基坑沉降预测的Logistic生长模型及其适用性研究

Applicability study on settlement prediction of foundation pit with Logistic growth model

基于基坑开挖沉降变形的特点,提出了基坑地面沉降的全过程及其发展可用Logistic生长模型来描述和预测。结合数理统计方法及原理,用线性回归方法获得了模型中的2个参数a,r,并比较了模型中参数K的3种估计方法。结合工程实例,应用结果表明:3种方法拟合参数较为接近,且精度都较高,其中以三点法最优。依据模型的数学意义,在基坑沉降发展的时间预测上,三点法和四点法较为接近,但预测效果差,而拐点法较前两者好。考虑到模型适用范围和预测精度等问题,根据混沌理论,研究了模型的适用范围和预测性能,当参数r(瞬时沉降速率)的取值范围在[0,2]之内,模型预测的最终沉降量是稳定的。

Based on settlement-deformation characteristics of foundation pit excavation, the settlement-time of foundation pit during the whole process of excavation can be described by Logistic model. Combined by statistic, two cocfl＇icients a, r in model are got by linear regression method and three methods for parameter K estimation of model are compared. According to practical engineering, and the application results indicated that three methods make good fitting precision, especially 3-peint method. According to mathematical meaning of model, yielding point method gives best evaluation in the case of settlement time-trend prediction, 3-point method has similar effect with 4-point method; however, the two are not better. Considering the range of applicability and prediction accuracy of model,the applicability and the prediction performance of the model are evaluated by using chaos theory. When parameter r, namely transient settlement rate, which is in the interval [0,2], the final settlement predicted by Logistic growth model is stable.