摘要
目前常用的均质土坡稳定性计算方法主要有瑞典条分法、Morgenstern-Price法、Bishop法、Janbu法、Sarma法等,这些方法基本都假设滑动面为圆弧,长期以来被当作公理沿袭下来。实际上,圆弧滑面只是观测得到的近似现象,并无确切证据表明滑面为理想的圆弧。在物理学和数学上已经证明,质点在只受重力、不计摩擦力的前提下沿曲线轨道下滑,历时最短的路径是最速降线(摆线)。类似地,土体沿滑面下滑遵循最小阻力原则,这具有与最速降线问题高度的相似性和可类比性,因此,对于均质土体,将最速降线作为最优滑面是合理且可行的。确定1条最速降线只需2个点,与其他曲线相比,大大减少了试算工作量,具有明显的优点。从理论推导和数值计算2个方面对最速降线的优越性进行了分析论证,通过编程实现了在CAD中生成最速降线,并将结果与圆弧滑面进行了对比。
The most widely applied analysis methods at present are Fellenius method,Morgenstern-Price method,Bishop method,Janbu method,Sarma method and so on in the stability computation of homogeneous slopes,which are based on arc sliding surface,and are accepted as an axiom.In fact,arc sliding surface is only an approximation from observation,and there is a lack of supporting evidence on the existence of ideal arc sliding surface.It has been proven in physics and mathematics that the optimum route for a mass particle in descent without friction except gravity along an orbit is brachistochrone curve(cycloid).Similarly,the slide of a soil mass is governed by the principle of least resistance,which is highly parallel to the brachistochrone curve problem,therefore the brachistochrone curve as optimum sliding surface is plausible and feasible for homogeneous soil.The determination of brachistochrone curve requires only two points,which is very economic in computation and superior compared to other curves.This thesis demonstrated the superiority of brachistochrone curve both by theoretical analysis and numeric computation,and realized the generation of brachistochrone curve by programming in CAD,and compared the results to arcs.
作者
张建永
马洪生
ZHANG Jianyong;MA Hongsheng(Sichuan Highway Planning,Survey,Design and Research Institute Ltd.,Chengdu 610041,China)
出处
《四川建筑科学研究》
2023年第5期47-53,共7页
Sichuan Building Science
基金
四川省交通运输科技项目(2020-A-01,2023-A-03)。
关键词
最速降线
土体
滑坡
滑面
brachistochrone curve
soil
landslide
sliding surface
