Modelling size effect on rock aggregates strength using a DEM bonded-cell model

Empirical evidence has shown that particle breakage affects the mechanical behaviour of granular materials. The source of this mechanism takes place at the particle scale, and the main consequence on the macromechanical behaviour is increasing compressibility. Due to the inverse correlation between particle size and particle crushing strength, coarse rockfill materials are particularly vulnerable to mechanical degradation due to particle breakage. However, such coarse materials do not fit in standard laboratory devices, and the alternative of large sample testing is usually unavailable or too expensive. Alternatively, recent works have proposed multi-scale approaches using the discrete element method (DEM) to carry out numerical testing of coarse crushable materials, although few studies have focused on size effects. This article presents the application of a DEM bonded-cell model to study particle size-strength correlation on angular rock aggregates. Each particle is modelled by a cluster of perfectly rigid polyhedral cells with Mohr–Coulomb contact law. Constant cell density within particles implies that the presence of potential fragmentation planes increases with size. Therefore, particle strength decreases with size. A comprehensive sensitivity analysis was carried out through 1477 particle crushing simulations in a given particle size. Based on published experimental data on calcareous rock aggregates, part of the simulations were used for calibration, and 97 additional simulations of a coarser size fraction were performed for validation. The results show a good agreement with the empirical data in terms of size effect and data scatter through Weibull statistics.

     

Response surface methodology for lead biosorption on Aspergillus terreus

A central composite face-centered design was used to study and to optimize lead biosorption from aqueous solution on Aspergillus terreus biomass. Four factors such as stirring speed, temperature, solution pH and biomass dose at different levels were studied.The hierarchical quadratic model were established by adding replicates at the central point and axial points to the initial full factorial design (2⁴). The percentage removal of lead was affected by biomass dose, pH, and interactions between pH and biomass dose, pH and stirring speed, pH and temperature. The hierarchical quadratic model described adequately the response surface based on the adjusted determination coefficient (R² _Adj= 0.97) and the adequate precision ratio (42.21). According to this model, the optimal conditions to remove lead completely from aqueous solutions (at initial lead concentration of 50 mg/L and solutions of 100 mL) with Aspergillus terreus were at pH 5.2, 50 °C, stirring speed of 102/min and a biomass dose of 139 mg.The response surface methodology can be used to determine the optimal conditions for metal adsorption on several adsorbents. In addition, results reported in this research demonstrated the feasibility of employing A. terreus as biosorbent for lead removal.