Showing papers on "Discontinuity (geotechnical engineering) published in 2007"

A simplified mesh-free method for shear bands with cohesive surfaces

Abstract: A simple methodology to model shear bands as strong displacement discontinuities in a mesh-free particle method is presented. The shear band is represented as a set of sheared particles. A sheared particle is developed through enrichment by tangential displacement discontinuities. The representation of the shear band as set of cohesive segments provides a simple and versatile model of shear bands. The loss of material stability is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation law acting on the discontinuity surface. The method is implemented for two and three dimensions. Examples of shear band progression in rate-dependent and rate-independent materials are presented, including the Kalthoff problem, where the transition from brittle fracture to shear banding is studied. Copyright © 2006 John Wiley & Sons, Ltd.

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Abstract: The strong discontinuity approach to modelling strain localization, combined with an enhanced strain element, has been used for more than a decade to model strain localization in materials including geomaterials. Most implementations of enhanced strain elements in the post-localization regime use very simple constitutive formulations along the discontinuity, such as linear softening or a constant friction coefficient. However, the softening relations can be much more complex for geomaterials. For rocks this softening is induced by micro-fractures coalescing into macroscopic cracks during a narrow time interval called ‘slip weakening.’ During this interval the cohesive resistance on the nucleating crack decays to zero while the frictional resistance increases. Furthermore, research has shown that the coefficient of friction for these materials is not constant, but in fact is a function both of the slip speed and the state of the material, including wear, temperature, and other factors. In this paper we augment the modelling capabilities of an enhanced strain element by incorporating a cohesive softening law and a popular rate- and state-dependent friction model commonly used for describing the constitutive properties of rocks and rock-like materials sliding along the fractured surface. Copyright © 2007 John Wiley & Sons, Ltd.

Seismic observations of transition-zone discontinuities beneath hotspot locations

Abstract: The seismic structure of the transition-zone discontinuities was studied beneath the forty-nine hotspot locations of the catalog of Courtillot et al. (2003), using a global data set of SS precursors. Some of these hotspots are proposed to originate from plumes rising in the upper mantle or from the core-mantle boundary region. I found thin transition zones in approximately two-thirds of the twenty-six hotspot locations for which precursor observations could be made. This observation agrees with the expectation for the olivine phase transition of a systematically thin transition zone in high-temperature regions. Other hotspot locations showed a clear deepening of both the 410- and 660-km discontinuities, which is consistent with a phase transition from majorite garnet to perovskite at a depth of 660 km. Predictions from mineral physics suggest that this transition is more important than the olivine phase transition in regions with high mantle temperatures. So, a hotspot location with a deep 410-km discontinuity in combination with either a shallow or deep 660-km discontinuity might be consistent with hot upwellings rising from the lower into the upper mantle. Hotspot locations with a shallow 410-km discontinuity are not in agreement with a positive thermal anomaly from the surface down to the mantle transition zone. This new interpretation of seismic discontinuities in the transition zone has important implications for our understanding of geodynamics in potential mantle plume location

Coupled hm analysis using zero-thickness interface elements with double nodes

Abstract: Coupled hydro-mechanical (HM) processes in pre-existing discontinuities (geological) and developing cracks (fractures) are important in many fields of engineering (e,g. Dams, Oil or Environmental). In these situations, flow through the discontinuity is influenced by its deformation through changes in the permeability and the storage capacity. At the same time, changes in fluid pressure result in changes in the effective stress distribution, and the subsequent closure, opening or even propagation of the discontinuity. The problem becomes more complicated when the medium that contains the discontinuity is porous, since fluid exchange between both may appear and HM coupling must be considered also in the porous domain. The thesis formulates the HM coupled problem in jointed or susceptible of fracturing geomaterials by means of the Finite Element Method (FEM) with "zero-thickness" interface elements and double nodes to discretize and describe the HM behavior of discontinuities. Each element (continuum and interface) is formulated in terms of the displacements (u) and the fluid pressure (p) at nodes. After assembly, a particular expression of the traditional "u-p" system of coupled equations is obtained, which is highly non-linear due to the strong dependence between the permeability and the aperture of discontinuities. Poro-elasticity is assumed in the continuum. The cubic law is considered to govern the longitudinal flow along an open discontinuity, whereas for a closed or filled discontinuity Darcy's law can be used along the plane. The influence of a transversal potential drop is introduced by means of a transversal transmissivity that takes into account the existence of impermeable material within a discontinuity. The constitutive model that relates effective stresses to relative displacements in the interface depends on the type of problem being analyzed (pre-existing joint: rock mechanics based model; developing crack: fracture mechanics based model). The "u-p"

On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids

Abstract: Bubbles rising in viscoelastic liquids may exhibit a jump discontinuity of the rise velocity as a critical bubble volume is exceeded. We carried out detailed experiments to investigate the occurrence of this discontinuity with single air bubble rising in various polymer solutions without influence of surfactants. The polymer solutions were characterized thoroughly by means of shear and elongational rheometry, as well as tensiometry. The experiments showed that a jump discontinuity can exist only if the non-dimensional group λE(g3ρ1/σ)1/4, found by dimensional analysis, exceeds a critical value. A universal correlation of non-dimensional numbers for the non-dimensional critical bubble volume at the jump discontinuity was found. The non-dimensional numbers represent the relevant rheological and dynamic liquid properties. This is the first time that the prediction of the critical bubble volume as well as the potential of the solution to exhibit a bubble rise velocity discontinuity becomes possible based on liquid properties only. In the correlation found, the relaxation time of the polymer solutions in elongational flow of the viscoelastic liquid was found to play a key role.

Three-dimensional fracture simulations based on the SDA

Abstract: A numerical model within the framework of a non-symmetric strong discontinuity approach (SDA) suitable for fracture simulations of plain concrete is presented. The model is based on the fixed crack concept and is formulated within the framework of elements with embedded discontinuities. Discontinuity segments of individual elements are considered to form a C0-continuous surface. Enforcement of continuity of the crack surface across adjacent elements is established by the so-called partial domain crack tracking algorithm (PDTA). Orientation of individual crack segments is derived from a non-local strain field. Within the present work emphasis is put on the formulation for the three-dimensional case. The implications on the respective algorithms are highlighted. The capabilities of the model are shown by means of numerical examples. Copyright © 2006 John Wiley & Sons, Ltd.

Whole mantle discontinuity structure beneath Hawaii

Abstract: [1] We examined mantle structure beneath the southeast Hawaiian Islands using multiple ScS reverberations from four earthquakes from the island of Hawaii and recorded at station KIP on the island of Oahu. We find an unusually deep 410-km discontinuity and a transition zone thickness of 227 km, corresponding to a temperature increase of 87 K above the global average. Other reflectors include a lid-low-velocity zone boundary, a weak 520-km discontinuity, and smaller discontinuities at 224 km, 288 km, and 1000 km. Whole mantle travel time is near the global average, which we attribute to an inclined or branching plume, lowermost mantle anisotropy, and estimate bias due to a possible ultra-low velocity zone atop the core.

Mapping the crustal structure under active volcanoes in central Tohoku, Japan using P and PmP data

Abstract: [1] We present high-resolution tomographic images of the crust under the active arc volcanoes in the central part of Northeast Japan (Tohoku) determined by using arrival times of first P waves and post-critically reflected waves from the Moho discontinuity (PmP). Results of detailed resolution analyses show that the addition of PmP data can improve significantly the resolution of the lower crustal structure. After the PmP data are included in the tomographic inversion, the low-velocity (low-V) anomalies in the lower crust under the active volcanoes can be better imaged. The low-V zones are clearly visible in the entire crust beneath the volcanoes extending from the surface down to the Moho discontinuity. Arc-magma related, deep, low-frequency microearthquakes are located around the low-V zones in the lower crust under the volcanoes, which occurrence is probably associated with the movement of fluid magma under the volcanoes.

Discontinuity Meshing for Radiosity

Abstract: The radiosity method is the most popular algorithm for simulating interre ection of light between di use surfaces. Most existing radiosity algorithms employ simple meshes and piecewise constant approximations, thereby constraining the radiosity function to be constant across each polygonal element. Much more accurate simulations are possible if linear, quadratic, or higher degree approximations are used. In order to realize the potential accuracy of higher-degree approximations, however, it is necessary for the radiosity mesh to resolve discontinuities such as shadow edges in the radiosity function. A discontinuity meshing algorithm is presented that places mesh boundaries directly along discontinuities. Such algorithms o er the potential of faster, more accurate simulations. Results are shown for three-dimensional scenes.

Melting in the Deep Upper Mantle Oceanward of the Honshu Slab

Abstract: We examine the upper mantle and transition zone beneath the western Pacific using multiple ScS reverberations. A low-velocity zone (LVZ) is found above the 410-km discontinuity oceanward of the subducting Honshu slab at an average depth of 356 km, with a thickness that ranges from 50 to 75 km assuming the LVZ continues to the 410-km discontinuity, which is locally elevated. The low-velocity region is evident in previous tomographic studies, and our results suggest that the anomaly is best explained by a layer of partial melt. The layer may be entrained from above by subduction or produced in situ by the combined effects of water and temperature. A self-consistent model that explains local P-wave velocities (Obayashi, M., Sugioka, H., Yoshimitsu, J., Fukao, Y., 2006. High temperature anomalies oceanward of subducting slabs at the 410-km discontinuity. Earth and Planetary Science Letters 243, 149–158) and our observations calls for a maximum temperature anomaly of ∼150 °C and a resulting maximum olivine water content after melting of 0.100 wt. %.

Imaging mantle discontinuities using least squares Radon transform

Abstract: [1] Differential traveltimes of SS precursors have been widely used to map large-scale mantle structure and depths of discontinuities. Measurements are commonly made by stacking individual records to increase the signal-to-noise ratio pertaining to these mild reflections. However, ray parameters of the SS precursors are typically less well constrained and undesired seismic arrivals with vastly different slownesses (for example, scattered waves) could potentially contaminate the time domain stacks. To overcome these pitfalls, we introduce a processing scheme based on the Radon transform and well-constrained inversions. Our method is particularly effective in suppressing background noise, constraining differential ray parameter and traveltime, and detecting weak reflected or converted phases. We apply the Radon-based method to delineate the discontinuity structure beneath the northeastern Pacific Ocean and the northwestern Canada. An elevated 410-km discontinuity and a thickened transition zone (252 km) are observed beneath the northern British Columbia, which may be caused by remnant oceanic lithosphere from the subduction of Kula-Farallon plate under North America. A thin transition zone is identified beneath the northern Pacific Ocean and its presence is supported by a low shear-velocity anomaly from recent tomographic models. The improved accuracy and resolution using the least squares Radon transform also offer clear evidence for a regional 520-km discontinuity and several mild reflectors in the depth ranges of 250–330 km and 900–1200 km. We do not observe a 220-km discontinuity beneath the study region.

Analysis of Critical Excavation Depth for a Jointed Rock Slope Using a Face-to-Face Discrete Element Method

Abstract: The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D-s and the natural slope angle alpha, the joint inclination angle theta as well as the strength parameters of the joints c(r) ,phi(r) is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.

Interaction of the bow shock with a tangential discontinuity and solar wind density decrease: Observations of predicted fast mode waves and magnetosheath merging

Abstract: [1] Shortly after 0600 UT on 7 April 2000 a tangential discontinuity (TD) in the solar wind passed the Advanced Composition Explorer satellite (ACE). It was characterized by a rotation of the interplanetary magnetic field (IMF) by ∼145° and more than a factor-of-2 decrease in the plasma density. About 50 min later, Polar encountered more complex manifestations of the discontinuity near noon in the magnetosheath outside the Northern Hemisphere cusp. On the basis of Polar observations, theoretical modeling, and MHD simulations we interpret the event as demonstrating that (1) a fast mode rarefaction wave was generated during the TD-bow shock interaction, (2) the fast wave carried a significant fraction of the density change to the magnetopause while the remainder stayed with the transmitted discontinuity, and (3) magnetic merging occurred between IMF field lines within the magnetosheath on opposite sides of the discontinuity's surface as it approached the magnetopause. Before the discontinuity passed the spacecraft, Polar detected ions accelerated antiparallel to B in the fast wave and perpendicular to B in a weak slow mode structure located adjacent to and just downstream of the fast wave. The antiparallel accelerated ions in the fast wave had no measurable ion-velocity dispersion signature, placing their source a few RE equatorward of Polar. Simulation results, a Walen test, detections of wave Poynting flux parallel to B, bidirectional electron heat flux, and ion velocity enhancements all indicate that the three ion bursts associated with the passage of the discontinuity were signatures of time-dependent, magnetic merging events within the magnetosheath.

The computational analysis of shallow depth tabular mining problems

Abstract: The evaluation of stress distributions and deformations in the vicinity of tabular mine layouts has been carried out routinely for many years using the displacement discontinuity boundary element method (DDM). In this approach, mine layouts are approximated as irregular shaped planar cracks (or slits) where the i?½widthi?½ of the crack, corresponding to the excavation height, is assumed to be negligible compared to the in-plane, lateral dimensions. Early implementations of this approach have employed square element tessellations with constant displacement discontinuity component values. This is generally restrictive when considering the analysis of irregular pillar layouts or the intersection of fault planes with excavations. This paper descriptionbes a general revision of this approach in which triangular or quadrilateral element shapes are introduced in conjunction with higher order variations of the displacement discontinuity shape functions. This facilitates an accurate evaluation of detailed stress and displacement components close to excavation surfaces and allows the investigation of local damage and failure behaviour associated with particular geological structures such as weak parting bands or weak layers. A method to embed these features in an efficient and accurate multi-level solution scheme is descriptionbed. This formulation can be extended to allow the analysis of shallow-depth pillar layout problems, facilitating the assessment of the interactive response and stability of shallow depth pillar layouts. A simple deformation model is introduced to facilitate the assessment of pillar failure and bursting potential in shallow mine layouts. The computational techniques descriptionbed here have been implemented in a computer code called TEXAN (Tabular EXcavation ANalyser) and are illustrated by the simulation of a particular multiple reef pillar mining problem in a shallow depth platinum mine.

Continuum mathematical modeling of slip weakening in geological systems

Abstract: [1] We describe a framework for mathematical modeling of slip weakening in an initially intact rock mass due to shear strain localization along any arbitrary slip plane. The modeling technique considered is based on continuum mechanics and may be cast directly into a standard nonlinear finite element algorithm for the analysis of prefailure and postfailure responses of geological systems in a boundary value problem. The prefailure behavior is represented by a continuum constitutive model; the postfailure behavior is characterized by frictional yielding on a slip surface with state- and velocity-dependent coefficient of friction. In the context of finite element analysis, slip planes are represented by an embedded strong discontinuity introduced into an initially intact finite element to signal the beginning of postfailure behavior. This paper focuses on the narrow time interval of slip weakening, from the moment the strong discontinuity has been embedded into a finite element until the relative slip has grown to a large enough value for the coefficient of friction to reach steady state. To this end, we formulate a linear slip weakening constitutive law in which the weakening component decays to zero at the same time that the frictional component increases to its value at residual state.

Deep Earth Structure – Transition Zone and Mantle Discontinuities

Abstract: We are discussing seismic observations of discontinuities in the upper-mantle materials between the crust–mantle boundary and the mantle transition zone The seismic techniques mainly used are receiver functions, ScS reverberations, and PP and SS precursors The signals used are small scattered phases caused by reflections or conversions of a main phase at a discontinuity The aim of these studies is to verify the elements of plate tectonics in greater detail Of special interest are the lithosphere–asthenosphere boundary and the midlithospheric discontinuity in cratons and thickness variations of the transition zone as indicator of lateral temperature changes Literature on seismic observations is discussed

Numerical implementation of a strain energy-based fracture model for HMA materials

Abstract: This work combines a new strain energy-based fracture criterion with a viscoelastic displacement discontinuity boundary element method to investigate crack growth in hot mix asphalt (HMA) materials. The study employs a fundamental crack growth threshold and simulates crack growth by accumulation of the dissipated creep strain energy (DCSE)—below this threshold, only healable micro-damage develops, and non-healable crack initiation or growth occurs, otherwise. A critical zone is introduced ahead of the crack tip to represent the portion of the material being damaged. Once the cumulative micro-damage inside the critical zone reaches the cracking threshold, the crack extends by the length of the critical zone. An HMA fracture simulator is developed by incorporating the DCSE threshold concept into a numerical framework based on a viscoelastic displacement discontinuity method, which has proven its convenience and efficiency in crack modeling. Numerical analyses are performed to predict piecewise crac...