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The present study addresses optimal design of reinforced concrete (RC) columns based on equivalent equations considering deformability regulations of ACI318-14 under axial force and uniaxial bending moment. This study contrary to common approaches working with trial and error approach in design, at first presents an exact solution for intensity of longitudinal reinforcement in column section by solving equivalent equation. Then, longitudinal and transverse reinforcement details are assessed regarding the previous step results and where achieving the lowest steel consumption design in the column is selected as the optimum. In addition to optimizing column cross-section dimension by implementing single-variable optimization methods, the effect of axial force, bending moment and concrete compressive strength variations on the column cross-section dimension, intensity of longitudinal reinforcement, construction costs and total weight of consumption steel have been investigated. The investigation on the validity of the proposed method was assessed and signified through comparison with the existed work in the literature. Finding an exact solution considering all regulations and constraints is the advantage of this method in determining optimized RC column.

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Predicting the bearing capability (q_rs) of geogrid-reinforced stone columns poses a significant challenge due to variations in soil and rock parameters across different locations. The behavior of soil and rock in one region cannot be generalized to other regions. Therefore, accurately predicting q_rs requires a complex and stable nonlinear equation that accounts for the complexity of rock engineering problems. This paper utilizes the Rock Engineering System (RES) method to address this issue and construct a predictive model.To develop the model, experimental data consisting of 219 data points from various locations were utilized. The input parameters considered in the model included the ratio between geogrid reinforced layers diameter and footing diameter (d/D), the ratio of stone column length to diameter (L/dsc), the q_rs of unreinforced soft clay (qu), the thickness ratio of Geosynthetic Reinforced Stone Column (GRSB) and USB to base diameter (t/D), and the settlement ratio to footing diameter (s/D). Following the implementation of the RES-based method, a comparison was made with other models, namely linear, power, exponential, polynomial, and multiple logarithmic regression methods. Statistical indicators such as root mean square error (RMSE), mean square error (MSE), and coefficient of determination (R2) were employed to assess the accuracy of the models. The results of this study demonstrated that the RES-based method outperforms other regression methods in terms of accuracy and efficiency.