Equilibrium Finite Element Method Research Articles

Seepage Analysis and Optimization of Reservoir Earthen Embankment with Double Textured HDPE Geo-Membrane Barrier

This research paper focuses on conducting a steady state seepage analysis along with the downstream slope factor of safety using the Modified Bishops method in a poorly compacted earthen embankment and optimizing the same reservoir earthen embankment in a case study located near Sadiyavav village in Junagadh district in Gujarat, India. The study site, situated at 21°32'06.5"N and 70°37'26.7"E, is renowned for its Asiatic lions. The analysis and optimization were performed with a double-textured High-Density Polyethylene (HDPE) Geo-membrane barrier. Previously, designs and numerical solutions proposed homogenous embankments and too poorly compacted with no drainage arrangements, which led to anisotropic conditions within the section and water seeping out, cutting the phreatic line. The paper presents the documented improvements in the factor of safety achieved through the seepage analysis and the optimization of the HDPE Geo-membrane barrier. Two improvement techniques were studied using the “Limiting Equilibrium-Finite Element Method” (LS-FEM). The first using (HDPE) Geo-membrane stabilized with gabions, and the second alternative using HDPE Geo-membrane with gabions in addition to rock toe. The study results showed improvements in the downstream slope stability for the two alternatives by 3% and 10%, respectively. Doi: 10.28991/CEJ-2023-09-11-07 Full Text: PDF

Equilibrium finite element and error estimation for frictional contact problem based on linear complementarity problem formulation

AbstractThis article proposes a novel equilibrium finite element method (EFEM) for equilibrated solution of frictional contact problem. The development of such EFEM is mainly two‐fold. On the one hand, the traction‐based equilibrium element is employed to construct the discrete equilibrated stress field. This equilibrium element, using edge tractions as basic variables, is found straightforward to deal with the friction and contact constraints on the contact surface. On the other hand, the Coulomb frictional contact problem is recast into a linear complementarity problem (LCP), with which the algebraic complementarity formulation can be obtained with the help of the constructed equilibrated stress field. A remarkable property of the proposed EFEM is that the equilibrated solution, in conjunction with the compatible solution of the traditional FEM, can provide reliable error estimation for frictional contact within the framework of dual analysis. Numerical examples are finally conducted to see the performance and the ability to reliable error estimation of the proposed EFEM.

An equilibrium finite element method for contact problem with application to strict error estimation

An equilibrium finite element method for contact problem with application to strict error estimation

Geotechnical Perspective on Dozer-Push Method in Coal Mining Operations

The rapid increase of technological development is currently playing a role in the mining industry. The dozer push exploitation method is an alternative to the conventional truck and shovel method. Heavy dozers have the ability to move large amounts of waste material in short distances at a low cost, while trucks and shovels will be more economical if over long distances. Geotechnical assessment becomes one of the critical considerations in making a decision plan and slope design for mining activities where the dozer push activities were carried out. Material conditions greatly affect slope stability, which can be defined as material behavior based on the physical and mechanical properties of the material. The slope stability analysis method used in this study was a combination of two methods, the Limit Equilibrium Method (LEM) and Finite Element Method (FEM). These two combinations of analytical methods will strengthen the justification of the geotechnical perspective. By understanding the behavior of the material on a slope, the risk of a slope failure can be controlled and minimized using a geotechnical perspective. The parameters that will be studied in this study are the physical and mechanical properties of the material against several conceptual design options

Evaluating Landslide Remediation Methods Used in the Carpathian Mountains, Poland

ABSTRACT The aim of this study was to evaluate the results of landslide remediation in the Polish Carpathians. The research for safeguarding the roads and infrastructure was conducted in the years 2005–2018 in nine landslide areas. The interpretation of engineering geology conditions was complex due to the soil-rock nature of the flysch sediment. Movements were activated after heavy rainfalls. In two cases, triggers were connected with the undercutting of the slope or external loading. The research methods included mapping, drilling, index, oedometer, direct shear tests, ground-penetrating radar scanning, and numerical modeling. To date, 15–59 series of inclinometer and piezometer network readings in 30 locations have been taken. Three online stations have been delivering continuous, nearly real-time data since May 2010. Displacements before the remediation ranged from a few millimeters to several centimeters. The proposed remediation methods included piles, micropiles, anchors, retaining walls, and drainage systems. Six stabilization projects were prepared and checked using the limit equilibrium method and finite element method modeling. The research shows that in five landslide areas, the proposed remedial works were effective. Two other partial stabilization works limited the scope of the movements but did not eliminate the risk. At two locations, only temporary repairs were conducted. Proper identification of the landslide triggers and activity is standard for the recognition of counteraction possibilities and could lower stabilization costs. The selected methods delivered data for remedial decisions. However, effective remediation of an active Carpathian landslide is difficult. It requires individually calibrated investigations, representative monitoring, and careful design of stabilization.

Stability analysis of two-layered non-homogeneous slopes

Natural slopes are non-homogeneous in nature, which behave differently than homogeneous slopes. The non-homogeneity in slopes exist in various ways, which include change in stratifications and/or shear strength parameters (cohesion, friction angle) with depth, presence of saturated–unsaturated zones, etc. This study is performed to show the effect of non-homogeneity due to different types of soils on the stability of two-layered slopes. Homogeneous and two-layered non-homogeneous models of soil slope are prepared with three different fine-grained and coarse-grained types of soils. Both the limit equilibrium method and finite element methods were used to evaluate the stability of the slopes and the results are presented in terms of safety factors along with the corresponding critical slip surfaces. Slopes with coarse-grained soil showed translational type of failure, while rotational failure was observed for fine-grained slopes.

Stability Analysis of River Dyke in Estuarine Environment

River dyke stability in estuarine environment is greatly influenced by the river stage fluctuations due to spring and neap tide variation in the zone of influence. The proposed river dyke will be located along the Nayachara island at the Rangafalla and Haldia end for protection of the proposed navigational channel across Nayachara, West Bengal, India. The navigational channel will connect the shipping route from Rangafalla to Haldia dock which the Kolkata Port Trust (KoPT) proposes as a long term solution for the shipping route to Haldia bypassing the existing troublesome route via Auckland and Jellingham, in order to reduce annual maintenance dredging burden to KoPT. The river dyke will be constructed artificially using sand as main core material. The soil profile of the site consists of mixture of river borne sand, silt and clay. The present site is located in a complex estuarine environment and the island has been formed due to siltation of very recent origin in geologic scale (about 70 years old). In this paper, stability analysis of proposed dyke for protection of the channel across Nayachara Island has been carried out using conventional limit equilibrium method and finite element method, considering the fluctuation of water level due to tidal effect. The factor of safety has been found out considering both drained and undrained conditions, simulating long term and short term stability of the dyke, respectively.

Landslide Simulation Using Limit Equilibrium and Finite Element Method

Slope stability analysis is one of the ancient tasks in the geotechnical engineering. There are two major methods; limit equilibrium method (LEM) and finite element method (FEM) that were used to analyze the factor of safety (FOS) to determine the stability of slope. The factor of safety will affect the remediation method to be underdesign or overdesign if the analysis method was not well chosen. This can lead to safety and costing problems which are the main concern. Furthermore, there were no statement that issued one of the analysis methods was more preferred than another. To achieve the objective of this research, the soil sample collected from landslide at Wang Kelian were tested to obtain the parameters of the soils. Then, those results were inserted into Plaxis and Slope/W software for modeling to obtain the factor of safety based on different cases such as geometry and homogenous of slope. The FOS obtained by FEM was generally lower compared to LEM but LEM can provide an obvious critical slip surface. This can be explained by their principles. Overall, the analysis method chosen must be based on the purpose of the analysis.

An extended shakedown theory on an elastic–plastic spherical shell

The article analyses one of possible optimization methodologies for ideal elastic–plastic structures at shakedown and its application for shallow spherical shells having prescribed geometry and affected by a variable repeated load (VRL) – a system of external forces that may vary independently of each other. The paper accepts that only time-independent upper and lower bounds of variations in external forces are given. The pronounced effect of external forces, i.e. in this context, possible histories of variations in forces, is not examined (the unloading phenomenon of cross-sections is ignored in the course of plastic deformation). The discussed concept of the structure at shakedown refers to the Melan theorem related to statically allowable admissible internal forces. Thus, for the discretization of the spherical shell, with the help of an assumption about small displacements, the equilibrium finite element method based on internal force approximation is applied. The limit axial force of the cross-section is supposed to be constant within the bounds of the finite element, and only the optimal distribution of limit internal forces among elements, according to the selected criterion, is in need of search. The article presents a discrete mathematical model for determining the optimal allocation problem with strength and stiffness requirements. The model conforms to the limit axial force of the shallow spherical shell of the variable repeated load and takes into account ultimate and serviceability limit states of EC3 with corresponding reliability levels. Structural optimization methods refer to extreme energy principles of mechanics and are illustrated with the numerical examples of spherical shell optimization.

Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

The rigid body limit equilibrium method (RBLEM) and finite element method (FEM) are two widely used approaches for rock slope’s stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety (FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory (DRT) is developed. With this theory, plastic complementary energy (PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope’s stability evaluation and reinforcement engineering practice in southwest of China.

Stable linear traction‐based equilibrium elements for elastostatics: Direct access to linear statically admissible stresses and quadratic kinematically admissible displacements for dual analysis

SummaryThis paper establishes the basic framework for the traction‐based equilibrium finite element method (traction‐based EFEM). Stable linear traction‐based equilibrium elements are formulated using the macro‐element technique. An arbitrary internal macro‐point renders a linear triangular element stable, while a stable linear quadrilateral element requires the macro‐point to locate at the intersection of diagonals. Then, a Lagrangian formulation is utilized to minimize the complementary energy under equilibrium constraints, and consequently, tractions as well as additional Lagrange multipliers are obtained. Linear statically admissible (SA) stresses are thereafter acquired from tractions. As for Lagrange multipliers, they turn out to coincide well with rigid‐body displacements in each element after simple modifications. With rigid‐body displacements and linear tractions known, quadratic displacements and the kinematically admissible (KA) counterpart thereof by recovery are obtainable. The knowledge of both SA stresses and KA displacements renders dual analysis directly applicable. That is to say, the traction‐based EFEM is featured with direct access to strict upper and lower bounds of strain energy and other quantities of interest. Copyright © 2014 John Wiley & Sons, Ltd.

Application Study on the Stability of Xiufengsi Landslide by Using Limit Equilibrium Method and Finite Element Method

Xiufengsi Landslide is an ancient landslide in Wushan County, Chongqing, China. Under natural condition, this landslide is stable. Due to the Three Gorges Reservoir, however, the water level in this region fluctuates within the range of [145 m, 175 m], periodically. Furthermore, an increasing number of residential quarters have been built on this landslide that also increase the possibility of occurrences of the landslide. Motivated by the government’s desire to take measures in control the landslide, we use two approaches to study the stability of this landslide. Under different computational conditions, the safety factors of the landslide are calculated by using limit equilibrium method and finite element method, respectively. Based on the comparison of the results, the stability of the landslide is analyzed more objectively and comprehensively. This work also lends insight into the landslide forecast.

Slope Stability Analysis with Finite Element Method

A slope is studied with limiting equilibrium method and finite element method comparatively. It is found that the results of the two methods are almost the same. The distribution of principal stress, maximal plastic strain, plastic zone, lateral displacement, vertical settlement and incremental of displacement can be investigated by FEM effectively, which make it easy to expediently choose the method of slope reinforcement and the position of strengthening.

Stability Analyses of Western Slopes in Jointed Rock Masses for GuangYang Highway

This paper presents the results of a study on a joint slope deformation affecting the western slope of the GuangYang highway (YangQuan, China). Fieldwork identified the ongoing deformational process and assisted in defining its mechanisms, evolution and controlling factors. Here we discuss how to use limit equilibrium methods to calculate the behavior of slopes and to use the finite element analysis to evaluate the stability, displacements of slopes and soil-slope stabilization interaction. The finite element method with shear strength reduction (SSR) technique is explained in Phase2D. This method is effective for the prediction of the stability of slope. Based on numerical comparisons between the limit equilibrium methods and finite element method, it is suggested that the finite element method with SSR technique is a reliable and maybe unique approach to evaluate the slope stability. The paper also took into account effectiveness of the large rain and seismic load. The results of the numerical analysis are consistent with the observed slope surface evidence.

Stability Analyses of an Earth Dam Using Limit Equilibrium and Finite Element Methods

The objective of this research is to study the relationships between the stability of earth dam and its soil strength parameters. The soil strength parameters include cohesion, unit weight of soil and angle of friction. GeoStudio, commercially available software, was used to obtain the overall factor of safety using limit equilibrium method (LEM) and finite element method (FEM). Tables to show the relationships among soil strength parameters for factor of safety 1.0 and 1.5 are presented in this paper.

Stability analysis and monitoring study of Jijia River landslide based on WebGIS

On the basis of in situ investigation and deformation monitoring of the Jijia River landslide (JJRL), the rigid body limit equilibrium method and finite element method (FEM) were used to analyze the stability of the JJRL; the grey system theory method was applied to forecast the deformation trend of the JJRL; and the information system about the landslide deformation and monitoring, and forecasting systems based on the platform of the Web Geographical Information System (WebGIS) were developed, which can be used to analyze in situ monitoring data and predict the deformation of the landslide. The study results can be summarized as follows: ➀ the JJRL is stable as a whole; the water content in the landslide has a great effect on its stability; ➁ the developed Web Geographical Information System has realized many functions, including inputting, computing, inquiry, analyzing, and the function of forecasting; it has also realized the functions of distance data management, analysis, and forecasting based on the WebGIS; ➂ the information resource can be shared by the WebGIS developed all over the world.

INCREMENTAL METHOD FOR UNLOADING PHENOMENON FIXATION AT SHAKEDOWN

Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.

An inflatable fabric beam finite element

AbstractInflatable structures made of modern textile materials with important mechanical characteristics can be inflated at high pressure (up to several hundreds kPa). For such values of the pressure they have a strong mechanical strength. The aim of the paper is to construct a new inflatable beam finite element able to predict the behaviour of inflatable structures made of beam elements. Experiments and analytical studies on inflatable fabric beams at high pressure have shown that their compliance is the sum of the beam compliance and of the yarn compliance. This new finite element is therefore obtained by the equilibrium finite element method and is modified into a displacement finite element. The stiffness matrix takes into account the inflation pressure. Comparisons between experimental and numerical results are shown and prove the accuracy of this new finite element for solving problems of inflatable beams at high pressure. Copyright © 2003 John Wiley & Sons, Ltd.

INCREMENTAL METHOD FOR UNLOADING PHENOMENON FIXATION AT SHAKEDOWN

Abstract Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.

Upper and lower bounds for evaluation of nonlinear fracture parameters

Bound theorems for estimating small strain nonlinear fracture parameters are proposed. It is found that the lower bound for the J-integral can be obtained by a compatible displacement finite element method. On the other hand, the upper bound of the I∗-integral, which is the dual counterpart of the J-integral, can be obtained by an equilibrium finite element method. To verify the theorems and avoid the difficulty of designing equilibrium finite element models, the popular Pian–Sumihara hybrid stress model is modified by incorporating a penalty-equilibrium constraint. Moreover, an incremental formulation of the I∗-integral for nonlinear finite element computation is developed. Numerical examples on different crack and loading configurations are presented. All the results indicate the validity of the theorems.