共振柱试验的非线性拟合研究
Study on Nonlinear Fitting Results of Resonant Column Test

土体动力参数是表征土动力特性的重要指标，对抗震计算具有重要影响。利用GCTS共振柱仪对淤泥、黏土、粉质黏土和粉砂进行共振柱试验，对Hardin—Drnevich提出的双曲线模型的模量比表达式进行线性拟合与改进的非线性拟合对比研究。结果表明：改进的非线性拟合得到的曲线较线性拟合曲线更加接近原始数据点；在低应变处，非线性拟合残差小于线性拟合残差，随着应变增加非线性拟合的残差接近线性拟合残差，在大应变处线性拟合残差小于非线性拟合的残差；改进的非线性拟合的最大动剪切模量Gdmax和参考剪应变γr的标准误差及置信区间宽度均比线性拟合的结果小；拟合优度评价指标表明改进非线性拟合效果优于线性拟合效果。将线性拟合结果作为非线性拟合方法的初始值的改进方法较线性拟合方法具有更高的准确性和稳定性，并具有更高的应用价值。
As important indexes for investigating soil dynamic characteristics, the dynamic parameters of soil play a significant role in seismic calculations. Using the GCTS resonant column device, resonant column experiments were carried out on silt, clay, silty clay, and silty sand. A comparative study was conducted on the modulus ratio expression of the hyperbolic model using a linear fitting method and improved nonlinear fitting method. The results show that the curves fitted by the nonlinear fitting method are closer to the original data points than the curves fitted by linear fitting method. In the low strain soil, the nonlinear fitting residual is less than the linear fitting residual, and with an increase of strain, the nonlinear fitting residual gets closer to linear fitting residual. In the large strain soil, the linear fitting residual is less than the nonlinear fitting residual. The standard error and confidence interval width of the maximum dynamic shear modulus Gdmax and reference shear strain γr, which was calculated by the nonlinear fitting method, are both smaller than the results calculated by the linear fitting method. The improved nonlinear fitting method has a higher accuracy, stability, and application value than the linear fitting method.