The geometric dimensions and bank profile shape of channels with boundaries containing particles on the verge of motion (threshold channels) are significant factors in channel design. In this study, extensive experimental work was done at different flow velocities to propose a reliable method capable of estimating stable channel bank profile. The proposed method is based on gene expression programming (GEP). Laboratorial datasets obtained from Mikhailova et al. (Hydro Tech Constr 14:714–722, 1980), Ikeda (J Hydraul Div ASCE 107:389–406 1981), Diplas (J Hydraul Eng ASCE 116:707–728, 1990) and Hassanzadeh et al. (J Civil Environ Eng 43(4):59–68, 2014) were used to train, test, validate and examine the GEP model in various geometric and hydraulic conditions. The obtained results demonstrate that the proposed model can estimate bank profile characteristics with great accuracy (determination coefficient of 0.973 and mean absolute relative error of 0.147). Moreover, for practical calculations of channel dimensions, the model provides a specific mathematical relationship to solve problems with different discharge rates (Q) and particles with various median grain sizes (D ). The proposed model’s performance is compared with 8 relationships suggested previously by researchers (based on empirical and theoretical analyses) and a relationship obtained using a nonlinear regression model with different experimental data. The polynomial VDM and two exponential functions, i.e. IKM and DIM, are introduced as the superior existing models. According to the present study results, the proposed GEP model can predict the bank profile shape trend well and similar to the experimental datasets. Sensitivity analysis was also applied to assess the impact of each input variable (x, Q and D 50 ) on the presented relationship. According to the current study, the GEP model provides a suitable equation for predicting the bank profile shape of stable channels.

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