Research on Slope Deformation Prediction Based on Fractional-Order Calculus Gray Model

Slope deformation prediction has important significance for slope prevention and control. Based on historical time series, the trend of displacement variation can be predicted in advance, and according to the development trend, risk warnings and treatment measures are proposed. The use of the mathematical model to predict slope deformation has been proved to be feasible by many studies; therefore, the choice of the predictive model and the practicability of the model are crucial issues in the prediction of slope deformation, and the mathematical prediction model used should be less complicated considering the practicality of the model. In view of slope deformation prediction, a fractional-order calculus gray model based on the coupling of gray theory and the fractional derivative method is proposed, which takes a deep foundation pit slope in Chongqing, Southwest China, as the study object. The fractional-order gray model is compared with the traditional gray models; therefore, the results show that the accuracy of slope deformation prediction based on the gray coupling model of cumulative displacement and fractional calculus is significantly higher than that of the conventional gray model, and its error is in the acceptable range compared with the actual monitoring data, which can meet the needs of engineering application. Compared with the traditional gray theory method, the gray coupling model of fractional-order calculus only increases the fractional derivative order, which is verified to be feasible, and can be used as a reference method for slope deformation prediction. It has a certain theoretical basis and a good application prospect in slope deformation prediction.