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 引用本文: 尹崇林, 吕爱钟. 水工圆形隧洞围岩衬砌摩擦滑动接触的新解法[J]. 力学学报, 2020, 52(1): 247-257.
Yin Chonglin, Lü Aizhong. A NEW SOLUTION FOR FRICTIONAL SLIP CONTACT BETWEEN SURROUNDING ROCK AND LINING IN A HYDRAULIC CIRCULAR TUNNEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 247-257.
 Citation: Yin Chonglin, Lü Aizhong. A NEW SOLUTION FOR FRICTIONAL SLIP CONTACT BETWEEN SURROUNDING ROCK AND LINING IN A HYDRAULIC CIRCULAR TUNNEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 247-257.

## A NEW SOLUTION FOR FRICTIONAL SLIP CONTACT BETWEEN SURROUNDING ROCK AND LINING IN A HYDRAULIC CIRCULAR TUNNEL

• 摘要: 在实际工程中,围岩和衬砌接触时,它们之间并非完全光滑,也并非可以承受任意大的摩擦力.如果围岩与衬砌之间的剪应力大于所能承受的最大静摩擦力,接触面间将发生切向滑动,定义接触面上产生最小滑动量的状态为衬砌的真实工作状态,这种接触即为摩擦滑动接触.以库仑摩擦模型模拟围岩和衬砌之间的摩擦滑动接触,在考虑支护滞后效应的前提下,利用平面弹性复变函数方法列出了应力边界条件、应力连续条件以及位移连续条件的方程, 再结合最优化理论,建立了具有一般性的摩擦滑动接触解法.在利用混合罚函数法求解最优化问题的过程中,减少了设计变量的个数,极大地简化了优化模型,提升了优化过程的迭代速度以及优化结果的精度.以此为基础,获得了围岩和衬砌相互作用下圆形水工隧洞的应力解析解.该方法可以求解光滑接触和完全接触两种极限情况,具有一般性.同时,利用一种精确的计算方法得到了不同情况下满足完全接触条件摩擦系数的阈值,还分析了衬砌和围岩边界上切向应力的变化规律.

Abstract: In practical engineering, when the surrounding rock and the lining contact with each other, the interface between the lining and the surrounding rock mass is not fully smooth, nor can it bear arbitrarily large friction. The tangential sliding will occur on the contact surface between the lining and the surrounding rock when the shear stress on the interface is greater than the maximum static friction. The state of the minimum relative sliding on the interface is considered as the true working state of the lining, and this kind of contact is called frictional slip contact. Coulomb friction model is used to simulate frictional slip contact between the lining and the surrounding rock mass. Under the premise of considering the mechanical process of the support delay, the equations of stress boundary condition, stress continuous condition and displacement continuous condition are listed by the plane elastic complex variable method. Combined with the optimization theory, a general frictional slip contact solution method is established. Furthermore, in the process of solving the optimization problem by the mixed penalty function method, the optimization model is greatly simplified by reducing the number of design variables, the iteration speed of the optimization process and the precision of the optimization results are improved. On this basis, the stress analytic solutions for a lined hydraulic circular tunnel under the interaction of the lining and the surrounding rock are derived. This method can simultaneously solve the two limiting contact cases of pure bond contact and pure slip contact and has generality. At the same time, the threshold of friction coefficient satisfying the pure bond contact under different conditions are obtained by using a precise calculation method. At last, the variation laws of tangential stresses on the boundaries of the lining and the surrounding rock are obtained.

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