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Mathematical Model and Numerical Method in Advanced Geotechnical Engineering and...
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Mathematical Model and Numerical Method in Advanced Geotechnical Engineering and Geomechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (15 August 2024) | Viewed by 5341

Special Issue Editors

Dr. Tuan A. Pham

E-Mail Website
Guest Editor
School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University, Edinburgh EH14 4AS, UK
Interests: mathematical models; geotechnical engineering; soil–structure interaction; numerical modelling; applied mechanics
Prof. Dr. Daniel Dias

E-Mail Website
Guest Editor
Geotechnical Engineering, Grenoble Alpes University, 38400 Grenoble, France
Interests: numerical modelling in geomechanics; soil/structure interaction; geotechnical engineering; soil mechanics; tunnels; dams; slopes; soil reinforcement
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Basic and advanced mathematics are usually necessary in civil engineering and other complex scientific fields. There would be no bridges, tunnels, roads, buildings, dams, or most mechanical things if mathematics had not been used to establish principles, compute measurements and limits, investigate variants, prove concepts, etc. In reality, mathematics is required for almost all numerical methods, software, and design principles. More importantly, the preliminary design process makes extensive use of the concepts that mathematics has fundamentally established. Mathematics will undoubtedly continue to be employed throughout the centuries and into the future. This Special Issue is primarily interested in works that provide new mathematical modellings, new applications, or a mix of both that advance the understanding of real-world problems. Papers using the presently available numerical techniques must show substantial innovation in the resolution of real-world issues. Research should be conducted on soil–structure interactions using applied mathematical models and  numerical methods. Papers addressing novel mathematical techniques for the analysis of soil–structure interaction are especially encouraged. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used to derive the results.

Dr. Tuan A. Pham
Prof. Dr. Daniel Dias
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical methods
  • analysis and simulation
  • soil–structure interaction
  • applied mechanics
  • quantitative models
  • numerical simulations

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Published Papers (3 papers)

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Research

22 pages, 5807 KiB  
Article
Analytical Solution for Bearing Capacity of Reinforced Strip Footings on Unsaturated Soils under Steady Flow
by Xudong Kang and De Zhou
Mathematics 2023, 11(17), 3746; https://doi.org/10.3390/math11173746 - 31 Aug 2023
Cited by 1 | Viewed by 1304
Abstract
The study of analytical solutions for the bearing capacity of reinforced soil foundations is a very important topic in engineering mathematics. Existing evaluations of the foundation-bearing capacity on reinforced soils are based on dry conditions, while many foundations are located on unsaturated soils [...] Read more.
The study of analytical solutions for the bearing capacity of reinforced soil foundations is a very important topic in engineering mathematics. Existing evaluations of the foundation-bearing capacity on reinforced soils are based on dry conditions, while many foundations are located on unsaturated soils in real engineering. In this paper, a new formula for the bearing capacity of reinforced strip footings on unsaturated soils is presented. Two sliding failure mechanisms are constructed based on the position of the reinforcement layer relative to the sliding surface. The distribution of apparent cohesion in the depth direction is calculated by considering the effect of matrix suction. By additionally considering the work conducted by the reinforcement and the contribution of the apparent cohesion, the bearing capacity formula is obtained using the upper bound theorem of limit analysis. The bearing capacity solution is obtained by adopting the sequential quadratic programming (SQP) algorithm. Comparing the results under two failure mechanisms, the optimal bearing capacity and the optimal embedment depth of reinforcement are obtained. The results of this paper are consistent with those of the existing literature. Finally, the effects of reinforcement embedment depth, effective internal friction angle, uniform load, and unsaturated soil parameters on the optimal bearing capacity are investigated through parametric analysis. This paper provides useful recommendations for the engineering application of reinforced strip footings on unsaturated soils. Full article
(This article belongs to the Special Issue Mathematical Model and Numerical Method in Advanced Geotechnical Engineering and Geomechanics)
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25 pages, 6066 KiB  
Article
An Analytical Framework for Assessing the Unsaturated Bearing Capacity of Strip Footings under Transient Infiltration
by Sheng Xu and De Zhou
Mathematics 2023, 11(16), 3480; https://doi.org/10.3390/math11163480 - 11 Aug 2023
Cited by 1 | Viewed by 1082
Abstract
The evaluation of the bearing capacity of strip footings generally assumes that the soil is either dry or fully saturated, which contradicts the actual condition in nature where the soil is often in a partially saturated state. Furthermore, infiltration has a significant impact [...] Read more.
The evaluation of the bearing capacity of strip footings generally assumes that the soil is either dry or fully saturated, which contradicts the actual condition in nature where the soil is often in a partially saturated state. Furthermore, infiltration has a significant impact on the shear strength of the soil. Following the upper bound theory of the limit analysis, this article provides a theoretical framework for assessing the bearing capacity under transient flow with linear variation in infiltration intensity for the first time. Firstly, the closed form of suction stress under linear transient infiltration is derived using Laplace transform and introduced into the Mohr–Coulomb criterion. A discrete failure mechanism with fewer variables and higher accuracy is provided to ensure kinematic admissibility. The upper bound solution for bearing capacity is obtained by solving the power balance equation. The present results are compared with results from the published literature and the finite element, confirming the validity and superiority of the theoretical framework provided. A parametric analysis is also conducted on three hypothetical soil types (fine sand, silt, and clay), and the results show that unsaturated transient infiltration has a positive influence on increasing the foundation bearing capacity. The magnitude of the influence is comprehensively controlled by factors such as soil type, saturated hydraulic conductivity, infiltration intensity, infiltration time, and water table depth. The increase in bearing capacity due to unsaturated transient infiltration can be incorporated into Terzaghi’s equation as a separate component presented in tabular form for engineering design purposes. Full article
(This article belongs to the Special Issue Mathematical Model and Numerical Method in Advanced Geotechnical Engineering and Geomechanics)
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24 pages, 10148 KiB  
Article
Global Sensitivity Analysis Method for Embankment Dam Slope Stability Considering Seepage–Stress Coupling under Changing Reservoir Water Levels
by Congcong Zhou, Zhenzhong Shen, Liqun Xu, Yiqing Sun, Wenbing Zhang, Hongwei Zhang and Jiayi Peng
Mathematics 2023, 11(13), 2836; https://doi.org/10.3390/math11132836 - 24 Jun 2023
Cited by 2 | Viewed by 2035
Abstract
Ensuring the long-term, efficient, and safe operation of reservoir dams relies on the slope stability of embankment dams. Periodic fluctuations of the reservoir water level due to reservoir scheduling operations make the slope of the reservoir bank vulnerable to instability. To investigate the [...] Read more.
Ensuring the long-term, efficient, and safe operation of reservoir dams relies on the slope stability of embankment dams. Periodic fluctuations of the reservoir water level due to reservoir scheduling operations make the slope of the reservoir bank vulnerable to instability. To investigate the influence of various factors and their interactions with embankment dam slope stability under changing reservoir water levels, a global sensitivity analysis method is proposed that accounts for seepage–stress coupling. An embankment dam in Shaanxi Province, China, is studied as an example, with COMSOL Multiphysics software simulating the seepage and slope stability of the dam under fluctuating reservoir water level conditions and seepage–stress coupling. The global sensitivity analysis of factors affecting dam slope stability is accomplished by combining Plackett–Burman and Box–Behnken experimental designs, with ANOVA determining the sensitivity of each factor and interaction term. The results demonstrate that during the impoundment period of the reservoir, the saturation line is concave, and the overall stability safety of the dam slope increases first and then tends to be stable, according to the coefficient. The internal friction angle φ, cohesion c, and soil density ρs represent the three most sensitive factors affecting the stability and safety of the dam slope, while c × ρs is a second-order interaction term with significant sensitivity to the stability and safety coefficient of the dam slope. The reservoir drainage period infiltration line is convex, and dam slope stability first reduced and then increased. The magnitude of water level change H, internal friction angle φ, cohesion c, and soil density ρs are the four most sensitive factors for the coefficient of safety of dam slope stability, while c × ρs, H × ρs, and φ × ρs are the second-order interaction terms with significant sensitivity to the coefficient of safety of dam slope stability. These research findings and methods can offer valuable technical support and reference for the investigation and evaluation of the stability of embankment dam slopes. Full article
(This article belongs to the Special Issue Mathematical Model and Numerical Method in Advanced Geotechnical Engineering and Geomechanics)
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