Equilibrium Method Research Articles

Slope stability modeling using limit equilibrium and finite element methods: A case study of the Adama City, Northern Main Ethiopian Rift

Slope failure is a prominent and recurring geohazard in numerous parts of Ethiopia, including Adama City, which is located in the Northern Main Ethiopian Rift (NMER). The city is surrounded by two ridges oriented in the NNE-SSW direction, which are susceptible to slope instability. Thus, this study is aimed at modeling slope stability along these two ridges using Finite Element Method (FEM) and Limit Equilibrium Method (LEM). The modeling was carried out on slopes of multifaceted geometry composed of eluvium soil, pumice, and moderately to highly-weathered ignimbrites. Critical slope sections were identified using satellite imagery and field manifestations such as slope toe condition and slope face tilting. Their geometries were then inferred from detailed geological cross-sections based on field data. Input parameters for the modeling, such as cohesion, friction angle, and elastic modulus, were calculated via Back Analysis using the Hoek-Brown criterion while unit weight and Poisson ratio were determined from empirical equations. For soil formations, the parameters were determined via standard laboratory experiments. The modeling was then carried out under different conditions, including dry, saturated, static, and dynamic conditions. Results from both LEM and FEM models revealed that three of the four analyzed slope segments were unstable under dynamic and saturated conditions, highlighting the influence and importance of precipitation and seismicity as triggering variables. Results from both methods tend to agree when the critical slip surface passes through a single geological material in both models. However, notable differences arise when the slip surface involves multiple geological materials. Under such conditions, LEM tends to yield higher FOS values compared to FEM. The results also showed that all unstable slopes were associated with the NNE-SSW striking fault of the study area, as inferred from failure surfaces generated from both models and field data. The study concluded that unstable slopes pose a serious risk to nearby residents and infrastructure, and as a remedy, it designed and recommended coupled benching and slope flattening.

Numerical Investigation of Bedding Rock Slope Potential Failure Modes and Triggering Factors: A Case Study of a Bridge Anchorage Excavated Foundation Pit Slope

The analysis of slope failure modes is essential for understanding slope stability. This study investigated the failure modes and triggering factors of a rock slope using the limit equilibrium method, finite differences method, and exploratory factor analysis. First, the limit equilibrium method was used to identify potential sliding surfaces. Then, the finite differences method was employed to study deformation and failure features in a slope. Stability factors were calculated considering specific conditions such as rainfall, prestressing loss, and earthquakes using the strength reduction method. Finally, exploratory factor analysis was utilized to identify the triggering factors of each failure mode. The results revealed that failure modes were categorized into two types based on the positions of the sliding surface. The main triggering factors for Failure Mode 1 were rainfall and prestress loss, while for Failure Mode 2 they were earthquake loading and prestress loss. This study offers a comprehensive exploration of potential failure modes and their triggering factors from mechanical and statistical perspectives, enriching our understanding of potential failure modes in rock slopes.

A Limit Equilibrium Method Based on Geostress Calculated by Implicit Stabilized Node-Based Smoothed Finite Element Method for Stability Analysis of Soil Slopes

A Limit Equilibrium Method Based on Geostress Calculated by Implicit Stabilized Node-Based Smoothed Finite Element Method for Stability Analysis of Soil Slopes

Monitoring Surface Deformations in a Fossil Landslide Zone and Identifying Potential Failure Mechanisms: A Case Study of Gümüşhane State Hospital.

The escalating occurrence of landslides has drawn increasing attention from the scientific community, primarily driven by a combination of natural phenomena such as unpredictable seismic events, intensified precipitation, and rapid snowmelt attributable to climate fluctuations, compounded by inadequacies in engineering practices during site selection. Within the scope of this investigation, contemporary geodetic techniques using the GNSS were employed to monitor structural and surface deformations in and around a hospital edifice situated within an ancient fossil landslide region. Additionally, inclinometer measurements facilitated the determination of slip circle parameters. A subsequent analysis integrated these datasets to scrutinize both the hospital structure and its surrounding slopes. In addition to the finite element method, four different limit equilibrium methods (Bishop, GLE-Morgenstern-Price, Spencer, and Janbu) were used in the evaluation of stability. Since the safety number determined in all analyses was <1, it was determined that the slope containing the hospital building was unstable. The movement has occurred again due to the additional load created by the hospital building built on the currently stable slope, the effect of surface and groundwater, and the improperly designed road route. As a result of geodetic monitoring, it was determined that the sliding speed on the surface was in the N-E direction and was approximately 3 cm, and this situation almost coincided with inclinometer measurements.

Influence of 3D subsurface flow on slope stability for unsaturated soils

The occurrence of rainfall-induced slope failures has become more frequent due to the effect of climate change. Hence, various studies have been conducted to analyse the effect of rainfall infiltration on slope stability. Physically-based hydrological models have been commonly used with slope stability models such as the infinite slope model to develop slope susceptibility maps. However, a combination of three-dimensional (3D) water balance model with 3D limit equilibrium method (LEM) has not been commonly used. Hence, in this study, a water balance model, GEOtop was used to investigate the influence of subsurface flow in unsaturated soil under extreme rainfall conditions on regional slope stability in 3D directions. The results from the GEOtop model were used as inputs for 3D LEM slope stability analysis performed using the Scoops3D software to obtain the factor of safety (FOS) map for the region. Four slopes within the region were then selected to be modelled in the two-dimensional (2D) seepage and slope stability analyses, SEEP/W and SLOPE/W. Results from the detailed study showed that the pore-water pressures (PWPs) from the 3D water balance analyses were found to be higher than the 2D seepage analyses. Under similar PWP conditions, the FOS from the 2D slope stability analysis was observed to be lower than the 3D analysis for two out of the four slopes. However, the combined 3D water balance and slope stability analyses produced lower FOS compared to the 2D seepage and slope stability analyses due to the higher PWPs in the 3D water balance analyses. Therefore, this study highlights the importance of considering the 3D subsurface flow in unsaturated soil given that it has a significant influence on the FOS of slopes.

Thermodynamic Properties of Sulfur in the CaO–AlO1.5–CeO1.5 Slag System at 1873 K

Elements with a high affinity for O and S in molten steel are desirable as deoxidizing and desulfurizing agents in the steel refining process, and Ce has attracted attention. In this study, the thermodynamic properties of sulfur in a CaO–AlO1.5–CeO1.5 slag system at 1873 K are investigated. A chemical equilibrium method using Cu is employed for these measurements. Sulfide capacities are determined in the CaO–AlO1.5–CeO1.5 system to show desulfurization ability; the precipitated phases are identified when large amounts of sulfur are added to the CaO–AlO1.5–CeO1.5 system; the solubility of CaS in the CaO–AlO1.5–CeO1.5 system is determined. It is suggested that the slag of this system can improve sulfur distribution while reducing the Al concentration in the steel.

Stability analysis of tunnel face considering the shape of excavation and reinforcement measures

In mountain tunnels, a series of advanced reinforcement measures are often employed to maintain the stability of the tunnel face, particularly in challenging geological conditions. However, there is a lack of design theories regarding the advanced support structure for uniquely shaped tunnel faces, necessitating further exploration. Based on the limit equilibrium method, this paper presents a derivation of the mechanical model for analyzing excavation face stability considering shape changes and bolts. Additionally, a design theory for horizontal glass fiber bolts in longitudinally inclined tunnel faces is established. The reinforcement effect of the pipe shed is further considered. Finally, the proposed model is validated, and parameter analysis is conducted to guide design practices.

Sorption kinetics of salt-in-porous-matrix composites: The effect of expanded natural graphite on cooling power

Sorption heat transformers and thermal energy storage systems are emerging technologies that utilize and store low-grade waste heat for heating and cooling applications. The performance of sorption systems is not only affected by systems’ operating conditions, and overall systems’ design but also by sorption material or composite parameters such as thermal diffusivity, composition, and pore structure, among others. In this study, CaCl2-based salt-in-porous-matrix composites of different compositions and coating thicknesses were synthesized. During synthesis, salt to silica gel and polyvinyl alcohol to silica gel ratios were fixed and the thermal additive (expanded natural graphite) to silica gel ratio was varied with care from 0 to 0.26 (or 0 to 20.5 wt.%, additive to silica gel ratio). The thickness of samples varied from 2.3 to 8.3 ± 0.1 mm. The composites were characterized by a transient plane source (thermal conductivity and thermal diffusivity), nitrogen adsorption porosimetry (specific surface area and total pore volume), and thermogravimetric sorption analysis (water sorption equilibrium) methods. A custom-built gravimetric large pressure jump (G-LPJ) testbed was used to study water sorption kinetics (water uptake vs. time) for selected samples. The thermal conductivity and diffusivity of the studied composite samples have shown significant enhancements, e.g., 240% (0.11 W/(m·K) vs. 0.37 W/(m·K)) and 310% (0.21 mm2/s vs. 0.87 mm2/s), respectively, by adding 12.5 wt.% expanded natural graphite (additive to silica gel ratio is 0.14) as a thermally conductive additive (additive to silica gel ratio) because of thermal percolation effect. This ratio of expanded natural graphite to silica gel was found to be optimal for studied composition. The results indicate that sorption composites with higher thermal diffusivity offer notably higher specific cooling power and improved sorption kinetics, compared to the composites without expanded natural graphite of the same thickness (850 W/kg vs. 480 W/kg at 70% water conversion for samples with thickness of 5.3 mm).

The determination of the solubility, enthalpy, and entropy of solutions of methyl Furan-2,5-Dimethylenedicarbamate and its hydrides in different solvents

The solubilities of methyl furan-2,5-dimethylenedicarbamate (FDC) and methyl tetrahydrofuran-2,5-dimethylenedicarbamate (THFDC) in dimethyl carbonate (DMC), anhydrous ethanol (EtOH) and benzene were studied using the static equilibrium method combined with high-performance liquid chromatography under atmospheric pressure at temperatures ranging from 278.15 K to 318.15 K. The experimental results demonstrate that the solubility of FDC and THFDC exhibits an upward trend as temperature increases. Among the six correlation models used, all of them (modified Apelblat equation, Buchowski-ksiazczak (λh) model, simplified two-parameter equation, polynomial equation, NRTL model and Wilson model) can effectively correlate the solubility data. Notably, the Wilson model demonstrates superior correlation performance compared to others in FDC system and the NRTL model demonstrates superior correlation performance compared to others in THFDC system. Using the modified Van’t Hoff equation and Gibbs equation, we calculated the apparent standard dissolution enthalpy (ΔHsol), the standard dissolution entropy change (ΔSsol), and the standard dissolution Gibbs energy (ΔGsol) for FDC and THFDC in different solvents. The research resulted indicate that all these dissolution processes are non-spontaneous, entropy-increasing endothermic processes. This study provides valuable reference data for crystallization and purification in industrial production.

Solubility measurements, correlations, DFT calculations, and thermodynamic properties of p-methylbenzyl alcohol in twelve organic solvents

This study had investigated the solubility of p-methylbenzyl alcohol (PMAL) by the static equilibrium method. Solubility data were determined in six common alcoholic solvents (methanol, ethanol, n-propanol, i-propanol, n-butanol, i-butanol) and non-alcoholic solvents (acetone, acetonitrile, ethyl formate, ethyl acetate, dichloromethane, 1,2-dichloroethane) over a temperature range of 278.15–313.15 K. The effect of temperature on PMAL solubility was significant in both solvent types, particularly in acetonitrile. Six thermodynamics models were employed to correlate the solubility data, with the modified Apelblat equation providing the best fit. The study also analyzed the factors influencing PMAL solubility by integrating the physicochemical properties of the solvents with Density Functional Theory calculations. The result suggested that multiple factors affect PMAL solubility in both solvent categories. Additionally, the electrostatic potential energy surfaces and the solvent–solute interaction energies were calculated based on Density Functional Theory. The order of interaction energies correlated with solubility trends. The calculated apparent thermodynamic properties, derived from the Van’t Hoff equation, revealed that the dissolution process was entropy-driven with heat absorption.

Slope Stability Analysis of Rockfill Embankments Considering Stress-Dependent Spatial Variability in Friction Angle of Granular Materials

Slope stability is a major safety concern of rockfill embankments. Since rockfills are incohesive materials, only friction angle is considered as a shear strength parameter in the slope stability analysis of rockfill embankments. Recently, it was found that confining pressure can significantly affect the mean value and variance of the friction angle of rockfills. Since the confining pressure spatially varies within a rockfill embankment, the effect of stress-dependent spatial variability in the friction angle of rockfills should be investigated for slope stability evaluation of rockfill embankments. In the framework of the Limit Equilibrium Method (LEM), an approach is proposed for the slope stability analysis of rockfill embankments considering the stress-dependent spatial variability in the friction angle. The safety factors of slope stability are computed with variable values of the friction angle at the bases of slices which are determined by the stress-dependent mean value and variance of the friction angle of rockfills. The slope stability of a homogeneous rockfill embankment is analyzed to illustrate the proposed approach, and a parametric analysis is carried out to explore the effect of variation in the parameters of the variance function of friction angle on slope stability. The illustrative example demonstrates that the stress-dependent spatial variability of friction angle along the slip surface is obvious and is affected by the location of the slip surface and the loading condition. The effects of the stress-dependent spatial variability of the friction angle on the slope stability of high rockfill embankments should be considered.

Seismic analysis of geosynthetic-reinforced soil walls in tiered configuration

Research on geosynthetic-reinforced soil (GRS) walls in tiered configurations is increasing gaining attention, with numerical methods being predominantly used in the past. In recent years, there has been a growing trend in conducting shaking table tests to further explore this area. However, traditional limit equilibrium (LE) methods are more preferred for design purposes. This study utilized a modified top-down approach, which is based on LE and pseudo-static methods to investigate the horizontal seismic force on the distribution of required tension along each reinforcement layer. The approach is initially extended from static analysis to seismic analysis for multitiered GRS walls. Parametric analyses are conducted to study the impacts that horizontal seismic coefficient, reinforcement length and spacing, internal friction angle of soil, height ratio of upper/lower tier, offset distance have on the internal stability of two-tiered GRS walls. Meanwhile, influences of wall batter and number of tiers on the critical offset distance for different seismic coefficients are assessed. Results indicate that the internal stability differs between the upper and lower tiers under seismic conditions, particularly with higher seismic forces, where the lower tier requires greater reinforcement tension to enhance its stability. Additionally, the critical offset distance grows with the increase in seismic coefficient, and it is sensitive to the internal friction angle of soil and the height ratio.

Optimasi Desain Geometri Lereng Material Old Dump Pada Usaha Penggalian Ulang Pit X PT. Bukit Asam Tbk

In doing slope design, it is necessary to pay attention to slope geometry and soil shear strength. Determination of slope geometry design also considers the balance between height and slope and production benefits. Research was conducted to analyze slope stability through physical and mechanical properties testing, limit equilibrium, and probabilistic Monte Carlo methods. The surface area of the Overburden stripping area in the 2024 RKP design is 8,172.79 m2. The production target is 2,000,000 tons of coal with a volume of overburden material that must be stripped of 29,000,000 BCM and obtained a Stripping Ratio value of 14.5. The results of the evaluation of the overall slope of the Old Dump material with an overall slope height of 66.582 m, a slope width of 447.69 m, an overall slope of 8.32˚ and a bench width of 25 m, a bench height of 6 m with a comparison ratio of 1:3 and a single slope angle of 18.43˚. Then the redesign was carried out and obtained recommendation results of 64.799 m overall slope height, 303.33 m slope width, 13.02˚ overall slope, and 25 m bench width, bench height at elevation 131-110 of 8 m with a comparison ratio of 1:2, single slope 26.57˚ and at elevation 110-50 of 8 m with a comparison ratio of 1:1.5, single slope 33.69˚.

Detection of Cliff Top Erosion Drivers through Machine Learning Algorithms between Portonovo and Trave Cliffs (Ancona, Italy)

Rocky coastlines are characterised by steep cliffs, which frequently experience a variety of natural processes that often exhibit intricate interdependencies, such as rainfall, ice and water run-off, and marine actions. The advent of high temporal and spatial resolution data, that can be acquired through remote sensing and geomatics techniques, has facilitated the safe exploration of otherwise inaccessible areas. The datasets that can be gathered from these techniques, typically combined with data from fieldwork, can subsequently undergo analyses employing/applying machine learning algorithms and/or numerical modeling, in order to identify/discern the predominant influencing factors affecting cliff top erosion. This study focuses on a specific case situated at the Conero promontory of the Adriatic Sea in the Marche region. The research methodology entails several steps. Initially, the morphological, geological and geomechanical characteristics of the areas were determined through unmanned aerial vehicle (UAV) and conventional geological/geomechanical surveys. Subsequently, cliff top retreat was determined within a GIS environment by comparing orthophotos taken in 1978 and 2022 using the DSAS tool (Digital Shoreline Analysis System), highlighting cliff top retreat up to 50 m in some sectors. Further analysis was conducted via the use of two Machine Learning (ML) algorithms, namely Random Forest (RF) and eXtreme Gradient Boosting (XGB). The Mean Decrease in Impurity (MDI) methodology was employed to assess the significance of each factor. Both algorithms yielded congruent results, emphasising that cliff top erosion rates are primarily influenced by slope height. Finally, a validation of the ML algorithm results was conducted using 2D Limit Equilibrium Method (LEM) codes. Ten sections extracted from the sector experiencing the most substantial cliff top retreat, as identified by DSAS, were utilised for 2D LEM analysis. Factor of Safety (FS) values were identified and compared with the cliff height of each section. The results from the 2D LEM analyses corroborated the outputs of the ML algorithms, showing a strong correlation between the slope instability and slope height (R2 of 0.84), with FS decreasing with slope height.

Evaluating the influence of backfilling on the stability of an abandoned room-and-pillar mine: a case study in northern Spain

Bodovalle is a siderite mine located in northern Spain that is currently in the closure phase. The mine was exploited using the room-and-pillar method. Subsidence processes have occurred previously and reached the surface because of the collapse of several pillars into the mine. To prevent such risky situations, the closure plan has been modified and the backfilling of some rooms has been considered. This study aimed to evaluate the global stability of room #1.1 after backfilling. This paper combines the use of traditional techniques, numerical modelling and remote sensing to achieve this objective. Limit equilibrium methods, LIDAR technology and numerical methods-based software were employed to evaluate the stability of rooms and pillars surrounding room #1.1 and considering different backfilling levels. In all possible backfilling scenarios involving room #1.1, the impact on the surface and neighboring rooms is negligible. In addition, no substantial changes in the safety factors and deformations of the neighboring rooms were observed for both studied levels of backfilling. Thus, backfilling is an adequate countermeasure to avoid subsidence.

How large is the collapsed area of ground collapse induced by tunnelling

ABSTRACT Ground collapse has frequently been reported in recent years, which poses a great threat to the safety of human beings and property. This study aims to determine the collapsing diameter and volume of tunnelling-induced ground collapse by analytical method. Firstly, assuming that the surface of collapsed block is sliding along a planar surface, and the sliding area is derived based on the limit equilibrium method. Then, the collapse volume is derived by combining with the equation of the collapse trajectory. Lastly, the proposed method is verified by a physical modelling test. The results show that (i) as the unit weight of soil, buried-depth and the radius of tunnel increase, the influencing diameter and collapse volume gradually increase; (ii) with the increase in the cohesion and friction angle of the soil, the influencing diameter and collapse volume gradually decrease. Dongquan Tunnel is taken as a case study, the influencing diameter of ground by using the proposed approach is compared with the one in practical engineering. This study provides a theoretical guideline to mark the collapse warning lines by the potential ground collapse area, which is induced by excavation of shallow-buried tunnels or underground structures.

Adsorption–desorption and leaching behavior of benzovindiflupyr in different soil types

Benzovindiflupyr is a succinate dehydrogenase inhibitor fungicide that targets mitochondrial function for disease control. In this study, we investigated the adsorption–desorption and leaching behavior of benzovindiflupyr in eight soil types using the batch equilibrium method and the soil column leaching method. A Freundlich model (r2 > 0.9959) was used to better characterize the adsorption-desorption process in eight soil types, with adsorption coefficients (KF-ads) ranging from 2.303 to 17.886. KF-ads was significantly and positively correlated (p < 0.05) with the organic carbon content. High temperatures and increased initial pH of aqueous solutions led to a decrease in benzovindiflupyr adsorption in the soil. The adsorption was also influenced by factors such as ionic strength, humic acid, surfactant type, microplastic type, and particle size and concentration. Moreover, benzovindiflupyr exhibited low leachability in all four soils selected, but different leaching solutions affected the risk of benzovindiflupyr migration to groundwater. Overall, this study provides insights into the adsorption characteristics of benzovindiflupyr in different soils and provides key information for environmental risk assessment.

Local Structure-Preserving Relaxation Method for Equilibrium of Charged Systems on Unstructured Meshes

Local Structure-Preserving Relaxation Method for Equilibrium of Charged Systems on Unstructured Meshes

Analisis Penggunaan Tanaman Vetiver terhadap Stabilitas Lereng pada Bendungan Way Sekampung

Problems that occur in the western part of As Way Sekampung have the potential for landslides to occur. Efforts used to handle slope strengthening by planting vetiver plants. The research method used to analyze slopes uses the limit equilibrium method on slip surface sections using the Morgenstren-Price method with the help of Geostudio 2023.1.0 software. SLOPE/W to get the safety factor under normal conditions and under seismic load conditions. By using a seismic load with a return period of 500 years (PE 10% in 50 years) with a Peak Ground Acceleration (PGA) value for the Way Sekampung Dam inundation area of 0,265 g. In vetiver plants, the root depth is simulated according to the top soil depth of 0,0 – 0,1 m. Soil planted with vetiver plants experienced an increase in the value of cohesion (c) by 74,42% and a decrease in the value of the angle of internal friction (φ˚) by 49,40%. The conclusion obtained was that slope stability in normal existing conditions was 4,525 and in normal vetiver plant strengthening conditions the safety factor increased to 4,529. Then, in the existing seismic conditions, the safety factor is 2,624 and in strengthening vetiver plants with seismic loads, the safety factor value increases to 2,626. It can be concluded that vetiver plants are able to strengthen slope conditions.

Solid-Liquid Phase Equilibria of the Pb2+, Ca2+, Mg2+//Cl--H2O Quaternary System and Its Subsystems at 303.2 K.

The solid-liquid phase equilibria of the ternary systems Pb2+, Ca2+//Cl--H2O, Pb2+, Mg2+//Cl--H2O, and Ca2+, Mg2+//Cl--H2O were investigated at atmospheric pressure and T = 303.2 K using the isothermal dissolution equilibrium method. Additionally, solid phase equilibria of the quaternary system Pb2+, Mg2+, and Ca2+//Cl--H2O were determined, and the corresponding stable phase diagrams and density-composition diagrams were constructed. The results indicate that the phase diagrams of Pb2+, Ca2+//Cl--H2O mainly consist of a ternary invariant point, two solubility curves, and four crystalline regions, while there are two ternary invariant points, three solubility curves, and six crystalline regions in the Pb2+, Mg2+//Cl--H2O and Ca2+, Mg2+//Cl--H2O systems. The results of the density-versus-w(CaCl2) plots of the various ternary systems confirm that the density of the equilibrium solution tends to go upward with the increase in the mass fraction of CaCl2. The density of various ternary systems reaches the maximum and equilibrium at the corresponding invariant point, and there is no significant change with the further increase in the CaCl2 mass fraction. Furthermore, the phase diagram of the Pb2+, Mg2+, Ca2+//Cl--H2O quaternary system includes two invariant points, five isothermal dissolution curves, and five crystalline regions. The order of the relative areas of the crystalline regions for the five salts is PbCl2 > CaCl2·2MgCl2·12H2O > 2PbCl2·3MgCl2·18H2O > MgCl2·6H2O > CaCl2·4H2O.