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.     

Modelling the poroelastoplastic behaviour of soils subjected to internal erosion by suffusion

Granular soils subjected to seepage flow may suffer suffusion, ie, a selective internal erosion. Extending the classical approach of poromechanics, we deduce a new form of the Clausius-Duhem inequality accounting for dissipation due to suffusion, and we deduce restrictions on the constitutive laws of the soil. We suggest (a) a possible coupling between the seepage forces and the suffusion kinetics and (b) an extension of an existing elastoplastic model for the skeleton mechanical behaviour. Numerical integrations of the elastoplastic model are carried out under drained axisymmetric triaxial and oedometric conditions. As a result, we prove that the extended model is able to qualitatively reproduce the suffusion induced strains and the strength reduction experimentally observed. Predictions on the oedometric behaviour of suffusive soils are also provided.     

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.     

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.     

Generalized strain probing of constitutive models

Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate‐independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane‐strain strain probe (PSSP), are used to generate 3‐D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto‐plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd.     

SANICLAY: simple anisotropic clay plasticity model

SANICLAY is a new simple anisotropic clay plasticity model that builds on a modification of an earlier model with an associated flow rule, in order to include simulations of softening response under undrained compression following K_o consolidation. Non‐associativity is introduced by adopting a yield surface different than the plastic potential surface. Besides, the isotropic hardening of the yield surface both surfaces evolve according to a combined distortional and rotational hardening rule, simulating the evolving anisotropy. Although built on the general premises of critical state soil mechanics, the model induces a critical state line in the void ratio–mean effective stress space, which is a function of anisotropy. To ease interpretation, the model formulation is presented firstly in the triaxial stress space and subsequently, its multiaxial generalization is developed systematically, in a form appropriate for implementation in numerical codes. The SANICLAY is shown to provide successful simulation of both undrained and drained rate‐independent behaviour of normally consolidated sensitive clays, and to a satisfactory degree of accuracy of overconsolidated clays. The new model requires merely three constants more than those of the modified Cam clay model, all of which are easily calibrated from well‐established laboratory tests following a meticulously presented procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

基于生物信息学探讨骨质疏松症与2型糖尿病的关系

目的：基于生物信息学探讨骨质疏松症与 2 型糖尿病的关系。方法：通过基因表达汇编（GEO）数据库检索骨质疏松症和2型糖尿病的相关数据集,并筛选骨质疏松症-2型糖尿病共同差异表达基因,将数据导入STRING数据库找寻关键基因,以一个单细胞测序数据集作为检验集验证关键基因细胞层面的表达水平,对筛选结果进行基因本体（GO）功能及京都基因与基因组百科全书（KEGG）通路富集分析,并对关键靶点、相关中药进行频数统计及功效分类。结果：骨质疏松症与 2 型糖尿病相关通路集中在 ErbB信号通路、丝活化蛋白激酶（MAPK）信号通路、神经营养素信号通路、NOD样受体信号通路。频数统计结果显示,与骨质疏松症-2型糖尿病关键基因相关的中药有51味,以功效分类,可分为清热解毒药、止痛药、祛风药、补虚药、止呕药。结论：骨质疏松症和2型糖尿病都是复杂的代谢性疾病,涉及众多基因表达网络和信号通路。尽管两种疾病存在复杂的基因网络背景,但是分析结果表明两种疾病之间仍存在高度重合的差异基因表达和信号通路。这表明两种疾病的分子机制密切相关,可能存在共同调控的靶点,因此这些靶点可能成为药物同时干预两种疾病的治疗靶点。     

南海北部主要经济鱼类体长与体重关系

文中根据1997～1999年和2001～2002年期间在南海北部底拖网调查的43种共33 389尾鱼的体长（叉长、肛长）和体重数据,应用统计分析方法对各鱼种体长与体重关系进行分析.结果表明,43种鱼分别隶属于4目16科25属,相关系数R^2的范围为0.764～0.993,相关系数R^2值相对较高,其中58%的R^2值超过0.95.幂指数b值范围为2.50～3.44,平均2.90.盒须图分析表明,50%的b值在2.79～3.01范围.经初步分析,43种主要经济鱼类中,有16种为等速生长、22种负的异速生长和5种正的异速生长.     

Study on copper complexing ligand concentrations in several China’s coastal waters

Copper complexing ligand concentrations in the Daya Bay, Qingdao coast, Jiaozhou Bay, South China Sea and Huanghe Estuary waters were determined by the anodic stripping voltammetry technique. The distribution regularity and the relationship with other parameters were discussed. The results were as follows: Copper complexing ligand concentrations of the South China Sea were a little higher than those of other sea areas, and they were apparently higher than those of the ocean. Compared with the subsurface layer (SSL) in the sea surface microlayer copper complexing ligand concentrations showed an enrichment phenomenon, of which the mechanism is similar to dissolved organic matter. The metal complexing ligand concentration profiles of the South China Sea showed that the value in the sea surface was the highest, then it decreased with depth accruing, and a higher value appeared at the bottom. Copper complexing ligand concentrations were higher than those of cadmium and lead. Ligands in each sea area exhibited a complicated property. In short, the distribution regularity of copper complexing ligand concentrations in China' s coastal waters was consistent with that of other regions in the world. Meanwhile, the positive relationship between the copper complexing ligand concentrations and biological oxygen demand, chemical oxygen demand, dissolved organic carbon, and viscosity were found clearly.