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Modeling the Fiber Addition Influence on the Small Strain Shear Modulus of Sand

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Abstract

The mechanical behavior of fiber reinforced soils has been extensively studied in the last decades. Previous studies have shown that inclusion of fibers increases the shear strength of the reinforced soil. However, the presence of fibers can reduce, in some cases, the stiffness of the composite material. In this paper, we study the change on the initial stiffness in alluvial sand reinforced with polypropylene fibers. A model based on Hertz elastic contact theory is developed in order to explain the trends of shear wave velocity and maximum shear modulus in the fiber reinforced sand as the fiber content varies. The model assumes that the shear wave is transmitted through elastic distortions at the contacts, so the stiffness of the contacts governs the initial shear modulus, which in turn is affected by fiber additions. Furthermore, the ratio between the amount of grain to fiber contacts and the total of contacts on the shear wave path influence the maximum shear modulus. An experimental testing program involving confined compression tests with shear wave velocity measurements of unreinforced and fiber-reinforced sand specimens was undertaken to validate the proposed model trends. The model predictions were found to be in good agreement with the experimental results.

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Abbreviations

α:

Ratio between fiber-to-grain contact stiffness and grain-to-grain contact stiffness

β:

Ratio of the number of fiber-to-grain contacts to the total of contacts

dg :

Soil grain diameter

df :

Fiber diameter

FC%:

Fiber content percentage

Gg :

Shear modulus of the soil grains

Gf :

Shear modulus of the fiber

Gmax :

Maximum shear modulus of soil without reinforcement

G′max :

Maximum shear modulus of fiber reinforced soil

G′′max :

Maximum shear modulus when all contacts are fiber-to-grain type

G*:

Effective shear modulus

γs :

Specific gravity of soil

γf :

Specific gravity of fiber

Lf :

Fiber length

μgg :

Grain-to-grain contact shear stiffness

μgf :

Fiber-to-grain contact shear stiffness

N:

Contact force

Nc :

Number of contacts

Ns :

Number of spheres

Ngg :

Number of grain-to-grain contacts

Ngf :

Number of fiber-to-grain contacts

νg :

Poisson ratio of the soil grains

νf :

Poisson ratio of the fiber

rc :

Contact radius between two spheres

r′c :

Contact radius between a sphere and a cylinder

ρ:

Soil bulk density

Vs :

Shear wave velocity

Ws :

Soil sample weight

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Acknowledgements

This research was financed by grants from the Science and Technology Secretary (Secretaría de Ciencia y Tecnología—SECyT) of the Universidad Nacional de Cordoba (UNC), Argentina. Its support is gratefully acknowledged.

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Authors and Affiliations

  1. Institute for Advanced Studies in Engineering and Technology, IDIT UNC-CONICET Córdoba, 5000, Córdoba, Argentina

    Paula V. Vettorelo

  2. Laboratorio de Geotecnia, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina

    Paula V. Vettorelo & Juan J. Clariá

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  1. Paula V. Vettorelo
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  2. Juan J. Clariá
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Correspondence to Paula V. Vettorelo.

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Vettorelo, P.V., Clariá, J.J. Modeling the Fiber Addition Influence on the Small Strain Shear Modulus of Sand. Indian Geotech J 48, 196–204 (2018). https://doi.org/10.1007/s40098-017-0251-9

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