The paper presents further developments of the boundary element technique for solving three-dimensional problems of piecewise homogeneous elastic media containing multiple cracks of arbitrary non-planar shapes (previous results were reported in [1, 2]). In the developed technique, the elastic fields are represented by integral identities. Triangular elements are used to discretize the boundaries and polynomial (linear and quadratic) approximations of the unknown variables are adopted. In-plane components of the fields and geometrical parameters are arranged in various complex-valued combinations to simplify the integration. No singular integrals are involved since the limit, as the field point approaches the boundary, is taken after the integration. Analytical integration over each element is reduced to that over the contour of the element via application of Cauchy- Pompeiu representation . The collocation method is used to set up the system of linear algebraic equations to find the boundary unknowns. Geoengineering applications of the method are discussed.
: A fully implicit method for coupled fluid flow and geomechanical deformation in fractured porous media is presented. Finite-volume and finite-element discretization schemes are used, respectively, for the flow and mechanics problems. The discrete flow and mechanics problems share the same conformal unstructured mesh. The network of natural fractures is represented explicitly in the mesh. The behavior of the fractured medium due to changes in the fluid pressure, stress, and strain fields is investigated. The methodology is validated using simple cases for which analytical solutions are available, and also using more complex "realistic" test cases.
In this paper, we compare methods of analysing the instability of an underground wedge that is characterised by uncertain parameters, and draw conclusions regarding the ability of the methods to propagate uncertainty through the problem. Assessment of underground rock wedge instability is a common problem in tunnelling and mining operations, and particularly during the early stages of a project may need to be performed when little or no objectively measured information is available. Such lack of information represents epistemic uncertainty, and although it is often analysed using an aleatory (e.g. probabilistic) model, this is known to be inappropriate. Here, we use the vertex method – an extension of interval mathematics – to show how epistemic uncertainty can be propagated through the analysis. We also discuss the implications of using the vertex method as a means of efficiently allocating resources to additional investigation and testing.
Because of relatively recent decisions by the current administration and its renewed assessment of the nuclear life-cycle, the various deep geologic disposal medium options are once again open for consideration. This paper focuses on addressing the favorable creep properties and behavior of rock salt, from the computational modeling perspective, as it relates to its potential use as a disposal medium for a deep geologic repository. The various components that make up a computational modeling capability to address the thermo-mechanical behavior of rock salt over a wide range of time and space are presented here. Several example rock salt calculations are also presented to demonstrate the applicability and validity of the modeling capability described herein to address repository-scale problems. The evidence shown points to a mature computational capability that can generate results relevant to the design and assessment of a potential rock salt HLW repository. The computational capability described here can be used to help enable fuel cycle sustainability by appropriately vetting the use of geologic rock salt for use as a deep geologic disposal medium.
Conventional stability analysis of rock slopes during earthquakes is often confined to vertically propagated ground motions. One of the main reasons for the limitation is due to the lack of a rational yet simple way to apply an input motion of a specific incident angle. In this study a method of ground motion input was implemented for this application in analyzing a jointed rock slope. In a nutshell, it involved extending a problem domain by wrapping it with an elastic region and converting the incident waves into nodal forces in addition to make a boundary non-reflecting. The approach is general, but here only the plane strain problem was tackled and thus only two dimensional P-wave was considered. A jointed rock is defined by an elastic modulus, a Poisson ratio, the joint orientations and the strength of the joints. A 1:1 jointed rock slope of 30 m in height was used as the base rock slope. An El Centro record of 1979 was employed as the base ground motion. Three incident angles were considered in the analysis. Results obtained indicated that incident angles do have a significant impact on the stability of a jointed rock slope, and the severity of the impact depended on the relative orientation of the incident wave with respect to that of the joints.
This paper presents a numerical implementation of the coupled hydro-thermal-mechanical logic in the commercial code FLAC3D. The numerical model uses the Boussinesq approximation in which fluid density variations are neglected in all but the body force term of the equation of motion. The numerical solution is compared to an analytical solution (obtained using stability analysis) for a convection cell in a confined layer heated from below. Numerical simulation examples are presented to illustrate the development of various cell configurations in a layered system heated from below. The numerical model can be applied to the analysis of geothermal groundwater convection in sedimentary basins. The study of the convection mechanism is important because it provides a natural heat exchanger that can be accessed without engineered hydraulic fracturing because of high natural permeability.
The present work initially presents an overview and the theoretical background of the Material Point Method (MPM) and details of its numerical implementation for coupled fluid-mechanical problems. This method is particularly useful when analyzing large strain problems in solid/fluid media including coupled problems, in particular, for geomechanical and geological media. The method possesses both Eulerian and Lagrangian characteristics which makes it suitable for the solution of a number of problems especially when compared to the usual techniques such as the Finite Element Method (FEM). Using the FEM, sometimes remeshing can make the analysis of certain problems particularly cumbersome. In particular, in the present work the MPM is used firstly for the determination of the complete failure pattern of openings, from the initiation until its complete closure, in two different scales, laboratory and tunnel lengths. This problem may involve large strains and contact situations. The last example includes fluid-mechanical coupling under dynamic conditions. Here, the dynamic effects associated with the impact of a rock block in a saturated porous media in a slope is evaluated.
The mechanical properties of rocks are essential for analysis of different problems during oil and gas drilling and production and future development. These properties are required for borehole stability, sand production, and select optimum flow rate during the completion stage and many other problems related with the short and long term mechanical stability of the well and the reservoir. The correct predictions may help in saving millions of dollars in drilling and completions costs, and may allow preventing long term and costly consequences. A common problem in oil and gas industry is the unavailability of the real core samples. To overcome this problem the engineers struggle to develop alternative sources of data via correlations, log measurements, etc. In this study, a simple scratching cell was developed and data produced was used to develop a correlation for predicting the unconfined compressive strength (UCS) for Saudi Arabian rocks.
The output of this paper is a great addition to the rock mechanics and petroleum engineering disciplines especially in Borehole instability problems during drilling of oil and gas wells.
The stress intensity factor at a fracture tip in a porous medium subjected to a fluid injection is studied. This factor evolves during the transient flow phase and tends to a limit value for the steady state. For simple fracture geometries without propagation and for constant injection pressures, finite element simulations show that this factor reaches its maximum value in the steady state regime. This result allows simplifying significantly the study and modeling of hydraulic fracture propagation because the determination of the steady flow solution is much easier and faster than the transient flow. In addition, some couplings between hydraulic and mechanical problems disappear under steady state flow and make it possible to establish some closed-form approximate expressions. These can be useful especially in the context of CO2 sequestration projects where the fluid injection is pressure-controlled.