## 1 Introduction  
With the continuous development of underground space and transportation facilities, underground construction processes will inevitably encounter existing pile foundations. Deep excavation and shield tunneling alter the initial stress state of soil, and the resulting lateral deformation of the soil will induce additional deformation and internal force on adjacent existing pile foundations. These will have serious consequences for engineering applications [1; 2; 3; 4]. The additional deformation of the existing pile foundations induced by nearby construction will affect the safety performance of superstructures. Consequently, it is crucial to assess the impacts of soil deformation on existing pile foundations before construction. Many researchers have investigated the effects of deep excavation and shield tunneling on adjacent existing pile foundations through field tests, model tests, numerical simulations, and theoretical analyses [5; 6; 7; 8; 9; 10; 11; 12; 13]. For the deformation of existing pile foundations located outside the pit, this is significantly affected by the deformation of the retaining structure induced by pit excavation [10]. Controlling the deformation of retaining structures can effectively limit the additional deformation of piles located outside the pit. Hence, current engineering projects mainly focus on reducing the deformation of retaining structures to mitigate the construction effects of deep excavation [14]. This method to reduce the deformation of retaining structures mainly includes enhancing the stiffness of the supporting system [15; 16], improving the soil properties [17], and excavating in subzones [18]. However, controlling the deformation of retaining structures depends heavily on the reasonableness of the design scheme and the accuracy of the preliminary evaluation of pile deformation, making it a passive control method [14]. Once the deformation of the pile exceeds the deformation control standard, the construction process must be interrupted, prolonging the construction period. For the deformation of existing pile foundations induced by shield tunneling, the soil loss during the tunneling process greatly impacts the deformation of pile foundations [19]. This soil loss can be effectively reduced by injecting cement paste into the soil layers (compensatory grouting technology), thereby controlling the deformation of neighboring pile foundations. Compensatory grouting technology has been widely used in building deflection correction [20; 21] and for reducing tunnel settlement [22], lateral displacement [23], etc. Compensatory grouting technology is a type of active control technology [14], mainly characterized by low construction investment, minimal impact on the construction period, a flexible control area, and a significant control effect. However, when directly grouted into soil, the cement paste is easy to split and infiltrate, resulting in a reduction in the grouting efficiency [24]. This makes it a challenge to accurately control the grouting area and achieve the expected effect. [PERSON] et al. [14] proposed a capsule grouting expansion technology, achieving the aim of a controllable grouting area through injecting cement paste in a capsule. The capsule is made of a puncture-resistant, high-strength, and non-ductile material, ensuring impermeability so that the injected cement paste does not penetrate the soil. Consequently, capsule grouting expansion technology can effectively control the volume and shape of the capsule. For the application of capsule grouting expansion technology, the capsule is presleeved onto a grouting pipe and vacuumed before being transported to the site. After drilling a hole at the desired location, the capsule and grouting pipe are inserted into the drilled hole to a predetermined depth. Fine sand is then used to backfill the void in the drilled hole.