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.     

Revisiting the existence of an effective stress for wet granular soils with micromechanics

A possible effective stress variable for wet granular materials is numerically investigated based on an adapted discrete element method (DEM) model for an ideal three‐phase system. The DEM simulations consider granular materials made of nearly monodisperse spherical particles, in the pendular regime with the pore fluid mixture consisting of distinct water menisci bridging particle pairs. The contact force‐related stress contribution to the total stresses is isolated and tested as the effective stress candidate for dense or loose systems. It is first recalled that this contact stress tensor is indeed an adequate effective stress that describes stress limit states of wet samples with the same Mohr‐Coulomb criterion associated with their dry counterparts. As for constitutive relationships, it is demonstrated that the contact stress tensor used in conjunction with dry constitutive relations does describe the strains of wet samples during an initial strain regime but not beyond. Outside this so‐called quasi‐static strain regime, whose extent is much greater for dense than loose materials, dramatic changes in the contact network prevent macroscale contact stress‐strain relationships to apply in the same manner to dry and unsaturated conditions. The presented numerical results also reveal unexpected constitutive bifurcations for the loose material, related to stick‐slip macrobehavior.     

An approximate method for evaluating the shear band thickness in saturated soils

A formula for the thickness of a shear band formed in saturated soils under a simple shear or a combined stress state has been proposed. It is shown that the shear band thickness is dependent on the pore pressure properties of the material and the dilatancy rate, but is independent of the details of the combined stress state. This is in accordance with some separate experimental observations. Copyright © 2004 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.     

有限元法与伪谱法混合求解弹性波动方程

在地震波场数值模拟中,有限差分法、有限元法和伪谱法都是常用的基本方法,但它们各有不同的适应性和优缺点,如有限差分法、有限元法都存在减弱网格频散和提高计算效率的矛盾,而伪谱法的网格频散小且计算效率高.有限差分法和伪谱法在处理地表结构复杂或地表剧烈起伏以及地下结构复杂的情况时存在较大的难度,而有限元法可较为理想地拟合起伏地表和任意弯曲界面,且可方便地处理自由边界条件和界面边界条件.尝试将有限元法和伪谱法相结合,形成地震波场数值模拟的一种混合方法,利用二者的优点,克服二者的缺点,达到既减弱网格频散又提高计算精度和效率的目的.并采用所谓的‘过度区域‘技术解决两种不同算法的衔接问题.模拟实例表明,给出的混合模拟方法不失为弹性波场数值模拟的一种有效方法.     

Non-Newtonian topographic relaxation on Europa

Models of topographic support on Europa by lateral shell thickness variations have previously assumed a Newtonian ice viscosity. Here I show that using a more realistic stress-dependent viscosity gives relaxation times which can be significantly different. Topography of wavelength 100 km cannot be supported by lateral shell thickness variations for ∼50 Myr, unless the shell thickness is <10 km or the ice grain size >10 mm. Shorter wavelength topography would require even thinner shells, but may be supported elastically. Global-scale variations in shell thickness, however, can be supported for geological timescales if the shell thickness is O(10 km).     

Mid-ultraviolet and optical photometry of helium stars

Mid-ultraviolet and optical photometric analysis of helium stars are presented. A linear relation exists between the effective temperature derived from model atmospheres and (1965-V)₀ index. The effective temperatures derived from (1965-V)₀ index are somewhat higher than that of MK spectral type estimates especially for late B-type helium objects.     

Chaotic Diffusion And Effective Stability of Jupiter Trojans

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T_L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T_Land the escape time, T_E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T_E=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T_LandT_E is found.     

青藏高原及邻近区域的S波三维速度结构

本文收集了WWSSN台网和我国台网中13个地震台站的长周期地震记录,用140条10-90s瑞利波频散曲线和作者提出的Tarantola-Backus面波频散层析成象方法,作了青藏高原及邻区的速度反演,得出该地区岩石层速度结构的三维图象.结果表明,1.在10-110km深度范围内,速度结构出现与大地构造特征相关的分区性,显示出四个构造单元:青藏块体、柴达木-巴颜喀拉-三江块体、塔里木块体和印度块体.2.高原内部,深度为10-70km内速度较低,莫霍界面呈不对称盆形分布,藏北那曲附近地壳厚度超过70km,高原边缘壳厚为45-50km,90-110km为高速异常,表明高原内部存在上地幔盖层.3.高原北部的班公湖断裂和东部的三江断裂系是该区重要的分界线,是岩石层结构存在明显差异的重要接触部位,可能是冈瓦纳古陆与欧亚古陆的缝合带.4.柴达木-巴颜喀拉-三江块体内部速度分布不均匀,地壳厚度由北向南从45km加深到60km;在深度90-110km存在一低速层.5.塔里木地块内速度随深度均匀增加,从地壳到上地幔110km内没有发现低速层.地壳厚度约50km.     

被断裂破坏的盖层封闭能力评价方法及其应用

断层对盖层的破坏主要表现为两个方面:一是减小了盖层的连续封盖面积,二是减小了盖层的厚度。盖层被断层破坏的主要影响因素有断层的断距、倾角和盖层厚度。通过对影响因素研究,提出了盖层有效断接厚度的新概念和计算方法。根据我国部分与断层有关的大-中型气田气柱高度资料,发现了有效断接厚度与所能封闭的最大气柱高度的对数线性关系,并由此提出了评价被断层破坏的盖层封闭能力的新方法。通过对库车坳陷库姆格列木群膏泥岩盖层的应用研究,所得结论与勘探实践完全吻合,证明所提出的评价方法是可行的。