Effective skeleton stress and void ratio for constitutive modeling of fiber-reinforced sand

Abstract

Inclusion of flexible fibers such as polypropylene and polyester is an effective method for soil improvement, as it significantly enhances the soil strength and ductility. A proper constitutive model is essential for assessing the stability and serviceability of fiber-reinforced slopes/foundations. A new method for constitutive modeling of fiber-reinforced sand (FRS) is proposed. It assumes that the strain of FRS is dependent on the deformation of the sand skeleton only, while the effective skeleton stress and effective skeleton void ratio, which should be used in describing the dilatancy, plastic hardening and elastic stiffness of FRS, are affected by fiber inclusion. The effective skeleton stress is dependent on the shear strain level, and the effective skeleton void ratio is affected by the fiber content and sample preparation method. A critical state FRS model in the triaxial stress space is proposed using the concept of effective skeleton stress and void ratio. Four parameters are introduced to characterize the effect of fiber inclusion on the mechanical behavior of sand, all of which can be easily determined based on triaxial test data on FRS, without measuring the stress-strain relationship of individual fibers. The model is validated by triaxial compression test results on four fiber-reinforced sands under loading conditions with various confining pressures, densities and stress paths. Potential improvement in the model for incorporating fiber orientation anisotropy is discussed.

Effect of sample preparation method on mechanical behaviour of fibre-reinforced sand

“…The model used in this study is developed based on the assumption that the strain of FRS is dependent on the deformation of the sand skeleton, while the effective skeleton stress (𝑝𝑠 and 𝑞𝑠) and effective skeleton void ratio 𝑒𝑠, which are used for describing the mechanical response of FRS (dilatancy, plastic hardening and elastic stiffness), are affected by fibre inclusion. Detailed discussions of the model have been presented in Gao et al (2020) and Gao and Diambra (2020). Some key equations are presented here to facilitate the discussion in this study.…”

“…and 𝜀𝑞 is the shear strain. 𝑝𝑐 is proposed based on the failure of FRS (Gao & Zhao, 2013;Gao et al, 2020):…”

“…where 𝑥 is a material constant, 𝜌𝑓=𝑣𝑓𝑣𝑠 with 𝑣𝑓 and 𝑣𝑠 being the specific volume of fibres and dry sand, respectively. The variable 𝜌𝑓 can be expressed in terms of the fibre weight content 𝑤𝑓 as below (Gao et al, 2020), which is more frequently used in the existing literature…”

“…The method for determining the sand parameters can be found in Li and Dafalias (2000). Once the model parameters for pure sand have been determined, the rest can be determined based on the triaxial compression test results on FRS (Gao et al, 2020).…”

“…For the MV samples, the model tends to give lower deviator stress before failure. This could be due to the model not being able to describe the evolution of mean effective skeleton stress 𝑝𝑓 with strain, which has also been discussed in Gao et al (2020). The four parameters for FRS can be used to infer the difference in the internal structure of FRS (Table 5).…”