[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117504-en":3,"doc-seo-117504-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117504,1099514067438,"River Wang","https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542",8,"Research & Report","Probabilistic analysis of active earth pressures in spatially variable soils using machine learning and confidence intervals","Probabilistic analysis framework for active earth pressures in soils with spatially varying friction angle and unit weight. Soil parameters are represented by log-normal random fields with spatial correlation lengths. Failure probabilities are computed by combining Monte Carlo simulations with finite element limit analysis, then accelerated using machine learning models such as Multivariate Adaptive Regression Splines to map key variability parameters to failure probability. Confidence intervals quantify prediction reliability, while adaptive finite element meshes capture irregular stochastic failure mechanisms. Parametric contour design charts support uncertainty-informed geotechnical decisions.","[www. nature.com/scientificreports](www. nature.com/scientificreports)  \nOPEN  \nProbabilistic analysis of active earth pressures in spatially variable soils using machine learning and confidence intervals  \nTran Vu-Hoang1, Tan Nguyen2􀀍, Jim Shiau3, Duy Ly-Khuong4,5 & Hung-Thinh Pham-Tran1  \nThis study introduces a probabilistic framework for assessing active earth pressures in soils exhibiting spatial variability in friction angles and unit weight. These properties are modeled using random fields with log-normal distributions and spatial correlation lengths. Monte Carlo simulations (MCS) are integrated with finite element limit analysis (FELA) to evaluate the failure probability under different design safety factors. To improve computational efficiency and prediction accuracy, machine learning models, such as Multivariate Adaptive Regression Splines (MARS), are utilized to predict failure probabilities based on key spatial variability parameters. A two-phase optimization approach, combining Random Search and Adaptive Sampling, is employed to refine the hyperparameters of the machine learning model. Confidence intervals are incorporated to quantify prediction reliability, providing engineers with robust decision-making tools under uncertainty. Furthermore, adaptive finite element meshes are applied to capture irregular stochastic failure mechanisms, offering deeper insights into the impact of spatial variability. The study produces parametric results in the form of practical contour design charts, aiding engineers in optimizing safety margins while accounting for soil variability. By combining computational methods, machine learning, and uncertainty quantification, this research enhances geotechnical design practices, ensuring more reliable and cost-effective solutions.  \nKeywords Random field, Probabilistic analysis, Limit analysis, Earth pressures, Machine learning, Confidence intervals, Spatial variability  \nAccurate estimation of active earth pressures is essential for the design and stability assessment of retaining walls. Classical methods, such as Rankine’s1 and Coulomb’s2 theories, have long served as the foundation for geotechnical analysis, providing simplicity and computational efficiency based on assumptions of homogeneous soil properties, linear pressure distributions, and smooth failure surfaces. More recent approaches, such as the rigorous solutions proposed by Nguyen3, Nguyen et al.4 have enhanced analytical precision. However, these methods often rely on key simplifications that do not fully account for real-world complexities, including spatial variability in soil properties, depth-dependent behaviors, and irregular failure mechanisms. Soils, shaped by processes such as weathering, deposition, and stress history, are inherently heterogeneous. Ignoring this variability can lead to designs that are either overly conservative or insufficiently robust, ultimately compromising the structural integrity of retaining walls5.  \nSpatial variability in soil parameters, such as unit weight and internal friction angle, plays a significant role in geotechnical performance6–8. Early studies by Fenton et al.9 demonstrated how random fields influence active pressure distributions and failure mechanisms, emphasizing the need for probabilistic models to address these uncertainties. Similarly, Phoon and Kulhawy10 highlighted the importance of quantifying geotechnical variability to enhance design reliability. Building on this foundation, Soubra and Macuh11 utilized kinematic limit analysis to derive active and passive pressure coefficients, while Al-Bittar and Soubra12 applied sparse polynomial chaos  \n1Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam. 2Smart Computing in Civil Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam.  \n3School of Engineering, University of Southern Queensland, Toowoomba, QLD 4350, Australia. 4Laboratory for Com","cbCaibFCcWEqGR0U","https://ap.wps.com/l/cbCaibFCcWEqGR0U","pdf",8859704,1,27,"English","en",105,"# Introduction\n## Background and limitations of classical methods\n## Need for spatial variability and probabilistic design\n# Proposed probabilistic framework\n## Random-field modeling of soil parameters\n## Monte Carlo simulation with finite element limit analysis\n## Machine learning acceleration and hyperparameter optimization\n## Confidence intervals and adaptive meshing\n# Results and engineering outputs\n## Parametric contour design charts\n## Implications for design reliability and cost effectiveness","[{\"question\":\"How are spatially variable soil properties modeled in this study?\",\"answer\":\"Friction angle and unit weight are modeled as random fields with log-normal distributions and spatial correlation lengths.\"},{\"question\":\"What numerical and computational methods are combined to estimate failure probability?\",\"answer\":\"Monte Carlo simulations are integrated with finite element limit analysis to evaluate failure probability under different design safety factors.\"},{\"question\":\"How does machine learning improve computational efficiency and accuracy?\",\"answer\":\"Machine learning models such as MARS are used to predict failure probabilities from key spatial variability parameters, with two-phase optimization (Random Search and Adaptive Sampling) refining hyperparameters.\"}]","Probabilistic analysis of active earth pressures in spatially variable soils using machine learning and confidence intervals | 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