Efficient block preconditioners for the coupled equations of pressure and deformation in highly discontinuous media     

Joachim Berdal Haga  Harald Osnes  Hans Petter Langtangen 《国际地质力学数值与分析法杂志》2011,35(13):1466-1482

Large‐scale simulations of flow in deformable porous media require efficient iterative methods for solving the involved systems of linear algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps in material properties, which is often the case in geological applications, such as basin evolution at regional scales. The success of iterative methods for this type of problems depends strongly on finding effective preconditioners. This paper investigates how the block‐structured matrix system arising from single‐phase flow in elastic porous media should be preconditioned, in particular for highly discontinuous permeability and significant jumps in elastic properties. The most promising preconditioner combines algebraic multigrid with a Schur complement‐based exact block decomposition. The paper compares numerous block preconditioners with the aim of providing guidelines on how to formulate efficient preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Low-velocity structure beneath Africa from forward modeling   总被引：1，自引：0，他引：1  

Sidao Ni  Xiaoming Ding  Donald V Helmberger  Michael Gurnis 《Earth and Planetary Science Letters》1999,170(4):21-507

Seismic waveforms observed in South Africa containing the first arrival crossover of S to SKS (70° to 110°) are analyzed. The data consist of analog records from the World Wide Seismographic Station Network (WWSSN) of deep events beneath South America. The S-waves arrive 2 to 3 s early relative to PREM at ranges from 70° to 95° and then become increasingly delayed, becoming 5 to 6 s late at 110°. The SKS phase is late by 3 to 5 s over the entire range. This pushes crossover between S and SKS, normally observed at about 81°, out about 2° to 3°, which is the most anomalous shift ever reported. To model such features, we modified Grand's tomography model [Grand et al., GSA Today 7 (1997) 1–7], and generated 2D synthetics to match the data. The overall shape and position of the lower mantle low-velocity anomaly proposed by Grand predicts good results if lower mantle anomalies are enhanced to a level of about 4%. This results in a complex tabular structure extending upward from the core–mantle boundary about 1500 km into the mantle. These features appear to be consistent with a large young plume which is erupting off the CMB.  相似文献   

Using modified state surface approach to select parameter values in the Barcelona basic model     

Xiong Zhang  Ming Xiao 《国际地质力学数值与分析法杂志》2013,37(12):1847-1866

The Barcelona basic model (BBM) successfully explained many key features of unsaturated soils and received extensive acceptance. It is also one of the few elastoplastic constitutive models for unsaturated soils that have been implemented within finite element codes and applied to the analysis of real boundary value problems. The BBM was proposed in incremental forms according to theories of soil plasticity in which individual aspects of the isotropic virgin behavior are controlled by multiple parameters, whereas at the same time, a single parameter controls more than one aspect of soil behavior. Although a variety of methods have been recently developed for calibrating model parameters for elastoplastic soil models, at present, there are no well‐established, simple, and objective methods for selecting parameter values in the BBM from laboratory tests. This has been one of the major obstacles to the dissemination of this constitutive model beyond the research context. This article presents an optimization approach especially developed for simple and objective identification of material parameters in the BBM. This is achieved by combining a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic stress conditions, with the Newton or quasi‐Newton method to simultaneously determine the five parameters governing isotropic virgin behavior in the BBM. The comparison between results using the proposed method and an existing method for the same laboratory tests was discussed from which the simplicity and objectivity of the proposed method were evaluated. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

Numerical modeling of fluid‐driven fractures in cohesive poroelastoplastic continuum     

E. Sarris  P. Papanastasiou 《国际地质力学数值与分析法杂志》2013,37(12):1822-1846

In this article, we investigate the main parameters that influence the propagation of a fluid‐driven fracture in a poroelastoplastic continuum. These parameters include the cohesive zone, the stress anisotropy, and the pore pressure field. The fracture is driven in a permeable porous domain that corresponds to weak formation by pumping of an incompressible viscous fluid at the fracture inlet under plane strain conditions. Rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fluid flow in the fracture is modeled by the lubrication theory. The movement of the pore fluid in the surrounding medium is assumed to obey the Darcy law and is of the same nature as the fracturing fluid. The cohesive zone approach is used as the fracture propagation criterion. The problem is modeled numerically with the finite element method to obtain the solution for the fracture length, the fracture opening, and the propagation pressure as a function of the time and distance from the pumping inlet. It is demonstrated that the plastic yielding that is associated with the rock dilation in an elastoplastic saturated porous continuum is significantly affected by the cohesive zone characteristics, the stress anisotropy, and the pore pressure field. These influences result in larger fracture profiles and propagation pressures due to the larger plastic zones that are developing during the fracture propagation. Furthermore, it is also found that the diffusion process that is a major mechanism in hydraulic fracture operations influences further the obtained results on the fracture dimensions, plastic yielding, and fluid pressures. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows     

Mohammad Hossein Bazyar  Adel Graili 《国际地质力学数值与分析法杂志》2012,36(16):1793-1812

The scaled boundary finite‐element method (SBFEM), a novel semi‐analytical technique, is applied to the analysis of the confined and unconfined seepage flow. This method combines the advantages of the finite‐element method and the boundary element method. In this method, only the boundary of the domain is discretized; no fundamental solution is required, and singularity problems can be modeled rigorously. Anisotropic and nonhomogeneous materials satisfying similarity are modeled without additional efforts. In this paper, SBFE equations and solution procedures for the analysis of seepage flow are outlined. The accuracy of the proposed method in modeling singularity problems is demonstrated by analyzing seepage flow under a concrete dam with a cutoff at heel. As only the boundary is discretized, the variable mesh technique is advisable for modeling unconfined seepage analyses. The accuracy, effectiveness, and efficiency of the method are demonstrated by modeling several unconfined seepage flow problems. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

P–T–t evidence for mechanisms of vertical tectonic motion in a contractional orogen: north-western US and Canadian Cordillera     

Whitney  Miller  & Paterson 《Journal of Metamorphic Geology》1999,17(1):75-90

The >1800 km long Coast Mountains–North Cascades orogen of the Canadian Cordillera and north-western US developed as a continental magmatic arc. Metamorphic rocks in the orogen contain widespread evidence for burial of supracrustal rocks to depths of c. 40 km, followed by nearly isothermal decompression to depths of <10 km. Near many shallowly-emplaced, mid-Cretaceous plutons, low-pressure contact metamorphic effects were overprinted by high-pressure regional metamorphic minerals and textures, as evidenced by kyanite±staurolite pseudomorphs after andalusite in metapelitic rocks. Therefore, near-pluton rocks record the loading history of the orogen. Metapelitic rocks not associated with plutons only preserve evidence for high-pressure conditions and/or high-temperature decompression, as indicated, for example, by sillimanite and cordierite after kyanite and garnet, respectively. Petrological evidence for burial and decompression is therefore recorded in different rocks. Various regions of the orogen differ in timing of metamorphism, the overall shape of P–T paths and the relative timing and regional extent of the high-pressure event, but most of these data and observations are consistent with thrusting and/or pure shear thickening as primary loading mechanisms throughout the orogen, as opposed to magma-dominated loading. This interpretation is further supported by comparison with thermal models, which demonstrate that the P–T paths are consistent with simultaneous thrusting and folding at a high initial geothermal gradient (35–40 °C km^?1) in much of the orogen. A high geothermal gradient supports tectonic models invoking intra-arc contraction and suggests that magmatism played an important role in regional temperature-time paths. This tectonic-thermal history may be typical of other contractional orogens and illustrates the importance of large vertical displacement of crust in magmatic arcs.  相似文献   

Flat boundaries and their effect on sand testing     

G. Marketos  Malcolm D. Bolton 《国际地质力学数值与分析法杂志》2010,34(8):821-837

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Prograde metamorphic sequence of REE minerals in pelitic rocks of the Central Alps: implications for allanite–monazite–xenotime phase relations from 250 to 610 °C     

E. JANOTS  M. ENGI  A. BERGER  J. ALLAZ  J.-O. SCHWARZ  C. SPANDLER 《Journal of Metamorphic Geology》2008,26(5):509-526

The distribution of REE minerals in metasedimentary rocks was investigated to gain insight into the stability of allanite, monazite and xenotime in metapelites. Samples were collected in the central Swiss Alps, along a well‐established metamorphic field gradient that record conditions from very low grade metamorphism (250 °C) to the lower amphibolite facies (～600 °C). In the Alpine metapelites investigated, mass balance calculations show that LREE are mainly transferred between monazite and allanite during the course of prograde metamorphism. At very low grade metamorphism, detrital monazite grains (mostly Variscan in age) have two distinct populations in terms of LREE and MREE compositions. Newly formed monazite crystallized during low‐grade metamorphism (<440 °C); these are enriched in La, but depleted in Th and Y, compared with inherited grains. Upon the appearance of chloritoid (～440–450 °C, thermometry based on chlorite–choritoid and carbonaceous material), monazite is consumed, and MREE and LREE are taken up preferentially in two distinct zones of allanite distinguishable by EMPA and X‐ray mapping. Prior to garnet growth, allanite acquires two growth zones of clinozoisite: a first one rich in HREE + Y and a second one containing low REE contents. Following garnet growth, close to the chloritoid–out zone boundary (～556–580 °C, based on phase equilibrium calculations), allanite and its rims are partially to totally replaced by monazite and xenotime, both associated with plagioclase (± biotite ± staurolite ± kyanite ± quartz). In these samples, epidote relics are located in the matrix or as inclusions in garnet, and these preserve their characteristic chemical and textural growth zoning, indicating that they did not experience re‐equilibration following their prograde formation. Hence, the partial breakdown of allanite to monazite offers the attractive possibility to obtain in situ ages, representing two distinct crystallization stages. In addition, the complex REE + Y and Th zoning pattern of allanite and monazite are essential monitors of crystallization conditions at relatively low metamorphic grade.  相似文献   

On the hydraulic intake shape factor for a circular opening located at an impervious boundary: Influence of inclined stratification     

A. P. S. Selvadurai 《国际地质力学数值与分析法杂志》2011,35(6):639-651

In this paper, we develop an exact closed form solution for a circular entry point located at the interface between an impermeable material and a stratified porous medium, where the principal plane of hydraulic isotropy is inclined to the interface. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Use of the Geometric Elements in Numerical Simulations     

Stéfan Renner  Bruno Sicardy 《Celestial Mechanics and Dynamical Astronomy》2006,94(2):237-248

We derive the transformations to convert the state vector in cartesian coordinates into geometric orbital elements (and conversely the geometric elements into the state vector) for a test particle moving around an oblate planet. These transformations arise from the epicyclic theory and are accurate to second order in eccentricity and inclination. This paper is written to be directly used for computational purposes, such as the numerical study of ring dynamics.  相似文献