Probability Density Functions as Botanical-Climatological Transfer Functions for Climate Reconstruction

We present a new procedure, the pdf method (pdf=probability density function), for reconstructing Quaternary climate utilizing botanical data. The procedure includes the advantages of the indicator species method by considering the fossil and modern presence and absence of taxa rather than their frequencies, thus avoiding the need for modern analog plant communities. Overcoming the problematic use of absolute limits to describe climate response ranges is the main progress of the pdf method in comparison to the indicator species method. This advantage results from estimating probability density functions (pdfs) for monthly mean January and July temperature conditional on the present day occurrence of single taxa. Gaussian distributions sufficiently approximate pdfs of many, although not all, studied taxa. On the assumption of statistical independence, the procedure calculates a joint pdf as the product of the pdfs of the individual taxa. This algorithm weights each taxon according to the extent of its climate response range expressed by its covariance structure. We interpret the maximum of the resulting pdf as the most likely climate and its confidence interval as the uncertainty range. To avoid an artificial reduction of uncertainty arising from the use of numerous similar pdfs, a preselection method is proposed based on the Mahalanobis distance between pdfs. The pdf method was applied to the Carpinus phase of a profile from Gröbern, Germany, that spans the last interglaciation (Eemian). The reconstructed most probable January and July temperatures of about 0.0°C and 18.4°C barely differ from the modern values of −0.5°C and 18.3°C.     

Dynamic soil–structure interaction analysis using Lanczos vectors with adaptive time integration technique

An analytical procedure to obtain the response of soil–structure interaction problems, time domain is described. The procedure makes use of large domain for descritization along with co-ordinate transformation using Lanczos vectors. The responses are obtained in time domain using an adaptive direct integration method. The scheme has the ability to estimate errors due to temporal discretization as well as co-ordinate transformation. The procedure has been applied to half-space problems and non-convex domains for validation of the scheme, and the scheme obeys causality condition in both the situations. The present method has all the advantages of time domain scheme which is local both in space and time with small computational effort. Copyright © 1999 John Wiley & Sons, Ltd.     

The use of microcomputers in the analysis of piles subjected to lateral loads and bending moments

A simple numerical procedure for the solution of the non-linear differential equation is presented. Such an equation with the appropriate boundary conditions is often encountered in the analysis of piles subjected to lateral loads and bending moments. The method is suitable for application using a microcomputer of limited memory capacity and the extension of the procedure to cover the solution to the equation ⁴+f(u, y) = 0 which governs the mode of deformation of slab-on-grades is possible and straight-forward.     

Sampling design optimization for spatial functions

A new procedure is presented for minimizing the sampling requirements necessary to estimate a mappable spatial function at a specified level of accuracy. The technique is based on universal kriging, an estimation method within the theory of regionalized variables. Neither actual implementation of the sampling nor universal kriging estimations are necessary to make an optimal design. The average standard errorand maximum standard error of estimationover the sampling domain are used as global indices of sampling efficiency. The procedure optimally selects those parameters controlling the magnitude of the indices, including the density and spatial pattern of the sample elements and the number of nearest sample elements used in the estimation. As an illustration, the network of observation wells used to monitor the water table in the Equus Beds of Kansas is analyzed and an improved sampling pattern suggested. This example demonstrates the practical utility of the procedure, which can be applied equally well to other spatial sampling problems, as the procedure is not limited by the nature of the spatial function.     

A Bayesian procedure for Probabilistic Tsunami Hazard Assessment

In this paper, a Bayesian procedure is implemented for the Probability Tsunami Hazard Assessment (PTHA). The approach is general and modular incorporating all significant information relevant for the hazard assessment, such as theoretical and empirical background, analytical or numerical models, instrumental and historical data. The procedure provides the posterior probability distribution that integrates the prior probability distribution based on the physical knowledge of the process and the likelihood based on the historical data. Also, the method deals with aleatory and epistemic uncertainties incorporating in a formal way all sources of relevant uncertainty, from the tsunami generation process to the wave propagation and impact on the coasts. The modular structure of the procedure is flexible and easy to modify and/or update as long as new models and/or information are available. Finally, the procedure is applied to an hypothetical region, Neverland, to clarify the PTHA evaluation in a realistic case.     

Automatic soil-boundary location from transect data

Spatially distributed soil data possess a short-range erratic variation, an irregular longer range pattern, and maybe multivariate. In order to reveal a pattern or meaning in them, they are usually classified by drawing boundaries. A method is described for determining boundaries automatically on transects. A small portion of a sampled transect is taken and divided about its midpoint, and Mahalanobis' generalized distance, Dor D²,between the two halves calculated from the sample data. The procedure is repeated for portions of the same length at positions one-sampling interval apart along the transect. High peaks on the resultant series of D² identify the boundaries. The length of portions is set equal to, or somewhat less than, the expected average distance between boundaries, and is determined by constructing correlograms of principal components. The lag distance over which fairly steady decay occurs is related closely to the distance between boundaries. The procedure is illustrated with data from a 6-km transect in Oxfordshire and shows good agreement with boundaries drawn by combined air-photo interpretation and field judgment. A means of extending the procedure to two dimensions is suggested.     

Stability of earth dam contaminated by chemical transport

When chemicals are introduced into the oil, they affect soil properties such as hydraulic conductivity and stress–strain behavior. In this study, several chloride concentrations are varied from 0 to 20 per cent to analyse the effect of chemicals on soil properties. A series of laboratory triaxial tests are performed on the cylindrical specimens of sand–bentonite mixture with different sodium chloride contents (5, 10, 15 per cent) by Nannapaneni. Deformation (elastic modulus, E) and strength (cohesion, c′, and angle of friction, ϕ′) parameters are obtained from the triaxial tests as functions of confining pressure and sodium chloride concentrations, and variations of parameters are incorporated into stability analysis. The stress–strain–strength behaviour based on the above strength parameters is introduced in a finite element procedure with a modified residual flow procedure (RFP). By integrating a slope stability procedure in the finite element method, the stability with time of earth dam contaminated by sodium chloride is examined. It is found that increasing sodium chloride concentration for the soil considered increases stability. However, the procedure is general and can allow stability analysis under the influence of other chemical which may lead to decrease in stability. Copyright © 1999 John Wiley & Sons, Ltd.     

Determination of Trace Element Mass Fractions in Ultramafic Rocks by HR‐ICP‐MS: A Combined Approach Using a Direct Digestion/Dilution Method and Preconcentration by Coprecipitation

A procedure is described for the determination of thirty‐seven minor and trace elements (LILE, REE, HFSE, U, Th, Pb, transition elements and Ga) in ultramafic rocks. After Tm addition and acid sample digestion, compositions were determined both following a direct digestion/dilution method (without element separation) and after a preconcentration procedure using a double coprecipitation process. Four ultramafic reference materials were investigated to test and validate our procedure (UB‐N, MGL‐GAS [GeoPT12], JP‐1 and DTS‐2B). Results obtained following the preconcentration procedure are in good agreement with previously published work on REE, HFSE, U, Th, Pb and some of the transition elements (Sc, Ti, V). This procedure has two major advantages: (a) it avoids any matrix effect resulting from the high Mg content of peridotite, and (b) it allows the preconcentration of a larger trace element set than with previous methods. Other elements (LILE, other transition elements Cr, Mn, Co, Ni, Cu, Zn, as well as Ga) were not fully coprecipitated with the preconcentration method and could only be accurately determined through the direct digestion/dilution method.     

Laser Ablation (U-Th-Sm)/He Dating of Zircons: Analytical Age Bias and its Consequence for Studying Detrital Zircon Populations

The in situ (U-Th-Sm)/He and U/Pb laser-ablation double-dating procedure is a valuable method that can provide a large dataset relatively efficiently in contrast with conventional bulk helium thermochronometry. In this study, we evaluate the potential age error associated with the double ablation procedure and report the in situ (U-Th-Sm)/He double-ablation dating of 249 zircons from the Fish Canyon Tuff locality. With LA-ICP-MS pseudo-depth profiling and 3D numerical modelling, we show that the concentric double-ablation procedure in minerals with U-Th-Sm zoning can generate a significant (U-Th-Sm)/He age error (positive or negative), resulting in over-scattering and/or an offset of the mean age. Pseudo-depth profiling is insufficient to predict the individual age error, partly because of the superimposed ablations. To evaluate the consequence of this inherent bias, we confront a synthetic age distribution to the error expected for U-Th-Sm zoned zircons analysed with double-ablation (U-Th-Sm)/He thermochronometry. As expected, a strong age bias causes the spreading of peak ages, downgrading the original signal. Yet, the throughput of the ablation-based method can allow intra- and inter-sample peak age identification and comparison, and the coupling of (U-Th-Sm)/He and U/Pb ages extends our ability to deconvolute a multimodal age spectrum.     

Determination of partial factors for the verification of the bearing capacity of shallow foundations under open channels

The limit state design method has been introduced into the design criteria for geotechnical structures. The current paper attempts to apply the reliability-based design method, at Level II, to the bearing capacity of the foundations of open channels from the viewpoint of the limit state design. To examine the applicability of the proposed procedure for practical structures, the reliability index is computed for evaluating the stability of the foundations of existing open channels designed by the conventional method. The conventional design procedure makes excessively safe side design. We applied the FORM to the existing open channels designed by the conventional design procedure, and consequently, large values of reliability index, 3 and 5 were obtained for clayey and sandy soils, respectively. Finally, the partial factors for the soil parameters have been determined, corresponding to the target reliability indices β _t =1, 3 and 4.     

On estimating the parameters in mixtures of circular normal distributions

The method of maximum likelihood used in analyzing data which are bimodal in the range (0, )is lengthy and not always successful. Two alternative methods are proposed and the results compared with those obtained by using the method of maximum likelihood on orientation data from clasts and shells. It is shown that a procedure based on the Method of Moments gives comparable results and is much more practicable.     

A new method of estimating the ratio between in situ rock stresses and tectonics based on empirical and probabilistic analyses

This paper describes a new procedure for assessing the ratio between in situ stresses in rock masses by means of K (K = σ_H / σ_v, being σ_H and σ_v principal stress) and tectonics for purposes of engineering geology and rock mechanics. The method combines the use of the logic decision tree and the empirical relationship between the Tectonic Stress Index, TSI, and a series of K in situ values obtained from an extensive database. The decision tree considers geological and geophysical factors affecting stress magnitudes both on the regional and local scale. The TSI index is defined by geological and geomechanical parameters. The method proposed provides an assessment of the magnitude of horizontal stresses of tectonic origin. Results for several regions of Europe are presented and the possible applications of the procedure are discussed.     

Chemical Separation of Tungsten and Other Trace Elements for TIMS Isotope Ratio Measurements Using Organic Acids

One requirement for isotope ratio measurement results with small measurement uncertainties is that the element of interest is effectively separated from the sample matrix. Efficient chemical separation of W from matrix components, especially Ti, can be challenging, particularly for large test portion masses (> 1 g). We present a new W separation procedure that takes advantage of the distinct complexation behaviour of Ti and W with citrate ligand in a moderately low pH, oxidising solution. This preparation procedure can reduce the Ti/W ratio of large (4–10 g) basaltic (i.e., high‐matrix) test portions by a factor of 10⁵, relative to their original compositions, in a two‐step separation procedure. The procedure additionally provides a separate, well‐purified Mo fraction. We show that optimal separation requires precise selection of reagent concentrations and sample load. The procedure was employed to determine the μ¹⁸²W composition of BHVO‐2 as ?6.7 ± 4.2 (2 standard deviation, 2s). The principles derived from this method may prove useful for chemical separation of other elements used for geochemical and cosmochemical applications given an appropriate selection of organic acid. Future successful applications of this method may reveal that the use of organic acids as procedural reagents is a currently under‐utilised tool for efficient chemical separation protocols.     

Efficient solution for matrix-fracture flow with multiple interacting continua

An efficient numerical procedure for implementing the multiple interacting continua (MINC) method for fractured porous media in a general-purpose multiphase simulator is presented. This procedure is substantially faster, requires less memory, is amenable to any n-component, multiphase non-isothermal package, and is readily adaptable for parallel processing computers. The present procedure results in a reduction of the computing time by a factor of the order of NMINC³ as compared to the band algorithm, where NMINC is the number of nested continua into which each matrix block is further discretized. The memory requirement approaches a reduction factor of the order of NMINC² for larger problems compared to the band algorithm. The code for the algorithm was structured so as to set up the time consuming, but independent, computations for each matrix block in a subroutine that was parallelized and tested using a Sequent machine accessed under a UNIX environment. For NMINC=10, total computing time was reduced by 33 per cent for the use of two versus one processor, with the savings increasing for increasing NMINC. The proposed procedure can be implemented with the same ease and efficiency in conjunction with any iterative or direct method, and the grid-blocks can be ordered in any non-standard manner such as in D-4, D-2, and others. Copyright © 1999 John Wiley & Sons, Ltd.     

Simplified procedure for reliability-based robust geotechnical design of drilled shafts in clay using spreadsheet

This paper provides a simplified procedure for reliability-based robust geotechnical design (RGD) using spreadsheet. In the RGD methodology, design robustness is achieved by adjusting “design parameters” without reducing the uncertainties in noise factors. This design approach generally involves a multi-objective optimisation, which is computationally challenging. To improve the efficiency of the RGD methodology, the design robustness is evaluated in terms of sensitivity index and the safety requirement is evaluated using mean value first order second moment (MFOSM). To ease the concern that the reliability index obtained with MFOSM may not be sufficiently accurate, a mapping function that relates MFOSM to a more accurate method such as first order reliability method is introduced. To further improve the efficiency of the proposed simplified RGD method, a new simplified procedure along with a more accurate robustness measure is developed that eliminates the need for multi-objective optimisation. With these modifications, the proposed simplified RGD method can efficiently be implemented in a single Excel spreadsheet. The proposed simplified method, which goes beyond any existing reliability-based RGD methods in terms of ease of use and computational efficiency, is illustrated in this paper with an example of robust design of drilled shaft in clay.     

Elasto-plastic analysis of an underground opening by FEM and coupled FEBEM

The elasto-plastic analysis of a circular underground opening using the finite element method (FEM), the coupled finite element and the boundary element method (FEBEM) is presented. The coupling procedure and elasto-plastic formulation are discussed. The effect of in situ stress ratio on yielded zone, displaced shape and principal stresses is presented. The results of FEBEM analysis are compared with those obtained from FEM. The computation time and the number of iterations as required by FEBEM and FEM are compared.     

Locating maximum variance segments in sequential data

An automated method is presented for the identification of peaks in sets of sequential data. The method is based upon the location of those segments with maximum variance and has the advantage of guarding against the masking of small-scale effects by large-scale effects. The procedure is illustrated with data taken as part of the National Uranium Resource Evaluation project.This work was performed under the auspices of the U.S. Energy Research and Development Administration, Grand Junction Office.     

Extraction of uranium ions from water: a rapid and convenient method using prepackaged ion exchange resins

Ion exchange resins are used successfully to extract and concentrate uranium ions from aqueous solutions although the procedures are time consuming. They utilize rather cumbersome resin columns, and consequently they have found little practical application in large geochemical surveys of isolated areas. An alternative approach using resin packages is proposed. The “package” is a teabag — convenient, cheap, disposable, and readily sealed. Laboratory and field tests indicate that the method combines simplicity, speed and economy with excellent precision and detection limits. Although the packaging procedure was designed specifically for the extraction of uranium from natural waters under field conditions, the method can be modified to extract elements other than uranium and presents a viable alternative to resin columns in a standard laboratory.     

Application of extended Kalman filter to back analysis of the natural stress state accounting for measuring uncertainties

In this work, we present a numerical procedure for determining the nature stress state in the rock mass around a tunnel. A finite element method is applied for analyzing the direct problems of tunneling during the back analysis of parameter estimation, in which a no‐tension elastic–plastic model is used to simulate the elastic–tensile and elastic–plastic‐tensile failure states which often occur in the cases of underground excavation in heavily jointed rock masses. By considering the natural stress state as random parameters of the tunneling system, the Kalman filter method is employed for feedback analysis to modify the parameter values in a statistical context, which uses the prior information in the process of estimation and employs a set of displacements obtained from field measurements. To verify the effectiveness of the proposed method of inverse analysis, the developed numerical procedure is applied to a synthetic example of deep tunnels in yielding rock masses. The relative importance of the a priori and updating information is investigated, as is the importance of their uncertainty. The results show great potential of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.