分段多项式拟合在动三轴试验数据处理中的应用

The application of piecewise polynomial fitting for processing cyclic triaxial testing data

动三轴采集的试验数据点(剪应变与动剪模量和阻尼比之间)具有离散性和有限性,为方便应用需要对数据点进行拟合,但现有经验公式不一定很好吻合试验数据。为得到不同剪应变与对应的动剪模量和阻尼比之间的关系,本文利用最小二乘原理,对渤海某海洋平台地基土进行动三轴试验获得的动剪模量、阻尼比与剪切应变的数据进行了分段多项式的拟合。数据处理过程是先对剪应变值进行了压缩处理,然后再分段低次多项式拟合,得到多项式拟合参数。通过此项改进解决了正规方程解中的病态问题,且拟合效果良好。

The recorded data by cyclic triaxial testing are discrete and limited, the relationships of data need to be fitted for easy use, however the present expirical equation is not available for testing data. To obtain the value of shear modulus and damping ratio for different shear strain, the piecewise polynomial fitting method is applied to normalized shear modulus and damping ratio versus shear strain based on least-square principle. The value of shear strain is converted to avoid the equation set ill-conditioned due to the great difference in shear strain magnitude. The fitting results is satisfactory by using the piecewise lower polynomial order fitting.