{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T14:48:25Z","timestamp":1774104505464,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T00:00:00Z","timestamp":1630627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52109139"],"award-info":[{"award-number":["52109139"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LQ20E080022"],"award-info":[{"award-number":["LQ20E080022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Soil arching, which occurs in the piled embankments, plays an important role in stress redistribution between the relatively soft subsoil and the stiffer piles. The formation of the soil arching depends on the differential settlement of the embankment fill above the pile and the subsoil. The soil arching effect is barely investigated in the literature from the perspective of differential settlement of piles and soils. Based on the discrete element method (DEM), this paper develops a classic trapdoor test model to investigate the differential settlement in piled embankment during the downward movement of the trapdoor, and to explore the formation mechanism of soil arching in equal settlement pattern by changing the width of the pile cap and the height of the embankment. Due to symmetry, only one section of the laboratory test model is simulated herein. It was found that the soil arching formed under the equal settlement pattern remained unchanged after a certain degree of development, and the height of the equal settlement did not change at 0.7(s-a), where s is the pile spacing, and a is the width of the pile cap. The height of the embankment (H) and the width of the pile cap (a) have a significant influence on the formation of the equal settlement pattern when the width of the trapdoor is kept constant. Both the decrease in \u201cH\u201d and the increase in \u201ca\u201d facilitate the differential settlement of the soil between the piles and the pile-soil, enabling the slip surface to develop upward gradually, thereby hindering the formation of the equal settlement pattern.<\/jats:p>","DOI":"10.3390\/sym13091627","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T23:55:22Z","timestamp":1630972522000},"page":"1627","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Soil Arching of Piled Embankment in Equal Settlement Pattern: A Discrete Element Analysis"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0580-1395","authenticated-orcid":false,"given":"Kangyu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China"}]},{"given":"Jun","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China"}]},{"given":"Xinquan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015, China"}]},{"given":"Yingjie","family":"Ning","sequence":"additional","affiliation":[{"name":"Zhejiang Jiaogong Group Co., Ltd., Hangzhou 310000, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1061\/(ASCE)GT.1943-5606.0000561","article-title":"Performance of pile-supported embankment over soft soil: Full-scale experiment","volume":"138","author":"Simon","year":"2012","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1139\/cgj-2014-0284","article-title":"Grouted gravel column supported highway embankment over soft clay: Case study","volume":"52","author":"Liu","year":"2015","journal-title":"Can. Geotech. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1680\/jgein.16.00002","article-title":"Field test of a geogrid-reinforced and floating pile-supported embankment","volume":"23","author":"Cao","year":"2016","journal-title":"Geosynth. Inter."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.compgeo.2017.09.006","article-title":"Effect of spatial variability on short- and long-term behaviour of axially-loaded cement-admixed marine clay column","volume":"94","author":"Pan","year":"2018","journal-title":"Comput. Geotech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"04019114","DOI":"10.1061\/(ASCE)GT.1943-5606.0002190","article-title":"Experimental investigation of soil arching mobilization and degradation under localized surface loading","volume":"145","author":"Han","year":"2019","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.geotexmem.2019.04.003","article-title":"Coupled numerical and experimental analyses of load transfer mechanismsin granular-reinforced platform overlying cavities","volume":"19","author":"Chalak","year":"2019","journal-title":"Geotext. Geomembr."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.geotexmem.2020.02.013","article-title":"Geosynthetic-reinforced soils above voids: Observation of soil and geosynthetic deformation mechanisms","volume":"49","author":"Elshafie","year":"2021","journal-title":"Geotext. Geomembr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1016\/j.geotexmem.2020.12.010","article-title":"Field study and numerical modelling for a road embankment built on soft soil improved with concrete injected columns and geosynthetics reinforced platform","volume":"49","author":"Ghosh","year":"2021","journal-title":"Geotext. Geomembr."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1007\/s12205-020-0625-x","article-title":"Lessons from Full-Scale Experiments on Piled Embankments with Different Geosynthetic Reinforcements","volume":"25","author":"Lee","year":"2021","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Terzaghi, K. (1943). Theoretical Soil Mechanics, Wiley.","DOI":"10.1002\/9780470172766"},{"key":"ref_11","first-page":"12","article-title":"Analysis of piled embankment","volume":"21","author":"Hewlett","year":"1988","journal-title":"Ground Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1680\/jgeot.16.P.266","article-title":"Finite-element analysis of arching in highway piled embankments subjected to moving vehicle loads","volume":"68","author":"Zhuang","year":"2018","journal-title":"Geotechnique"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"04018195","DOI":"10.1061\/(ASCE)GM.1943-5622.0001341","article-title":"Discrete and continuum numerical modeling of soil arching between piles","volume":"19","author":"Tran","year":"2019","journal-title":"Int. J. Geomech."},{"key":"ref_14","unstructured":"Alonso, J., Moya, M., Asensio, L., de la Morena, G., Galve, J.P., and Navarro, V. (2020). A catenary model for the analysis of arching effect in soils and its application to predicting sinkhole collapse. G\u00e9otechnique, 1\u201346."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.1007\/s11440-019-00902-x","article-title":"\u201cSoil arching\u201d for piled embankments: Insights from stress redistribution behaviour of DEM modelling","volume":"15","author":"Lai","year":"2020","journal-title":"Acta Geotech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"103365","DOI":"10.1016\/j.compgeo.2019.103365","article-title":"Simplified method for estimating vertical stress-settlement responses of piled embankments on soft soils","volume":"119","author":"Rui","year":"2020","journal-title":"Comput. Geotech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/j.geotexmem.2020.11.001","article-title":"Comparison and evaluation of analytical models for the design of geosyntheticreinforced and pile-supported embankments","volume":"49","author":"Pham","year":"2021","journal-title":"Geotext. Geomembr."},{"key":"ref_18","first-page":"818","article-title":"Berechnung von geokunstst off between trags chichten \u00fcber pfahlelementen","volume":"74","author":"Kempfert","year":"1997","journal-title":"Bautechnik"},{"key":"ref_19","first-page":"80","article-title":"Calculation and Behaviour of Unreinforced and Reinforced Bearing Layers over Point- or Line-Shaped Bearing Elements","volume":"77","author":"Zaeske","year":"2002","journal-title":"Bauingenieur"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.geotexmem.2013.07.005","article-title":"An analytical model for arching in piledembankments","volume":"39","author":"Bezuijen","year":"2013","journal-title":"Geotext. Geomembr."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.geotexmem.2014.10.002","article-title":"Validation ofanalytical models for the design of basal reinforced piled embankments","volume":"43","author":"Bezuijen","year":"2015","journal-title":"Geotext. Geomembr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"04013005","DOI":"10.1061\/(ASCE)GT.1943-5606.0000998","article-title":"Investigation of soil arching with centrifuge tests","volume":"140","author":"Iglesia","year":"2014","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.compgeo.2015.12.006","article-title":"Evolution of soil arching; 2D DEM simulations","volume":"73","author":"Rui","year":"2016","journal-title":"Comput. Geotech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1520\/GTJ20150130","article-title":"Investigation of soil-arching development in dense sand by 2D model tests","volume":"39","author":"Rui","year":"2016","journal-title":"Geotech. Test. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s11440-011-0152-5","article-title":"Experimental and discrete element modeling studies of the trapdoor problem: Influence of the macro-mechanical frictional parameters","volume":"7","author":"Chevalier","year":"2012","journal-title":"Acta Geotech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.geotexmem.2011.12.002","article-title":"Visualization of soil arching on reinforced embankment with rigid pile foundation using X-ray CT","volume":"32","author":"Eskisar","year":"2012","journal-title":"Geotext. Geomembr."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1007\/s11440-019-00769-y","article-title":"Experimental study of soil arching effect under seepage condition","volume":"14","author":"Xu","year":"2019","journal-title":"Acta Geotech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3208\/sandf.45.15","article-title":"Soft ground improvement by vertical rigid piles twodimensional physical modelling and comparison with current design methods","volume":"45","author":"Jenck","year":"2005","journal-title":"Soils Found."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.geotexmem.2007.05.004","article-title":"An experimental investigation of soil arching within basal reinforced and unreinforced piled embankments","volume":"26","author":"Chen","year":"2008","journal-title":"Geotext. Geomembr."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1631\/jzus.A1500302","article-title":"Visualization of the formation and features of soil arching within a piled embankment by discrete element method simulation","volume":"17","author":"Lai","year":"2016","journal-title":"J. Zhejiang Univ.-Sci. A"},{"key":"ref_31","unstructured":"BSI (British Standards Institution) (2010). Code of Practice for Strengthened\/Reinforced Soils and Other Fills, BSI. BSI: BS8006-1."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1680\/geot.9.P.113","article-title":"Three-dimensional finite-element analysis of arching in a piled embankment","volume":"62","author":"Zhuang","year":"2012","journal-title":"G\u00e9otechnique"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.compgeo.2009.02.001","article-title":"Discrete element modelling of a granular platform supported by piles in soft soil-validation on a small scale model test and comparison to a numerical analysis in a continuum","volume":"36","author":"Jenck","year":"2009","journal-title":"Comput. Geotech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1061\/(ASCE)GM.1943-5622.0000050","article-title":"DEM analysis of stresses and deformations of geogrid-reinforced embankments over piles","volume":"12","author":"Han","year":"2012","journal-title":"Int. J. Geomech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"103662","DOI":"10.1016\/j.compgeo.2020.103662","article-title":"Effect of particle shape on the development of 2D soil arching","volume":"125","author":"Chen","year":"2020","journal-title":"Comput. Geotech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"e12148","DOI":"10.1111\/nrm.12148","article-title":"Optimization analysis of the factors affecting the soil arching effect between landslide stabilizing piles","volume":"31","author":"He","year":"2018","journal-title":"Nat. Resour. Model."},{"key":"ref_37","unstructured":"Itasca (2016). Particle Flow Code in Two Dimensions, Version 5.0, Itasca Consulting Group Inc."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1680\/geot.1979.29.1.47","article-title":"A discrete numerical model for granular assemblies","volume":"29","author":"Cundall","year":"1979","journal-title":"Geotechnique"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ijsolstr.2019.03.035","article-title":"A 3D-DEM investigation of the mechanism of arching within geosynthetic-reinforced piled embankment","volume":"187","author":"Badakhshan","year":"2020","journal-title":"Int. J. Solids Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/S0266-352X(03)00064-8","article-title":"An efficient technique for generating homogeneous specimens for DEM studies","volume":"30","author":"Jiang","year":"2003","journal-title":"Comput. Geotech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1061\/(ASCE)1090-0241(2002)128:1(44)","article-title":"Numerical analysis of geosynthetic-reinforced and pile-supported earth platforms over soft soil","volume":"128","author":"Han","year":"2002","journal-title":"J. Geotech. Geoenviron. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1627\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:56:01Z","timestamp":1760165761000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1627"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,3]]},"references-count":41,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["sym13091627"],"URL":"https:\/\/doi.org\/10.3390\/sym13091627","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,3]]}}}