基于Mindlin解的压力型锚杆锚固段的受力分析

Mechanical analysis of anchorage segment of pressure-type cable based on the Mindlin solution

假设锚杆为与周围介质相同的材料,视锚杆作用的岩土体为弹性半空间位移体;基于Mindlin位移解,求出集中力作用下周围岩土体沿锚固体的轴向位移;根据压力型锚杆锚固段的受力状态,计算锚固体在轴向荷载作用下压缩变形,利用锚固体与周围岩土体变形协调假定,推导出锚固段轴向应力和剪应力分布的理论解。经过与已有现场试验实测数据对比分析,验证了理论解的可行性,并在此基础上讨论了相关岩土参数对锚固段轴向应力和剪应力的影响。锚杆现场试验和理论分析结果表明:压力型锚杆的锚固段所受轴向应力和剪应力与锚固力成正比;压力型锚杆的锚固段所受剪应力的分布形式受周围岩土体弹模、泊松比以及锚固体与周围岩土体界面的内摩擦角等因素的影响。其中周围岩土体的弹模影响最大。

Assuming that cable has the same material properties with the surrounding rock soil and there is a displacement in an elastic half-space occurred for the rock and soil mass reinforced with cable, axial displacement of surrounding rock soil mass along cable under anchorage force was calculated based on Mindlin displacement solution. Based on the stress state of anchorage segment of pressure-type cable, the compression deformation of anchorage body under axial load was also obtained. Theoretical solutions for the distribution of axial stress and shear stress on anchorage segment of pressure-type cable were derived on the assumption of a compatible deformation between anchorage body and surrounding rock soil mass. After comparing with the existed data of in-situ test, theoretical solutions proved to he feasible. On this basis, the influence of related mechanical parameters of rock and soil on shear stress and axial stress were discussed. Experimental and theoretical analysis results indicated that the axial normal stress and shear stress on anchorage segment of pressure-type cable were proportional to anchorage force, and several factors including elastic modulus, Poisson ratio of rock soil mass and internal friction between anchorage segment and rock soil mass had influence on the distribution patterns of shear stress, among which elastic modulus of rock soil mass exerted the greatest impact.