## 1 Introduction  
When highway tunnels pass through urban areas, they often face problems such as tight land use, fragile geological environment, and high sensitivity of the surrounding environment. Therefore, it is necessary to strictly control the stress release ratio and reduce the disturbance to the surrounding rock to minimize the impact on the surrounding environment [1]. The double-arch tunnel is one of the most commonly used construction methods for urban highway tunnels because of its beautiful section, land saving and relatively small impact on the surrounding environment [2; 3; 4; 5]. Due to a large number of underground pipelines in urban areas, the underground excavation causes stress redistribution in surrounding rock and soil, which inevitably affects the deformation of land surface and surrounding pipelines. If the pipelines were damaged or failed, not only the safety of engineering construction is threatened, but also the normal production and life of urban residents are greatly affected [6; 7]. Therefore, it is of great significance to study the response mechanism of the underground pipeline to underground excavation. Extensive researches have been conducted on the influence of underground excavation on adjacent pipelines and fruitful results have been achieved. The studies on existing pipeline deformation mainly include analytical, experimental, and numerical simulation methods. An analytical method has a rigorous derivation process and reliable mathematical basis, which can provide simple and clear solutions to engineering. Based on Winkler elastic foundation beam theory, [PERSON] [8] proposed an analysis and calculation model of pipeline deformation caused by stratum movement induced by tunnel excavation, and analyzed the joint angle and bending stress of the pipeline when the pipeline moved perpendicular to the parallel stratum. [PERSON] et al. [9] obtained the modified Winkler foundation modulus by using the elastic continuum solution, so that the Winkler system and the elastic continuum system obtained similar maximum bending moments in the natural stratum settlement dimension Gaussian distribution. [PERSON] [10] studied the distribution of pipeline bending moment caused by tunnel excavation, and obtained the prediction formula of pipeline bending moment according to the geometrical shape of pipeline and tunnel and the ground movement at the same depth of the pipeline. [PERSON] et al. [11,12] compiled a TURISK program to calculate the strain of underground pipelines according to the stratum bending strain and axial strain caused by engineering excavation. [PERSON] et al. [13] studied the influence of deep foundation pit excavation on adjacent underground pipelines in Lurie medical research center in Chicago by comparing theoretical calculation with measured data. [PERSON] [14] deduced pipeline displacement based on stratum deformation and studied the influence of subway excavation on adjacent pipelines. Using nonlinear regression method, [PERSON] et al. [15] established the approximate equation of stability load factor and safety factor of the square tunnel in anisotropic heterogeneous clay, and also established the design equation of stability analysis of shallow buried unlined circular tunnel [16]. The tests on double-arch tunnels and pipelines included field tests and laboratory tests. Due to multi-uncontrollable factors and high cost, few studies were performed on field tests. Using the method of field measurement, [PERSON] et al. [7] systematically studied the attenuation law of blasting seismic waves in soil and the vibration response of buried pipelines. [PERSON] et al. [17] studied the influence of shield tunnel construction on the deformation of buried pipelines and the relationship between the deflection of pipelines and pipeline damage by analyzing the monitoring data of shield tunnel construction. Laboratory test has been widely used in the influence of tunnel excavation on adjacent pipelines because of their convenient operation, low cost and high controllability. [PERSON] et al.