Discussion of dislocation phenomena of resistance and load in formula for stability safety factor
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摘要: 岩土结构稳定安全系数应为抗力之和除以荷载之和。国内外相关标准中稳定安全系数计算公式存在着5类抗力与荷载错位、不符合安全系数定义现象：①条分法部分条块产生的抗滑力被计入了分母,如果与滑动力相减则形成第1类错位现象,相加则产生第2类；锚杆抗力切向分量被放在了分母中与滑动力相减亦形成第1类；②把水压力等荷载放在了分子与抗力相减,产生了第3类错位现象；第3类分别与第1,2类作用叠加,产生了第4,5类错位现象；③第1类与第3类造成安全系数计算结果虚高,导致工程有时安全储备不足；第2类造成安全系数虚低,可能会导致较大浪费；第4,5类加大了公式计算结果的不确定性,其中第4类会进一步造成安全系数虚高；④这些错位的计算公式可修正并概化为一个统一公式。Abstract: The stability safety factor of geotechnical structure shall be the sum of resistance divided by the sum of loads. There are five kinds of dislocation phenomena between resistance and load in the formula for calculating the stability safety factor in the worldwide relevant standards, and they are inconsistent with the definition of safety factor. (1) The anti-sliding force produced by some soil strips in the slice method is included in the denominator, and the first type of dislocation will be formed if it minuses the sliding force. The second type of dislocation will be formed if it pluses the sliding force. If the tangential component of anchor resistance is placed in the denominator to minus the sliding force, the first type of dislocation will be formed as well. (2) The third type of dislocation will be formed if water pressures and other pressures are placed in the numerator and subtracted from the resistance, and when the third type works together with the first and second types respectively, they result in the fourth and fifth types. (3) The first and third types result in a virtual height of safety factor calculation, which leads to insufficient safety in engineering sometimes. The second type results in a virtual lower safety factor, which may lead to great waste. The fourth and fifth types increase the uncertainty of calculated results, and the fourth kind will further cause the virtual height of safety factor. (4) These dislocated formulas can be modified and generalized into a unified formula.
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Keywords:
- stability safety factor /
- load /
- resistance /
- dislocation /
- slice method /
- sliding force
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图 5 基坑锚固条分法稳定分析简图
Figure 5. Stability analysis of anchorage foundation pits by slice method
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图 9 挡墙抗水平滑移稳定分析简图
Figure 9. Stability analysis of retaining walls against horizontal sliding
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图 11 锚固结构Kranz法稳定分析简图
Figure 11. Stability analysis of anchorage structures by Kranz method
表 1 K1=1.30时K0及δ1随n的变化
Table 1 Variation of K0 and δ1 with n while K1 = 1.30
n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 3.5 K0 1.30 1.27 1.24 1.22 1.20 1.18 1.17 1.16 1.15 1.14 1.13 1.05 δ1/% 0 3 5 7 9 10 11 12 13 14 15 23 
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表 2 K2=1.30时K0及δ1随n的变化
Table 2 Variation of K0 and δ1 with n while K2 = 1.30
n 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 K0 1.30 1.46 1.65 1.86 2.10 2.40 2.76 3.24 3.78 4.57 5.55 δ2/% 0 -11 -21 -30 -38 -46 -53 -60 -66 -72 -77
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表 3 K3=1.30时K0及δ3随n的变化
Table 3 Variation of K0 and δ3 with n while K3 = 1.30
n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 K0 1.30 1.27 1.23 1.19 1.16 1.13 1.10 1.08 1.05 1.02 1.00 δ3/% 0 3 6 9 12 15 18 21 24 27 30
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表 4 K4及K0随n的变化
Table 4 Variation of K4 and K0 with n
n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 K4 1.30 1.34 1.40 1.47 1.57 1.70 1.90 2.23 2.90 4.90 40.9 K0 1.30 1.28 1.26 1.25 1.24 1.23 1.23 1.22 1.22 1.22 1.21
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