三维加筋边坡地震稳定性上限分析

基于极限分析上限定理,考虑均匀加筋和三角形加筋两种加筋模式,采用拟静力分析方法推导了一定边坡高度条件下的三维加筋边坡临界加筋强度的计算公式。通过与已有文献结果的对比,验证了所提方法的正确性,并讨论了边坡宽高比、水平和竖向地震力系数对三维边坡稳定性的影响。结果表明:地震力作用下边坡临界加筋强度随边坡宽高比的增大而增加,但其变化速率逐渐减小,当边坡宽高比大于10时,三维边坡加筋强度与二维情况相近;随着水平地震作用的增大,三维边坡临界加筋强度呈非线性增大;随着竖向地震作用的增大,临界加筋强度大致呈线性增加,且随着坡角的增大,竖向地震作用对临界加筋强度的影响更加显著;两种加筋模式下的边坡临界加筋强度值变化规律一致,且三角形加筋模式所需的加筋强度较小,效果较优。最后,针对实际工程提出了一些工程建议。

Upper bound analysis of seismic stability of 3D reinforced slopes

Based on the upper bound theorem of limit analysis, the stability of the three-dimensional reinforcement slopes was investigated by using the pseudo-static analysis method under the horizontal and vertical seismic forces. Both uniform reinforcement and triangular reinforcement patterns were considered, and analytical expression was derived to calculate the required critical reinforcement strength to prevent the failure of reinforced slopes. The validity of this method was verified by comparing with the results of existing literature, and the effects of the ratio of slope width to height and horizontal and vertical seismic force coefficients on the stability of three-dimensional reinforced slopes were discussed. The results show that with the increase of the ratio of slope width to height, the critical reinforcement strength of the slopes increases under seismic forces, but the changing rate gradually decreases. When the ratio of slope width to height is larger than 10, the critical reinforcement strength of the 3D slopes is similar to that of the 2D cases. With the increase of horizontal seismic force, the critical reinforcement strength of 3D slopes increases nonlinearly. While, with the increase of vertical seismic force, the value of the critical reinforcement strength increases approximately linearly. In addition, with the increase of slope angle, the effect of vertical seismic force on the critical reinforcement strength becomes more significant. The changing rule of the critical reinforcement strength under two reinforcement modes is consistent. Moreover, the stability values of triangular reinforcement mode is always smaller than that of uniform reinforcement mode, and is more conducive to maintaining the stability of the slopes. Finally, some engineering suggestions are proposed for practical projects.