# Prediction of Pile Axial Bearing Capacity Using Artificial Neural Network and Random Forest
## 1 Introduction  
In applied engineering, piles have been used as the foundation elements, in which the axial bearing capacity of the pile (P\({}_{\text{u}}\)) is considered as the most important parameter in the design of pile foundation. Normally, the axial bearing capacity of piles can be determined by five approaches, namely the static analysis, dynamic analysis, dynamic testing, pile load testing, and in-situ testing [1]. Out of these methods, the pile load test is considered as the best method to determine the pile bearing capacity. However, such a method is time-consuming, and the costs are often difficult to justify for ordinary or small projects, whereas other methods have lower accuracy. As a result, several approaches have been developed to predict the axial bearing capacity of pile or to enhance the prediction accuracy. The nature of these methods included some simplifications, assumptions, or empirical approaches with respect to the soil stratigraphy, soil-pile structure interactions, and the distribution of soil resistance along the pile. In such studies, the test results were used as complementary elements to improve the prediction accuracy. Meanwhile, the European standard (Euro code 7) [2] recommends using the following ground field tests: DP (dynamic probing test), SS (press-in and screw-on probe test), SPT (standard penetration test), PMT (pressure meter tests), PLT (plate loading test), DMT (flat dilatometer test), FVT (field vane test), CPTu (cone penetration tests with the measurement of pore pressure). Among the above indicators, the SPT is commonly used to determine the bearing capacity of piles [3]. Several propositions relying on the results of SPT have been proposed to predict the bearing capacity of piles, including the empirical equations derived from the works of [PERSON] [4], [PERSON] and [PERSON] [5], [PERSON] [6], [PERSON] and [PERSON] [7], [PERSON] et al. [8]. In general, the pile diameter, SPT blow counts along the pile shaft, and at the tip of the pile have been used in these equations. Besides, [PERSON] and [PERSON] [9] proposed a formula to estimate the pile bearing capacity for different types of soil, namely sand, and silt. [PERSON] [10] has presented an empirical formula, including the adjustment factors for sandy and clay soils. Last but not least, the Architectural Institute of Japan (AIJ) [11] has a recommendation using an experimental formula, taking into account the effects of soil type or the use of SPT value for sandy soil and untrained shear strength of soil (C\({}_{\text{u}}\)) for clayey soil. Overall, traditional methods or empirical equations attempted to include a few key parameters to predict the pile strength. However, if the input parameters of pile geometry and soil properties increased, these methods were impossible to use. In recent years, a widespread development in the use of information technology in civil engineering has paved the way for many promising applications, especially the use of machine learning (ML) approaches to solve practical engineering problems [12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. Moreover, different ML techniques have been used, for instance, decision tree [22], hybrid artificial intelligence approaches [23; 24; 25], artificial neural network (ANN) [26; 27; 28; 29; 30; 31], adaptive neuro-fuzzy inference system (ANFIS) [32; 33], and support vector machine (SVM) [34] in solving many real-world problems, including the prediction of behavior of piles. Precisely, [PERSON] et al. [35] developed a K-nearest neighbors (KNN) model to estimate the soil parameters required for foundation design. In another work, [PERSON] et al. [36; 37] presented an ANN model to predict the friction capacity of driven piles in clays, which was trained by on-field data records. Besides, [PERSON] et al. [38; 39; 40; 41] developed an ANN model for driven piles and drilled shafts using a series of in-situ load tests as well as CTP results. [PERSON] et al.