倾斜坡顶黄土边坡垂直裂隙深度计算方法

垂直裂隙在黄土层中发育极为普遍,为研究黄土边坡坡顶垂直裂隙深度的问题,改进传统裂隙法中存在的缺陷,分别建立单裂隙与多裂隙滑动模型,并结合边坡滑动后垂直裂隙后壁形成的垂直张拉段土体自稳特点,采用极限平衡法对2种滑动模型进行受力分析,建立边坡极限状态方程;并进一步利用最优值法对方程进行求解,推导出黄土边坡倾斜坡顶垂直裂隙极...

Calculation Method for the Vertical Crack Depth of a Loess Slope with an Inclined Crest

To study the depth of a vertical crack in a loess slope and improve the flaws in the traditional crack method, single- and multi-crack sliding models were established. In addition, the limit equilibrium method was used to analyze the stress of the sliding models, considering that the vertical tension section formed behind the crack could be stabilized after sliding. The calculation formula for the limit depth of the vertical crack on the top of the slope was derived by analyzing the limit state equation of the slope using the optimal value method. According to the calculation program, the variations in crack depth by the effects of different factors could be obtained. The upper-bound theorem of limit analysis and practical engineering examples were used to verify the formula. Results show that the limit depth of the vertical crack is twice that of the traditional crack depth for a single-crack slope and is independent of the slope inclination angle β. However, for a multi-crack slope, the limit depth of vertical cracks is more complex than that of a single-crack slope, where its value is related to the soil bulk density γ, cohesion c, internal friction angle φ, slope inclination angle β, and geological survey parameter L₂. The crack influence coefficient k_K decreases with an increase in β and increases with an increase in φ and γL₂/c, whereas the angle α between the sliding surface and horizontal plane increases with an increase in β and φ and decreases with an increase in γL₂/c. However, β has little influence on k_K and α. The accuracy of the formula is verified by the upper-bound theorem of limit analysis. With a sliding slope along the Huang-Yan Expressway taken as an example, the relative error between the calculation results and field measurement results is 3.76%, thus proving the reliability of the formula.