Abstract
The stress–dilatancy relationship could be employed as the foundation to develop a constitutive model for polypropylene fiber-reinforced (PFR) soils. In this study, a number of triaxial compression tests were carried out to investigate the effect of uniform distributed fiber reinforcements on the stress dilatancy relationship of Nan**g sand. A new parameter representing the increase in the effective confining stress \(\sigma _{\rm FR}\) was introduced to describe the stress–dilatancy of PFR sand, and a new stress–dilatancy relationship was proposed for PFR sand based on Rowe’s stress–dilatancy equation for granular materials. Moreover, the stress–dilatancy relationships in the conventional triaxial compression, extension and plane stain conditions were discussed in this paper. The stress–dilatancy relationship is validated against a series of triaxial tests on Nan**g sand and Hostun RF sand mixed with discrete polypropylene fibers. It is shown that the predicted results are in a good agreement with the experimental results.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11440-019-00834-6/MediaObjects/11440_2019_834_Fig12_HTML.png)
Data adapted from Diambra et al. [5]
Similar content being viewed by others
References
Bolton M (1986) The strength and dilatancy of sands. Géotechnique 36(1):65–78
Consoli NC, Casagrande MDT, Coop MR (2007) Performance of a fibre-reinforced sand at large shear strains. Géotechnique 57(9):751–756
Diambra A, Ibraim E (2015) Fibre-reinforced sand: interaction at the fibre and grain scale. Géotechnique 65(4):296–308
Diambra A, Russell AR, Ibraim E, Wood DM (2007) Determination of fibre orientation distribution in reinforced sands. Géotechnique 57(7):623–628
Diambra A, Ibraim E, Wood DM, Russell A (2010) Fibre reinforced sands: experiments and modelling. Geotext Geomembr 28(3):238–250
Gray DH, Al-Refeai T (1986) Behavior of fabric-versus fiber-reinforced sand. J Geotech Eng 112(8):804–820
Heineck KS, Coop MR, Consoli NC (2005) Effect of microreinforcement of soils from very small to large shear strains. J Geotech Geoenviron Eng 131(8):1024–1033
Hendry MT, Sharma JS, Martin CD, Barbour SL (2012) Effect of fibre content and structure on anisotropic elastic stiffness and shear strength of peat. Can Geotech J 49(4):403–415
Houlsby G (1991) How the dilatancy of soils affects their behaviour. In: Proceedings of 10th European conference on soil mechanics and foundation engineering, Florence
Kruyt N, Rothenburg L (2016) A micromechanical study of dilatancy of granular materials. J Mech Phys Solids 95:411–427
Landva A, La Rochelle P (1983) Compressibility and shear characteristics of radforth peats. ASTM Spec Tech Publ 820:157–191
Li M, He H, Senetakis K (2017) Behavior of carbon fiber-reinforced recycled concrete aggregate. Geosynth Int 24(5):480–490
Madhusudhan BN, Baudet BA, Ferreira PMV, Sammonds P (2017) Performance of fiber reinforcement in completely decomposed granite. J Geotech Geoenviron Eng 143(8):04017038
Maher MH, Gray DH (1990) Static response of sands reinforced with randomly distributed fibers. J Geotech Eng 116(11):1661–1677
Maheshwari BK, Singh HP, Saran S (2012) Effects of reinforcement on liquefaction resistance of solani sand. J Geotech Geoenviron Eng 138(7):831–840
Reynolds O (1885) On the dilatancy of media composed of rigid particles in contact with experimental illustrations. Philos Mag Ser 5 20(127):469–481
Rifai SM, Miller CJ (2009) Theoretical assessment of increased tensile strength of fibrous soil undergoing desiccation. J Geotech Geoenviron Eng 135(12):1857–1862
Rowe PW (1962) The stress–dilatancy relation for static equilibrium of an assembly of particles in contact. Proc R Soc Lond A Math Phys Eng Sci 269(1339):500–527
Santos AD, Consoli N, Heineck K, Coop M (2010) High-pressure isotropic compression tests on fiber-reinforced cemented sand. J Geotech Geoenviron Eng 136(6):885–890
Santos APS, Consoli NC, Baudet BA (2010) The mechanics of fibre-reinforced sand. Géotechnique 60(10):791–799
Tang C, Shi B, Gao W, Chen F, Cai Y (2007) Strength and mechanical behavior of short polypropylene fiber reinforced and cement stabilized clayey soil. Geotext Geomembr 25(3):194–202
Tang CS, Shi B, Zhao LZ (2010) Interfacial shear strength of fiber reinforced soil. Geotext Geomembr 28(1):54–62
Wan RG, Guo PJ (2004) Stress dilatancy and fabric dependencies on sand behavior. J Eng Mech 130(6):635–645
Wood DM, Diambra A, Ibraim E (2016) Fibres and soils: a route towards modelling of root–soil systems. Soils Found 56(5):765–778
Zornberg JG (2002) Discrete framework for limit equilibrium analysis of fibre-reinforced soil. Géotechnique 52(8):593–604
Acknowledgements
The authors would like to acknowledge the supports provided by the National Natural Science Foundation of China (No. 11402109) and the Natural Science Foundation of Jiangsu Province (No. BK20130909). The authors appreciate the comments made by the reviewer which help improve the quality of the manuscript. The authors would like to thank Dr. Dan Su, Dr. Zhu Song and Dr. Weiyun Chen for valuable comments and suggestions on the paper. Yuxia Kong thanks the China Scholarship Council for supporting her time in residence at RMIT University under visiting scholar award 201808320020.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kong, Y., Zhou, A., Shen, F. et al. Stress–dilatancy relationship for fiber-reinforced sand and its modeling. Acta Geotech. 14, 1871–1881 (2019). https://doi.org/10.1007/s11440-019-00834-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11440-019-00834-6