基于相关函数理论的动模量和阻尼比计算新方法

基于相关函数理论，提出一种新的计算动三轴试验动模量和阻尼比的方法。假设土体为黏弹性体，采用自相关函数分析应力、应变波形的平均幅值，进而计算动模量；采用互相关函数分析应变滞后于应力时程波形的相位差，进而计算阻尼比。利用饱和珊瑚砂、南京细砂和原状粉质黏土的不排水应变控制分级循环加载试验数据，分析结果表明：动模量和阻尼比计算的相关函数法对不同土样具有普适性；应变幅值小于1×10?4时，相关函数法计算动模量及阻尼比的精度明显优于传统的滞回圈法；应变幅值大于1×10?3时，土体呈现强非线性特性，应力-应变滞回圈不对称，相关函数法计算的阻尼更为可靠。

An new method for calculation of dynamic modulus and damping ratio based on theory of correlation function

Based on the theory of correlation function, a new method for calculating the dynamic modulus and damping ratio of dynamic triaxial test is proposed. Based on viscoelastic constitutive model, the amplitudes of strain and stress can be captured by analyzing the autocorrelative function of strain and stress variations with time, respectively. Thus, the dynamic modulus can be calculated. The damping ratio is determined through the characterization of the phase lag between the strain and stress time-histories which can be captured by the cross-correlation function. A series of undrained multistage strain-controlled cyclic triaxial test was conducted on saturated coral sand, Nanjing fine sand, and a type of undisturbed silty clay. The dynamic modulus and damping ratios were calculated from the experimental results using both the correlation function (CF) method and the conventional hysteresis loop (HL) method. The results show that the CF method is applicable for the calculation of dynamic modulus and damping ratio of different types of soils. The results show that the precision of the CF method for the modulus and damping ratio is significantly higher than that of the HL method within the strain amplitude of 1×10?4. When the strain amplitude is greater than 1×10?3, because of the strong nonlinearity of soil as well as the asymmetry of the stress-strain hysteresis loop, the damping ratio of soil calculated by the CF method is more reliable.