Showing papers on "Discontinuity (geotechnical engineering) published in 2015"

Mechanisms and geologic significance of the mid-lithosphere discontinuity in the continents

Abstract: The continents have a puzzling structure — a transition occurs at mid-lithospheric depths. A synthesis of geological data indicates that stress-induced sliding along crystal grain boundaries may be responsible for the transition.

Thickness of the lithosphere beneath Turkey and surroundings from S-receiver functions

Abstract: . We analyze S-receiver functions to investigate variations of lithospheric thickness below the entire region of Turkey and surrounding areas. The teleseismic data used here have been compiled combining all permanent seismic stations which are open to public access. We obtained almost 12 000 S-receiver function traces characterizing the seismic discontinuities between the Moho and the discontinuity at 410 km depth. Common-conversion-point stacks yield well-constrained images of the Moho and of the lithosphere–asthenosphere boundary (LAB). Results from previous studies suggesting shallow LAB depths between 80 and 100 km are confirmed in the entire region outside the subduction zones. We did not observe changes in LAB depths across the North and East Anatolian faults. To the east of Cyprus, we see indications of the Arabian LAB. The African plate is observed down to about 150 km depth subducting to the north and east between the Aegean and Cyprus with a tear at Cyprus. We also observed the discontinuity at 410 km depth and a negative discontinuity above the 410, which might indicate a zone of partial melt above this discontinuity.

A simplified three-dimensional displacement discontinuity method for multiple fracture simulations

Abstract: The displacement discontinuity method (DDM) developed by Crouch (Int J Numer Methods Eng 10:301–343, 1976) is a popular form of the boundary element method and is widely used to model hydraulic fracture propagation. The two-dimensional displacement discontinuity method (2D DDM) has limitations with regard to the simulation of some practical fracture problems, which often require accounting for the three-dimensional (3D) nature of the fracture. A 2D method with a 3D correction factor proposed by Olson (The initiation, propagation, and arrest of joints and other fractures, vol 231. Geological Society of London Special Publication, London, pp 73–87, 2004) is able to account for 3D effects of a single fixed-height, embedded fracture. However, this correction factor proves inadequate for describing multiple fracture interaction. Greater accuracy is clearly possible with a truly three-dimensional displacement discontinuity method (3D DDM), but such an approach requires significantly higher computational time and memory, especially for simulating multiple fracture propagation. To enhance calculation efficiency and reduce memory usage, a novel, simplified 3D DDM approach is proposed. This method is simplified from 3D DDM through excluding non-vertical fractures and vertical components of shear stress, as well as eliminating the need for discretization in the vertical (height) direction by applying correction factors to improve fracture-induced stresses. The correction factors are derived from the analytical plane strain solution for a uniformly loaded, isolated, vertical fracture of finite height and infinite length. The simplified method not only can calculate displacement discontinuities and induced stresses for single 3D fracture, but also can accurately and efficiently solve the problem of multiple 3D interacting fracture, improving computational efficiency by more than one thousand times compared with the standard 3D method. This model has been used to simulate the propagation of multiple fractures for horizontal wells. The approach should be generally applicable to other 3D boundary element methods to enhance computation efficiency.

Rock slope stability analysis using photogrammetric data and DFN–DEM modelling

Abstract: Structural and mechanical analyses of rock mass are key components for rock slope stability assessment. The complementary use of photogrammetric techniques and numerical models coupling discrete fracture networks with the discrete element method (DEM) provides a methodology that can be applied to assess the mechanical behaviour of realistic three-dimensional (3D) configurations for which fracture persistence cannot be assumed. A real case has been studied to show the complete methodology from the acquisition of the photogrammetric data to the numerical modelling of the potential progressive failure process occurring in the rock mass. Using a 3D mapping system and its associated structural mapping tool Sirovision, the topography and the discontinuity set of an unstable rock block located in a limestone layer of the Mount N,ron, located in the French Alps, were imported into a DEM code specially enhanced for the modelling of pre-fractured rock masses. A stability analysis has been carried out, emphasizing the contribution of rock bridge failure through a mixed shear-tensile failure process to the generation of new failure surfaces. This addresses limitations in methodologies using only shear strength reduction method. It is believed that the proposed methodology can strengthen the basis for a more comprehensive stability analysis of complex fractured rock slopes.

Theoretical Analyses of MFL Signal Affected by Discontinuity Orientation and Sensor-Scanning Direction

Abstract: To improve the accuracy of the magnetic flux leakage (MFL) nondestructive testing in practical applications, we analyzed the MFL signal characteristics affected by discontinuity orientation and sensor-scanning direction. On the basis of magnetic dipole theory, the descriptions for the MFL field distributions of discontinuities in arbitrary orientations were established, indicating that the MFL density increases with the discontinuity orientation increasing from 0 to $\pi $ /2 and that magnetic flux always flows through the discontinuity perpendicularly, which was verified by relevant experiments. Further, the influence of the sensor-scanning direction on MFL signal features was analyzed and it was found that the MFL component signal parallel to scanning direction increases, the MFL component signal perpendicular to scanning direction falls, the MFL component signal perpendicular to discontinuity stays the same, and the widths of test signals become narrow, when the angle between the discontinuity orientation and sensor-scanning direction increases.

Numerical simulation of interaction between hydraulic and natural fractures in discontinuous media

Abstract: In this study, the displacement discontinuity formulation is used to solve the problem of interaction between hydraulic fractures (HF) and natural fractures (NF). Furthermore, a numerical program (2DFPM) is developed to study the mechanical activation of a NF because of the propagation of the HF. The accuracy of the numerical method is enhanced using the higher-order displacement variation along the HF and the special crack tip element near its ends. The maximum tangential stress criterion is implemented to predict the HF propagation path, and the stages of hydraulic fracturing tip approaching, coalescence and fluid penetration along the NF are modeled. The tangential stress around the NF with different contact modes (bonded, sliding and opening) is calculated by coupling the finite difference and boundary element methods. The location of secondary tensile fracture that re-initiates along the opposite side of NF is determined, and the key parameters that have great influence on interaction process are discussed. The results show that position, distance and inclination of the HF relative to the pre-existing discontinuity have a strong influence on the HF propagation path.

Characterization of the effect of normal load on the discontinuity morphology in direct shear specimens using X-ray micro-CT

Abstract: Discontinuities in brittle geomaterials, including concrete and rock, represent localized zones of weakness and enhanced hydraulic transmissivity that often control the hydromechanical behavior of the medium. The shearing of discontinuities and the resulting morphological changes can significantly alter this behavior. In this work, a procedure is developed to characterize sheared discontinuity replicas as a function of the applied normal load using X-ray micro-computed tomography (micro-CT) imagery. A specimen design and testing procedure that facilitates CT scanning is presented along with an image processing procedure to quantify the morphological changes in the specimens. Subsequently, the results of direct shear testing and image-based measurements of mean fracture aperture, surface area, median effective aperture, and the preferential orientation of fracture void space are presented and discussed. Application of the procedure developed herein yields characteristics of the morphology of sheared discontinuities that were previously not possible to obtain or that were time consuming to collect with destructive sectioning methods.

On the equivalence between traction- and stress-based approaches for the modeling of localized failure in solids

Abstract: This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., discontinuities localized in an elastic solid and strain localization of an inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, i.e., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given a priori. The bi-directional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (J2), Drucker–Prager, Mohr–Coulomb and many other frequently employed criteria recovered as its particular cases.

Numerical Analysis on the Optimization of Hydraulic Fracture Networks

Abstract: The clear understanding of hydraulic fracture network complexity and the optimization of fracture network configuration are important to the hydraulic fracturing treatment of shale gas reservoirs. For the prediction of hydraulic fracture network configuration, one of the problems is the accurate representation of natural fractures. In this work, a real natural fracture network is reconstructed from shale samples. Moreover, a virtual fracture system is proposed to simulate the large number of small fractures that are difficult to identify. A numerical model based on the displacement discontinuity method is developed to simulate the fluid-rock coupling system. A dimensionless stress difference that is normalized by rock strength is proposed to quantify the anisotropy of crustal stress. The hydraulic fracturing processes under different stress conditions are simulated. The most complex fracture configurations are obtained when the maximum principle stress direction is perpendicular to the principle natural fracture direction. In contrast, the worst results are obtained when these two directions are parallel to each other. Moreover, the side effects of the unfavorable geological conditions caused by crustal stress anisotropy can be partly suppressed by increasing the viscous effect of the fluid.

Combined continuum damage‐embedded discontinuity model for explicit dynamic fracture analyses of quasi‐brittle materials

Abstract: SUMMARY In this paper, a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi-brittle failure phenomena. The model is capable of describing the rate-dependent behavior in dynamics and the three phases in failure of quasi-brittle materials. The first phase is always linear elastic, followed by the second phase corresponding to fracture-process zone creation, represented with rate-dependent continuum damage with isotropic hardening formulated by utilizing consistency approach. The third and final phase, involving nonlinear softening, is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions. The proposed model is capable of describing the rate-dependent ductile to brittle transition typical of cohesive materials (e.g., rocks and ice). The model is implemented in the finite element setting by using the CST elements. The displacement jump vector is solved for implicitly at the local (finite element) level along with a viscoplastic return mapping algorithm, whereas the global equations of motion are solved with explicit time-stepping scheme. The model performance is illustrated by several numerical simulations, including both material point and structural tests. The final validation example concerns the dynamic Brazilian disc test on rock material under plane stress assumption. Copyright © 2014 John Wiley & Sons, Ltd.

Size Distribution for Potentially Unstable Rock Masses and In Situ Rock Blocks Using LIDAR-Generated Digital Elevation Models

Abstract: In this paper, two analytical procedures which are independent from the existence of empirical data are presented for the calculation of (1) the size distribution of potentially unstable rock masses that expresses the potential rockfall size distribution, including big volumes corresponding to potential rare events with low susceptibility of failure and (2) the in situ block distribution on the slope face. Two approaches are, respectively, used. The first one involves the detection of kinematically unstable surfaces on a digital elevation model (DEM) and on orthophotos and the calculation of the volumes resting on them. For the second one the in situ block volumes formed by the intersection of the existing discontinuity sets are calculated using a high-resolution DEM. The procedures are presented through an application example at the country of Andorra and in particular at the chute of Forat Negre. The results from the first procedure indicate that it is kinematically possible to have mobilized volumes of some thousands of cubic meters; however, these are considered rare events with low susceptibility of failure. The size distribution of potentially unstable rock masses for big volume events was well fitted by a power law with an exponent of −0.5. The in situ block distribution on the slope face from the second procedure, assuming three types of intersection between the joints of the existing discontinuity sets and two extreme cases of discontinuity persistence, was also found to follow a power law, but with an exponent of −1.3. The comparison with the observed in the field block volume distribution on the slope face indicates that in reality discontinuities have a very high persistence and that considering only their visible trace length overestimates volumes, which is conservative.

A coupled numerical–experimental study of the breakage process of brittle substances

Abstract: Pre-existing cracks in brittle substances seem to be the main cause of their breakage under various loading conditions. In the present paper, a coupled numerical–experimental analysis of crack propagation, cracks coalescence, and breakage process of brittle substances such as rocks and rock-like samples have been studied. The numerical analyses are accomplished using a numerical code based on the Higher order Displacement Discontinuity Method for Crack (HDDMCR2D) analysis. A quadratic displacement discontinuity variation along each boundary element is assumed to evaluate the Mode I and Mode II stress intensity factors. Based on the linear elastic fracture mechanics theory, the maximum tangential stress criterion (i.e., a mixed mode fracture criterion) is implemented in the HDDMCR2D code for predicting the crack initiation and its direction of propagation (cracks propagation path). Some numerical and analytical problems in finite and infinite planes are solved numerically by the proposed numerical method, and the results are compared in different tables illustrating the accuracy and validity of the numerical results. Experimental tests are also being done to evaluate the final breakage path and cracks initiation and cracks coalescence stresses in rock-like specimens containing two random cracks. The numerical and experimental results obtained from the tested specimens show a good agreement between the corresponding values and demonstrate the accuracy and effectiveness of the approach.

Simulation of crack coalescence mechanism underneath single and double disc cutters by higher order displacement discontinuity method

Abstract: The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics (LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method. The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs. The effects of specific disc parameters (except speed) on the thrust force F r, the rolling force F r, and the specific energy E S are investigated. It has been shown that the specific energy (energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth P d (i.e. S/P d ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.

A regional-scale discontinuity in western sicily revealed by a multidisciplinary approach. A new piece for understanding the geodynamic puzzle of the southern Mediterranean.†

Abstract: The results of an integrated stratigraphic, structural, geophysical, and geochemical study reveal the presence of a crustal discontinuity in western Sicily that, at present, runs roughly N-S along a band from San Vito Lo Capo to Sciacca (SVCS). The boundary between the two zones of this discontinuity is nearly orthogonal to the main thrust propagation of the Sicilian thrust-and-fold belt. The different Permian to Tertiary sedimentary evolution recorded by the two zones appears related to this discontinuity, with thick carbonate platforms in the western sector facing deep-water successions in the eastern one. The presence of Upper Triassic reefs, huge megabreccias bodies, and widespread submarine volcanisms along the transition zone suggest the presence of a long lasting weakness zone. This zone has been reactivated episodically as transpressional and/or transtensional faults in relation to the different geodynamic stress acting in central Mediterranean area in different epochs. We speculate that this transition zone has represented a segment of the passive margin of the Ionian Tethys. During the Maghrebian convergence a different style of deformation has affected the two sectors floored by different sedimentary multilayers. The orthogonal-to-oblique differential convergence between the two sectors has resulted in right-lateral transpressional motions, leading to oblique thrusting of deep-water-derived thrusts onto platform-derived thrusts associated with clockwise rotations. The oblique convergence is still ongoing as demonstrated by the seismicity of the area, by the geothermal field with high mantle-derived helium fluxes and by the GPS measurements collected by different authors.

SPH procedures for modeling multiple intersecting discontinuities in geomaterial

Abstract: Summary A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic-plastic constitutive model. Free-sip, no-slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system. The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.