The load transfer approach is a simple but efficient method to analyze the pile response under compression or uplifted load [21]. The load-transfer method incorporates the complex nonlinear pile-soil interaction behavior [22]. Many nonlinear load-transfer functions have been proposed to model the pile-soil interaction, such as the bilinear model [23], the exponential function model [24; 25], the softening model [26] and the hyperbolic model [27]. For practical purposes, the hyperbolic model is commonly used in the load-transfer method to evaluate the pile response [17; 27]. Consequently, the load-transfer method incorporating the hyperbolic load-transfer method is adopted. This paper proposes a semi-analytical approach to evaluate the load-displacement behavior of a single uplift pile considering the effects of excavation. First, the pile response during the excavation unloading and pile loading stages was analyzed. The relationship between pile displacement and soil displacement was determined. Then, based on the load-transfer method, a semi-analytical approach incorporating excavation effects was proposed and implemented using an iterative algorithm.