Analysis of mobilized stress ratio of gap-graded granular materials in direct shear state considering coarse fraction effect

Abstract

Weathered rockfill materials, characterized by a mixture of soil matrix and rock aggregates, are widely distributed in mountainous areas. These soils are frequently used for subgrade or riprap in engineering practice, and the mobilized shear strength is crucial for analyzing the displacement and stability of these geo-structures. A series of direct shear tests are performed on a gap-graded soil with a full range of coarse fraction. The behavior of gap-graded soils is analyzed, and a simple model is proposed for the evolution of mobilized stress ratio during direct shearing process based on mixture theory. The change of inter-aggregate configuration is incorporated by introducing a structure variable which increases with coarse fraction and decreases approximately linearly with the overall horizontal shear strain in double logarithmic plot. It reasonably reflects a gradually transformation from a matrix-sustained structure into an aggregate-sustained one with the increase of coarse fraction. The model has four parameters, and at least two direct shear tests need to be done for the calibration. Validation of the model is done by using the test data in this work and those from the literature.

Appendix 1

There are two types of structure according to the coarse fraction, matrix-sustained structure, and aggregate-sustained structure. In this study, we deal with the matrix-sustained structure, and the structure of the fine matrix is relatively uniform without macro-voids (Fig. 3). Therefore, volume of voids in mixtures can be well represented by the volume of voids in fine matrix, and the overall deformation of gap-graded mixtures relies on the decrease of volume of voids in fines. The mixture can be divided into three parts: (1) the solid phase of fine matrix (denoted as V_sm), (2) the volume of voids in fine matrix (denoted as V_vm), and (3) the volume of coarse aggregates (denoted as V_a). Suppose that the volume of solid phase of fine matrix is one unit (i.e., V_sm = 1). The volume of voids in fine matrix is

$$ V_{\text{vm}} = e_{\text{m}} $$

(15)

where e_m is the void ratio of fine matrix. From the definition of the void ratio of aggregates e_a,

$$ V_{\text{a}} = \frac{{V_{\text{sm}} { + }V_{\text{vm}} }}{{e_{\text{a}} }} = \frac{{1 + e_{\text{m}} }}{{e_{\text{a}} }} $$

(16)

Hence, the coarse fraction and overall void ratio at the transitional point can be derived according to its definition:

$$ \tilde{\psi }_{a} = \frac{{V_{\text{a}} }}{{V_{\text{sm}} + V_{\text{a}} }} = \frac{{1{ + }e_{\text{m}} }}{{1 + e_{\text{m}} + e_{{\hbox{min} ,{\text{a}}}} }} $$

(17)

$$ \tilde{e} = \frac{{V_{\text{vm}} }}{{V_{\text{sm}} + V_{\text{a}} }} = \frac{{e_{\text{m}} e_{{\hbox{min} ,{\text{a}}}} }}{{1 + e_{\text{m}} + e_{{\hbox{min} ,{\text{a}}}} }} $$

(18)

The overall void ratio can be derived according to its definition:

$$ e = \frac{{V_{\text{vm}} }}{{V_{\text{sm}} + V_{\text{a}} }} = \frac{{e_{\text{m}} }}{{1 + V_{\text{a}} }} $$

(19)

The dry mass of the fines m_s and aggregates m_a is

$$ m_{\text{s}} = \rho_{s} V_{\text{sm}} ;\;\;m_{\text{a}} = \rho_{\text{a}} V_{\text{a}} $$

(20)

Suppose that the density of fines and aggregates is the same, the coarse fraction is derived as:

$$ \psi_{a} = \frac{{m_{\text{a}} }}{{m_{\text{s}} + m_{\text{a}} }} = \frac{{\rho_{\text{a}} V_{\text{a}} }}{{\rho_{\text{s}} V_{\text{sm}} + \rho_{\text{a}} V_{\text{a}} }} = \frac{{V_{\text{a}} }}{{1 + V_{\text{a}} }} $$

(21)

The following equations can be derived from Eq. (19) and Eq. (21):

$$ e_{\text{m}} = \frac{e}{{1 - \psi_{a} }};\;\;V_{\text{a}} = \frac{{\psi_{a} }}{{1 - \psi_{a} }} $$

(22)

The volume fraction of aggregates is defined as:

$$ \phi_{a} = \frac{{V_{\text{a}} }}{{V_{\text{sm}} + V_{\text{vm}} + V_{\text{a}} }} = \frac{{V_{\text{a}} }}{{1 + e_{\text{m}} + V_{\text{a}} }} $$

(23)

Substituting Eq. (22) into Eq. (23), it gives:

$$ \phi_{a} = \frac{{\psi_{a} }}{1 + e} $$

(24)