Analytic solutions for soil-structure interaction in layered media

The total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil-structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented.     

Ultrahigh-pressure metamorphism and tectonics

Abstract Recognition of several ultrahigh-pressure (UHP) metamorphic terranes in continental collision belts has revolutionized the concept of geodynamic processes. In order to facilitate better communication and focus among active investigators, the Task Group III-6 of the International Lithosphere Program'Ultrahigh-Pressure Metamorphism and Geodynamics in Collision-type Orogenic Belts'held the first two day workshop at Stanford University in December, 1994. Petrotectonic settings, mineral paragenesis, geochronoldgy, and geochemical characteristics of UHP rocks from several recognized and suspected UHP terranes were addressed. This special issue presents 11 papers from the more than 50 contributions from the 88 participants representing 15 countries. Many challenging petrotectonic and petrochemical problems remain to be investigated. These include detailed P-T time paths for both the UHP unit and adjacent units, the role of fluids at mantle depths, deep seismic profiles and mechanisms and rate of exhumation of the UHP unit.     

Petrology and retrograde P-T path for eclogites of the Maksyutov Complex, Southern Ural Mountains, Russia

Abstract The Maksyutov Complex, situated in the southern Ural Mountains of Russia, is the first location where quartz aggregates within garnets exhibiting radial fractures were identified as coesite pseudomorphs (Chesnokov & Popov 1965). The complex consists of two tectonic units: a structurally lower eclogite-bearing schist unit and an overlying meta-ophiolite unit. Both units show evidence for multiple stages of metamorphism and deformation. The high-pressure metamorphism of the eclogite-bearing schist unit, discussed in this report, is suspected to be related to a collision between the Russian platform and a fragment of the Siberian continent during the early Cambrian. At least three stages of metamorphism (M_1-3) and two stages of deformation (S₁ and S₂) were observed in thin sections: M₁) garnet (Alm_55-60, Prp_22-28, Grs_16-20) + omphacite (Jd_46-56) + phengite (Si ≅ 3.5) + rutile; M₂) garnet + glaucophane ± lawsonite + white mica; and M₃) epidote + chlorite ± albite ± actinolite + white mica. Observed mineral parageneses define a retrograde P-T path for the eclogite. Mineral assemblages within the most representative eclogite from the lower unit of the Maksyutov Complex indicate minimum peak pressures of 15 kbar at temperatures of approximately 600°C. If the presence of coesite pseudomorph is confirmed, the peak ultrahigh-pressure metamorphism may be as high as 27 kbar at 615°C.     

Titanium solubility in coexisting garnet and clinopyroxene at very high pressure: the significance of exsolved rutile in garnet

Exsolution microstructures including ilmenite±garnet in clinopyroxene and rutile in garnet are common in clinopyroxenite and eclogite from the Sulu ultrahigh-pressure (UHP) terrane. In order to understand the phase relations and Ti solubility in both garnet and clinopyroxene in a natural TiO₂-bearing system, several experiments at 5-15 GPa, 1000-1400°C were carried out using the multianvil high-pressure apparatus. The Hujianlin ilmenite-rich garnet clinopyroxenite showing exsolution microstructure was selected as starting material, because it closely approaches a composition lying in the TiO₂-CaO-MgO-FeO-Al₂O₃-SiO₂ system. Except for minor melt in one experiment at 1400°C and 5 GPa, other run products contain majoritic garnet+clinopyroxene±ilmenite (or rutile) and exhibit neoblastic texture. With increasing pressure, Ti and Ca, Mg and Si contents of neoblastic garnet increase with decreasing Al. The principal coupled substitutions are Ca²⁺Ti⁴⁺→2Al³⁺ and Si⁴⁺Mg²⁺→2Al³⁺ responding to majorite component increase. Titanium solubility (0.8-4.5 wt% as TiO₂) in garnet and Grt_Ti/Cpx_Ti ratio have a pronounced positive correlation with pressure between 5 and 15 GPa. On the other hand, the coexisting clinopyroxene contains low Ti (0.17-0.53 wt% as TiO₂), and shows no significant pressure effect. Rutile exsolution in garnet is coupled to that of pyroxene exsolution; both are exsolved from majoritic garnet on decompression. Therefore, the amount of such exsolved lamellae is a potential indicator of high-pressure metamorphism in exhumed rocks, whereas the TiO₂ content of clinopyroxene coexisting with garnet is not sensitive to pressure change.     

Fixed-frequency Stokes wave expansion

The study describes a new fixed-frequency Stokes wave theory that differs from previous Stokes wave theories that fix the wave number. The present wave expansion analytically reveals that the wavelength increases with wave height and exceeds than the wavelength obtained by linear wave theory. A method proposed to comparably transform the wave celerity of Fenton's [Fenton, J.D., 1985. A fifth-order Stokes theory for steady waves. Journal of Waterway, Port, Coastal and Ocean Engineering 111, 216–234.] wave theory to the present one. A direct calculation of the wavelength is introduced for practical solutions, avoiding the need to solve a nonlinear equation using an iterative numerical method.     

Sensitivity of high-resolution tropical cyclone intensity forecasts to surface flux parameterization

Surface flux parameterization schemes used in current dynamic models are primarily based upon measurements at low and moderate wind speeds. Recent studies show that these parameterization schemes may be incorrect at high wind speeds (e.g., tropical cyclone forecasts). Five high-resolution numerical model experiments are designed to assess the sensitivity of tropical cyclone intensity forecasts to changes in the surface flux parameterization. The sensitivity experiments are conducted by running 48 h forecasts of the Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS) for six selected tropical cyclones with individual modifications to surface flux calculation that include: (1) limiting the surface stress for wind speeds greater than 33 m s⁻¹, or 64 knots (kt); (2) computing the stress at the top of the model bottom grid layer (MBGL) by averaging results from surface layer similarity and turbulence mixing parameterization for wind speeds greater than 33 m s⁻¹; (3) increasing the roughness lengths for heat and moisture transfer by a factor of ten; (4) setting the roughness lengths for heat and moisture transfer to 1/10 of the momentum roughness length; and (5) cooling the sea surface temperature (SST) by a prescribed rate at high winds. Averaged responses for the six storms to these sensitivity tests show that: (i) the limit on surface stress at high winds significantly increases the cyclone intensity in 48 h forecasts; (ii) the averaged surface layer stress at high winds increases the cyclone intensity but to a much lesser degree than limiting the surface stress; (iii) large increases in the roughness lengths for heat and moisture transfer are needed to significantly impact the intensity forecast; (iv) the different roughness length formula for surface transfer coefficients notably increases C _h/C _d ratio from 0.59 to 0.79 for 25 m s⁻¹ and 0.41 to 0.75 for 50 m s⁻¹ that significantly increases the predicted cyclone intensity; and (v) cooling of the SST by −5.8°C in 48 h reduces the maximum surface wind speed by −32 kt, or 16.5 m s⁻¹, at 48 h forecast. These results suggest that a surface flux parameterization scheme suitable for tropical cyclone intensity forecast must correctly model the leveling-off character of surface stress and C _h/C _d ratio at high winds. All modifications to surface flux calculation have little influence on 48 h track forecasts, even though they may significantly impact the intensity forecasts.

Petrological characterization and tectonic significance of retrogressed garnet peridotites, Raobazhai area, North Dabie Complex, east-central China

The Raobazhai ultramafic body of the North Dabie Complex is re-interpreted as a mantle-derived peridotitic slice enclosed in, and isofacially metamorphosed with, surrounding granulite-to-amphibolite facies gneisses. The ultramafic sheet consists mainly of metaharzburgite, but includes subunits of metadunite and mylonitic lherzolite. The rocks contain spinel but neither garnet nor plagioclase. However, in the mylonitic lherzolite, fine-grained intergrowths of spinel, orthopyroxene and clinopyroxene outline domains resembling the habit of garnet in two dimensions; broad-beam microprobe analyses imply pseudomorphs after a pyropic garnet precursor. The mineral assemblage of the metadunite and metaharzburgite is: olivine (Fo₉₂)+orthopyroxene (En₉₂)+tremolitic-to-magnesiohornblende+Mg–Al-chromite, indicating amphibolite facies recrystallization. The mineral assemblage of the mylonitic lherzolite is: olivine (Fo₉₀)+orthopyroxene (En₉₀)+clinopyroxene+Cr-bearing spinel+pargasitic amphibole, indicative of granulite-to-amphibolite facies metamorphism. Phase equilibria and geothermometric estimations show that the Raobazhai meta-ultramafics have undergone at least three stages of recrystallization: (I) 950–990 °C, (II) 750–860 °C, and (III) 670–720 °C, assuming equilibrium in the spinel peridotite stability field ( c. 6–15 kbar), although an early, high-pressure stage (≥18 kbar) is probable, based on the inferred garnet pseudomorphs. Petrochemical and geothermobarometric data suggest that the ultramafic slice represents a fragment of the mantle wedge, tectonically incorporated into subducted continental crust and re-equilibrated at granulite-to-amphibolite facies conditions while being exhumed to shallow levels.