Age and early metamorphic history of the Sanbagawa belt: Lu–Hf and P–T constraints from the Western Iratsu eclogite

Two distinct age estimates for eclogite-facies metamorphism in the Sanbagawa belt have been proposed: (i) c.  120–110 Ma based on a zircon SHRIMP age for the Western Iratsu unit and (ii) c.  88–89 Ma based on a garnet–omphacite Lu–Hf isochron age from the Seba and Kotsu eclogite units. Despite the contrasting estimates of formation ages, petrological studies suggest the formation conditions of the Western Iratsu unit are indistinguishable from those of the other two units—all ∼20 kbar and 600–650 °C. Studies of the associated geological structures suggest the Seba and Western Iratsu units are parts of a larger semi-continuous eclogite unit. A combination of geochronological and petrological studies for the Western Iratsu eclogite offers a resolution to this discrepancy in age estimates. New Lu–Hf dating for the Western Iratsu eclogite yields an age of 115.9 ± 0.5 Ma that is compatible with the zircon SHRIMP age. However, petrological studies show that there was significant garnet growth in the Western Iratsu eclogite before eclogite facies metamorphism, and the early core growth is associated with a strong concentration of Lu. Pre-eclogite facies garnet (Grt1) includes epidote–amphibolite facies parageneses equilibrated at 550–650 °C and ∼10 kbar, and this is overgrown by prograde eclogite facies garnet (Grt2). The Lu–Hf age of c.  116 Ma is strongly skewed to the isotopic composition of Grt1 and is interpreted to reflect the age of the pre-eclogite phase. The considerable time gap ( c.  27 Myr) between the two Lu–Hf ages suggests they may be related to separate tectonic events or distinct phases in the evolution of the Sanbagawa subduction zone.     

P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

An explicit representation of steady state response of a beam on an elastic foundation to moving harmonic line loads

A closed‐form deflection response of a beam rest is presented in this paper using the integral transform method. The theory of linear partial differential equations is used to represent the deflection of beam subjected to a moving harmonic line load in integration form. The solution is finally carried out using the inverse Fourier transform. To evaluate the integration analytically, poles of the integrand are identified with the help of algebraic equation theory. Residue theorem is then utilized to represent the integration as a contour integral in the complex plane. Closed‐form deflections and numerical results are provided for different combinations of load frequency and velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

Metamorphic phase relations in orthopyroxene-bearing granitoids: implication for high-pressure metamorphism and prograde melting in the continental crust

In this work, the factors controlling the formation and preservation of high-pressure mineral assemblages in the metamorphosed orthopyroxene-bearing metagranitoids of the Sandmata Complex, Aravalli-Delhi Mobile Belt (ADMB), northwestern India have been modelled. The rocks range in composition from farsundite through quartz mangerite to opdalite, and with varying K₂O, Ca/(Ca + Na)_rock and FeO_tot + MgO contents. A two stage metamorphic evolution has been recorded in these rocks.
An early hydration event stabilized biotite with or without epidote at the expense of magmatic orthopyroxene and plagioclase. Subsequent high-pressure granulite facies metamorphism (∼15 kbar, ∼800 °C) of these hydrated rocks produced two rock types with contrasting mineralogy and textures. In the non-migmatitic metagranitoids, spectacular garnet ± K-feldspar ± quartz corona was formed around reacting biotite, plagioclase, quartz and/or pyroxene. In contrast, biotite ± epidote melting produced migmatites, containing porphyroblastic garnet incongruent solids and leucosomes.
Applying NCKFMASHTO T–M (H₂O) and P–T pseudosection modelling techniques, it is demonstrated that the differential response of these magmatic rocks to high-pressure metamorphism is primarily controlled by the scale of initial hydration. Rocks, which were pervasively hydrated, produced garnetiferous migmatites, while for limited hydration, the same metamorphism formed sub-solidus garnet-bearing coronae. Based on the sequence of mineral assemblage evolution and the mineral compositional zoning features in the two metagranitoids, a clockwise metamorphic P–T path is constrained for the high-pressure metamorphic event. The finding has major implications in formulating geodynamic model of crustal amalgamation in the ADMB.     

Transient‐state groundwater flow in various geometries with wells at arbitrary positions: analytical methods

We have developed a method for analytically solving the porous medium flow equation in many different geometries for horizontal (two‐dimensional), homogeneous and isotropic aquifers containing impermeable boundaries and any number of pumping or injection wells located at arbitrary positions within the system. Solutions and results are presented for rectangular and circular aquifers but the method presented here is easily extendible to many geometries. Results are also presented for systems where constant head boundary conditions can be emulated internal to the aquifer boundary. Recommendations for extensions of the present work are briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd.     

The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

量子化学方法研究氯代苯酚类化合物对水生物毒性的构效关系

对20个氯代苯酚类化合物进行了CNDO/2量子化学计算,讨论了化合物电子结构与其对水生物翻车鱼(Bluegill)、花鳉鱼(Guppy)、和虾(Shrimp)半致死量之间的关系,分别获得了表示其构效关系的三个线性方程,它们的显著性均远高于α=0.01水平。结果表明:氯代苯酚化合物苯环上碳原子的兀电荷之和(∑Qπ_R)越大苯环上碳原子的净电荷之和(∑Q_R)越大,或LUMO轨道能(E_(LUMO))越低,均使化合物对Bluegill和Guppy水生物的毒性增大;而化合物苯环上羟基邻位的碳原子的兀电荷布居(P_3)越大,同时HOMO轨道能E_(HOMO)越高,则化合物对Shrimp毒性也越大。据此,可预测氯代苯酚类化合物对上述三种水生物的毒性。