A Temperature-Dependent Model for Ultimate Bearing Capacity of Energy Piles in Unsaturated Fine-Grained Soils
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 147, Issue 11
Abstract
This study presents an analytical framework to estimate the change in ultimate bearing capacity of energy piles in unsaturated fine-grained soils under drained mechanical loading conditions after drained heating. The framework was developed by extending conventional methods for the ultimate bearing capacity of piles in unsaturated soils to temperature-dependent conditions, where thermally induced changes in the characteristics of the unsaturated soil and soil–pile interface are considered. Specifically, the thermally induced variations in matric suction and effective saturation profiles with depth were incorporated into calculations of the shaft capacity and the end bearing capacity of piles in unsaturated soils. The proposed ultimate bearing capacity model is validated against experimental data for an energy pile loaded to failure in unsaturated Bonny silt, and a good match between measured and predicted values was obtained. A parametric study was carried out to evaluate the effects of infiltration rate and pile aspect ratio (i.e., pile embedment length/pile diameter) on the ultimate bearing capacity of energy piles in unsaturated clay and silt layers subjected to temperatures ranging from 5°C to 45°C. For both soils, the shaft, end bearing, and ultimate bearing capacities vary with an increase in temperature. At the reference temperature, the shaft, end, and ultimate bearing capacities vary monotonically with pile embedment length, while at elevated temperatures they vary nonmonotonically with pile embedment depth. At a given temperature, the parametric study shows that the bearing capacity of energy piles in clay decreases with increasing downward infiltration of water into the soil profile surrounding the energy pile, while in silt it may decrease or increase depending on pile embedment length. The ultimate bearing capacity increases with a decrease in pile aspect ratio at all temperatures. Estimates of the ultimate bearing capacity of energy piles in unsaturated fine-grained soils from the framework are a critical part of thermomechanical soil–structure interaction analyses needed to design energy piles, so this study contributes toward the widespread application of this emerging technology in practice.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. CMMI-1634748. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
References
Akrouch, G. A., M. Sánchez, and J. L. Briaud. 2014. “Thermo-mechanical behavior of energy piles in high plasticity clays.” Acta Geotech. 9 (3): 399–412. https://doi.org/10.1007/s11440-014-0312-5.
Akrouch, G. A., M. Sánchez, and J. L. Briaud. 2016. “An experimental, analytical and numerical study on the thermal efficiency of energy piles in unsaturated soils.” Comput. Geotech. 71 (Jan): 207–220. https://doi.org/10.1016/j.compgeo.2015.08.009.
Başer, T., Y. Dong, A. M. Moradi, N. Lu, K. Smits, S. Ge, D. Tartakovsky, and J. S. McCartney. 2018. “Role of nonequilibrium water vapor diffusion in thermal energy storage systems in the vadose zone.” J. Geotech. Geoenviron. Eng. 144 (7): 04018038. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001910.
Behbehani, F., and J. S. McCartney. 2020a. “Impacts of unsaturated conditions on the ultimate axial capacity of energy piles.” In Vol. 195 of Proc., EUnsat 2020: The 4th European Conf. on Unsaturated Soils, 04005. Les Ulis, France: EDP Sciences.
Behbehani, F., and J. S. McCartney. 2020b. “Simulation of the thermo-hydraulic response of energy piles in unsaturated soils.” In Vol. 205 of Proc., 2nd Int. Conf. on Energy Geotechnics (ICEGT-2020), 05002. Les Ulis, France: EDP Sciences.
Bishop, A. W. 1959. “The principle of effective stress.” Teknisk Ukeblad 106 (39): 859–863.
Bourne-Webb, P. J., B. Amatya, K. Soga, T. Amis, C. Davidson, and P. Payne. 2009. “Energy pile test at Lambeth College, London: Geotechnical and thermodynamic aspects of pile response to heat cycles.” Géotechnique 59 (3): 237–248. https://doi.org/10.1680/geot.2009.59.3.237.
Brandl, H. 2006. “Energy foundations and other thermo-active ground structures.” Géotechnique 56 (2): 81–122. https://doi.org/10.1680/geot.2006.56.2.81.
Brooks, R. H., and A. T. Corey. 1964. Hydraulic properties of porous media. Fort Collins, CO: Colorado State Univ.
Burland, J. B. 1973. “Shaft friction of piles in clay-a simple fundamental approach.” Ground Eng. 6 (3): 30–42.
Campbell, G. S., J. D. Jungbauer Jr., W. R. Bidlake, and R. D. Hungerford. 1994. “Predicting the effect of temperature on soil thermal conductivity.” Soil Sci. 158 (5): 307–313. https://doi.org/10.1097/00010694-199411000-00001.
Cao, T. C., S. K. Thota, F. Vahedifard, and A. Amirlatifi. 2021. “A temperature-dependent model for thermal conductivity function of unsaturated soils.” In Proc., 2021 Int. Foundations Congress and Equipment Exposition, IFCEE 2021, 89–98. Reston, VA: ASCE. https://doi.org/10.1061/9780784483428.010.
Chandler, R. J. 1968. “The shaft friction of piles in cohesive soils in terms of effective stress.” Civ. Eng. Public Works Rev. 60 (708): 48–51.
Chen, D., and J. S. McCartney. 2017. “Parameters for load transfer analysis of energy piles in uniform nonplastic soils.” Int. J. Geomech. 17 (7): 04016159. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000873.
Constantz, J. 1982. “Temperature dependence of unsaturated hydraulic conductivity of two soils.” Soil Sci. Soc. Am. J. 46 (3): 466–470. https://doi.org/10.2136/sssaj1982.03615995004600030005x.
Di Donna, A., A. Ferrari, and L. Laloui. 2016a. “Experimental investigations of the soil–concrete interface: Physical mechanisms, cyclic mobilization, and behaviour at different temperatures.” Can. Geotech. J. 53 (4): 659–672. https://doi.org/10.1139/cgj-2015-0294.
Di Donna, A., and L. Laloui. 2013. “Soil response under thermomechanical conditions imposed by energy geostructures.” In Energy geostructures: Innovation in underground engineering, 3–21. Hoboken, NJ: Wiley.
Di Donna, A., A. F. R. Loria, and L. Laloui. 2016b. “Numerical study of the response of a group of energy piles under different combinations of thermo-mechanical loads.” Comput. Geotech. 72 (Feb): 126–142. https://doi.org/10.1016/j.compgeo.2015.11.010.
Dorsey, N. E. 1940. Properties of ordinary water substance. New York: Reinhold.
Elzeiny, R., M. T. Suleiman, S. Xiao, M. A. A. Qamar, and M. Al-Khawaja. 2020. “Laboratory-scale pull-out tests on a geothermal energy pile in dry sand subjected to heating cycles.” Can. Geotech. J. 57 (11): 1754–1766. https://doi.org/10.1139/cgj-2019-0143.
Fu, Z. 2017. “Thermo-hydro-mechanical effects on the behaviour of unsaturated soil-structure interfaces and the numerical analysis of energy piles.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Ottawa.
Fuentes, R., N. Pinyol, and E. Alonso. 2016. “Effect of temperature induced excess porewater pressures on the shaft bearing capacity of geothermal piles.” Geomech. Energy Environ. 8 (Dec): 30–37. https://doi.org/10.1016/j.gete.2016.10.003.
Gardner, W. R. 1958. “Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.” Soil Sci. 85 (4): 228–232. https://doi.org/10.1097/00010694-195804000-00006.
Georgiadis, K., D. M. Potts, and L. Zdravkovic. 2003. “The influence of partial soil saturation on pile behaviour.” Géotechnique 53 (1): 11–25. https://doi.org/10.1680/geot.2003.53.1.11.
Goode, J. C., III, and J. S. McCartney. 2015. “Centrifuge modeling of end-restraint effects in energy foundations.” J. Geotech. Geoenviron. Eng. 141 (8): 04015034. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001333.
Graham, J., N. Tanaka, T. Crilly, and M. Alfaro. 2001. “Modified Cam-clay modelling of temperature effects in clays.” Can. Geotech. J. 38 (3): 608–621. https://doi.org/10.1139/t00-125.
Grant, S. A. 2003. “Extension of temperature effects model for capillary pressure saturation relations.” Water Resour. Res. 39 (1): SBH 1–SBH 10. https://doi.org/10.1029/2000WR000193.
Grant, S. A., and A. Salehzadeh. 1996. “Calculation of temperature effects on wetting coefficients of porous solids and their capillary pressure functions.” Water Resour. Res. 32 (2): 261–270. https://doi.org/10.1029/95WR02915.
Haar, L., J. S. Gallagher, and G. S. Kell. 1984. NBS/NRC steam table. New York: Hemisphere Publishing Corporation.
Hueckel, T., R. Pellegrini, and C. Del Olmo. 1998. “A constitutive study of thermo-elasto-plasticity of deep carbonatic clays.” Int. J. Numer. Anal. Methods Geomech. 22 (7): 549–574. https://doi.org/10.1002/(SICI)1096-9853(199807)22:7%3C549::AID-NAG927%3E3.0.CO;2-R.
Kalantidou, A., A. M. Tang, J. Pereira, and G. Hassen. 2012. “Preliminary study on the mechanical behaviour of heat exchanger pile in physical model.” Géotechnique 62 (11): 1047–1051. https://doi.org/10.1680/geot.11.T.013.
Knellwolf, C., H. Peron, and L. Laloui. 2011. “Geotechnical analysis of heat exchanger piles.” J. Geotech. Geoenviron. Eng. 137 (10): 890–902. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000513.
Kramer, C. A., and P. Basu. 2014. “Performance of a model geothermal pile in sand.” In Proc., 8th Int. Conf. on Physical Modelling in Geotechnics, edited by C. Gaudin and D. White, 771–777. Leiden, Netherlands: CRC Press/Balkema.
Laloui, L., and A. F. R. Loria. 2019. Analysis and design of energy geostructures: Theoretical essentials and practical application. London: Academic Press.
Laloui, L., M. Nuth, and L. Vulliet. 2006. “Experimental and numerical investigations of the behaviour of a heat exchanger pile.” Int. J. Numer. Anal. Methods Geomech. 30 (8): 763–781. https://doi.org/10.1002/nag.499.
Li, C., G. Kong, H. Liu, and H. Abuel-Naga. 2019. “Effect of temperature on behaviour of red clay–structure interface.” Can. Geotech. J. 56 (1): 126–134. https://doi.org/10.1139/cgj-2017-0310.
Lide, D. R. 1995. Handbook of chemistry and physics. 75th ed. New York: CRC Press.
Liu, H. L., C. L. Wang, G. Q. Kong, and A. Bouazza. 2019. “Ultimate bearing capacity of energy piles in dry and saturated sand.” Acta Geotech. 14 (3): 869–879. https://doi.org/10.1007/s11440-018-0661-6.
Loria, A. F. R., A. Gunawan, C. Shi, L. Laloui, and C. W. W. Ng. 2015. “Numerical modelling of energy piles in saturated sand subjected to thermo-mechanical loads.” Geomech. Energy Environ. 1 (Apr): 1–15. https://doi.org/10.1016/j.gete.2015.03.002.
Loveridge, F. A., G. Narsilio, M. Sánchez, and J. S. McCartney. 2019. “Energy geostructures: A review of analysis approaches, in situ testing and model scale experiments.” Geomech. Energy Environ. 22 (May): 100173. https://doi.org/10.1016/j.gete.2019.100173.
Lu, N., and Y. Dong. 2015. “Closed-form equation for thermal conductivity of unsaturated soils at room temperature.” J. Geotech. Geoenviron. Eng. 141 (6): 04015016. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001295.
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): 1–14. https://doi.org/10.1029/2009WR008646.
Lu, N., and D. V. Griffiths. 2004. “Profiles of steady-state suction stress in unsaturated soils.” J. Geotech. Geoenviron. Eng. 130 (10): 1063–1076. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(1063).
McCartney, J. S., N. H. Jafari, T. Hueckel, M. Sanchez, and F. Vahedifard. 2019. “Emerging thermal issues in geotechnical engineering.” In Geotechnical fundamentals for addressing new world challenges, edited by N. Lu and J. K. Mitchell, 275–317. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-06249-1_10.
McCartney, J. S., and K. D. Murphy. 2017. “Investigation of potential dragdown/uplift effects on energy piles.” Geomech. Energy Environ. 10 (Jun): 21–28. https://doi.org/10.1016/j.gete.2017.03.001.
McCartney, J. S., and J. E. Rosenberg. 2011. “Impact of heat exchange on side shear in thermo-active foundations.” In Geo-Frontiers 2011: Advances in Geotechnical Engineering, 488–498. Reston, VA: ASCE.
Murphy, K. D., and J. S. McCartney. 2014. “Thermal borehole shear device.” ASTM Geotech. Test. J. 37 (6): 1040–1055. https://doi.org/10.1520/GTJ20140009.
Murphy, K. D., J. S. McCartney, and K. S. Henry. 2015. “Evaluation of thermo-mechanical and thermal behavior of full-scale energy foundations.” Acta Geotech. 10 (2): 179–195. https://doi.org/10.1007/s11440-013-0298-4.
Ng, C. W. W., C. Shi, A. Gunawan, L. Laloui, and H. L. Liu. 2015. “Centrifuge modelling of heating effects on energy pile performance in saturated sand.” Can. Geotech. J. 52 (8): 1045–1057. https://doi.org/10.1139/cgj-2014-0301.
Olgun, C. G., T. Y. Ozudogru, S. L. Abdelaziz, and A. Senol. 2015. “Long-term performance of heat exchanger piles.” Acta Geotech. 10 (5): 553–569. https://doi.org/10.1007/s11440-014-0334-z.
Ozudogru, T. Y., C. G. Olgun, and C. F. Arson. 2015. “Analysis of friction induced thermo-mechanical stresses on a heat exchanger pile in isothermal soil.” Geotech. Geol. Eng. 33 (2): 357–371. https://doi.org/10.1007/s10706-014-9821-0.
Philip, J. R. 1969. “Theory of infiltration.” In Vol. 5 of Advances in hydroscience, 215–296. Amsterdam, Netherlands: Elsevier.
Philip, J. R., and D. A. De Vries. 1957. “Moisture movement in porous materials under temperature gradients.” EOS, Trans. Am. Geophys. Union 38 (2): 222–232. https://doi.org/10.1029/TR038i002p00222.
Pillsbury, A. F. 1950. “Effects of particle size and temperature on the permeability of sand to water.” Soil Sci. 70 (4): 299–300. https://doi.org/10.1097/00010694-195010000-00005.
Ravera, E., M. Sutman, and L. Laloui. 2020. “Load transfer method for energy piles in a group with pile–soil–slab–pile interaction.” J. Geotech. Geoenviron. Eng. 146 (6): 04020042. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002258.
Saggu, R., and T. Chakraborty. 2015. “Cyclic thermo-mechanical analysis of energy piles in sand.” Geotech. Geol. Eng. 33 (2): 321–342. https://doi.org/10.1007/s10706-014-9798-8.
Skempton, A. W. 1959. “Cast in-situ bored piles in London clay.” Géotechnique 9 (4): 153–173. https://doi.org/10.1680/geot.1959.9.4.153.
Suryatriyastuti, M. E., H. Mroueh, and S. Burlon. 2013. “Numerical analysis of the bearing capacity of thermoactive piles under cyclic axial loading.” Chap. 7 in Energy geostructures: Innovation in underground engineering, edited by L. Laloui and A. Di Donna. Hoboken, NJ: Wiley.
Suryatriyastuti, M. E., H. Mroueh, and S. Burlon. 2014. “A load transfer approach for studying the cyclic behavior of thermo-active piles.” Comput. Geotech. 55 (Jan): 378–391. https://doi.org/10.1016/j.compgeo.2013.09.021.
Thota, S. K. 2020. “Temperature effects on unsaturated soils: Constitutive relationships and emerging geotechnical applications.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Mississippi State Univ.
Thota, S. K., T. C. Cao, and F. Vahedifard. 2021. “Poisson’s ratio characteristic curve of unsaturated soils.” J. Geotech. Geoenviron. Eng. 147 (1): 04020149. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002424.
Thota, S. K., T. D. Cao, F. Vahedifard, and E. Ghazanfari. 2019. “Stability analysis of an unsaturated silty slope under nonisothermal conditions.” In Proc., Geo-Congress 2019: Geotechnical Materials, Modeling, and Testing, 844–852. Reston, VA: ASCE. https://doi.org/10.1061/9780784482124.085.
Thota, S. K., and F. Vahedifard. 2020. “A model for ultimate bearing capacity of piles in unsaturated soils under elevated temperatures.” In Vol. 205 of Proc., E3S Web of Conf., 05003. Les Ulis, France: EDP Sciences. https://doi.org/10.1051/e3sconf/202020505003.
Thota, S. K., and F. Vahedifard. 2021. “Stability analysis of unsaturated slopes under elevated temperatures.” Eng. Geol. 294: 106317. https://doi.org/10.1016/j.enggeo.2021.106317.
Uchaipichat, A. 2005. “Experimental investigation and constitutive modelling of thermo-hydro-mechanical coupling in unsaturated soils.” Ph.D. thesis, School of Civil and Environmental Engineering, Univ. of New South Wales.
Uchaipichat, A. 2012. “Variation of pile capacity in unsaturated clay layer with suction.” Electron. J. Geotech. Eng. 17: 2425–2433.
Uchaipichat, A. 2013. “Pile capacity in silt layer under elevated temperature.” Electron. J. Geotech. Eng. 18: 5499–5505.
Vahedifard, F., T. D. Cao, E. Ghazanfari, and S. K. Thota. 2019. “Closed-form models for nonisothermal effective stress of unsaturated soils.” J. Geotech. Geoenviron. Eng. 145 (9): 04019053. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002094.
Vahedifard, F., T. D. Cao, S. K. Thota, and E. Ghazanfari. 2018. “Nonisothermal models for soil–water retention curve.” J. Geotech. Geoenviron. Eng. 144 (9): 04018061. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001939.
Vahedifard, F., D. Leshchinsky, K. Mortezaei, and N. Lu. 2016. “Effective stress-based limit equilibrium analysis for homogeneous unsaturated slopes.” Int. J. Geomech. 16 (6): D4016003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000554.
Vahedifard, F., S. K. Thota, T. D. Cao, R. A. Samarakoon, and J. S. McCartney. 2020. “A temperature-dependent model for small-strain shear modulus of unsaturated soils.” J. Geotech. Geoenviron. Eng. 146 (12): 04020136. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002406.
Vanapalli, S. K., and Z. N. Taylan. 2012. “Design of single piles using the mechanics of unsaturated soils.” Int. J. GEOMATE 2 (1): 197–204.
Vasilescu, A. R., A. L. Fauchille, C. Dano, P. Kotronis, R. Manirakiza, and P. Gotteland. 2019. “Impact of temperature cycles at soil–concrete interface for energy piles.” In Proc., Int. Symp. on Energy Geotechnics, 35–42. Cham, Switzerland: Springer.
Wang, B., A. Bouazza, D. Barry-Macaulay, M. R. Singh, M. Webster, C. Haberfield, and S. Baycan. 2012. “Field and laboratory investigation of a heat exchanger pile.” In Proc., GeoCongress 2012: State of the Art and Practice in Geotechnical Engineering, 4396–4405. Reston, VA: ASCE.
Wang, W., R. A. Regueiro, and J. S. McCartney. 2015. “Coupled axisymmetric thermo-poro-mechanical finite element analysis of energy foundation centrifuge experiments in partially saturated silt.” Geotech. Geol. Eng. 33 (2): 373–388. https://doi.org/10.1007/s10706-014-9801-4.
Watson, K. M. 1943. “Thermodynamics of the liquid state.” Ind. Eng. Chem. 35 (4): 398–406. https://doi.org/10.1021/ie50400a004.
Xiao, S., M. T. Suleiman, and J. S. McCartney. 2014. “Shear behavior of silty soil and soil-structure interface under temperature effects.” In Proc., Geo-Congress 2014: Geo-characterization and Modeling for Sustainability, 4105–4114. Reston, VA: ASCE.
Yavari, N., A. M. Tang, J. M. Pereira, and G. Hassen. 2016. “Effect of temperature on the shear strength of soils and the soil–structure interface.” Can. Geotech. J. 53 (7): 1186–1194. https://doi.org/10.1139/cgj-2015-0355.
Yazdani, S., S. Helwany, and G. Olgun. 2019. “Influence of temperature on soil–pile interface shear strength.” Geomech. Energy Environ. 18 (Jun): 69–78. https://doi.org/10.1016/j.gete.2018.08.001.
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Journal of Geotechnical and Geoenvironmental Engineering
Volume 147 • Issue 11 • November 2021
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© 2021 American Society of Civil Engineers.
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Received: Oct 23, 2020
Accepted: Jul 20, 2021
Published online: Sep 13, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 13, 2022
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