Mechanical Analysis of Rock Bolts under Action of Tension and Shearing in Bedding Rock Slopes
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摘要:
锚杆能够显著增强顺层岩质边坡的稳定性.基于顺层边坡结构效应，应用锚杆加固顺层边坡的力学模型，根据结构力学理论和变形协调关系，建立拉剪作用下全长粘结型锚杆加固顺层边坡抗剪计算的理论分析方法.与相关试验数据进行了比较验证，结果表明顺层边坡锚固抗力模型计算结果与试验结果比较一致，验证了理论模型的合理性.讨论了锚杆倾角、锚杆直径、灌浆体强度、结构面内摩擦角、剪胀角等对加锚顺层岩体抗剪性能的影响.分析表明：锚杆锚固抗力模型能够较好地反映锚杆轴力及横向剪切力对顺层岩质边坡的抗剪作用.锚杆倾角越大，锚杆总的抗力呈减小趋势，而锚杆抗力随剪胀角增大而增加；当锚杆倾角等于内摩擦角时，锚杆抗力达到最大；锚杆抗力随锚杆直径增加而增大；当锚杆直径不变时，锚杆抗力随灌浆体抗压强度增大而有所减小.
Abstract:Bolting is one of the important methods to harness the bedding rock slopes. The stability of the rock can be strengthened by rock bolts. The mechanical model of bolted bedding rock slope is employed to analyses the behavior of the rock bolt. The force method approach and the deformation compatibility principles are used to model the contribution of the axial and shear bolt forces at the intersection between the bolt and the joint plane. The theoretical analyses of the shearing resistance for the fully grouted rock bolts in the bedding rock slope are evaluated in the action of axial and shear loads. Comparisons and validations were carried out between the shearing resistance mechanical model predictions and the experimental data. It is shown that the data of the both methods have a good agreement. The effects of bolt inclination, the length of shearing deformation, bolt diameter, the grout compressive strength, and the internal friction angle of the joint plane on the shear strength of the bolted bedding rocks are investigated in detail. The results show that the bolt shearing resistance model expresses the contribution of the axial force and shearing force of the bolts to the shear strength of the bedding rock slopes. The total resistance is reduced with the larger of the bolt inclination. With increasing of the dilation angle, the rock bolt resisting force increases. When the inclination of rock bolt equals to the friction angle, the bolt contribution to resist the rock movement is the maximum value.The greater the diameter of the bolts, the larger the bolt resistance. The resistance of the rock bolt will have a little reduction with the increasing of the grout compressive strength for a certain diameter of the bolt.
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图 2 锚杆在岩体剪切作用下的反对称变形
Fig. 2. Antisymmetric deflection for the rock bolt under shearing action
图 3 锚杆剪切变形段计算模型
a.三角形分布荷载；b.均匀分布荷载
Fig. 3. Computing model of the bolt for the deflection length
图 7 锚杆抗力值理论与试验结果变化曲线对比
Fig. 7. Comparison between theoretical and experimental data curves for rock bolts
图 8 不同剪胀角下锚杆抗力与倾角和内摩擦角的变化关系
Fig. 8. Relationships among the support force, the inclination, and the inner friction angle under different dilation angles
图 9 不同直径锚杆抗力与倾角和灌浆强度的变化关系
Fig. 9. Relationships among the support force, the inclination, and the grout strength under different rock bolt diameters
表 1 试验材料参数
Table 1. Mechanical parameters of meterials
材料 弹性模量
E(GPa)泊松比
μ屈服强度
fy(MPa)抗压强度
fc(MPa)直径
(mm)锚杆 186.0 0.18 505 - 8 岩体 31.5 0.20 - 33.0 - 灌浆 13.0 0.15 - 45.5 - 
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表 2 锚杆抗力理论与试验结果对比
Table 2. Comparison of theoretical data with experimental results for rock bolt resistances
工况 试验值(kN) 文献(Ranjbarnia, 2022)(kN) 本文(kN) $ \alpha $=45°，φ=42.1° 30.4 29.1 31.8 $ \alpha $=60°，φ=38.7° 27.6 26.3 28.7 $ \alpha $=75°，φ=42.5° 25.6 23.1 26.7 $ \alpha $=90°，φ=36.4° 13.7 13.3 14.9
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