中文摘要：

自由变形法是地下压力拱（隧道衬砌）结构内力计算的基本方法之一,适用于淤泥、流沙、完全塑形或软土介质等理想松软地层的水下隧道或软塑土层压力拱的内力计算。本文推导出整体圆形衬砌自由变形法内力计算的力法过程及其严格理论解,为后续发展的弹性抗力、椭圆变形、弹性铰等同类方法提供对比参考,以明确公式计算的理论来源,便于理论拓展。通过实例对比地铁浅埋衬砌压力拱自由变形法的理论计算、实测与数值模拟。结果显示,该方法进行整体式衬砌的内力计算过程明确,其理论结果可应用于狮子洋半岩半土复合地层及南京地铁砂性土及黏性土层衬砌计算,可为类似工程设计必要的理论包络值提供参考,具有一定的工程实用性。

英文摘要：

The FFD（Free-Form Deformation）method is one of the basic methods for structural internal force calculation of underground pressure arches（tunnel lining）.Conventionally speaking,it is suitable for internal force calculation of underwater tunnels in ideal yielding strata of mud,running sand and completely remodeling or soft soil media and is suitable for internal force calculation of pressure arches in plastic soft soil.In this paper,the process for calculating structural internal forces of the monolithic circular lining with the FFD method was deduced and its rigorous theoretical solution was obtained to provide reference for comparison with the subsequently developed similar methods,such as the elastic resistance,elliptical deformation and elastic hinges etc,and to make clear the theoretical source of formula calculation for further continuation.Through application of the FFD method in an example of shallow subway pressure arch lining,theoretical calculation,field measurement and numerical simulation were compared.The results show as follows：By applying the FFD method,the process for calculating the internal forces of the monolithic lining is made clear and definite and the theoretical results can be utilized in calculation of the tunnel lining in the cases of the Shiziyang half rock and half soil composite layers and Nanjing Metro sand and clay layers;reference can be provided for theoretical envelope values essential to engineering design;the FFD method is of certain engineering practicality.