Response to the discussion on “Recommendations for extension and re-calibration of an existing sand constitutive model taking into account varying non-plastic fines content” by Md. Mizanur Rahman, S. R. Lo

Abstract

The author of this paper wishes to express his appreciation to Rahman and Lo for their time and effort in studying the paper and preparing the discussion. In sequel, the main questions are answered. Wei and Yang [17] experimentally studied the role of particle shape in the liquefaction of clean sand and sand–fines mixtures. They showed that the average shape of particles in both coarse and fines phases plays a central role in liquefaction vulnerability of sand–fines mixtures. In Fig.1, 5% by weight of glass beads (as wellrounded particles) and crushed glass (as angular particles) of the same material and particle gradation were added to clean coarse Toyoura and Fujian sands. By observing a dramatic difference between the behaviors shown in each part of the figure, the influence of particle shape on the behavior of binary granular soils can be confirmed. Vahidi-Nia et al. [14] studied the drained behavior of binary granular mixtures by using direct shear apparatus. In that study, angular fine sand was added to two coarse sands of the same gradation, but different grain shapes. Based on the result of experiments, fines participation factor (i.e., β) was estimated and the results are drawn in Fig. 2 .I nFig. 2(a), β increases linearly with fines content when both coarse and fine phases are angular. However in Fig. 2(b), β varies with fines content in a non-linear manner when angular fine sand was added to sub-rounded coarse sand. Moreover, it is observed that β values are generally greater in the latter case. Yang and Wei [15] introduced a conceptual classification to explain the influence of particle shape on the mechanical behavior of binary granular soils. They defined four extremes representing four different typical inter-particle contact mechanisms of particles interaction in binary mixtures (see Fig. 3). Type I portrays the interaction (i.e., contact, movement, and rotation) of a well-rounded fine particle with respect to a well-rounded coarse particle. Type II shows the interaction of a well-rounded fine particle with respect to an angular coarse particle. Type III presents the interaction of an angular fine particle with respect to a well-rounded coarse particle. Finally, Type IV portrays the interaction of an angular fine particle with respect to an angular coarse particle. Among these four extremes, Type I is the case in which, particles easily relocate and rearrange. On the other side of the spectrum, Type IV is the most difficult case for particles to relocate and rearrange [15]. Therefore, mixtures in Type I and Type IV, respectively, have the most unstable and the most stable structures against the static