Fractal dimension of pore space in carbonate samples from Tushka area (Egypt)

To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P _c and cumulative fraction V _c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V _c and relaxation time T ₂ show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S _por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S _por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.     

How water use of <Emphasis Type="Italic">Salix</Emphasis><Emphasis Type="Italic">psammophila</Emphasis> bush depends on groundwater depth in a semi-desert area

To investigate the groundwater levels changes effects on the transpiration of Salix psammophila (S. psammophila) bush, systemic measurements of meteorological conditions, sap flow of S. psammophila, soil water contents and groundwater levels were conducted in the Hailiutu River catchment, NW of China. Based on the collected field data, Hydrus-1D software package was used to calibrate water movement for root uptake in the saturated–unsaturated zone. The soil hydraulic parameters and root uptake function parameters were calibrated. The simulated results of soil water contents and sap flow fitted well with the observed ones. Based on the calibrated hydraulic parameters, different groundwater levels were imposed at the low boundary to simulate the groundwater levels changes effects on the transpiration. The relationship between ratio of actual transpiration and potential (T/T _p) and groundwater water table depth was established. The results shows that the ratio of actual transpiration and potential transpiration decreases with groundwater table depth increase as inverse ‘S’ shape. And the turn point is corresponding to the extinct depth, i.e., no groundwater contribution to S. psammophila transpiration. To further verify this phenomenon is universal, the soil hydraulic parameters were replaced with the other five groups in the calibrated forward model. The results confirmed the similar changes of T _a/T _p with the groundwater levels changed, i.e. inverse ‘S’ shape. However, the extinction depth is different corresponding to different soil hydraulic parameters. So, the research results indicated the relationship between transpiration and groundwater levels is non-linear function.     

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.     

Structural systematics of Ge substitution in primitive pyroxenes

Pyroxenes of general stoichiometry Mg(Ge _x Si_1?x )O₃ were encountered in attempts to synthesise Ge-substituted talcs at 0.2 GPa, 650–700 °C. Orthopyroxenes (Pbca) of compositions x = 0.21, 0.30, and 0.34 were identified, and also a P2₁/c clinopyroxene of composition x = 0.63, and C2/c clinopyroxenes of compositions x = 0.91 and 1. End-member clinoenstatite MgSiO₃-P2₁/c synthesised at 16 GPa, 1300 °C and transformed from C2/c was also included in the study. Crystal structure refinements using single-crystal XRD data showed that unit-cell parameters vary linearly with Si–Ge for the Pbca and P2₁/c pyroxenes, both of which have two symmetrically non-equivalent tetrahedral chains. Refinement of Si–Ge occupancies at tetrahedral sites showed that the two chains of all primitive pyroxenes have very different compositions, with X_Ge(TB) ? X_Ge(TA). This difference arises from the greater flexibility of the B-chain to rotate in response to tetrahedral expansion due to increasing Ge content. The TA-M2 shared polyhedral edge imposes significant constraints on the flexibility of the A-chain, which can accommodate much less Ge than the B-chain. Linear trends of cell parameters, site occupancies, and structural parameters for the primitive pyroxenes, when extrapolated to published data for MgGeO₃–Pbca, extend across the entire Si–Ge join.     

Seismic source characteristics in Kachchh and Saurashtra regions of Western India: <Emphasis Type="Italic">b</Emphasis>-value and fractal dimension mapping of aftershock sequences

Seismic source characteristics in the Kachchh rift basin and Saurashtra horst tectonic blocks in the stable continental region (SCR) of western peninsular India are studied using the earthquake catalog data for the period 2006–2011 recorded by a 52-station broadband seismic network known as Gujarat State Network (GSNet) running by Institute of Seismological Research (ISR), Gujarat. These data are mainly the aftershock sequences of three mainshocks, the 2001 Bhuj earthquake (M _w 7.7) in the Kachchh rift basin, and the 2007 and 2011 Talala earthquakes (M _w ≥ 5.0) in the Saurashtra horst. Two important seismological parameters, the frequency–magnitude relation (b-value) and the fractal correlation dimension (D _c) of the hypocenters, are estimated. The b-value and the D _c maps indicate a difference in seismic characteristics of these two tectonic regions. The average b-value in Kachchh region is 1.2 ± 0.05 and that in the Saurashtra region 0.7 ± 0.04. The average D _c in Kachchh is 2.64 ± 0.01 and in Saurashtra 2.46 ± 0.01. The hypocenters in Kachchh rift basin cluster at a depth range 20–35 km and that in Saurashtra at 5–10 km. The b-value and D _c cross sections image the seismogenic structures that shed new light on seismotectonics of these two tectonic regions. The mainshock sources at depth are identified as lower b-value or stressed zones at the fault end. Crustal heterogeneities are well reflected in the maps as well as in the cross sections. We also find a positive correlation between b- and D _c-values in both the tectonic regions.     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

Heterogeneity of hydraulic conductivity and Darcian flux in the submerged streambed and adjacent exposed stream bank of the Beiluo River,northwest China

Recognizing the heterogeneity of hydraulic conductivity and hyporheic flow is critical for understanding contaminant transfer and biogeochemical and hydrological processes involving streams and aquifers. In this study, the heterogeneity of hydraulic conductivity and Darcian flux in a submerged streambed and its adjacent exposed stream banks were investigated in the Beiluo River, northwest China. In the submerged streambed, Darcian flux was estimated by measurement of vertical hydraulic conductivity (K _v) and vertical head gradient (VHG) using in-situ permeameter tests. On exposed stream banks, both horizontal hydraulic conductivity (K _h) and K _v were measured by on-site permeameter tests. In the submerged streambed, K _v values gradually decreased with depth and the higher values were concentrated in the center and close to the erosional bank. Compared to the exposed stream banks, the K _v values were higher in the streambed. From stream stage to the topmost layer of tested sediment, through increasing elevation, the K _h values increased on the erosional bank, while they decreased on the depositional bank. The values of VHG along the thalweg illustrate that downwelling flux occurred in the deepest area while upwelling flux appeared in the other areas, which might result from the change of streambed elevation. The higher value of the Darcian flux in the submerged streambed existed near the erosional bank.     

High-pressure displacive phase transition of a natural Mg-rich pigeonite

A high-pressure single-crystal X-ray diffraction study has been carried out on a P2₁/c natural Mg-rich pigeonite sample with composition ca. Wo₆En₇₆Fs₁₈ using a diamond anvil-cell. The unit-cell parameters were determined at 14 different pressures to 7.14 GPa. The sudden disappearance of the b-type reflections (h + k = odd) and a strong discontinuity (about 2.8%) in the unit-cell volume indicated a first-order P2₁/c–C2/c phase transition between 4.66 and 4.88 GPa. The P(V) data of the P2₁/c phase were fitted to 4.66 GPa by a third-order Birch–Murnaghan equation of state (BM3 EoS), whereas the limited number of experimental data collected within the C2/c phase between 4.88 and 7.14 GPa were fitted using the same equation of state but with K′ constrained to the value obtained for the P2₁/c fitting. The equation of state coefficients are V ₀ = 424.66(6) ų, K _T0 = 104(2) GPa and K′ = 8(1) for the P2₁/c phase, and V ₀ = 423.6(1) ų, K _T0 = 112.4(8) GPa, and K′ fixed to 8(1) for the C2/c phase. The axial moduli for a, b, and c for the P2₁/c phase were obtained using also a BM3-EoS, while for the C2/c phase only a linear calculation could be performed, and therefore the same approach was applied for comparison also to the P2₁/c phase. In general the C2/c phase exhibits axial compressibilities (β _c > β _a >> β _b) lower than those of the P2₁/c phase (β _b > β _c ≈ β _a; similar to those found in previous studies in clinopyroxenes and orthopyroxenes). The lower compressibility of the C2/c phase compared with that of the P2₁/c could be ascribed to the greater stiffness along the b direction. A previously published relationship between P _c and M2 average cation radius (i.r.) has been updated using all the literature data on P2₁/c clinopyroxene containing large cations at M2 site and our new data. The following weighted regression was obtained: P _c (GPa) = 26(4) ? 28(5) ×  i.r (Å), R ² = 0.97. This improved equation can be used to predict the critical pressure of natural P2₁/c clinopyroxene samples just knowing the composition at M2 site.     

Behavior of 10-Å phase at low temperatures

The thermal evolution of 10-Å phase Mg₃Si₄O₁₀(OH)₂·H₂O, a phyllosilicate which may have an important role in the storage/release of water in subducting slabs, was studied by X-ray single-crystal diffraction in the temperature range 116–293 K. The lattice parameters were measured at several intervals both on cooling and heating. The structural model was refined with intensity data collected at 116 K and compared to the model refined at room temperature. As expected for a layer silicate on cooling in this temperature range, the a and b lattice parameters undergo a small linear decrease, α _a  = 1.7(4) 10^?6 K^?1 and α _b  = 1.9(4) 10^?6 K^?1, where α is the linear thermal expansion coefficient. The greater variation is along the c axis and can be modeled with the second order polynomial c _T  = c ₂₉₃(1 + 6.7(4)10^?5 K^?1ΔT + 9.5(2.5)10^?8 K^?2(ΔT)²) where ΔT = T ? 293 K; the monoclinic angle β slightly increased. The cell volume thermal expansion can be modeled with the polynomial V _T  = V ₂₉₃ (1 + 8.0 10^?5 K^?1 ΔT + 1.4 10^?7 K^?2 (ΔT)²) where ΔT = T ? 293 is in K and V in ų. These variations were similar to those expected for a pressure increase, indicating that T and P effects are approximately inverse. The least-squares refinement with intensity data measured at 116 K shows that the volume of the SiO₄ tetrahedra does not change significantly, whereas the volume of the Mg octahedra slightly decreases. To adjust for the increased misfit between the tetrahedral and octahedral sheets, the tetrahedral rotation angle α changes from 0.58° to 1.38°, increasing the ditrigonalization of the silicate sheet. This deformation has implications on the H-bonds between the water molecule and the basal oxygen atoms. Furthermore, the highly anisotropic thermal ellipsoid of the H₂O oxygen indicates positional disorder, similar to the disorder observed at room temperature. The low-temperature results support the hypothesis that the disorder is static. It can be modeled with a splitting of the interlayer oxygen site with a statistical distribution of the H₂O molecules into two positions, 0.6 Å apart. The resulting shortest O_bas–O_W distances are 2.97 Å, with a significant shortening with respect to the value at room temperature. The low-temperature behavior of the H-bond system is consistent with that hypothesized at high pressure on the basis of the Raman spectra evolution with P.     

Absorption in the H(93–95)<Emphasis Type="Italic">α</Emphasis> and H(78–79)<Emphasis Type="Italic">α</Emphasis> recombination lines in the HII region of the quasar 3C 345

Absorption of the synchrotron emission of the quasar 3C 345 in the continuum and H(93–95)α and H(78–79)α radio recombination lines is studied. The upper limit for absorption in the H(93–95)α lines is T_al/T_ac < 0.7%; absorption in the H(78–79)α lines with antenna temperature T_al = 25 mK, linewidth Δf = 5.3 ± 0.08 MHz, and T_al/T_ac ≥ 0.3% has been detected. A correction to the redshift Δz = 0.00135 ± 0.00008 (z = 0.59365) has been determined.     

Spatial information of soil hydraulic conductivity and performance of cokriging over kriging in a semi-arid basin scale

Unlike the studies in small parcels by systematic measurements, the spatial variability of soil properties is expected to increase in those over relatively large areas or scales. Spatial variability of soil hydraulic conductivity (K _h) is of significance for the environmental processes, such as soil erosion, plant growth, transport of the plant nutrients in a soil profile and ground water levels. However, its variability is not much and sufficiently known at basin scale. A study of testing the performance of cokriging of K _h compared with that of kriging was conducted in the catchment area of Sarayköy II Irrigation Dam in Cank?r?, Turkey. A total of 300 soil surface samples (0–10 cm) were collected from the catchment with irregular intervals. Of the selected soil properties, because the water-stable aggregates (WSA) indicated the highest relationship with the hydraulic conductivity by the Pearson correlation analysis, it is used as an auxiliary variable to predict K _h by the cokriging procedure. In addition, the sampling density was reduced randomly to n = 175, n = 150, n = 75 and n = 50 for K _h to determine if the superiority of cokriging over kriging would exist. Statistically, the results showed that all reduced K _h was as good as the complete K _h when its auxiliary relations with WSA were used in cokriging. Particularly, the results of the “Relative Reduction in MSE” (RMSE) revealed that the reduced data set of n = 75 produced the most accurate map than the others. In this basin-scaled study, there was a clear superiority of the cokriging procedure by the reduction in data although a very undulating topography and topographically different aspects, two different land uses with non-uniform vegetation density, different parent materials and soil textures were present in the area. Hence, using the statistically significant auxiliary relationship between K _h and WSA might bring about a very useful data set for watershed hydrological researches.     

The radio brightness distribution along the solar limb observed on the Siberian Solar Radio Telescope

The radio brightness distribution at 5.2 cm has been obtained along the entire solar limb down to a level of 0.01 of brightness temperature at the disk center T ₀ ^c during the solar minimum. The measurements are based on strip scans from the Siberian Solar Radio Telescope. Data reduction included model fitting of an actual solar scan for each position angle. The maximum limb brightness, 1.37 T ₀ ^c , in the derived distribution is at equatorial direction, where the radio radius exceeds the photosphere radius by 7%. Toward the poles, the brightness peak and radio radius gradually decrease to 1.01 T ₀ ^c and 1.005 R₀. The derived two-dimensional brightness distribution was used to calculate radio radius as a function of position angle for several wavelengths from 4 to 31.6 cm. These dependences are consistent with RATAN-600 observations at position angles 0° and 25°.     

Effects of salt solutions on the hydro-mechanical behavior of compacted GMZ01 Bentonite

In this study, the effects of salinity of infiltrating solutions on the swelling strain, compressibility, and hydraulic conductivity of compacted GMZ01 Bentonite were investigated. After swelling under vertical load using either distilled water or NaCl solutions with concentrations of 0.1, 0.5 M, and 1 M, laboratory oedometer tests were conducted on the compacted GMZ01 Bentonite. Based on the oedometer test results, hydraulic conductivity was determined using the Casagrande’s method. Results show that the swelling strain of highly compacted GMZ01 Bentonite decreases as the concentration of NaCl solution increases. The compression index C _c ^* increases and then turns to decrease with an increase in the vertical stress or a decrease in the void ratio for different solutions, and the C _c ^* decreases as the concentration of NaCl solution increases. The secondary consolidation coefficient C _α increases linearly with the increase of the compression index C _c ^* . Furthermore, a bi-linear relationship between the swelling index C _s ^* and the secondary consolidation coefficient C _α can be characterized clearly. The hydraulic conductivity increases as the concentration of NaCl solution increases, however, this increase can be prevented if a high confining stress is applied.     

Time constant of hydraulic-head response in aquifers subjected to sudden recharge change: application to large basins

Analytical formulae are proposed to describe the first-order temporal evolution of the head in large groundwater systems (such as those found in North Africa or eastern Australia) that are subjected to drastic modifications of their recharge conditions (such as those in Pleistocene and Holocene times). The mathematical model is based on the hydrodynamics of a mixed-aquifer system composed of a confined aquifer connected to an unconfined one with a large storage capacity. The transient behaviour of the head following a sudden change of recharge conditions is computed with Laplace transforms for linear one-dimensional and cylindrical geometries. This transient evolution closely follows an exponential trend exp(?t/τ). The time constant τ is expressed analytically as a function of the various parameters characterizing the system. In many commonly occurring situations, τ depends on only four parameters: the width a _c of the main confined aquifer, its transmissivity T _c, the integrated storage situated upstream in the unconfined aquifer M?=?S _u a _u, and a curvature parameter accounting for convergence/divergence effects. This model is applied to the natural decay of large aquifer basins of the Sahara and Australia following the end of the mid-Holocene humid period. The observed persistence of the resource is discussed on the basis of the time constant estimated with the system parameters. This comparison confirms the role of the upstream water reserve, which is modelled as an unconfined aquifer, and highlights the significant increase of the time constant in case of converging flow.     

Elastic behavior of vanadinite,Pb<Subscript>10</Subscript>(VO<Subscript>4</Subscript>)<Subscript>6</Subscript>Cl<Subscript>2</Subscript>, a microporous non-zeolitic mineral

The high-pressure behavior of a vanadinite (Pb₁₀(VO₄)₆Cl₂, a = b = 10.3254(5), c = 7.3450(4) Å, space group P6₃/m), a natural microporous mineral, has been investigated using in-situ HP-synchrotron X-ray powder diffraction up to 7.67 GPa with a diamond anvil cell under hydrostatic conditions. No phase transition has been observed within the pressure range investigated. Axial and volume isothermal Equations of State (EoS) of vanadinite were determined. Fitting the P–V data with a third-order Birch-Murnaghan (BM) EoS, using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 681(1) Å³, K ₀ = 41(5) GPa, and K′ = 12.5(2.5). The evolution of the lattice constants with P shows a strong anisotropic compression pattern. The axial bulk moduli were calculated with a third-order “linearized” BM-EoS. The EoS parameters are: a ₀ = 10.3302(2) Å, K ₀(a) = 35(2) GPa and K′(a) = 10(1) for the a-axis; c ₀ = 7.3520(3) Å, K ₀(c) = 98(4) GPa, and K′(c) = 9(2) for the c-axis (K ₀(a):K ₀(c) = 1:2.80). Axial and volume Eulerian-finite strain (fe) at different normalized stress (Fe) were calculated. The weighted linear regression through the data points yields the following intercept values: Fe _a (0) = 35(2) GPa for the a-axis, Fe _c (0) = 98(4) GPa for the c-axis and Fe _V (0) = 45(2) GPa for the unit-cell volume. The slope of the regression lines gives rise to K′ values of 10(1) for the a-axis, 9(2) for the c-axis and 11(1) for the unit cell-volume. A comparison between the HP-elastic response of vanadinite and the iso-structural apatite is carried out. The possible reasons of the elastic anisotropy are discussed.     

Nonlinear consolidation in randomly heterogeneous highly compressible aquitards

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. The effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards is investigated by means of one-dimensional Monte Carlo numerical simulations where the lower boundary represents the effect of an instant drop in hydraulic head due to groundwater pumping. Two thousand realizations are generated for each of the following parameters: hydraulic conductivity (K), compression index (C _c), void ratio (e) and m (an empirical parameter relating hydraulic conductivity and void ratio). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system when compared to a nonlinear consolidation model with deterministic initial parameters. The deterministic solution underestimates the ensemble average of total settlement when initial K is random. In addition, random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady-state conditions.     

New models to predict rock failure by linking the volume dilatant point with the peak stress point

The rock mass failure process can be divided into several distinct deformation stages: the compaction stage, elastic stage, stable failure stage, accelerated failure stage, and post-peak stage. Although each stage has been well studied, the relationship among the stages has not been established. Here, we establish two models which are the Strain model Q and Energy density model S by using the renormalization group theory and investigate the mechanical relationship between the volume dilatant point and peak stress point on the rock stress-strain curve. Our models show that the strain ratio (ε _f /ε _c ) and energy ratio (E _f /E _c ) at the volume dilatant point and peak stress point are solely functions of the shape parameter m. To verify our models, we further studied the failure process of rock specimens through several uniaxial compression experiments and found that the relationship between ε _f /ε _c or E _f /E _c and m shares a notably similar pattern to that from our theoretical model. However, the ε _f /ε _c and E _f /E _c values in our experiments are slightly smaller than those predicted by the models. In brief, we demonstrate that our models can be used to predict the failure process of the laboratory-scale hard brittle rock samples.     

Nonlinear radial pulsations of Wolf-Rayet stars

The evolution of Population I stars with initial masses 60 M _⊙ ≤ M _ZAMS ≤ 120 M _⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y _c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T _eff ～ 10⁵ K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T _eff ≈ 10⁵ K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M _⊙ to M = 6 M _⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 10⁵ K.     

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.