Sensitivity analysis method of swelling of paleo-clay based on rough set theory and response surface method
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摘要: 评价老黏土膨胀性等级时出现的误差主要源于多因素在参数统计上的不确定性，对此提出老黏土膨胀敏感性分析方法。结合粗糙集理论分析各因素的敏感性并确立主导因素，进而构建老黏土膨胀性等级的多因素定量评价模型，随后通过响应面法，分析主导因素间参数不确定性的交互作用对评价结果的影响。襄阳城区老黏土研究表明，自由膨胀率和体缩率为影响评价结果的主导与次主导因素，二者参数变化产生的交互作用对膨胀性评价等级影响较显著。当体缩率统计值较大时，随着自由膨胀率的上升，膨胀性评价等级变幅较大，偏大的自由膨胀率将高估老黏土的膨胀性，致使评价过于保守，偏小的自由膨胀率则会对其低估，导致结果较不可信；而当体缩率统计值较小时，评价等级随自由膨胀率的上升变化不大，因此评价结果较为准确。所得结论可为老黏土膨胀性评价与分类工作提供参考。Abstract: The error in evaluating the swelling grade of paleo-clay is mainly due to the statistical uncertainty of many factors.Therefore, a sensitivity analysis method for the swelling of old clay is proposed.Based on rough set theory, this paper analyzes the sensitivity of various factors to the swelling properties of paleo-clay and establishes the dominant factors, and then constructs a multi-factor quantitative evaluation model for the swelling properties of paleo-clay.Subsequently, the influence law of the interaction between dominant factors on the evaluation grade is analyzed.The study of the paleo-clay in Xiangyang urban area shows that the free expansion rate and the volume shrinkage rate are the dominant and secondary dominant factors affecting the expansion evaluation, and the interaction between the change of two has a significant impact on the expansion evaluation grade.When the statistical value of volume shrinkage rate is large, as the free expansion rate rises, the swelling evaluation grade changes greatly.A large free expansion rate may overestimate the swelling of the paleo-clay, causing the evaluation to be too conservative, and the free expansion rate is too small.The expansion rate may be underestimated, resulting in less credible results; when the statistical value of volume shrinkage rate is small, the expansion evaluation grade does not change much with the increase of the free expansion rate, so the evaluation result more accurate.The conclusions obtained can provide references for the evaluation and classification of paleo-clay swelling.
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Key words:
- paleo-clay /
- swelling /
- uncertainty /
- rough set theory /
- response surface method /
- sensitivity analysis
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图 3 模糊评价值的预测值与实际值分布图
Figure 3. Distribution diagram of predicted and actual values for fuzzy evaluation value
图 4 自由膨胀率与线缩率的交互作用响应图
a.AB响应面; b.AB等高线
Figure 4. Response graph of interaction between free expansion rate and linear shrinkage rate
图 5 自由膨胀率与体缩率的交互作用响应图
a.AB响应面; b.AC等高线
Figure 5. Response graph of interaction between free expansion rate and volume shrinkage rate
图 6 线缩率与体缩率的交互作用响应图
a.BC响应面; b.BC等高线
Figure 6. Response graph of interaction between linear shrinkage rate and volume shrinkage rate
表 1 老黏土试样物理指标
Table 1. Indices of physical properties for paleo-clay
土样编号 W/% Fs/% WL/% Ip δsi/% δv/% TY01 24.20 49.7 41.0 19.2 4.07 17.2 TY02 24.80 49.7 38.6 16.2 6.07 16.7 TY03 24.16 52.4 39.0 16.7 4.50 17.7 TY04 24.80 45.0 35.9 15.9 4.78 15.9 TY05 25.6 58.3 42.5 19.0 5.61 18.7 TY06 25.31 60.0 39.7 17.1 5.20 15.0 TY07 25.10 45.0 40.5 16.1 4.10 16.2 TY08 24.66 42.3 37.7 20.0 4.68 18.2 TY09 24.52 34.0 34.1 14.5 2.50 7.4 TY10 28.10 76.0 52.5 23.5 6.50 19.2 注：W.天然含水量；Fs.自由膨胀率；WL.液限；Ip.塑性指数；δsi.线缩率；δv.体缩率；下同 
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表 2 试样数据离散规则
Table 2. The rule of data discretization
分类标准 非膨胀 弱膨胀 中膨胀 强膨胀 1 2 3 4 WL/% ≤40 40~45 45~50 50~60 Ip ≤10 10~18 18~25 25~32 Fs/% ≤40 40~65 65~90 90~115 δv/% ≤8 8~16 16~23 23~30 δsi/% ≤2 2~5 5~8 8~11 W/% 45~55 35~45 25~35 ≤25
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表 3 物理指标离散元数值
Table 3. Discrete element values of physical properties
土样编号 W/% Fs/% WL/% Ip δsi/% δv/% TY01 4 2 2 3 2 3 TY02 4 2 1 2 3 3 TY03 4 2 1 2 2 3 TY04 4 2 1 2 2 2 TY05 3 2 2 3 3 3 TY06 3 2 1 2 3 2 TY07 3 2 2 2 2 3 TY08 4 2 1 3 2 3 TY09 4 1 1 2 2 1 TY10 3 3 4 3 3 3
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表 4 隶属函数边界值
Table 4. Rule of data discretization
边界值 σ1 σ2 σ3 σ4 WL/% 40 45 50 60 Ip 10 18 25 32 Fs/% 40 65 90 115 δv/% 8 16 23 30 δsi/% 2 5 8 11
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表 5 老黏土膨胀性评价标准
Table 5. Evaluation standard for expansion degree of paleo-clay
D 评价等级 D 评价等级 1.00~1.25 非膨胀 2.50~2.75 中主弱次 1.25~1.50 非主弱次 2.75~3.25 中膨胀 1.50~1.75 弱主非次 3.25~3.50 中主强次 1.75~2.25 弱膨胀 3.50~3.75 强主中次 2.25~2.50 弱主中次 3.75~4.00 强膨胀
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表 7 响应面试验变量与水平
Table 7. Factors and levels of response surface test
因素 水平 -1 0 1 A-Fs/% 34 55 76 B-δsi/ % 2.5 4.5 6.5 C-δv/% 7.4 13.3 19.2
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表 8 响应面试验设计与结果
Table 8. Design and results of response surface test
方案 Fs/% δsi/ % δv/% D 1 34 4.5 7.4 1.767 2 34 2.5 13.3 1.799 3 76 6.5 13.3 2.664 4 55 2.5 19.2 2.270 5 55 4.5 13.3 2.153 6 55 4.5 13.3 2.153 7 76 2.5 13.3 2.375 8 55 6.5 19.2 2.560 9 55 2.5 7.4 1.820 10 55 4.5 13.3 2.153 11 76 4.5 7.4 2.257 12 55 4.5 13.3 2.153 13 34 6.5 13.3 2.098 14 76 4.5 19.2 2.769 15 55 4.5 13.3 2.153 16 34 4.5 19.2 2.210 17 55 6.5 7.4 2.112
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表 9 响应面模型的方差分析
Table 9. Variance analysis of response surface model
来源 平方和 自由度 均方和 F值 P值 模型 1.23 9 0.14 649.86 < 0.000 1 A-Fs 0.60 1 0.60 2 860.28 < 0.000 1 B-δsi 0.17 1 0.17 815.19 < 0.000 1 C-δv 0.43 1 0.43 2 043.41 < 0.000 1 AB 2.5×10-5 1 2.5×10-5 0.12 0.740 1 AC 1.2×10-3 1 1.2×10-3 5.77 0.047 3 BC 1.0×10-6 1 1.0×10-6 4.8×10-3 0.946 9 A2 0.021 1 0.021 99.84 < 0.000 1 B2 4.6×10-4 1 4.6×10-4 2.19 0.182 4 C2 3.1×10-3 1 3.1×10-3 14.68 0.006 4 R2=0.998 8 RAdj2=0.997 3 RPred2=0.980 9
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