[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121503-en":3,"doc-seo-121503-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"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},121503,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Indirect models for SWCC parameters - reducing prediction uncertainty with machine learning","The soil–water characteristic curve (SWCC) is essential for modelling water and hazardous-material transport in the vadose zone, yet direct SWCC measurement is often laborious and slow. This work develops probabilistic indirect models that predict SWCC parameters from easily measured inputs such as particle-size distributions and porosity. A joint normal model provides an initial predictive framework, but with excessively high uncertainty. Multiple machine-learning strategies are then evaluated to reduce variability, including dependence of variation scale on predictors, ANN-based nonlinear dependence, additional predictive features, and larger training data. The final model is tested on a separate sample set to limit overfitting.","Computers and Geotechnics 177 (2025) 106823  \nContents lists available at ScienceDirect  \nComputers and Geotechnics  \njournal [homepage: www.elsevier.com/locate/compgeo](homepage: www.elsevier.com/locate/compgeo)  \n| Indirect models for SWCC parameters: reducing prediction uncertainty with   machine learning\u003Cbr>Xuzhen He a,*, Guoqing Caib,c, Daichao Shenga\u003Cbr>a School of Civil and Environmental Engineering, University of Technology Sydney, NSW 2007, Australia b Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing 100044, China c School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China |  |  |\n| --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |\n| Keywords:\u003Cbr>Probabilistic indirect model Machine learning\u003Cbr>Soil–water characteristic curve |  | The soil–water characteristic curve (SWCC) is crucial for modelling the transport of water and hazardous materials in the vadose zone. However, measuring SWCC is often cumbersome and time-consuming. This paper introduces indirect models that predict SWCC parameters in probabilistic distributions using easily measurable quantities such as particle-size distributions and porosity. This paper starts with building a joint normal model and the derived conditional probability from it serves as a predictive model. However, this model had extremely high prediction uncertainty. To reduce such uncertainty, various machine-learning techniques were explored, including introducing the dependence of variation scale on predictors, using artificial neural networks (ANN) to model nonlinear dependence, incorporating additional predictive features, and generating a larger dataset. The final machine-learning model successfully reduces prediction variability and has been rigorously tested on a separate set of samples to prevent overfitting. |\n\n1. Introduction  \nConstitutive models are essential for predicting and designing geotechnical structures (Dafalias and Taiebat, 2016; He, et al., 2020). However, even with a “perfect” model, the effectiveness and accuracy of numerical predictions depend largely on having reliable input parameters for these models. For predicting water flow and the movement of hazardous materials through the vadose zone, the soil–water characteristic curve (SWCC) and its parameters are crucial (Fredlund and Rahardjo, 1993; Zhou et al., 2012; Cai et al., 2020). Unfortunately, these parameters are difficult to measure directly, and flow permeability can vary by several orders of magnitude across the full range of saturation. Numerous laboratory and field methods exist to measure unsaturated soil hydraulic parameters, but these methods are often cumbersome and time-consuming (Chen et al., 2024).  \nIn practice, it is easier to conduct simpler tests and estimate these SWCC parameters indirectly using empirical models. By treating pores as “idealised” cylindrical pores, Laplace’s law (Fredlund and Rahardjo, 1993) can link pressure heads to pore sizes. The pore sizes of soils are related to particle-size distributions (PSD), packing state (i.e., fabric, primarily porosity), and organic matter content. Consequently, it is sensible to build indirect models and estimate SWCC parameters from  \nmeasurements of these attributes (Sakaki et al., 2014; Zhai et al., 2020b; Zhang et al., 2022b; Es-haghi et al., 2023; Satyanaga et al., 2024).  \nThe most straightforward indirect models are deterministic empirical equations. For instance, Sakaki et al. (2014) demonstrated the relationship between the air entry value and characteristic particle sizes such as d30 and d50, which represent the particle sizes at which the mass cumulative percentages (MCP) are 30 % and 50 %, respectively. However, since predictors like particle-size distribution and porosity do not encompass all the necessary information to fully determine the water retention capability of soils, it is not expected to have a very accurate prediction using these models. Instead, the","cbCaiqUgcLCGNeya","https://ap.wps.com/l/cbCaiqUgcLCGNeya","pdf",14555062,1,15,"English","en",105,"# Introduction\n## Role of SWCC parameters in geotechnical modelling\n## Indirect prediction from particle-size distribution and porosity\n## Deterministic vs probabilistic indirect models\n## Objective and approach using machine-learning techniques","[{\"question\":\"Why are SWCC parameters important, and why are they difficult to obtain directly?\",\"answer\":\"SWCC parameters govern modelling of water flow and hazardous-material movement in the vadose zone. Direct measurement is difficult and time-consuming, and flow permeability can vary by orders of magnitude across saturation states.\"},{\"question\":\"What indirect inputs are used to predict SWCC parameters?\",\"answer\":\"The proposed indirect modelling uses easily measurable quantities such as particle-size distributions and porosity (packing state), which are linked to pore sizes and thus to water retention behaviour.\"},{\"question\":\"How does the paper reduce prediction uncertainty compared with a simple probabilistic model?\",\"answer\":\"It first builds a joint normal model that yields a conditional probability predictive framework, which has high uncertainty. Then it evaluates machine-learning methods—variation-scale dependence, ANN for nonlinear relationships, added predictive features, and a larger dataset—and validates the final model on separate samples to prevent overfitting.\"}]","Indirect models for SWCC parameters - reducing prediction uncertainty with machine learning | PDF",1785735977,38,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"indirect-models-for-swcc-parameters-reducing-prediction-uncertainty-with-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/indirect-models-for-swcc-parameters-reducing-prediction-uncertainty-with-machine-learning/121503/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are SWCC parameters important, and why are they difficult to obtain directly?","Question",{"text":75,"@type":76},"SWCC parameters govern modelling of water flow and hazardous-material movement in the vadose zone. Direct measurement is difficult and time-consuming, and flow permeability can vary by orders of magnitude across saturation states.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What indirect inputs are used to predict SWCC parameters?",{"text":80,"@type":76},"The proposed indirect modelling uses easily measurable quantities such as particle-size distributions and porosity (packing state), which are linked to pore sizes and thus to water retention behaviour.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the paper reduce prediction uncertainty compared with a simple probabilistic model?",{"text":84,"@type":76},"It first builds a joint normal model that yields a conditional probability predictive framework, which has high uncertainty. 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