Discrete numerical modelling of rockfill dams

The aim of this study is to obtain quantitative information on the behaviour of rockfill used in embankment dams, and particularly on the influence of block breakage on the displacement field, from a numerical analysis using the Distinct element method. A methodology is set up to define the resistance of the 2D particles so that the same probability of breaking blocks may be reproduced as in a 3D material. The model uses the discrete element code PFC^2D (Itasca Consulting Group Inc., PFC2D (Particle Flow Code in Two Dimensions), Version 3.0, 2002) and considers breakable clusters of 2D balls. The different parameters are determined from experimental data obtained from laboratory tests performed on rock blocks. The model is validated by comparing the results of the simulation of shearing tests with actual triaxial tests on rockfill material published in the literature. The numerical analysis of block crushing in an actual dam is proposed in the last part of this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Naturally acidic and metalliferous waters at unmined volcanogenic massive sulfide deposits in the Bonnifield mining district, Alaska Range, east-central Alaska

The Bonnifield district hosts 26 tmmined volcanogenic massive sulfide （VMS） occurrences. Environmental geochemical samples of water and stream sediment were collected at several occurrences, concentrating on the two best-exposed and largest deposits, Red Mountain （RM） and Sheep Creek （SC）. Limited samples were also collected at the poorly exposed WTF deposit. The deposits are Late Devonian to Early Mississippian, and are hosted by felsic metavolcanic and carbonaceous schist members of the Totatlanika Schist or Keevy Peak Fm. Spring and stream waters at RM and SC have pH values commonly 〈3.5 （as low as 2.4 at RM and 2.5 at SC）, high conductivity （up to 11000 μS/cm）, and very high （Is to 100s mg/L） dissolved contents of Al, Cd, Co, Cu, Fe, Ni, and Pb. Waters at RM are characterized by extremely high REE contents （summed REE median 3200 μg/L, n=33）. At both RM and SC, pyrite oxidation and dissolution produce low pH waters that interact with and dissolve bedrock minerals, resulting in acidic, metal-laden, naturally degraded streams that are mostly devoid of aquatic life. Ferricrete is common. In contrast, WTF barely produces a surficial environmental footprint, mostly due to topography and relief. RM and SC are well exposed in the areas of relatively high relief, and both exhibit extensive areas of quartz-sericite-pyrite-alteration. While WTF shares many of the same deposit-and alteration characteristics, it is concealed by tundra in a large, nearly flat area. Surface water at WTF is absent and outcrops are sparse. Even though WTF is roughly the same size as Red Mountain （both around 3 million tonnes） and has similar base- and precious-metal grades, the surficial geochemical manifestation of WTF is minimal. However, exposure through mining of the altered, mineralized rock at WTF potentially could initiate the same processes of pyrite oxidation, acid generation, and mineral dissolution that are observed naturally at RM and SC.     

Analysis of a rigid footing lying on three-layered soil using the finite difference method

A numerical procedure is described for the analysis of the vertical deformation and the stress distribution of the strip footings on layered soil media. Three layers of soil with different stiffness are considered with the middle soil layer the thinnest and most stiff layer. The soil media is discretized and using the theory of elasticity, the governing differential equations are obtained in terms of vertical and horizontal displacements. These equations along with appropriate boundary and continuity conditions are solved by using the finite difference method. The vertical and horizontal displacements, strains and stresses are found at various nodes in the soil media. Parametric studies are carried out to study the effect of the placement depth of the middle soil layer, the relative ratios of the moduli of deformation of the soil layers on the vertical displacement of the footing and the vertical stress distribution. These studies reveal that the middle thin but very stiff layer acts like a plate and redistributes the stresses on the lower soft soil layer uniformly. The displacement on the top and bottom of the middle soil layer is almost the same showing that the compression of the middle layer is negligible as it is very stiff.     

Performance of Mortar and Chemical Grout Injection into Surrounding Soil When Slurry Pipe-jacking Method is Used

Small-diameter shallow tunnels are often being built by using the slurry pipe-jacking method. This system involves the pushing or thrusting of a drivage machine and concrete pipes into the ground. Chemical grout injection into the surrounding soil around the tunnel is carried out after the drivage and pushing processes are finished. The purpose of the chemical grout injection is to maintain permanent stability of the surrounding soil. However, the behavior of the chemical grouting material in the surrounding soil around the tunnel and the amount of optimum injection is not clearly understood. From these points of view, this paper discusses the performance of the chemical grouting material, when it is injected into the surrounding soil around the tunnel, by means of 2-D Eulerian–Lagrangian seepage analysis. Moreover, the effectiveness of the chemical grout injection was evaluated by using the non-linear finite element method. This investigation show when the range of the grouted zone is designed; it is necessary that the relationship between Young’s modulus of the soil/grouted zone and the confining stress be taken into consideration in order to establish effective, economical and safe chemical grout injection system. Understanding the performance of the seepage/dispersion behavior of the chemical grout and the characteristics of soil/ grouted zone is also important.     

Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.     

Traction image method for irregular free surface boundaries in finite difference seismic wave simulation

In this study, we propose a new numerical method, named as Traction Image method, to accurately and efficiently implement the traction-free boundary conditions in finite difference simulation in the presence of surface topography. In this algorithm, the computational domain is discretized by boundary-conforming grids, in which the irregular surface is transformed into a 'flat' surface in computational space. Thus, the artefact of staircase approximation to arbitrarily irregular surface can be avoided. Such boundary-conforming gridding is equivalent to a curvilinear coordinate system, in which the first-order partial differential velocity-stress equations are numerically updated by an optimized high-order non-staggered finite difference scheme, that is, DRP/opt MacCormack scheme. To satisfy the free surface boundary conditions, we extend the Stress Image method for planar surface to Traction Image method for arbitrarily irregular surface by antisymmetrically setting the values of normal traction on the grid points above the free surface. This Traction Image method can be efficiently implemented. To validate this new method, we perform numerical tests to several complex models by comparing our results with those computed by other independent accurate methods. Although some of the testing examples have extremely sloped topography, all tested results show an excellent agreement between our results and those from the reference solutions, confirming the validity of our method for modelling seismic waves in the heterogeneous media with arbitrary shape topography. Numerical tests also demonstrate the efficiency of this method. We find about 10 grid points per shortest wavelength is enough to maintain the global accuracy of the simulation. Although the current study is for 2-D P-SV problem, it can be easily extended to 3-D problem.