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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 the characteristics of settlement and deformation of foundation pit excavation, the whole process of foundation pit ground subsidence and its development can be described and predicted by Logistic growth model. Combined with the mathematical statistics method and principle, the two parameters a and r in the model were obtained by linear regression, and three kinds of estimation methods of the parameter K in the model were compared. Combined with engineering examples, application results show that the fitting parameters of the three methods are relatively close, and the precision is high, of which the three-point method is the best. According to the mathematical meaning of the model, the three-point method and the four-point method are close to each other in time prediction of foundation pit settlement, but the prediction effect is poor, while the inflection point method is better than the former two. Considering the problems such as the scope of the model and the accuracy of the prediction, the applicability and prediction performance of the model are studied according to the chaos theory. When the range of the parameter r (instantaneous sedimentation rate) is within [0, 2], the final model prediction The settlement is stable.