Advances in Numerical Computation and Mathematical Modelling for Mechanics and Dynamics in Geotechnical Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 406

Special Issue Editors


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Guest Editor
School of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, China
Interests: rock dynamics; numerical simulation; constitutive model; couple field analysis
Special Issues, Collections and Topics in MDPI journals
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Interests: mining; rock blasting; statistical learning; predictive modeling; statistics; tunneling; machine learning
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
School of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, China
Interests: rock/soil mechanics; numerical simulation; multi-physics coupling; high performance computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With the excavation of geotechnical engineering in deep strata and complex geological environments, a large number of engineering problems, such as dynamic failure of rock mass or soil, geothermal damage to rock mass, rockbust, and microseism, will strengthen the need for reliable numerical, mathematical, and engineering monitoring methods in analysis, evaluation, and design processes.

Deformations in rock and soil masses, disaster evolution, and underground structural damage can all be analyzed from the perspectives of mechanics and dynamics, and solved efficiently with the aid of advanced numerical computation and mathematical models, underscoring the universality and applicability of integrating cutting-edge mathematical theories and computational tools across diverse practical scenarios. Original research papers, reviews, and case studies related to basic theories and advanced engineering applications are welcome.

Topics of interest include, but are not limited to, the following:

  1. New dynamical system models or constitutive relations capturing the nonlinear, time-dependent mechanical behavior of rock or soil, including new constitutive models, metaheuristic-based system modeling, and advanced numerical schemes;
  2. Dynamic and static analysis of coupled multi-physics processes in rock/soil systems, such as thermo–hydro–mechanical–chemical (THMC) interactions, stability and bifurcation analysis, and dynamic/static system responses;
  3. Application of nonlinear dynamics, stability theory, and computational methods to predict, control, and optimize geotechnical engineering performance under complex loading and environmental conditions.

Dr. Jiadong Qiu
Dr. Jian Zhou
Dr. He Liu
Guest Editors

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Keywords

  • dynamic/static responses of rock-soil system
  • dynamic and static constitutive models
  • advanced numerical methods for dynamic and static analyses
  • nonlinear dynamics
  • multi-physical field numerical simulation
  • AI-driven rock dynamic/ static analysis
  • structural stability analysis
  • development and improvement of FEM/DEM

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Published Papers (1 paper)

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Research

20 pages, 13321 KB  
Article
Limit Analysis Theory and Numerical Simulation Study on the Cover Thickness of Tunnel Crown in Soil–Rock Strata
by Fang Ji, Qinshan Wang, Hongtao Wang, Yaotao Yuan, Zhenxiang Hao, Ping Liu and Rongli Liu
Mathematics 2025, 13(20), 3293; https://doi.org/10.3390/math13203293 - 15 Oct 2025
Viewed by 223
Abstract
When constructing subway tunnels in composite strata consisting of overlying soil and underlying rock, placing the tunnel within the overburden rock strata and setting a certain thickness of safety cover rock on top is an effective way to ensure the safety of tunnel [...] Read more.
When constructing subway tunnels in composite strata consisting of overlying soil and underlying rock, placing the tunnel within the overburden rock strata and setting a certain thickness of safety cover rock on top is an effective way to ensure the safety of tunnel construction and the stability of the surrounding rock. However, there is currently no unified understanding or standard regarding the safe overburden thickness of the tunnel and its general rules. To investigate the effect of changes in the roof overlying rock thickness on the surrounding rock stability of subway tunnels, this study is based on the typical soil–rock strata of an underground tunnel section of Jinan Metro Line 4 in China. A total of 4 different conditions for the thickness of the overlying soil layer were considered, and 48 comparison schemes were designed. A systematic study of numerical simulation comparisons of tunnel excavation under different cover rock thicknesses was conducted. The deformation and plastic zone evolution characteristics of the surrounding rock were revealed under different cover rock thicknesses, and the existence of an optimal cover rock thickness range for tunnel crowns in soil–rock strata was identified. Based on this, a theoretical analysis model for the failure of the tunnel roof overlying rock was constructed. Using the upper-bound approach limit analysis method, the theoretical formula for the critical overburden thickness of the tunnel crown was derived. The influence of different rock mechanical parameters and tunnel design parameters on the critical overburden thickness was analyzed. The results were compared with numerical simulation results to verify the effectiveness of the proposed method. The research findings provide theoretical references for selecting reasonable buried depths and support designs for mining-bored tunnels in soil–rock composite strata. Full article
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