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This paper aims to study the interplay between a risk-averse national brand manufacturer's (NBM) selling mode decision and a risk-neutral e-platform's private brand (PB) introduction decision.

A game theory model is used to solve selling mode decision, that is whether transform the selling mode from the wholesale mode to the marketplace mode, and PB introduction decision, that is, whether introduce the PB.

The results show that for the NBM, under certain condition, the NBM's selling mode decision is not affected by the e-platform's PB introduction decision. High revenue-sharing rate is conducive only when the difference in consumer preference between the PB and the national brand (NB) is small. The NBM's risk aversion will improve the applicability of the marketplace mode. For the e-platform, high PB preference of consumers and risk-averse behavior of the NBM is not conducive to PB introduction. For the supply chain, scenarios that the NB monopolizes the market under the wholesale mode and PB introduction under the marketplace mode should be prevented. PB introduction under the wholesale mode will become the only equilibrium with the increase of risk aversion of the NBM. Finally, the authors extend the scenario that consumers prefer the PB and the e-platform is risk-averse enterprise and find that PB introduction under the wholesale mode is detrimental to the NBM but beneficial to the supply chain. The impact of consumers' PB preference on the e-platform's PB introduction is opposite to the basic model. The impact of the e-platform's risk aversion on game equilibrium is opposite to that of the NBM's risk aversion.

This paper is first to study selling mode decision and PB introduction decision when considering enterprises' risk-averse attitude.

Current modellings of granular collapse are lack of considering the effect of soil density. This paper aims to present a numerical method to analyse the collapse of granular column based on the critical-state soil mechanics.

In the proposed method, a simple critical-state based constitutive model is first adopted and implemented into a finite element code using the coupled Eulerian–Lagrangian technique for large deformation analysis. Simulations of column collapse with various aspect ratios are then conducted for a given initial soil density. The effect of aspect ratio on the final size of deposit morphology, dynamical collapse profiles and the stable region is discussed comparing to experimental results. Moreover, complementary simulations with various initial soil densities on each aspect ratio are conducted.

Simulations show that a lower value of initial density leads to a lower final deposit height and a longer run-out distance. The simulated evolutions of kinetic energy and collapsing profile with time by the proposed numerical approach also show clearly a soil density-dependent collapse process.

To the end, this study can improve the understanding of column collapse in different aspect ratios and soil densities, and provide a computational tool for the analysis of real scale granular flow.

The originality of this paper is proposed in a numerical approach to model granular column collapse considering the influences of aspect ratio and initial void ratio. The proposed approach is based on the finite element platform with coupled Eulerian–Lagrangian technique for large deformation analysis and implementing the critical-state based model accounting for the effect of soil density.