Dynamic stiffness matrices for two circular foundations     

Gin-Show Liou 《地震工程与结构动力学》1994,23(2):193-210

A systematic procedure is presented for generating dynamic stiffness matrices for two independent circular foundations on an elastic half-space medium. With the technique reported in References 1–3, the analytic solution of three-dimensional (3D) wave equations satisfying the prescribed traction due to the vibration of one circular foundation can be found. Since there are two analytic solutions for two prescribed tractions due to the vibrations of two circular foundations, the principle of superposition must be used to obtain the total solution. The interaction stresses (prescribed tractions) are assumed to be piecewise linear in the r-directions of both cylindrical co-ordinates for the two circular foundations. Then, the variational principle and the reciprocal theorem are employed to generate the dynamic stiffness matrices for the two foundations. In the process of employing the variational principle, a co-ordinate transformation matrix between two cylindrical co-ordinate systems is introduced. Some numerical results of dynamic stiffness matrices for the interaction of two identical rigid circular foundations are presented in order to show the effectiveness and efficiency of the present method, and some elaborations for its future extensions are also discussed.  相似文献   

Petrology of the diamond-grade eclogite in the Kokchetav Massif, northern Kazakhstan   总被引：2，自引：0，他引：2  

K. Okamoto  J. G. Liou and  Y. Ogasawara 《Island Arc》2000,9(3):379-399

Abstract The Kokchetav Massif of northern Kazakhstan is unique because of the abundant occurrence of microdiamond inclusions in garnet, zircon and clinopyroxene of metasediments. In order to determine precise pressure–temperature (P–T) conditions, we have systematically investigated mineral inclusions and the compositions of major silicates in Ti–clinohumite–garnet peridotite and diamond-grade eclogite from Kumdy–Kol. It was found that garnet peridotites from Kumdy–Kol contain assemblages of garnet, olivine, Ti–clinohumite and ilmenite. The garnet contains inclusions that are indicative of both ultrahigh pressure (UHP) and retrograde conditions. Inclusions of hydrous phases such as chlorite, amphibole and zoisite were formed at the post-UHP stage. The study also found that eclogite from Kumdy–Kol contains albite–augite symplectites after omphacitic pyroxene. The core of pyroxene (sodic augite) contains high K₂O (up to 1wt%; average 0.24wt%). Phengite is included in the core. Applying the K₂O-in-augite geobarometry, which is based on recent experiments, and the garnet–clinopyroxene (Grt–Cpx) geothermometer for peak metamorphism, the eclogites yield P–T estimates of > 6 GPa and > 1000 °C, and the diamond-grade eclogites yield lower temperature estimates at 900–1000 °C and 5 GPa.  相似文献   

Analysis of atmospheric and ionospheric structures using the GPS/MET and CHAMP radio occultation database: a methodological review     

Y. A. Liou  A. G. Pavelyev  J. Wickert  T. Schmidt  A. A. Pavelyev 《GPS Solutions》2005,9(2):122-143

Since 1995, the global positioning system (GPS) has been exploited by the means of the radio occultation (RO) method to obtain the vertical profiles of refractivity, temperature, pressure, and water vapor in the neutral atmosphere and electron density in the ionosphere. Applying the RO method to the study of the Earths atmosphere was demonstrated for the first time with the GPS/MET experiment. Since then, several satellites with GPS receivers, suitable for RO experiments, have been launched including Oersted, SUNSAT, CHAMP, SAC-C, and GRACE. Future RO investigations that are planned now include FORMOSAT3/COSMIC and Terra-SAR missions. New elements in the RO technology are required to meet the goals of improving the accuracy and broadening the potential of the RO method. In this paper, a methodological review of RO investigations is presented to emphasize new directions in applying the RO method: measuring the vertical gradients of the refractivity in the atmosphere and electron density in the lower ionosphere, determination of the temperature regime in the upper stratosphere, investigation of the internal wave activity in the atmosphere, and study of the ionospheric disturbances on a global scale. These new directions may be relevant for investigating the relationships between processes in the atmosphere and mesosphere, the study of thermal regimes in the intermediate heights of the upper stratosphere—lower mesosphere, and the analysis of the influence of the space weather phenomena on the lower ionosphere.  相似文献   

Petrogenesis of UHP metamorphic rocks from Qinglongshan, southern Sulu, east-central China   总被引：23，自引：0，他引：23  

Zeming Zhang  Yilin Xiao  Fulai Liu  J.G. Liou  Jochen Hoefs 《Lithos》2005,81(1-4):189-207

Five kinds of UHP metamorphic rocks, including eclogite, orthogneiss, paragneiss, schist and quartzite are exposed in the Qinglongshan roadcut, southern Sulu orogenic belt of eastern central China. They comprise metamorphic supracrustal rocks with bimodal volcanic characteristics and continental affinity, and granitic intrusive associations. The preservation of coesite inclusions and/or its pseudomorphs in eclogite and other rocks indicate that they have been subjected to in-situ UHP metamorphism. Four stages of metamorphism were recognized by combining petrographic observations and compositions of minerals from various UHP rocks. Prograde epidote-amphibolite facies, UHP coesite–eclogite facies, post UHP quartz–eclogite facies, and retrograde amphibolite facies assemblages delineate an inferred P–T path with a clockwise trajectory and a retrograde event characterized by the coupling of decompression with a temperature decrease. Garnet porphyroblasts in UHP eclogites display a complex growth zoning and mineral distribution, and record a crucial segment of the prograde and retrograde metamorphic evolution. The preservation of growth zoning in eclogitic and gneissic garnets suggests that the UHP rocks had a short residence time before retrograde metamorphism and a very high uplift rate in order to preserve the prograde growth zoning.  相似文献   

Ultrahigh pressure metamorphic rocks from the Chinese Continental Scientific Drilling Project: I. Petrology and geochemistry of the main hole (0–2,050 m)     

Zeming Zhang  Yilin Xiao  Jochen Hoefs  J. G. Liou  Klaus Simon 《Contributions to Mineralogy and Petrology》2006,152(4):421-441

The main hole (MH) of the Chinese Continental Scientific Drilling Project (CCSD) in southern Sulu has penetrated into an ultrahigh-pressure (UHP) metamorphic rock slice which consists of orthogneiss, paragneiss, eclogite, ultramafic rock and minor schist. Recovered eclogites have a UHP metamorphic mineral assemblage of garnet + omphacite + rutile ± phengite ± kyanite ± coesite ± epidote. Ultramafic rocks contain garnet + olivine + clinopyroxene + orthopyroxene ± Ti-clinohumite ± phlogopite. Gneisses and schists contain an amphibolite-facies paragenesis, but their zircons have coesite, garnet, omphacite (or jadeite) and phengite inclusions, indicating that eclogites and gneisses have been subjected to in situ UHP metamorphism. Using available geothermobarometers, P–T estimates of 3.1–4.4 GPa and 678–816°C for eclogites were obtained. If surface outcrops and neighboring shallow drill holes are considered together, we suggest that a huge supracrustal rock slab (> 50 km long × 100 km wide × 5 km deep) was subducted to a depth > 100 km and then exhumed to the surface. The depth interval (0–2,050 m) of the CCSD-MH can be divided into six lithological units. Unit 1 consists of alternating layers of quartz-rich and rutile-rich eclogites, with thin interlayers of gneiss and schist. Eclogites of unit 1 are characterized by Nb, Ta, Sr and Ti depletions, low Mg number and general LREE enrichment. Unit 2 comprises rutile- and ilmenite-rich eclogite and minor “normal” eclogite and is characterized by high TiO₂, total Fe, V, Co and Sr, and very low SiO₂, alkali, Zr, Ba, Nb, Ta and total REE contents, and LREE-depleted REE patterns with slightly positive Eu anomalies. Unit 3 contains ultramafic rock and minor MgO-rich eclogite. Protoliths of UHP rocks from units 1, 2 and 3 represent a layered mafic to ultramafic intrusion at crustal depth. Units 4 and 6 consist of interlayered eclogite and paragneiss; the eclogites are characterized by Th, U, Nb, Ta and Ti depletion and K enrichment and LREE-enriched REE patterns. Paragneisses show Nb, Ta, Sr and Ti depletions and LREE-enriched REE patterns occasionally with slightly negative Eu anomalies, indicating that their protoliths represent metamorphic supracrustal series. Unit 5 consists mainly of orthogneisses, showing distinct Nb, Ta, Sr and Ti depletions, and LREE-enriched REE patterns with pronounced negative Eu anomalies, suggesting granitic protoliths. In conclusion it is proposed that the southern Sulu UHP belt consists of a series of meta-supracrustal rocks, a layered mafic–ultramafic complex and granites.  相似文献   

Geochronology and tectonic significance of Middle Proterozoic granitic orthogneiss, North Qaidam HP/UHP terrane, Western China   总被引：4，自引：0，他引：4  

C. G. Mattinson  J. L. Wooden  J. G. Liou  D. K. Bird  C. L. Wu 《Mineralogy and Petrology》2006,88(1-2):227-241

Summary Amphibolite-facies para- and orthogneisses near Dulan, in the southeast part of the North Qaidam terrane, enclose minor ultra-high pressure (UHP) eclogite and peridotite. Field relations and coesite inclusions in zircons from paragneiss suggest that felsic, mafic, and ultramafic rocks all experienced UHP metamorphism and a common amphibolite-facies retrogression. Ion microprobe U–Pb and REE analyses of zircons from two granitic orthogneisses indicate magmatic crystallization at 927 ± Ma and 921 ± 7 Ma. Zircon rims in one of these samples yield younger ages (397–618 Ma) compatible with partial zircon recrystallization during in-situ Ordovician-Silurian eclogite-facies metamorphism previously determined from eclogite and paragneiss in this area. The similarity between a 2496 ± 18 Ma xenocrystic core and 2.4–2.5 Ga zircon cores in the surrounding paragneiss suggests that the granites intruded the sediments or that the granite is a melt of the older basement which supplied detritus to the sediments. The magmatic ages of the granitic orthogneisses are similar to 920–930 Ma ages of (meta)granitoids described further northwest in the North Qaidam terrane and its correlative west of the Altyn Tagh fault, suggesting that these areas formed a coherent block prior to widespread Mid Proterozoic granitic magmatism.  相似文献   

Use of geochemical modeling to evaluate the hydraulic connection of aquifers: a case study from Chianan Plain, Taiwan   总被引：1，自引：0，他引：1  

Hsueh-Yu Lu  Tsung-Kwei Liu  Wen-Fu Chen  Tsung-Ren Peng  Chung-Ho Wang  Meng-Hsun Tsai  Tai-Sheng Liou 《Hydrogeology Journal》2008,16(1):139-154

Aquifers are generally composed of highly permeable layers that can conduct a considerable amount of groundwater. Traditionally, aquifer units are correlated through the concept of lithostratigraphy. For low-permeable aquifers, it is difficult to define the spatial distribution of hydrogeological units, and this study attempts to use geochemical modeling to identify the groundwater flow paths in an area of Taiwan. Multiple geochemical analyses, including groundwater chemistry; stable isotopic compositions of hydrogen, oxygen and carbon; and radiocarbon contents were performed. Using these parameters as the constraints of geochemical models, the hydraulic connection was examined between pairs of possibly interlinked wells along four selected cross sections, and the conceptual groundwater model was accordingly established. The resultant model suggests that the hydraulic connection between aquifers should be correlated with the concept of chronological stratigraphy, especially for low-permeable, unconsolidated aquifers. Using Darcy’s law, the hydraulic conductivities of the fine-sand aquifers were estimated to be between 3.14 × 10⁻⁵ and 1.80 × 10⁻⁴ m/s, which are roughly one order of magnitude higher than those derived by in situ pumping tests. The substantial extraction of groundwater over a long period in the studied area could accelerate groundwater flow, leading to an overestimation of the aquifer permeability.

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Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.

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Résumé En règle générale, les aquifères sont constitués de couches très perméables capables de conduire des quantités d’eau considérables. Les unités aquifères sont traditionnellement corrélées d’un point de vue lithostratigraphique. Dans le cas des aquifères à faible perméabilité, il s’avère difficile de définir une distribution spatiale des unités hydrogéologiques, et cette étude tente d’utiliser la modélisation géochimique pour identifier les cheminements des eaux souterraines dans un secteur de Taiwan. Plusieurs analyses géochimiques ont été réalisées ; elles incluent la chimie des eaux souterraines, les isotopes stables de l’hydrogène, de l’oxygène et du carbone et l’abondance en carbone 14. En utilisant ces paramètres comme contraintes pour les modèles géochimiques, les liaisons hydrauliques entre les puits potentiellement interconnectés ont été étudiées deux par deux, le long de quatre coupes présélectionnées, et le modèle conceptuel a été établi en conséquence. Ce modèle résultant suggère que les connexions hydrauliques inter-aquifères devraient être corrélées avec les concepts stratigraphiques, surtout pour les aquifères non consolidés à faible perméabilité. Les perméabilités dans les aquifères de sables fins ont été estimées par la loi de Darcy entre 3.14 × 10⁻⁵ et 1.80 × 10⁻⁴ m/s, soit environ un ordre de grandeur au-dessus de celles issues des tests de pompage sur site. L’exploitation substantielle des eaux souterraines sur une longue période dans la zone d’étude peut accélérer les écoulements souterrains, menant à une surestimation de la perméabilité de l’aquifère.

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Resumen Los acuíferos están generalmente compuestos de capas muy permeables que pueden conducir una cantidad considerable de agua subterránea. Tradicionalmente, se ponen en correlación las unidades acuíferas a través del concepto de litoestratigrafía. Para los acuíferos de baja-permeabilidad, es difícil de definir la distribución espacial de unidades hidrogeológicas y este estudio intenta usar modelamiento geoquímico para identificar las direcciones del flujo de agua subterránea en un área de Taiwán. Se realizó el análisis geoquímico múltiple, incluyendo la química del agua subterránea, la composición de isótopos estables de hidrógeno, oxígeno y carbono, y el contenido de radiocarbono. Usando estos parámetros como limitantes de modelos geoquímicos, la conexión hidráulica se examinó entre pares de pozos posiblemente interrelacionados, a lo largo de cuatro cortes transversales seleccionados y de acuerdo con esto se estableció el modelo conceptual del agua subterránea. El modelo resultante sugiere que la conexión hidráulica entre los acuíferos deba interrelacionarse con el concepto de estratigrafía cronológica, sobre todo para los acuíferos sin consolidar de baja permeabilidad. Usando la ley de Darcy, se estimaron las conductividades hidráulicas de los acuíferos de arena fina obteniendo valores entre 3.14 × 10⁻⁵ y 1.80 × 10⁻⁴ m/s, las cuales son aproximadamente un orden de magnitud mayor, que aquéllos obtenidos in situ por las pruebas de bombeo. La extracción considerable de agua subterránea durante un periodo largo en el área estudiada, podría acelerar el flujo de agua subterránea, llevando a una sobrestimación de la permeabilidad en los acuíferos.

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