Stability assessment of the Pekmez landslide area: a comparison of the 2D Limit Equilibrium Method (2D LEM), 2D Finite Element Method (2D FEM), and 3D Finite Element Method (3D FEM)

A comprehensive understanding of slope stability is essential for ensuring the safety and durability of structures built on or near slopes and mitigating the risks associated with landslides and slope failures. Slope stability is typically evaluated using the factor of safety (FOS) based on the critical slip surfaces. The calculation of FOS is commonly executed using Limit Equilibrium Method (LEM) by dividing the slope into several vertical slices. However, the stability analyses using Finite Element Method (FEM) have gained significant attention in geotechnical engineering due to their ability to simulate slope behaviour and predict stability accurately by employing mathematical models and computational algorithms. Hence, this paper aims to analyse the FOS of the unreinforced slope using 2D FEM and 3D FEM conducted through computer software while examining the influence of different mesh coarseness. Besides that, the formation of critical slip surfaces and the displacement behaviour of the slope are also presented. A slope geometry model was analysed using PLAXIS 2D and PLAXIS 3D with different mesh coarseness. The findings were compared and discussed. The findings reveal that the values of FOS generated by 3D FEM are slightly larger compared to 2D FEM analysis, ranging from 1.27% to 2.56%. On the other hand, the effect of mesh coarseness indicates that coarser mesh sizes yield higher FOS values compared to finer mesh sizes. The shape, location and depth of the critical slip surfaces are consistent for each analysis in both methods. However, the maximum displacement values differ for each mesh coarseness, as the locations of maximum total displacement are identified at different nodes due to varying numbers of elements but still within the same potential failure zone. Overall, this comparative study is crucial in ensuring the validity of the performed analyses. Understanding the capabilities and limitations of 2D and 3D numerical analyses to achieve reliable and accurate results is important to balance mesh coarseness and computational efficiency.

Finite Element Method (FEM) is widely used in geotechnical engineering for analyzing soil-structure interactions, slope stability, and foundation performance. While 2D FEM is a common approach due to its efficiency and simplicity, 3D FEM provides a more realistic representation of geotechnical problems by incorporating the third spatial dimension. This study compared the results of 2D and 3D FEM analyses to determine whether the inclusion of the third dimension significantly affects computational outcomes for the same geotechnical model. To investigate this, two case studies are conducted: (1) a slope stability analysis in both 2D and 3D, and (2) a settlement analysis in both 2D and 3D. The results show that problems that inherently follow a 2D assumption, such as slope stability, 3D modeling does not provide significant advantages, making 2D analysis a sufficient and efficient approach. However, settlement analysis is inherently a 3D problem due to stress distribution and spatial soil deformations, meaning that a 2D model cannot accurately capture real behavior. The study highlights the importance of choosing the appropriate FEM approach based on problem characteristics. While 2D FEM remains a powerful tool for many geotechnical applications, complex deformation patterns and anisotropic effects in problems like settlement require 3D modeling for accurate predictions. These findings provide engineers with practical guidelines for optimizing computational resources while ensuring reliability in geotechnical design.

To clarify the effects of seismic response of concrete gravity dams under large earthquake, finite element method (FEM) analyses were carried out. In analyses, the height of dam and material properties of concrete and basement rock are same. The 2-dimensional (2D) and the 3-dimensional (3D) FEM model were made and used in earthquake response analyses. The contraction joints between dam block are concerned in 3D non-linear FEM analysis. In the case of same height of dam, the numerical results of damage states and placements in dam are different between 2D FEM model and 3D FEM model, due to the effect of difference in vibration mode of dam. In the 2D FEM model, the damage of top in cross-section becomes remarkable. In the 3D FEM model, the damage of attachment between dam body and basement rock at high-elevation becomes remarkable. The damage of 3D FEM model is smaller than that of 2D FEM model for the same acceleration level of earthquake. The influence of seismic response on contraction joints of 3D non-linear FEM dam model is smaller, which is as same as that of 3D linear FEM dam model. From the above results, the 2D FEM model gives a conservative assessment compared to the 3D FEM model.

For openhole completions in a weak sand formation, the failure of completion tubing frequently occurs under the loading from formation subsidence resulting from production. This paper investigates the integrity of completion tubing in this environment using the 3D finite element method (FEM). An elastoplastic analysis was performed on four sets of completion tubing using 3D FEM. A porous elastoplastic model was used to model the mechanical behavior of a weak sand formation. The interaction between the completion tubing and the sand formation was modeled with frictional contact constraints. The inclination angles of the completion tubing are set at 15°, 35°, 50°, and 75°. With a given geostress field and pressure depletion from production, the numerical results obtained with the 3D FEM model include subsidence of the sand formation, distribution of the equivalent plastic strain, and von Mises equivalent stress within the completion tubing and its deformed mesh. The principal conclusions include:major loading factors affecting tubing failure are the axial pulling force and the bending moment or normal pressure applied on the external surface of the formation subsidence;including an extendable tubing section can release the axial tensile stress caused by production-induced formation subsidence, and thus keep the tubing intact;various scenarios have been checked for a safe pore pressure depletion value with a variation of tubing parameters values. This work presents a best practice for estimating the completion tubing integrity under subsidence loading by using a 3D FEM tool. Introduction For openhole completions in a weak sand formation, the failure of completion tubing frequently occurs under the loading from formation subsidence arising from production. In the past decades, a few researchers investigated this topic. Green (1991) discussed the subsidence that occurred in a Gulf Coast field and introduced his subsidence measurement technique; this technique uses existing downhole wireline tools configured to provide high-resolution results. Salamy et al. (1999) investigated the monitoring of wellbore stability caused by production and compaction. Earles et al. (2011) introduced a new generation compaction monitoring device, a fiber optic support device called 'real time monitoring compaction system'. Dudley et al. (2009) introduced their works on subsidence prediction by using an integrated method that combines geomechanical core testing, field monitoring, and 3D numerical modeling. Hoang et al. (2010) reported their work on pore pressure depletion-related reservoir compaction and its effect on the design of multilateral horizontal wells. Furui et al. (2010) reported their work on the stability of openhole, cemented liner and uncemented liner completions in a highly compacted chalk formation. Various scenarios of liner collapse were investigated numerically. Shen (2010) reported his work on numerical modeling and analysis to subsidence prediction and casing integrity induced by pore pressure depletion. Hilbert et al. (2011) introduced their works on geomechanical modeling and analysis used to assess the risk of compaction-induced deformation and the potential failure of horizontal gravel pack completion in a field that is located in deep water but at a shallow depth below the seafloor. This work presents the results of the numerical stress analysis for tubing and the formations in which the tubing lies. The completion tubings of four wells are involved in this work: A15, A35, A50, and A75. The number in the well name indicates the inclination angle of that well. For example, well A15 has inclination angle of 15°. This study investigates the integrity of completion tubing under loads from the formation caused by production and subsidence. The complete study includes data derivation from results of 1D analysis with Drillworks® Finite Element Method (FEM) modeling and analysis. Numerical calculations were performed with Abaqus 3D Finite Element software on the mechanical behavior of completion tubing under subsidence loading.

PurposeTo determine the optimal dimensions for a stacked micro‐channel using the genetic algorithms (GAs) under different flow constraints.Design/methodology/approachGA is used as an optimization tool for optimizing the thermal resistance of a stacked micro‐channel under different flow constraints obtained by using the one dimensional (1D) and two dimensional (2D) finite element methods (FEM) and by thermal resistance network model as well (proposed by earlier researcher). The 2D FEM is used to study the effect of two dimensional heat conduction in the micro‐channel material. Some parametric studies are carried out to determine the resulting performance of the stacked micro‐channel. Different number of layers of the stacked micro‐channel is also investigated to study its effect on the minimum thermal resistance.FindingsThe results obtained from the 1D FEM analysis compare well with those obtained from the thermal resistance network model. However, the 2D FEM analysis results in lower thermal resistance and, therefore, the importance of considering the conduction in two dimensions in the micro‐channel is highlighted.Research limitations/implicationThe analysis is valid for constant properties fluid and for steady‐state conditions. The top‐most surfaces as well as the side surfaces of the micro‐channel are considered adiabatic.Practical implicationsThe method is very useful for practical design of micro‐channel heat‐sinks.Originality/valueFEM analyses of stacked micro‐channel can be easily implemented in the optimization procedure for obtaining the dimensions of the stacked micro‐channel heat‐sinks for minimum thermal resistance.

This study investigates the slope stability of Bingöl open-pit iron mine slopes using 3D limit equilibrium and finite element methods. The pit benches are 3 m wide and 6 m high, with an overall slope angle of 38°. The geological composition comprises slightly to moderately weathered and heavily jointed phyllite, micaschist, and gneiss. Shear strength parameters were determined through back analyses of already failed sections using the Hoek-Brown failure criterion and Geological Strength Index (GSI). Factor of safety values for static and dynamic conditions were calculated using 3D limit equilibrium and 2D finite element analyses. Results show good agreement between the two methods, with benches in the northern section exhibiting a significant decrease in safety factor under dynamic conditions, indicating near-limit equilibrium slopes.

Rotation patterns of a mangle-type magnetic field source optimized via covariance matrix adaptation evolution strategy with 3D finite element method

Background:Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties.Materials and Methods:A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses.Results:For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced.Conclusion:This shows that the force level required for non-linear analysis is lesser than that of linear analysis.

this paper proposes an effective design process for matching axial length between stator and rotor of high temperature superconducting synchronous motor (HTSSM) using two-dimension (2D) finite element method (FEM), magnetic network method (MNM) and three-dimension (3D) finite element method. During this process, 2D FEM is used to get distributional parameter in short time by selecting some representative 2D plane in 3D geometrical space. MNM are more efficient and faster, which is build after accepting some useful conclusion by 2D FEM. 3D FEM is used to makes necessary adjustment, and the result also verify the validity of the former methods, because of its accuracy. The design process is performed in the 1MW HTSSM design for search proper axial length of stator and rotor. The results provide strong direction in different design period, which verify the validity of the method.

2D finite element method (FEM) has been used in the asphalt pavement mechanics calculation. In order to analyze its rationality, elastic multilayer theory has been applied to analyze the asphalt pavement mechanical response under double circular vertical uniformly distributed load. Deflection, tensile stress on pavement bottom and compression strain on top of subgrade calculated based on elastic multilayer theory is compared with the results using 2D FEM. The analysis results show that deflection, tensile stress on pavement bottom and compression strain on top of subgrade computed by 2D FEM have discrepancy with the results by elastic multilayer theory. The discrepancy of maximum tensile stress between elastic multilayer theory and 2D FEM improves along with the increase of structural layer depth, but the two methods can get similar variation of the results. It is seen that applying 2D FEM without any analysis to calculate asphalt pavement mechanics is inaccurate and unreasonable.

Slope stability for soft clay is a hard problem in practice. In this paper, 2D and 3D finite element method (FEM) based on elastoplastic model are used to calculate the stress and displacement distribution in the soft clay slope under gravity and uniform load at the slope top. Stability analyses indicate that 3D boundary effect varies with the stress level of the slope. When the slope is stable, end effect of 3D space is not remarkable. When the stability decreases, end effect occurs; when the slope is at limiting state, end effect reaches maximum. The failure mode will not be the same if the slope is under different stress states; furthermore, a standard to evaluate slope failure with FEM calculation is established. The slope failure form caused by accumulative load is different from that caused by slope strength insufficiency. The energy causing slope failure spreads preferentially along Y-Z section. When the failure resistance capability reaches the limiting state, the energy can extend along X-axis direction. The 3D effect of the slope under uniform load on the top is related to the ratio of load influence width to slope height, and the effect is remarkable with the decrease of the ratio.

PurposeThe interbar current of a squirrel-cage induction motor (IM) flows in the steel sheets when the secondary conductor is not insulated from the laminated steel sheets. It was reported that the interbar current loss was increased when skewing the rotor core. This paper aims to analyze a skewed IM using the three-dimensional (3D) finite element method. The effects of rotor skew on the interbar current are clarified.Design/methodology/approachIn this paper, a skewed squirrel-cage IM is analyzed in three patterns of skewed angle. The calculated results were compared with each other. If all laminated steel sheets are divided by the mesh with actual thickness, the huge calculation time is required. In the method applied in the study, several steel sheets are divided by the mesh with the actual thickness and some steel sheets are assumed to be the steel lump between them to shorten the calculation time.FindingsThe paper describes that the distribution of interbar current loss when rotor is skewed is different from that when rotor is not skewed. In addition, the paper suggests that the larger the skew angle becomes, the larger the interbar current loss becomes.Originality/valueIn this paper, a skewed IM with the consideration of the interbar current in the laminated steel sheets was analyzed using the 3D finite element method. The influences of the rotor skew on the interbar current are clarified.

During the rolling process, temperature is an important factor that affects the die and the work-piece in metal forming procedure. The metal deformation is often carried along with the variety of temperature. Moreover, mechanical energy of plastic deformation is converted into heat during the metal deformation process. Thus, it is necessary to couple the deformation and thermal behaviors in an integrated manner in numerical simulation so as to improve the simulation accuracy. In this paper, we use a 3D rigid-plastic Finite Element Method (FEM) to simulate the hot rolling process by coupling the thermal effects. Based on the 3D FEM model, integrated equations of coupling velocity and temperature fields are formulated. The uniform of integrated equations is obtained by re-indexing the combination sequences and then a modified coupling method is proposed to solve the resulted equations. The numerical experiments are carried on the real data collected from a steel plant. A good agreement between the numerical result and measured value shows the availability of the proposed coupling method.

This paper presents a modeling and simulation of transient heat transfer process in the human eye with a tumour. A three dimensional (3D) finite element method is applied to obtain the solution of a boundary value problem for a transient heat transfer model in the human eye. The human eye is modeled as a composition of several homogeneous regions. The Ritz method in the finite element method is used for solving heat differential equation. Applying the boundary conditions, the heat radiation condition and the Robin condition on the cornea surface of the eye and on the outer part of sclera are used, respectively. Simulation results of heat transfer for three dimensional model of human eye with a tumour show the effect of tumour on transient heat distribution.

An integrated fatigue assessment approach of rail welds using dynamic 3D FE simulation and strain monitoring technique