基于“S-指数”数学模型的建筑地基沉降预测研究

Research on prediction of building foundation settlement based on S-exponential mathematical model

对建筑地基的沉降趋势进行了分析和预测,首先分析了建筑地基的沉降规律,之后将常用的Logistic曲线(S曲线)模型与指数曲线模型进行优化,提出了'S-指数'数学模型,并从数学角度对模型进行了理论分析,最后基于建设综合勘察研究设计院有限公司提供的实测沉降数据对模型进行了数值验证。数值实验结果显示,'S-指数'模型的数据拟合效果较好,相关系数平均为0.9965,相对误差平均为0.4855%,将该模型与S曲线模型、指数曲线模型进行对比,其拟合精度更高、预测结果更符合实际,表明该模型的适应性更强,可在实际建筑工程中用于地基沉降安全诊断和趋势预测。

The settlement trend of the building foundation is analyzed and forecasted.Firstly,the settlement law of building foundation is analyzed.Secondly,the mathematical model of'S-exponential'is put forward,which is optimized by the Logistic curve(S curve)model and the exponential curve model,and the theoretical analysis of the model is carried out from the mathematical point of view.Finally,the numerical verification of the model is conducted based on the measured settlement data provided by the CIGIS(CHINA)LIMITED.The experimental results of the measured data show that the data fitting effect of the'S-exponential'model is better,the correlation coefficient is 0.9965 and the average relative error is 0.4855%.The model is compared with the S curve model and the exponential curve model.The accuracy of the model is higher and the prediction results are more practical.It shows that the model is more adaptable and can be used for the foundation settlement safety diagnosis and trend prediction in the actual construction engineering.