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Mathematics
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Numerical Modeling and Simulation in Geomechanics
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Numerical Modeling and Simulation in Geomechanics

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (28 June 2024) | Viewed by 2622

Special Issue Editors

Dr. Kwai Kwan (Henry) Wong

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Guest Editor
LTDS (UMR- CNRS 5513), Université de Lyon, ENTPE, rue Maurice Audin, 69120 Vaulx-en-Velin, France
Interests: consititutive models; multiphysics behaviour of geostructures and geostructures
Special Issues, Collections and Topics in MDPI journals
Prof. Yung-Ming Cheng

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Guest Editor
School of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China
Interests: numerical methods; discrete element analysis; slope and pile; deep excavation
Dr. Chin Leo

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Guest Editor
School of Engineering, Design and Built Environment, Western Sydney University, Penrith, Australia
Interests: soil dynamics; foundations; retaining structures; soil stabilization and computational geomechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Xiaoqin Lei

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Guest Editor
Institute of Mountain Hazards & Environment, Chengdu, China
Interests: multiphysics behaviour of geostructures and geostructures; material point method

Special Issue Information

Dear Colleagues,

The advent of high-speed digital computers and the development of new theories have significantly changed the professional approach of engineers. Many computational tools in the form of commercial or free-access codes based on these new theories have been developed by researchers and subsequently made available to professional engineers. Numerical resolution of many complex problems has become a routine task in engineering design offices. It would be useful to inform the engineering community at regular intervals on the latest developments of such numerical methods and tools.

This Special Issue focuses on the modelling and simulation of coupled problems in geomechanics concerning the general behaviour of geomaterials and geo-structures, where two or more physical phenomena simultaneously intervene: thermal, mechanical, chemical, hydraulic, osmotic, capillarity, phase-change, etc.

Papers are invited from those who work on the development of new numerical methods or on the application of existing tools and methods to analyse challenging cases.

We look forward to receiving your submissions.

Dr. Kwai Kwan (Henry) Wong
Prof. Yung-Ming Cheng
Dr. Chin Leo
Dr. Xiaoqin Lei
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

  • multi-physics behaviour
  • coupled physical phenomena
  • finite elements
  • smoothed particle hydrodynamics (SPH)
  • material point method (MPM)
  • discrete elements
  • boundary elements

Published Papers (4 papers)

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Research

17 pages, 20176 KiB  
Article
Computation of Green’s Function in a Strongly Heterogeneous Medium Using the Lippmann–Schwinger Equation: A Generalized Successive Over-Relaxion plus Preconditioning Scheme
by Yangyang Xu, Jianguo Sun and Yaoda Shang
Mathematics 2024, 12(13), 2066; https://doi.org/10.3390/math12132066 - 1 Jul 2024
Viewed by 345
Abstract
The computation of Green’s function is a basic and time-consuming task in realizing seismic imaging using integral operators because the function is the kernel of the integral operators and because every image point functions as the source point of Green’s function. If the [...] Read more.
The computation of Green’s function is a basic and time-consuming task in realizing seismic imaging using integral operators because the function is the kernel of the integral operators and because every image point functions as the source point of Green’s function. If the perturbation theory is used, the problem of the computation of Green’s function can be transformed into one of solving the Lippmann–Schwinger (L–S) equation. However, if the velocity model under consideration has large scale and strong heterogeneity, solving the L–S equation may become difficult because only numerical or successive approximate (iterative) methods can be used in this case. In the literature, one of these methods is the generalized successive over-relaxation (GSOR) iterative method, which can effectively solve the L–S equation and obtain the desired convergent iterative series. However, the GSOR iterative method may encounter slow convergence when calculating the high-frequency Green’s function. In this paper, we propose a new scheme that utilizes the GSOR iterative with a precondition to solve the complex wavenumber L–S equation in a slightly attenuated medium. The complex wavenumber with imaginary components localizes the energy of the background Green’s function and reduces its singularity by enabling exponential decay. Introduction of the preconditioning operator can further improve the convergence speed of the GSOR iterative series. Then, we provide a preconditioned generalized successive over-relaxation (pre-GSOR) iterative format. Our numerical results show that if an appropriate damping factor and a proper preconditioning operator are selected, the method presented here outperforms the GSOR iterative for the real wavenumber L–S equation in terms of the convergence speed, accuracy, and adaptation to high frequencies. Full article
(This article belongs to the Special Issue Numerical Modeling and Simulation in Geomechanics)
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15 pages, 6840 KiB  
Article
Dynamic Binary-Medium Model for Jointed Rock Subjected to Cyclic Loading
by Mingxing Liu, Enlong Liu, Xingyan Liu and Qingsong Zheng
Mathematics 2024, 12(11), 1765; https://doi.org/10.3390/math12111765 - 6 Jun 2024
Viewed by 376
Abstract
Revealing the damage mechanism of jointed rocks under a cyclic loading and formulating the corresponding dynamic constitutive model to meet the requirements for the evaluation of anti-vibration safety for critical engineering construction and operation is an essential, urgent and basic subject. Based on [...] Read more.
Revealing the damage mechanism of jointed rocks under a cyclic loading and formulating the corresponding dynamic constitutive model to meet the requirements for the evaluation of anti-vibration safety for critical engineering construction and operation is an essential, urgent and basic subject. Based on the breakage mechanics for geological material, jointed rock is considered as a binary-medium material composed of the bonded elements and frictional elements. The bonded elements are regarded as elastic-brittle elements, and the frictional elements are regarded as elastic-plastic elements. Firstly, the static binary-medium model for jointed rock is established based on the homogenization method and by introducing the breakage ratio and the strain concentration coefficient. Then, the dynamic binary-medium model for jointed rock under cyclic loads is established considering the nonlinear damage effect resulting from cyclic loads. The breakage ratio formula is improved, and the Drucker–Prager criterion is introduced. During the unloading stage, it is supposed that the breakage ratios and strain concentration coefficients remain unchanged and the stress–strain ratios of both bonded elements and frictional elements are constant. The model is verified by static and dynamic triaxial tests of jointed rock samples with an interpenetrated joint. It is found that the model can describe the nonlinear stress–strain characteristics of a jointed rock subjected to cyclic loads relatively well and can reflect the effects of cyclic loading on the deformation and damage, including the lateral deformation characteristics. Meanwhile, the typical three-stage (varying from sparse to dense to sparse) evolution laws of the stress–strain curves are also reflected relatively well. Full article
(This article belongs to the Special Issue Numerical Modeling and Simulation in Geomechanics)
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19 pages, 5733 KiB  
Article
A Numerical Analysis of the Non-Uniform Layered Ground Vibration Caused by a Moving Railway Load Using an Efficient Frequency–Wave-Number Method
by Shaofeng Yao, Wei Xie, Jianlong Geng, Xiaolu Xu and Sen Zheng
Mathematics 2024, 12(11), 1750; https://doi.org/10.3390/math12111750 - 4 Jun 2024
Viewed by 504
Abstract
The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory [...] Read more.
The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory model is proposed to quickly obtain the numerical results without losing accuracy. The track is regarded as a composite Euler–Bernoulli beam resting on the layered ground, and the spatial heterogeneity of the ground soil is considered. The ground dynamic characteristics of an elastic, layered, non-uniform foundation are investigated, and numerical results at three typical train speeds are reported based on the developed Fortran computer programs. The results show that as the soil homogeneity coefficient increases, the peak acceleration continuously decreases in the transonic case, while it gradually increases in the supersonic case, and the ground acceleration spectrum at a far distance obviously decreases; the maximum acceleration occurs at the track edge, and a local rebound in vibration attenuation occurs in the supersonic case. Full article
(This article belongs to the Special Issue Numerical Modeling and Simulation in Geomechanics)
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16 pages, 3949 KiB  
Article
Influence of Internal Erosion on Rainfall-Induced Instability of Layered Deposited-Soil Slopes
by Xiaoqin Lei, Weiyu Zhang, Xiaoqing Chen and Liu Ming
Mathematics 2023, 11(20), 4348; https://doi.org/10.3390/math11204348 - 19 Oct 2023
Cited by 1 | Viewed by 913
Abstract
Layered deposited-soil slopes are widely distributed in mountainous terrain. The rainfall-induced instability of layered deposited-soil slopes is not only controlled by the unsaturated infiltration process but also by the seepage-induced internal-erosion process within the deposited soils. In this paper, the main physical processes [...] Read more.
Layered deposited-soil slopes are widely distributed in mountainous terrain. The rainfall-induced instability of layered deposited-soil slopes is not only controlled by the unsaturated infiltration process but also by the seepage-induced internal-erosion process within the deposited soils. In this paper, the main physical processes within two-layer deposited-soil slopes under rainfall infiltration are summarized, and a coupled seepage–erosion finite element model is established to analyze the interactions between the rainfall infiltration process and the internal-erosion process within layered deposited-soil slopes. This finite element model was validated by simulating the coupled seepage–erosion process in a one-dimensional layered soil column. Then, serials of two-dimensional coupled seepage–erosion simulations were conducted to investigate the rainfall-induced seepage–erosion patterns, as well as their impact on the stability evolution of the layered deposited slopes. It was shown that the rainfall-induced seepage–erosion accelerate the water infiltration into the slope and facilitate the generation of subsurface stormflow near the layer interface, which will weaken the soils around the layer interface and accelerate the slope failure process inevitably. Special attention should be paid to the rainfall-induced seepage–erosion effect when evaluating the stability of layered deposited-soil slopes. Full article
(This article belongs to the Special Issue Numerical Modeling and Simulation in Geomechanics)
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