{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T08:42:45Z","timestamp":1789634565888,"version":"build-2803163510"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T00:00:00Z","timestamp":1773964800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:00:00Z","timestamp":1777939200000},"content-version":"vor","delay-in-days":46,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Reliability-based design (RBD) of tunnel concrete linings in weak rocks is challenging due to the uncertainty of geomechanical parameters and the ground\u2013support interaction. This study introduces a transparent and efficient framework that integrates three key components: (1) implicit ground\u2013support equilibrium analysis based on the Convergence\u2013Confinement Method (CCM), (2) probabilistic evaluation of the safety factor (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:SF$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), reliability index (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:\\beta\\:$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), and failure probability (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:{P}_{f}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ) and (3) a data-driven surrogate model based on artificial intelligence for rapid parametric analysis. The uncertainties of the rock mass and concrete linings are treated through Monte Carlo sampling, and the outcomes are benchmarked against the First-Order Reliability Method (FORM) to verify accuracy and potential bias. The results are transformed into decision-making charts linking the thickness and compressive strength of concrete linings to target\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:\\beta\\:\/{P}_{f}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    levels, thus providing risk-consistent objectives instead of a fixed safety factor criterion. Two types of linings are considered: conventional concrete (with an average uniaxial compressive strength of 20\u00a0MPa) and fiber-reinforced reactive powder concrete (FRPC, with an average uniaxial compressive strength of 65\u00a0MPa, developed by the research team). The findings demonstrate that increasing thickness and material quality significantly reduce\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:{P}_{f}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , achieving the reliability thresholds required for final tunnel support (2E-5). This effect is more critical at smaller thicknesses and with lower-quality materials. The use of FRPC also leads to a considerable reduction in\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\:{P}_{f}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    at intermediate thicknesses, making it an efficient option when construction constraints limit thickness increase. The surrogate model successfully reproduces probabilistic trends with high consistency and slight conservatism. Ultimately, the integrated CCM\u2013reliability\u2013artificial intelligence framework bridges the gap between deterministic design and risk management, delivering economical and resilient tunnel lining designs in weak rocks.\n                  <\/jats:p>","DOI":"10.1038\/s41598-026-44903-9","type":"journal-article","created":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T05:14:22Z","timestamp":1773983662000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["AI-assisted reliability-based design framework for tunnel concrete linings in weak rocks"],"prefix":"10.1038","volume":"16","author":[{"given":"Jafar","family":"Khani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamid Reza","family":"Nejati","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kamran","family":"Goshtasbi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sina","family":"Rostamabadi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arsalan","family":"Mahmoodzadeh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,20]]},"reference":[{"key":"44903_CR1","first-page":"15","volume":"1","author":"K Terzaghi","year":"1946","unstructured":"Terzaghi, K. 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