# Effects of New Tunnelling on a Buried Pipeline with Joints and Its Detachment
## 1 Introduction  
With the extraordinary increase in population and subsequent transport networks, the construction of infrastructure involving underground excavations is undergoing an uncommon period of prosperity. Such excavations inevitably cause ground movements, leading to the longitudinal responses of buried pipelines. Research shows that the primary causes of fractures in pipelines are corrosion and system disturbance due to seismic excitations [1; 2; 3] and ground movement, which arise from traffic loading, ground temperature and moisture changes, as well as adjacent excavation such as trenching or tunnelling [4; 5; 6; 7; 8; 9; 10]. Initially, experimental studies were carried out to measure the deformation of the ground and buried pipelines during the tunnelling and to provide more insight into the mechanism of soil-pipe interaction [11; 12; 13; 14]. With the development of computer technology, a series of numerical simulations were conducted to model the experimental test and to estimate the response of a buried pipeline. The complex soil-pipeline interaction can be taken into account by numerical simulations with the complex geological and geometrical conditions and construction process in practice [15; 16; 17; 18]. In addition to numerical simulations, analytical solutions are less time-consuming and easier for practical utilization. The interaction between the pipeline and the soil is usually analyzed by using the subgrade reaction analysis. This method assumes that the buried pipeline is an elastic beam resting on an elastic foundation model [19; 20; 21; 22]. The beam usually uses Bernoulli-Euler beam theory in which straight lines or planes, normal to the neutral beam axis, remain straight after deformation. This theory neglects the effect of transverse shear deformations and is relevant only to slender beams. The Winkler foundation model, widely used in subgrade reaction analysis, is characterized by theassumption that the pressure in the foundation is proportional to the deflection at the very point and is independent of pressures or deflections elsewhere. This simpler foundation model can be easily applied and gives satisfactory results in many practical situations. However, it is a rather crude approximation without considering the continuity or cohesion of the soil. Two-parameter elastic foundation models, including the Pasternak foundation model, are adopted herein to overcome this deficiency. Meanwhile, pipelines with joints are often overlooked in related research. For the interaction analysis to be of any practical use, equal importance should be given to adequately defining the strength and deformation properties of the pipelines, their joints and the surrounding soil. Some scholars [23; 24; 25; 26; 27; 28] consider the jointed pipeline as a continuous pipeline with additional local rotations at the joints. [PERSON] et al. [29] provide a mathematical model to estimate the mechanical behaviors of the existing tunnels with bending stiffness and shearing stiffness reduction at the movement joints. What is more, the detachment of the underlying soil potentially occurs beneath the jointed pipeline, which inevitably causes nonlinearity. Due to the unknown contact location, the detachment is highly nonlinear even in the range of small deformation and linear elastic behavior. The existing solutions to this problem are highly sophisticated mathematical analyses. Some distinct approaches may be found in the literature: direct approaches, numerical simulations and mathematical models [30; 31; 32; 33; 34; 35; 36; 37; 38]. To deal with the problem, a set of transcendental equations or inequalities, and an iterative technique is utilized in all approaches. The finite difference method [39; 40; 41] of the numerical approach is utilized herein, which has emerged as a powerful and effective technique to study many problems arising in beams in material mechanics. Compared with the aforementioned research, we provide a novel mathematical model to simulate the joints on the buried pipeline.