Engineering Geology最新文献

{"title":"Deformation characteristics and influencing factors of loess fill foundation based on InSAR technique","authors":"Siyuan Ren,&nbsp;Haiman Wang,&nbsp;Wankui Ni,&nbsp;Anzhi Shen","doi":"10.1016/j.enggeo.2025.108098","DOIUrl":"10.1016/j.enggeo.2025.108098","url":null,"abstract":"<div><div>Ground subsidence is a common urban geological hazard in several regions worldwide. The settlement of loess fill foundations exhibits more complex subsidence issues under the coupled effects of geomechanical and seepage-driven processes. This study selected 21 ascending Sentinel-1 A radar images from April 2023 to October 2024 to monitor the loess fill foundation in Shaanxi, China. To minimize errors caused by the orbital phase and residual flat-earth phase, this research combined PS-InSAR technology with the three-threshold method to improve the SBAS-InSAR processing workflow, thereby exploring time-series deformation of the loess fill foundation. Compared with conventional SBAS-InSAR technology, the improved SBAS-InSAR technique provided more consistent deformation time-series results with leveling data, effectively capturing the deformation characteristics of the fill foundation. Additionally, geographic information system (GIS) spatial analysis techniques and statistical methods were employed to analyze the overall characteristics and spatiotemporal evolution of the ground surface deformation in the study area. On the other hand, the major drivers of the subsidence in the study area were also discussed based on indoor experiments and engineering geological data. The results showed gradual and temporal shifts of the subsidence center toward areas with the maximum fill depths. In addition, two directions of uneven subsidence were observed within the fill foundation study area. The differences in the fill depth and soil properties caused by the building foundation construction were the main factors contributing to the uneven settlement of the foundations. Foundation deformation was also positively and negatively affected by surface water infiltration. This study integrates remote sensing and engineering geological data to provide a scientific basis for accurately monitoring and predicting loess fill foundation settlement. It also offers practical guidance for regional infrastructure development and geological hazard prevention.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"353 ","pages":"Article 108098"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gas permeability and microscopic mechanisms of Xanthan gum-amended compacted lean clay as a gas barrier material","authors":"Ying-Zhen Li ,&nbsp;Jia-Lei Wan ,&nbsp;Fei Jin ,&nbsp;Krishna R. Reddy ,&nbsp;Ning-Jun Jiang ,&nbsp;Yan-Jun Du","doi":"10.1016/j.enggeo.2025.108095","DOIUrl":"10.1016/j.enggeo.2025.108095","url":null,"abstract":"<div><div>Compacted clays are extensively used as cover barriers to control rainfall infiltration and upward migration of greenhouse gases at municipal solid waste landfills and volatile organic compounds at industrially contaminated sites. Xanthan gum (XG) amendment offers a green and low-carbon solution to improve gas breakthrough pressure and reduce gas permeability of compacted clays, sustainably improve earthen structures. This study aimed to systematically investigate the effects of XG amendment on gas breakthrough pressure, gas permeability, and hydraulic conductivity of compacted clay liners. The gas breakthrough pressure increased from 0.6 kPa to 2.2 kPa (improve ∼4 times) and the gas permeability decreased from 2.2 × 10⁻¹⁴ m² to 4.8 × 10⁻¹⁶ m² (reduce ∼200 times) when the XG dosage increased from 0 % to 2 % and apparent degree of saturation was 100 %. Hydraulic conductivity of XG-amended soil at 1 % XG dosage was 2.6 × 10⁻¹⁰ m/s, which was 3 % of the value measured in unamended soil. Mechanisms of enhanced gas barrier and hydraulic performance were interpreted by the combined effects of (i) soil pore filling substantiated by the analyses of scanning electron microscopy and pore size distribution; (ii) high viscosity of XG hydrogels, validated by the measurement of rheological properties; and (iii) increased diffuse double layer thickness of the amended soils evidenced by the zeta potential analysis.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"353 ","pages":"Article 108095"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimation of volumetric block proportions from 1D boring of bim-materials considering different block forms","authors":"Han Zhang ,&nbsp;Chengyou Huang ,&nbsp;Lehua Wang ,&nbsp;Yining Cao ,&nbsp;Daniela Boldini","doi":"10.1016/j.enggeo.2025.108094","DOIUrl":"10.1016/j.enggeo.2025.108094","url":null,"abstract":"<div><div>Understanding the mechanical behavior of block-in-matrix geomaterials (bim-materials) is crucial for estimating the stability and designing reinforcements for natural slopes. This behavior is primarily influenced by the volumetric block proportion (<em>VBP</em>). Typically, the <em>VBP</em> is estimated using in-situ 1D boring data, which can differ from the actual 3D <em>VBP</em>. To address this discrepancy, uncertainty factors were introduced by Medley (1997) and subsequently refined by Napoli et al. (2022a) to estimate the actual 3D <em>VBP</em> from the linear block proportion (<em>LBP</em>) obtained via 1D boring. In this study, the coefficient of variation (<em>COV</em>) is further refined by incorporating the effects of block morphology. Actual 3D block geometries were reconstructed using CT scanning, focusing on four typical block geometries: spheroidal, prolate, oblate, and blade shapes. A novel method for generating virtual 3D block assembly models was developed, achieving an 86 % reduction in the time required to generate a 3D block assembly model for a 42 % <em>VBP</em> configuration by minimizing the number of blocks to be assessed and optimizing vertex checks. In total, 88 block assembly models were established with varying <em>VBP</em>s, block forms, and engineering dimensions (<em>L</em>_<em>c</em>), to examine their effects on <em>COV</em> values. The updated <em>COV</em> values were then applied to estimate <em>VBP</em> in bim-materials in the Scott Dam and Shuping landslide case studies. The reliability of these <em>COV</em> values was confirmed by comparison with previous studies by Medley and Napoli et al. under similar conditions. The analysis revealed that <em>COV</em> values decrease with increasing sampling length (<em>N</em>) and <em>VBP</em>, reflecting the lower heterogeneity of block distributions. Spheroidal blocks exhibit the highest <em>COV</em> values, while blade and oblate blocks show the lowest. Notably, <em>VBP</em> and block form were found to have a significant impact on <em>COV</em> values, particularly within the 13 % to 32 % <em>VBP</em> range, whereas the influence of engineering dimensions <em>L</em>_<em>c</em> is minimal. The updated <em>COV</em> values provide a more means of estimating actual <em>VBP</em> from in-situ borehole <em>LBP</em> measurements. This improvement is critical for enhancing the accuracy of stability assessments in engineering projects involving bim-materials.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"353 ","pages":"Article 108094"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hydraulic conductivity model incorporating adsorption and capillarity for unsaturated/frozen soil","authors":"Yijie Wang ,&nbsp;Yandi Wu ,&nbsp;Liming Hu ,&nbsp;Pierre-Yves Hicher ,&nbsp;Zhen-Yu Yin","doi":"10.1016/j.enggeo.2025.108093","DOIUrl":"10.1016/j.enggeo.2025.108093","url":null,"abstract":"<div><div>Hydraulic conductivity is a key parameter for describing seepage-related issues in soils. The soil water retention, soil water freezing, and soil water flow are essentially dominated by adsorption and capillarity. However, these mechanisms have not been effectively incorporated into a unified hydraulic conductivity model. This study proposes a hydraulic conductivity model based on the Navier-Stokes equations and capillary bundle model, which is applicable to both unsaturated and frozen soils. By considering the different influences of adsorption and capillarity on water flow and water freezing, the model can predict the hydraulic conductivities of soils in different states and distinguish the contributions of capillary flow and film flow to the total permeability. Benefiting from the consideration of physical mechanisms, the proposed model can use any of the soil water characteristic curve, the soil freezing characteristic curve, or the particle size distribution as input. The model achieves better prediction accuracy than existing models that do not consider the film flow and its reliability is validated through extensive experimental data including various sands, silts, and lean clays. This study not only provides an effective tool for predicting hydraulic conductivity but also highlights the underlying physical connections between soil water retention, soil water freezing, and seepage.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"353 ","pages":"Article 108093"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A big indirect data – Informed probabilistic method for three-dimensional site reconstruction","authors":"Zhiyong Yang ,&nbsp;Xueyou Li ,&nbsp;Xiaohui Qi ,&nbsp;Zhijun Liu","doi":"10.1016/j.enggeo.2025.108097","DOIUrl":"10.1016/j.enggeo.2025.108097","url":null,"abstract":"<div><div>Three-dimensional (3D) reconstruction of a sparse measurement site is of paramount significance for the safety assessments or designing of the geotechnical structures. However, this task is often challenging because the site investigation data generally are sparse due to the limit budget, leading to large statistical uncertainties in the soil parameters. The challenge is further exacerbated by computational issues such as inversion or decomposition of the large correlation matrix, which frequently arises when dealing with large-scale 3D sites. To address these challenges, this paper proposes a novel big indirect data-informed three-dimensional site reconstruction method using hybrid Bayesian theory. The proposed method first constructs the probability distribution functions (PDFs) of the soil parameters of the big indirect data collected from worldwide historical sites and the soil parameters of the targeted site using the Gibbs sampler. The two PDFs are then integrated to form a hybrid PDF of the target site. Based on the hybrid PDF, the three-dimensional site is reconstructed with consideration of spatial variabilities of the soil parameters using multiple multivariate conditional random fields. The Kronecker product is utilized to decompose the large autocorrelation matrix into several small matrices that can be easily handled. A virtual site and a real site in Huizhou, China are employed to demonstrate the capability of the proposed method. The results show that the proposed method can effectively reduce the statistical uncertainty of soil parameters caused by sparse measurement. It offers a transformative tool that utilizes generic geotechnical big indirect data to supplement sparse local data, enabling effective 3D site construction.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"353 ","pages":"Article 108097"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Physical vulnerability assessment procedures for confined and unconfined (unreinforced) clay brick masonry buildings due to mass movements, rigid foundation","authors":"Alfer L. Silva-Ceron,&nbsp;Jorge A. Prieto,&nbsp;Marco F. Gamboa","doi":"10.1016/j.enggeo.2025.108091","DOIUrl":"10.1016/j.enggeo.2025.108091","url":null,"abstract":"<div><div>While climate change and urban development in mountainous terrain continue to impact society through geo-mass transport phenomena, quantitative risk models must evolve and be communicated as clearly as possible to enhance the social appropriation of knowledge. Recent advancements in mass movement risk analysis equate external hazard intensity measures with the internal strength of buildings. However, procedures for estimating building capacity and developing fragility curves remain less well-defined, particularly for masonry buildings, which are among the most common construction types worldwide, especially in less developed regions, and where laboratory or field data may be scarce. Fragility curves relate hazard intensity to the probability of reaching or exceeding a level of physical damage and have thus become essential tools in vulnerability and risk assessments related to natural hazards. This paper presents a procedure for deriving structural damage thresholds through fragility curves for mass movements, featuring the following characteristics: it is not based on seismic design parameters, does not require excessive computational resources, and is straightforward to implement. Recognizing that damage during a mass movement event may depend not only on the structural strength of buildings —assuming a rigid foundation— but also on ground resistance, which can cause permanent deformations, this study focuses on the rigid, fixed foundation scenario. The method incorporates geometrical and mechanical parameters along with their associated uncertainties, and provides damage state thresholds as functions of momentum flux and mass movement height for two typical wall types: unconfined, unreinforced clay brick masonry (URM) and confined clay brick masonry (CM).</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"352 ","pages":"Article 108091"},"PeriodicalIF":6.9,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Instability mechanism of reservoir landslides under combined effects of water level fluctuations and rainfall","authors":"Jing-kun Qu ,&nbsp;Qing-yang Zhu ,&nbsp;Shun-chao Qi ,&nbsp;Jia-wen Zhou","doi":"10.1016/j.enggeo.2025.108092","DOIUrl":"10.1016/j.enggeo.2025.108092","url":null,"abstract":"<div><div>With the continued development of water resources in Southwest China, fluctuations in water levels and rainfall have triggered numerous landslides. The potential hazards posed by these events have garnered considerable attention from the academic community, making it imperative to elucidate the landslide mechanisms under the combined influence of multiple factors. This study integrates laboratory tests and numerical simulations to explore the instability mechanisms of landslides under the combined effects of rainfall and fluctuating water levels, as well as to compare the impacts of different factors. Results indicate that the sensitivity of landslide deformation decreases as the number of water level fluctuations increases, exhibiting a gradually stabilizing tendency. However, the occurrence of a heavy rainfall event can reactivate previously stabilized landslides by increasing pore water pressure and establishing a positive feedback loop with rainfall infiltration. This process reduces boundary constraints at the toe of the slope, promotes the development of an overhanging surface, and ultimately leads to overall instability and landslide disaster. Under the same rainfall intensities, the presence of water level fluctuations prior to rainfall significantly shortens the time for the landslide to reach a critical state. The key mechanisms contributing to landslide failure include terrain modification, fine particle erosion, and outward water pressure, all of which generates substantial destabilizing forces. This research offers valuable insights for the monitoring, early warning, and risk mitigation of landslides that have already experienced some degree of deformation in hydropower reservoir areas.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"352 ","pages":"Article 108092"},"PeriodicalIF":6.9,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluating the combined influence of anisotropy and weathering on strength behavior of gneissic rocks in Himachal Pradesh, India: Insights from chemical weathering indices","authors":"Honey Kaushal,&nbsp;Aditya Singh,&nbsp;Narendra Kumar Samadhiya","doi":"10.1016/j.enggeo.2025.108086","DOIUrl":"10.1016/j.enggeo.2025.108086","url":null,"abstract":"<div><div>The present study examines the combined effect of anisotropic foliations and weathering on the strength and deformation characteristics of the three grades of weathered Himalayan gneiss (fresh, slightly, and moderately weathered) from Kullu, Himachal Pradesh, India. The study's novelty is that it links the triaxial strength of weathered gneiss with suitable chemical weathering indices (Plagioclase Index of Alteration (PIA), Chemical Index of Weathering (CIW), and Loss of Ignition (LOI)). The study reports the output of extensive experimental work containing uniaxial, triaxial compression, Brazilian tensile, and point load strength testing on three grades of weathered gneiss at five different anisotropic foliations (0°, 30°, 45°, 60°, and 90°). The observations report that anisotropic foliations and weathering affect the strength of gneissic rocks under unconfined and confined conditions. The weathering decreases gneissic rock's uniaxial, Brazilian tensile, and triaxial strengths. The U-shaped strength anisotropy curve is noticed in all grades of weathered gneiss under both uniaxial and triaxial states. The linear relations were observed between the triaxial strength and appropriate indices of chemical weathering. These relations help to obtain the strength of the anisotropic rock at different anisotropy angles using data from powder XRF. The powder XRF tests are relatively easier to execute as sample preparations have no physical dimensions restrictions. In the absence of the required number of perfect cores (specimens) of L/D ratio two, the correlations enable approximate strength assessment for rock engineering projects. Owing to these relationships, the study identifies the suitable modified Hoek-Brown anisotropic rock failure criterion that is modified to consider the effect of weathering using appropriate indices of chemical weathering for the Himalayan gneiss. The coefficient of determination (<em>R</em>^<em>2</em>) was calculated to be 0.93 for the proposed modification.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"352 ","pages":"Article 108086"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hydro-mechanical interactions in CO2 storage: Critical parameters influencing coal mine at Shenhua's CCS site","authors":"Keyao Lin ,&nbsp;Ning Wei ,&nbsp;Yao Zhang ,&nbsp;Shengnan Liu ,&nbsp;Muhammad Ali ,&nbsp;Wendong Wang ,&nbsp;Quan Chen ,&nbsp;Yongsheng Wang","doi":"10.1016/j.enggeo.2025.108087","DOIUrl":"10.1016/j.enggeo.2025.108087","url":null,"abstract":"<div><div>The co-development of saline aquifers and coal seams in sedimentary basins results in geomechanical conflicts when concurrently exploited in shared subsurface strata. However, reliable assessments of CO₂ storage effects on coal mines are limited by uncertainties associated with the mechanical and physical characteristics of deep rock formations. Studies have developed advanced hydraulic-mechanical (HM) coupling frameworks for CO₂ storage in saline aquifers or coal seams; however, no study has quantitatively linked parameter uncertainties to coal mine stability thresholds under CO₂ injection pressures, a gap addressed in this study. This study investigated the critical parameters governing coal mine stability under CO₂ injection at the Shenhua CCS site. A coupled MRST-FLAC3D model was developed to simulate HM interactions, and Tornado analysis and response surface methodology were performed to evaluate 17 parameters, with <span><math><mi>F</mi></math></span>-values quantifying their significance. Predictive models for CO₂ plume radius (<span><math><mi>R</mi></math></span>) and vertical displacement (<span><math><mi>U</mi></math></span>) were established, revealing three key findings: (1) reservoir porosity had the dominant effect on <span><math><mi>R</mi></math></span> variations (73.6), exceeding the influences of reservoir permeability (34.16) and reservoir thickness (0.95) by orders of magnitude; (2) <span><math><mi>U</mi></math></span> was most sensitive to the caprock Poisson's ratio (1, 240.22), followed by the caprock Young's modulus (1, 019.59), Biot's coefficient (707.8), interbedded mudstone-sandstone Poisson's ratio (367.22), and reservoir permeability (289.45); (3) the <span><math><mi>R</mi></math></span> and <span><math><mi>U</mi></math></span> models robustly predicted CO₂ migration and stratum deformation across diverse geological conditions. These findings provide a quantitative framework for optimizing CO₂ storage integrity and coal mine safety in tectonically active basins, with implications for global CCS projects facing similar resource conflicts.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"352 ","pages":"Article 108087"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The optimal control problem for stability analysis of general slopes","authors":"Hong Zheng,&nbsp;Pingwei Jiang","doi":"10.1016/j.enggeo.2025.108089","DOIUrl":"10.1016/j.enggeo.2025.108089","url":null,"abstract":"<div><div>In general, a slope is a statically indeterminate system of infinite order. In the framework of limit equilibrium methods, where the slip body is treated as a rigid body, non-physical assumptions about the internal forces must be introduced to make the system statically determinate. Different assumptions lead to distinct limit equilibrium methods, all of which can bring the slope into a limit equilibrium state. Although so-called rigorous methods (satisfying all equilibrium conditions) produce relatively small variations in the factor of safety, none of these methods guarantees a statically admissible force system a priori, which leads to inefficiencies in slope stabilization design. By defining the normal stress on the slip surface at the limit equilibrium state and the critical sliding direction vector as control variables, with the factor of safety as the state variable, this study demonstrates that the slope stability analysis can be reduced to an optimal control problem of integral equations. The state equations represent the limit equilibrium equations of the slip body, while the cost functional depends on the specific problem. In this study, the cost functional is defined as the factor of safety of slip body, derived from Pan's maximum principle applied to the stability analysis of the given slip body. By solving this optimal control problem, the critical sliding direction and safety factor for a three-dimensional asymmetric slip body are obtained simultaneously, along with a statically admissible force system. The analysis of several classical examples and a well-known real case demonstrates the accuracy and robustness of the optimal control model proposed in this paper.</div></div>","PeriodicalId":11567,"journal":{"name":"Engineering Geology","volume":"352 ","pages":"Article 108089"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}