A composite foundation refers to an artificial foundation formed by strengthening or replacing part of the natural foundation during the foundation treatment process. In this type of foundation, both the foundation soil and the reinforcing material work together to bear the load. The strength and modulus of the reinforcing material are higher than those of the in situ soil. The reinforcing material is divided into horizontal and vertical components, with a vertical component being commonly referred to as a pile. One type of vertical reinforced composite foundation is the soil–cement mixed (SCM) pile composite foundation.
In the field of engineering construction, SCM piles have been extensively researched and utilized as one of the most efficient methods for strengthening soft soil foundations. They may also successfully minimize the settling of soft soil foundations. The prediction of the ultimate bearing capacity (UBC) of SCM pile composite foundations is one of the important applications in intelligent geotechnical engineering. Its accuracy can assist engineers in understanding the foundation’s bearing capacity under various conditions, thereby guiding the civil engineering design and construction processes to ensure the safety and stability of the project. The soil between the piles and the piles themselves constitute the final bearing capacity of an SCM pile composite foundation. The primary determinants are the characteristics of the pile (such as its length, diameter, spacing, and structural integrity), the soil properties in the vicinity, the rate of pile–soil interaction, and the thickness of the mattress. At present, the methods used for predicting the UBC of SCM pile composite foundations primarily consist of field experiments [
1], numerical simulations [
2,
3], and analytical calculations [
4]. Nevertheless, these approaches are plagued by issues such as high costs, lengthy durations, and low precision. As a result, a method for estimating the UBC of an SCM pile composite foundation can be identified. This method significantly reduces the need for labor and materials, while providing prediction accuracy that meets construction design requirements. Under flexible foundation loads, the bearing capacity of a composite foundation equals the bearing capacity of a single pile [
5]. At present, the methods used to predict carrying capacity include the Gaussian process regression prediction (GPR) [
6], BP neural network algorithm [
7,
8,
9,
10], support vector machine method [
11,
12], least square support vector machine method, random forest method (RF) [
13], polynomial regression method, and grey system method [
14], among others. However, each algorithm has certain limitations. The backpropagation neural network (BPNN) model is an intelligent information processing system with a strong nonlinear mapping capability. Through the learning and training of large-capacity samples, its strong self-adaptive learning ability can constantly adjust network parameters, providing significant advantages in addressing nonlinear problems. In fact, the determination of its weights and thresholds is random, which can affect the stability of training results, leading to a decrease in predictive performance. Nguyen et al. [
15] proposed a hybrid machine learning model for predicting the load–displacement characteristics of bored piles. They utilized 1650 sets of static load test sample data to establish the complex relationship between design parameters and the load–displacement response of piles. Furthermore, the reliability of the model was rigorously verified using independent datasets. Nguyen et al. [
16] utilized a feedforward neural network (FFNN) to investigate the ultimate axial bearing capacity of pre-stressed precast high-strength concrete (PHC) joint piles. They employed the regularization backpropagation technique (BRB) for network training, and the resulting output values closely matched the measured values, showcasing the robustness and reliability of the FFNN model. EL et al. [
17] developed a novel multi-hybrid optimization model based on Design of Experiments (DoE), which combined reverse-propagated neural networks and genetic algorithms (GAs) to optimize the parameters of a BP neural network and process parameters. Ren et al. [
18] developed a new technique for calculating the UBC of pile foundations by optimizing BPNN utilizing the adaptive genetic algorithm and the adaptive particle swarm optimization algorithm. Shen et al. [
19] proposed a new group optimization approach for microchannel resistance factor prediction by combining BP with the Particle Swarm Evolution (PSE) algorithm. Liu et al. [
20] combined the chaos optimization method and gradient descent method to create a novel search optimization method. They developed a prediction model for the bearing capacity of SCM pile composite foundations based on chaotic optimization and neural networks. This model demonstrates high prediction accuracy and is both simple and feasible. Nguyen et al. [
21] suggested a novel hybrid approach to estimate a pavement roughness index that combines several meta-heuristic optimization techniques, including the firefly algorithm, genetic algorithm, and particle swarm optimization. The approach is built on an adaptive network fuzzy reasoning system. The model was validated using the derived correlation coefficient and root-mean-square error with 2811 samples. Qi et al. [
22] developed an artificial neural network-based bearing capacity prediction model for CFG pile composite foundations using the BPNN model in the design and calculation of the piles’ bearing capacity. The anticipated bearing capacity value of the composite foundation reached the required accuracy during the network’s learning and training process. Chen et al. [
23] used a BPNN to predict the bearing capacity of rammed and expanded pile composite foundations and obtained satisfactory results after training the samples. However, the determination of BPNN weights and thresholds is random, which can affect the stability of training accuracy. Therefore, in this study, the weight and threshold are optimized using a hybrid optimization approach. The combined prediction model, incorporating optimal weights and thresholds, demonstrates high accuracy and stability.
This paper combines the IRMO algorithm with the SA algorithm and uses MATLAB R2018a software to design a hybrid meta-heuristic optimization algorithm, SA-IRMO, which has the advantages of both self-feedback and local jump. The built-in parameters (weights and thresholds) of BPNN are optimized by the SA-IRMO algorithm, and a prediction model of UBC for SCM pile composite foundations is established. The model can also be used to predict the UBC of other composite foundations. In this paper, static load test data of SCM pile composite foundations were collected for model training, verification and testing. The input parameters selected were pile length, pile diameter, pile spacing, cement incorporation ratio, pile soil replacement rate, mattress thickness, weighted average weight of soil around the pile, weighted average cohesion, and internal friction angle, and the output parameter was UBC. The input data were preprocessed (62 datasets after processing) and divided into training set/verification set/test set = 4:1:1 for training simulation. The predicted data were compared with the actual value, and the predicted results were in good agreement with a high degree of fitting (R = 0.9978). In order to prove the effectiveness of the established SA-IRMO-BPNN forecasting model, the research results were compared with other well-known UBC forecasting models, and the results of the prediction in this paper showed lower RMSE and MAE values and higher R and VAF values, indicating that the prediction performance of the model in this paper was better. At the same time, two sets of independent data from the literature were used to verify the performance of the model in this paper, and the verification results showed that the model in this paper had good performance. The research content of this paper is of great significance for guiding the civil engineering design and construction processes and determining the safety and stability of projects.