最小势能原理在关键层挠度计算中的应用

关键层对上覆岩层的变形起控制作用并与受其直接控制的岩层形成组合梁结构协调变形,依此原理可算得将关键层视为四边简支的弹性薄板时板中面承受的均布荷载,因此可用关键层的变形代替组合梁结构的变形。将承受等效荷载时缓慢下沉的关键层视为平衡体系,依据平衡体系势能最小的原理求得注浆前后关键层的最大挠度和最大拉应力的方向。离层注浆是控制地表变形的有效方法,注浆前后地表的沉陷变形与关键层的挠曲变形密切相关,在忽略表土层对沉陷起弱化作用的前提下可用注浆前后关键层最大挠度的变化间接的反映离层注浆的减沉效果。通过该理论计算得出的减沉值和实测数据较为接近,验证了采用最小势能原理进行注浆前后关键层挠度值计算的可行性。为关键层注浆前后的挠度计算和注浆减沉的效果评价提供了新的方法和思路。

The application of the minimum potential energy principle in the calculation of the deflection of the key layer

The key strata control the deformation of the overlying rock,the key strata and the rocks that directly controlled by the key strata form an composite beam structure have the coordination deformation,the uniform load of the surface of the plate which can be seen as an elastic thin plate with four simply supported edges can be calculated according to this principle,so the deformation of the composite beam structure can be insteaded by the key strat＇s,the slowly sinking key strata can be seen as an balance system with the equivalent uniform load on its surface,the maximum deflection and maximum tensile stress direction of the key strat before and after grouting can be known based on the principle of minimum potential energy. Abscission layer grouting is an effective method to control the deformation of the surface,the subsidence deformation of the surface relate to the deformation of the key strata before and after grouting closely,the abscission layer grouting＇s reducing effect can be reflected indirectly by the change of the key strata＇s maximum deflection before and after grouting on the premise of ignoring the weakening effect of the topsoil in subsidence. The value of the deflection reducing effection from calculation is relatively close to the measured data verifies the principle of minimum potential energy is feasibile to calculate the deflection values of the key layer before and after grouting. It provides a new method for the deflection calculation of the key layer and the reduce effect of grouting.