Spatial relationships of multivariate data

Spatial factor analysis (SFA) is a multivariate method that determines linear combinations of variables with maximum autocorrelation at a given lag. This is achieved by deriving estimates of auto-/cross-correlations of the variables and calculating the corresponding eigenvectors of the covariance quotient matrix. A two-point spatial factor analysis model derives factors by the formation of transition matrixU comparing auto-/cross-correlations at lag 0,R ₀, with those at a specified lag d,R _d, expressed asU _d=R ₀ ^–1 R_d. The matrixU _d can be decomposed into its spectral components which represent the spatial factors. The technique has been extended to include three points of reference. Spatial factors can be derived from the relationship:

An experimental study of the diffusion of oxygen in quartz and albite using an overgrowth technique

Diffusion rates of¹⁸O tracer in quartz ( c, 1 Kb H₂O) and Amelia albite ( 001, 2 Kb H₂O) have been measured, using Secondary Ion Mass Spectrometry (SIMS). A new technique involving hydrothermal deposition of labelled materials has removed the possibility of pressure solution-reprecipitation processes adversely affecting the experiments. Reported diffusion constants are:-quartz ( c), ,Q=98±7 KJ mol^–1 (600–825° C, 1 Kb); Amelia albite ( 001), ,Q=85±7 KJ mol^–1, (400–600° C, 2 Kb). Measured quartz¹⁸O diffusivities decrease discontinuously at the- transition, reflecting strong structural influences. The reported albite data agree with previously recorded studies, but-quartz data indicate significantly lower activation energies. Possible causes of this discrepancy, and some geological consequences, are noted.     

The crystal structure of a triclinic roscherite

Summary The crystallography of roscherite is more complicated than previously thought. Single crystal X-ray work on material from Foote Mine (California) gave triclinic symmetry. The unit cell corresponding to the one adopted for monoclinic roscherite hasa=15.921,b=11.965,c=6.741 Å, =91°04, =94°21, =89°59 1/2, space group . The least-squares refinement of the structure using 2380 non zero reflections with anisotropic temperature factors resulted in a conventional reliability factorR=0.060.The X-ray study indicates the formula while that proposed for monoclinic roscherite is The atomic arrangements of both varieties of roscherite are very similar. The lowering of symmetry is caused by the segregation of the trivalent cations into only half of the sites of a monoclinic point position. Crystallochemical considerations suggest that the symmetry of roscherite does not depend on the kind of trivalent cations occupying the 6-coordinated position, but rather by the ratio between trivalent and divalent metal ions.

---

Die Kristallstruktur eines triklinen Roscherites

Zusammenfassung Die Kristallographie des Roscherites ist komplizierter als man bisher annahm. Einkristall-Röntgenuntersuchungen an Material von Foote Mine (Kalifornien) ergaben trikline Symmetrie. Die Elementarzelle, welche der für monoklinen Roscherit angenommenen entspricht, hata=15,921,b=11,965,c=6,741 Å, =91°04, =94°21, =89°59 1/2, Raumgruppe . Die Verfeinerung der Struktur mit der Methode der kleinsten Quadrate ergab unter Verwendung anisotroper Temperaturfaktoren für 2380 beobachtete Reflexe einen konventionellen ZuverlässigkeitsindexR=0,060.Die Röntgenuntersuchung weist auf die Formel , während für monoklinen Roscherit vorgeschlagen wurde. Die Atomanordnungen beider Abarten des Roscherites sind sehr ähnlich. die Symmetrieerniedrigung wird dadurch hervorgerufen, daß die dreiwertigen Kationen nur die Hälfte der Positionen einer monoklinen Punktlage besetzen. Kristallchemische Überlegungen weisen darauf hin, daß die Symmetrie nicht von der Art der dreiwertigen Kationen, welche eine 6-koordinierte Punktlage besetzen, abhängt, sondern vielmehr von dem Mengenverhältnis zwischen 3-wertigen und 2-wertigen Metallionen.

---

---

With 1 Figure     

Manganese olivine I: Electrical conductivity

To investigate the point defect chemistry and the kinetic properties of manganese olivine Mn₂SiO₄, electrical conductivity () of single crystals was measured along either the [100] or the [010] direction. The experiments were carried out at temperatures T=850–1200 °C and oxygen fugacities atm under both Mn oxide (MO) buffered and MnSiO₃ (MS) buffered conditions. Under the same thermodynamic conditions, charge transport along [100] is 2.5–3.0 times faster than along [010]. At high oxygen fugacities, the electrical conductivity of samples buffered against MS is 1.6 times larger than that of samples buffered against MO; while at low oxygen fugacities, the electrical conductivity is nearly identical for the two buffer cases. The dependencies of electrical conductivity on oxygen fugacity and temperature are essentially the same for conduction along the [100] and [010] directions, as well as for samples coexisting with a solid-state buffer of either MO or MS. Hence, it is proposed that the same conduction mechanisms operate for samples of either orientation in contact with either solid-state buffer.The electrical conductivity data lie on concave upward curves on a log-log plot of vs , giving rise to two regimes with different oxygen fugacity exponents. In the low- regime , the exponent, m, is 0, the MnSiO₃-activity exponent, q, is 0, and the activation energy, Q, is 45 kJ/mol. In the high regime 10^{ - 7} {\text{atm}}} \right)$$ " align="middle" border="0"> , m=1/6, q=1/4–1/3, and Q=45 and 200 kJ/mol for T<1100 °c=" and=">T>1100 °C, respectively.     

Use of Pitzer Equations to Examine the Formation of Mercury(II) Hydroxide and Chloride Complexes in NaClO<Subscript>4</Subscript> Media

The thermodynamic stability constants for the hydrolysis and formation of mercury (Hg²⁺) chloride complexes

H<Subscript>2</Subscript>O diffusion in peralkaline to peraluminous rhyolitic melts

The diffusion of water in a peralkaline and a peraluminous rhyolitic melt was investigated at temperatures of 714–1,493 K and pressures of 100 and 500 MPa. At temperatures below 923 K dehydration experiments were performed on glasses containing about 2 wt% H₂O _t in cold seal pressure vessels. At high temperatures diffusion couples of water-poor (<0.5 wt% H₂O _t ) and water-rich (~2 wt% H₂O _t ) melts were run in an internally heated gas pressure vessel. Argon was the pressure medium in both cases. Concentration profiles of hydrous species (OH groups and H₂O molecules) were measured along the diffusion direction using near-infrared (NIR) microspectroscopy. The bulk water diffusivity () was derived from profiles of total water () using a modified Boltzmann-Matano method as well as using fittings assuming a functional relationship between and Both methods consistently indicate that is proportional to in this range of water contents for both bulk compositions, in agreement with previous work on metaluminous rhyolite. The water diffusivity in the peraluminous melts agrees very well with data for metaluminous rhyolites implying that an excess of Al₂O₃ with respect to alkalis does not affect water diffusion. On the other hand, water diffusion is faster by roughly a factor of two in the peralkaline melt compared to the metaluminous melt. The following expression for the water diffusivity in the peralkaline rhyolite as a function of temperature and pressure was obtained by least-squares fitting:

An almandine garnet isograd in the Rogers Pass area,British Columbia: The nature of the reaction and an estimation of the physical conditions during its formation

In the Rogers Pass area of British Columbia the almandine garnet isograd results from a reaction of the form: 5.31 ferroan-dolomite+8.75 paragonite+4.80 pyrrhotite+3.57 albite+16.83 quartz+1.97 O₂=1.00 garnet+16.44 andesine+1.53 chlorite+2.40 S₂+1.90 H₂O+10.62 CO₂. The coefficients of this reaction are quite sensitive to the Mn content of ferroan-dolomite.Experimental data applied to mineral compositions present at the isograd, permits calculation of two intersecting P, T equilibrium curves. P=29088–39.583 T is obtained for the sub-system paragonite-margarite (solid-solution), plagioclase, quartz, ferroan-dolomite, and P=28.247 T–14126 is obtained for the sub-system epidote, quartz, garnet, plagioclase. These equations yield P=3898 bars and T=638° K (365° C). These values are consistent with the FeS content of sphalerite in the assemblage pyrite, pyrrhotite, sphalerite and with other estimates for the area.At these values of P and T the composition of the fluid phase in equilibrium with graphite in the system C-O-H-S during the formation of garnet is estimated as: bars, bars, bars, bars, bars, bars, bars, bars, , bars, bars.     

A Coupled Riverine-Marine Fractionation Model for Dissolved Rare Earths and Yttrium

Fractionation of yttrium (Y) and the rare earth elements (REEs) begins in riverine systems and continues in estuaries and the ocean. Models of yttrium and rare earth (YREE) distributions in seawater must therefore consider the fractionation of these elements in both marine and riverine systems. In this work we develop a coupled riverine/marine fractionation model for dissolved rare earths and yttrium, and apply this model to calculations of marine YREE fractionation for a simple two-box (riverine/marine) geochemical system. Shale-normalized YREE concentrations in seawater can be expressed in terms of fractionation factors ( _ij ) appropriate to riverine environments ( ) and seawater ( ):

Impact of land use change on groundwater quality in a typical karst watershed of southwest China: a case study of the Xiaojiang watershed,Yunnan Province

The impact of land-use change on the quality of groundwater in the Xiaotjiang watershed, China was assessed for the period 1982–2004. Groundwater samples were collected from 30 monitoring points across the watershed, and were representative of the various changes, determined by remote sensing and geographical information systems. The results indicate that 610 km² (60% of the total watershed area) were subject to land-use change during the period. The most important changes were the conversion of 135 km² of forested land to cultivated land, and 211 km² of unused land to cultivated land. The main impact was ascribed to diffuse pollution from fertilizers applied to newly cultivated land, and from building development. Overall the groundwater pH value was significantly increased, as were the concentrations of ions , , , , and Cl⁻ in groundwater whilst the concentrations of Ca²⁺ and declined. More precisely, in the regions where forested land and unused land were converted into cultivated land, the pH value and the concentrations of Mg²⁺, , , , , Cl⁻ increased whilst the concentrations of Ca²⁺ and declined. However in the region where cultivated land was converted into construction land, the pH value and the concentrations of Ca²⁺, Mg²⁺, , , , , , Cl⁻ increased.

---

Résumé  L’impact des changements de l’utilisation du territoire sur la qualité de l’eau souterraine dans le bassin versant de Xiaojiang, en Chine, a été évalué de 1982 à 2004. Des échantillons d’eau souterraine ont été récoltés à partir de 30 points d’observation éparpillés sur le bassin, représentant les divers changements déterminés par télédétection et système d’information géographique. Les résultats indiquent que 610 km² (soit 60% de la surface du bassin) ont été sujets à des modifications de l’utilisation du territoire sur cette période. Les changements les plus importants furent la conversion de 135 km² de forêt et 211 km² de terres inutilisées en terres cultivées. Le principal impact est attribué à la pollution diffuse des engrais utilisés en agriculture et pour les batiments. De manière générale le pH de l’eau souterraine a augmenté significativement, ainsi que les concentrations des ions , , , , et Cl⁻, tandis que les concentration en Ca²⁺ et ont diminué. Plus précisément dans les régions transformées en terres cultivées, la valeur du pH et les concentrations en Mg²⁺, , , , , Cl⁻ ont augmenté tandis que les concentrations en Ca²⁺ et ont diminué. Toutefois dans les régions cultivées converties en zones de construction, le pH et les concentrations en Ca²⁺, Mg²⁺, , , , , , Cl⁻ ont augmenté.

---

Resumen  El impacto del cambio en uso de la tierra en la calidad del agua en la cuenca Xiaojiang, China fue evaluado para el periodo 1982–2004. Muestras de agua subterránea fueron tomadas de 30 puntos de monitoreo a través de la cuenca, y fueron representativas de los múltiples cambios, determinados por sensores remotos y sistemas de información geográfica. Los resultados indican que 610 km² (60% del área total de la cuenca) estaban sujetos a cambios de uso de la tierra durante el periodo estudiado. Los cambios más importantes fueron la conversión de 135 km² de bosques a tierra cultivada, y 211 km² de tierra sin uso (ociosa) a tierra cultivada. El impacto principal fue causado por contaminación difusa de fertilizantes aplicados a la tierra recientemente cultivada, y a desarrollo de construcciones. En general el pH en agua subterránea creció significantemente, al igual que las concentraciones de los iones , , , , y Cl⁻ en agua subterránea mientras que las concentraciones de Ca²⁺ y decrecieron. Mas precisamente, en las regiones donde bosque y tierra ociosa fueron convertidas en tierra cultivada, el valor de pH y las concentraciones de Mg²⁺, , , , , Cl⁻ crecieron mientras las concentraciones de Ca²⁺ y decrecieron. Sin embargo en la región donde tierra cultivada fue convertida en construcciones, el valor de pH y las concentraciones de Ca²⁺, Mg²⁺, , , , , , Cl⁻ crecieron.

     

Carbon isotope fractionation between calcite,graphite and CO2: an experimental study

The partitioning of stable carbon isotopes between calcite, graphite and CO₂ was experimentally determined at temperatures from 500 to 1200 °C and 1 to 15 kbar pressure. Attainment of carbon isotope equilibrium in CO₂-calcite runs was proven by achieving the same fractionation from isotopically opposite directions. The resultant CO₂-calcite fractionation curve for carbon differs from Bottinga's calculation by 1.2 and confirms recent experiments of Chacko et al. and Mattey et al. In CO₂-graphite experiments equilibrium fractions were extrapolated by applying the partial-exchange technique of Northrop and Clayton and by optimizing the contribution of surface reaction in graphite. CO₂-graphite fractionations at temperatures up to 800 °C are in fair agreement with Bottinga's calculation, but yield a surprisingly high fractionation of 5 at upper mantle temperatures. The combination of CO₂-calcite (carbon) and CO₂-graphite fractionation results in a new experimentally determined calcite-grapite fractionation curve, expressed by the equation:

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Water in microcrystalline quartz of volcanic origin: Agates

Agates of volcanic origin, containing the different quartz species, fibrous, length-fast chalcedony (CH), granular fine quartz (FQ), and fibrous, length-slow, to lepidospheric quartzine (QN), have been investigated to evaluate possible relations between microstructure, i.e. crystallite size and texture, refractive indices, densities, contents of trace elements and of water, as well as dehydration behaviour. By means of near infrared spectroscopy, total water contents , could be differentiated quantitatively into contents of molecular water, , and silanole-group water, . Despite the low total water contents of the agates studied ( between 1 and 2 wt.%), near infrared spectroscopy results in reliable data on and .Wall-layering CH consists of fibrous quartz crystals and exhibits higher C-ratios, , than horizontally layered FQ which consists predominantly of granular quartz crystals (C _CH=0.45±0.11 (N=6), C _FQ=0.36±0.10 (N=4). This result is interpreted to be due to analogy with the behaviour of C-ratios in fluid phase-deposited opals-AN (hyalithe) and liquid phase-deposited opals-AG (non-crystalline opal) or -CT (common opal) (Langer and Flörke 1974).Translucent layers of CH show mostly lower refractive indices, when measured parallel than when measured perpendicular to the axes of the quartz fibers. The same is true for milky layers of CH. Crystallite sizes are smaller in the latter than in the former.For all samples studied, exists a positive correlation between at% (1/2Ca+1/2Mg+Na+K+Li) and at% (Al³⁺+Fe³⁺). This indicates that at least parts of (A1³⁺+ Fe³⁺) substitute for Si in the quartz structure. The charge is balanced by incorporation of di- and mono-valent cations in structural interstices. When the quantity at % H⁺, as obtained from , is included into the sum at% (1/2 Me²⁺+Me⁺), the above correlation is destroyed. This result could be indicative for a strong concentration of the Si-OH groups in the surface of the quartz microcrystallites.     

Fe2⇄Mg2 and TiAl2⇄MgSi2 exchange reactions between clinopyroxenes and silicate melts

The interdependence of the Fe(Mg)_–1 (e.g., FeO-MgO in silicate melt; CaFeSi₂O₆-CaMgSi₂O₆ in pyroxene) and TiAl₂(MgSi₂)_–1 exchange reactions between silicate melts and coexisting Ca-pyroxene has been examined. High-calcium clinopyroxenes were grown in 1 atmosphere melting and crystallization experiments on rock powders spanning the composition range tholeiite to melilitite (1,0922+Mg²⁺ exchange and suggest that at given values of extent of Fe(Mg)_–1 substitution is strongly coupled with the TiAl₂(MgSi₂)_–1 substitution in pyroxenes near the five-component space CaMg(Si₂O₆-CaFe(Si)₂O₆-CaTi(Al)₂O₆-CaFe(Al,Si)₂O₆-CaAl(Al,Si)₂O₆. The inferred stabilization of Ti in iron-rich relative to magnesium pyroxene is consistent with the operation of Fe²⁺Ti⁴⁺ intervalence charge transfer interactions (e.g., Rossman 1980) and observations on zoning in natural titanaugites (e.g., Tracy and Robinson 1977). Although the rims of some pyroxenes grown in some melting experiments exhibit prominent zoning in TiAl₂(MgSi₂)_–1, the average values of inferred from the compositions of these pyroxenes, together with those of the relatively homogeneous pyroxenes produced in crystallization experiments, exhibit a 11 correlation with values of derived from the solution model of Ghiorso et al. (1983) with a standard error of 750 calories. The Ti contents of Ca-rich pyroxenes crystallizing from a wide range of natural silicate liquids can therefore be predicted.     

Aluminum partitioning between olivine and ultrabasic silicate liquid to 6 GPa

Trace element analyses of 1-atm and high-pressure experiments show that in komatiite and peridotite, the olivine (OL)/liquid (L) distribution coefficient for Al₂O₃ ( ) increases with pressure and temperature. Olivine in equilibrium with liquid accepts as much as 0.2 wt% Al₂O₃ in solution at 6 GPa. Convergence to equilibrium compositions at this high level is shown by cation diffusion of Al into synthetic forsterite crystals of low-Al contents in the presence of melt. Convergence to low-Al equilibrium compositions at lower P and T is shown by diffusion of Al out of synthetic forsterite with high initial Al content. Isobaric and isothermal experimental data subsets reveal that temperature and pressure variations both have real effects on . Variation in silicate melt composition has no detectable effect on within the limited range of experimentally investigated mixtures. Least-squares regression for 24 experiments, using komatiite and peridotite, performed at 1 atm to 6 GPa and 1300 to 1960°C, gives the best fit equation: Increase in with increasingly higher-pressure melting is consistent with incorporation of a spinel-like component of low molar volume into olivine, although other substitutions possibly involving more complex coupling cannot be ruled out. High P-T ultrabasic melting residues, if pristine, may be recognized by the high calculated from microprobe analyses of Al₂O₃ concentrations in residual olivines and estimated Al₂O₃ concentration in the last liquid removed. In general the low levels of Al in natural olivine from mantle xenoliths suggest that pristine residues are rarely recovered.     

Systematic study of liquidas phase relations in olivine melilitite +H2O +CO2 at high pressures and petrogenesis of an olivine melilitite magma

Near-liquidus phase relationships of a spinel lherzolite-bearing olivine melilitite from Tasmania were investigated over a P, T range with varying , , and . At 30 kb under MH-buffered conditions, systematic changes of liquidus phases occur with increasing ( = CO₂/CO₂ +H₂O+olivine melilitite). Olivine is the liquidus phase in the presence of H₂O alone and is joined by clinopyroxene at low . Increasing eliminates olivine and clinopyroxene becomes the only liquidus phase. Further addition of CO₂ brings garnet+orthopyroxene onto the liquidus together with clinopyroxene, which disappears with even higher CO₂. The same systematic changes appear to hold at higher and lower pressures also, only that the phase boundaries are shifted to different . The field with olivine- +clinopyroxene becomes stable to higher with lower pressure and approaches most closely the field with garnet+orthopyroxene+clinopyroxene at about 27 kb, 1160 °C, 0.08 and 0.2 (i.e., 6–7% CO₂+ 7–8% H₂O). Olivine does not coexist with garnet+orthopyroxene+clinopyroxene under these MH-buffered conditions. Lower oxygen fugacities do not increase the stability of olivine to higher and do not change the phase relationships and liquidus temperatures drastically. Thus, it is inferred that olivine melilitite 2927 originates as a 5% melt (inferred from K_{2 O} and P₂O₅ content) from a pyrolite source at about 27kb, 1160 dg with about 6–7% CO₂ and 7–8% H₂O dissolved in the melt. The highly undersaturated character of the melt and the inability to find olivine together with garnet and orthopyroxene on the liquidus (in spite of the close approach of the respective liquidus fields) can be explained by reaction relationships of olivine and clinopyroxene with orthopyroxene, garnet and melt in the presence of CO₂.     

APL computer programs for thermodynamic calculations of equilibria in P-T-X CO 2 space

APL computer programs for the thermodynamic calculation of devolatilization and solid-solid equilibria operate using stored values for the molar volume and entropy of solids, the free energies of H₂O and CO₂, and the free energies of formation for 110 geologically-important phases. P-T-X _{CO 2} calculations of devolatilization equilibria can be made at pressures from 0.2 through 10 kb, and temperatures from 200 through 1,000° C. P-T-X calculations of solid-solid equilibria may be accomplished at pressures to 30 kb and temperatures to 1,000° C. Calculations can be extrapolations from experimental points, or direct calculations from thermochemical data alone. Options are available in these programs to consider effects of: real vs. ideal gas mixing, thermal expansion and compressibility, solid solution, fluid pressure differing from solid pressure, and uncertainties in high-temperature entropies.A collection of thermodynamic data programs accompanies the programs for calculating P-T-X _{CO 2} equilibria. Over a wide range of physical conditions, the data functions report free energies, entropies, fugacities of H₂O and CO₂, high temperature entropies of solids, and activities of components in H₂O-CO₂ mixtures.List of Symbols Activity of H₂O and CO₂ - G_f Free energy of formation of a phase from elements - G_r Free energy change of reaction - G _r ^o Standard state free energy change of a reaction - Free energies of pure H₂O and CO₂ - H _r ^o Standard state enthalpy change for a reaction - K Equilibrium constant - R Gas constant - S _r ^o Standard state entropy change of reaction - S _s ^o Standard state entropy change of solids in a reaction - V_s ^o Standard state volume change of a reaction - V_s ^o Standard state volume change of solids in a reaction - Mole fraction of H₂O and CO₂ - Activity coefficient of H₂O and CO₂     

Titania precipitation in sapphire containing iron and titanium

Titania, TiO₂, precipitation in natural blue sapphire (Fe, Ti: -Al₂O₃) has been investigated using high resolution and analytical transmission electron microscopy. The structure and habit of the TiO₂ precipitate depends on both the Ti⁴⁺ concentration and the temperature at which the precipitate formed. Tetragonal TiO₂ (Rutile) grows at 1350° C but at 1150° C an orthorhombic non-equilibrium TiO₂ polymorph precipitates. Both TiO₂ polymorphs nucleate in the (0001)s plane as lens shaped discs twinned along their diameter. The crystallographic alignment of each type of TiO₂ precipitate with respect to the -Al₂O₃ host matrix provides a high degree of structural coherency with minimal lattice mismatch. Electron diffraction analysis established the following precipitate/host orientation relationships: tetragonal TiO₂: {011}r {11 07B;100}r(0001)s and 01 r10 0s twinned along the (011)r planeand orthorhombic TiO₂: {021}{11 0}s, {100}(0001)s and 0 2 10 0s twinned along the (021) plane.     

Foundations of cable car towers upon alpine glaciers

This paper presents a design approach for strip footings upon glacier ice. Safety against ultimate limit state is proved by the geotechnical slip-line field solution by Prandtl. Glacier ice at 0°C can be modelled as purely cohesive material. Statistical evaluation of uniaxial compression tests with high strain rate revealed a mean value of the cohesion of 600 kPa and a characteristic value c _k = 355 kPa (5% fractile). With a coefficient of variation V _c = 0.3, the partial safety factor turns out to be γ _c = 1.9. An approximate solution for estimating the creep settlement rate is presented to check the serviceability limit state: with the width b of the strip foundation, p the foundation pressure and for ice at 0°C. Experiences on Stubai glacier with grate shaped footings showed that creep settlements occurring per year due to maximum foundation pressures 250 kPa did not influence the operation and the maintenance of the cable cars.