条形浅基础极限承载力的滑移线解

Slip-line Solution to Ultimate Bearing Capacity of Shallow Strip Footings

[目的]基于极限平衡理论,提出了一种求解一般条件下条形浅基础极限承载力的精确方法。[方法]地基土被视为服从Mohr-Coulomb屈服准则的理想弹塑性材料,并且假定它是各向同性的、均匀的以及不可压缩或不可膨胀的理想连续介质。通过分析基础与土之间的相对运动和相互作用,将条形浅基础极限承载力问题分为两类问题。建立一个以总竖向极限承载力为目标函数的最小值模型,进而采用滑移线法求解极限承载力而无需事先对塑性区和非塑性楔作任何假定,还提出一种工程上方便实用的简化方法。此外,重点研究了基础两侧均布荷载相同的第一类问题,推导出Terzaghi极限承载力方程的适用条件以及其三个承载力系数的理论精确解,提出一个新承载力方程替代Terzaghi方程,并且通过无量纲分析提出几何力学相似原理。[结果]研究结果表明:当基础完全光滑时,研究得到的总竖向极限承载力与现有方法得到的结果相当吻合;然而当基础完全粗糙时,现有方法低估了极限承载力。[结论]经典的Prandtl机构并不是无重土地基上完全光滑基础极限承载力问题的塑性破坏机构。

[Introduction]Based on the limit equilibrium theory,an accurate approach is proposed to solve the ultimate bearing capacity of shallow strip footings under general conditions.[Method]The foundation soil is considered to be an ideal elastic-plastic material,which obeys the Mohr-Coulomb yield criterion,and is assumed to be an ideal continuous medium that is isotropic,homogeneous and incompressible or non-expansive.Through analyzing the relative motion and interaction between the footing and soil,the problem of the ultimate bearing capacity of shallow strip footings is divided into two categories.A minimum model with the total vertical ultimate bearing capacity as its objective function is established to solve the ultimate bearing capacity using the slip-line method with no need to make any assumptions on the plastic zone and non-plastic wedge in advance.A convenient and practical simplified method is also proposed for practical engineering purposes.Furthermore,the first category of the problem in the case of the same uniform surcharges on both sides of footing is the focus of the study:the applicable conditions of Terzaghi′s ultimate bearing capacity equation as well as the theoretical exact solutions to its three bearing capacity factors are derived,and a new bearing capacity equation is put forward as a replacement for Terzaghi′s equation.The geometric and mechanical similarity principle is proposed by a dimensionless analysis.[Result]The results show that for perfectly smooth footings,the total vertical ultimate bearing capacity obtained by the present method is in good agreement with those by existing methods;whereas for perfectly rough footings,the existing methods underestimate the ultimate bearing capacity.[Conclusion]The classic Prandtl mechanism is not the plastic failure mechanism of the ultimate bearing capacity problem of perfectly smooth footings on weightless soil.