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.     

Morphology and Luminosity Segregations in Galaxy Groups

We study morphology and luminosity segregation of galaxies in groups. We analyze the two catalogs of (∼2×400) groups which have been identified in the Nearby Optical Galaxy sample, by means of hierarchical and percolation `friends-of-friends' methods. We find that earlier-type (brighter) galaxies are more clustered and lie closer to the group centers, both in position and in velocity, than later-type (fainter) galaxies. Spatial segregations are stronger than kinematical segregations. These effects are generally detected at the ≳3-sigma level, with the exception of morphological segregation in velocity, which is the weakest effect. Our main results are confirmed by the analysis of statistically more reliable groups (with at least five members), and are strengthened by the detection of segregation in both hierarchical and percolation catalogs. Luminosity segregation is shown to be independent of morphology segregation. Our conclusions agree with a continuum of segregation properties of galaxies in systems, from low-mass groups to massive clusters. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

The carbohydrates in relation to mineralogic and granulometric composition of surface sediments in the karst estuary (River Krka estuary,Yugoslavia)

The investigation of mineral, granulometric and chemical composition of sediments of the River Krka estuary (Yugoslavia) were performed in order to elucidate the origin of the sediments and the pattern of sedimentation. Estuarine surface sediments were found to be fine-grained with a bimodal distribution. Environmental conditions in estuarine sediments favour conservation of the organic matter (anoxic conditions). The carbohydrates in the sediments were investigated to determine whether they are of terrigenous or authigenous origin. Glucose, galactose, mannose, xylose, rhamnose, glucosamine and glucuronic acid were detected in the sediments. Their mutual relationship indicates a preferentially terrigenous source of sedimented organic material in estuarine sediments.     

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.     

Plant distribution at the mobile dune scale and its relevance to soil properties and topographic features

A survey was conducted in an 11-year recovery mobile dune (RMD11) and a 20-year recovery mobile dune (RMD20), in Horqin Sandy Land, Northern China, to determine plant distribution at the mobile dune scale and its relevance to soil properties and topographic features. The results showed that (1) vegetation cover and species number increased from dune top to bottom in the restoration process of mobile dune; (2) the average value of soil organic C, total N, pH, relative height of sampling site, very fine sand content and soil water contents (40−60 and 60−80 cm) of RMD11 were less than that of RMD20, respectively, and there were significant differences (P < 0.05) between the two dunes; (3) soil resources were redistributed by shrub restoration and relative height of sampling site on dune. The distribution of sand pioneer plant, Agriophyllum squarrosum, was positively related to the relative height of sampling site and soil water content, while that of other herbaceous plants was positively related to soil nutrients in the restoration process of mobile dune. These results suggest that at mobile dune scale, plant distributions are determined by a combination of soil properties and topographic feature. Much effort should be made to preserve the interdune lowland and to improve the level of soil nutrients on mobile dune.