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振动波在土介质中传播包含呈幂函数关系的几何衰减和呈指数函数关系的阻尼衰减两方面,针对振动波衰减的两种性质,提出Hyperbola-Logistic组合模型来描述振动波沿地表的传播。实例分析表明,Hyperbola-Logistic组合模型既可以用来预测地面位移、速度、加速度及振级的衰减,又可以预测高架桥段、路堤段及地下列车引起的地面振动。Hyperbola-Logistic组合模型具有较高的拟合精度,相关系数R均在0.95以上,决定系数R2均在0.90以上,它对振动衰减的拟合是可信的。通过对比,文中模型无论数值大小还是分布趋势,都能更好地预测列车引起的地面振动。
According to the two properties of vibration wave attenuation, the vibrational wave propagates in the soil medium including the geometric attenuation in the power function relationship and the damping attenuation in exponential relation. The Hyperbola-Logistic model is proposed to describe the propagation of the vibration wave along the surface. The case study shows that the Hyperbola-Logistic model can be used to predict the ground displacement, velocity, acceleration and vibration attenuation as well as ground vibration caused by viaduct section, embankment section and underground train. The Hyperbola-Logistic model has higher fitting accuracy, the correlation coefficient R is above 0.95 and the coefficient of determination R2 is above 0.90, which is credible for the fitting of vibration attenuation. By comparison, the model in this paper can better predict the ground-induced vibration caused by trains, regardless of the magnitude of the values or distribution trends.