Solution of the Ultimate Bearing Capacity at the Tip of a Pile in Anisotropic Discontinuous Rock Mass Based on the Hoek–Brown Criterion
Publication: International Journal of Geomechanics
Volume 21, Issue 2
Abstract
An analytical method will be proposed to investigate the bearing mechanism of piles in an anisotropic discontinuous rock mass. Based on the characteristic line method, the discontinuous part of the rock is considered as the boundary condition of the plastified zone, and Riemann's invariant governing equation will be applied at the boundary conditions to link these boundaries. It was found that four different failure mechanisms exist that depend on the inclination angle of weakness planes (χ): (1) conditioned by the planes of weakness in the intermediate zone (MC), (2) conditioned by the planes of weakness close to Boundary 2 in the active zone (M2), (3) conditioned by the planes of weakness close to Boundary 1 in the passive zone (M1), and (4) not conditioned by the planes of weakness (MI). Each pile failure mechanism contains four failure modes under different pile embedment and geostatic loads: (1) deep pile with minor overburden (DL), (2) deep pile and large overburden (DH), (3) semideep pile and small overburden (SL), and (4) semideep pile and large overburden (SH). Therefore, 16 pile failure modes exist and are distinguished by χ and the embedment ratios (n). The friction angles of the weakness planes (φ) have significant effects on the pile failure mechanisms. Under the failure mechanism of MC, M2, and M1, the peak of the percentage of pile bearing capacity in anisotropic discontinuous rock over that in isotropic continuous rock (NβP,DL/NβP,MI ) increased with φ.
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Acknowledgments
The authors are grateful to the support of National Key R&D Program of China (2016YFC0800200), and the National Natural Science Foundation of China (Grant Nos. 51778571, 51578500, and 51578426). This paper has also received funding from the European Union's Horizon 2020 MARIE SKLODOWSKA-CURIE RESEARCH AND INNOVATION STAFF EXCHANGEMARIE SKLODOWSKA-CURIE RESEARCH AND INNOVATION STAFF EXCHANGE Program under Grant No. 778360.
Notation
The following symbols are used in this paper:
- hm
- average overburden load in ground;
- mi
- parameter of the Hoek and Brown criterion;
- tensile strength of the planes of weakness;
- α
- angle for the assumed virtual failure surface;
- αA
- angle for the assumed virtual failure surface for Boundary A;
- αA
- angle for the assumed virtual failure surface for Boundary A;
- αB
- angle for the assumed virtual failure surface for Boundary A;
- αB
- angle for the assumed virtual failure surface for Boundary B;
- β
- strength modulus for the rock mass;
- γ
- intermediate parameter;
- γA
- intermediate parameter for Boundary A;
- γA
- intermediate parameter for Boundary A;
- γB
- intermediate parameter for Boundary B;
- γB
- intermediate parameter for Boundary B;
- ɛ
- angle that forms the main major stress with the inclination of the ground;
- ζ
- tensile strength coefficient of the rock mass;
- ρ
- instantaneous friction angles of rocks;
- ρ1
- instantaneous friction angles of rocks for Boundary 1;
- ρA
- instantaneous friction angle for Boundary A;
- ρB
- instantaneous friction angle for Boundary B;
- failure stress for Boundary A;
- failure stress for Boundary B;
- φ
- friction angles of the planes of weakness;
- χ
- inclination angles of the planes of weakness; and
- ω
- intermediate angle.
References
Cai, Y., B. Xu, Z. Cao, X. Geng, and Z. Yuan. 2020. “Solution of the ultimate bearing capacity at the tip of a pile in inclined rocks based on the Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 125: 104140. https://doi.org/10.1016/j.ijrmms.2019.104140.
Carter, J. P., and F. H. Kulhawy. 1988. Analysis and design of drilled shaft foundation socketed into rock. Rep. No. EL-5918. Palo Alto, CA: Electric Power Research Institute.
Coates, D. F. 1967. Rock mechanics principles. Monograph 874. Ottawa: Dept. of Energy, Mines and Resources, Mines Branch, Queen’s printer.
De Beer, E. E. 1970. “Experimental determination of the shape factors and the bearing capacity factors of sand.” Géotechnique 20 (4): 387–411. https://doi.org/10.1680/geot.1970.20.4.387.
England, M., P. Cheesman, J. A. Lawrence, M. Preene, U. L. Lawrence, and R. Buckley. 2018. “Recent experiences of full scale static pile load testing in chalk.” In Engineering in Chalk, 129–134. London: ICE Publishing.
Fatehnia, M., and G. Amirinia. 2018. “A review of genetic programming and artificial neural network applications in pile foundations.” Int. J. Geo-Eng. 9 (1): 2. https://doi.org/10.1186/s40703-017-0067-6.
Galindo, R. A., A. Serrano, and C. Olalla. 2017. “Ultimate bearing capacity of rock masses based on modified Mohr-Coulomb strength criterion.” Int. J. Rock Mech. Min. Sci. 100 (93): 215–225. https://doi.org/10.1016/j.ijrmms.2016.12.017.
Hoek, E., and E. T. Brown. 1980. “Empirical strength criterion for rock masses.” J. Geotech. Geoenviron. Eng. 106 (GT9): 1013–1035.
Huang, B., Y. Zhang, X. Fu, and B. Zhang. 2018. “Study on visualization and failure mode of model test of rock-socketed pile in soft rock.” Geotech. Test. J. 42 (6): 1624–1639. https://doi.org/10.1520/GTJ20170348.
Kulhawy, F. H., and R. E. Goodman. 1980. “Design of foundations on discontinuous rock.” In Vol. 1 of Proc., Int. Conf. on Struct Found on Rock, 209–220. Sydney, Australia: University of Sydney.
Meyerhof, G. G. 1951. “The ultimate bearing capacity of foudations.” Géotechnique 2 (4): 301–332. https://doi.org/10.1680/geot.1951.2.4.301.
Murlidhar, B. R., R. K. Sinha, E. T. Mohamad, R. Sonkar, and M. Khorami. 2020. “The effects of particle swarm optimisation and genetic algorithm on ANN results in predicting pile bearing capacity.” Int. J. Hydromechatronics 3 (1): 69–87. https://doi.org/10.1504/IJHM.2020.105484.
O’Neill, M. W., and L. C. Reese. 1999. Drilled shafts: Cons- truction procedures and design methods. FHWA Publication No. FHWA-IF-99-025. McLean, VA: Federal Highway Administration.
Pells, P. J. 1977. “Theoretical and model studies related to the bearing capacity of rock.” In Sydney Group of Australian Geomechanics Society. Sydney, Australia: Institution of Engineers.
Roh, Y., G. Kim, I. Kim, and J. Lee. 2019. “Effects of rock-support and inclined-layer conditions on load carrying behavior of piled rafts.” Geomech. Geoeng. 18 (4): 363–371. https://doi.org/10.12989/gae.2019.18.4.363.
Rowe, R. K., and H. H. Armitage. 1987. “A design method for drilled piers in soft rock.” Can. Geotech. J. 24 (1): 126–142. https://doi.org/10.1139/t87-011.
Serrano, A., and C. Olalla. 1994. “Ultimate bearing capacity of rock masses.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (2): 93–106. https://doi.org/10.1016/0148-9062(94)92799-5.
Serrano, A., and C. Olalla. 1996. “Allowable bearing capacity of rock foundations using a non-linear failure criterium.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 (4): 327–345. https://doi.org/10.1016/0148-9062(95)00081-X.
Serrano, A., and C. Olalla. 1998a. “Ultimate bearing capacity of an anisotropic discontinuous rock mass. Part I: Basic modes of failure.” Int. J. Rock Mech. Min. Sci. 35 (3): 301–324. https://doi.org/10.1016/S0148-9062(97)00337-9.
Serrano, A., and C. Olalla. 1998b. “Ultimate bearing capacity of an anisotropic rock mass. Part II: Procedure for its determination.” Int. J. Rock Mech. Min. Sci. 35 (3): 325–348. https://doi.org/10.1016/S0148-9062(97)00338-0.
Serrano, A., and C. Olalla. 2002a. “Ultimate bearing capacity at the tip of a pile in rock. Part 1: Theory.” Int. J. Rock Mech. Min. Sci. 39 (7): 833–846. https://doi.org/10.1016/S1365-1609(02)00052-7.
Serrano, A., and C. Olalla. 2002b. “Ultimate bearing capacity at the tip of a pile in rock. Part 2: Application.” Int. J. Rock Mech. Min. Sci. 39 (7): 847–866. https://doi.org/10.1016/S1365-1609(02)00053-9.
Serrano, A., C. Olalla, and R. A. Galindo. 2014. “Ultimate bearing capacity at the tip of a pile in rock based on the modified Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 71: 83–90. https://doi.org/10.1016/j.ijrmms.2014.07.006.
Serrano, A., C. Olalla, and R. A. Galindo. 2016. “Ultimate bearing capacity of an anisotropic discontinuous rock mass based on the modified Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 83: 24–40. https://doi.org/10.1016/j.ijrmms.2015.12.014.
Serrano, A., C. Olalla, and J. González. 2000. “Ultimate bearing capacity of rock masses based on the modified Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 37 (6): 1013–1018. https://doi.org/10.1016/S1365-1609(00)00028-9.
Sokolovsky, V. V. 1956. Statics of loose medium. London: Butterworth.
Teng, W. C. 1962. Foundation design. Englewood Cliffs, NJ: Prentice-Hall.
Vipulanandan, C., A. Hussain, and O. Usluogulari. 2007. “Parametric study of open core-hole on the behavior of drilled shafts socketed in soft rock.” In Geo-Denver 2007, Geotechnical Special Publication 158, edited by W. Camp, R. Castelli, D. F. Laefer, and S. Paikowsky, 1–10. Reston, VA: ASCE.
Yang, X. L., and J. H. Yin. 2005. “Upper bound solution for ultimate bearing capacity with a modified Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 42 (4): 550–560. https://doi.org/10.1016/j.ijrmms.2005.03.002.
Yang, X. L., and J. H. Yin. 2006. “Linear Mohr-Coulomb strength parameters from the non-linear Hoek–Brown rock masses.” Int. J. Non Linear Mech. 41 (8): 1000–1005. https://doi.org/10.1016/j.ijnonlinmec.2006.08.003.
Zhang, L., and H. H. Einstein. 1998. “End bearing capacity of drilled shafts in rock.” J. Geotech. Geoenviron. Eng. 124 (7): 574–584. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:7(574).
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Published In
International Journal of Geomechanics
Volume 21 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: May 11, 2020
Accepted: Sep 15, 2020
Published online: Dec 7, 2020
Published in print: Feb 1, 2021
Discussion open until: May 7, 2021
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