Abstract
A uniaxial strain-softening constitutive model for fiber-reinforced soils is developed based on the disturbed state concept (DSC). The response in the relatively intact state is assumed to satisfy the Duncan–Chang model obtained from the prepeak stress–strain curve, while the fully adjusted state response satisfies the linear model obtained by an extension of the residual strength. The apparent stress–strain curve is a weighted average response derived from the two aforementioned response curves by a disturbance function that acts as the weight. The peak of the stress–strain curve and the postpeak stable point are assumed as the starting and ending points of the disturbance, respectively, which assign a reasonable physical sense to the parameters in the disturbance function. Comparisons of stress–strain curves and peak strength reveal that for a specified fiber, fiber content exhibits a greater influence on the reinforcement effect than fiber length. Five required parameters that vary with fiber content are used in the DSC model. Five sets of uniaxial compression test data of different fiber-reinforced soils are evaluated, and a high consistency between the stress–strain curves predicted by the DSC model and the test curves is noted. Both the consistency index δ and the energy absorption capacity reveal a satisfactory description of the fiber reinforcement effect.
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Acknowledgments
The work was supported by the National Natural Science Foundation of China (Grant Nos. 51878551, 51478385, and 51778528). Their support is greatly appreciated.
Notation
The following symbols are used in this paper:
- Ac
- area of the FA part;
- At
- total area of the material element;
- D
- disturbance function;
- Da
- disturbance value at different loading moments;
- Du
- limit value of the disturbance function;
- Ei
- initial tangent modulus;
- M
- postpeak modulus;
- N
- number of axial stress points of the stress–strain curve;
- axial stress of the FA state;
- axial stress of the RI state;
- XEi
- axial stress of the stress–strain curve measured by the uniaxial compression test;
- XPi
- axial stress of the predicted stress–strain curve;
- average value of the axial stress at each point of the measured stress–strain curve;
- Δ
- test-prediction difference;
- η
- fiber content;
- δ
- consistency index;
- σa
- apparent stress of the material;
- σFA
- stress in the FA state of the material element;
- σRI
- stress in the RI state of the material element;
- Σp
- peak strength;
- σr
- residual strength;
- σult
- ultimate strength;
- ɛ1
- axial strain;
- axial strain of the RI state;
- ɛp
- axial strain corresponding to the peak strength; and
- axial strain of the maximum curvature point of the postpeak curve.
References
ASTM. 2016. Standard test method for unconfined compressive strength of cohesive soil. ASTM D2166/D2166M-16. West Conshohocken, PA: ASTM.
ASTM. 2017. Standard practice for classification of soils for engineering purposes (unified soil classification system). ASTM D2487-17e1. West Conshohocken, PA: ASTM.
Aymerich, F., L. Fenu, and P. Meloni. 2012. “Effect of reinforcing wool fibres on fracture and energy absorption properties of an earthen material.” Constr. Build. Mater. 27 (1): 66–72. https://doi.org/10.1016/j.conbuildmat.2011.08.008.
Desai, C. S. 2000. Mechanics of materials and interfaces: The disturbed state concept. 1st ed. Boca Raton, FL: CRC Press.
Desai, C. S. 2007. “Unified DSC constitutive model for pavement materials with numerical implementation.” Int. J. Geomech. 7 (2): 83–101. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:2(83).
Desai, C. S., S. Somasundaram, and G. Frantziskonis. 1986. “A hierarchical approach for constitutive modelling of geologic materials.” Int. J. Numer. Anal. Methods Geomech. 10 (3): 225–257. https://doi.org/10.1002/nag.1610100302.
Desai, C. S., and J. Toth. 1996. “Disturbed state constitutive modeling based on stress-strain and nondestructive behavior.” Int. J. Solids Struct. 33 (11): 1619–1650. https://doi.org/10.1016/0020-7683(95)00115-8.
Dhar, S., and M. Hussain. 2019. “The strength behaviour of lime-stabilised plastic fibre-reinforced clayey soil.” Road Mater. Pavement Des. 20 (8): 1757–1778. https://doi.org/10.1080/14680629.2018.1468803.
Diambra, A., and E. Ibraim. 2014. “Modelling of fibre–cohesive soil mixtures.” Acta Geotech. 9 (6): 1029–1043. https://doi.org/10.1007/s11440-013-0283-y.
Diambra, A., E. Ibraim, D. M. Wood, and A. R. Russell. 2010. “Fibre reinforced sands: Experiments and modelling.” Geotext. Geomembr. 28 (3): 238–250. https://doi.org/10.1016/j.geotexmem.2009.09.010.
di Prisco, C., and R. Nova. 1993. “A constitutive model for soil reinforced by continuous threads.” Geotext. Geomembr. 12 (2): 161–178. https://doi.org/10.1016/0266-1144(93)90004-8.
Duncan, J. M., and C. Y. Chang. 1970. “Nonlinear analysis of stress and strain in soils.” J. Soil Mech. Found. Div. 96 (5): 1629–1653. https://doi.org/10.1061/JSFEAQ.0001458.
Garg, A., S. Bordoloi, S. Mondal, J. J. Ni, and S. Sreedeep. 2020. “Investigation of mechanical factor of soil reinforced with four types of fibers: An integrated experimental and extreme learning machine approach.” J. Nat. Fibers 17 (5): 650–664. https://doi.org/10.1080/15440478.2018.1521763.
Geiser, F., L. Laloui, L. Vulliet, and C. S. Desai. 1997. “Disturbed state concept for partially saturated soils.” InProc., 6th Int. Symp. on Numerical Models in Geomechanics, 129–133. Rotterdam, Netherlands: Balkema.
Ghazavi, M., and M. Roustaie. 2010. “The influence of freeze–thaw cycles on the unconfined compressive strength of fiber-reinforced clay.” Cold Reg. Sci. Technol. 61 (2–3): 125–131. https://doi.org/10.1016/j.coldregions.2009.12.005.
Gray, D. H., and H. Ohashi. 1983. “Mechanics of fiber reinforcement in sand.” J. Geotech. Eng. 109 (3): 335–353. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:3(335).
Hejazi, S. M., M. Sheikhzadeh, S. M. Abtahi, and A. Zadhoush. 2012. “A simple review of soil reinforcement by using natural and synthetic fibers.” Constr. Build. Mater. 30: 100–116. https://doi.org/10.1016/j.conbuildmat.2011.11.045.
Hu, C., X. Weng, C. Liu, L. Jiang, and W. Li. 2021. “Performance of polypropylene fiber-reinforced solidified soil.” Adv. Civ. Eng. 2021: 8859358. https://doi.org/10.1155/2021/8859358.
Jewell, R. A., and C. P. Wroth. 1987. “Direct shear tests on reinforced sand.” Geotechnique 37 (1): 53–68. https://doi.org/10.1680/geot.1987.37.1.53.
Kar, R., and P. Pradhan. 2011. “Strength and compressibility characteristics of randomly distributed fiber-reinforced soil.” Int. J. Geotech. Eng. 5 (2): 235–243. https://doi.org/10.3328/IJGE.2011.05.02.235-243.
Kumar, A., B. S. Walia, and J. Mohan. 2006. “Compressive strength of fiber reinforced highly compressible clay.” Constr. Build. Mater. 20 (10): 1063–1068. https://doi.org/10.1016/j.conbuildmat.2005.02.027.
Langroudi, S. G., A. Zad, and A. M. Rajabi. 2021. “Improvement of sandy soil to prevent hydraulic failure using BCF fibers and geotextiles.” Arab. J. Geosci. 14 (17): 1–16. https://doi.org/10.1007/s12517-021-07986-4.
Lewis, C. D. 1982. “Industrial and business forecasting methods: A practical guide to exponential smoothing and curve fitting.” Oxford, UK: Butterworth-Heinemann.
Liu, H., and H. I. Ling. 2012. “Seismic responses of reinforced soil retaining walls and the strain softening of backfill soils.” Int. J. Geomech. 12 (4): 351–356. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000051.
Michalowski, R. L. 2008. “Limit analysis with anisotropic fibre-reinforced soil.” Geotechnique 58 (6): 489–501. https://doi.org/10.1680/geot.2008.58.6.489.
Michalowski, R. L., and J. Cermak. 2002. “Strength anisotropy of fiber-reinforced sand.” Comput. Geotech. 29 (4): 279–299. https://doi.org/10.1016/S0266-352X(01)00032-5.
Neeraja, V. S., K. Geetha Manjari, and G. L. Sivakumar Babu. 2014. “Numerical analysis of effect of orientation of fibers on stress–strain response of fiber reinforced soil.” Int. J. Geotech. Eng. 8 (3): 328–334. https://doi.org/10.1179/1939787913Y.0000000023.
Patel, S. K., and B. Singh. 2017. “Strength and deformation behavior of fiber-reinforced cohesive soil under varying moisture and compaction states.” Geotech. Geol. Eng. 35 (4): 1767–1781. https://doi.org/10.1007/s10706-017-0207-y.
Prabakar, J., and R. S. Sridhar. 2002. “Effect of random inclusion of sisal fibre on strength behaviour of soil.” Constr. Build. Mater. 16 (2): 123–131. https://doi.org/10.1016/S0950-0618(02)00008-9.
Rabab’ah, S., O. A. Hattamleh, H. Aldeeky, and B. A. Alfoul. 2021. “Effect of glass fiber on the properties of expansive soil and its utilization as subgrade reinforcement in pavement applications.” Case Stud. Constr. Mater. 14: e00485. https://doi.org/10.1016/j.cscm.2020.e00485.
Ranjan, G., R. M. Vasan, and H. D. Charan. 1996. “Probabilistic analysis of randomly distributed fiber-reinforced soil.” J. Geotech. Eng. 122 (6): 419–426. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:10(986).
Sivakumar Babu, G. L., and A. K. Vasudevan. 2008. “Strength and stiffness response of coir fiber-reinforced tropical soil.” J. Mater. Civ. Eng. 20 (9): 571–577. https://doi.org/10.1061/(ASCE)0899-1561(2008)20:9(571).
Tang, C., B. Shi, W. Gao, F. Chen, and Y. Cai. 2007. “Strength and mechanical behavior of short polypropylene fiber reinforced and cement stabilized clayey soil.” Geotext. Geomembr. 25 (3): 194–202. https://doi.org/10.1016/j.geotexmem.2006.11.002.
Toth, J. C. 1994. Development of lunar ceramic composites, testing and constitutive modeling, including cemented sand. Tucson, AZ: Univ. of Arizona.
Tran, V. D. H., M. A. Meguid, and L. E. Chouinard. 2015. “Three-dimensional analysis of geogrid-reinforced soil using a finite-discrete element framework.” Int. J. Geomech. 15 (4): 04014066. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000410.
Vanapalli, S. K., W. S. Sillers, and M. D. Fredlund. 1998. “The meaning and relevance of residual state to unsaturated soils.” In Proc., of the 51st Canadian Geotechnical Conf., 4–7. Edmonton, Canada: The Canadian Geotechnical Society.
Wang, Y., P. Guo, F. Dai, X. Li, Y. Zhao, and Y. Liu. 2018. “Behavior and modeling of fiber-reinforced clay under triaxial compression by combining the superposition method with the energy-based homogenization technique.” Int. J. Geomech. 18 (12): 04018172. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001313.
Wang, Y., P. Guo, H. Lin, X. Li, Y. Zhao, B. Yuan, Y. Liu, and P. Cao. 2019. “Numerical analysis of fiber-reinforced soils based on the equivalent additional stress concept.” Int. J. Geomech. 19 (11): 04019122. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001504.
Wang, Y. X, P. P. Guo, W. X. Ren, B. X. Yuan, H. P. Yuan, Y. L. Zhao, S. B. Shan, and P. Cao. 2017. “Laboratory investigation on strength characteristics of expansive soil treated with jute fiber reinforcement.” Int. J. Geomech. 17 (11): 04017101. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000998.
Wang, Z., F. Jacobs, and M. Ziegler. 2016. “Experimental and DEM investigation of geogrid–soil interaction under pullout loads.” Geotext. Geomembr. 44 (3): 230–246. https://doi.org/10.1016/j.geotexmem.2015.11.001.
Wang, Z., F. Jacobs, M. Ziegler, and G. Yang. 2020. “Visualisation and quantification of geogrid reinforcing effects under strip footing loads using discrete element method.” Geotext. Geomembr. 48 (1): 62–70. https://doi.org/10.1016/j.geotexmem.2019.103505.
Wen, K., C. Bu, S. Liu, Y. Li, and L. Li. 2018. “Experimental investigation of flexure resistance performance of bio-beams reinforced with discrete randomly distributed fiber and bamboo.” Constr. Build. Mater. 176: 241–249. https://doi.org/10.1016/j.conbuildmat.2018.05.032.
Willmott, C. J. 1981. “On the validation of models.” Phys. Geogr. 2 (2): 184–194. https://doi.org/10.1080/02723646.1981.10642213.
Xu, J., Z. Wu, H. Chen, L. Shao, X. Zhou, and S. Wang. 2021. “Triaxial shear behavior of basalt fiber-reinforced loess based on digital image technology.” KSCE J. Civ. Eng. 25 (10): 3714–3726. https://doi.org/10.1007/s12205-021-2034-1.
Yang, G., H. Liu, P. Lv, and B. Zhang. 2012. “Geogrid-reinforced lime-treated cohesive soil retaining wall: Case study and implications.” Geotext. Geomembr. 35: 112–118. https://doi.org/10.1016/j.geotexmem.2012.09.001.
Yang, K. H., W. M. Yalew, and M. D. Nguyen. 2016. “Behavior of geotextile-reinforced clay with a coarse material sandwich technique under unconsolidated-undrained triaxial compression.” Int. J. Geomech. 16 (3): 04015083. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000611.
Yang, X., and S. K. Vanapalli. 2021. “Model for predicting the variation of shear stress in unsaturated soils during strain-softening.” Can. Geotech. J. 58 (10): 1513–1526. https://doi.org/10.1139/cgj-2020-0312.
Yetimoglu, T., and O. Salbas. 2003. “A study on shear strength of sands reinforced with randomly distributed discrete fibers.” Geotext. Geomembr. 21 (2): 103–110. https://doi.org/10.1016/S0266-1144(03)00003-7.
Zhao, Y., X. Ling, W. Gong, P. Li, G. Li, and L. Wang. 2020. “Mechanical properties of fiber-reinforced soil under triaxial compression and parameter determination based on the Duncan–Chang model.” Appl. Sci. 10 (24): 9043. https://doi.org/10.3390/app10249043.
Zhu, H. H., C. C. Zhang, C. S. Tang, B. Shi, and B. J. Wang. 2014. “Modeling the pullout behavior of short fiber in reinforced soil.” Geotext. Geomembr. 42 (4): 329–338. https://doi.org/10.1016/j.geotexmem.2014.05.005.
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Received: Nov 10, 2021
Accepted: Feb 7, 2022
Published online: May 3, 2022
Published in print: Jul 1, 2022
Discussion open until: Oct 3, 2022
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