The precise estimation and forecast of the safety factor (SF) in civil engineering applications is considered as an important issue to reduce engineering risk. The present research investigates new artificial intelligence (AI) techniques for the prediction of SF values of retaining walls, as important and resistant structures for ground forces. These structures have complicated performances in dynamic conditions. Consequently, more than 8000 designs of these structures were dynamically evaluated. Two AI models, namely the imperialist competitive algorithm (ICA)-artificial neural network (ANN), and the genetic algorithm (GA)-ANN were used for the forecasting of SF values. In order to design intelligent models, parameters i.e., the wall thickness, stone density, wall height, soil density, and internal soil friction angle were examined under different dynamic conditions and assigned as inputs to predict SF of retaining walls. Various models of these systems were constructed and compared with each other to obtain the best one. Results of models indicated that although both hybrid models are able to predict SF values with a high accuracy and they can be introduced as new models in the field, the retaining wall performance could be properly predicted in dynamic conditions using the ICA-ANN model. Under these conditions, a combination of engineering design and artificial intelligence techniques can be used to control and secure retaining walls in dynamic conditions.

Seepage is one of the most challenging issues in some procedures such as design, construction, and operation of embankment or earth fill dams. The purpose of this research is to develop a new solution based on governing equations to solve the seepage problem in an effective way. Therefore, by implementing the equations in the programming environment, more than 24,000 models were designed to be applicable to different conditions. Input data included different parameters such as slopes in upstream and downstream, embankment width, soil permeability coefficient, height, and freeboard. With the use of this big data, a new process was developed to provide simple mathematical models for the seepage rate analysis. The study first used intelligent models to simulate the seepage behavior. Finally, the accuracy of the models was optimized using a new metaheuristic algorithm. This led to the ultimate flexibility of the final model presented as a new solution capable of evaluating different conditions. Finally, using the best model, new mathematical relationships were developed based on this methodology. This new solution can be used as a proper alternative to the governing equations of seepage rate estimation. Another advantage of the proposed model is its high flexibility that can be well applied to engineering design in this field, which was not possible using the initial equations.

This research focuses on developing hybrid intelligence techniques to predict the bearing capacity of circular foundations using the most effective parameters. In this regard, a database involving 968 test circular foundations involving different rock properties, soil characteristics, and foundation radius has been prepared by laboratory tests for training and testing the new model presented in this study. For adequately considering various factors, the several parameters of depth (D) in m, density of soil (DS) in gr/cm³, internal angle of friction (IAF) in degree, cohesion of soil (CS) in kg/cm², and foundation radius (FR) in m were considered as the input of the model and bearing capacity in kg/cm² was considered as the target parameter. Three main strategies were addressed in this study. First, four well-known machine learning algorithms, Artificial Neural Network (ANN), Bagging Regressor (BR), Least Squares Support Vector Machine (LSSVM), and Gradient Boosting Regressor (GBR), were adopted to predict bearing capacity. Second, a novel and robust mathematical computation named dimensional analysis (DA) theorem was integrated with machine learning techniques to improve the accuracy and performance of the models by decreasing the number of inputs. Third, based on DA implementation, a rational mathematical formula using gene expression programming (GEP) was structured to anticipate bearing capacity. Furthermore, the sensitivity analysis process specified the impact of the five effective factors. The results of this study demonstrate the effectiveness of integrating DA with machine learning models to predict the BC of circular foundations. Among the developed models, the DA-LSSVM model showed superior performance, achieving an R² of 0.998 and 0.996 for training and testing, respectively, indicating high prediction accuracy. The results indicated that the IAF was the most sensitive factor with r = 0.709, while CS was the least sensitive with r = -0.087. A graphical user interface (GUI) app has been designed to apply the proposed models in this study conveniently. In the last step of this process, the GUI and the DA-based machine learning models were implemented by analyzing two examples. According to the findings, the GUI may be employed to make a reliable and speedy projection of the bearing capacity of circular foundations by considering a variety of input parameters.