Influence of physical and geometrical parameters on three-dimensional load transfer mechanism at tunnel face Ricardo A.M.P. Gomes and Tarcisio B. Celestino Abstract: Three-dimensional discretizations used in numerical analyses of tunnel construction normally include excavation step lengths much shorter than tunnel cross-section dimensions. Simulations have usually worked around this problem by using excavation steps that are much larger than the actual physical steps used in a real tunnel excavation. In contrast, the analyses performed in this study were based on finely discretized meshes capable of reproducing the excavation lengths actually used in tunnels, and the results obtained for internal forces are up to 100% greater than those found in other anal- yses available in the literature. Whereas most reports conclude that internal forces depend on support delay length alone, this study shows that geometric path dependency (reflected by excavation round length) is very strong, even considering linear elasticity. Moreover, many other solutions found in the literature have also neglected the importance of the relative stiffness between the ground mass and support structure, probably owing to the relatively coarse meshes used in these studies. The analyses presented here show that relative stiffness may account for internal force discrepancies in the order of 60%. A dimensionless expression that takes all these parameters into account is presented as a good approximation for the load transfer mechanism at the tunnel face. Key words: tunneling, three-dimensional, stress transfer, internal forces, support delay. Re ´sume ´: Les discre ´tisations 3-D utilise ´es en analyse nume ´rique pour la construction de tunnels incluent normalement des longueurs qui repre ´sentent les e ´tapes d’excavation qui sont assez petites par rapport au diame `tre du tunnel. Les simulations ont normalement contourne ´ le proble `me en utilisant des e ´tapes d’excavation qui sont beaucoup plus grande que les e ´tapes physiques re ´elles. Cependant, les analyses effectue ´es dans cette e ´tude sont base ´es sur un maillage finement discre ´tise ´ ca- pable de reproduire les longueurs d’excavation re ´ellement utilise ´es dans les tunnels, et les re ´sultats obtenus pour les forces internes sont jusqu’a ` 100% plus e ´leve ´es que celles obtenues dans les autres analyses disponibles dans la litte ´rature. Tandis que la plupart des e ´tudes concluent que les forces internes de ´pendent seulement du temps de l’attente avant l’installation du soute `nement, cette e ´tude de ´montre que la de ´pendance du cheminement de la ge ´ome ´trie (refle ´te ´e par la longueur circu- laire d’excavation) est tre `s forte, me ˆme lorsqu’on conside `re l’e ´lasticite ´ line ´aire. De plus, plusieurs autres solutions trouve ´es dans la litte ´rature ont aussi ne ´glige ´ l’importance de la rigidite ´ relative entre le sol et la structure de soute `nement, possible- ment a ` cause des dimensions pluto ˆt grossie `res du maillage. Les analyses pre ´sente ´es dans cet article montrent que la rigidite ´ relative peut e ˆtre responsable de diffe ´rences de l’ordre de 60% dans les forces internes. Une expression sans dimension qui conside `re tous ces parame `tres est pre ´sente ´e en tant que bonne approximation pour le me ´canisme de transfert de charge sur la face. Mots-cle ´s : tunnel, trois dimensions, transfert de contraintes, forces internes, de ´lai pour l’installation du soute `nement. [Traduit par la Re ´daction] Introduction Tunnel support structure is a key aspect of underground construction operations planning as it affects cost, installa- tion time, and — in particular — safety during excavation. However, gaining a fuller understanding of the load transfer process in these structures has been restricted because of the complexity of the phenomena involved, such as the time de- pendency of material behavior (in the case of shotcrete) and the three-dimensional character of the mechanism at the face, and the many peculiarities related to the way in which a tunnel cross section’s geometric characteristics evolve in sequential excavation processes or ground-mass constitutive models. Advances in numerical modeling and computer processing power have helped improve the understanding of the load transfer mechanism, but many of the mechanism’s aspects remain to be clarified. Despite their three-dimensional char- acter, plane strain analyses have been used to investigate the transfer mechanism, after making certain simplifications and with certain limitations. Convergence–confinement methods have also often been used. Wong et al. (2006) developed an analytical convergence– confinement model to simulate the behavior of a support consisting of grouted bolts. Discrete bolts were assimilated Received 3 September 2006. Accepted 13 January 2009. Published on the NRC Research Press Web site at cgj.nrc.ca on 8 July 2009. R.A.M.P. Gomes and T.B. Celestino. 1,2 Sa ˜o Carlos Engineering School, University of Sa ˜o Paulo, Av. Trabalhador Sa ˜o-Carlense 400, 13566-590 Sa ˜o Carlos, SP, Brazil. 1 Corresponding author (e-mail: tbcelest@usp.br). 2 Present address: Themag Engenharia Ltda., Sa ˜o Paulo, Brazil. 855 Can. Geotech. J. 46: 855–868 (2009) doi:10.1139/T09-016 Published by NRC Research Press