摘要
根据极限平衡条分法所满足的平衡条件,将现有13种极限平衡条分法分为4大类:M类(仅考虑对选定求矩中心的力矩平衡)、VM类(考虑垂直方向力的平衡和对选定求矩中心的力矩平衡)、HV类(考虑水平方向力的平衡和垂直方向力的平衡)和HVM类(考虑所有平衡条件)。其中,M类(瑞典法)有显式解,VM类(简化Bishop法)有隐式的安全系数表达式,迭代并不困难。将现有极限平衡条分法对条间力的假定表示成统一形式,根据力和力矩的平衡,推导出十分简明的条间力递推方程和条间力矩递推方程。根据条间力递推方程,建立了传统意义上(保持原有方法所满足的平衡条件、对条间力的假定和未知量不变)基于力平衡(HV类)的安全系数统一求解格式。根据条间力递推方程和条间力矩递推方程,通过Newton-Raphson法建立了传统意义上基于严格平衡(HVM类)的安全系数统一求解格式。不但便于程序的编写,而且有利于不同方法优缺点的比较和理解。
The currently used 13 limit equilibrium methods of slices are classified into four types based on the equilibrium conditions. These are type M with only considering moment equilibrium condition about specified center,type VM with considering vertical force equilibrium condition and moment equilibrium condition about specified center,type HV with considering both horizontal and vertical force equilibrium condition,and type HVM with considering horizontal and vertical force equilibrium condition as well as moment equilibrium condition about specified center. Type M, Sweden method,has explicit solution. Type VM, simplified Bishop method, has inexplicit expression for the safety factor whose iteration is not difficult. For the first time,the assumptions regarding the inter-slice force associated with the existing limit equilibrium methods of slices are expressed in the unified formulation. The simple and clear recurrent equations of the inter-slice forces and inter-slice moments are derived based on force equilibrium and moment equilibrium. The unified calculation formulation for the safety factor based on force equilibrium (type HV) in the context of conventional methods of slices is developed based on the recurrent equation of the inter-slice forces which keeps the equilibrium conditions and the assumptions regarding the inter-slice force and unknowns. Based on the recurrent equations of the inter-slice forces and inter-slice moments,the unified calculation formulation for the safety factor based on rigorous equilibrium (type HVM) in the context of conventional methods of slices is developed by Newton-Raphson method. Unified calculation formulation facilitates the development of programming and the comparison among the advantages and disadvantages of different methods.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2004年第16期2836-2841,共6页
Chinese Journal of Rock Mechanics and Engineering
关键词
岩土力学
边坡稳定
条分法
条间力递推方程
分类
rock and soil mechanics,slope stability,slice method, recurrent equation of inter-slice forces,recurrent equation of inter-slice moments,safety factor,unified calculation formulation
