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An elastoplastic evaluation of the stress state around cylindrical openings based on a closed multiaxial yield surface. (English) Zbl 1272.74067
Summary: There are many applications encountered in geo-engineering where there is a need to evaluate the stress state around circular openings. This paper presents a new analytical solution for evaluating the stresses around a cylindrical excavation in an elastoplastic medium defined by the closed \(\mathrm{MSDP}_{u}\) yield surface. The proposed formulation takes into account the 3D stress geometry with a plasticity criterion that intersects the mean stress axis on the positive (compressive) and negative (tensile) sides. The results shown here illustrate how the stress distribution and yielding zone size are affected by various influence factors. Validation of the proposed formulation is made by comparing calculated results with existing analytical solutions and a numerical simulation.
MSC:
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74L10 Soil and rock mechanics
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[1] Obert, Rock Mechanics and the Design of Structures in Rock (1967)
[2] Ward, Ground supports for tunnels in weak rocks, Géotechnique 28 (2) pp 133– (1978)
[3] Marchetti, Analysis of circular tunnels in soft ground, Tunnels and Tunnelling 18 pp 45– (1986)
[4] Maury, Comprehensive Rock Engineering Principles, Practice and Projects 1 pp 369– (1993)
[5] Hoek, Support of Underground Excavations in Hard Rock (1995)
[6] Martin, Observations of brittle failure around a circular test tunnel, International Journal of Rock Mechanics and Mining Sciences 34 (7) pp 1065– (1997)
[7] Li, Estimation des contraintes dans les roches à partir de l’écaillage autour de trous de forage, Revue Française de Géotechnique 89 pp 3– (1999)
[8] Aubertin, Études et Recherches R-312 (2002)
[9] Abdel-Meguid, Three-dimensional analysis of unlined tunnels in rock subjected to high horizontal stress, Canadian Geotechnical Journal 40 pp 1208– (2003)
[10] Obara, Measurements of induced stress and strength in the near-field around a tunnel and associated estimation of the Mohr-Coulomb parameters for rock mass strength, International Journal of Rock Mechanics and Mining Sciences 41 (5) pp 761– (2004)
[11] Hawkes, Assessing the mechanical stability of horizontal boreholes in coal, Canadian Geotechnical Journal 44 (7) pp 797– (2007)
[12] Sari, Rock mass response model for circular openings, Canadian Geotechnical Journal 44 (7) pp 891– (2007)
[13] Fenner, Untersuchungen zur Erkenntnis des Gebirgsdruckes, Glückauf 74 pp 681– (1938)
[14] Labasse, Les pressions de terrains dans les mines de huiles, Revue Universelle des Mines Séries 9 5 (3) pp 78– (1949)
[15] Jaeger, Fundamentals of Rock Mechanics (1979)
[16] Brown, Ground response curves for rock tunnels, Journal of Soil Mechanics and Geotechnical Engineering 109 (1) pp 15– (1983)
[17] Cristescu, Rock Rheology (1989) · doi:10.1007/978-94-009-2554-0
[18] Kastner, Über den echten Gebirgsdruck beim Bau tiefliengender Tunnel, Osterreich Bauzeitschrift 10 (11) (1949)
[19] Salençon, Expansion quasi-statique d’une cavité à symétrie sphérique ou cylindrique dans un milieu elastoplastique, Annales des Ponts et Chaussées 3 pp 175– (1966)
[20] Salençon, Contraction quasi-statique d’une cavité à symétrie sphérique ou cylindrique dans un milieu elastoplastique, Annales des Ponts et Chaussées 4 pp 231– (1969)
[21] Egger, Advances in Rock Mechanics, Proceedings of the Third Congress of the International Society for Rock Mechanics 2 pp 1007– (1974)
[22] Florence, Axisymmetric compression of a Mohr-Coulomb medium around a circular hole, International Journal for Numerical and Analytical Methods in Geomechanics 2 (4) pp 367– (1978) · Zbl 0384.73077
[23] Schwartz, The State of the Art in Rock Mechanics, Proceedings of the Twenty-First U.S. Symposium on Rock Mechanics pp 787– (1980)
[24] Wang, Ground response of circular tunnel in poorly consolidated rock, Journal of Geotechnical Engineering 122 (9) pp 703– (1996)
[25] Carranza-Torres, The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion, International Journal of Rock Mechanics and Mining Sciences 36 pp 777– (1999)
[26] Carranza-Torres, Application of the convergence-confinement method of tunnel design to rock masses that satisfy the Hoek-Brown criterion, Tunnelling and Underground Space Technology 15 (2) pp 187– (2000)
[27] Sharan, Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media, International Journal of Rock Mechanics and Mining Sciences 40 pp 817– (2003)
[28] Sharan, Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock, International Journal of Rock Mechanics and Mining Sciences 42 pp 542– (2005)
[29] Sharan, Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock, International Journal of Rock Mechanics and Mining Sciences 45 pp 78– (2008)
[30] Carranza-Torres, Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion, International Journal of Rock Mechanics and Mining Sciences 41 pp 480– (2004)
[31] Parka, Analytical solution for a circular opening in an elastic-brittle-plastic rock, International Journal of Rock Mechanics and Mining Sciences 43 pp 616– (2006)
[32] Detournay, Two-dimensional elastoplastic analysis of a long, cylindrical cavity under non-hydrostatic loading, International Journal of Rock Mechanics and Mining Sciences 24 (4) pp 197– (1987)
[33] Chen, Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures, International Journal for Numerical and Analytical Methods in Geomechanics 23 (8) pp 779– (1999) · Zbl 0943.74016
[34] Carranza-Torres, Mining and Tunnelling Innovation and Opportunity 1 pp 283– (2002)
[35] Li, Formulation and application of a general inelastic locus for geomaterials with variable porosity, Canadian Geotechnical Journal 42 (2) pp 601– (2005)
[36] Aubertin, A multiaxial stress criterion for short term and long term strength of isotropic rock media, International Journal of Rock Mechanics and Mining Sciences 37 pp 1169– (2000)
[37] Aubertin, A porosity-dependent inelastic criterion for engineering materials, International Journal of Plasticity 20 (12) pp 2179– (2004) · Zbl 1125.74312
[38] Hiramatsu, Stress around a shaft or level excavated in ground with a three-dimensional stress state, Memoirs of the Faculty of Engineering, Kyoto University 24 pp 56– (1962)
[39] Hiramatsu, Determination of the stress in rock unaffected by boreholes or drifts, from measured strains or deformations, International Journal of Rock Mechanics and Mining Sciences 5 (1) pp 337– (1968) · doi:10.1016/0148-9062(68)90005-3
[40] Brady, Rock Mechanics for Underground Mining (1993)
[41] Li, Implementation and application of a new elasto-plastic model based on a multiaxial criterion to assess the stress state around backfilled openings, ASCE International Journal of Geomechanics (2007)
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