基于Davidenkov骨架曲线的土体动力本构关系及其参数研究

以描述土体一维动应力-应变幅值关系的Davidenkov骨架曲线为基础,采用Mahing法则,构造了土体加载再卸载的一维动应力-应变关系滞回曲线;采用破坏剪应变幅上限值作为分界点,对Davidenkov骨架曲线用分段函数法进行修正,纠正了Davidenkov骨架曲线随着剪应变幅值的增大而不能趋近于破坏剪应力上限值的缺点;对修正后的Davidenkov骨架曲线和所构造的加载再卸载一维动应力-应变关系滞回曲线,推导了阻尼比的计算公式。讨论了Davidenkov模型参数值的变化对动剪切模量比G/Gmax–γ曲线和阻尼比D–γ曲线形状的影响规律,提出了综合考虑土的G/Gmax–γ和D–γ试验曲线的Davidenkov模型参数拟合方法,并采用该方法给出了南京及其邻近地区各类土的G/Gmax–γ和D–γ曲线的Davidenkov模型参数的拟合值,结果表明:与常规拟合法的拟合结果相比,本文拟合法对G/Gmax–γ和D–γ试验曲线的拟合结果更加合理,尤其是阻尼比D–γ试验曲线的拟合结果。

Developed nonlinear dynamic constitutive relations of soils based on Davidenkov skeleton curve

Based on Davidenkov skeleton curve of the one dimensional dynamic stress-strain relation, the dynamic shear stress-strain curves were constituted by using Mashing rules. The Davidenkov skeleton curve was corrected by using sectional functions, and the upper limit of failure shear strain amplitude was used as the sectional point. The modified skeleton curve could approach the upper limit of failure shear stress when shear strain amplitude approached infinite. The equations used to calculate damping ratio were derived. The effects of fitting parameters A, B and γ 0 on the curves of dynamic shear modulus ratio and damping ratio versus shear strain amplitude(G/Gmax–γ and D–γ ) were studied systematically. Based on these studies, a new fitting method was suggested to fit the tested G/Gmax–γ and D–γ curves. It is obvious that the new fitting method is better than the current methods to fit the tested G/Gmax–γ and D–γ curves of soils in Nanjing city. The reference values of fitting parameters A, B and γ 0 are given to fit the G/Gmax–γ and D–γ curves of soils tested by free vibration column apparatus.