Theoretical investigation of the effects of consolidation on contaminant transport through clay barriers

Consolidation of clayey contaminant barriers such as landfill liners has been postulated as a cause of early breakthrough of contaminants. In this paper we theoretically investigate this proposition. For this purpose a sophisticated one‐dimensional, large‐deformation model of coupled mechanical consolidation and solute transport is employed. This new model is a generalization of existing coupled consolidation and solute transport models described in the literature. It takes into account both non‐linearities in geometry as well as constitutive relations. The latter relate the compressibility, hydraulic conductivity and coefficient of effective diffusivity to the deformation of the soil. The model is applied to a case study of a clay liner and geomembrane system. Results obtained from numerical solution of the model equations are compared with those from various simplified models, including a ‘diffusion only’ (i.e. a rigid soil) model traditionally used in contaminant barrier design. For barriers incorporating low compressibility soils (as for many well compacted clays), there is little difference between contaminant transit (i.e. breakthrough) times predicted by the two models. However, for contaminant barriers incorporating more compressible soils, consolidation is shown to significantly accelerate transport. These results indicate the potential importance of accounting for the effects of soil consolidation and highlight the limitations of existing models when modelling solute transport through composite barriers utilizing soft soils. Based on these limited results, we suggest a possible way of taking into account soil consolidation using simplified models. Copyright © 2008 John Wiley & Sons, Ltd.     

Phase Relations and Stability of Magnetoplumbite- and Crichtonite-Series Phases under Upper-Mantle P-T Conditions: an Experimental Study to 15 GPa with Implications for LILE Metasomatism in the Lithospheric Mantle

High-pressure–high-temperature experiments were performedin the range 7–15 GPa and 1300–1600°C to investigatethe stability and phase relations of the K- and Ba-dominantmembers of the crichtonite and magnetoplumbite series of phasesin simplified bulk compositions in the systems TiO₂–ZrO₂–Cr₂O₃–Fe₂O₃–BaO–K₂Oand TiO₂–Cr₂O₃–Fe₂O₃–BaO–K₂O. Both seriesof phases occur as inclusions in diamond and/or as constituentsof metasomatized peridotite mantle xenoliths sampled by kimberlitesor alkaline lamprophyres. They can accommodate large ion lithophileelements (LILE) and high field strength elements (HFSE) on awt % level and, hence, can critically influence the LILE andHFSE budget of a metasomatized peridotite even if present onlyin trace amounts. The Ba and K end-members of the crichtoniteseries, lindsleyite and mathiasite, are stable to 11 GPa and1500–1600°C. Between 11 and 12 GPa, lindsleyite breaksdown to form two Ba–Cr-titanates of unknown structurethat persist to at least 13 GPa. The high-pressure breakdownproduct of mathiasite is a K–Cr-titanate with an idealizedformula KM₇O₁₂, where M = Ti, Cr, Mg, Fe. This phase possessesspace group P6₃/m with a = 9·175(2) Å, c = 2·879(1)Å, V = 209·9(1) ų. Towards high temperatures,lindsleyite persists to 1600°C, whereas mathiasite breaksdown between 1500 and 1600°C to form a number of complexTi–Cr-oxides. Ba and K end-members of the magnetoplumbiteseries, hawthorneite and yimengite, are stable in runs at 7,10 and 15 GPa between 1300 and 1400°C coexisting with anumber of Ti–Cr-oxides. Molar mixtures (1:1) of lindsleyite–mathiasiteand hawthorneite–yimengite were studied at 7–10GPa and 1300–1400°C, and 9–15 GPa and 1150–1400°C,respectively. In the system lindsleyite–mathiasite, onehomogeneous Ba–K phase is stable, which shows a systematicincrease in the K/(K + Ba) ratio with increasing pressure. Inthe system hawthorneite–yimengite, two coexisting Ba–Kphases appear, which are Ba rich and Ba poor, respectively.The data obtained from this study suggest that Ba- and K-dominantmembers of the crichtonite and magnetoplumbite series of phasesare potentially stable not only throughout the entire subcontinentallithosphere but also under conditions of an average present-daymantle adiabat in the underlying asthenosphere to a depth ofup to 450 km. At still higher pressures, both K and Ba may remainstored in alkali titanates that would also be eminently suitablefor the transport of other ions with large ionic radii. KEY WORDS: crichtonite; magnetoplumbite; high-P–T experiments; phase relations; upper mantle     

A scale-explicit model for checking directional consistency in multi-resolution spatial data

Multi-resolution spatial data always contain the inconsistencies of topological, directional, and metric relations due to measurement methods, data acquisition approaches, and map generalization algorithms. Therefore, checking these inconsistencies is critical for maintaining the integrity of multi-resolution or multi-source spatial data. To date, research has focused on the topological consistency, while the directional consistency at different resolutions has been largely overlooked. In this study we developed computation methods to derive the direction relations between coarse spatial objects from the relations between detailed objects. Then, the consistency of direction relations at different resolutions can be evaluated by checking whether the derived relations are compatible with the relations computed from the coarse objects in multi-resolution spatial data. The methods in this study modeled explicitly the scale effects of direction relations induced by the map generalization operator – merging, thus they are efficient for evaluating consistency. The directional consistency is an essential complement to topological and object-based consistencies.     

Evolving fluid composition during prograde metamorphism in subduction zones: A new approach using carbonate-bearing assemblages in the pelitic system

The changing XCO₂ in fluids during the progressive metamorphism in Sanbagawa belt of the Cretaceous subduction zone, Japan, was estimated by a newly proposed method. The subduction zone meta-sediments are characterized commonly by four-phase assemblages in the CaO–NaAlO₂–KAlO₂–Al₂O₃ system with excess quartz and a CO₂–H₂O binary fluid phase. Using the common assemblage of calcite–albite–muscovite–clinozoisite, XCO₂ of the fluid was estimated to be from about 0.0001–0.0005 (the lowest grade chlorite zone), through 0.004–0.01 (garnet zone), 0.01–0.05 (albite–biotite zone) to 0.06–0.2 (oligoclase–biotite zone).The paragenetic relationship of meta-sediments from the subduction zones was compared in a wide P–T range to cover the stability fields of aragonite and jadeite. As a result, an excellent P–T–XCO₂ relationship was delineated to serve as a quantitative monitor for the evolving fluid composition during the progressive metamorphism in subduction zones.     

Slope stability analysis based on the direct comparison of driving forces and resisting forces

The paper disproves a commonly accepted concept that the slope stability problem cannot be correctly solved without invoking the auxiliary static assumptions. The given slope stability analysis is based on the direct comparison of the driving force tending to induce a movement of the slope mass and the mobilized resisting force. A problem of separating the driving forces from the resisting forces is resolved by subdividing an area of the assumed slide mass into two segments wherein the driving forces dominate over the resisting forces at the first segment and vice versa at the other. The slope stability is assessed by the stability index that is equal to a ratio between the resisting forces and driving forces. The stability problem is reduced to determining and analyzing a distribution of the interslice force along the slip line length. A system of recurrence dependencies involving the components of the interslice force and the vertical coordinates of the thrust line is derived from the complete system of the slice equilibrium equations (equilibrium of the horizontal and vertical forces and the force moment equilibrium). This system falls into two subsystems of relations one of which involves only the components of the interslice force. From this it follows that a distribution of the interslice force does not depend on the thrust line position. The slope safety factor regulated by the design manuals for mobilizing the soil shear strength along the slip line is prescribed in advance. A computer program is developed for solving the governing recurrence relations and computing the slope stability index. The applicability of the program is confirmed by solving the problem on a calculation of the critical safety factor for three shapes of the slip line (a circular arc, and a cubic and quadratic parabola) and the stability problem of the real inhomogeneous slope consisting of four layers. Copyright © 2008 John Wiley & Sons, Ltd.     

Order relation correction experiments for probability kriging

Consideration of order relations is key to indicator kriging, indicator cokriging, and probability kriging, especially for the latter two methods wherein the additional modeling of cross-covariance contributes to an increased chance of violating order relations. Herein, Gaussian-type curves are fit to estimates of the cumulative distribution function (cdf) at data quantiles to: (1) yield smoothed estimates of the cdf; and (2) to correct for violations of order relations (i.e., to correct for situations wherein the estimate of the cdf for a larger quantile is less than that for a smaller quantile). Smoothed estimates of the cdf are sought as a means to improve the approximation to the integral equation for the expected value of the regionalized variable in probability kriging. Experiments show that this smoothing yields slightly improved estimation of the expected value (in probability kriging). Another experiment, one that uses the same variogram for all indicator functions, does not yield improved estimates.Presented at the 25th Anniversary Meeting of the IAMG, Prague, Czech Republic, October 10–15, 1993.     

球面四元三角网的三拓扑数计算

讨论了任意球面三角格网p的三拓扑数计算.任意球面三角格网p的三拓扑数是指和该球面三角格网互为三邻近的目标球面三角格网的个数,它是讨论球面栅格区域局部拓扑不变量的重要参数,也是描述和推断球面栅格拓扑关系首先要解决的问题.