## 1 Introduction  
Soil compaction is important for rapid urban and industrial development. Rolling dynamic compaction (RDC) has been found to be useful for the compaction of soils and is now widely used globally [1]. It involves towing a non-circular module, whose designs have three, four, or five sides, behind a tractor. As the module rotates, it imparts energy and compacts the soil as it falls to the ground [2]. Compared with a conventional smooth drum roller, RDC is able to compact soil to deeper depths (>3 m) with a relatively faster speed [3]. Hence, RDC is extensively used in civil engineering construction, including situ densification of existing fills, airports and land reclamation projects, reconstruction of rural roads, and in the mining and agricultural sectors [4; 5; 6; 7; 8]. To assess the effectiveness of RDC, many researchers have conducted field tests of soil settlement [9], soil pressure [10], and vector velocities of the rolling module [11]. Due to the fact that some measurements are difficult to realize or are not fully controlled in field tests, physical scale model tests have been utilized to quantify the performance of RDC with respect to various soil types, roller speeds, and masses [3; 12]. Although model tests are more controllable than field tests, small-scale model tests are still impaired by scaling and boundary effects [13]. To complement field and modeling tests, several researchers have developed numerical models to assess the effectiveness of RDC [2; 14; 15; 16; 17]. [PERSON] et al. [14] investigated the behavior of a full-size RDC model using the finite element method (FEM). The numerical results were validated against field results, and they showed encouraging results in terms of simulating soil responses induced by RDC. Nevertheless, since the FEM model is based on continuum rather than particulate analysis, soil particles are difficult to simulate. In order to overcome the limitations of the FEM, several researchers have switched to the discrete element method (DEM) to mimic the behavior of granular materials [18; 19; 20]. [PERSON] et al. [15; 16; 17] developed a FEM-DEM-based model to simulate the behavior of the RDC of three-sided and four-sided impact rollers. In addition, machine learning algorithms were applied to the study of RDC in some works. [PERSON] et al. [21; 22] suggest an approach to predict density improvement at a specified depth below ground level due to RDC based on artificial neural networks. Despite this research, there is still a dearth of prediction studies of soil settlements induced by RDC. Settlement prediction in a large-construction project is an important issue for rapid and cost-effective construction. Since machine learning algorithms have proven to be efficient and reliable tools for solving complex geotechnical engineering issues, they have been employed in recent years as prediction models in subterranean geotechnical applications. Many scholars have attempted to predict soil settlements. [PERSON] et al. [23] used a genetic algorithm (GA) back-analysis method to predict the settlement of multi-layered thick, soft soil. [PERSON] et al. [24] combined a threshold regression (TR) theory approach with an improved support vector machine (SVM) to establish a dam top settlement prediction model. [PERSON] et al. [25] used the sinusoidal algorithm (SA) to optimize a regularized extreme learning machine (RELM) in order to develop a prediction model for ground settlement around a foundation pit. However, existing researches cannot be applied to the prediction of settlement induced by RDC due to the large variation in the effectiveness of different foundation improvement methods. In addition, RDC can cause uneven settlement of soils, which may be detrimental torprojects. It is evident that it is necessary to establish an effective prediction method for soil settlements induced by RDC.