LIMIT ANALYSIS OF PERMANENT DISPLACEMENT FOR SLOPE CONSIDERING THE TENSILE STRENGTH OF SOIL
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摘要: 通过野外观测与室内试验发现，边坡后缘往往存在拉应力区。拉应力区的存在会影响边坡的稳定性，而地震荷载的存在会放大这种影响。分析拉应力区对边坡稳定性的影响，当前主要采用的方式为：对强度准则中抗拉强度进行折减（即张拉截断）。文章通过极限分析上限原理和拟静力法，推导出边坡临界加速度计算方程。以边坡在不同参数组合下的位移系数为基础，输入实测地震波，采用改进的Newmark法对边坡进行位移分析。文章算例的结果表明：拉应力区的存在会大大降低边坡临界加速度，土体在完全张拉截断下的临界加速度对边坡可能会产生超过50%的折减。拉应力区的存在也可以使永久位移达到传统的摩尔库伦理论计算值的2倍之多。文中所有的结果皆以图表形式展示，非常便于理解以及读取数据。Abstract: Through field observation and laboratory experiment, it is found that the stability of the slope is influenced by the existence of tensile stress zone in the back edge of the slope, while the influence is amplified by the existence of seismic load. To analyze the impact of tensile stress zone on the stability of slope, the main method used at present is to reduce the tensile strength in the strength criterion (i.e., tension cut-off). According to the upper limit principle of limit analysis and the quasi-static method, the calculation equation of the critical acceleration of the slope is derived. Based on the displacement coefficients of the slope under different parameter combinations, the measured seismic wave was input and the improved Newmark method was used to analyze the displacement of the slope. The results show that the critical acceleration of the slope can be greatly reduced by the existence of the tensile stress area, and the critical acceleration of the soil mass under the complete tension cut-off may produce more than 50% reduction of the slope. The existence of the tensile stress zone can also make the permanent displacement as much as twice the value calculated by the traditional Mohr-Coulomb yield criterion. All of the results in this article are presented in graphical form, which is very easy to understand and read.
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Key words:
- seismic load /
- limit analysis /
- tension cut-off /
- critical acceleration /
- permanent displacement
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图 1 不同破坏机制下的土体包络线
a—经典M-C包络线；b—土体张拉截断包络线；
c—完全张拉截断包络线；
$φ$—内摩擦角; c—粘聚力; σ—法向应力; τ—剪应力;
δ—破裂角; δu—法相速度分量; δw—水平速度分量;
ft、f3t—单轴抗拉强度; f′t—一维的部分折减的抗拉强度; fc—一维抗压强度Figure 1. Soil envelopes under different failure mechanisms
图 2 土体受张拉截断影响的边坡
H—坡高；Kh—水平向地震系数；δm—初始破裂角；mg—坡体重力；v—非连续速度
Figure 2. The slope with tension strength cut-off
图 3 不同参数下边坡临界加速度(张拉截断边坡中，抗拉强度系数ξ=0)
a—内摩擦角$φ$=10°下的坡体临界加速度；b—内摩擦 $φ$=20°下的坡体临界加速度；c—内摩擦角$φ$=30°下的坡体临界加速度
Figure 3. The critical accelerations of three slopes under different parameters (ξ=0 for full tension strength cut-off)
图 4 不同抗拉强度系数ξ对应的边坡临界加速度
Figure 4. The critical accelerations of the slope corresponding to different tensile strength coefficient ξ
图 5 二维张拉截断边坡旋转机制
a—坡体破坏机制；b—坡体位移原理图
Figure 5. The rotation mechanism of the slope with two-dimensional tnsion-cut off
图 6 不同抗拉强度系数ξ下的地震位移系数
a—临界加速度kc=0.1；b—临界加速度kc=0.2；c—临界加速度kc=0.3
Figure 6. Seismic displacement coefficients under different tensile strength coefficient ξ
图 7 El Centro Array站台记录Imperial Valley地震的水平分量
Figure 7. Horizontal components of Imperial Velley earthquake recorder by EI Centro Array Station
图 8 Imperial Valley地震的下的边坡永久位移
Figure 8. The corresponding earthquake-induced permanent displacements under Imperial Valley earthquake
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