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Stability analysis of complex double-sided slope
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摘要: 实际工程中边坡常呈现出复杂的几何结构，利用有限元强度折减法讨论了3种边界条件下凹凸坡结构和不同坡度组合情况双面边坡的安全系数和破坏特性，并与单面平直边坡进行对比分析。研究发现：在本次计算条件下，双面边坡垂直放坡时，单面平直边坡的安全系数大于凸坡；对于凸坡其他情况，全约束边界条件下安全系数最大，与平直边坡相比提高了约3%。所有形式的凹坡的安全系数均大于平直边坡，其中，全曲面凹坡在全约束边界条件下安全系数提高了近10%，约为其余形式凹坡的2倍。当双面边坡横纵坡度不等时，边坡沿危险坡面产生滑移，决定边坡整体稳定性的因素为较陡的坡度；坡度相等时，边界条件对双面边坡破坏模式的影响较为明显，不同边界条件将导致边坡不同的破坏形态，在半约束条件下，双面边坡只沿法向约束一侧产生滑移破坏，而另外两种约束条件下，其破坏区域均为对称形状。Abstract: In practice, slopes often have complex geometries. Therefore, the 3D finite element analysis with strength reduction method was used to study the safety factors and failure characteristics of double-sided slopes which have concave or convex structures with different gradient combinations under three boundary conditions, and the results are compared with those of flat slopes. It is shown that comparing with the flat slope, the safety factor of the convex vertical side slope is less than that of the flat slope. For other convex slopes, the safety factor under rough-rough boundary condition is increased by about 3%. However, for concave slopes, the safety factor is higher than that of the flat slope, and the safety factor of the curved surface slope with 1∶2 gradient under rough-rough boundary condition is the largest, and is higher than that of the flat slope by nearly 10%, and about twice as much as that of other structure of concave slopes with the same gradient. When the gradients of two sides are different, the slope will slip along the side with the large slope angle. When the gradients of two sides are equal, the slope failure area is affected by the boundary condition type. Under smooth-rough conditions, the sliding failure occurs on the constrained side, while under the other two boundary conditions, the failure area is symmetrical.
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Key words:
- double-sided slope /
- concave-convex structure /
- gradient /
- boundary condition /
- stability
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图 3 形式1边坡在3种边界条件下的安全系数
Figure 3. Safety factors of the 1st slope under three boundary conditions
图 4 形式2，3和4边坡在3种边界条件下的安全系数
Figure 4. Safety factors of the 2nd, 3rd and 4th slopes under three boundary conditions
图 5 凸边坡与单面平直边坡安全系数关系
Figure 5. Relationship between the safety factors of the convex and single-sided straight slopes
图 6 凹边坡与单面平直边坡安全系数关系
Figure 6. Relationship between the safety factors of the concave and single-sided straight slopes
图 7 全约束边界条件下4种形式边坡的等效位移云图
Figure 7. Displacement zone of four slopes under rough-rough boundary condition
图 8 全约束边界条件下5种工况边坡的等效位移云图
Figure 8. Displacement zone of five cases under rough-rough boundary condition
图 9 纵向坡度与边坡安全系数的关系曲线
Figure 9. Relationship between longitudinal gradient and safety factor
图 10 纵向坡度与
$\left( {{F_{\rm s{\text{凹}}/{\text{凸}}}} - {F_{\rm s{\text{直}}}}} \right)/{F_{\rm s{\text{直}}}} \times 100$ %的关系曲线Figure 10. Relationship between
$\left( {{F_{\rm s{\text{凹}}/{\text{凸}}}} - {F_{\rm s{\text{直}}}}} \right)/{F_{\rm s{\text{直}}}} \times 100 \%$ and longitudinal gradient
图 11 纵向坡度与
$ \left(F_{\rm S R / R R}-F_{\rm S S}\right) / F_{\rm S S} \times 100 \% $ 的关系曲线Figure 11. Relationship between
$ \left(F_{\rm S R / R R}-F_{\rm S S}\right) / F_{\rm S S} \times 100 \% $ and longitudinal gradient
图 12 不同约束条件下边坡的位移云图
Figure 12. Displacement zone of slopes under different boundary conditions
表 1 边坡体边界类型对应的约束情况
Table 1. Boundary conditions of slopes
平面 SS SR（凸） SR（ 凹） RR（凸） RR（凹） X=0 法向约束 法向约束 法向约束 法向约束 固定约束 X=W1+S+W2 法向约束 固定约束 法向约束 固定约束 法向约束 Y=0 法向约束 法向约束 固定约束 法向约束 固定约束 Y= W1+S+W2 法向约束 法向约束 法向约束 固定约束 法向约束 Z=0 固定约束 固定约束 固定约束 固定约束 固定约束 
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