Generalized stress field in granular soils heap with RayleigheRitz method

The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.

Wmic-GMTS and Wmic-GMERR criteria for micron-scale crack propagation in red-bed soft rocks under hydraulic action

Micron-scale crack propagation in red-bed soft rocks under hydraulic action is a common cause of engineering disasters due to damage to the hard rockesoft rockewater interface.Previous studies have not provided a theoretical analysis of the length,inclination angle,and propagation angle of micron-scale cracks,nor have they established appropriate criteria to describe the crack propagation process.The propagation mechanism of micron-scale cracks in red-bed soft rocks under hydraulic action is not yet fully understood,which makes it challenging to prevent engineering disasters in these types of rocks.To address this issue,we have used the existing generalized maximum tangential stress(GMTS)and generalized maximum energy release rate(GMERR)criteria as the basis and introduced parameters related to micron-scale crack propagation and water action.The GMTS and GMERR criteria for micronscale crack propagation in red-bed soft rocks under hydraulic action(abbreviated as the Wmic-GMTS and Wmic-GMERR criteria,respectively)were established to evaluate micron-scale crack propagation in redbed soft rocks under hydraulic action.The influence of the parameters was also described.The process of micron-scale crack propagation under hydraulic action was monitored using uniaxial compression tests(UCTs)based on digital image correlation(DIC)technology.The study analyzed the length,propagation and inclination angles,and mechanical parameters of micron-scale crack propagation to confirm the reliability of the established criteria.The findings suggest that the Wmic-GMTS and Wmic-GMERR criteria are effective in describing the micron-scale crack propagation in red-bed soft rocks under hydraulic action.This study discusses the mechanism of micron-scale crack propagation and its effect on engineering disasters under hydraulic action.It covers topics such as the internal-external weakening of nano-scale particles,lateral propagation of micron-scale cracks,weakening of the mechanical properties of millimeter-scale soft rocks,and resulting interface damage at the engineering scale.The study provides a theoretical basis for the mechanism of disasters in red-bed soft-rock engineering under hydraulic action.

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

ON THE RESPONSE FUNCTIONALS OF MATERIALS FOR THE IRREVERSIBLE PROCESSES OF THERMODYNAMICS

Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equations of the general-ized stress and entropy associated ivith the time and temperature are derived for the irreversible process of thermoviscoelastic-plastic materials. As an example, the response functionals of Maxwell viscoelastic materials are obtained.

Extending application of asymmetric semi-circular bend specimen to investigate mixed mode Ⅰ/Ⅱ fracture behavior of granite

The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.However,there are few studies on the fracture toughness determination of rock materials.In this work,a series of fracture tests were performed with the ASCB specimens made of granite.The onset of fracture,crack initiation angle and crack propagating trajectory was analyzed in detail combined with several mixed mode fracture criteria.The influence of the crack length on the mode Ⅰ/Ⅱ fracture toughness was studied.A comparison between the fracture toughness ratios predicted by varying criteria and experimental results was conducted.The relationship between experimentally determined crack initiation angles and curves of the generalized maximum tangential stress(GMTS)criterion was obtained.The fracture process of the specimen was recorded with the high-speed camera.The shortcomings of the ASCB specimens for the fracture toughness determination of rock materials were discussed.The results may provide a reference for analysis of mixed mode I and II fracture behavior of brittle materials.

LARGE EDDY SIMULATION (LES) OF TURBULENT FLOW BY FINITE DIFFERENCE METHOD

A Large Eddy Simulation (LES) technique was applied to solve the turbulentchannel flow for Re_τ = 150 . Three types of turbulence models are employed, such as theSmagorinsky model, the Dynamic Sub-Grid Scale(SGS) model and the Generalized Normal Stress (GNS)model. The simulated data in time series for the LES were averaged in both time and space to carryout the statistical analysis. Results of LES were compared with that of a DNS. As an application, aLES technique was used for 2D body in order to check the validation by investigating the turbulentvortical motion around the afterbody with a slant angle.