寒区预制混凝土衬砌梯形渠道弹性冻土地基梁模型

Elastic frozen soil foundation beam model for trapezoidal canal lined with concrete precast slabs in cold regions

基于Winkler弹性地基梁理论及有限杆单元的思想,以单块预制板为研究对象构建其挠曲线微分方程并求解;在此基础上,考虑冻土-结构接触界面及预制板间填缝处的协调变形与相互作用,引入端部边界条件及板间连续性条件,同时砂浆填缝处弯矩为零,将多块预制板联系起来,构建预制混凝土衬砌梯形渠道弹性冻土地基梁模型。再由切向静力平衡条件导出切向控制方程并求解,最终获得衬砌板各截面法向冻胀位移与切向位移的解析表达式。以新疆北部某梯形渠道为例,对衬砌各截面法向冻胀位移、切向位移、接触面法向应力、切向冻结力及上表面应力进行计算。结果表明:本文模型计算的法向冻胀位移与观测值符合良好,与弹性支承法、杆系有限元法计算结果相比更接近观测值。上表面应力估算的易开裂范围与实地调查结果基本相符,表明了模型的合理性。由于存在不连续断面即砂浆填缝,衬砌板法向冻胀位移、接触面法向应力、截面弯矩和上表面应力均存在一定的起伏,出现正负交替现象。顶推力作用下坡板各截面均存在切向位移,且自坡脚向坡顶非线性减小,在坡顶达到最小值。

Based on Winkler elastic foundation beam theory and finite beam element method,the deflection differential equation for a single prefabricated slab is put forward and solved.On this basis,considering interaction between frozen soil and concrete lining plate and interaction between precast slabs,elastic frozen soil foundation beam model of trapezoidal canal lined with precast slabs is proposed through introducing end boundary conditions,continuity conditions between slabs and conditions that bending moment on joints is zero.The tangential governing equation is derived from tangential static equilibrium condition.Then analytic expressions for both normal and tangential frost heave displacement of concrete lining plates are presented.By taking a trapezoidal canal in north Xinjiang as prototype,normal frost heave displacement,tangential displacement,normal stress on contact interface,tangential freezing force and upper surface stress of each section of lining plates are calculated.The results prove that the normal frost heave displacement calculated by the presented method are in good agreement with observed value and is better than that calculated by elastic support method and finite beam element method.The cracking range estimated by analyzing distribution of upper surface stress of lining plate is basically consistent with field investigation.Due to discontinuity of lining plates,distribution of normal frost heave displacement,stress on contact interface,bending moment and upper surface stress of concrete lining plates all show some fluctuations,and there are positive and negative alternating phenomena.There is tangential displacement in each cross-section of slope plate of the canal caused by pushing force,and tangential displacement decreases nonlinearly from slope toe to the top of slop,then the minimum is reached at the top of the slope plate.