三轴试验中砂土刚度的统计和回归分析及应用

砂土的密度和应力状态对其刚度有很大的影响。计算岩土工程中许多硬化土体模型都是基于邓肯?张模型得出的，没有考虑到密度对砂土刚度的影响。而在极致密或松散的砂土的三轴压缩过程中，剪切应变的上升会引起密度的显著变化。为了评估粒径分布、密度及应力状态对砂土刚度的影响，使用统计和回归方法对来自莫斯科和明斯克的15个建筑工地的962个土壤样本的各向同性三轴试验数据进行分析。基于密度和应力状态参数的影响，提出了评估不同粒径砂土刚度的经验方程。对来自欧洲、印度和美国的冲积土和陆地土试验的比较分析表明，其砂土的刚度与莫斯科和明斯克的砂土在同一范围。所提出的方程可用于初步估计有限元法计算里的刚度参数，也可应用于岩土工程模型（允许考虑刚度的变化、水平和垂直分布）。此外，还提出了基于邓肯?张模型的半经验关系。当密度的变化影响土的刚度时，该半经验关系可为受到大变形和（或）复杂加载路径影响的松散和非常致密的砂土提供更为真实的结果。一般来说，岩土工程师可将获得的结果应用于更为复杂的土体模型设计中。

Statistical and regression analyses of sands stiffness in triaxial tests and application of the results

The density and stress state significantly impact on the sand stiffness. Many of hardening soil models used for geotechnical computation are based on Duncan-Chang model and do not consider the influence of density on the soil stiffness. In course of triaxial compression of very dense or loose sands, the shear strains rise induces significant changes in density. In order to evaluate the effects of grain size distribution, density, and stress state on stiffness, the results of 962 isotropic triaxial tests on soil samples from 15 Moscow and Minsk construction sites were processed using statistical and regression analysis. As a result, empirical equations enabling evaluation of the effects of density and stress state on stiffness of sands with different particle size distribution were proposed. Comparative analysis of tests performed on alluvial and continental soils from Europe, India, and the United States sites showed that the sand stiffness is in the same range as sands from Moscow and Minsk sites. Proposed equations can be applied for preliminary estimation of the stiffness parameters for finite element method calculation and also can be used in geotechnical models that allow variability, horizontal and vertical distribution of stiffness to be taken into account. Additionally, the semi-empirical relationship based on the Duncan-Chang model, is proposed. The relationship provides more realistic results for loose and extra dense sands affected by large deformations and/or complex loading paths, when the changes in density influence soil stiffness. Generally, geotechnical engineers may utilize the obtained results to apply them to design of complex soil models.