Three-dimensional elastic analysis by the displacement discontinuity method with boundary division into triangular leaf elements

Kuriyama, Ken; Mizuta, Yoshiaki

doi:10.1016/0148-9062(93)90704-h

Cited by 54 publications

(43 citation statements)

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“…This modeling method is based on the analytical solution of a triangular dislocation (TD) element in an elastic full-space (Yoffe, 1960). The TD elements allow us to discretize any curved surface, such as topography and the geometry of complex sources without any discontinuity (Kuriyama and Mizuta, 1993;Maerten et al, 2005). In our model, we simulate the pressurization of the source by defining a traction boundary condition at the source TD elements.…”

Section: Source Modelingmentioning

confidence: 99%

Satellite radar data reveal short-term pre-explosive displacements and a complex conduit system at VolcÃ¡n de Colima, Mexico

et al. 2014

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The geometry of the volcanic conduit is a main parameter controlling the dynamics and the style of volcanic eruptions and their precursors, but also one of the main unknowns. Pre-eruptive signals that originate in the upper conduit region include seismicity and deformation of different types and scales. However, the locality of the source of these signals and thus the conduit geometry often remain unconstrained at steep sloped and explosive volcanoes due to the sparse instrumental coverage in the summit region and difficult access. Here we infer the shallow conduit system geometry of Volcán de Colima, Mexico, based on ground displacements detected in high resolution satellite radar data up to 7 h prior to an explosion in January 2013. We use Boundary Element Method modeling to reproduce the data synthetically and constrain the parameters of the deformation source, in combination with an analysis of photographs of the summit. We favor a two-source model, indicative of distinct regions of pressurization at very shallow levels. The horizontal location of the upper pressurization source coincides with that of post-explosive extrusion. The pattern and degree of deformation reverses again during the eruption; we therefore attribute the displacements to transient (elastic) pre-explosive pressurization of the conduit system. Our results highlight the geometrical complexity of shallow conduit systems at explosive volcanoes and its effect on the distribution of pre-eruptive deformation signals. An apparent absence of such signals at many explosive volcanoes may relate to its small temporal and spatial extent, partly controlled by upper conduit structures. Modern satellite radar instruments allow observations at high spatial and temporal resolution that may be the key for detecting and improving our understanding of the generation of precursors at explosive volcanoes.

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Section: Source Modelingmentioning

confidence: 99%

Satellite radar data reveal short-term pre-explosive displacements and a complex conduit system at VolcÃ¡n de Colima, Mexico

et al. 2014

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“…The analytical solutions for a TD in a full-space contain artefact singularities on the extensions of the sides of the TD (Kuriyama & Mizuta 1993). Similar difficulties also exist in the general solution of the previous section.…”

Section: Developing An Artefact-free Solution For a Td In A Full-spacementioning

confidence: 87%

“…The other shortcoming of the Yoffe (1960) approach is related to the Burgers function producing multiple outputs at a single calculation point, as first considered by Brown (1975). Crouch & Starfield (1983) developed an alternate solution for a TD in a full-space, which was later utilized in a BEM implementation developed by Kuriyama & Mizuta (1993). The latter also reported the existence of singularities on the extensions of the sides of the TD, which is considered to be a major shortcoming of the method.…”

Section: Improvements On and Comparison To Earlier Workmentioning

confidence: 99%

“…Our solutions can be used as the basis for other numerical methods, such as the BEM, which utilize TDs as fundamental elements. Inverting the coseismic surface deformation for the slip on complex curved faults associated with earthquakes (Maerten et al 2005), analysing the deformations and stress fields of volcanoes arising from fractures and pressurized reservoirs underneath realistic edifice topographies (Cayol & Cornet 1997), and evaluating the excavation-induced displacements and stresses near man-made cavities (Kuriyama & Mizuta 1993) are a few examples of the possible applications of this approach.…”

Section: Application Possibilitiesmentioning

confidence: 99%

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Triangular dislocation: an analytical, artefact-free solution

Nikkhoo

Walter

2015

Geophysical Journal International

106

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S U M M A R YDisplacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space R 3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.Key words: Geomechanics; Kinematics of crustal and mantle deformation. I N T RO D U C T I O NCrustal deformations associated with earthquakes, volcanoes, landslides and human activities can be observed at a high level of detail using modern geodetic techniques, including synthetic aperture radar interferometry (InSAR) and GPS (Segall 1997;Bürgmann et al. 2000). These deformation data are often analysed using modelling techniques that are typically very computationally intense. The primary objective of such modelling is to understand the underlying processes through indirect imaging of the so-called sources, such as seismogenic faults, magma chambers and other reservoirs. The position and geometry of these sources, as well as the slip or the forces acting on them, are typically regarded as the source parameters. The source parameters, in other words, the outputs of the implemented modelling, are relevant to earthquake aftershock studies, the assessment of volcanic eruption precursors, tsunami modelling and many other applications (Feigl et al. 2002).The majority of methods that are applied for crustal deformation modelling are based on the theory of elasticity in general and the concept of dislocations in particular (Segall 2010). Elastic dislocation theory concerns the state of deformations in a strained solid body that is subject to the action of a dislocation embedded inside it (Love 1944). The Volterra model (Volterra 1907) describes a dislocation as a surface of displacement discontinuity with a uniform distribution of the slip throughout. The edges of the Volterra dislocation, also known as ...

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“…Bui (1977), Weaver (1977), Lin'kov and Mogilevskaya (1986), Luchi and Rizzuti (1987), Kuriyama and Mizuta (1993), Chen and Gross (1997), Chen and Lee (2001), Frangi et al (2002), Lo et al (2005). There are also various papers on three-dimensional crack propagation, e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

Geomechanical Simulation of Fluid-Driven Fractures

Makhnenko¹,

Nikolskiy²,

Mogilevskaya³

et al. 2012

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The project supported graduate students working on experimental and numerical modeling of rock fracture, with the following objectives: (a) perform laboratory testing of fluid-saturated rock; (b) develop predictive models for simulation of fracture; and (c) establish educational frameworks for geologic sequestration issues related to rock fracture. These objectives were achieved through (i) using a novel apparatus to produce faulting in a fluid-saturated rock; (ii) modeling fracture with a boundary element method; and (iii) developing curricula for training geoengineers in experimental mechanics, numerical modeling of fracture, and poroelasticity.4 EXECUTIVE SUMMARYCarbon storage technologies offer a means of reducing CO 2 emissions and mitigating climate change. These new technologies will require a workforce educated in geomechanics. To this end, the project supported graduate students working on geomechanical simulation of fluid-driven fractures with the following objectives:1. Measure elastic and inelastic response of fluid-saturated rock 2. Develop predictive models for simulation of fluid-driven fractures 1. Deformation and damage of a porous, fluid-saturated rock under drained and undrained conditions were investigated. A plane-strain apparatus was modified in order to conduct tests with water-saturated rock specimens and to measure the pore pressure within the rock. Transducers within the apparatus were calibrated at the various loading states and the compliances of the system were determined. Plane strain compression and conventional triaxial compression tests were performed at different confining pressures under air-dry, drained, and undrained conditions. The behavior of the rock was evaluated within the framework of linear poroelasticity. Dilatant hardening and contractant softening was investigated from undrained experiments, where pore pressure was measured throughout the failure process. The parameters that govern the inelastic deformation of fluid-saturated rock, i.e. dilatancy angle β, friction coefficient µ, poroelastic coefficient K eff , shear modulus G, and inelastic hardening modulus H, were calculated for the drained response. The constitutive model predicts the undrained inelastic response of the rock fairly well, almost up to the peak load if compared with the undrained test that had the same effective mean stress at the onset of inelasticity. Knowledge of dilatant hardening behavior is essential for the proper assessment of underground structures, such as long-term CO 2 storage facilities.2. The boundary element method (BEM) is based on the boundary integral representation equivalent to the differential equation governing a specific physical problem. Such representation is possible when the so-called fundamental solution of the governing differential equation is available. The fundamental solution satisfies the differential equation everywhere in the domain except one point where it is singular. In the case of linear isotropic and homogeneous elasticity, the fundamental solution...

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Three-dimensional elastic analysis by the displacement discontinuity method with boundary division into triangular leaf elements

Cited by 54 publications

References 1 publication

Satellite radar data reveal short-term pre-explosive displacements and a complex conduit system at VolcÃ¡n de Colima, Mexico

Satellite radar data reveal short-term pre-explosive displacements and a complex conduit system at VolcÃ¡n de Colima, Mexico

Triangular dislocation: an analytical, artefact-free solution

Geomechanical Simulation of Fluid-Driven Fractures

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