| Multi-frame foundation beam with anchor bolts has been widely used in high slope engineering in red beds soft rock as a flexible retaining structures. Under earthquake action, the structure has good supporting effect. Based on a high slope engineering of express highway in Suining-Ziyang-Meishan, Sichuan Province, China, dynamic response of side slopes which reinforced by the multi-frame foundation beam with anchor bolts and failure mode are analyzed through numerical simulation. And then using the limit analysis, safety factor of the anchored slope and the corresponding potential slip surface are deduced. The permanent displacement of the anchored slope is figured out by using Newmark’s sliding block analysis method. Specifically, the main contents and research results are as follows:(1) Numerical simulation of FLAC3D method is carried out to analyze the laws of the dynamic responses of multi-bench high slopes. And laws of the dynamic feature of multi-frame foundation beam with anchor bolts are obtained by analyzing PGA, the stress state in slope body, the maximum shear strain increment, and the horizontal displacement under earthquake action. This paper reveals seismic wave characteristics as the amplitude, the frequency spectrum, the duration and the vertical value of seismic wave, which affect the supporting results of the multi-bench framed anchor under earthquake action. Anchor length, anchor diameter, anchor angle, and the spacing of frame beam on the slope supporting effects under earthquake action are also analyzed detailedly, and it indicates that the optimal anchor length is 10 m (0.1g amplitude) and 12m (0.2g amplitude). It shows that there is optimal dip angle of anchor, and the spacing of the beam out of plane is 3m but the spacing in plane is 2.5m.(2) According to the plastic limit analysis upper bound theorem, the mathematic expression of the safety factor and yielding acceleration of slope supported by the structure are deduced as per the analysis of the energy consumption for the logarithmic spiral and straight line sliding surface, respectively. Safety factors of the anchored slopes calculated by plastic limit analysis are close to those of pseudo-static approach. The safety factors are linearly increasing with design axial force of anchor bolt growing; approximately linearly reducing with the increasing of anchors’dip angle; approximately linearly increasing with the increasing of platform’s width; linearly increasing with the increasing of slope’s cohesion force; approximately exponentially increasing with the increasing of internal friction angle; nonlinearly decreasing with the increasing of horizontal seismic action’s acceleration factor; and approximately linearly increasing with the increasing of vertical seismic action’s acceleration factor. Generally, five elements have the most prominent influence on slope’s safety factor. They are the designing axial force of anchors, width of platform, the cohesion of slope, the internal friction angle of slope, and the acceleration factor of horizontal seismic action.(3) Based on the concept of yielding acceleration speed, the permanent displacement of the high slope reinforced by multi-frame foundation beam with anchor bolts is deduced. The rationality is verificated by numerical simulation and the Ambraseys’ multiple regression method.This study draws some conclusions about dynamic response of side slopes reniforced by multi-frame foundation beam with anchor bolts and calculation method of safety factor and permanent displacement of the anchored slope. It can provide theoretical guidances and references for aseismic design of high slope strengthened by the structure. |
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