Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Influence of spatial variability on unsaturated hydraulic properties

  • Tan, Xiaohui (School of Resources and Environmental Engineering, Hefei University of Technology) ;
  • Fei, Suozhu (School of Resources and Environmental Engineering, Hefei University of Technology) ;
  • Shen, Mengfen (Zhejiang University of Technology) ;
  • Hou, Xiaoliang (School of Resources and Environmental Engineering, Hefei University of Technology) ;
  • Ma, Haichun (School of Resources and Environmental Engineering, Hefei University of Technology)
  • Received : 2019.05.27
  • Accepted : 2020.11.18
  • Published : 2020.12.10
⟨ Previous Next ⟩

Abstract

To investigate the effect of spatial variability on hydraulic properties of unsaturated soils, a numerical model is set up which can simulate seepage process in an unsaturated heterogeneous soil. The unsaturated heterogeneous soil is composed of matrix sand embedded with a small proportion of clay for simulating the heterogeneity. Soil-water characteristic curve and unsaturated hydraulic conductivity curve of the unsaturated soil are expressed by Van Genuchten model. Hydraulic parameters of the matrix sand are considered as random fields. Different autocorrelation lengths (ACLs) of hydraulic parameter of the matrix sand and different proportions of clay are assumed to investigate the influence of spatial variability on the equivalent hydraulic properties of the heterogeneous soil. Four model sizes are used in the numerical experiments to investigate the influence of scale effects and to determine the sizes of representative volume element (RVE) in the numerical simulations. Through a number of Monte Carlo simulations of unsaturated seepage analysis, the means and the coefficients of variations (COVs) of the equivalent hydraulic parameters of the heterogeneous soil are calculated. Simulations show that the ACL and model size has little influence on the means of the equivalent hydraulic parameters, but they have a large influence on the COVs of the equivalent hydraulic parameters. The size of an RVE is mainly affected by the ACL and the proportion of heterogeneity. The influence of spatial variability on the hydraulic parameters of the heterogeneous unsaturated soil can be used as a guidance for geotechnical reliability analysis and design related to unsaturated soils.

Keywords

Acknowledgement

The financial supports from the National Natural Science Foundation, China (41572282, 41972278) are greatly appreciated and acknowledged.

References

  1. Ahmed, A.A. (2009), "Stochastic analysis of free surface flow through earth dams", Comput. Geotech., 36(7), 1186-1190. http://doi.org/10.1016/j.compgeo.2009.05.005.
  2. Botros, F.E., Harter, T., Onsoy, Y.S., Tuli, A. and Hopmans, J.W. (2009), "Spatial variability of hydraulic properties and sediment characteristics in a deep alluvial unsaturated zone", Vadose Zone J., 8(2), 276-289. http://doi.org/10.2136/vzj2008.0087.
  3. Chen, P.Y., Chen, C.H., Hsu, N.S., Wu, C.M. and Wen, J.C. (2012), "Influence of heterogeneity on unsaturated hydraulic properties:(1) local heterogeneity and scale effect", Hydrol. Process., 26, 3593-3603. http://doi.org/10.1002/hyp.8449.
  4. Ching, J.Y. and Phoon, K.K. (2013), "Effect of element sizes in random field finite element simulations of soil shear strength", Comput. Struct., 126(1), 120-134. http://doi.org/10.1016/j.compstruc.2012.11.008.
  5. Cho, S.E. (2007), "Effects of spatial variability of soil properties on slope stability", Eng. Geol., 92(3), 97-109. http://doi.org/10.1016/j.enggeo.2007.03.006.
  6. Cho, S.E. (2012), "Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation", Eng. Geol., 133-134(3), 30-39. http://doi.org/10.1016/j.enggeo.2012.02.013.
  7. Dou, H.Q., Han, T.C., Gong, X.N. and Zhang, J. (2014), "Probabilistic slope stability analysis considering the variability of hydraulic conductivity under rainfall infiltrationredistribution conditions", Eng. Geol., 183(1-13), 1-13. http://doi.org/10.1016/j.enggeo.2014.09.005.
  8. Fan, H. and Liang, R. (2013), "Reliability-based design of axially loaded drilled shafts using Monte Carlo method", Int. J. Numer. Anal. Meth. Geomech., 37(14), 2223-2238. https://doi.org/10.1002/nag.2131.
  9. Fei, S.Z., Tan, X.H., Wang, X., Du, L.F. and Sun, Z.H. (2019), "Evaluation of soil spatial variability by micro-structure simulation", Geomech. Eng., 17(6), 565-572. http://doi.org/10.12989/gae.2019.17.6.565.
  10. Firouzianbandpey, S., Griffiths, D.V., Ibsen, L.B. and Andersen, L.V. (2014), "Spatial correlation length of normalized cone data in sand: case study in the north of Denmark", Can. Geotech. J., 51(8), 844-857. http://doi.org/10.1139/cgj-2013-0294.
  11. Fredlund, D.G. and Houston, S.L. (2009), "Protocol for the assessment of unsaturated soil properties in geotechnical engineering practice", Can. Geotech. J., 46(6), 694-707. http://doi.org/10.1139/T09-010.
  12. Fredlund, D.G. and Xing, A. (1994), "Equations for the soil-water characteristic curve", Can. Geotech. J., 31(521-32), 521-532. https://doi.org/10.1139/t94-061.
  13. Fredlund, D.G., Sheng, D.C. and Zhao, J.D. (2011), "Estimation of soil suction from the soil-water characteristic curve", Can. Geotech. J., 48(2), 186-198. https://doi.org/10.1139/T10-060.
  14. Fredlund, D.G., Xing, A., Fredlund, M.D. and Barbour, S.L. (1995), "The relationship of the unsaturated soil shear strength to the soil-water characteristic curve", Can. Geotech. J., 33(3), 440-448. https://doi.org/10.1139/t96-065.
  15. Fredlund, M. and Gitirana, J.G. (2011), "Probabilistic methods applied to unsaturated numerical modeling", Geotech. Geol. Eng., 29(2), 217-223. http://doi.org/10.1007/s10706-011-9391-3.
  16. Gong, W., Juang, C.H., Khoshnevisan, S. and Phoon, K.K. (2016), "R-LRFD: Load and resistance factor design considering robustness", Comput. Geotech., 74, 74-87. https://doi.org/10.1016/j.compgeo.2015.12.017.
  17. Griffiths, D.V., Paiboon, J., Huang, J. and Fenton, G.A. (2012), "Homogenization of geomaterials containing voids by random fields and finite elements", Int. J. Solids Struct., 49(14), 2006-2014. http://doi.org/10.1016/j.ijsolstr.2012.04.006.
  18. Gui, S.X., Zhang, R.D., Turner, J.P. and Xue, X.Z. (2000), "Probabilistic slope stability analysis with stochastic soil hydraulic conductivity", J. Geotech. Geoenviron. Eng., 126(1), 1-9. http://doi.org/10.1061/(ASCE)1090-0241.
  19. Heshmati, A.A. and Motahari, M.R. (2015), "Modeling the dependency of suction stress characteristic curve on void ratio in unsaturated soils", KSCE J. Civ. Eng., 19(1), 91-97. http://doi.org/10.1007/s12205-013-1185-0.
  20. Itasca Consulting Group, Inc. (2008), FLAC Version 6.0 Manual, Minneapolis, Minnesota, U.S.A.
  21. Javankhoshdel, S., Bathurst, R.J. and Cami, B. (2018), "Influence of model type, bias and input parameter variability on reliability analysis for simple limit states with two load terms", Comput. Geotech., 97, 78-89. https://doi.org/10.1016/j.compgeo.2018.01.002.
  22. Ji, J., Liao, H.L. and Low, B.K. (2012), "Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations", Comput. Geotech., 40(3), 135-146. http://doi.org/10.1016/j.compgeo.2011.11.002.
  23. Jiang, S.H., Li, D.Q., Zhou, C.B. and Phoon, K.K. (2014), "Slope reliability analysis considering effect of autocorrelation functions", Chin. J. Geotech. Eng., 36(3), 508-518. http://doi.org/10.11779/CJGE201403014.
  24. Jimenez, R. and Sitar, R. (2009), "The importance of distribution types on finite element analyses of foundation settlement", Comput. Geotech., 36(3), 474-483. https://doi.org/10.1016/j.compgeo.2008.05.003.
  25. Johari, A. and Mehrabani, L.A. (2016), "System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method", Int. J. Rock Mech. Min. Sci., 82, 61-70. http://doi.org/10.1016/j.ijrmms.2015.12.002.
  26. Kim, Y.M. and Jeong, S.S. (2017), "Modeling of shallow landslides in an unsaturated soil slope using a coupled model", Geomech. Eng., 13(2), 353-370. http://doi.org/10.12989/gae.2017.13.2.353.
  27. Le, T.MH., Gallipoli, D., Sanchez, M. and Wheeler, S.J. (2012), "Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments", Int. J. Numer. Anal. Met., 36(8), 1056-1076. http://dx.doi.org/10.1002/nag.1047.
  28. Lombardi, M., Cardarilli, M. and Raspa, G. (2017), "Spatial variability analysis of soil strength to slope stability assessment", Geomech. Eng., 12(3), 565-572. http://doi.org/10.12989/gae.2019.17.6.565.
  29. Mahmood, K., Kim, J.M., Khan, H., Safdar, M. and Khan, U. (2018), "The probabilistic stability analysis of saturatedunsaturated MH and CL soil slope with rainfall infiltration", KSCE J. Civ. Eng., 22(5), 1742-1749. http://doi.org/10.1007/s12205-017-1052-5.
  30. Moradi, F., Moosavi, A.A. and Moghaddam, B.K. (2016), "Spatial variability of water retention parameters and saturated hydraulic conductivity in a calcareous Inceptisols (Khuzestan province of Iran) under sugarcane cropping", Arch. Agron. Soil Sci., 62(12), 1686-1699. https://doi.org/10.1080/03650340.2016.1164308.
  31. Mualem, Y. (1976), "A new model for predicting the hydraulic conductivity of unsaturated porous media", Water Resour. Res., 12(3), 513-522. https://doi.org/10.1029/WR012i003p00513.
  32. Nemes, A., Schaap, M.G., Leij, F.J. and Wosten, J.H.M. (2001), "Description of the unsaturated ydraulic database UNSODA version 2.0", J. Hydrol., 251, 151-162. https://doi.org/10.1016/S0022-1694(01)00465-6.
  33. Onyejekwe, S., Kang, X. and Ge, L. (2016), "Evaluation of the scale of fluctuation of geotechnical parameters by autocorrelation function and semivariogram function", Eng. Geol., 214, 43-49. http://doi.org/10.1016/j.enggeo.2016.09.014.
  34. Paiboon, J., Griffiths, D.V., Huang, J. and Fenton, G.A. (2013), "Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements", Int. J. Solids Struct., 50(20-21), 3233-3241. http://doi.org/10.1016/j.ijsolstr.2013.05.031.
  35. Papaioannou, I. and Straub, D. (2012), "Reliability updating in geotechnical engineering including spatial variability of soil", Comput. Geotech., 42, 44-51. http://doi.org/10.1016/j.compgeo.2011.12.004.
  36. Pereiral, J.H. and Fredlund, D.G. (2000), "Volume change behavior of collapsible compacted gneiss soil", J. Geotech. Geoenviron. Eng., 126(10), 907-916. http://doi.org/10.1061/(ASCE)10900241(2000)126:10(907).
  37. Phoon, K.K., Santoso, A. and Quek, S.T. (2010), "Probabilistic Analysis of Soil-Water Characteristic Curves", J. Geotech. Geoenviron. Eng., 136(3), 445-455. http://doi.org/10.1061/(ASCE)GT.1943-5606.0000222.
  38. Sillers, W.S. and Fredlund, D.G. (2001), "Statistical assessment of soil-water characteristic curve models for geotechnical engineering", Can. Geotech. J., 38(6), 1297-1313. http://doi.org/10.1139/t01-066.
  39. Srivastava, A., Babu, G.L.S. and Halda, S. (2010), "Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis", Eng. Geol., 110(3-4), 93-101. http://doi.org/10.1016/j.enggeo.2009.11.006.
  40. Stefanou, G. (2008), "The stochastic finite element method: Past, present and future", Comput. Method Appl. M., 198(9-12), 1031-1051. http://doi.org/10.1016/j.cma.2008.11.007.
  41. Sudret, B. and Kiureghian, A.D. (2002), "Comparison of finite element reliability methods", Probabilist. Eng. Mech., 17(4), 337-348. http://doi.org/10.1016/S0266-8920(02)00031-0.
  42. Tan, X.H., Bi, W.H., Hou, X.L. and Wang, W. (2011), "Reliability analysis using radial basis function networks and support vector machines", Comput. Geotech., 38(2), 178-186. https://doi.org/10.1016/j.compgeo.2010.11.002.
  43. Tan, X.H., Hu, M.Z., Juang, C.H., Li, P. and Shen, M.F. (2018), "Evaluation of the Autocorrelation Distance of Unsaturated Soils", Proceedings of the GeoShanghai 2018 International Conference: Multi-physics Processes in Soil Mechanics and Advances in Geotechnical Testing, Shanghai, China, May.
  44. Tan, X.H., Wang, X., Khoshnevisan, S., Hou, X.L. and Zha, F.S. (2017), "Seepage analysis of earth dams considering spatial variability of hydraulic parameters", Eng. Geol., 228, 260-269. http://doi.org/10.1016/j.enggeo.2017.08.018.
  45. Tan, X.H., Xin, Z.Y., Shen, M.F., Wang, X.E. and Xu, Q. (2014), "Study of soil-water characteristics of expansive soil under moisture adsorption and expansion condition", Rock Soil Mech., 35(12), 3352-3360. http://doi.org/10.11779/CJGE201507004.
  46. Van Genuchten, M.T. (1980), "A closed form equation predicting the hydraulic conductivity of unsaturated soils", Soil Sci. Soc. Am. J., 44(5), 892-898. http://doi.org/10.2136/sssaj1980.03615995004400050002x.
  47. Vanapalli, S.K., Fredlund, D.G. and Pufahl, D.E. (1996), "The relationship between the soil-water characteristic curve and the unsaturated shear strength of a compacted glacial till", Geotech. Test. J., 19(3), 259-268. http://doi.org/10.1520/GTJ10351J.
  48. Vanmarke, E.H. (1977), "Probabilistic modeling of soil profiles", J. Geotech. Eng., 103(11), 1227 -1246.
  49. Vogel, T., van Genuchten, M.T.H. and Cislerova, M. (2001), "Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions", Adv. Water Resour., 24, 133-144. https://doi.org/10.1016/S0309-1708(00)00037-3.
  50. Wang, T., Zhou, G.Q., Wang, J.Z., Zhao, X.D. and Yin, L.J. (2018), "Stochastic analysis for uncertain deformation of foundations in permafrost regions", Geomech. Eng., 14(6), 589-600. http://doi.org/10.12989/gae.2018.14.6.589.
  51. Wang, Y.Q., Shao, M.A., Han, X.W. and Liu, Z.P. (2015), "Spatial variability of soil parameters of the van Genuchten model at a regional scale", Clean-soil Air Water, 43(2), 271-278. https://doi.org/10.1002/clen.201300903.
  52. Wu, C.M., Chen, P.Y., Chen, C.H., Hsu, N.S. and Wen, J.C. (2012), "Influence of heterogeneity on unsaturated hydraulic properties (2) - percentage and shape of heterogeneity", Hydrol. Process, 26, 3604-3613. http://doi.org/10.1002/hyp.8448.
  53. Wu, L.Z., Huang, R.Q. and Xu, Q. (2012), "Incorporating Hysteresis in One-dimensional Seepage Modeling in Unsaturated Soils", KSCE J. Civ. Eng., 16(1), 69-77. http://doi.org/10.1007/s12665-015-4890-9.
  54. Zhu, H., Zhang, L.M., Zhang, L.L. and Zhou, C.B. (2013), "Twodimensional probabilistic infiltration analysis with a spatially varying permeability function", Comput. Geotech., 48(4), 249-259. http://doi.org/10.1016/j.compgeo.2012.07.010.