{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T06:36:01Z","timestamp":1773902161065,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation for Science and Technology for the PhD scholarship","award":["PRT\/BD\/151571\/2021"],"award-info":[{"award-number":["PRT\/BD\/151571\/2021"]}]},{"name":"Foundation for Science and Technology for the PhD scholarship","award":["UIDB\/04625\/2020"],"award-info":[{"award-number":["UIDB\/04625\/2020"]}]},{"name":"research unit CERIS","award":["PRT\/BD\/151571\/2021"],"award-info":[{"award-number":["PRT\/BD\/151571\/2021"]}]},{"name":"research unit CERIS","award":["UIDB\/04625\/2020"],"award-info":[{"award-number":["UIDB\/04625\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sustainability"],"abstract":"<jats:p>Unsupported excavations are frequently performed in several geological and geotechnical projects, particularly for constructing roads and railways, and they are often carried out in different materials. The design of such cuts in soils needs the determination of representative values of its mechanical properties, particularly of the strength parameters, and the application of adequate safety factors. The procedure should ensure a sustainable design of those cuts, allowing for economical solutions that guarantee a low probability of geological\u2013geotechnical failure. This paper assesses the reliability of unsupported cuts in soils, under drained conditions, assuming a Mohr\u2013Coulomb strength criterion. Statistical meshes are generated considering the spatial variability of the friction angle and of the true effective cohesion, which are assumed to be uncorrelated. In this process, typical values of the coefficients of variation and of the horizontal and vertical scales of fluctuation are applied. Soil characterisation is simulated in each statistical mesh, and the characteristic values of the strength parameters are determined using statistical methods. Unsupported cuts of different heights and inclinations are designed using typical safety factors. Slope stability analyses are carried out using Random Finite Element Limit Analysis. The uncertainty in the actions is considered, and the probability of failure is determined by direct reliability analysis. The results show the relevance of the ratio between the scale of fluctuation and the excavation depth, the slope inclination, and the characteristic value of the soil strength parameters on the probability of failure. Values of adequate safety factors are proposed towards obtaining an appropriate probability of failure, compatible with the sustainable design of the cuts.<\/jats:p>","DOI":"10.3390\/su162310596","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T09:18:32Z","timestamp":1733217512000},"page":"10596","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Soil Strength Parameters for the Sustainable Design of Unsupported Cuts Under Drained Conditions Using Reliability Analysis"],"prefix":"10.3390","volume":"16","author":[{"given":"Fl\u00e1vio","family":"Rog\u00e9rio","sequence":"first","affiliation":[{"name":"DEC, Instituto Superior Polit\u00e9cnico Tundavala, Rua Patrice Lumumba, <i>n<\/i>\u00b0 30, Lubango CP 298, Angola"},{"name":"NOVA School of Science and Technology, 2829-516 Caparica, Portugal"}]},{"given":"Nuno","family":"Guerra","sequence":"additional","affiliation":[{"name":"NOVA School of Science and Technology, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2835-2780","authenticated-orcid":false,"given":"Armando","family":"Ant\u00e3o","sequence":"additional","affiliation":[{"name":"CERIS, NOVA School of Science and Technology, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0800-6979","authenticated-orcid":false,"given":"M\u00e1rio","family":"Vicente da Silva","sequence":"additional","affiliation":[{"name":"NOVA School of Science and Technology, 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"key":"ref_1","unstructured":"Basu, D., Puppala, A., Misra, A., and Chittoori, B. (2013, January 2\u20136). Sustainability in Geotechnical Engineering. Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical, Paris, France. Available online: https:\/\/www.cfms-sols.org\/sites\/default\/files\/Actes\/3171-3174.pdf."},{"key":"ref_2","unstructured":"(2004). EN1997-1. Eurocode 7: Geotechnical Design\u2014Part 1: General Rules, CEN, European Committee for Standardization."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1139\/t70-032","article-title":"Safety factors and the probability distribution of soil strength","volume":"7","author":"Lumb","year":"1970","journal-title":"Can. Geotech. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1139\/t70-047","article-title":"Safety factors in soil mechanics","volume":"7","author":"Meyerhof","year":"1970","journal-title":"Can. Geotech. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0167-4730(82)90015-7","article-title":"Limit states design in geotechnical engineering","volume":"1","author":"Meyerhof","year":"1982","journal-title":"Struct. Saf."},{"key":"ref_6","unstructured":"Santamarina, J.C., Altschaeffl, A.G., and Chameau, J.L. (2024, September 01). Reliability of Slopes: Incorporating Qualitative Information. National Research Council (U.S.), Transportation Research Board, Report TRR 1343. Available online: http:\/\/onlinepubs.trb.org\/Onlinepubs\/trr\/1992\/1343\/1343-001.pdf."},{"key":"ref_7","unstructured":"Baecher, G.B., and Christian, J.T. (2003). Reliability and Statistics in Geotechnical Engineering, John Wiley & Sons."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0266-352X(99)00042-7","article-title":"Selection of characteristic values and partial factors in geotechnical designs to Eurocode 7","volume":"26","author":"Orr","year":"2000","journal-title":"Comput. Geotech."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ching, J., Phoon, K.K., Chen, K.F., Orr, T.L., and Schneider, H.R. (2020). Statistical determination of multivariate characteristic values for Eurocode 7. Struct. Saf., 82.","DOI":"10.1016\/j.strusafe.2019.101893"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/17499518.2021.1975301","article-title":"What is a characteristic value for soils?","volume":"16","author":"Phoon","year":"2022","journal-title":"Georisk Assess. Manag. Risk Eng. Syst. Geohazards"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1139\/t99-038","article-title":"Characterization of geotechnical variability","volume":"36","author":"Phoon","year":"1999","journal-title":"Can. Geotech. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cao, Z., Wang, Y., and Li, D. (2017). Probabilistic Approaches for Geotechnical Site Characterization and Slope Stability Analysis, Springer.","DOI":"10.1007\/978-3-662-52914-0"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kulhawy, F., Prakoso, W., and Phoon, K. (2020). Uncertainty in basic laboratory and field properties of geomaterials. Geotechnical Engineering Education and Training, CRC Press.","DOI":"10.1201\/9781003078623-53"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Phoon, K.K., Shuku, T., and Ching, J. (2023). Uncertainty, Modeling, and Decision Making in Geotechnics, CRC Press.","DOI":"10.1201\/9781003333586"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1061\/AJGEB6.0000518","article-title":"Reliability of Earth Slopes","volume":"103","author":"Vanmarcke","year":"1977","journal-title":"J. Geotech. Eng. Div."},{"key":"ref_16","unstructured":"Mostyn, G.R., and Soo, S. (1992, January 3\u20137). The effect of auto-correlation on the probability of failure of slopes. Proceedings of the Effect of Auto-Correlation on the Probability of Failure of Slopes, Christchurch, New Zealand. Available online: https:\/\/www.issmge.org\/uploads\/publications\/89\/99\/6ANZ_095.pdf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1061\/(ASCE)1090-0241(2004)130:5(507)","article-title":"Probabilistic Slope Stability Analysis by Finite Elements","volume":"130","author":"Griffiths","year":"2004","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.enggeo.2007.03.006","article-title":"Effects of spatial variability of soil properties on slope stability","volume":"92","author":"Cho","year":"2007","journal-title":"Eng. Geol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.compgeo.2009.08.005","article-title":"Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c\u2032\u03d5 soil","volume":"37","author":"Suchomel","year":"2010","journal-title":"Comput. Geotech."},{"key":"ref_20","first-page":"17","article-title":"Probabilistic analysis of a spatially variable c\u2032\u2212\u03d5\u2032 slope","volume":"50","author":"Chok","year":"2015","journal-title":"Aust. Geomech. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Agbaje, S., Zhang, X., Ward, D., Dhimitri, L., and Patelli, E. (2022). Spatial variability characteristics of the effective friction angle of Crag deposits and its effects on slope stability. Comput. Geotech., 141.","DOI":"10.1016\/j.compgeo.2021.104532"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Chuaiwate, P., Jaritngam, S., Panedpojaman, P., and Konkong, N. (2022). Probabilistic Analysis of Slope against Uncertain Soil Parameters. Sustainability, 14.","DOI":"10.3390\/su142114530"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Peng, P., Li, Z., Zhang, X., Liu, W., Sui, S., and Xu, H. (2023). Slope Failure Risk Assessment Considering Both the Randomness of Groundwater Level and Soil Shear Strength Parameters. Sustainability, 15.","DOI":"10.3390\/su15097464"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yang, R., Huang, J., Griffiths, D.V., Meng, J., and Fenton, G.A. (2019). Optimal geotechnical site investigations for slope design. Comput. Geotech., 114.","DOI":"10.1016\/j.compgeo.2019.103111"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1139\/cgj-2018-0060","article-title":"Importance of soil property sampling location in slope stability assessment","volume":"56","author":"Yang","year":"2019","journal-title":"Can. Geotech. J."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jiang, S.H., Papaioannou, I., and Straub, D. (2020). Optimization of Site-Exploration Programs for Slope-Reliability Assessment. Asce-Asme J. Risk Uncertain. Eng. Syst. Part Civ. Eng., 6.","DOI":"10.1061\/AJRUA6.0001042"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yang, R., Huang, J., and Griffiths, D.V. (2022). Optimal geotechnical site investigations for slope reliability assessment considering measurement errors. Eng. Geol., 297.","DOI":"10.1016\/j.enggeo.2021.106497"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1139\/cgj-2018-0149","article-title":"Assessment of reliability-based design of stable slopes","volume":"56","author":"Day","year":"2019","journal-title":"Can. Geotech. J."},{"key":"ref_29","unstructured":"Knuuti, M., and L\u00e4nsivaara, T. (2019, January 26\u201330). Performance of Variable Partial Factor approach in a slope design. Proceedings of the 13th International Conference on Applications of Statistics and Probability in Civil Engineering(ICASP13), Seoul, Republic of Korea."},{"key":"ref_30","unstructured":"L\u00e4nsivaara, T., and Poutanen, T. (2013, January 2\u20136). Slope stability with partial safety factor method. Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, Paris, France. Available online: https:\/\/www.cfms-sols.org\/sites\/default\/files\/Actes\/1823-1826.pdf."},{"key":"ref_31","unstructured":"Kavvadas, M., Karlaftis, M., Fortsakis, P., and Stylianidi, E. (2009, January 5\u20139). Probabilistic analysis in slope stability. Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering: The Academia and Practice of Geotechnical Engineering, Alexandria, Egypt."},{"key":"ref_32","unstructured":"Vicente da Silva, M., and Ant\u00e3o, A.N. (2023, February 02). Software Mechpy. Available online: http:\/\/geocluster.dec.fct.unl.pt\/mechpy\/."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Sim\u00f5es, J.T., Neves, L.C., Ant\u00e3o, A.N., and Guerra, N.M.C. (2014). Probabilistic analysis of bearing capacity of shallow foundations using three-dimensional limit analyses. Int. J. Comput. Methods, 11.","DOI":"10.1142\/S0219876213420085"},{"key":"ref_34","unstructured":"Rantanen, T. (2016). Influence of the Variability of Soil Properties on the Stability of Shallow Tunnels in Soils Under Undrained Eonditions. [Master\u2019s Thesis, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa]. (In Portuguese)."},{"key":"ref_35","unstructured":"Andrade Viana, L., Ant\u00e3o, A., Vicente da Silva, M., and Guerra, N. (2019., January 1\u20136). The application of limit analysis to the study of basal failure of deep excavations in clay considering the spatial distribution of soil strength. Proceedings of the XVII European Conference on Soil Mechanics and Geotechnical Engineening, Icelandic Geotechnical Society, Reykjav\u00edk, Iceland. Available online: https:\/\/www.ecsmge-2019.com\/uploads\/2\/1\/7\/9\/21790806\/0909-ecsmge-2019_viana-v2.pdf."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Sim\u00f5es, J., Neves, L.C., Ant\u00e3o, A.N., and Guerra, N.M. (2020). Reliability assessment of shallow foundations on undrained soils considering soil spatial variability. Comput. Geotech., 119.","DOI":"10.1016\/j.compgeo.2019.103369"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1061\/AJGEB6.0000517","article-title":"Probabilistic Modeling of Soil Profiles","volume":"103","author":"Vanmarcke","year":"1977","journal-title":"J. Geotech. Eng. Div."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Fenton, G.A., and Griffiths, D.V. (2008). Risk Assessment in Geotechnical Engineering, John Wiley & Sons.","DOI":"10.1002\/9780470284704"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Vicente da Silva, M., Deusdado, N., and Ant\u00e3o, A.N. (2020). Lower and upper bound limit analysis via the alternating direction method of multipliers. Comput. Geotech., 124.","DOI":"10.1016\/j.compgeo.2020.103571"},{"key":"ref_40","first-page":"239","article-title":"Comparison of three methods for selecting values of input variables in the analysis of output from a computer code","volume":"21","author":"McKay","year":"1979","journal-title":"Technometrics"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0167-4730(02)00039-5","article-title":"On Latin hypercube sampling for structural reliability analysis","volume":"25","author":"Olsson","year":"2003","journal-title":"Struct. Saf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0266-8920(97)00013-1","article-title":"Improvements to and limitations of Latin hypercube sampling","volume":"13","author":"Huntington","year":"1998","journal-title":"Probabilistic Eng. Mech."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1680\/geolett.11.00018","article-title":"The use of adaptive finite-element limit analysis to reveal slip-line fields","volume":"1","author":"Martin","year":"2011","journal-title":"G\u00e9Otechnique Lett."},{"key":"ref_44","unstructured":"ISSMGE-TC304 (2021, March 02). State of the art review of inherent variability and uncertainty in geotechnical properties and models. International Society of Soil Mechanics and Geotechnical Engineering (ISSMGE)\u2014Technical Committee TC304 \u2018Engineering Practice of Risk Assessment and Management\u2019. Available online: https:\/\/issmge.org\/files\/reports\/TC304-State-of-the-art-review-of-inherent-variability-and-uncertainty-in-geotechnical-properties-and-models.pdf."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Cami, B., Javankhoshdel, S., Phoon, K.K., and Ching, J. (2020). Scale of Fluctuation for Spatially Varying Soils: Estimation Methods and Values. Asce-Asme J. Risk Uncertain. Eng. Syst. Part Civ. Eng., 6.","DOI":"10.1061\/AJRUA6.0001083"}],"container-title":["Sustainability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2071-1050\/16\/23\/10596\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:45:57Z","timestamp":1760114757000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2071-1050\/16\/23\/10596"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"references-count":45,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["su162310596"],"URL":"https:\/\/doi.org\/10.3390\/su162310596","relation":{},"ISSN":["2071-1050"],"issn-type":[{"value":"2071-1050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,3]]}}}