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.     

Analytical study of ground motion caused by seismic wave propagation across faulted rock masses

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.     

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.     

影响鸢乌贼手钓上钩率的因子探讨

根据印度洋西北部鸢乌贼（Sym plectoteuthis oualaniensis）作业渔场的现场调查数据．分析了作业水深、作业时段、摄食等级和月相等因子对手钓上钩率的影响。统计表明．晚上、午夜和凌晨3个不同时段和不同作业水深对手钓上钩率均有显著性影响。3个时段中，其摄食等级呈先低后高再低的现象。午夜和凌展，上钩率的变化趋势与摄食等级的变化趋势呈显著的负相关。在月相的影响下．离朔日三四天之前，手钓产量呈上升趋势；离望日五六天之前。手钓产量呈明显的下降趋势。     

AGGLOMERATION AND RADIATION EFFECT OF THE PULL OF URBANIZATION

In order to explore the train of thought for China‘s urbanizing development and coordinated rural eco-nomic development, and to find good ways of solving rural problems through urbanization, this paper absorbs the push-and-pull forces theory and the systematic dynamic theory in the traditional population migration theories, views urbanization as a dynamic system, makes research on the push-and-pull mechanism of urbanization. The pulling power of urbanization is analyzed according to two aspects, the agglomeration effect and the radiation effect of cities. The agglomeration effect provides continuous propelling force for urbanization, and the radiation effect further accelerates the urbanization process by pushing forward the development of rural economy. Of course, the slow de-velopment of urbanization can result in the hindrance to rural economic development.     

Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

GRADATION AND ASSESSMENT OF DAMAGE DEGREE OF NATURAL LANDSCAPE IN XING, AN COUNTY, GUANGXI

A new technique designed to help quantify the degree of damage to the landscape from one area to another shows a close relationship between population density and the degree of landscape damage. The technique establishes a scale of damage from 0 to 5 (zero = no damage; 5 = severe damage) using data from aerial photographs, land-use maps, and field data. The related formula allows one to compare the relative degree of damage across regions using a combination of an absolute index, a theoretical index, a relative index, and population density. Xing'an County is used to demonstrate the technique.     

Opposition polarimetry and photometry of S- and E-type asteroids

The first results of the observational program devoted to simultaneous investigation of asteroid polarimetric and photometric opposition phenomena are presented. UBVRI polarimetric and V-band photometric observations of the S-type Asteroid 20 Massalia and the E-type Asteroids 214 Aschera and 620 Drakonia were carried out in 1996-1999 down to phase angles of 0.08°, 0.7°, and 1.2°, correspondingly. The S-type Asteroid 20 Massalia is characterized by the pronounced brightness opposition surge with an amplitude larger than that observed for the E-type asteroids. A sharp peak of negative polarization at small phase angles was not observed for this asteroid. The value of polarization degree at phase angle α<1° is less than 0.5% for both S and E types. The negative polarization branches of S and especially E-asteroids have an asymmetrical shape. The phase angle at which the polarization minimum occurs is close to the angle at which non-linear increase begins in the asteroid magnitude phase curves. A relation of the observed effects to the mechanism of coherent backscattering is discussed.     

Synthetic SH seismograms in a laterally varying medium by the discrete wavenumber method

Summary. We present a new method to calculate the SH wavefield produced by a seismic source in a half-space with an irregular buried interface. The diffracting interface is represented by a distribution of body forces. The Green's functions needed to solve the boundary conditions are evaluated using the discrete wavenumber method. Our approach relies on the introduction of a periodicity in the source-medium configuration and on the discretization of the interface at regular spacing. The technique developed is applicable to boundaries of arbitrary shapes and is valid at all frequencies. Some examples of calculation in simple configurations are presented showing the capabilities of the method.