General Model for the Uniaxial Tensile Strength Characteristic Curve of Unsaturated Soils
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 147, Issue 7
Abstract
Characterization of tensile strength is critical to investigate the influence of desiccation and tensile cracks on the structural integrity of natural and artificial earthen structures and slopes. Although several models for the prediction of tensile strength of unsaturated soils have been proposed in the literature, critical gaps remain regarding a comprehensive model describing the tensile behavior of all soil types over a wide range of suction. This paper presents a general model for the tensile strength characteristic curve (TSCC) which establishes a relationship between the tensile strength versus water content in unsaturated soils. The proposed model is applicable to various soil types ranging from clean sands to silty and clayey soils. Tensile strength is characterized using the suction stress concept, and the TSCC model is built upon the concept that changes in tensile strength with water content (or degree of saturation) are primarily dominated by two distinct water retention mechanisms of capillarity and adsorption. Differences in the characteristics of capillary and adsorptive mechanisms and interparticle forces cause dissimilarities in the resultant TSCC in different soil types. Thus, a two-part suction stress characteristic curve (SSCC) was incorporated into the development of the TSCC to separately account for and distinguish interparticle forces and the resultant tensile strength under capillary and adsorptive mechanisms. The model was validated against laboratory-measured tensile strength reported in the literature for 10 soils, and was found to capture the tensile behavior of sandy, silty, and clayey soils well. Compared with several alternative models, the predictive accuracy of the proposed model was greater, particularly for clayey soils at low water contents (high suction). This superior performance can be attributed to properly accounting for the effect of adsorption mechanism, which is significant in clays.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
References
Abdollahi, M., F. Vahedifard, M. Abed, and B. A. Leshchinsky. 2021. “Effect of tension crack formation on active earth pressure encountered in unsaturated retaining wall backfills.” J. Geotech. Geoenviron. Eng. 147 (2): 06020028. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002434.
Ajaz, A., and R. H. G. Parry. 1975. “Stress–strain behaviour of two compacted clays in tension and compression.” Géotechnique 25 (3): 495–512. https://doi.org/10.1680/geot.1975.25.3.495.
Albrecht, B. A., and C. H. Benson. 2001. “Effect of desiccation on compacted natural clays.” J. Geotech. Geoenviron. Eng. 127 (1): 67–75. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:1(67).
Alonso, E. E., J.-M. Pereira, J. Vaunat, and S. Olivella. 2010. “A microstructurally based effective stress for unsaturated soils.” Géotechnique 60 (12): 913–925. https://doi.org/10.1680/geot.8.P.002.
Amarasiri, A. L., and J. K. Kodikara. 2013. “Numerical modeling of desiccation cracking using the cohesive crack method.” Int. J. Geomech. 13 (3): 213–221. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000192.
Amarasiri, A. L., J. K. Kodikara, and S. Costa. 2011. “Numerical modelling of desiccation cracking.” Int. J. Numer. Anal. Methods Geomech. 35 (1): 82–96. https://doi.org/10.1002/nag.894.
Ayad, R., J.-M. Konrad, and M. Soulié. 1997. “Desiccation of a sensitive clay: Application of the model CRACK.” Can. Geotech. J. 34 (6): 943–951.
Banin, A., and A. Amiel. 1970. “A correlative study of the chemical and physical properties of a group of natural soils of Israel.” Geoderma 3 (3): 185–198. https://doi.org/10.1016/0016-7061(70)90018-2.
Bishop, A. W. 1959. “The principle of effective stress.” Teknisk Ukeblad 39: 859–863.
Bishop, A. W., and V. K. Garga. 1969. “Drained tension tests on London clay.” Géotechnique 19 (2): 309–313. https://doi.org/10.1680/geot.1969.19.2.309.
Cheng, Q., C.-S. Tang, H. Zeng, C. Zhu, N. An, and B. Shi. 2020. “Effects of microstructure on desiccation cracking of a compacted soil.” Eng. Geol. 265 (Feb): 105418. https://doi.org/10.1016/j.enggeo.2019.105418.
Cho, G. C., and J. C. Santamarina. 2001. “Unsaturated particulate materials—Particle-level studies.” J. Geotech. Geoenviron. Eng. 127 (1): 84–96. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:1(84).
Delage, P.,and J. Graham. 1996. “Mechanical behaviour of unsaturated soils: Understanding the behaviour of unsaturated soils requires reliable conceptual models.” In Vol. 3 of Proc. 1st Int. Conf. on Unsaturated Soils, UNSAT’95. Crowthorne, UK: Transport Research Laboratory.
Fisher, R. 1926. “On the capillary forces in an ideal soil; correction of formulae given by WB Haines.” J. Agric. Sci. 16 (3): 492–505. https://doi.org/10.1017/S0021859600007838.
Fredlund, D., N. R. Morgenstern, and R. Widger. 1978. “The shear strength of unsaturated soils.” Can. Geotech. J. 15 (3): 313–321. https://doi.org/10.1139/t78-029.
Fredlund, D. G., and N. R. Morgenstern. 1977. “Stress state variables for unsaturated soils.” J. Geotech. Geoenviron. Eng. 103 (5): 447–466. https://doi.org/10.1061/AJGEB6.0000423.
Fredlund, D. G., and H. Rahardjo. 1993. Soil mechanics for unsaturated soils. New York: Wiley.
Frydman, S. 1964. “The applicability of Brazilian (indirect tension) test to soils.” Aust. J. Appl. Sci. 15 (4): 335–343.
Gens, A., and E. Alonso. 1992. “A framework for the behaviour of unsaturated expansive clays.” Can. Geotech. J. 29 (6): 1013–1032. https://doi.org/10.1139/t92-120.
Haines, W. B. 1925. “Studies in the physical properties of soils: II. A note on the cohesion developed by capillary forces in an ideal soil.” J. Agric. Sci. 15 (4): 529–535. https://doi.org/10.1017/S0021859600082460.
Hueckel, T., B. Mielniczuk, M. S. El Youssoufi, L. B. Hu, and L. Laloui. 2014. “A three-scale cracking criterion for drying soils.” Acta Geophys. 62 (5): 1049–1059. https://doi.org/10.2478/s11600-014-0214-9.
Ingles, O. 1962. “Bonding forces in soils. Part 3. Theory of tensile strength for stabilised and naturally coherent soils.” In Proc., 1st Australian Road Research Board Conf.; Canberra, ACT, 1025–1047. Vermont, VIC: Australian Road Research Board.
Jindal, P., J. Sharma, and R. Bashir. 2016. “Effect of pore-water surface tension on tensile strength of unsaturated sand.” Indian Geotech. J. 46 (3): 276–290. https://doi.org/10.1007/s40098-016-0184-8.
Karathanasis, A. D., and B. F. Hajek. 1982. “Revised methods for rapid quantitative determination of minerals in soil clays.” Soil Sci. Soc. Am. J. 46 (2): 419–425. https://doi.org/10.2136/sssaj1982.03615995004600020042x.
Kemper, W. D. 1960. “Water and ion movement in thin films as influenced by the electrostatic charge and diffuse layer of cations associated with clay mineral surfaces.” Soil Sci. Soc. Am. J. 24 (1): 10–16. https://doi.org/10.2136/sssaj1960.03615995002400010013x.
Kim, T.-H., and C. Hwang. 2003. “Modeling of tensile strength on moist granular earth material at low water content.” Eng. Geol. 69 (3–4): 233–244. https://doi.org/10.1016/S0013-7952(02)00284-3.
Kodikara, J., and S. Costa. 2013. “Desiccation cracking in clayey soils: Mechanisms and modelling.” In Multiphysical testing of soils and shales. New York: Springer.
Kodikara, J. K., and X. Choi. 2006. A simplified analytical model for desiccation cracking of clay layers in laboratory tests. In Proc., 4th Int. Conf. on Unsaturated Soils. Reston, VA: ASCE.
Koliji, A., L. Vulliet, and L. Laloui. 2010. “Structural characterization of unsaturated aggregated soil.” Can. Geotech. J. 47 (3): 297–311. https://doi.org/10.1139/T09-089.
Konrad, J.-M., and R. Ayad. 1997. “Desiccation of a sensitive clay: field experimental observations.” Can. Geotech. J. 34 (6): 929–942. https://doi.org/10.1139/t97-063.
Lachenbruch, A. H. 1961. “Depth and spacing of tension cracks.” J. Geophys. Res. 66 (12): 4273–4292. https://doi.org/10.1029/JZ066i012p04273.
Lakshmikantha, M., P. C. Prat, and A. Ledesma. 2012. “Experimental evidence of size effect in soil cracking.” Can. Geotech. J. 49 (3): 264–284. https://doi.org/10.1139/t11-102.
Lambe, T. W. 1960. Soil stabilization. Washington, DC: Highway Research Board.
Li, H.-D., C.-S. Tang, Q. Cheng, S.-J. Li, X.-P. Gong, and B. Shi. 2019. “Tensile strength of clayey soil and the strain analysis based on image processing techniques.” Eng. Geol. 253 (Apr): 137–148. https://doi.org/10.1016/j.enggeo.2019.03.017.
Lin, B., and A. B. Cerato. 2014. “Applications of SEM and ESEM in microstructural investigation of shale-weathered expansive soils along swelling-shrinkage cycles.” Eng. Geol. 177 (Jul): 66–74. https://doi.org/10.1016/j.enggeo.2014.05.006.
Lu, N. 2016. “Generalized soil water retention equation for adsorption and capillarity.” J. Geotech. Geoenviron. Eng. 142 (10): 04016051. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001524.
Lu, N., J. W. Godt, and D. T. Wu. 2010. “A closed-form equation for effective stress in unsaturated soil.” Water Resour. Res. 46 (5). https://doi.org/10.1029/2009WR008646.
Lu, N., and M. Khorshidi. 2015. “Mechanisms for soil-water retention and hysteresis at high suction range.” J. Geotech. Geoenviron. Eng. 141 (8): 04015032. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001325.
Lu, N., T.-H. Kim, S. Sture, and W. J. Likos. 2009. “Tensile strength of unsaturated sand.” J. Eng. Mech. 135 (12): 1410–1419. https://doi.org/10.1061/%28ASCE%29EM.1943-7889.0000054.
Lu, N., and W. J. Likos. 2004. Unsaturated soil mechanics. New York: Wiley.
Lu, N., and W. J. Likos. 2006. “Suction stress characteristic curve for unsaturated soil.” J. Geotech. Geoenviron. Eng. 132 (2): 131–142. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131).
Lu, N., B. Wu, and C. P. Tan. 2007. “Tensile strength characteristics of unsaturated sands.” J. Geotech. Geoenviron. Eng. 133 (2): 144–154. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:2(144).
Lu, N., and C. Zhang. 2019. “Soil sorptive potential: Concept, theory, and verification.” J. Geotech. Geoenviron. Eng. 145 (4): 04019006. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002025.
Lutenegger, A., and A. Rubin. 2008. “Tensile strength of some compacted fine-grained soils.” In Unsaturated soils: Advances in geo-engineering: Proc., 1st European Conf. E-UNSAT 2008, edited by D. G. Toll, C. E. Augarde, D. Gallipoli, and S. J. Wheeler, 411–415. London: CRC Press.
Mathews, J., and R. L. Walker. 1970. In Vol. 501 of Mathematical methods of physics. New York: WA Benjamin.
McQueen, I. S., and R. F. Miller. 1974. “Approximating soil moisture characteristics from limited data: Empirical evidence and tentative model.” Water Resour. Res. 10 (3): 521–527. https://doi.org/10.1029/WR010i003p00521.
Morris, P. H., J. Graham, and D. J. Williams. 1992. “Cracking in drying soils.” Can. Geotech. J. 29 (2): 263–277. https://doi.org/10.1139/t92-030.
Nahlawi, H., S. Chakrabarti, and J. Kodikara. 2004. “A direct tensile strength testing method for unsaturated geomaterials.” Geotech. Test. J. 27 (4): 356–361. https://doi.org/10.1520/GTJ11767.
Narvaez, B., M. Aubertin, and F. Saleh-Mbemba. 2015. “Determination of the tensile strength of unsaturated tailings using bending tests.” Can. Geotech. J. 52 (11): 1874–1885. https://doi.org/10.1139/cgj-2014-0156.
Öberg, A., and G. Sällfors. 1997. “Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve.” Geotech. Test. J. 20 (1): 40–48. https://doi.org/10.1520/GTJ11419J.
Omidi, G. H., J. C. Thomas, and K. W. Brown. 1996. “Effect of desiccation cracking on the hydraulic conductivity of a compacted clay liner.” Water Air Soil Pollut. 89 (1): 91–103. https://doi.org/10.1007/BF00300424.
Or, D., and M. Tuller. 2002. “Cavitation during desaturation of porous media under tension.” Water Resour. Res. 38 (5): 19-1–19-14. https://doi.org/10.1029/2001WR000282.
Orr, F. M., L. E. Scriven, and A. P. Rivas. 1975. “Pendular rings between solids: meniscus properties and capillary force.” J. Fluid Mech. 67 (4): 723–742. https://doi.org/10.1017/S0022112075000572.
Peron, H., L. Laloui, T. Hueckel, and L. B. Hu. 2009. “Desiccation cracking of soils.” Eur. J. Environ. Civ. Eng. 13 (7–8): 869–888. https://doi.org/10.1080/19648189.2009.9693159.
Philip, J. R. 1977. “Unitary approach to capillary condensation and adsorption.” J. Chem. Phys. 66 (11): 5069–5075. https://doi.org/10.1063/1.433814.
Pietsch, W. B. 1968. “Tensile strength of granular materials.” Nature 217 (5130): 736–737. https://doi.org/10.1038/217736a0.
Romero, E., and P. H. Simms. 2008. “Microstructure investigation in unsaturated soils: A review with special attention to contribution of mercury intrusion porosimetry and environmental scanning electron microscopy.” Geotech. Geol. Eng. 26 (6): 705–727. https://doi.org/10.1007/s10706-008-9204-5.
Rumpf, H. C. H. 1970. “Zur theorie der zugfestigkeit von agglomeraten bei kraftuebertragung an kontaktpunkten.” Chem. Ing. Tech. 42 (8): 538–540. https://doi.org/10.1002/cite.330420806.
Salimi, K., A. Cerato, F. Vahedifard, and G. Miller. 2021. “Tensile strength of compacted clays during desiccation under elevated temperatures.” Geotech. Test. J. 44 (4). https://doi.org/10.1520/GTJ20200114.
Santamarina, J. C. 2003. “Soil behavior at the microscale: Particle forces.” In Proc., Symp. Soil Behavior and Soft Ground Construction Honoring Charles C. “Chuck” Ladd . Reston, VA: ASCE. https://doi.org/10.1061/40659(2003)2.
Schubert, H. 1975. “Tensile strength of agglomerates.” Powder Technol. 11 (2): 107–119. https://doi.org/10.1016/0032-5910(75)80036-2.
Schubert, H. 1982. Kapillarität in porösen festsoffsystemen. Berlin: Springer.
Snyder, V. A., and R. D. Miller. 1985. “Tensile strength of unsaturated soils.” Soil Sci. Soc. Am. J. 49 (1): 58–65. https://doi.org/10.2136/sssaj1985.03615995004900010011x.
Sridharan, A., and G. V. Rao. 1973. “Mechanisms controlling volume change of saturated clays and the role of the effective stress concept.” Géotechnique 23 (3): 359–382. https://doi.org/10.1680/geot.1973.23.3.359.
Stirling, R. A., P. Hughes, C. T. Davie, and S. Glendinning. 2015. “Tensile behaviour of unsaturated compacted clay soils—A direct assessment method.” Appl. Clay Sci. 112–113.
Tamrakar, S. B., Y. Toyosawa, T. Mitachi, and K. Itoh. 2005. “Tensile strength of compacted and saturated soils using newly developed tensile strength measuring apparatus.” Soils Found. 45 (6): 103–110. https://doi.org/10.3208/sandf.45.103.
Tang, C.-S., X.-J. Pei, D.-Y. Wang, B. Shi, and J. Li. 2015. “Tensile strength of compacted clayey soil.” J. Geotech. Geoenviron. Eng. 141 (4): 04014122. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001267.
Tang, G. X., and J. Graham. 2000. “A method for testing tensile strength in unsaturated soils.” Geotech. Test. J. 23 (3): 377–382. https://doi.org/10.1520/GTJ11059J.
Trabelsi, H., M. Jamei, H. Zenzri, and S. Olivella. 2012. “Crack patterns in clayey soils: Experiments and modeling.” Int. J. Numer. Anal. Methods Geomech. 36 (11): 1410–1433. https://doi.org/10.1002/nag.1060.
Tuller, M., and D. Or. 2005. “Water films and scaling of soil characteristic curves at low water contents.” Water Resour. Res. 41 (9). https://doi.org/10.1029/2005WR004142.
Tuller, M., D. Or, and L. M. Dudley. 1999. “Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores.” Water Resour. Res. 35 (7): 1949–1964. https://doi.org/10.1029/1999WR900098.
Vanapalli, S. K., D. G. Fredlund, and D. E. Pufahl. 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. https://doi.org/10.1520/GTJ10351J.
Varsei, M., G. A. Miller, and A. Hassanikhah. 2016. “Novel approach to measuring tensile strength of compacted clayey soil during desiccation.” Int. J. Geomech. 16 (6): D4016011. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000705.
Venkataramana, K., B. H. Rao, and D. Singh. 2009. “A critical review of the methodologies employed for determination of tensile strength of fine-grained soils.” J. Test. Eval. 37 (2): 115–121. https://doi.org/10.1520/JTE101989.
Vesga, L. F. 2009. “Direct tensile-shear test (DTS) on unsaturated kaolinite clay.” Geotech. Test. J. 32 (5): 397–409. https://doi.org/10.1520/GTJ101563.
Yin, P., and S. K. Vanapalli. 2018. “Model for predicting tensile strength of unsaturated cohesionless soils.” Can. Geotech. J. 55 (9): 1313–1333. https://doi.org/10.1139/cgj-2017-0376.
Zeh, R., and K. Witt. 2005. “Suction-controlled tensile strength of compacted clays.” In Proc., of the Int. Conf. on Soil Mechanics and Geotechnical Engineering, 2347. Princeton, NJ: Citeseer.
Zhang, C., and N. Lu. 2018. “What is the range of soil water density? Critical reviews with a unified model.” Rev. Geophys. 56 (3): 532–562. https://doi.org/10.1029/2018RG000597.
Zhang, C., and N. Lu. 2020. “Unified effective stress equation for soil.” J. Eng. Mech. 146 (2): 04019135. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001718.
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Journal of Geotechnical and Geoenvironmental Engineering
Volume 147 • Issue 7 • July 2021
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Received: Aug 10, 2020
Accepted: Mar 18, 2021
Published online: May 14, 2021
Published in print: Jul 1, 2021
Discussion open until: Oct 14, 2021
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