双参数地基中隧道下穿既有管线的显式解析解分析  

Explicit solution analysis of tunnel excavation under existing pipelines on the double-parameter foundation

作　　者：黄明华 周钲霖 HUANG Minghua;ZHOU Zhenglin(MOE Key Laboratory of Building Safety and Energy Efficiency,Hunan University,Changsha 410082,China;College of Civil Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学建筑安全与节能教育部重点实验室,长沙410082 [2]湖南大学土木工程学院,长沙410082

出　　处：《安全与环境学报》2023年第6期1852-1858,共7页Journal of Safety and Environment

基　　金：国家重点研发计划项目(2019YFC1511100);湖南省科技重大专项项目(2019GK1010);长沙市自然科学基金项目(kq2208031)。

摘　　要：针对隧道下穿诱发既有管线响应问题,基于Pasternak地基模型推导管线变形控制微分方程,并采用朗斯基行列式和常数变易法给出全定义域内管线挠度、转角、弯矩和剪力的显式解析解。结合工程实例,将该方法所得管线挠度与实测数据及已有文献结果进行对比,对显式解析解的可行性和优异性进行验证。此外,分析了沉降槽宽度参数和剪切层刚度系数对管线响应的影响。结果表明:所提方法给出的管线挠度与实测数据吻合较好;随沉降槽宽度参数增大,管线响应范围扩大,管线挠度增加,管线最大转角先增大后减小,管线最大弯矩值和最大剪力值减小;随剪切层刚度系数增大,管线响应范围受到影响较小,管线挠度在隧道中轴线附近范围增加,管线转角在峰值附近范围增大,管线弯矩最大值和剪力最大值减小。Aiming to predict the response of the existing pipeline induced by down-crossing tunneling,this study firstly formulated the governing differential equation for the deformation of the pipeline based on the Pasternak foundation model.To directly solve the equation,a series of parameter transformations were carried out to obtain a new governing differential equation that is easy to deal with mathematically.Then,the general solution for the homogeneous equation was solved,and the special solution was obtained by combining the Wronskian,the variation of constants,and the solving formula for the error function.Combined with the special solution and the general solution for the homogeneous equation,the general solution of the governing differential equation for the deformation of the pipeline was obtained.Finally,the values of the undetermined coefficients in the general solution were obtained according to the boundary conditions of the pipeline,from which the explicit analytical solution for deflection of the pipeline in the full definition domain was obtained.The explicit analytical solutions for the rotation angle,bending moment,and shear force of the pipeline in the full definition domain were obtained by calculating the first,second,and third derivatives for the deflection equation.Based on the engineering example,the deflection calculated by the method of this paper was compared with the measurement data and results of existing literature,which verified the feasibility and superiority of the calculation.In addition,the effects of the width parameter of the settlement trough and the stiffness coefficient of the shear layer on the response of the pipeline were analyzed.The results show that the calculated results of deflection are in good agreement with the measurement data.With increasing the width parameter of the settlement trough,the response range and deflection of the pipeline increase,the maximum rotation angle of the pipeline first increases and then decreases,and the maximum bending moment and maximum shea

关 键 词：安全工程 隧道下穿 既有管线 管线响应 PASTERNAK地基 显式解析解 

分 类 号：X951[环境科学与工程—安全科学]