{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T10:05:04Z","timestamp":1781517904437,"version":"3.54.1"},"reference-count":36,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["2208085ME149"],"award-info":[{"award-number":["2208085ME149"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>This study proposes a method for determining 3-D limit equilibrium solutions. The method, inspired by Sarma, introduces the horizontal seismic coefficient as a slope failure parameter and implements a modification of the normal stress over the slip surface. Four equilibrium equations are used to solve the problem without compromising the accuracy of the calculations: three force equilibrium equations in the x, y, and z directions and a moment equilibrium equation in the vertical (z) direction. The reliable factor of safety can be determined by calculating the minimum value of the horizontal seismic coefficient. Furthermore, we analyzed several typical examples of symmetric and asymmetric slopes, finding good consistency with the existing literature. This consistency indicates the reliability of the factor of safety we obtained. The proposed method is favored due to its straightforward principle, convenient operation, fast convergence, and ease of programming.<\/jats:p>","DOI":"10.1371\/journal.pone.0287998","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T18:15:20Z","timestamp":1688062520000},"page":"e0287998","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Solving the general 3-D safety factor by combining Sarma\u2019s idea with the assumption of normal stress distribution over the slip surface"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9955-8981","authenticated-orcid":true,"given":"Linghui","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kunlin","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"pone.0287998.ref001","article-title":"The safety factor of an elastic-plastic body in plane strain","author":"D Drucker","year":"1951","journal-title":"Journal of Applied Mathematics"},{"issue":"2","key":"pone.0287998.ref002","first-page":"157","article-title":"Soil mechanics and plastic analysis or limit design","volume":"10","author":"DC Drucker","year":"1952","journal-title":"Journal of Applied Mathematics"},{"key":"pone.0287998.ref003","article-title":"Calculation of the stability of earth dams","author":"W Fellenius","year":"1936","journal-title":"In Transactions of the 2nd congress on large dams, Washington, DC"},{"issue":"6","key":"pone.0287998.ref004","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1680\/geot.1999.49.6.835","article-title":"Slope stability analysis by strength reduction.","volume":"49","author":"E Dawson","year":"1999","journal-title":"Geotechnique"},{"issue":"3","key":"pone.0287998.ref005","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1002\/nag.1610090302","article-title":"Three dimensional analysis of slope stability","volume":"9","author":"D Leshchinsky","year":"1985","journal-title":"International Journal for Numerical Analytical Methods in Geomechanics"},{"issue":"1","key":"pone.0287998.ref006","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1680\/geot.1955.5.1.7","article-title":"The use of the slip circle in the stability analysis of slopes.","volume":"5","author":"AW Bishop","year":"1955","journal-title":"G\u00e9otechnique"},{"issue":"1","key":"pone.0287998.ref007","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1680\/geot.1965.15.1.79","article-title":"The analysis of stability of general slip surface.","volume":"15","author":"NR Morgenstern","year":"1965","journal-title":"G\u00e9otechnique"},{"issue":"1","key":"pone.0287998.ref008","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1680\/geot.1967.17.1.11","article-title":"A method of analysis of the stability of embankments assuming parallel inter-slice forces","volume":"17","author":"E. 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