Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.     

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

We investigate our ability to assess transfer of hexavalent chromium, Cr(VI), from the soil to surface runoff by considering the effect of coupling diverse adsorption models with a two‐layer solute transfer model. Our analyses are grounded on a set of two experiments associated with soils characterized by diverse particle size distributions. Our study is motivated by the observation that Cr(VI) is receiving much attention for the assessment of environmental risks due to its high solubility, mobility, and toxicological significance. Adsorption of Cr(VI) is considered to be at equilibrium in the mixing layer under our experimental conditions. Four adsorption models, that is, the Langmuir, Freundlich, Temkin, and linear models, constitute our set of alternative (competing) mathematical formulations. Experimental results reveal that the soil samples characterized by the finest grain sizes are associated with the highest release of Cr(VI) to runoff. We compare the relative abilities of the four models to interpret experimental results through maximum likelihood model calibration and four model identification criteria (i.e., the Akaike information criteria [AIC and AIC_C] and the Bayesian and Kashyap information criteria). Our study results enable us to rank the tested models on the basis of a set of posterior weights assigned to each of them. A classical variance‐based global sensitivity analysis is then performed to assess the relative importance of the uncertain parameters associated with each of the models considered, within subregions of the parameter space. In this context, the modelling strategy resulting from coupling the Langmuir isotherm with a two‐layer solute transfer model is then evaluated as the most skilful for the overall interpretation of both sets of experiments. Our results document that (a) the depth of the mixing layer is the most influential factor for all models tested, with the exception of the Freundlich isotherm, and (b) the total sensitivity of the adsorption parameters varies in time, with a trend to increase as time progresses for all of the models. These results suggest that adsorption has a significant effect on the uncertainty associated with the release of Cr(VI) from the soil to the surface runoff component.     

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.     

Canonical theory of perturbations using eccentric anomaly as independent variable

It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy.     

中国古生教授学会微体古生物学分会举行代表大会和学术年会

中国古生教授学会微体古生物学分会举行代表大会和学术年会中国古竽物学会微体古物学分会第五次会员代表大分暨第六次不术年会于１９９６年１月２４日到３０日在福州市召开。来自全国地质、石油、煤炭的和产、科研和大学的１００多位代表参加了这次大会和学术研讨。大会共...     

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.