考虑阻尼修正的Pyke滞回模型研究

Modified Pyke's hysteretic model considering damping ratio

阻尼比反映了土体滞回耗能的特性,是土的重要动力特性参数。土的滞回本构模型能同时真实反映土的动剪模量衰减和阻尼比非线性变化特性,是保证场地及土–结构体系动力响应分析精确度的关键。针对经典的Pyke滞回本构模型,基于文献实测的动剪模量曲线和阻尼比曲线,研究了其对土体阻尼比的预测精确度,发现Pyke模型在大应变幅值时将显著高估土的阻尼比。针对此缺陷,结合前人提出的基于阻尼的滞回曲线方程和Pyke模型加卸载准则,提出了考虑阻尼修正的D-Pyke滞回模型。该模型假设双曲线形滞回曲线的饱满程度由形状系数确定,而后者则由当前加载曲线的滞回应变幅值所对应的实测阻尼比确定。滞回曲线的应变幅值与应力幅值之间通过骨架曲线相互关联,而应力幅值则由Pyke所建议的加卸载准则确定。通过针对粉质黏土的循环单剪试验结果,验证了D-Pyke模型相比于Pyke模型能够更为合理地同时模拟土的非线性动剪模量和阻尼比特性。模型同时继承了Pyke模型能更好地模拟土的循环加载棘轮效应、加卸载准则简单的优点,可为随机动力荷载作用下土体响应问题分析提供合理的本构行为模拟。

The damping ratio is a dynamic soil property that indicates the capacity of energy dissipation under cyclic loadings, and it plays an important role in dynamic response analysis of sites and soil-structure systems. Based on the dynamic shear modulus curves and damping ratio curves in the references, the accuracy of damping ratio predicted by Pyke’s model is studied, and it is found that the predicted damping ratio by Pyke’s model largely exceeds the measured damping ratio in the range of large strain amplitude. A modified Pyke’s model for accurate simulation of damping ratio of soils, named as D-Pyke model, is proposed, which combines the damping ratio-based hysteretic curve equations with the unloading-reloading rules of the original Pyke’s model. The new model assumes that the fullness of the hyperbolic hysteresis curve is determined by the shape-factor that is determined from the experimental damping ratio curves according to the shear-strain amplitude of the current hysteretic loading curve. The shear-strain amplitude of the current hysteretic loading curve is calculated from the shear-stress amplitude based on the skeleton curve of soils, and the shear-stress amplitude is determined according to Pyke’s rules. Based on the results of cyclic simple shear tests on a silty clay, it is verified that the D-Pyke model simulates the nonlinear shear modulus and damping ratio properties more reasonably than the original Pyke’s model. The D-Pyke model inherits the advantages of Pyke’s model, i.e., it simulates well the ratcheting effects of soils under cyclic loadings, and it obeys simple unloading/reloading criteria under irregular loadings. The proposed model can provide a more reasonable constitutive simulation method for the analysis of soil response under stochastic loading.