A Simple Method for Predicting the Response of Single Energy Pile Considering Temperature Variation of Pile–Soil Interface
Publication: International Journal of Geomechanics
Volume 23, Issue 2
Abstract
To capture the influence of temperature variation of pile–soil interface on the response of a single energy pile, numerical simulation and theoretical analysis were adopted in this paper. The temperature variation mechanism of a single energy pile was clarified using numerical simulation, and the temperature variation model of the pile–soil interface was established. Considering the influence of temperature variation on the conventional load transfer model of the pile–soil interface, the improved hyperbolic functions were proposed, and the parameters related to the improved load transfer model were determined. To predict the response of a single energy pile considering the temperature variation of the pile–soil interface, an iterative algorithm was developed using load transfer methods. Comparisons of the load-settlement response of three well-documented cases between the present computation results and the results derived from other methods were made to verify the reliability of the calculation method. Furthermore, a parameter analysis was carried out to assess the influence of soil properties and the parameters related to the load transfer models on the thermomechanical response of a single energy pile.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This work was supported by the Young Experts of Taishan Scholar Project of Shandong Province (No. tsqn202103163), the National Natural Science Foundation of China (Nos. 52078278 and 52278358), and the program of Qilu Young Scholars of Shandong University. Great appreciation goes to the editorial board and the reviewers of this paper.
Notation
The following symbols are used in this paper:
- a
- parameters of the temperature variation model;
- aT
- parameters of the hyperbolic model of pile–soil interface;
- b
- parameters of the temperature variation model;
- bT
- parameters of the hyperbolic model of pile–soil interface;
- c
- cohesion of soil beneath the pile base;
- Es
- elastic modulus of surrounding soil;
- fb
- parameters of the hyperbolic model of pile the base;
- gb
- parameters of the hyperbolic model of the pile base;
- Gb
- shear modulus of soil beneath the pile base;
- H0
- height from pile end to the model bottom;
- H1
- height from the bottom of heat exchange tube to the model bottom;
- kb
- initial compressive stiffness of the pile base;
- ksT
- initial shear stiffness of the pile–soil interface;
- K0
- coefficient of static earth pressure;
- L0
- initial pile length;
- Ln
- length of pile segment n;
- LT
- pile length subjected to temperature effect;
- n
- pile segment;
- Nc
- dimensionless coefficients related to the soil cohesion and earth pressure on the pile shaft;
- Nq
- dimensionless coefficients related to the soil cohesion and earth pressure on the pile shaft;
- Pbn
- pile base load of pile segment n;
- Ptn
- pile top load of pile segment n;
- qb
- pile end resistance;
- qbu
- ultimate base resistance of pile;
- r0
- initial pile radius;
- rT
- pile radius subjected to temperature effect;
- Rbf
- failure ratio of base resistance ranged;
- Rsf
- failure ratio of unit skin friction;
- sb
- pile end displacement;
- sbn
- pile end displacement of pile segment n;
- scn
- initial displacement at the midpoint in length direction of pile segment n;
- modified displacement at the midpoint of pile segment n;
- stn
- displacement at the top of pile segment n;
- ST(z)
- pile–soil relative displacement of energy piles at a given depth z;
- T(z)
- temperature of the pile–soil interface at a depth z;
- T0
- initial temperature of the pile–soil interface;
- T1
- temperature of exchange liquid;
- V0
- initial pile volume;
- VT
- pile volume subjected to temperature effect;
- z
- depth;
- α
- coefficient of linear thermal expansion;
- β
- coefficient of volumetric thermal expansion;
- γ
- unit weight of soil;
- ΔauT
- apparent limit relative displacement;
- ΔuT
- pile-soil ultimate relative displacement;
- Δr
- radial deformation of the pile subjected to temperature effect;
- ΔT
- temperature variation of the pile–soil interface;
- Δz
- axial deformation of energy pile;
- ζ
- coefficient of interface friction;
- ζc
- coefficients related to the internal friction angle of soil;
- ζq
- coefficients related to the internal friction angle of soil;
- σh
- horizontal stress;
- σrT
- radial temperature stress of the pile–soil interface;
- τfT
- shear strength of the pile–soil interface;
- τT(z)
- unit skin friction of energy piles;
- τT(zi)
- shaft resistance of energy piles at a depth zi;
- (zn)
- modified shaft resistance of pile segment n;
- τuT
- ultimate shear stress of the pile–soil interface;
- υb
- Poisson’s ratio of soil beneath the pile base;
- υs
- Poisson’s ratio of surrounding soil;
- φ
- internal friction angle of soil;
- χ
- parameter of the connection between ΔauT and ΔuT; and
- ψ
- angle between compaction core boundary of soil beneath the pile base and horizontal plane.
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.
Alonso, E. E., A. Josa, and A. Ledesma. 1984. “Negative skin friction on piles: A simplified analysis and prediction procedure.” Géotechnique 34 (3): 341–357. https://doi.org/10.1680/geot.1984.34.3.341.
Bourne-Webb, P. J., B. Amatya, and K. Soga. 2013. “A framework for understanding energy pile behaviour.” Proc. Inst. Civ. Eng. Geotech. Eng. 166 (2): 170–177. https://doi.org/10.1680/geng.10.00098.
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.
Bozis, D., K. Papakostas, and N. Kyriakis. 2011. “On the evaluation of design parameters effects on the heat transfer efficiency of energy piles.” Energy Build. 43 (4): 1020–1029. https://doi.org/10.1016/j.enbuild.2010.12.028.
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.
Chen, R. P., W. H. Zhou, W. P. Cao, and Y. M. Chen. 2007. “Improved hyperbolic model of load-transfer for pile–soil interface and its application in study of negative friction of single piles considering time effect.” [In Chinese.] Chin. J. Geotech. Eng. 29 (6): 824–830.
Eskilson, P., and J. Claesson. 1988. “Simulation model for thermally interacting heat extraction boreholes.” Numer. Heat Transfer 13 (2): 149–165. https://doi.org/10.1080/10407788808913609.
Faizal, M., A. Bouazza, C. Haberfield, and J. S. McCartney. 2018. “Axial and radial thermal responses of a field-scale energy pile under monotonic and cyclic temperature changes.” J. Geotech. Geoenviron. Eng. 144 (10): 04018072. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001952.
Fang, P. F., X. Gao, Y. Lou, R. H. Zhang, X. Y. Xie, Z. J. Wang, and D. Y. Zhu. 2021. “Field test on the bearing behaviors of geothermal energy piles in natural service under the summer condition.” [In Chinese.] Chin. J. Rock Mech. Eng. 40 (5): 1032–1042.
Gao, J., X. Zhang, J. Liu, K. S. Li, and J. Yang. 2008. “Thermal performance and ground temperature of vertical pile-foundation heat exchangers: A case study.” Appl. Therm. Eng. 28 (17): 2295–2304. https://doi.org/10.1016/j.applthermaleng.2008.01.013.
Ingersoll, L. R., F. T. Adler, H. J. Plass, and A. C. Ingersoll. 1950. “Theory of earth heat exchangers for the heat pump.” Heat. Pip. Air Condition. 22: 113–122.
Janbu, N. 1976. “Static bearing capacity of friction piles.” In Vol. 1 of Proc., 6th European Conf., on Soil Mechanics and Foundation Engineering, 479–482. TU Wien: Institute fuer Grundbau Und Bodenmechanik.
Jiang, G., R. F. Li, H. Wang, G. Chen, H. W. Lu, and D. Shao. 2019. “Numerical analysis of the bearing capacity of floating energy piles during the full process of thermal-mechanical coupling.” [In Chinese.] Chin. J. Rock Mech. Eng. 38 (12): 2525–2534.
Kishida, H., and M. Uesugi. 1987. “Tests of the interface between sand and steel in the simple shear apparatus.” Géotechnique 37 (1): 45–52. https://doi.org/10.1680/geot.1987.37.1.45.
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.
Mimouni, T., and L. Laloui. 2014. “Towards a secure basis for the design of geothermal piles.” Acta Geotech. 9 (3): 355–366. https://doi.org/10.1007/s11440-013-0245-4.
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.
Liang, F., L. Chen, and J. Han. 2009. “Integral equation method for analysis of piled rafts with dissimilar piles under vertical loading.” Comput. Geotech. 36 (3): 419–426. https://doi.org/10.1016/j.compgeo.2008.08.007.
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.
Liu, S.-W., Q.-Q. Zhang, C.-Y. Cui, R.-F. Feng, and W. Cui. 2021. “A simplified approach for the response of pile groups composed of dissimilar piles.” Structures 34: 4548–4559. https://doi.org/10.1016/j.istruc.2021.10.063.
Luo, J., H. Zhao, S. Gui, W. Xiang, J. Rohn, and P. Blum. 2016. “Thermo-economic analysis of four different types of ground heat exchangers in energy piles.” Appl. Therm. Eng. 108: 11–19. https://doi.org/10.1016/j.applthermaleng.2016.07.085.
Luo, X. Q., G. B. Liu, Y. D. Zheng, F. Qian, and M. Zhou. 2019. “A load transfer model of energy pile–soil interfaces under temperature variation.” [In Chinese.] Chin. J. Rock Mech. Eng. 38 (1): 171–179.
Man, Y., H. Yang, N. Diao, J. Liu, and Z. Fang. 2010. “A new model and analytical solutions for borehole and pile ground heat exchangers.” Int. J. Heat Mass Transfer 53 (13): 2593–2601. https://doi.org/10.1016/j.ijheatmasstransfer.2010.03.001.
MHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China). 2018. Technical standrad for utilization of geothermal energy through piles. JGJ/T 438-2018. Beijing: MHURD.
Najma, A., and J. Sharma. 2021. “Incremental load transfer analysis of an energy pile under arbitrary mechanical and thermal loads.” Geomech. Energy Environ. 28: 100243. https://doi.org/10.1016/j.gete.2021.100243.
Olia, A. S. R., and D. Peric. 2021. “Thermomechanical soil-structure interaction in single energy piles exhibiting reversible interface behavior.” Int. J. Geomech. 21 (5): 04021065. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002014.
Ouyang, Y., K. Soga, and Y. F. Leung. 2011. “Numerical back-analysis of energy pile test at lambeth college, London.”" In Geo-Frontiers 2011: Advances in Geotechnical Engineering, Geotechnical Special Publication 211, edited by J. Han and D. E. Alzamora, 440–449. Reston, VA: ASCE.
Pasten, C., and J. C. Santamarina. 2014. “Thermally induced long-term displacement of thermoactive piles.” J. Geotech. Geoenviron. Eng. 140 (5): 70–75. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001092.
Randolph, M. F., and C. P. Wroth. 1978. “Analysis of deformation of vertically loaded piles.” J. Geotech. Eng. 104 (12): 1465–1488.
Saberi, M., C. D. Annan, and J. M. Konrad. 2017. “Constitutive modeling of gravelly soil–structure interface considering particle breakage.” J. Eng. Mech. 143 (8): 04017044.
Saberi, M., C.-D. Annan, and J.-M. Konrad. 2018. “A unified constitutive model for simulating stress-path dependency of sandy and gravelly soil–structure interfaces.” Int. J. Non Linear Mech. 102: 1–13. https://doi.org/10.1016/j.ijnonlinmec.2018.03.001.
Shi, X., J. S. Zhang, B. Liu, F. Meng, and G. D. Deng. 2015. “Experimental research on shearing properties of interface between red clay and concrete.” J. Cent. South Univ. 46 (5): 1826–1831.
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: 378–391. https://doi.org/10.1016/j.compgeo.2013.09.021.
Sutman, M., C. G. Olgun, and L. Laloui. 2019. “Cyclic load–transfer approach for the analysis of energy piles.” J. Geotech. Geoenviron. Eng. 145 (1): 04018101. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001992.
Sutman, M., G. Speranza, A. Ferrari, P. Larrey-Lassalle, and L. Laloui. 2020. “Long-term performance and life cycle assessment of energy piles in three different climatic conditions.” Renewable Energy 146: 1177–1191. https://doi.org/10.1016/j.renene.2019.07.035.
Vesic, A. S. 1973. “Analysis of ultimate loads of shallow foundations.” J. Soil Mech. Found. Div. 99 (1): 45–73. https://doi.org/10.1061/JSFEAQ.0001846.
Wong, K. S., and C. I. Teh. 1995. “Negative skin friction on piles in layered soil deposits.” J. Geotech. Eng. 121 (6): 457–465. https://doi.org/10.1061/(ASCE)0733-9410(1995)121:6(457).
Zhang, Q. Q., S. C. Li, F. Y. Liang, M. Yang, and Q. Zhang. 2014. “Simplified method for settlement prediction of single pile and pile group using a hyperbolic model.” Int. J. Civ. Eng. 12 (2): 179–192.
Zhang, Q.-Q., S.-W. Liu, R-F. Feng, and X.-M. Li. 2019. “Analytical method for prediction of progressive deformation mechanism of existing piles due to excavation beneath a pile-supported building.” Int. J. Civ. Eng. 17 (6): 751–763. https://doi.org/10.1007/s40999-018-0309-9.
Zhang, Q.-Q., S.-W. Liu, S.-M. Zhang, J. Zhang, and K. Wang. 2016. “Simplified non-linear approaches for response of a single pile and pile groups considering progressive deformation of pile-soil system.” Soils Found. 56 (3): 473–484. https://doi.org/10.1016/j.sandf.2016.04.013.
Zhang, Q.-Q., and Z.-M. Zhang. 2012. “Simplified calculation approach for settlement of single pile and pile groups.” J. Comput. Civ. Eng. 26 (6): 750–758. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000167.
Zong, C. F., D. Shao, Y. P. Huang, Q. Wu, G. Jiang, and Z. Song. 2019. “Research on energy pile load transfer analysis method considering radial temperature effect.” J. Disaster Prev. Mitigation Eng. 39 (4): 658–664.
Zong-Ze, Y, Z. Hong, and X. Guo-Hua. 1995. “A study of deformation in the interface between soil and concrete.” Comput. Geotech. 17 (1): 75–92. https://doi.org/10.1016/0266-352X(95)91303-L.
Information & Authors
Information
Published In
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 26, 2022
Accepted: Sep 7, 2022
Published online: Dec 13, 2022
Published in print: Feb 1, 2023
Discussion open until: May 13, 2023
ASCE Technical Topics:
- Continuum mechanics
- Deformation (mechanics)
- Design (by type)
- Energy methods
- Engineering fundamentals
- Engineering mechanics
- Foundations
- Geotechnical engineering
- Load factors
- Load transfer
- Mathematics
- Measurement (by type)
- Models (by type)
- Numerical models
- Parameters (statistics)
- Pile foundations
- Piles
- Solid mechanics
- Statistics
- Stress (by type)
- Structural analysis
- Structural design
- Structural engineering
- Structural mechanics
- Temperature effects
- Temperature measurement
- Thermal loads
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Tuan A. Pham, Melis Sutman, A Simplified Method for Bearing-Capacity Analysis of Energy Piles Integrating Temperature-Dependent Model of Soil–Water Characteristic Curve, Journal of Geotechnical and Geoenvironmental Engineering, 10.1061/JGGEFK.GTENG-11095, 149, 9, (2023).