DOI QR코드

DOI QR Code

Probabilistic bearing capacity of circular footing on spatially variable undrained clay

  • 투고 : 2022.12.20
  • 심사 : 2024.07.03
  • 발행 : 2024.07.10

초록

The present paper investigates the spatial variability effect of soil property on the three-dimensional probabilistic characteristics of the bearing capacity factor (i.e., mean and coefficient of variation) of a circular footing resting on clayey soil where both mean and standard deviation of undrained shear strength increases with depth, keeping the coefficient of variation constant. The mean trend of undrained shear strength is defined by introducing the dimensionless strength gradient parameter. The finite difference method along with the random field and Monte Carlo simulation technique, is used to execute the numerical analyses. The lognormal distribution is chosen to generate random fields of the undrained shear strength. In the study, the potential failure of the structure is represented through the failure probability. The influences of different vertical scales of fluctuation, dimensionless strength gradient parameters, and coefficient of variation of undrained shear strength on the probabilistic characteristics of the bearing capacity factor and failure probability of the footing, along with the probability and cumulative density functions, are explored in this study. The variations of failure probability for different factors of safety corresponding to different parameters are also illustrated. The results are presented in non-dimensional form as they might be helpful to the practicing engineers dealing with this type of problem.

키워드

참고문헌

  1. Al-Bittar, T. and Soubra, A. -H. (2013), "Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion", Int. J. Numer. Anal. Methods Geomech., 37(13), 2039-2060. https://doi.org/10.1002/nag.2120. 
  2. Bai, T., Yang, H., Chen, X., Zhang, S. and Jin, Y. (2020), "In-situ monitoring and reliability analysis of an embankment slope with soil variability", Geomech. Eng., 23(3), 261-273. https://doi.org/10.12989/gae.2020.23.3.261. 
  3. Benmoussa, S., Benmebarek, S. and Benmebarek, N. (2021), "Bearing capacity factor of circular footings on two-layered clay soils", Civ. Eng. J., 7(5), 775-785. https://doi.org/10.28991/cej-2021-03091689. 
  4. Bishop, A.W. (1966), "The strength of soils as engineering materials", Geotechnique, 16(2), 91-130. https://doi.org/10.1680/geot.1966.16.2.91. 
  5. Bransby, M.F. and Randolph, M.F. (1998), "Combined loading of skirted foundations", Geotechnique, 48(5), 637-655. https://doi.org/10.1680/geot.1998.48.5.637. 
  6. Charlton, T.S. and Rouainia, M. (2017), "A probabilistic approach to the ultimate capacity of skirted foundations in spatially variable clay", Struct. Saf., 65, 126-136. https://doi.org/10.1016/j.strusafe.2016.05.002. 
  7. Cho, S.E. (2010), "Probabilistic assessment of slope stability that considers the spatial variability of soil properties", J. Geotech. Geoenviron. Eng., 136(7), 975-984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309. 
  8. Choudhuri, K. and Chakraborty, D. (2021), "Probabilistic Bearing Capacity of a Pavement Resting on Fibre Reinforced Embankment Considering Soil Spatial Variability", Front. Built Environ., 7, 628016. https://doi.org/10.3389/fbuil.2021.628016. 
  9. Choudhuri, K. and Chakraborty, D. (2022), "Probabilistic analyses of three-dimensional circular footing resting on two-layer c-ϕ soil system considering soil spatial variability", Acta Geotech., 17(12), 5739-5758. https://doi.org/10.1007/s11440-022-01701-7. 
  10. Choudhuri, K. and Chakraborty, D. (2023) "Risk assessment of three-dimensional bearing capacity of a circular footing resting on spatially variable sandy soil", Iran. J. Sci. Technol. - Trans. Civ. Eng., 47(6), 3681-3698. https://doi.org/10.1007/s40996-023-01129-3. 
  11. Choudhuri, K. and Chakraborty, D. (2024), "Probability-based analyses of bearing capacity of square and rectangular footings resting on sandy soil considering rotational anisotropy", Acta Geotech., 1-22. https://doi.org/10.1007/s11440-024-02297-w. 
  12. Chwala, M. and Kawa, M. (2021), "Random failure mechanism method for assessment of working platform bearing capacity with a linear trend in undrained shear strength", J. Rock Mech. Geotech. Eng., 13(6), 1513-1530. https://doi.org/10.1016/j.jrmge.2021.06.004. 
  13. Das, S. and Chakraborty, D. (2024), "Influence of rotated anisotropy and spatial variability of undrained clay on bearing capacity of strip footings under eccentric loading", Comput. Geotech., 172, 106443. https://doi.org/10.1016/j.compgeo.2024.106443. 
  14. Deng, Z.P., Pan, M., Niu, J.T., Jiang, S.H. and Qian, W.W. (2021), "Slope reliability analysis in spatially variable soils using sliced inverse regression-based multivariate adaptive regression spline", Bull. Eng. Geol. Environ., 80, 7213-7226. https://doi.org/10.1007/s10064-021-02353-9. 
  15. Deng, Z.P., Pan, M., Niu, J.T. and Jiang, S.H. (2022), "Full probability design of soil slopes considering both stratigraphic uncertainty and spatial variability of soil properties", Bull. Eng. Geol. Environ., 81(5), 195. https://doi.org/10.1007/s10064-022-02702-2. 
  16. El-Ramly, H., Morgenstern, N.R. and Cruden, D.M. (2003), "Probabilistic stability analysis of a tailings dyke on presheared clay-shale", Can. Geotech. J., 40(1), 192-208. https://doi.org/10.1139/t02-095. 
  17. EN1990 (2002), Basis of structural design, European Committee for Standardization; Brussels, Belgium. 
  18. Fenton, G.A. and Griffiths, D.V. (2002), "Probabilistic foundation settlement on spatially random soil", J. Geotech. Geoenviron. Eng., 128(5), 381-390. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:5(381). 
  19. FLAC3D (2012), Fast Lagrangian analysis of continua, version 5.01: user's and theory manuals, Itasca Consulting Group Inc., Minneapolis, USA. 
  20. Griffiths, D.V., Fenton, G.A. and Manoharan, N. (2002), "Bearing capacity of rough rigid strip footing on cohesive soil: probabilistic study", J. Geotech. Geoenviron. Eng., 128(9), 743-755. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743). 
  21. Griffiths, D.V. and Fenton, G.A. (2004), "Probabilistic slope stability analysis by finite elements", J. Geotech. Geoenviron. Eng., 130(5), 507-518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507). 
  22. Griffiths, D.V. and Fenton, G.A. (2009), "Probabilistic settlement analysis by stochastic and random finite-element methods", J. Geotech. Geoenviron. Eng., 135(11), 1629-1637. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000126. 
  23. Haldar, S. and Sivakumar Babu, G.L. (2008), "Effect of soil spatial variability on the response of laterally loaded pile in undrained clay", Comput. Geotech., 35, 537-547. https://doi.org/10.1016/j.compgeo.2007.10.004. 
  24. Halder, K. and Chakraborty, D. (2020a), "Influence of soil spatial variability on the response of strip footing on geocell-reinforced slope", Comput. Geotech., 122, 103533. https://doi.org/10.1016/j.compgeo.2020.103533. 
  25. Halder, K. and Chakraborty, D. (2020b) "Probabilistic bearing capacity of strip footing on reinforced anisotropic soil slope", Geomech. Eng., 23(1), 15-30 https://doi.org/10.12989/gae.2020.23.1.015. 
  26. Houlsby, G.T. and Martin, C.M. (2003), "Undrained bearing capacity factors for conical footings on clay", Geotechnique, 53(5), 513-520. https://doi.org/10.1680/geot.2003.53.5.513. 
  27. Jamshidi Chenari, R. and Mahigir, A. (2014), "The effect of spatial variability and anisotropy of soils on bearing capacity of shallow foundations", Civ. Eng. Infrastruct. J., 47(2), 199-213. https://doi.org/10.7508/ceij.2014.02.004. 
  28. Jamshidi Chenari, R. and Alaie, R. (2015), "Effects of anisotropy in correlation structure on the stability of an undrained clay slope", Georisk, 9(2), 109-123. https://doi.org/10.1080/17499518.2015.1037844. 
  29. Jha, S.K. (2016), "Reliability-based analysis of bearing capacity of strip footings considering anisotropic correlation of spatially varying undrained shear strength", Int. J. Geomech., 16(5), 06016003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000638. 
  30. Jiang, S.H. and Huang, J. (2018), "Modeling of non-stationary random field of undrained shear strength of soil for slope reliability analysis", Soils Found., 58(1), 185-198. https://doi.org/10.1016/j.sandf.2017.11.006. 
  31. Jiang, S.H., Huang, J., Griffiths, D.V. and Deng, Z.P. (2022), "Advances in reliability and risk analyses of slopes in spatially variable soils: A state-of-the-art review". Comput. Geotech., 141, 104498. https://doi.org/10.1016/j.compgeo.2021.104498. 
  32. Kasama, K. and Whittle, A.J. (2016), "Effect of spatial variability on the slope stability using Random Field Numerical Limit analysis", Georisk, 10(1), 42-54. https://doi.org/10.1080/17499518.2015.1077973. 
  33. Kawa, M. and Pula, W. (2020), "3D bearing capacity probabilistic analyses of footings on spatially variable c-ϕ soil", Acta Geotech., 15(6), 1453-1466. https://doi.org/10.1007/s11440-019-00853-3. 
  34. Khatri, V.N. and Kumar, J. (2009), "Bearing capacity factor Nc under ϕ = 0 condition for piles in clays", Int. J. Numer. Anal. Methods Geomech., 33(9), 1203-1225. https://doi.org/10.1002/nag.763. 
  35. Krishnan, K. and Chakraborty, D. (2022), "Probabilistic study on the bearing capacity of strip footing subjected to combined effect of inclined and eccentric loads", Comput. Geotech., 141, 104505,. https://doi.org/10.1016/j.compgeo.2021.104505. 
  36. Kusakabe, O., Suzuki, H. and Nakase, A. (1986), "An upper bound calculation on bearing capacity of a circular footing on a non-homogeneous clay", Soils Found., 26(3), 143-148. https://doi.org/10.3208/sandf1972.26.3_143. 
  37. Li, D.Q., Qi, X.H., Phoon, K.K., Zhang, L.M. and Zhou, C.B. (2014), "Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes", Struct. Saf., 49, 45-55. https://doi.org/10.1016/j.strusafe.2013.08.005. 
  38. Li, D.Q., Qi, X.H., Cao, Z.J., Tang, X.S., Zhou, W., Phoon, K.K. and Zhou, C.B. (2015), "Reliability analysis of strip footing considering spatially variable undrained shear strength that linearly increases with depth", Soils Found., 55(4), 866-880. https://doi.org/10.1016/j.sandf.2015.06.017. 
  39. Li, Y., Liu, K., Zhang, B. and Xu, N. (2019), "Reliability of shape factors for bearing capacity of square footings on spatially varying cohesive soils", Int. J. Geomech., 20(3), 04019195. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001614. 
  40. Li, T., Gong, W. and Tang, H. (2021), "Three-dimensional stochastic geological modeling for probabilistic stability analysis of a circular tunnel face", Tunn. Undergr. Sp. Tech., 118, 104190. https://doi.org/10.1016/j.tust.2021.104190. 
  41. Li, T., Pan, Q., Shen, Z. and Gong, W. (2022), "Probabilistic stability analysis of a tunnel face in spatially random Hoek-Brown rock masses with a multi-tangent method", Rock Mech. Rock Eng., 55(6), 3545-3561. https://doi.org/10.1007/s00603-022-02821-y. 
  42. Lombardi, M., Cardarilli, M. and Raspa, G. (2017), "Spatial variability analysis of soil strength to slope stability assessment", Geomech. Eng., 12(3), 483-503. https://doi.org/10.12989/gae.2017.12.3.483. 
  43. Luo, Z., Atamturktur, S., Cai, Y. and Juang, C.H. (2011), "Reliability analysis of basal- heave in a braced excavation in a 2-D random field", Comput. Geotech., 39, 27-37. https://doi.org/10.1016/j.compgeo.2011.08.005. 
  44. Lumb, P. (1966), "The variability of natural soils", Can. Geotech. J., 3(2), 74-97. https://doi.org/10.1139/t66-009. 
  45. Majumder, M. and Chakraborty, D. (2021), "Three-dimensional numerical analysis of under-reamed pile in clay under lateral loading", Innov. Infrastruct. Solut., 6(2), 1-17. https://doi.org/10.1007/s41062-020-00428-2. 
  46. Sivakumar Babu, G.L. and Mukesh, M.D. (2004), "Effect of soil variability on reliability of soil slopes", Geotechnique, 54(5), 335-337. https://doi.org/10.1680/geot.2004.54.5.335. 
  47. Shen, Z., Jin, D., Pan, Q., Yang, H. and Chian, S.C. (2020), "Probabilistic analysis of strip footings on spatially variable soils with linearly increasing shear strength", Comput. Geotech., 126, 103653. https://doi.org/10.1016/j.compgeo.2020.103653. 
  48. Shen, Z., Jin, D., Pan, Q., Yang, H. and Chian, S.C. (2021), "Effect of soil spatial variability on failure mechanisms and undrained capacities of strip foundations under uniaxial loading", Comput. Geotech., 139, 104387. https://doi.org/10.1016/j.compgeo.2021.104387. 
  49. Shu, S., Gao, Y. and Wu, Y. (2020), "Probabilistic bearing capacity analysis of spudcan foundation in soil with linearly increasing mean undrained shear strength", Ocean Eng., 204, 106800. https://doi.org/10.1016/j.oceaneng.2019.106800. 
  50. Srivastava, A. and Sivakumar Babu, G.L. (2009), "Effect of soil variability on the bearing capacity of clay and in slope stability problems", Eng. Geol., 108(1-2), 142-152. https://doi.org/10.1016/j.enggeo.2009.06.023. 
  51. Srivastava, A. and Sivakumar Babu, G.L. (2011), "Deflection and buckling of buried flexible pipe-soil system in a spatially variable soil profile", Geomech. Eng., 3(3), 169-188. https://doi.org/10.12989/gae.2011.3.3.169. 
  52. The MathWorks Inc. (2020), MATLAB (R2020b), version 9.9, Massachusetts, United States. https://www.mathworks.com
  53. U.S. Army Corps of Engineers (USACE) (1997), Engineering and design: Introduction to probability and reliability methods for use in geotechnical engineering, Eng. Circ. 1110-2-547, U.S. Dept. of the Army, Washington, DC. 
  54. Wu, Y., Zhou, X., Gao, Y., Zhang, L. and Yang, J. (2019), "Effect of soil variability on bearing capacity accounting for nonstationary characteristics of undrained shear strength", Comput. Geotech., 110, 199-210. https://doi.org/10.1016/j.compgeo.2019.02.003. 
  55. Wu, Y., Zhou, X., Gao, Y. and Shu, S. (2020), "Bearing capacity of embedded shallow foundations in spatially random soils with linearly increasing mean undrained shear strength", Comput. Geotech., 122, 103508. https://doi.org/10.1016/j.compgeo.2020.103508. 
  56. Yi, J.T., Huang, L.Y., Li, D.Q. and Liu, Y. (2020), "A largede-formation random finite-element study: failure mechanism and bearing capacity of spudcan in a spatially varying clayey seabed", Geotechnique, 70(5), 392-405. https://doi.org/10.1680/jgeot.18.P.171. 
  57. Yoo, C. (2016), "Effect of spatial characteristics of a weak zone on tunnel deformation behavior", Geomech. Eng., 11(1), 41-58. https://doi.org/10.12989/gae.2016.11.1.041. 
  58. Zhao, C., Gong, W., Li, T., Juang, C.H., Tang, H. and Wang, H. (2021), "Probabilistic characterization of subsurface stratigraphic configuration with modified random field approach", Eng. Geol., 288, 106138. https://doi.org/10.1016/j.enggeo.2021.106138. 
  59. Zhu, D., Griffiths, D.V., Huang, J. and Fenton, G.A. (2017), "Probabilistic stability analyses of undrained slopes with linearly increasing mean strength", Geotechnique, 67(8), 733-746. https://doi.org/10.1680/jgeot.16.P.223.