Coupled stress-flow

Experimental studies on coupled stress- flow of single rock fractures... 

Hybrid model of Discrete Fracture Network (DFN) and Discrete Element Method (DEM) for coupled stress-flow analysis of rock slope stability (Wang, 2000) ... 

In terms of numerical methods, the dominance by FEM with equivalent continuum approach might not be most suitable for sparsely or moderately fractured hard rocks and more advanced methods and codes using discrete approach are needed. The issue of applicability of the equivalent media approach, the associated scale effects, and uncertainty evaluations need to be fully explored. The processes are dominated by coupled stress-flow problems and effects of thermo-chemical effects need more attention. More works for soils, clays, sands and other similar media, which are equally, if not more, important in the fields of geo-engineering and environments, seem also needed. 

For the basic equations of coupled stress-flow analysis mentioned above, it is very difficult to solve them in closed-form. The transposition method of progression and integration can only be applied for problems of boundary value problems of simple geometry and boundary conditions. Therefore the finite element method (FEM) is used to solve the coupled partial differential equations in this paper. 

The FEM modelling was applied for the simulating the dam behaviour with coupled stress-flow effects under different loading cases according to the water level variations. The tangential displacements of Longyangxia dam s typical dam section on April 16, 1989, April 16, 1990, and April 16, 1996, and December 31, 1999 were calculated and compared with measured data. The results are listed in Table 2 and illustrated in Figure 4. 

The couple stress method can be used for modeling a special case of micro-polar fluids, i.e., the two-phase flow, wherein the constitutive equation is given by [22,34-38]... 

C.J. Greenshields, H.G. Weller, A. Ivankovic, The Finite Volume Method for Coupled Fluid Flow and Stress Analysis, Computer Modeling and Smubtion in Engineering, 4, (1999), 213-218. 

Fig. 2 shows a horizontal cross-section through NGFs coupled shear flow test (CSFT) cell. This biaxial cell allows fractured samples (14 x 12 x 5 cm) to be displaced by a maximum 8 mm under controlled fracture normal stresses and temperatures up to 80°C. Variation in fracture aperture (dilation) is measured by a total of four displacement gages, whereas shear displacement is measured by a total of two gages. The flow measurements, as illustrated in Fig. 2, measure the total flow in the direction of the fracture plane and do not differentiate between fracture and matrix flow. To quantify the matrix flow component, tests on non-fractured samples with the same principal geometry as the fractured tests and under the same stress conditions, were conducted in the CSFT cell. 

Fig. 3 shows a vertical cross-section of NGI s triaxial coupled shear flow test (TCSFT) cell. This modified triaxial cell allows higher confining stresses and the testing of smaller samples compared to the CSFT cell. The tested samples had a diameter of... 

In the case of heat transfer analysis, axial temperature distribution, shown in Figure 3 are specified for the surfaces of both He and sulfuric flow cannels, considering heat transfer coefficients. And outer surface of block is modeled as adiabatic condition. Figures 5 and 6 show the temperature and the stress distributions in the block, respectively. The stress shown in Figure 6 is a coupled stress with thermal stress and static stress caused by the operating pressure difference between He and sulfuric acid. Analytical conditions are as follows ... 

Su B, Zhan M and Wang Y. 1997. Experimental study on the coupled stress and fluid flow in fractured rock masses. Chinese J. of Geotech. Engng., 19(4), pp. 73-77. 

Wu Y. 1996. The coupled stress-ground water flow-model for jointed rock mass. J. of Geological Hazards Environmental... 

Wu Y and Zhang Z. 1996. An application of generalized double porosity media model for coupled stress and groundwater flow analysis in fractured rock mass. J. of Engineering Geology, 1(3), pp. 40-46. 

How large a cavity can exist at depth in an intact sandstone or in a dilated and yielded sand This question is a coupled mechanics-flow issue involving seepage forces acting at the local scale (cm), pore pressure variations acting at a larger scale (m), and stress redistribution at all scales. 

Oda, M., 1986. An Equivalent Continuum Model for Coupled Stresses and Fluid Flow Analysis in Jointed Rock Masses, Water Resour. Res. 22,... 

Oda, M., 1986. An equivalent continuum model for coupled stress and fluid flow analysis and jointed rock masses. Water Resources Research, V. 22, No. 13, pp. 1845-1856. 

Recognizing the importance of the coupled hydro-mechanical effects on the performance of civil engineering structures involving fractured rocks, the stress-flow coupling mechanism of the dam-foundation system at Longyangxia site was simulated using a three-dimensional Finite Element code, supported by two visco-elastic constitutive models to represent the time-dependent material behaviour of the dam concrete and the foundation rock. The calculated results were concord with the measured ones and helped to interpret the causes of this continuous displacement at the 13" dam section of the Longyangxia hydropower project, towards the left bank. 

The dynamics of the molten material in the extrusion head is a quite complex process involving the melting point of the materials coupled with flow processes and stresses which are in part related to the viscosity and surface energy as well as the design of the extruder. Most 3D printers use shear thinning materials that follow power-law viscosity models (7.4) ... 

Because stress corrosion cracking is a localized corrosion process, involving the spatial separation of the local anode (in the crack) and the local cathode (on the external surfaces), the phenomenon of IGSCC is expected to fall under the theoretical umbrella of the Differential Aeration Hypothesis (DAH), as depicted in Fig. 82. The DAH, which was first postulated by Evans in the 1920s and which has since been recognized as the theoretical basis for essentially all localized corrosion phenomena requires that, in order to maintain the spatial separation between the local anode and local cathode, a positive ionic coupling current flows through... 

When limiting our attention to low-molecular-weight nematics, we may expect that, in general, flow has the following effects (1) it alters the distribution of molecular orientations about the nematic axis (director) and (2) it affects the director itself. In other words, the velocity v(r) and the director n(r) are coupled under flow of nematic solutions. Next, we first present the expressions for stress, then discuss some important features of the Ericksen-Leslie theory, and finally show relationships existing between the six Leslie coefficients and three molecular parameters appearing in the Doi theory. The presentation of the entire Ericksen-Leslie theory (Ericksen 1960 Leslie 1966, 1968, 1979) is beyond the scope of this chapter. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

The concepts of interface rheology are derived from the rheology of three-dimensional phases. Characteristic for the interface rheology is the coupling of the motions of an interface with the flow processes in the bulk close to the interface. Thus, in interface rheology the shear and dilatational stresses of the interface are in equilibrium with the corresponding shear stress in the bulk. An important feature is the compressibility of the adsorption layer of an interface in contrast, the flow elements of the bulk are incompressible. As a result, compression or dilatation of the adsorption layer of a soluble surfactant is associated with desorption and adsorption processes by which the interface tends to reinstate the adsorption equilibrium with the bulk phase. 

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