Risk Factor Based Design of Cantilever Retaining Walls

Sensitivity analysis of geotechnical random variables on potential failure modes (overturning, sliding, bearing capacity and eccentricity) of a cantilever retaining wall reveals that high sensitivity of a particular variable on a particular mode of failure does not necessarily imply a remarkable contribution to the overall failure probability. The present paper aims to combine probability of failure (P _f ) of each failure mode and sensitivity of the random variables to these failure modes and introduces a new factor, called Probabilistic Risk Factor (R _f ) for each random variable. P _f is calculated by Monte Carlo Simulation and sensitivity analysis of each random variable is calculated based on normalized F-Statistics value. R _f is a reduction factor which takes into account the variations of random variables and hence can be directly implemented in design by the designers. The random variables (friction angle and unit weight of backfill soil; and friction angle, unit weight and cohesion of foundation soil), when divided by R _f and applied in design, yield a structure which is safe against variations of the random variables. It is observed that R _f of friction angle (φ ₁ ) of backfill increases and cohesion (c ₂ ) of foundation soil decreases with an increase in variation of φ ₁ , while R _f for unit weights (γ ₁ and γ ₂ ) of both the soil and friction angle of foundation soil (φ ₂ ) remains almost constant. Finally, design guidelines for different variations of φ ₁ are provided based on the proposed methodology, which proves to be cost effective.     

Influence of Randomly Distributed Coir Fibers on Shear Strength of Clay

The use of natural fibers such as coir for soil improvement is highly attractive in countries where such materials are locally and economically obtainable, in view of the preservation of natural environment and cost effectiveness. This paper discusses shear strength of clay reinforced with randomly distributed coir fibers based on a series of consolidated undrained triaxial compression tests. Test results show that major principal stress at failure for clay-coir fiber matrix increases with increase in fiber content (W _f ) and fiber aspect ratio (A _r ). For all the combinations of fiber contents and aspect ratios, failure principal stress envelope exhibits a curvilinear variation with a transition at a confining stress, known as critical confining stress. Separate regression analyses have been performed for observations below and above critical confining stress to develop mathematical models, which consider fiber content, aspect ratio, confining stress and plain soil characteristics as the input parameter, to predict major principal stress at failure for the clay-fiber composite. In general, the study identifies that the inclusion of discrete coir fibers in random fashion significantly improves the shear strength of clay and hence could be effectively used for the cases where in-place mixing of soil with fibers is possible (e.g., pavement sub-grade, landfill liner, small embankment). The developed regression models may be used in the design phase for the rough estimation of shear strength of the composite.     

Pressure induced phase transition in Mg2GeO4 as determined by frequency dependent complex electrical resistivity measurements

The phase transition of Mg₂GeO₄ from the olivine structure (α-phase) to the spinel structure (γ-phase) was determined by complex electrical resistivity measurements in the frequency range 10 Hz up to 100 kHz. The stability fields of the α- and the γ-phase were confirmed up to 2.05 GPa in the temperature range 845° C–1400° C. Based on volume resistivity data, a decrease of about a factor of 5 was found at the α-γ phase transition. Activation energies of electrical conduction E _a at 1.05 GPa and 2.05 GPa were calculated using the volume resistivities (?) and the relaxation times (τ). The values range from 1.98 eV up to 2.78 eV. The relative dielectric permeability increases with increasing temperature. This is is due to crystal defects and charge transport mechanisms.     

Characteristic scale of heterogeneity of seismically active fault and its manifestation in scaling of earthquake source spectra

Previously, similarity of source spectra of Kamchatka earthquakes with respect to the common corner frequency f_c1 and the expressed deviations from similarity for the second f_c2 and the third f_c3 corner frequencies were revealed. The value of f_c3 reflects the characteristic size L_is of fault surface; correspondingly, L_is ≈ v_rT_is, where v_r is the rupture speed and T_is ≈ 1/f_c3 is characteristic time. The estimates of f_c3 are used for normalizing f_c1 and f_c2. In this way one obtains dimensionless rupture temporal parametres τ₁ and τ₂ and can further study the dependence τ₂ (τ₁). The growth of a rupture is considered as a process of aggregation of elementary fault spots of the size L_is. The dimensionless width of the random front of aggregation is on the order of τ₂. The relationship τ₂ (τ₁) approximately follows power law with exponent β. The estimates of β derived from earthquake populations of Kamchatka, USA and Central Asia (β = 0.35–0.6) agree with values expected from the known Eden’s theory of random aggregation growth and from its generalizations.     

The effective stochastization time in stellar systems

Stochastization in stellar systems is analyzed in the framework of the paradigm of Krylov and Gurzadyan-Savvidi. The use of a Holtsmark distribution for the random forces with a Rastorguev-Sementsov cutoff confirms that τ _e /τ _c ∝ N ^1/5, where τ _c is the crossing time, τ _e is the effective stochastization time, and N is the number of stars. More oblate systems evolve more rapidly, and rotation slows stochastization. The need for a cutoff does not arise if a Petrovskaya distribution is adopted for the random forces (although applying a cutoff does not change the results). In this case, τ _e /τ _c varies with N approximately as N ^0.3. It is found theoretically that τ _e /τ _c ∝ N ^1/3/(lnN)^1/2 for large N. Thus, the evolutionary scale found is close to that proposed earlier by Genkin.     

Cosmological tests based on the abundance of galaxy clusters

We present a new normalization for the linear density-perturbation spectrum in a multi-parameter model of the Universe. Using the differential mass function for the nearly galaxy clusters obtained from optical data, we have constructed a functional relation between the dispersion of the density contrast σ ₈ on the scale 8h ^?1 Mpc and the cosmological parameters Ω _m , Ω_Λ, h, n, f _v for each of three theoretical approximations of the mass function: Press-Schechter, Sheth-Tormen and Jenkins. An extended class of models of the Universe with general spatial curvature include four parameters for the matter components: baryons (Ω _b ), “cold” dark matter (Ω _c ), “hot” dark matter (Ω _v ), and the vacuum energy (Ω_Λ). It is shown that the most accurate normalization of the power spectrum is achieved with the Sheth-Tormen approximation.     

Twist of magnetic fields in solar active regions

We study the twist properties of photospheric magnetic fields in solar active regions using magnetographic data on 422 active regions obtained at the Huairou Solar Observing Station in 1988–1997. We calculate the mean twist (force-free field α_f) of the active regions and compare it with the mean current-helicity density of these same active regions, h _c =B _∥·(?×B)_∥. The latitude and longitude distributions and time dependence of these quantities is analyzed. These parameters represent two different tracers of the α effect in dynamo theory, so we might expect them to possess similar properties. However, apart from differences in their definitions, they also display differences associated with the technique used to recalculate the magnetographic data and with their different physical meanings. The distributions of the mean α_f and h _c both show hemispherical asymmetry—negative (positive) values in the northern (southern) hemisphere—although this tendency is stronger for h _c. One reason for these differences may be the averaging procedure, when twists of opposite sign in regions with weak fields make a small contribution to the mean current-helicity density. Such transequatorial regularity is in agreement with the expectations of dynamo theory. In some active regions, the average α_f and h _c do not obey this transequatorial rule. As a whole, the mean twist of the magnetic fields α_f of active regions does not vary significantly with the solar cycle. Active regions that do not follow the general behavior for α_f do not show any appreciable tendency to cluster at certain longitudes, in contrast to results for h _c noted in previous studies. We analyze similarities and differences in the distributions of these two quantities. We conclude that using only one of these tracers, such as α_f, to search for signatures of the α effect can have disadvantages, which should be taken into account in future studies.     

Multiple response surfaces for slope reliability analysis

This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second‐order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability p_f. The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the p_f values estimated from multiple response surfaces agree well with those p_f values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation (λ) values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS‐based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of 2-D Random Field Discretization on Failure Probability and Failure Mechanism in Probabilistic Slope Stability

This paper investigates, using the random field theory and Monte Carlo simulation, the effects of random field discretization on failure probability, p _f, and failure mechanism of cohesive soil slope stability. The spatial sizes of the discretized elements in random field Δx, Δy in horizontal and vertical directions, respectively, are assigned a series of combinational values in order to model the discretization accuracy. The p _f of deterministic critical slip surface (DCSS) and that of the slope system both are analyzed. The numerical simulation results have demonstrated that both the ratios of Δy/λ _y (λ _y  = scale of fluctuation in vertical direction) and Δx/λ _x (λ _x  = scale of fluctuation in horizontal direction) contribute in a similar manner to the accuracy of p _f of DCSS. The effect of random field discretization on the p _f can be negligible if both the ratios of Δx/λ _x and Δy/λ _y are no greater than 0.1. The normalized discrepancy tends to increase at a linear rate with Δy/λ _y when Δx/λ _x is larger than 0.1, and vice versa for p _f of DCSS. The random field discretization tends to have more considerable influence on the p _f of DCSS than on that of the slope system. The variation of p _f versus λ _x and λ _y may exhibit opposite trends for the cases where the limit state functions of slope failure are defined on DCSS and on the slope system as well. Finally, the p _f of slope system converges in a more rapid manner to that of DCSS than the failure mechanism does to DCSS as the spatial variability of soil property grows from significant to negligible.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

High resolution electron microscopic studies on ferrosilite III

High resolution transmission electron microscopic (HRTEM) studies on ferrosilite (Fs) III confirmed the periodicity nine (p=9) of the tetrahedral chains in this silicate. Various chain periodicity faults (CPFs) have been observed and faults with “elfer” units (p′=11) dominate. CPFs with p′?9 were observed and are interpreted as pyroxene like slabs. Synthesis of Fs III under extended run duration demonstrated that Fs III actually is the stable phase in the system FeSiO₃ at high pressures and high temperatures. However, the stability fields of Fs III and orthoferrosilite might be separated by a narrow field of a FeSiO₃ polymorph with “elfer” single chain. This field has not been bracketed so far. New structure variants of Fs are discussed. Reconnaissance experiments on the kinetics of CPFs are reported.     

Seismic vertical uplift capacity of horizontal strip anchors using pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis to determine the seismic vertical uplift capacity of a horizontal strip anchor using upper bound limit analysis. However, in the literature, the pseudo-static approach was used by few researchers to compute the seismic vertical pullout resistance, where the real dynamic nature of earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of uplift factor f_γE are determined for different magnitudes of soil friction angle, soil amplification, embedment ratio and seismic acceleration coefficients both in the horizontal and vertical directions. It is observed that the uplift factor f_γE decreases significantly with the increase in seismic accelerations and amplification but increases with the increase in embedment ratio. The results are compared with the existing values in the literature and the significance of the present methodology for designing the horizontal strip anchor is discussed. In presence of vertical earthquake acceleration and amplification of vibration, the present values of f_γE compare reasonably well with the existing pseudo-static values obtained by modifying the horizontal acceleration coefficient.     

The spectra of hard radiation from radio pulsars

The kinetic equation for the distribution function of relativistic electrons is solved taking into account quasi-linear interactions with waves and radiative processes. Mean values of the pitch angles ψ are calculated. If the particles of the primary beam with Lorentz factors γ_b～10⁶ are resonant, then the condition γ_bψ_b?1 is satisfied, the particle distribution is described by the function f _‖(γ) ∝ γ^?4, and the synchrotron radiation spectrum is characterized by the spectral index α=3/2. On the other hand, if a cyclotron resonance is associated with particles of the high-energy tail of the secondary plasma (γ_t～10⁵), then γ_tψ_t?1, and the distribution function has two parts—f _‖(γ) ∝ γ and f _‖(γ) ∝ γ^?2—which correspond to the spectral indices α₁=+1 and α₂=?0.5. This behavior is similar to that observed for the pulsar B0656+14. The predicted frequency of the maximum ν_m=7.5×10¹⁶ Hz coincides with the peak frequency for this pulsar. The model estimate for the total synchrotron luminosity of a typical radio pulsar with hard radiation L _s =3×10³³ erg/s is in agreement with observed values.     

Measurements of the scattering of pulsar radio emission

Measurements of the broadening of pulsar pulses by scattering in the interstellar medium are presented for a complete sample of 100 pulsars with Galactic longitudes from 6° to 311° and distances to three kiloparsec. The dependences of the scattering on the dispersion measure (τ _sc(DM) ∝ DM^α), frequency (τ _sc(v) ∝ v ^?γ ), Galactic longitude, and distance to the pulsar are analyzed. The dependence of the scattering on the dispersion measure in the near-solar neighbourhood can be represented by the power law τ _sc(DM) ∝ DM^2.2±0.1). Measurements at the low frequencies 111, 60, and 40 MHz and literature data are used to derive the frequency dependence of the scattering (τ _sc(v) ∝ V ^?γ ) over a wide frequency interval (covering a range of less than 10: 1) with no fewer than five frequencies. The index for the frequency dependence, γ = 4.1 ± 0.3, corresponds to a normal distribution for inhomogeneities in the turbulence in the scattering medium. Based on an analysis of the dependence of the scattering on the distance to the pulsar and on Galactic longitude, on average, the turbulence level C _n ² is the same in all directions and at all distances out to about three kpc, testifying to the statistical homogeneity of the turbulence of the scattering medium in the near-solar region of the Galaxy.     

Rheology of aqueous magnetite suspensions in uniform magnetic fields

Non-magnetized suspensions of magnetite particles with concentrations in excess of 30% by mass and particle size less than 75 μm exhibit Bingham plastic behaviour. When exposed to external magnetic fields of strengths in excess of 41 × 10⁻⁴ T, the rheological behaviour of the suspensions departs from the Bingham model and can be described by a Herschel–Bulkley model of the form τ = τ₀ + kγⁿ. The value of the index n was found to range from 0.38 to 0.9, depending on the magnetic field strength, solids concentration and particle size and correlations are proposed for the apparent viscosity of magnetized suspensions as a function of magnetic field strength and solids concentration.     

Discrete multifractals

The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions but it also provides insight into the relationships between fractals, bifractals, and multifractals.     

Horizontal magnetic fields in the solar photosphere

Two-dimensional simulations of time-dependent solar magnetogranulation are used to analyze the horizontal magnetic fields and the response of the synthesized Stokes profiles of the IR FeI λ1564.85 nm line to the magnetic fields. The 1.5-h series of MHD models used for the analyses reproduces a region of the magnetic network in the photosphere with an unsigned magnetic flux density of 192 G at the solar surface. According to the magnetic-field distribution obtained, the most probable absolute strength of the horizontal magnetic field at an optical depth of τ ₅ = 1(τ ₅ denotes τ at λ = 500 nm) is 50 G, while the mean value is 244 G. On average, the horizontal magnetic fields are stronger than the vertical fields to heights of about 400 km in the photosphere due to their higher density and the larger area they occupy. The maximum factor by which the horizontal fields are greater is 1.5. Strong horizontal magnetic flux tubes emerge at the surface as spots with field strengths of more than 500 G. These are smaller than granules in size, and have lifetimes of 3–6 min. They form in the photosphere due to the expulsion of magnetic fields by convective flows coming from deep subphotospheric layers. The data obtained qualitatively agree with observations with the Hinode space observatory.     

Aqueous dissolution,solubilities and thermodynamic stabilities of common aluminosilicate clay minerals: Kaolinite and smectites

Determinations of the aqueous solubilities of kaolinite at pH 4, and of five smectite minerals in suspensions set between pH 5 and 8, were undertaken with mineral suspensions adjusted to approach equilibrium from over- and undersaturation. After 1,237 days, Dry Branch, Georgia kaolinite suspensions attained equilibrium solubility with respect to the kaolinite, for which K_eq = (2.72 ± 0.35) × 10⁷. The experimentally determined Gibbs free energy of formation (ΔG_f,298⁰) for the kaolinite is −3,789.51 ± 6.60 kj mol⁻¹. Equilibrium solubilities could not be determined for the smectites because the composition of the solution phase in the smectite suspensions appeared to be controlled by the formation of gibbsite or amorphous aluminum hydroxide and not by the smectites, preventing attempts to determine valid ΔG_f⁰ values for these complex aluminosilicate clay minerals. Reported solubility-based ΔG_f⁰ determinations for smectites and other variable composition aluminosilicate clay minerals are shown to be invalid because of experimental deficiencies and of conceptual flaws arising from the nature of the minerals themselves. Because of the variable composition of smectites and similar minerals, it is concluded that reliable equilibrium solubilities and solubility-derived ΔG_f⁰ values can neither be rigorously determined by conventional experimental procedures, nor applied in equilibriabased models of smectite-water interactions.     

Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading

The stability of tunnels is an important problem in geotechnical engineering. Most of the previous studies dealing with the stability of unlined tunnels are deterministic in nature and do not consider the soil spatial variability. This study investigates the influence of spatial variability on the undrained stability of an unlined circular tunnel, using Random Adaptive Finite Element Limit Analysis (RAFELA). The effect of spatial variability is investigated for tunnels having two different ratios of γD/c_u, for different spatial correlation lengths and tunnel depths. The results indicate that the effect of spatial variability depends on γD/c_u and the depth of the tunnel.     

Sources of the global magnetic field of the Sun

Data on the global magnetic field (GMF) of the Sun as a star for 1968–1999 are used to determine the correlation of the GMF with the radial component of the interplanetary magnetic field (IMF) |B _r|; all data were averaged over a half year. The time variations in the GMF |H| are better correlated with variations in |B _r|; than the results of extrapolating the field from the “source surface” to the Earth’s orbit in a potential model based on magnetic synoptic maps of the photosphere. Possible origins for the higher correlation between the GMF and IMF are discussed. For both the GMF and IMF, the source surface actually corresponds to the quiet photosphere—i.e., background fields and coronal holes—rather than to a spherical surface artificially placed ≈2.5 R _⊙ from the center of the Sun, as assumed in potential models (R _⊙ is the solar radius). The mean effective strength of the photospheric field is about 1.9 G. There is a nearly linear dependence between |H| and |B _r|. The strong correlation between variations in |H| and |B _r| casts doubt on the validity of correcting solar magnetic fields using the so-called “saturation” factor δ^?1 (for magnetograph measurements in the λ 525.0 nm FeI line).