New Model for Predicting Permanent Strain of Granular Materials in Embankment Subjected to Low Cyclic Loadings
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 146, Issue 9
Abstract
Estimating the permanent strain of granular materials in embankments subjected to cyclic loading is a major challenge for transport engineering projects. In practice, the development of permanent strain can be divided into two periods, postcompaction and secondary cyclic compression. In this study, the existing literature on prediction of permanent strain is reviewed in detail, and the key advantages and limitations of each model are presented and discussed. Based on the gaps identified in the existing literature, a new model for predicting the permanent strain of granular materials under low cyclic loadings is proposed. This model defines two new terms, “representative cycle number” and “reference strain line,” to distinguish the postcompaction and secondary cyclic compression periods accurately. Specifically, the new model correlates the stress states, first with the accumulated strain at the end of the postcompaction period, and then with the strain rate in the secondary cyclic compression period, with good accuracy. This model eliminates the requirement for static compression tests, which are normally needed for the existing models. The new model also avoids the determination of resilient modulus, which is not a competent definitive parameter for evaluating the performance of granular materials. Further, the new model is validated by predicting the permanent strain development of two types of granular materials that are adopted in pavement subgrade and railway subgrade, respectively, in cyclic triaxial tests. The new model is applied in a trial for predicting the long-term settlement of a full-scale physical model of railway embankment under cyclic loading. The results indicate that the new model can effectively capture and accurately predict the permanent strain of testing materials under various stress states and testing conditions. It is also proved that the practical value of the new model is promising. The effects of moisture content, particle size distribution, and compaction degree were not considered, and further studies are recommended to investigate these factors.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This work was supported by a Key Project Grant (Grant No. U1234204) from National Natural Science Foundation of China via PolyU Shenzhen Research Institute, and Hong Kong Polytechnic University (PolyU), China. The authors acknowledge financial support from the Research Institute for Sustainable Urban Development, PolyU. This work was also supported by General Research Fund (GRF) (PolyU 152196/14E, PolyU 152209/17E). Financial support from PolyU grants (1-BBAG, 1-ZVCR. 1-ZVEH. 4-BCAU, 4-BCAW, 4-BCB1, 5-ZDAF) is acknowledged. The Research Centre for Urban Hazards Mitigation of Faculty of Construction and Environment, PolyU, also provided support.
References
AASHTO. 2007. Standard method of test for determining the resilient modulus of soils and aggregate material. AASHTO T307. Washington, DC: AASHTO.
Abu-Farsakh, M., G. Souci, G. Z. Voyiadjis, and Q. Chen. 2012. “Evaluation of factors affecting the performance of geogrid-reinforced granular base material using repeated load triaxial tests.” J. Mater. Civ. Eng. 24 (1): 72–83. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000349.
ASTM. 2011. Standard practice for classification of soils for engineering purposes (unified soil classification system). ASTM D2487-11. West Conshohocken, PA: ASTM.
Barksdale, R. D. 1972. “Laboratory evaluation of rutting in base course materials.” In Proc., 3rd Int. Conf. on the Structural Design of Asphalt Pavements, 11–15. Ann Arbor, Mich: Cushing-Malloy.
Bonaquist, R. F., and M. W. Witczak. 1997. “A comprehensive constitutive model for granular materials in flexible pavement structures.” In Proc., 8th Int. Conf. on Asphalt Pavements, 783–802. Seattle: Univ. of Washington Press.
CEN (European Committee for Standardization). 2004. Cyclic load triaxial test for unbound mixtures. EN 13286-7. Brussels, Belgium: CEN.
Chazallon, C., P. Hornych, and S. Mouhoubi. 2006. “Elastoplastic model for long-term behavior modeling of unbound granular materials in flexible pavements.” Int. J. Geomech. 6 (4): 279–289. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:4(279).
Chen, R. P., J. M. Chen, and H. L. Wang. 2014. “Recent research on the track-subgrade of high-speed railways.” J. Zhejiang Univ. Sci. A 15 (12): 1034–1038. https://doi.org/10.1631/jzus.A1400342.
Chen, W. B., W. Q. Feng, and J. H. Yin. 2020a. “Effects of water content on resilient modulus of a granular material with high fines content.” Constr. Build. Mater. 236 (Mar): 117542. https://doi.org/10.1016/j.conbuildmat.2019.117542.
Chen, W. B., W. Q. Feng, J. H. Yin, and L. Borana. 2020b. “LVDTs-based radial strain measurement system for static and cyclic behavior of geomaterials.” Measurement 155 (Apr): 107526. https://doi.org/10.1016/j.measurement.2020.107526.
Chen, W. B., W. Q. Feng, J. H. Yin, L. Borana, and R. P. Chen. 2019a. “Characterization of permanent axial strain of granular materials subjected to cyclic loading based on shakedown theory.” Constr. Build. Mater. 198 (Feb): 751–761. https://doi.org/10.1016/j.conbuildmat.2018.12.012.
Chen, W. B., K. Liu, Z. Y. Yin, and J. H. Yin. 2020c. “Crushing and flooding effects on one-dimensional time-dependent behaviors of a granular soil.” Int. J. Geomech. 20 (2): 04019156. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001560.
Chen, W. B., J. H. Yin, and W. Q. Feng. 2019b. “A new double-cell system for measuring volume change of a soil specimen under monotonic or cyclic loading.” Acta Geotech. 14 (1): 71–81. https://doi.org/10.1007/s11440-018-0629-6.
Chen, W. B., J. H. Yin, W. Q. Feng, L. Borana, and R. P. Chen. 2018. “Accumulated permanent axial strain of a subgrade fill under cyclic high-speed railway loading.” Int. J. Geomech. 18 (5): 04018018. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001119.
Chinese Standard. 2009. Code for design of high speed railway. TB10621. Beijing: Ministry of Railways of the People’s Republic of China.
Feng, W. Q., J. H. Yin, X. M. Tao, F. Tong, and W. B. Chen. 2017. “Time and strain-rate effects on viscous stress–strain behavior of plasticine material.” Int. J. Geomech. 17 (5): 04016115. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000806.
Gidel, G., P. Hornych, J. J. Chauvin, D. Breysse, and A. Denis. 2001. “A new approach for investigating the permanent deformation behaviour of unbound granular material using the repeated load triaxial apparatus.” Bull. de Liaison des Laboratoires des Ponts et Chaussées 233: 5–21.
Gu, F., Y. Q. Zhang, X. Luo, H. Sahin, and R. L. Lytton. 2017. “Characterization and prediction of permanent deformation properties of unbound granular materials for pavement ME design.” Constr. Build. Mater. 155 (Nov): 584–592. https://doi.org/10.1016/j.conbuildmat.2017.08.116.
Hicher, P., A. Daouadji, and D. Fedghouche. 1999. “Elastoplastic modelling of the cyclic behaviour of granular materials.” In Proc., Int. Workshop on Modeling and Advanced Testing for Unbound Granular Materials, 161–168. Rotterdam, Netherlands: Balkema.
Huurman, M. 1997. “Permanent deformation in concrete block pavements.” Ph.D. thesis, Faculteit der Civiele Techniek, Univ. of Delft.
Jiang, H. G., X. C. Bian, J. Q. Jiang, and Y. M. Chen. 2016. “Dynamic performance of high-speed railway formation with the rise of water table.” Eng. Geol. 206 (May): 18–32. https://doi.org/10.1016/j.enggeo.2016.03.002.
Jin, Y. F., Z. Y. Yin, Z. X. Wu, and W. H. Zhou. 2018. “Identifying parameters of easily crushable sand and application to offshore pile driving.” Ocean Eng. 154 (Apr): 416–429. https://doi.org/10.1016/j.oceaneng.2018.01.023.
Khedr, S. 1985. “Deformation characteristics of granular base course in flexible pavements.” Transp. Res. Rec. 1043: 131–138.
Korkiala-Tanttu, L. 2005. “A new material model for permanent deformations in pavements.” In Proc., 7th Int. Conf. on Bearing Capacity of Roads and Airfields, BCRRA’05. London: Taylor & Francis.
Lackenby, J., B. Indraratna, G. R. McDowell, and D. Christie. 2007. “Effect of confining pressure on ballast degradation and deformation under cyclic triaxial loading.” Géotechnique 57 (6): 527–536. https://doi.org/10.1680/geot.2007.57.6.527.
Lashine, A. K., S. F. Brown, and P. S. Pell. 1971. Dynamic properties of soils. Nottingham, UK: Dept. of Civil Engineering, Univ. of Nottingham.
Lekarp, F., and A. Dawson. 1998. “Modelling permanent deformation behaviour of unbound granular materials.” Constr. Build. Mater. 12 (1): 9–18. https://doi.org/10.1016/S0950-0618(97)00078-0.
Lekarp, F., U. Isacsson, and A. Dawson. 2000. “State of the art. II: Permanent strain response of unbound aggregates.” J. Transp. Eng. 126 (1): 76–83. https://doi.org/10.1061/(ASCE)0733-947X(2000)126:1(76).
Lekarp, F., I. R. Richardson, and A. Dawson. 1996. “Influences on permanent deformation behavior of unbound granular materials.” Transp. Res. Rec. 1547 (1): 68–75.
Lu, M., and G. R. McDowell. 2006. “Discrete element modelling of ballast abrasion.” Géotechnique 56 (9): 651–655. https://doi.org/10.1680/geot.2006.56.9.651.
Lu, M., and G. R. McDowell. 2008. “Discrete element modelling of railway ballast under triaxial conditions.” Geomech. Geoeng. Int. J. 3 (4): 257–270. https://doi.org/10.1080/17486020802485289.
Lu, M., and G. R. McDowell. 2010. “Discrete element modelling of railway ballast under monotonic and cyclic triaxial loading.” Géotechnique 60 (6): 459–467. https://doi.org/10.1680/geot.2010.60.6.459.
Mohammad, L., A. Herath, M. Rasoulian, and Z. Zhang. 2006. “Laboratory evaluation of untreated and treated pavement base materials from a repeated load permanent deformation test.” In Proc., CD-ROM of the 85th Transportation Research Board Annual Meeting. Washington, DC: Transportation Research Board.
Paute, J. L., A. R. Dawson, and P. J. Galjjard. 1996a. “Recommendations for repeated load triaxial test equipment and procedure for unbound granular materials.” In Proc., European Symp. on Flexible Pavements, Euroflex 1993, 27–47. Rotterdam, Netherlands: A.A. Balkema.
Paute, J. L., P. Hornych, and J. P. Benaben. 1996b. “Repeated load triaxial testing of granular materials in the French Network of Laboratories des Ponts et Chaussées.” In Proc., European Symp. Flexible Pavements, Euroflex 1993. Rotterdam, Netherlands: A.A. Balkema.
Pérez, I., and J. Gallego. 2010. “Rutting prediction of a granular material for base layers of low-traffic roads.” Constr. Build. Mater. 24 (3): 340–345. https://doi.org/10.1016/j.conbuildmat.2009.08.028.
Pérez, I., L. Medina, and M. G. Romana. 2006. “Permanent deformation models for a granular material used in road pavements.” Constr. Build. Mater. 20 (9): 790–800. https://doi.org/10.1016/j.conbuildmat.2005.01.050.
Puppala, A. J., L. N. Mohammad, and A. Allen. 1999. “Permanent deformation characterization of subgrade soils from RLT test.” J. Mater. Civ. Eng. 11 (4): 274–282. https://doi.org/10.1061/(ASCE)0899-1561(1999)11:4(274).
Rahman, M. S., and S. Erlingsson. 2015a. “A model for predicting permanent deformation of unbound granular materials.” Road Mater. Pavement Des. 16 (3): 653–673. https://doi.org/10.1080/14680629.2015.1026382.
Rahman, M. S., and S. Erlingsson. 2015b. “Predicting permanent deformation behaviour of unbound granular materials.” Int. J. Pavement Eng. 16 (7): 587–601. https://doi.org/10.1080/10298436.2014.943209.
Sharp, R. 1983. “Shakedown analyses and the design of pavement under moving surface load.” Ph.D. thesis, School of Civil and Mining Engineering, Univ. of Sydney.
Shi, X. S., and J. Zhao. 2020. “Practical estimation of compression behavior of clayey/silty sands using equivalent void-ratio concept.” J. Geotech. Geoenviron. Eng. 146 (6): 04020046. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002267.
Sweere, G. T. H. 1990. “Unbound granular bases for roads.” Ph.D. thesis, Faculty of Civil Engineering, Univ. of Delft.
Tao, M. J., L. N. Mohammad, M. D. Nazzal, Z. J. Zhang, and Z. Wu. 2010. “Application of shakedown theory in characterizing traditional and recycled pavement base materials.” J. Transp. Eng. 136 (3): 214–222. https://doi.org/10.1061/(ASCE)0733-947X(2010)136:3(214).
Theyse, H. L. 2000. “The development of mechanistic-empirical permanent deformation design models for unbound pavement materials from laboratory accelerated pavement data.” In Proc., 5th Int. Symp. on Unbound Aggregates in Road, UNBAR 5, 285–293. Rotterdam, Netherlands: A.A. Balkema.
Thompson, M. R., and K. L. Smith. 1990. “Repeated triaxial characterization of granular bases.” Transp. Res. Rec. 1278: 7–17.
Tseng, K. H., and R. L. Lytton. 1989. “Prediction of permanent deformation in flexible pavement materials.” In Implication of aggregates in design, construction, and performance of flexible pavements, 154–172. West Conshohocken, PA: ASTM.
Tutumluer, E., D. Mishra, and A. Butt. 2009. Characterization of Illinois aggregates for subgrade replacement and subbase. Urbana, IL: Univ. of Illinois Urbana-Champaign.
Vallerga, B. A., H. B. Seed, C. L. Monismith, and R. S. Cooper. 1956. Effect of shape, size and surface roughness of aggregate particles on the strength of granular materials. In Proc., Symp. on Road and Paving Materials, 63–76. West Conshohocken, PA: ASTM.
Wang, H. L., R. P. Chen, S. Qi, W. Cheng, and Y. J. Cui. 2018. “Long-term performance of pile-supported ballastless track-bed at various water levels.” J. Geotech. Geoenviron. Eng. 144 (6): 04018035. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001890.
Wang, P., Z. Karatza, and C. Arson. 2019. “DEM modelling of sequential fragmentation of zeolite granules under oedometric compression based on XCT observations.” Powder Technol. 347 (Apr): 66–75. https://doi.org/10.1016/j.powtec.2019.02.050.
Werkmeister, S. 2003. “Permanent deformation behaviour of unbound granular materials in pavement constructions.” Ph.D. thesis, Faculty of Civil Engineering, Dresden Univ. of Technology.
Wolff, H., and A. T. Visser. 1994. “Incorporating elasto-plasticity in granular layer pavement design.” Proc. Inst. Civ. Eng. Transport 105 (4): 259–272. https://doi.org/10.1680/itran.1994.27137.
Xiao, Y. J. 2014. “Performance-based evaluation of unbound aggregates affecting mechanistic response and performance of flexible pavements.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Illinois at Urbana-Champaign.
Xiao, Y. J., Z. Zhang, L. X. Chen, and K. Y. Zheng. 2018a. “Modeling stress path dependency of cyclic plastic strain accumulation of unbound granular materials under moving wheel loads.” Mater. Des. 137 (Jan): 9–21. https://doi.org/10.1016/j.matdes.2017.10.024.
Xiao, Y. J., K. Y. Zheng, L. X. Chen, and J. F. Mao. 2018b. “Shakedown analysis of cyclic plastic deformation characteristics of unbound granular materials under moving wheel loads.” Constr. Build. Mater. 167 (Apr): 457–472. https://doi.org/10.1016/j.conbuildmat.2018.02.064.
Xiong, H., F. Nicot, and Z. Y. Yin. 2017. “A three-dimensional micromechanically based model.” Int. J. Numer. Anal. Methods Geomech. 41 (17): 1669–1686. https://doi.org/10.1002/nag.2692.
Yin, Z. Y., C. S. Chang, and P. Hicher. 2010. “Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand.” Int. J. Solid Struct. 47 (14–15): 1933–1951. https://doi.org/10.1016/j.ijsolstr.2010.03.028.
Yin, Z. Y., Y. F. Jin, J. S. Shen, and P. Y. Hicher. 2018a. “Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement.” Int. J. Numer. Anal. Methods Geomech. 42 (1): 70–94. https://doi.org/10.1002/nag.2714.
Yin, Z. Y., Z. X. Wu, and P. Y. Hicher. 2018b. “Modeling the monotonic and cyclic behavior of granular materials by an exponential constitutive function.” J. Eng. Mech. 144 (4): 04018014. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001437.
Yin, Z. Y., Q. Xu, and C. S. Chang. 2013. “Modeling cyclic behavior of clay by micromechanical approach.” J. Eng. Mech. 139 (9): 1305–1309. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000516.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 146 • Issue 9 • September 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Oct 9, 2019
Accepted: Apr 22, 2020
Published online: Jun 29, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 29, 2020
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.