Shear Strength of Sands Reinforced with Polypropylene Fibers

Abstract

The inclusion of oriented or randomly distributed discrete elements, such as fibers, to reinforce soil has recently attracted increasing attention in geotechnical engineering. The present paper studies the shear strength parameters of reinforced sands, consisting of different mean grain sizes. The polypropylene fiber volumetric content of the sands ranges from 0.1 to 0.5 %. Specifically, a series of direct shear tests were conducted to determine the peak and residual shear strength parameters of unreinforced and reinforced sands. Laboratory results showed that fiber reinforcement substantially improved the residual strength of fine sands of medium dense state. On the contrary, reinforced sands of high dense state appeared to exhibit negligible strength increment. Based on the experimental results, a non-linear regression analysis was performed to correlate the shear strength of reinforced sand with some descriptor variables.

Appendix

The derivation of Eq. 1 is based on the hypothetical case that after the addition of fibers, the total mass of solids and the volume of voids (V_v) remain unchanged. This assumption leads to the following expression:

Total mass (before) = Total mass (after)

$$ \gamma_{\text{s}} \cdot {\text{V}}_{\text{s}} = \gamma_{\text{s}} \cdot {\text{V}}_{\text{s}}^{\prime } + \gamma_{\text{f}} \cdot {\text{V}}_{\text{f}} $$

(7)

where γ_s and γ_f are the density of solids and fibers, respectively. V_s is the initial volume of solids, V ^′_s is the volume of solids after the mixing (V ^′_s  < V_s) and V_f is the volume of the fibers.

The total volume of composite is defined as:

$$ {\text{V}}_{\text{total}} = {\text{V}}_{\text{s}}^{\prime } + {\text{V}}_{\text{f}} + {\text{V}}_{\text{v}} $$

(8)

Note that the fiber concentration by volume is ρ_v = V_f/V_total and fiber concentration by weight is ρ_f = W_f/W_s, where W_f and W_s are the mass of fibers and the solids, respectively.

The void ratio of the composite is:

$$ {\text{e}}_{\text{o}} = {\text{V}}_{\text{v}} /({\text{V}}_{\text{s}}^{\prime } + {\text{V}}_{\text{f}} ) $$

(9)

According to the required void ratio of the composite and the fiber concentration by volume, the fiber concentration by weight can be calculated by using Eqs. (7) through (9).

Rearrangement of Eq. (7) and (8) gives:

$$ {\text{V}}_{\text{s}}^{\prime } = (\gamma_{\text{s}} {\text{V}}_{\text{s}} - \gamma_{\text{f}} {\text{V}}_{\text{f}} )/\gamma_{\text{s}} $$

(10)

$$ {\text{V}}_{\text{v}} = {\text{V}}_{\text{total}} - {\text{V}}_{\text{s}}^{\prime } - {\text{V}}_{\text{f}} $$

(11)

By substituting Eqs. (10) and (11) into (9), the following is obtained:

$$ {\text{e}}_{\text{o}} = \frac{{\frac{{{\text{V}}_{\text{f}} }}{{\rho_{\text{v}} }} - \frac{{\gamma_{\text{s}} \cdot {\text{V}}_{\text{S}} - \gamma_{\text{f}} \cdot {\text{V}}_{\text{f}} }}{{\gamma {\text{s}}}} - {\text{V}}_{\text{f}} }}{{\frac{{\gamma_{\text{s}} \cdot {\text{V}}_{\text{S}} - \gamma_{\text{f}} \cdot {\text{V}}_{\text{f}} }}{{\gamma_{\text{s}} }} + {\text{V}}_{\text{f}} }} $$

(12)

Equation (12) can be transformed into:

$$ {\text{e}}_{\text{o}} = \frac{{\left( {\frac{{{\text{W}}_{\text{f}} }}{{\gamma_{\text{f}} \cdot \rho_{\text{v}} }} - \frac{{{\text{W}}_{\text{S}} - {\text{W}}_{\text{f}} }}{{\gamma_{\text{s}} }} - \frac{{{\text{W}}_{\text{f}} }}{{\gamma_{\text{f}} }}} \right) \cdot \frac{1}{{{\text{W}}_{\text{S}} }}}}{{\left( {\frac{{{\text{W}}_{\text{S}} - {\text{W}}_{\text{f}} }}{{\gamma_{\text{s}} }} + \frac{{{\text{W}}_{\text{f}} }}{{\gamma_{\text{f}} }}} \right) \cdot \frac{1}{{{\text{W}}_{\text{S}} }}}} $$

(13)

Equation (13) now becomes:

$$ {\text{e}}_{\text{o}} = \frac{{\frac{{\rho_{\text{f}} }}{{\gamma_{\text{f}} \cdot \rho_{\text{v}} }} - \frac{{1 - \rho_{\text{f}} }}{{\gamma_{\text{s}} }} - \frac{{\rho_{\text{f}} }}{{\gamma_{\text{f}} }}}}{{\frac{{1 - \rho_{\text{f}} }}{{\gamma_{\text{s}} }} + \frac{{\rho_{\text{f}} }}{{\gamma_{\text{f}} }}}} $$

(14)

Rearrangement of Eq. (14) results in the explicit expression for the fiber concentration by weight ρ_f.