Advances in Numerical Computation and Mathematical Modeling for Geotechnical Engineering

1. Introduction

The field of geotechnical engineering is experiencing a transformative period driven by the increasing complexity of in situ projects and the need for operations in challenging geological environments [1,2,3,4]. As engineering activities extend into deeper strata and more complex geological conditions, practitioners face unprecedented challenges, including groundwater seepage control, dynamic rock mass failure analysis, geothermal effects on rock stability, and microseismic monitoring [5,6,7,8,9]. These multifaceted problems demand sophisticated numerical computation, mathematical modeling, and engineering monitoring methodologies that can provide reliable solutions for analysis, evaluation, and design processes [10,11].

This Special Issue, “Advances in Numerical Computation and Mathematical Modeling for Geotechnical Engineering”, addresses the critical need for advanced computational tools in geotechnical engineering practice. The collection focuses on the development and application of cutting-edge numerical computation and modeling methods for geotechnical monitoring, analysis, and theoretical prediction. By assembling high-quality original research papers, comprehensive case studies, and innovative methodological contributions, this Special Issue aims to bridge the gap between fundamental mathematical theories and practical computer-based applications in geotechnical engineering.

The rapid pace of global urbanization and infrastructure development has generated an unprecedented demand for reliable geotechnical solutions [12]. Modern projects such as deep excavations for underground transportation systems, high-rise building foundations in challenging soil conditions, and the exploitation of deep mineral resources all require accurate prediction of ground behavior under complex, multi-axial loading conditions. While traditional empirical methods remain valuable, they often prove inadequate when addressing the multi-physics nature of contemporary geotechnical problems, which involve coupled processes, material heterogeneity, and time-dependent behavior [13,14].

Recent advances in computational power and numerical algorithms have revolutionized our understanding and predictive capabilities in geotechnical behavior analysis. The development of sophisticated constitutive models capable of capturing complex stress–strain relationships in soils and rocks, combined with advanced numerical methods including the Finite Element Method (FEM), Discrete Element Method (DEM), and innovative hybrid approaches, has fundamentally transformed our analytical capabilities [10,11,15,16,17,18]. These computational tools enable engineers to comprehensively consider previously intractable factors, such as material heterogeneity, non-linear behavior, time-dependent effects, and complex coupled processes.

2. An Overview of Published Articles

This Special Issue encompasses a comprehensive range of research topics that reflect the current frontiers and emerging trends in computational geotechnics. These contributions can be categorized into several key thematic areas that collectively advance the state-of-the-art in numerical modeling and mathematical analysis.

Zhang et al. [19] utilized laboratory experiments and the Universal Distinct Element Code (UDEC) to explore the influence of the compressive strength of joint walls on the shear deformation behavior of rock discontinuities. The numerical results demonstrated good consistency with the experimental findings. At the microscopic level, the study revealed that roughness and normal stress are the main factors influencing the shear dilation process of discontinuities, and parameters such as dilation magnitude and shear strength are constrained by joint wall strength.

The application of advanced mathematical models in geotechnical engineering represents a mature yet continuously evolving field that successfully bridges theoretical analysis and practical engineering applications [20]. Liao et al. [21] proposed an innovative comprehensive evaluation methodology that integrates an improved grey correlation–Delphi model with validity and reliability coefficients. This sophisticated approach is specifically designed to address the inherent challenges in both quantitative and qualitative evaluation of loess slope stability—a critical issue in many regions worldwide where loess deposits are prevalent. The proposed method effectively overcomes the subjective dependence and index selection redundancy that characterize traditional evaluation approaches, demonstrating high reliability and providing a valuable mathematical framework for comprehensive geological slope assessment. This contribution is particularly significant given the increasing frequency of slope failures in loess regions and the need for more objective, scientifically based evaluation tools.

The integration of artificial intelligence and machine learning techniques with traditional numerical methods represents one of the most exciting and rapidly developing areas in computational geotechnics [22,23,24,25]. Sui, et al. [26] introduced a groundbreaking artificial intelligence algorithm based on a stacking integration strategy for predicting fragmentation size in open-pit bench blasting operations. This innovative AI algorithm effectively integrates Random Forest and XGBoost models, achieving significantly higher predictive accuracy compared to traditional single machine learning approaches. The research demonstrates the potential of ensemble learning methods in addressing complex geotechnical prediction problems where multiple variables and non-linear relationships are involved. This work has direct applications in mining engineering, where accurate prediction of blast fragmentation is crucial for optimizing extraction processes and minimizing environmental impact.

3. Conclusions

This Special Issue represents a significant contribution to the field of computational geotechnics, showcasing innovative research that addresses both fundamental scientific questions and practical engineering challenges. These papers presented here demonstrate the power of numerical computation and mathematical modeling in solving complex geotechnical problems, from the microscale behavior of soil particles to the large-scale response of geological systems. As we face increasingly complex engineering challenges in an era of climate change and sustainable development, the role of advanced computational methods in geotechnical engineering will only grow in importance. The research presented in this Special Issue provides the foundation for future developments, offering novel tools and insights that will enable engineers to design safer, more efficient, and more sustainable geotechnical solutions.