Evolution Stage Division of Landslide Based on Analysis of Multivariate Time Series
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摘要: 滑坡的时间-位移曲线一般具有3个阶段特征，即初始变形阶段、等速变形阶段和加速变形阶段，不同演化阶段加速度具有不同的变化特点.目前往往是依据对加速度曲线特征的分析来人为划分演化阶段，缺少相应的理论支持和定量计算.针对上述问题，选取月降雨量、月库水位高程变化量对滑坡的累计位移建立多因素的时间序列预测模型.然后利用Chow分割点检验理论，以所建模型中F和LR统计量最大值点作为分割点对滑坡演化阶段进行划分.以新滩滑坡和三峡库区白水河滑坡为例，利用累计位移、降雨及库水位变化数据进行计算验证.结果表明，对多元时间序列模型进行Chow分割点检验可对滑坡的演化阶段进行准确划分，为滑坡的临滑预警预报提供重要判据.Abstract: Curves of cumulative displacement vs. time of the landslide generally include the stages of the initial deformation, constant speed deformation and accelerated deformation. Different deformation stages have their own different acceleration characteristics. Now the evolution of landslide can be divided by analyzing the characteristics of acceleration curve. But it lacks theoretical basis and quantitative calculation. To the above problems, the rainfall of current month and reservoir level fluctuation of current month are selected as influencing factors, and the multivariate time series model is adopted to predict the cumulative displacement. Taking the maximum points of F statistic and log-likelihood ratio statistic of the multivariate time series model as segmentation points divides the evolution stages of landslide based on the theory of Chow breakpoint test. This model is used to deal with the data of cumulative displacement, rainfall and reservoir level fluctuation of Xintan landslide and Baishuihe landslide in the Three Gorges reservoir area. The results indicate that the Chow breakpoint test on the multivariate time series prediction model based on the inducing factors and the landslide displacement has certain validity and application value. This division of the landslide evolution stage can provide an important criterion for the early-warning prediction of landslide.
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图 7 白水河滑坡ZG118监测点累计位移-时间曲线
Fig. 7. Accumulated displacement-time curve of monitoring point ZG118 of Baishuihe landslide
图 8 白水河滑坡库水位高程监测曲线
Fig. 8. Curve of reservoir level elevation vs. time of Baishuihe landslide
图 9 白水河滑坡ZG118监测点加速度-时间曲线
Fig. 9. Acceleration-time curve of monitoring point ZG118 of Baishuihe landslide
表 1 新滩滑坡F统计量和LR统计量值
Table 1. F statistic and log-likelihood ratio statistic values of Xintan landslide
月份 F统计量 相应概率值P LR统计量 相应概率值P 1979-10 2.31 0.0371 4.80 0.0302 1979-11 2.39 0.0346 4.95 0.0280 1979-12 2.33 0.0364 4.84 0.0297 1981-12 5.62 0.0056 11.00 0.0041 1982-01 5.92 0.0044 11.53 0.0031 1982-02 5.94 0.0043 11.58 0.0031 1982-03 6.06 0.0039 11.80 0.0027 1982-04 6.25 0.0033 12.13 0.0023 1982-05 6.25 0.0033 12.13 0.0023 1982-06 6.28 0.0032 12.19 0.0023 1982-07 6.05 0.0039 11.77 0.0028 1982-08 6.97 0.0018 13.40 0.0012 1985-05 4.68 0.0092 9.24 0.0099 
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表 2 白水河滑坡F统计量和LR统计量值
Table 2. F statistic and log-likelihood ratio statistic values of Baishuihe landslide
月份 F统计量 相应概率值P LR统计量 相应概率值P 2004-08 15.88 0.0000 34.45 0.0000 2004-09 9.40 0.0001 23.95 0.0000 2004-10 5.22 0.0049 15.12 0.0017 2004-11 5.98 0.0024 16.89 0.0007 2004-12 6.05 0.0023 17.06 0.0007 2005-01 6.16 0.0021 17.30 0.0006 2007-02 6.10 0.0019 17.23 0.0006 2007-03 6.26 0.0016 17.61 0.0005 2007-04 9.32 0.0001 24.08 0.0000 2007-05 11.17 0.0000 27.53 0.0000 2007-06 13.82 0.0000 32.04 0.0000 2007-07 6.26 0.0016 17.61 0.0005
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