层状结构岩体顺层斜坡滑移-弯曲失稳计算探讨

中-陡倾顺层斜坡在下端被阻挡及嵌固时可能产生滑移-弯曲型结构变形与屈曲失稳,但以前失稳分析采用的力学模型的边界条件及变形形态对地质原型的符合性较为不足。因顺层斜坡上部平直段与下部屈曲段是一个连续的整体,弯曲段边界条件及变形形态的合理对正确建立挠曲线方程和临界屈曲失稳分析均非常重要。在分析了顺层斜坡地质原型变形形态的基础上,由考虑自重的阻滑端固定的斜置等厚弹性板梁模型,提出了以地质原型变形形态抽象出相应边界条件的分析方法,及理论上求解挠曲线的适定三阶微分方程。鉴于弯曲段长度可现场测知,以所分析的边界条件拟定了简便合理的、曲线形态能较好反映地质原型变形形态的多项式近似挠曲线。通过势能泛函的平衡稳定判断方法,滑移-弯曲破坏的临界条件得到确定,失稳临界弯曲长度计算式较符合工程实际。

Studies on Estimate of Sliding-bending Rupture of Bedded Rock Slopes

When the slopes' foot was fixed,the middle-dipping to steep-dipping angle bedded rock slopes may take place a sort of destabilization named sliding-bending deformation and buckling yielding rupture.In former studies,the confining conditions and curving shapes in mechanical models were not according with the prototype slopes preferably.In fact,the rational boundary conditions and curving shapes are important to establish differential equation for bending equilibrium state and to analyze the critical condition of buckling.According to the investigated deforming state of prototype slopes in-situ,the buckling mode of curve and the confining conditions was analyzed.It is indicated that,the bending curve is not asymmetrical and there will not have moment of flexure on the top of the bending section.Based on a slantwise constant-thick beam which foot is fixed,and took deadweight of bending section to account,a theoretical differential equation of third order for buckling equilibrium state was established.As bending length and deformation state can be deserved in prototype slopes,a convenient and rational approximate polynomial bending curve was put forward,which accord with the confining boundary conditions preferably.By means of potential energy method,the criterion for equilibrium stability was put forward,and the critical bending length can be deserved.Its applications accord to practice projects to a certain extent.