Application of micropolar plasticity to post failure analysis in geomechanics

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy–Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Zircon U–Pb age, trace element and Hf isotope composition of Kongling terrane in the Yangtze Craton: refining the timing of Palaeoproterozoic high-grade metamorphism

U–Pb age, trace element and Hf isotope compositions of zircon were analysed for a metasedimentary rock and two amphibolites from the Kongling terrane in the northern part of the Yangtze Craton. The zircon shows distinct morphological and chemical characteristics. Most zircon in an amphibolite shows oscillatory zoning, high Th/U and ¹⁷⁶Lu/¹⁷⁷Hf ratios, high formation temperature, high trace element contents, clear negative Eu anomaly, as well as HREE-enriched patterns, suggesting that it is igneous. The zircon yields a weighted mean ²⁰⁷Pb/²⁰⁶Pb age of 2857 ± 8 Ma, representing the age of the magmatic protolith. The zircon in the other two samples is metamorphic. It has low Th/U ratios, low trace element concentrations, variable HREE contents (33.8 ≥ Lu_N≥2213; 14.7 ≤ Lu_N/Sm_N ≤ 354) and ¹⁷⁶Lu/¹⁷⁷Hf ratios (0.000030–0.001168). The data indicate that the zircon formed in the presence of garnet and under upper amphibolite facies conditions. The metamorphic zircon yields a weighted mean ²⁰⁷Pb/²⁰⁶Pb age of 2010 ± 13 Ma. These results combined with previously obtained Palaeoproterozoic metamorphic ages suggest a c. 2.0 Ga Palaeoproterozoic collisional event in the Yangtze Craton, which may result from the assembly of the supercontinent Columbia. The zircon in two samples yields weighted mean two-stage Hf model ( T _DM2) ages of 3217 ± 110 and 2943 ± 50 Ma, respectively, indicating that their protoliths were mainly derived from Archean crust.     

Pressure-induced incipient amorphization of α-quartz and transition to coesite in an eclogite from Antarctica: a first record and some consequences

Monocrystalline quartz inclusions in garnet and omphacite from various eclogite samples from the Lanterman Range (Northern Victoria Land, Antarctica) have been investigated by cathodoluminescence (CL), Raman spectroscopy and imaging, and in situ X‐ray (XR) microdiffraction using the synchrotron. A few inclusions, with a clear‐to‐opalescent lustre, show ‘anomalous’ Raman spectra characterized by weak α‐quartz modes, the broadening of the main α‐quartz peak at 465 cm^?1, and additional vibrations at 480–485, 520–523 and 608 cm^?1. CL and Raman imaging indicate that this ‘anomalous’α‐quartz occurs as relicts within ordinary α‐quartz, and that it was preserved in the internal parts of small quartz inclusions. XR diffraction circular patterns display irregular and broad α‐quartz spots, some of which show an anomalous d‐spacing tightening of ～2%. They also show some very weak, hazy clouds that have d‐spacing compatible with coesite but not with α‐quartz. Raman spectrometry and XR microdiffraction characterize the anomalies with respect to α‐quartz as (i) a pressure‐induced disordering and incipient amorphization, mainly revealed by the 480–485 and 608‐cm^?1 Raman bands, together with (ii) a lattice densification, evidenced by d‐spacing tightening; (iii) the cryptic development of coesite, 520–523 cm^?1 being the main Raman peak of coesite and (iv) Brazil micro‐twinning. This ‘anomalous’α‐quartz represents the first example of pressure‐induced incipient amorphization of a metastable phase in a crustal rock. This issue is really surprising because pressure‐induced amorphization of metastable α‐quartz, observed in impactites and known to occur between 15 and 32 GPa during ultrahigh‐pressure (UHP) experiments at room temperature, is in principle irrelevant under normal geological P–T conditions. A shock (due to a seism?) or a local overpressure at the inclusion scale (due to expansion mismatch between quartz and its host mineral) seem the only geological mechanisms that can produce such incipient amorphization in crustal rocks. This discovery throws new light on the modality of the quartz‐coesite transition and on the pressure regimes (non‐lithostatic v. lithostatic) during high‐pressure/UHP metamorphism. In particular, incipient amorphization of quartz could favour the quartz‐coesite transition, or allow the growth of metastable coesite, as already experimentally observed.     

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.     

Solution to the rotation of the elastic earth by method of rigid dynamics

Hamiltonian mechanics is applied to the problem of the rotation of the elastic Earth. We first show the process for the formulation of the Hamiltonian for rotation of a deformable body and the derivation of the equations of motion from it. Then, based on a simple model of deformation, the solution is given for the period of Euler motion, UT1 and the nutation of the elastic Earth. In particular it is shown that the elasticity of the Earth acts on the nutation so as to decrease the Oppolzer terms of the nutation of the rigid Earth by about 30 per cent. The solution is in good agreement with results which have been obtained by other, different approaches.     

Porphyroblast inclusion-trail orientation data: eppure non son girate*!

Extensive examination of large numbers of spatially orientated thin sections of orientated samples from orogens of all ages around the world has demonstrated that porphyroblasts do not rotate relative to geographical coordinates during highly non-coaxial ductile deformation of the matrix subsequent to their growth. This has been demonstrated for all tectonic environments so far investigated. The work also has provided new insights and data on metamorphic, structural and tectonic processes including: (1) the intimate control of deformation partitioning on metamorphic reactions; (2) solutions to the lack of correlation between lineations that indicate the direction of movement within thrusts and shear zones, and relative plate motion; and (3) a possible technique for determining the direction of relative plate motion that caused orogenesis in ancient orogens.     

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.     

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.     

Chemical alteration of tephra in the depositional environment: theoretical stability modelling

The study of the chemical stability of vitreous material in aqueous media is well‐established. There has to date been little consideration of the implications of variations in the chemical durability of tephra in Quaternary tephrochronology. Chemical alteration can take the form of cationic leaching from the matrix, or complete destruction of the silica network, either of which could constrain the ability to chemically identify distal tephra. Here we apply established models of vitreous durability to the published chemical analyses of a large number of Icelandic tephras in order to predict their relative durabilities under equivalent conditions. This suggests that some important tephras have relatively poor chemical stability, and that rhyolitic tephras are, in general, more stable than basaltic. We conclude that tephras should be expected to show predictable differential chemical stability in the post‐depositional environment. Copyright © 2003 John Wiley & Sons, Ltd.