Aiming at fully considering the influence of bolt length on stability of flysch layered slope, safety factors and failure modes of layered slope with different dip angles of bedding plane and equal-length bolts were analyzed by finite element limit analysis code Optum G2. Then bolt length distribution was optimized to obtain the bolt combination which has minimum total bolt length without reducing safety factor. The results show that as the bolt length increases from 1m to 28m, the safety factor of layered slope keeps constant first and then increases and finally keeps constant or increases first and then keeps constant. As the dip angle increases from 0° to 90°, the effective bolt length of layered slope increases first and then decreases and then increases. The maximum effective bolt length is 26m and the minimum one is 12m corresponding to slopes with 20° and 40° dip angles respectively. As the dip angle increases from 0° to 90°, the limit increase rate of safety factor increases first and then decreases and then increases, which ranges from 38% to 97%. As the bolt length increases from 1m to 28m, the movement of failure surface could divide into three stages: First, failure surface is same to that of slope without bolt. Second, failure surface moves deeper as bolt length increases. Third, failure surface changes from a deep one to a shallow one suddenly and then keeps unchanged. The critical bolt length of last two stages is the effective bolt length. Through the optimization of bolt length distribution, bolt materials could be saved with saving rates ranging up to 36%. The optimization result is closely related to the failure mode of slope without bolt. That means, the deeper the failure surface of the slope without bolt is, the longer optimized bolt needed to cross the failure surface is.


Flysch is a kind of marine sedimentary structure generating from the process of sedimentation, which is very common in Europe and south china. Flysch rock is a typical layered rock, which is generally composed of interlaced sandstone, shale and mudstone. Flysch rock has obvious layered structure and anisotropic characteristic and the soft rock in it such as mudstone is easy to be weathered by water and air (Jaeger, J. C. et al., 1960; Marinos, P. et al., 2001; Zhao, Z. et al., 2016; Wu, X. et al., 2017; Qiu, T. Q. et al., 2018). The layer structure and characteristic of easy-weathering make flysch layered slope have different stability and failure mechanism comparing with isotropic slope. Along the South-North Highway constructed by CRBC in Montenegro, there are 20 kilometers line crossing flysch area. The photos of flysch layered slopes in Montenegro are shown in Fig. 1.

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