Prediction of compressive strength of the welded matrix-rock mixture by meso-inclusion theory

Abstract

As a special and widely distributed geological material, the matrix-rock mixture (block-in-matrix texture) has been worldwide focused on its complex physical and mechanical properties for 25 years. However, the macro-meso mechanical relationship of matrix-rock mixture has not been well clarified so far, leading to the unclear understanding of its mechanical behavior. In this paper, the welded matrix-rock mixture is considered as a two-phase composite material, and a mesoscopic mechanical method is presented for calculating the uniaxial compressive strength (UCS). The influence of volumetric block proportion of rock (VBP) and mechanical contrast of meso components (i.e. UCS ratio (SR) and modulus ratio (MR) of rock to matrix) on the strength and the failure mechanism of the matrix-rock mixture is illustrated by the meso-inclusion theory. To avoid the rock damage in the welded mixture, it is suggested that the SR of rock to matrix should be larger than 1.5 for the low stiffness ratio of rock to matrix (e.g. MR ≤ 5), while for the mixture with high stiffness contrast (e.g. 5 < MR < 100) the SR of rock to matrix should be larger than 2. For the common case of strong rock-weak matrix mixture, the reinforced effect of VBP is positive with the MR of rock to matrix but seems to be insignificant when MR > 100. Meanwhile, the Weibull function is adopted to describe the strength property of the matrix in view of its strength randomness contributing to the matrix-rock mixture. It is shown that the strength evolution of the mixtures can be effectively predicted by the present model considering the Weibull distributed strength of the matrix, based on the comparison with the published experimental data and the discussion of existed empirical formulas.