物质点强度折减法边坡失稳判据选择方法

蒋先平; 张鹏; 卢艺伟; 刘磊磊; 张明辉

doi:10.19509/j.cnki.dzkq.2021.0075

物质点强度折减法边坡失稳判据选择方法

doi: 10.19509/j.cnki.dzkq.2021.0075

蒋先平^1,,
张鹏^{2a, 2b},
卢艺伟¹,
刘磊磊^{2a, 2b, ,},
张明辉¹

基金项目:

国家自然科学基金青年基金项目 41902291

湖南省自然科学基金项目 2020JJ5704

中南大学中央高校基本科研业务费专项资金项目 2021zzts0810

详细信息

作者简介:
蒋先平(1980—)，男，高级工程师，主要从事复杂地质条件下的岩土工程设计方法方面的研究工作。E-mail: 41555767@qq.com

通讯作者:
刘磊磊(1987—)，男，副教授，主要从事地质灾害防治与风险控制方面的研究工作。E-mail: csulll@foxmail.com

中图分类号: P642.22
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出版历程
- 收稿日期: 2021-04-07

Slope failure criterion for the strength reduction material point method

Jiang Xianping^1
,,
Zhang Peng^{2a, 2b},
Lu Yiwei¹,
Liu Leilei^{2a, 2b
, ,},
Zhang Minghui¹

摘要

摘要: 用物质点强度折减法求解边坡安全系数时, 需要选择一定的失稳判据, 而采用不同的失稳判据获得的安全系数通常存在一定差异。为此, 采用物质点强度折减法对两个边坡算例进行了稳定性分析, 对比研究了文献中常用的4种边坡失稳判据(计算不收敛、特征点位移突变、塑性应变贯通及界限值判据)在计算边坡安全系数时的合理性及适用性。同时, 将Spencer极限平衡法获得的安全系数作为参考, 进一步验证了结果的合理性与准确性。结果表明: ①数值计算的收敛性不能作为边坡失稳判据; ②将特征点位移突变视为边坡失稳判据时, 获得的安全系数与极限平衡法获得的结果基本一致, 故特征点位移突变可以作为边坡失稳判据; ③塑性应变贯通和边坡最大位移随迭代时间步趋于稳定的界限值不宜单独作为边坡失稳判据。
- 边坡稳定性分析 /
- 物质点法 /
- 强度折减法 /
- 失稳判据 /
- 安全系数
Abstract: It is necessary to select an instability criterion for the material point strength reduction method (SRMPM) to solve the slope safety factor (F_s), and there are some differences in the obtained F_s values with different instability criteria. To examine the rationality and applicability of the four common instability criteria (i.e., calculation nonconvergence, displacement mutation of the feature point, transfixion of the plastic zone and the limit value), this paper uses the SRMPM to analyse the stability of two slope examples. The F_s obtained by the Spencer limit equilibrium method (LEM) is taken as a reference to further verify the rationality and accuracy of the results. The results show that ① the material point calculation is convergent, so the calculation nonconvergence cannot be used as the slope instability criterion; ② when the displacement mutation of the feature is regarded as the criterion of slope instability, the F_s is basically consistent with the LEM, so the displacement mutation of the feature point can be used as the slope instability criterion; and ③ the limit value and the transfixion of the plastic zone cannot be used alone as the slope instability criterion.
- slope stability analysis /
- material point method /
- strength reduction method /
- failure criterion /
- factor of safety

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图 1 算例1边坡几何尺寸

Figure 1. Slope geometry of example 1

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图 2 算例2边坡几何尺寸

Figure 2. Slope geometry of example 2

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图 3 边坡特征点位移随折减系数变化曲线

Figure 3. Variation curve of slope characteristic point displacement with reduction coefficient

下载: 全尺寸图片幻灯片

图 4 不同强度折减系数下的等效塑性应变区(算例1)

Figure 4. Equivalent plastic strain zone for different F_t values (example 1)

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图 5 不同强度折减系数下的等效塑性应变区(算例2)

Figure 5. Equivalent plastic strain zone for different F_t values (example 2)

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图 6 不同折减系数下计算时间步与特征点最大位移曲线

Figure 6. Curve of calculation steps and maximum displacement under different reduction coefficients

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图 7 同一折减系数下算例2边坡塑性应变随计算时间步分布图

Figure 7. Plastic strain zone with calculation steps for example 2 under the same reduction coefficient

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图 8 算例2边坡潜在滑动面

Figure 8. Potential sliding surface of example 2

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表 1 边坡基本计算参数

Table 1. Fundamental calculation parameters of slope

土体参数	算例1^[25]	算例2^[37]
重度γ/(kN·m^-2)	20	20
内摩擦角φ/(°)	12.38	20
黏聚力c/kPa	20	15
弹性模量E/kPa	100	100
泊松比υ	0.35	0.30
膨胀角ψ/(°)	0	9

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表 2 不同方法得到的安全系数

Table 2. F_s obtained by various methods

方法	算例1(F_s)	算例2(F_s)
Spencer极限平衡法	0.996^[38]	1.593
有限元法(塑性区贯通)	0.98^[38]	—
有限元法(位移突变)	0.99^[38]	1.60^[39]
有限元法(计算不收敛)	1.06^[38]	—

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表 3 不同折减系数下算例1和2边坡位移

Table 3. Displacement of example 1 and 2 for different F_t

	F_t	y_A，y_C/m	x_A, x_C/m	x_B, x_D/m
算例1	0.95	0.013	0.001	0.003
	0.96	0.014	0.002	0.003
	0.97	0.015	0.002	0.004
	0.98	0.016	0.003	0.004
	0.99	0.019	0.005	0.005
	1.00	0.026	0.010	0.008
	1.01	1.313	0.923	0.426
	1.02	1.384	0.977	0.169
	1.03	1.484	1.051	0.500
算例2	1.10	0.018	0.000	0.002
	1.20	0.019	0.000	0.003
	1.30	0.020	0.002	0.004
	1.40	0.020	0.003	0.005
	1.50	0.024	0.006	0.007
	1.60	0.028	0.012	0.016
	1.70	0.054	0.041	0.060
注：表中y_A和y_C分别为算例1和算例2的坡顶点竖向位移，x_A和x_C分别为算例1和算例2的坡顶点横向位移，x_B和x_D分别为算例1和算例2的坡脚点横向位移

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