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.     

Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity

This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.     

Going underground: in search of Carboniferous coal forests

The development of coal forests during the Carboniferous is one of the best-known episodes in the history of life. Although often reconstructed as steamy tropical rainforests, these ancient ecosystems were a far cry from anything we might encounter in the Amazon today. Bizarre giant club-mosses, horsetails and tree ferns were the dominant plants, not flowering trees as in modern rainforests. At their height, coal forests stretched all the way from Kansas to Kazakhstan, spanning the entire breadth of tropical Pangaea. Most of what we know of their biodiversity and ecology has been quite literally mined out of the ground through two centuries of hard labour. Without coal mining, our knowledge would be greatly impoverished. Over the past few years, we've been exploring underground coal mines in the United States, where entire forested landscapes have been preserved intact over huge areas. Never before have geologists had the opportunity to walk out through mile upon mile of fossilized forest. In this feature article, we describe some of our recent explorations and attempt to shed new light on these old fossils.     

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.     

A techno-economic comparison of power systems for autonomousunderwater vehicles

This paper compares lead-acid batteries, sodium-sulfur batteries, solid polymer fuel cells and closed-cycle diesel engines for autonomous underwater vehicle (AUV) applications. The service is described in terms of a parametric mission and life cycle. A generic AUV is used as a basis for comparison. Power systems are evaluated by two criteria: (1) submerged endurance capability and (2) life cycle cost. This study determines categories of service for which each power system is preferred. The solid polymer fuel cell can provide greater submerged endurance than other power systems examined. For extremely long duration AUV missions, the fuel cell is the required system, indicating a possible market niche for today's fuel cell technology. Considering cost projections for each power system, the results also show that the SPFC can become cost-competitive with conventional technologies, particularly for services characterized by high levels of utilization     

Effect of element size on the static finite element analysis of steep slopes

The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher‐order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd.     

Oxygen isotopic compositions and origins of calcium‐aluminum‐rich inclusions and chondrules

Abstract— Primary minerals in calcium‐aluminum‐rich inclusions (CAIs), Al‐rich and ferromagnesian chondrules in each chondrite group have δ¹⁸O values that typically range from ?50 to +5%0. Neglecting effects due to minor mass fractionations, the oxygen isotopic data for each chondrite group and for micrometeorites define lines on the three‐isotope plot with slopes of 1.01 ± 0.06 and intercepts of ?2 ± 1. This suggests that the same kind of nebular process produced the ¹⁶O variations among chondrules and CAIs in all groups. Chemical and isotopic properties of some CAIs and chondrules strongly suggest that they formed from solar nebula condensates. This is incompatible with the existing two‐component model for oxygen isotopes in which chondrules and CAIs were derived from heated and melted ¹⁶O‐rich presolar dust that exchanged oxygen with ¹⁶O‐poor nebular gas. Some FUN CAIs (inclusions with isotope anomalies due to fractionation and unknown nuclear effects) have chemical and isotopic compositions indicating they are evaporative residues of presolar material, which is incompatible with ¹⁶O fractionation during mass‐independent gas phase reactions in the solar nebula. There is only one plausible reason why solar nebula condensates and evaporative residues of presolar materials are both enriched in ¹⁶O. Condensation must have occurred in a nebular region where the oxygen was largely derived from evaporated ¹⁶O‐rich dust. A simple model suggests that dust was enriched (or gas was depleted) relative to cosmic proportions by factors of ～10 to >50 prior to condensation for most CAIs and factors of 1–5 for chondrule precursor material. We infer that dust‐gas fractionation prior to evaporation and condensation was more important in establishing the oxygen isotopic composition of CAIs and chondrules than any subsequent exchange with nebular gases. Dust‐gas fractionation may have occurred near the inner edge of the disk where nebular gases accreted into the protosun and Shu and colleagues suggest that CAIs formed.     

Large‐ion lithophile element fractionation during the early differentiation of Mars and the composition of the martian primitive mantle

Abstract— Basaltic shergottites display a systematic decrease in K/Th, K/U, and K/La ratios with increasing K content. These trends are interpreted as mixing lines between relatively young martian magmas derived from highly depleted mantle sources and an ancient large‐ion lithophile (LIL) element‐enriched crustal component. One implication of this is that a substantial fractionation of these ratios occurs during the early crustal differentiation on Mars. Isotopic evidence from SNC meteorites and compositional data from Pathfinder and orbital gamma ray spectroscopy suggest that in excess of 50% of the LIL element complement of Mars resides in the crustal reservoir. If so, the primitive mantle of Mars is significantly more volatile‐depleted (i.e., lower K/Th, K/U, K/La) than previously thought but probably (though not necessarily) still less volatile‐depleted than the primitive mantle of the Earth. The La/Th ratios of virtually all SNC meteorites are subchondritic, including those with the most severe LREE‐depletion. Extrapolation of the basaltic shergottite trend suggests that both the depleted mantle end member and the enriched crustal end member have subchondritic La/Th ratios. This is in contrast with the Earth where basalts from LIL element‐depleted sources such as MORB have superchondritic La/Th ratios, complementary to the subchondritic ratios of the continental crust. Accordingly, assuming that the refractory elements are in chondritic proportions for the Mars primitive mantle, an additional major geochemical reservoir must exist on Mars that may not yet have been sampled.