土钉支护季节冻土区边坡冻胀效应耦合模型建立及求解

Establishment and solution of a soil and nailing interaction model of slopes in seasonal frozen soil areas considering frost heaving effect

为了研究季节冻土区边坡冻胀效应下土钉支护结构沿土钉长度方向的剪应力和轴力分布变化规律,首先,基于传热学理论及固液两相共存的导热微分方程得到冻结锋面移动变化规律,结合冻胀率公式进一步推导得到寒区边坡自由冻胀变形计算公式;其次,将土钉对边坡的支护作用视为无穷多个沿着土钉长度方向上的剪切分布力,考虑到边坡冻结时冻结层与未冻土层的刚度差异性,通过坐标变换后将刚度当层法与Mindlin解相结合推导双刚度层边坡内部有剪切集中力作用时钉土相互作用接触面上任一点的位移解析解;最后,基于钉土二者相互作用位移协调条件,建立关于土钉长度方向剪切分布力的黎曼积分方程,通过闭Newton-Cotes法的复合梯形积分公式及MATLAB软件编程对算例求解分析,获得土钉轴力分布规律,并利用数值解和实测值进行对比验证,此外还分析冻胀率、初始含水量等参数对土钉长度方向剪应力及轴力分布影响。结果表明:本文耦合计算方法得到土钉轴力分布形式与现场实测、数值模拟结果在总体趋势上基本一致,表明耦合计算法是合理可行的;土钉长度方向的剪应力及轴力分布规律符合中性点理论,轴力曲线呈现出两头小中间大的抛物线状,其最大值对应出现在剪应力为零的位置处,此外边坡土体冻胀率、初始含水量、土钉长度等因素均对土钉长度方向的剪应力及轴力的影响不容忽视。研究结果可为寒区边坡冻胀作用下土钉支护结构设计提供有益科学参考。

In order to study the distributions of shear stress and axial force along the length direction of soil nailing of slopes in cold regions considering frost heaving effect,in this paper,the movement law of the freezing front is discussed based on the heat transfer theory and the differential equation of solid-liquid two-phase coexistence,and the calculation formula of free frost heaving deformation of a slope in cold regions is further derived according to the formula of frost heaving rate. On this basis,regarding the supporting effect of soil nailing on slopes as shear distributed force along the length direction of soil nailing and considering the stiffness difference between the frozen layer and the unfrozen soil layer of a slope,the displacement analytical solution of any point on the interface of nail and soil interaction is derived by combining the stiffness layer method with Mindlin solution after coordinate transformation. Finally,Based on the displacement compatibility condition of soil and nailing interaction,the Riemann integral equation of the shear distribution force along the length direction of soil nail is established. The axial force distribution of soil nailing is obtained by using the compound trapezoidal integral formula of closed Newton-Cotes method and MATLAB software programming,and verified by comparing the numerical solutions and the measured values. In addition,the influence of the frost heaving rate and the initial water content on the shear stress and axial force distributions along the length direction of soil nailing is analyzed.The results show that the distribution of the axial force of soil nailing obtained by the developed coupling calculation method is basically consistent with the numerical simulation results and the measured values,indicating that the coupling calculation method is reasonable and feasible. It is also revealed that the distributions of the shear stress and the axial force along the length direction of soil nail conform to the neutral point theory,the axial force curve presents a parabola shape with small ends and large middle,and the maximum axial force appears at the position where the shear stress is zero. The influence of the frost heaving rate,the initial water content and the nailing length on the shear stress and the axial force along the length direction of soil nailing can not be ignored. The research results can provide a useful scientific reference for the design of soil nailing support structure of slopes in cold region under frost heaving condition.