Showing papers on "Discontinuity (geotechnical engineering) published in 2011"

Thermomechanical forcing of deep rock slope deformation: 1. Conceptual study of a simplified slope

Abstract: [1] Thermo-elastic rock slope deformation is often considered to be of relatively minor importance and limited to shallow depths subject to seasonal warming and cooling. In this study, we demonstrate how thermomechanical (TM) effects can drive rock slope deformation at greater depths below the annual thermal active layer. Here in Part 1 of two companion papers, we present 2D numerical models of a simplified slope subject to annual surface temperature cycles. The slope geometry and discontinuity sets are loosely based on the Randa instability considered in detail in Part 2. Results show that near-surface thermo-elastic stresses can propagate to depths of 100 m and more as a result of topography and elasticity of the rock mass. Shear dislocation along discontinuities can have both a reversible component controlled by discontinuity compliance and, provided that the stress state is sufficiently close to the strength limit, an irreversible component (i.e., slip). Induced slip increments are followed by stress redistribution resulting in the propagation of slip fronts. Thus, deformation and progressive rock slope failure can be driven solely by thermomechanical forcing. The influence of TM-induced stress changes becomes stronger for increasing numbers of critically stressed discontinuities and is enhanced if failure of discontinuities involves slip-weakening. The net TM effect acts as a meso-scale fatigue process, involving incremental discontinuity slip and hysteresis driven by periodic loading.

Seismic response of a single and a set of filled joints of viscoelastic deformational behaviour

Abstract: Rock joints are often filled with weak medium, for example, saturated clay or sand, of viscoelastic nature. Their effects on wave propagation can be modelled as displacement and stress discontinuity conditions. The viscoelastic behaviour of the filled joint can be described by either the Kelvin or the Maxwell models. The analytical solutions for wave propagation across a single joint are derived in this paper by accounting for the incident angle, the non-dimensional joint stiffness, the non-dimensional joint viscosity and the acoustic impedance ratio of the filled joint. It is shown that the viscoelastic behaviour results in dissipation of wave energy and frequency dependence of the reflection and transmission coefficients. Based on curve fitting of the experimental data of P-wave propagation across a single joint filled with saturated sand, both the Kelvin and Maxwell models are found to reproduce the behaviour of the filled joint, in terms of the amplitude and frequency contents. Then, wave transmission across a filled joint set is studied with the virtual wave source method and the scattering matrix method, where multiple wave reflections among joints are taken into account. It is shown that the non-dimensional joint spacing and the number of joints have significant effects on the transmission coefficients.

A discrete fracture model for two-phase flow with matrix-fracture interaction

Abstract: This article introduces a model for incompressible, two-phase flow in a porous medium with a fracture. The model is an extension to the case of two-phase flow of the model for single phase flow described in [1]. The model is a discrete fracture model in which the fractures are treated as interfaces of dimension n - 1 but in which there is fluid exchange between the fracture and the surrounding rock matrix. The matrix domain is effected by the fracture flow through a Robin type boundary condition along both sides of the fracture, while the fracture takes into account the flow in the matrix by means of a source term representing the discontinuity across the fracture of the flux. Twophase flow is modeled using the global pressure formulation in which the unknowns are the global pressure and the wetting phase saturation; see [2]. The case of different rock types in the (n - 1)-dimensional fracture domain and in the n-dimensional matrix rock domain is considered.

Hydraulic-Fracture Propagation in a Naturally Fractured Reservoir

Abstract: This paper (SPE 128715) was accepted for presentation at the SPE Oil and Gas India Conference and Exhibition, Mumbai, India, 20–22 January 2010, and revised for publication. Original manuscript received 17 February 2010. Revised manuscript received 20 July 2010. Paper peer approved 17 August 2010. Summary We present the results of numerical modeling that quantify the physical mechanisms of mechanical activation of a natural fault because of contact with a pressurized hydraulic fracture (HF). We focus on three stages of interactions: HF approaching, contact, and subsequent infiltration of the fault. Fracture interaction at the contact is shown to depend on four dimensionless parameters: net pressure in the HF, in-situ differential stress, relative angle between the natural fault and the HF, and friction angle of the natural fault. A numerical model based on the displacement discontinuity method (DDM) allowing for fracture closure and Mohr-Coulomb friction was used to calculate the displacements and stresses along the natural fracture as a result of the interaction with the pressurized HF. The analysis of the total stress state along the fault during the HF coalescence stage makes it possible to define a criterion for reinitiation of a secondary tensile crack from the natural fault. We show that the most probable location for tensile-crack initiation is the end of the open zone of the fault where the highest tension peak is generated by the HF contact. In our numerical analysis, we study the magnitude of maximum tensile stress and its position along the fault for a wide range of key dimensionless parameters. Given real reservoir properties, these measurements can be used to detect the possible fracturing scenarios in naturally fractured reservoirs. Using simplified uncoupled modeling of fluid penetration into the fault after the contact with the HF, we demonstrate that either an increase or a decrease of the tensile stress at the opposite side of the fault can be realized depending on the ratio of increments of net pressure and the fluid front as it penetrates the natural fault.

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

Abstract: South Peak is a 7-Mm3 potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.

Geometrical Acoustics I: The Theory of Weak Shock Waves

Abstract: In the first part the discontinuity conditions in an arbitrary continuous material are deduced for a general (i.e., possibly curved) discontinuity surface. It is then shown that only three types of discontinuities are possible—shocks, contact discontinuities, and phase‐change fronts. In the second part the acoustic discontinuity conditions are deduced and specialized to a perfect fluid without heat conduction. Then a first‐order partial differential equation is obtained for the location of an acoustic shock front. This equation can be solved, as in optics, by means of rays. The variation of shock strength along a ray is then determined (this is one main result of this paper). Coefficients of reflection and transmission for an acoustic shock at a contact discontinuity in the basic flow are also obtained. Finally, the results are exemplified by an analysis of the shock tube.

Frictional slip plane growth by localization detection and the extended finite element method (XFEM)

Abstract: This paper is concerned with developing a numerical tool for detecting instabilities in elasto-plastic solids (with an emphasis on soils) and inserting a discontinuity at these instabilities allowing the boundary value problem to proceed beyond these instabilities. This consists of implementing an algorithm for detection of strong discontinuities within a finite element (FE) framework. These discontinuities are then inserted into the FE problem through the use of a displacement field enrichment technique called the extended finite element method (XFEM). The newly formed discontinuities are governed by a Mohr–Coulomb frictional law that is enforced by a penalty method. This implementation within an FE framework is then tested on a compressive soil block and a soil slope where the discontinuity is inserted and grown according to the localization detection. Copyright © 2010 John Wiley & Sons, Ltd.

Analysis of stochastic seismic wave interaction with a slippery rock fault

Abstract: Stochastic seismic wave interaction with a slippery rock fault is studied, based on the principle of conservation of momentum at the wave fronts along the fault. By using the displacement discontinuity method, the wave propagation equations are derived for incident longitudinal-(P-) and shear-(S-) waves, respectively. This is an extension of the study by Li and Ma (2010) for blast-induced wave propagation across a linear rock joint. Stochastic seismic waves are generated from a frequency spectrum and used to analyze the seismic wave interaction with a rock fault having a Coulomb-slip behavior. Parametric studies are carried out to investigate the effect of the intensity and impinging angle of the incident seismic waves on wave propagation across a slippery rock fault. Results show that the transmission of the incident P-wave is almost not affected by the fault, on the contrary, this is not the case for an incident S-wave, due to the occurrence of a relative slip which is related to the impinging angle of the incident S-wave. A quantitative study is presented which is of help in understanding the propagation and attenuation laws of seismic waves in discontinuous rock masses.

Continuous-discontinuous formulation for ductile fracture

Abstract: In this contribution, a continuum-discontinuum model for ductile failure is presented. The degradation of material properties through deformation is described by a Continuum Damage Mechanics model, which uses a non-local integral formulation to avoid mesh dependence. In the final stage of failure, the damaged zone is replaced by a macro crack for a more realistic representation of the phenomenon. The inclusion of the discontinuity surfaces is performed by the XFEM and Level Set Method to avoid the spurious damage growth typical of this class of models.

Bifurcation analysis for a rate-sensitive, non-associative, three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials: Part I. Small strain

Abstract: Localized deformations such as shear bands, compaction bands, dilation bands, combined shear/compaction or shear/dilation bands, fractures, and joint slippage are commonly found in geomaterials like soil and rock. Thus, modeling their inception, development, and propagation, and effect on mechanical response of the body or structure is important. The paper will focus on one, now classical, analysis method for modeling the inception of these localized deformations for a rate-sensitive, non-associative, three-invariant, isotropic/kinematic hardening cap plasticity model. Bifurcation analysis, in terms of continuous and discontinuous conditions (Int. J. Solids Struct. 1980; 16:597–605), provides the mathematical conditions under which a localized deformation mode could be admissible, and it should not to be confused with attempting to model the microstructural evolution of the geomaterial as it transitions from a nearly uniform to localized deformation response at a material point. Analysis determines that continuous and discontinuous bifurcation are different for weak discontinuity and the same for strong discontinuity, and such conditions are identified for the plasticity model. Rate sensitivity will preclude bifurcation regardless of viscosity value. Numerical examples demonstrate various plasticity model features that enable detection of localization using bifurcation analysis. All analyses are conducted currently in the small strain regime. Copyright © 2010 John Wiley & Sons, Ltd.

A new approach to plane failure of rock slope stability based on water flow velocity in discontinuities for the Latian dam reservoir landslide

Abstract: The stability of slopes is always of great concern in the field of rock engineering. The geometry and orientation of pre-existing discontinuities show a larger impact on the behavior of slopes that is often used to describe the measurement of the steepness, incline, gradient, or grade of a straight line. One of the structurally controlled modes of failure in jointed rock slopes is plane failure. There are numerous analytical methods for the rock slope stability including limit equilibrium, stress analysis and stereographic methods. The limiting equilibrium methods for slopes under various conditions against plane failure have been previously proposed by several investigators. However, these methods do not involve water pressure on sliding surfaces assessments due to water velocity and have not yet been validated by case study results. This paper has tried to explore the effects of forces due to water pressure on discontinuity surfaces in plane failure through applying the improved equations. It has studied the effect of water flow velocity on sliding surfaces in safety factor, as well. New equations for considering water velocity (fluid dynamics) are presented. To check the validity of the suggested equations, safety factor for a case study has been determined. Results show that velocity of water flow had significant effect on the amount of safety factor. Also, the suggested equations have higher validity rate compared to the current equations.

3-D Discontinuity Orientations using Combined Optical Imaging and LiDAR Techniques

Abstract: The importance of the collection and analysis of data on discontinuities cannot be overemphasized. Problems which include sampling difficulties, risks, limited access to rock faces and exposures, and the delay in data collection has led to a high need for data collection tools and analysis techniques that can overcome these problems. Great developments have been made towards automated measurements using both optical imaging and LiDAR scanning methods but there is still more room for improvement. Discontinuities manifest themselves as „facets‟ that can be measured by LiDAR or fracture „traces‟ that can be measured from optical imaging methods. LiDAR scanning alone cannot measure „traces‟ neither can optical imaging methods measure „facets‟. This is complicated by the fact that both „facets‟ and „traces‟ are often present in the same rock cut, making the selection of an appropriate measuring tool very difficult if not impossible. In this paper, we present our research on the development of robust software to determine 3-D discontinuity orientations from combined LiDAR and optical imaging techniques. Figure 1.1. (a) Example of wedge , (b) planar , and (c) toppling failures along road cuts. discontinuity plane, is assigned to a discontinuity set by using cluster analysis. Cluster analysis techniques are described in detail by Maerz and Zhou [5, 8, 9, 10,11]. The orientations can be and have been traditionally measured using manual compass and clinometer methods. These methods are however slow, tedious and cumbersome, and in some cases dangerous because of potential falling rock, and are often limited to easily accessible locations like the base of the slope. Figure 1.2: Orthogonal nature of joint sets. Measurements of the “cracks” or discontinuities are displayed in Figure 1.3 Figure 1.3: Projections of vectors normal to discontinuity plane on a unit lower hemisphere, clustered into three sets. Once having identified the graphical or computational techniques can be used to determine the kinematic feasibility of failure (Figure 1.4) and standard modeling techniques such as limiting equilibrium analysis can be used to determine if failure will indeed take place (Figure 1.5). Figure 1.4: Planar failure geometry (left) and graphical method of determining if slide failure is kinematically possible [6]. Figure 1.5: Limiting equilibriums analysis applied to planar features (left) and wedge features (right) [6]. 1.3. Surface Expressions of Discontinuities The discontinuities or cracks in the rock mass, when exposed in an outcrop or cut manifest themselves in one of two ways, often in both ways on the same exposure: 1. On flat planar rock cuts, the intersection of the plane of the discontinuity and the planar rock cut results in a visible line (fracture trace) that lies on both planes (Figure 1.6). 2. On rock cuts that are irregular, the actual faces of the discontinuities are exposed. These fracture surfaces can be considered to be like “facets” on a cut precious stone (Figure 1.6). There are emerging techniques to measure joint orientations for each of these situations, however, two completely different techniques are required for the two types of discontinuity expressions. What is worse is that, in at least one of the methods, the mere presence of the opposite type of fracture expression makes the technique unusable. Even though often both expressions are present, there is to date no legitimate way to combine the two techniques. (a) (b) (c)

Formation and Growth of the Crack in Bonded Joints Under Mode I Fracture: Substrate Deflection at Crack Vicinity

Abstract: Adhesive bonding is now commonly used in aircraft, cars, boats, etc. In these applications, thin panels are often bonded. In such thin structures, heterogeneous mechanical loading along the bondline edge (or potential crack front) is likely to arise due to 3D structural effects. The crack front and its vicinity is a special region, in that it is where structural properties of the adherend material meet those of the adhesive (discontinuity). To investigate the stress distribution in this region, we have observed the deflection of a flexible adherend in an asymmetric wedge bonded joint loaded in Mode I. A sensitive laser profilometry technique was used to observe the main vertical beam displacement and curvature along the length, as well as the resulting transverse, or anticlastic effect, due to Poisson's ratio. From this analysis is evaluated the heterogeneous tensile stress distribution in the adhesive in the vicinity of the crack front.

Extended Finite Element Method for hygro-mechanical analysis of crack propagation in porous materials

Abstract: In computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Folding in regions of extension

Abstract: SUMMARY Many extension zones have been subjected to folding and shortening in a direction perpendicular to the stretching. Such deformation can be accounted for by the extension of a thin superficial elastic layer overlying a substrate that has small elastic moduli or that deforms in a viscous regime. Laboratory experiments are used to document the wavelength and amplitude of the folds for a range of geometrical configurations. Folding is observed even for very small amounts of extension (less than 1 per cent) with characteristics that are consistent with finite-amplitude scaling laws. Because of the intrinsically 3-D nature of the deformation field, the size of the region affected by folding and the direction of the fold axes depend on the orientation of the extension with respect to the rigid blocks that bound the deforming region. For regions of extension where the elastic thickness is about 10 km, as in the Basin and Range province for example, it is predicted that folding occurs with wavelengths in a 20–40 km range, such that it induces little deformation in the lower crust and maintains a flat Moho discontinuity. These predictions are consistent with the observations. The characteristics of faulting that is associated with such deformation are discussed.

Extended finite element simulation of crack propagation in fractured rock masses

Abstract: The extended finite element method (XFEM) is a new numerical method for modelling discontinuity. The application of XFEM in simulating crack propagation in rock masses is investigated. This method greatly eases the modelling of crack propagation as no remeshing is required. The application of XFEM to rock mechanics is presented. A two‐dimensional and a three‐dimensional numerical examples are compared with the experimental results from the literature and good agreements are reached. The XFEM proves to be a promising powerful tool in modelling discontinuities in rock masses.