基于多元线性回归模型的冻土强度影响因素 显著性分析

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。

Significant analysis of the influence factors on strength of frozen soil base on multivariable linear regression model

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.