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Underground roadway excavation is a complex process, especially roadway curved excavation. In addition, the rationality of the design of coal mine roadway excavation scheme directly affects the speed of roadway excavation. The more reasonable the scheme design, the more conducive to rapid excavation. In order to avoid the influence of invalid construction on the efficiency of roadway excavation, this paper studies the forming of roadway bend. Based on the analysis of the tunneling process of the roadway curve, the mathematical model of the roadway curve is established. Taking the turning radius of the roadway curve as the evaluation index, the influence of various factors on the roadway curve excavation is analyzed. The research shows that the radius of the roadway curve increases with the increase of the feed rate, the working space position of the roadheader and the required width of the roadway, and decreases with the increase of the working space angle. Then, combined with the advantages of KNN algorithm, an interpolation model for calculating the radius of the curve is established based on RBF algorithm, and the radius of the tunnel curve is reconstructed and predicted. It provides a basis for the rational design of the construction process of the roadway bend and a reliable numerical algorithm for the design of the radius of the roadway bend. It also provides a theoretical basis for improving the efficiency of high roadway excavation in coal mines.