{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T20:35:56Z","timestamp":1785530156460,"version":"3.56.0"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T00:00:00Z","timestamp":1757462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Institute Science and Technology Project","award":["PJ24073"],"award-info":[{"award-number":["PJ24073"]}]},{"name":"Guangxi Institute Science and Technology Project","award":["2020TD005"],"award-info":[{"award-number":["2020TD005"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Innovation Capability Support Plan","award":["PJ24073"],"award-info":[{"award-number":["PJ24073"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Innovation Capability Support Plan","award":["2020TD005"],"award-info":[{"award-number":["2020TD005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Laboratory triaxial tests are essential for studying sandy soil behavior but have limited ability to capture localized deformation and microstructural evolution. The discrete element method (DEM) overcomes these limitations by enabling particle-scale analysis, where boundary conditions can critically affect simulation results. This study employed DEM-based triaxial compression simulations to compare rigid wall and flexible membrane boundaries for sand specimens with initial porosities of 35.5%, 38.2%, 40.8%, and 41.5% under confining pressures of 50, 100, and 150 kPa. The analyses covered macroscopic stress\u2013strain and volumetric responses, shear band morphology, local porosity evolution, and contact force fabric. The results indicate that rigid and flexible boundaries produce similar pre-peak responses, but differ markedly in post-peak behavior and volumetric strain. Rigid boundaries constrain lateral deformation, induce stress concentrations, and underestimate post-peak strength, while flexible membranes apply confining pressure more uniformly and reproduce realistic bulging and porosity evolution. Based on these findings, rigid boundaries are suitable for dense sands when post-peak strength is not a concern, and for loose sands at small strains, whereas flexible membranes are necessary to capture volumetric contraction and realistic post-peak responses. This work provides mechanistic insights into boundary effects and offers a basis for more efficient selection of boundary conditions in DEM triaxial simulations.<\/jats:p>","DOI":"10.3390\/sym17091499","type":"journal-article","created":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T08:43:54Z","timestamp":1757493834000},"page":"1499","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multi-Scale Analysis of Sand Behavior Under Rigid and Flexible Membrane Boundaries in DEM Triaxial Compression"],"prefix":"10.3390","volume":"17","author":[{"given":"Jiesheng","family":"Li","sequence":"first","affiliation":[{"name":"China Energy Engineering Group Guangxi Electric Power Design Institute Co., Ltd., Nanning 530007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaole","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"},{"name":"Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering, Xi\u2019an 710055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Youyi","family":"Yu","sequence":"additional","affiliation":[{"name":"China Energy Engineering Group Guangxi Electric Power Design Institute Co., Ltd., Nanning 530007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jin","family":"Liang","sequence":"additional","affiliation":[{"name":"China Energy Engineering Group Guangxi Electric Power Design Institute Co., Ltd., Nanning 530007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6530-7236","authenticated-orcid":false,"given":"Pengyuan","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"},{"name":"Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering, Xi\u2019an 710055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1680\/geot.2004.54.3.187","article-title":"Evolution of shear bands in sand","volume":"54","author":"Gudehus","year":"2004","journal-title":"Geotechnique"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1061\/(ASCE)1090-0241(2000)126:6(495)","article-title":"Shear Band Formation in Plane Strain Experiments of Sand","volume":"126","author":"Alshibli","year":"2000","journal-title":"J. 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