边坡稳定性联合评价方法

摘要: 借助MATLAB优化工具箱, 考虑土性参数变异性影响, 采用二次多项式序列响应面法求解边坡可靠指标和对应的安全系数, 并用可靠指标对应的失效概率对安全系数进行折减计算, 采用可靠指标与折减概率安全系数联合评价方法对边坡稳定性进行综合评价, 将计算结果和滑裂面图示与传统定值方法和二元指标方法的中值安全系数折减法进行对比分析。对比结果表明: 在土性参数变异性较大时, 即便传统定值方法计算出的安全系数明显大于1, 也会存在较大失稳风险; 但该方法利用失效概率对安全系数进行折减的过程, 实质是提取安全系数中可信部分的过程, 剔除了其中由于忽略不确定性因素而放大边坡稳定性的成分, 从而保证了评价结论的可靠性。
- 道路工程 /
- 边坡稳定性 /
- 安全系数 /
- 可靠指标 /
- 响应面法
Abstract: With MATLAB optimization toolbox, the parameter variability of soil was considered, the reliability index and corresponding safety factor of slope were computed by using response surface method(RSM)with quadratic sequence, and the safety factor was reduced by using the corresponding failure probability of the reliability index. A combined evaluation method, named reliability index and reduction safety factor evaluation method, was set up, the stability of slope was evaluated, and the calculation result and the failure surfaces obtained by the method were compared with the results obtained by traditional certification method and median reduction method of safety factor in dual index method. Comparison result indicates that slope may be unreliable with a safety factor(greater than 1)calculated by using traditional method when the parameter variability of soil is larger. In the present method, the reliable part of the safety factor is gotten by the reducing process, simultaneity, the unreliable part resulted from ignoring the uncertainty is deleted, so it can give a reasonable evaluation for practical slope.
- road engineering /
- slop stability /
- safety factor /
- reliability index /
- RSM

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图 1 例1参数与滑裂面

Figure 1. Parameters and slipping surfaces of example 1

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图 2 例2参数与滑裂面

Figure 2. Parameters and slipping surface of example 2

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表 1 例1计算参数

Table 1. Calculation parameters of example 1

土性参数		c/kPa	φ/(°)	γ/(kN·m^-3)
平均值		35.0	15.0	17.50
小变异情况	变异系数	0.1	0.1	0.02
小变异情况	标准差	3.5	1.535	0.35
大变异情况	变异系数	0.3	0.2	0.10
大变异情况	标准差	10.5	3.068	1.75

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表 2 例1计算结果

Table 2. Calculation result of example 1

坡度/(°)	坡高/m	变异性	β_min	F_{β_min}	F $_{β_{\min}}^{0}$	中值法F_min
20	10	小	8.080	2.451	2.451	2.577
	10	大	1.486	2.593	2.415	2.577
	20	小	5.657	1.699	1.699	1.808
	20	大	1.284	1.782	1.604	1.808
45	10	小	5.234	1.719	1.719	1.858
	10	大	0.913	1.737	1.423	1.858
	20	小	0.879	1.079	0.874	1.135
	20	大	0.169	1.079	0.612	1.135
60	10	小	4.099	1.488	1.488	1.759
	10	大	0.719	1.492	1.140	1.759
	20	小	5.01×10^-5	1.009	0.505	1.087
	20	大	9.99×10^-5	1.009	0.505	1.087

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表 3 例2计算参数

Table 3. Calculation parameters of example 2

土层	土性参数		c/kPa	φ/(°)	γ/(kN·m^-3)
上层土	平均值		40.00	18.00	17.64
	小变异情况	变异系数	0.06	0.08	0.01
	小变异情况	标准差	2.40	1.44	0.18
	大变异情况	变异系数	0.20	0.10	0.05
	大变异情况	标准差	8.00	1.80	0.88
下层土	平均值		8.00	30.00	21.56
	小变异情况	变异系数	0.06	0.08	0.01
	小变异情况	标准差	0.48	2.40	0.22
	大变异情况	变异系数	0.20	0.10	0.05
	大变异情况	标准差	1.60	3.00	1.08

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表 4 例2计算结果

Table 4. Calculation result of example 2

中值安全系数		F_min=1.249 0
变异性	β_min	F_{β_min}	F⁰_{β_min}	文献[7]
小	4.703 4	1.225	1.224 99	1.249 0
大	1.746 4	1.037	0.995 10	1.249 0
注: 文献[[7]]为利用二元指标体系方法计算得到的安全系数值。

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参考文献(11)

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