基于多元线性回归模型的冻土强度影响因素显著性分析
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摘要
为定量分析土质、含水率、温度和应变速率等因素对冻土强度的影响,本文根据公开发表的试验数据,应用多元线性回归模型对冻土强度影响因素进行了显著性分析。分析结果表明,在仅考虑线性影响条件下,温度和土性是影响冻土强度的主要因素,影响强度分别为0.632和0.193,含水率对冻土强度也有显著性影响,影响强度为-0.577。为探明各影响因素对冻土强度的非线性作用,在保留强度Taylor展开二次项的条件下,通过变量代换,将非线性项进行线性化,并利用多元线性回归模型进行了进一步分析。分析结果表明含水率与温度对冻土强度的影响包含线性、非线性和交叉影响项三项,应变率对冻土强度的影响仅包含非线性和交叉影响项。各因素对冻土强度的影响程度可用偏回归系数定量描述。
To quantitative analyze the impact of soil type, moisture content, temperature and strain rate, etc. on strength of frozen soil, a significance analysis of influence factors on strength of frozen soil was carried out with multiple linear regression models based on the published experimental data in this study. The results show that the main factors influencing the strength of frozen soil are temperature and soil property, with the impact intensity of 0.632 and 0.193, respectively, when considering linear effect only. Moisture content also has significant effect with the intensity of-0.577. In order to investigate the nonlinear effect of the impact factors on strength of frozen soil, the nonlinear term is linearized by variable substitution under the condition of retaining second order of Taylor expansion of strength, and the multiple linear regression model is used to analyze furtherly. The analytical results show that the impacts of moisture content and temperature on the strength of frozen soil include linear, nonlinear and cross impacts, while the strain rate on strength contains only nonlinear and cross impacts. The impact intensity of the factors on the strength of frozen soil could be quantitatively described by partial regression coefficient.
To quantitative analyze the impact of soil type, moisture content, temperature and strain rate, etc. on strength of frozen soil, a significance analysis of influence factors on strength of frozen soil was carried out with multiple linear regression models based on the published experimental data in this study. The results show that the main factors influencing the strength of frozen soil are temperature and soil property, with the impact intensity of 0.632 and 0.193, respectively, when considering linear effect only. Moisture content also has significant effect with the intensity of-0.577. In order to investigate the nonlinear effect of the impact factors on strength of frozen soil, the nonlinear term is linearized by variable substitution under the condition of retaining second order of Taylor expansion of strength, and the multiple linear regression model is used to analyze furtherly. The analytical results show that the impacts of moisture content and temperature on the strength of frozen soil include linear, nonlinear and cross impacts, while the strain rate on strength contains only nonlinear and cross impacts. The impact intensity of the factors on the strength of frozen soil could be quantitatively described by partial regression coefficient.
引文
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[12] Ma Wei,Wu Ziwang,Chang Xiaoxiao,et al.Strength characteristics of frozen soil under high confining pressure[J].Journal of Glaciology and Geocryology,1996,18(3):268-272.[马巍,吴紫汪,常小晓,等.高围压下冻结砂土的强度特性[J].冰川冻土,1996,18(3):268-272.]
[13] Ma Wei,Wang Dayan,Chang Xiaoxiao.Stress-strain modeling for frozen soils subjected to K0 consolidation under various confining pressures[J].Progress in Natural Science,2004,14(3):344-348.[马巍,王大雁,常小晓.模拟K0固结后不同初始围压下冻土应力-应变特性研究[J].自然科学进展,2004,14(3):344-348.]
[14] Xu Xiangtian,Bai Ruiqiang,Lai Yuanming,et al.Experimental study on mechanical properties of saline frozen silty sand[J].Journal of China Coal Society,2016,41(4):836-842.[徐湘田,白瑞强,赖远明,等.含盐冻结粉质砂土力学性质的试验研究[J].煤炭学报,2016,41(4):836-842.]
[15] Xu Xiangtian,Lai Yuanming,Dong Yuanhong,et al.Laboratory investigation on strength and deformation characteristics of ice-saturated[J].Cold Regions Science and Technology,2011,69(1):98-104.
[16] Hu Kai,Chen Xiaoqing.Experimental study on the effect of nano-silicon on frozen clay sand strength[J].Journal of Glaciology and Geocryology,2017,39(3):602-608.[胡凯,陈晓清.纳米硅对冻结黏性砂土强度影响试验研究[J].冰川冻土,2017,39(3):602-608.]
[17] Li Shunqun,Gao Lingxia,Chai Shouxi.Significance and interaction of factors on mechanical properties of frozen soil[J].Rock and Soil Mechanics,2012,33(4):1173-1177.[李顺群,高凌霞,柴寿喜.冻土力学性质影响因素的显著性和交互作用研究[J].岩土力学,2012,33(4):1173-1177.]
[18] Zhang Zhaotai.The mechanical properties tests in deep frozen soil and calculation of frozen wall[D].Huainan:Anhui University of Science and Technology,2006:38-40.[张照太.深土冻土力学性能试验研究及工程应用[D].淮南:安徽理工大学,2006:38-40.]
[19] Li Haipeng,Lin Chuannian,Zhang Junbing,et al.Uniaxial compressive strength of saturated frozen clay at constant strain rate[J].Chinese Journal of Geotechnical Engineering,2004,26(1):105-109.[李海鹏,林传年,张俊兵,等.饱和冻结黏土在常应变率下的单轴抗压强度[J].岩土工程学报,2004,26(1):105-109.]
[20] Chang Xiaoxiao,Ma Wei,Sheng Yu,et al.Effects of experimental conditions on mechanical index of frozen soils[J].Journal of Glaciology and Geocryology,1995,17(Suppl 1):151-155.[常小晓,马巍,盛煜,等.试验条件对冻土力学指标的影响[J].冰川冻土,1995,17(增刊1):151-155.]
[2] Ma Qinyong.Tensile strength,uniaxial compressive strength test on artificially frozen soils[J].Rock and Soil Mechanics,1996,17(3):76-81.[马芹永.人工冻土单轴抗拉、 抗压强度的试验研究[J].岩土力学,1996,17(3):76-81.]
[3] Sun Xingliang,Wang Ren,Hu Mingjian,et al.Triaxial strength and deformation properties of frozen silty clay under low confining pressure[J].Rock and Soil Mechanics,2005,26(10):102-106.[孙星亮,汪稔,胡明鉴,等.低围压下冻结粉质粘土的三轴强度及变形分析[J].岩土力学,2005,26(10):102-106.]
[4] Chang Xiaoxiao,Ma Wei,Wang Dayan.Study on the strength of frozen clay at high confining pressures[J].Journal of Glaciology and Geocryology,2007,29(4):636-639.[常小晓,马巍,王大雁.高围压下冻结粘土的抗压强度试验研究[J].冰川冻土,2007,29(4):636-639.]
[5] Chen Youliang,Wang Ming,Xu Shan,et al.Tensile and compressive strength tests on artificial frozen soft clay in Shanghai[J].Chinese Journal of Geotechnical Engineering,2009,31(7):1046-1051.[陈有亮,王明,徐珊,等.上海人工冻结软黏土抗压抗拉强度试验研究[J].岩土工程学报,2009,31(7):1046-1051.]
[6] Huo Ming,Wang Shuangjie,Zhang Jinzhao,et al.Experimental study on influences of water content and temperature on mechanical properties of ice-rich frozen soil[J].Journal of Hydraulic Engineering,2010,39(10):1165-1172.[霍明,汪双杰,章金钊,等.含水率和温度对高含冰量冻土力学性质的影响[J].水利学报,2010,39(10):1165-1172.]
[7] Cai Zhengyin,Wu Zhiqiang,Huang Yinghao,et al.Experimental study on the factors influencing the uniaxial compressive strength of frozen soil[J].Journal of Glaciology and Geocryology,2015,37(4):1002-1008.[蔡正银,吴志强,黄英豪,等.冻土单轴抗压强度影响因素的试验研究[J].冰川冻土,2015,37(4):1002-1008.]
[8] Huang Xing,Li Dongqing,Ming Feng,et al.Experimental study of the compressive and tensile strengths of artificial frozen soil[J].Journal of Glaciology and Geocryology,2016,38(5):1346-1352.[黄星,李东庆,明锋,等.冻土的单轴抗压、 抗拉强度特性试验研究[J].冰川冻土,2016,38(5):1346-1352.]
[9] Niu Jiangyu,Jin Pengwei,Li Dongwei,et al.Study of the uniaxial compressive strength of frozen saline sandy soil[J].Journal of Glaciology and Geocryology,2015,37(2):428-433.[牛江宇,靳鹏伟,李栋伟,等.冻结盐渍砂土单轴强度特性研究[J].冰川冻土,2015,37(2):428-433.]
[10] Cai Zhengyin,Wu Zhiqiang,Huang Yinghao,et al.Influence of water and salt contents on strength of frozen soils[J].Chinese Journal of Geotechnical Engineering,2014,36(9):1580-1586.[蔡正银,吴志强,黄英豪,等.含水率和含盐量对冻土无侧限抗压强度影响的试验研究[J].岩土工程学报,2014,36(9):1580-1586.]
[11] Li Hongsheng,Yang Haitian,Chang Cheng,et al.The strain rate sensitivity analysis of compression strength of frozen soil[J].Journal of Glaciology and Geocryology,1995,17(1):40-48.[李洪升,杨海天,常成,等.冻土抗压强度对应变速率敏感性分析[J].冰川冻土,1995,17(1):40-48.]
[12] Ma Wei,Wu Ziwang,Chang Xiaoxiao,et al.Strength characteristics of frozen soil under high confining pressure[J].Journal of Glaciology and Geocryology,1996,18(3):268-272.[马巍,吴紫汪,常小晓,等.高围压下冻结砂土的强度特性[J].冰川冻土,1996,18(3):268-272.]
[13] Ma Wei,Wang Dayan,Chang Xiaoxiao.Stress-strain modeling for frozen soils subjected to K0 consolidation under various confining pressures[J].Progress in Natural Science,2004,14(3):344-348.[马巍,王大雁,常小晓.模拟K0固结后不同初始围压下冻土应力-应变特性研究[J].自然科学进展,2004,14(3):344-348.]
[14] Xu Xiangtian,Bai Ruiqiang,Lai Yuanming,et al.Experimental study on mechanical properties of saline frozen silty sand[J].Journal of China Coal Society,2016,41(4):836-842.[徐湘田,白瑞强,赖远明,等.含盐冻结粉质砂土力学性质的试验研究[J].煤炭学报,2016,41(4):836-842.]
[15] Xu Xiangtian,Lai Yuanming,Dong Yuanhong,et al.Laboratory investigation on strength and deformation characteristics of ice-saturated[J].Cold Regions Science and Technology,2011,69(1):98-104.
[16] Hu Kai,Chen Xiaoqing.Experimental study on the effect of nano-silicon on frozen clay sand strength[J].Journal of Glaciology and Geocryology,2017,39(3):602-608.[胡凯,陈晓清.纳米硅对冻结黏性砂土强度影响试验研究[J].冰川冻土,2017,39(3):602-608.]
[17] Li Shunqun,Gao Lingxia,Chai Shouxi.Significance and interaction of factors on mechanical properties of frozen soil[J].Rock and Soil Mechanics,2012,33(4):1173-1177.[李顺群,高凌霞,柴寿喜.冻土力学性质影响因素的显著性和交互作用研究[J].岩土力学,2012,33(4):1173-1177.]
[18] Zhang Zhaotai.The mechanical properties tests in deep frozen soil and calculation of frozen wall[D].Huainan:Anhui University of Science and Technology,2006:38-40.[张照太.深土冻土力学性能试验研究及工程应用[D].淮南:安徽理工大学,2006:38-40.]
[19] Li Haipeng,Lin Chuannian,Zhang Junbing,et al.Uniaxial compressive strength of saturated frozen clay at constant strain rate[J].Chinese Journal of Geotechnical Engineering,2004,26(1):105-109.[李海鹏,林传年,张俊兵,等.饱和冻结黏土在常应变率下的单轴抗压强度[J].岩土工程学报,2004,26(1):105-109.]
[20] Chang Xiaoxiao,Ma Wei,Sheng Yu,et al.Effects of experimental conditions on mechanical index of frozen soils[J].Journal of Glaciology and Geocryology,1995,17(Suppl 1):151-155.[常小晓,马巍,盛煜,等.试验条件对冻土力学指标的影响[J].冰川冻土,1995,17(增刊1):151-155.]
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