m 法幂级数解计算系数的修订建议  

Suggested Revision for Calculating Coefficients of Power Series Solution for m Method

作　　者：缪云 王旭东 MIAO Yun;WANG Xudong(School of Civil Engineering and Architecture,Jiangsu Open University,Nanjing 210036,China;College of Transportation Engineering,Nanjing Tech University,Nanjing 211816,China)

机构地区：[1]江苏开放大学建筑工程学院,南京210036 [2]南京工业大学交通运输工程学院,南京211816

出　　处：《铁道标准设计》2024年第12期100-105,148,共7页Railway Standard Design

基　　金：江苏省高等学校基础科学(自然科学)研究面上项目(22KJD560002);江苏省高职院校教师专业带头人高端研修项目(2022GRFX012)。

摘　　要：国内工程设计规范和手册中水平受荷桩计算均采用m法幂级数解,该方法主要源自二十世纪六七十年代《铁路标准设计通讯》的若干论文,计算系数则来自前苏联列宁格勒运输桥梁设计院。根据水平受荷桩m法的基本方程确定的幂级数解,对水平位移、转角、弯矩、剪力计算系数以及相应的衍生系数进行计算。计算结果表明,计算系数的精度与截断误差和舍入误差相关。现行TB 10093—2017《铁路桥涵地基和基础设计规范》附录D给出的5位小数的计算系数表中,部分计算系数存在误差,尤其是在换算深度小于0.5 m时,衍生计算系数差异更为明显。通过舍入误差与计算系数精度的对比分析,给出满足级数解精度的计算项数取值,建议计算系数采用科学计数的表述方式和有效位数,保证利用计算系数表进行水平受荷桩计算分析的正确性。建议在规范修订时对计算系数表进行更正。The m method power series solution is commonly used for calculating laterally loaded piles in domestic engineering design codes and manuals.This method is primarily derived from several papers published in the 1960s and 1970s in Railway Standard Design Communication,and the calculation coefficients originate from Leningrad Transport Bridge Design Institute in the former Soviet Union.Based on the basic equation of the m method for laterally loaded piles,this study used the power series solution to calculate coefficients for the horizontal displacement,rotation angle,bending moment,shear force,and their corresponding derived coefficients.The results showed that the accuracy of these coefficients was related to truncation and rounding errors.The current table of coefficients with 5 decimal places,provided in Appendix D of Code for Design on Subsoil and Foundation of Railway Bridge and Culvert(TB 10093—2017)contained some errors.These discrepancies,especially in the derived coefficients,became more pronounced when the conversion depth was less than 0.5 m.Through a comparative analysis of rounding errors and coefficient accuracy,the study proposed an appropriate number of terms to satisfy the accuracy requirements of the power series solution.It was recommended that the calculation coefficients be presented in scientific notation with an appropriate number of significant figures to ensure accuracy when using the coefficient table for laterally loaded pile analysis.Correction to the coefficient table was suggested for the upcoming revision of the code.

关 键 词：桥梁 桩基础 水平受荷桩 M法 幂级数解 计算系数 舍入误差 

分 类 号：U24[交通运输工程—道路与铁道工程] TU473.1[建筑科学—结构工程]