An extended micromechanical-based plastic damage model for understanding water effects on quasi-brittle rocks

Water effects on the mechanical properties of rocks have been extensively investigated through experiments and numerical models.However,few studies have established a comprehensive link between the microscopic mechanisms of water-related micro-crack and the constitutive behaviors of rocks.In this work,we shall propose an extended micromechanical-based plastic damage model for understanding weakening effect induced by the presence of water between micro-crack’s surfaces on quasi-brittle rocks,based on the Mori-Tanaka homogenization and irreversible thermodynamics framework.Regarding the physical mechanism,water strengthens micro-crack propagation,which induces damage evolution during the pre-and post-stage,and weakens the elastic effective properties of rock matrix.After proposing a special calibration procedure for the determination of model parameters based on the laboratory compression tests,the proposed micromechanical-based model is verified by comparing the model predictions to the experimental results.The model effectively captures the mechanical behaviors of quasibrittle rocks subjected to the weakening effects of water.

ANALYSIS ON THE COHESIVE STRESS AT HALF INFINITE CRACK TIP

The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function . The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are given.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

Validation of surface coating with nanoparticles to improve the flowability of fine cohesive powders

Fluidization of fine cohesive powders is seriously restricted by the strong interparticle cohesion. The rational combination of nanoparticles with fine cohesive powders is expected to obtain composite par- ticles with improved flowability. In this work, we firstly reviewed the sandwich and three-point contact models regarding the fundamental principles of nano-additives in reducing cohesiveness. Based on these previous models, the effects of the size of nanoparticles, their agglomeration and coverage on the surface of cohesive powders in reducing interparticle forces were theoretically analyzed. To validate the the- ory effectiveness for the irregularly shaped cohesive powders, an extreme case of cubic powders coated with silica nanoparticles was fabricated, and the flowability of the composite particles was determined experimentally. Ultimately, based oN force balance of a single particle, a semi-theoretical criterion for predicting the fluidization behavior of coated powders was developed to guide the practical applications of improving the flowability of cohesive powders through structural design and modulation.

Two-fluid modeling of Geldart A particles in gas-fluidized beds

We have investigated the effect of cohesion and drag models on the bed hydrodynamics of Geldart A particles based on the two-fluid （TF） model. For a high gas velocity U0 = 0.03 m/s, we found a transition from the homogeneous fluidization to bubbling fluidization with an increase of the coefficient C1, which is used to account for the contribution of cohesion to the excess compressibility. Thus cohesion can play a role in the bed expansion of Geldart A particles. Apart from cohesion, we have also investigated the influence of the drag models. When using the Wen and Yu drag correlation with an exponent n = 4.65, we find an under-prediction of the bed expansion at low gas velocities （U0 = 0.009 m/s）. When using a larger exponent （n = 9.6）, as reported in experimental studies of gas-fluidization, a much better agreement with the experimental bed expansion is obtained. These findings suggest that at low gas velocity, a scale-down of the commonly used drag model is required. On the other hand, a scale-up of the commonly used drag model is necessary at high gas velocity （U0 = 0.2 and 0.06 m/s）. We therefore conclude that scaling the drag force represent only an ad hoc way of repairing the deficiencies of the TF model, and that a far more detailed study is required into the origin of the failure of the TF model for simulating fluidized beds of fine powders.

Simulations of ice jam thickness distribution in the transverse direction

River ice often forms in the cold regions of northern hemisphere which can lead to ice jams （or ice dams）. Water level can be significantly raised due to ice jams. As a consequence, disastrous ice flooding may be resulted, such as the ice jam flooding in the Nechako River in Prince George in winter 2007-2008. In the present study, the equations describing the ice jam thickness in the transverse direction are derived. The impact of the secondary vortex is considered while the cohesive force within ice cubes is neglected in the model. The relationship between the parameter β and the total water depth is established based on the assumption that all other variables except the velocities are kept constant on the same cross section. By using the parameter β and the developed equations, the ice jam thickness in the transverse direction can be predicted. The developed model is used to simulate the ice jam thickness in the transverse direction at the Hequ Reach of the Yellow River in China. The simulated ice jam thicknesses agree well with the field measurements on different cross sections.