Analytical solution for 1D consolidation under haversine cyclic loading

Presented and discussed in this paper is an exact analytical solution of the nonhomogeneous partial differential equation governing the conventional one‐dimensional consolidation under haversine repeated loading. The derived analytical solution to the 1D consolidation equation is compared with the numerical solution of the same consolidation problem via FEM. The series solution takes into account the frequency of repeated loading through a dimensionless time factor T₀. The paper reveals that an increase in the frequency of imposed repeated haversine loading (a decrease in period of repeated loading) causes an increase in the number of cycles required to achieve the steady state, whereas the effect of frequency on the maximum excess pore water pressure at the bottom of a clay layer with permeable top and impermeable bottom for the range of frequencies studied is generally insignificant. The effective stress at the bottom of the clay deposit with permeable top and impermeable bottom increases with time but with some fluctuations without changing the sign. These fluctuations become more pronounced for increasing values of T₀. An increase in T₀ also causes an increase in maximum effective stress. Copyright © 2013 John Wiley & Sons, Ltd.     

Impact of desalination plants brine injection wells on coastal aquifers

A new methodology is developed in assessing environmental impacts of desalination plants discharging brine into the ground. The main environmental problem of the desalination of seawater is the brine disposal. The brine is commonly discharged into the sea or injected into a saline aquifer. In the case of injection into the ground, it is necessary to design a disposal system in a way that respects the environment and is sustainable. Laboratory and computational methods have been utilized to simulate the unsteady three-dimensional (3D) phenomena of subsurface brine disposal. The computational software used is SEAWAT, which is a 3D unsteady variable-density flow simulation model. The model is first used to simulate the laboratory results, and good agreement is achieved. Then, hypothetical problems are designed and simulated of groundwater extraction and brine disposal by desalination stations. The major purpose of these hypothetical problems is to delineate a methodology and to create design charts for design and management of production and injection well fields for coastal desalination plants. Several design charts have been developed with 36 scenarios for two well configurations created by four design parameters: relative salt concentration (RSC), production and injection rates (Q _d , Q _r ), well spacing (S), and simulation period (T).     

Rock media mathematical models processing

This paper reports on mathematical models of rock media processing and on their use in designing open pit coal mines. Spatial mathematical model of rock media was processed on a 25 km² model site, incorporating 918 borehole logs. The model is capable of providing information concerning the geological structure of every point of the investigated area by plotting geological cross-sections along given lines or by plotting contour lines of the surface or the base for thickness of chosen lithological strata. The computation of one point of a grid involves the following steps: Borehole logs are numericaly coded. The geological structure at an arbitrarily chosen pointP is computed as follows. All borehole logs inside the circle (P; R) are used to compute theZ-coordinate of the ground atP by some interpolation formula chosen from those contained in the program system. Next, we check what stratum occurs topmost at boreholes inside the circle and which is most probable as the top stratumC ₁ atP. TheZ-coordinate of theC ₁ stratum surface atP is computed. Then what strata occur underC ₁ stratum and which of them is the most probable stratumC ₂ is determined. The process of computation is repeated until a sequence of strataC _i atP andZ _i coordinates of their surfaces is ascertained. The interpolation formulas included in the system are proper linear combination of PAF (polynomial approximations formulas, linear or quadratic and weighted) and WAF (weighted average formulas). Among the various interpolation formulas, some proved more useful for tectonic fault lines, others for ordinary sedimentary surfaces.     

New Approach for Estimation of Static and Seismic Active Earth Pressure

To estimate static and seismic active earth pressure (P_ad) on a rigid retaining wall, numerical analyses using different step sizes have been carried out in this paper, based on the modified Culmann line method by considering Coulomb’s planar rupture surface. Equivalent pseudo-static seismic forces are considered in the analysis. A new concept of modified unit weight by considering ground surcharge is introduced under static and seismic conditions. By numerical analysis, area of soil (A) has been estimated to obtain the ratio of A/A₀ where A₀ is θh², θ is the angle between retaining structure and ground surface and h is the vertical height of the wall. This ratio remains constant for a particular type of soil and has been used to estimate the maximum active earth pressure using force diagram. Results are provided in tabular form for easy calculation of the coefficient of static and seismic active earth pressure. Present results by considering the new technique, compares well with the results obtained by earlier researchers.     

Petrological constraints on the eclogite- and blueschistfacies metamorphism and P-T-t paths in the Western Alps*

Phase relationships in the model mafic system and geothermobarometry allow discrimination of four main groups of high-P rocks in the nappes of the Western Alps: very high-P eclogite-facies (including kyanite eclogites and coesite-pyrope assemblages), eclogite-facies (paragonite-zoisite eclogites), high-T blueschist-facies (glaucophane-garnet ± lawsonite assemblages) and low-T blueschist-facies (glaucophane-lawsonite ± pumpellyite assemblages). The blueschist-facies-eclogite-facies transition is promoted chiefly by increasing T, low bulk X_Mg and relatively low μ_H2O. The variety of assemblages and the heterogeneous approach to equilibrium observed in the Alpine rocks are not only constrained by the intersection of the reaction surfaces in P-T-X space, but also by the effect and timing of the processes which control kinetics (i.e. pervasive deformation and fluid infiltration). The faster rate of dehydration reactions relative to hydration reactions along with the fact that different bulk compositions crossed the reaction curves at different temperatures (and times), all may have induced μ_H2O gradients and contributed to the heterogeneous distribution of deformation through a process of reaction-enhanced ductility. Also mass-transfer may have been an effective process in determining the type of high-P assemblage in particular rock volumes. As regards the P-T-t paths, only the post-climax histories are recorded well in the Alpine nappes. Post-eclogitic exhumation paths at decreasing temperatures characterize structurally higher nappes which were first subducted during the early-Alpine (Cretaceous) event. In contrast, more or less isothermal decompression paths characterize structurally deeper nappes formed by westward propagation of the underthrust surfaces during the early-Alpine event and the subsequent meso-Alpine (Palaeogene) collision between the ‘European’and ‘African’plates. In the Western Alps, prevalent eclogite-facies conditions were attained during the metamorphic climax of the early-Alpine subduction, while blueschist-facies recrystallization characterizes the early-Alpine exhumation of the eclogitized units and the subsequent intracontinental underthrusts linked to the meso-Alpine continental collision.     

The effect of internal gas pressurization on volcanic edifice stability: evolution towards a critical state

Results from simple physical and numerical models investigating the effects of increased internal pore‐fluid pressures of a Mohr–Coulomb volcanic edifice are presented. Physical experiments make use of a heap built from angular sand on top of a stiff substrate of variable angle, with the provision for injection of internal fluid (gas) pressures into the base. The resulting failure geometries arising from internal pressurization of the model appear similar to some natural examples of sector collapse. Two‐dimensional limit equilibrium models analysing 42 500 possible failure surfaces were run with internal pressures (P₀) in the range 5–35 MPa, and show that the potential critical failure surface migrates to increasingly deeper levels with increasing internal pressure. Although internal pressurization alone is unlikely to reduce the factor of safety (F_S) below unity, the edifice is driven towards a state of criticality that will render in susceptible to any internal or external perturbations.     

Artificial neural network approach for estimation of surface specific humidity and air temperature using multifrequency scanning microwave radiometer

Microwave sensor MSMR (Multifrequency Scanning Microwave Radiometer) data onboard Oceansat-1 was used for retrieval of monthly averages of near surface specific humidity (Q _a) and air temperature (T _a) by means of Artificial Neural Network (ANN). The MSMR measures the microwave radiances in 8 channels at frequencies of 6.6, 10.7, 18 and 21 GHz for both vertical and horizontal polarizations. The artificial neural networks (ANN) technique is employed to find the transfer function relating the input MSMR observed brightness temperatures and output (Q _a andT _a) parameters. Input data consist of nearly 28 months (June 1999 – September 2001) of monthly averages of MSMR observed brightness temperature and surface marine observations ofQ _a andT _a from Comprehensive Ocean-Atmosphere Data Set (COADS). The performance of the algorithm is assessed with independent surface marine observations. The results indicate that the combination of MSMR observed brightness temperatures as input parameters provides reasonable estimates of monthly averaged surface parameters. The global root mean square (rms) differences are 1.0‡C and 1.1 g kg⁻¹ for air temperature and surface specific humidity respectively.     

Spatial distribution of soil shear-wave velocity and the fundamental period of vibration – a case study of the Saguenay region,Canada

The spatial distribution of soil shear-wave velocity and the fundamental period of vibration were selected as input parameters for the determination of potential seismic site effects in the Saguenay region, Canada. The methodology used in this study involved three clear steps. First, a 3D geological model of the surficial deposits was built taking into consideration the type, spatial distribution and thickness of the deposits. Second, representative average V_s values were determined for each of the major soil units. Finally, the average shear-wave velocity from the ground surface to bedrock (V_sav), the shear-wave velocity of the upper 30 m (V_s30) and the fundamental site resonance period (T₀) were calculated over a regular grid for the study area. The results include the spatial distribution of the fundamental site resonance period, the average shear-wave velocity in the first 30 m of the ground and the spatial distribution of National Building Code of Canada seismic soil classes for the Saguenay region.     

Anisotropic Scaling Models of Rock Density and the Earth’s Surface Gravity Field

In this paper we consider an anisotropic scaling approach to understanding rock density and surface gravity which naturally accounts for wide range variability and anomalies at all scales. This approach is empirically justified by the growing body of evidence that geophysical fields including topography and density are scaling over wide range ranges. Theoretically it is justified, since scale invariance is a (geo)dynamical symmetry principle which is expected to hold in the absence of symmetry breaking mechanisms. Unfortunately, to date most scaling approaches have been self-similar, i.e., they have assumed not only scale invariant but also isotropic dynamics. In contrast, most nonscaling approaches recognize the anisotropy (e.g., the strata), but implicitly assume that the latter is independent of scale. In this paper, we argue that the dynamics are scaling but highly anisotropic, i.e., with scale dependent differential anisotropy. By using empirical density statistics in the crust and a statistical theory of high Prandtl number convection in the mantle, we argue that is a reasonable model for the 3-D spectrum (K is the horizontal wavevector and K is its modulus, k _z is a vertical wavenumber), (s,H _z ) are fundamental exponents which we estimate as (5.3,3), (3,3) in the crust and mantle, respectively. We theoretically derive expressions for the corresponding surface gravity spectrum. For scales smaller than ≈100 km, the anisotropic crust model of the density (with flat top and bottom) using empirically determined vertical and horizontal density spectra is sufficient to explain the (Bouguer) g _z spectra. However, the crust thickness is highly variable and the crust-mantle density contrast is very large. By considering isostatic equilibrium, and using global gravity and topography data, we show that this thickness variability is the dominant contribution to the surface g _z spectrum over the range ≈100–1000 km. Using estimates of mantle properties (viscosity, thermal conductivity, thermal expansion coefficient, etc.), we show that the mantle contribution to the mean spectrum is strongest at ≈1000 km and is comparable to the variable crust thickness contribution. Overall, we produce a model which is compatible with both the observed (horizontal and vertical) density heterogeneity and surface gravity anomaly statistics over a range of meters to several thousand kilometers.     

A volume-conserving representation of cell faces in corner point grids

Corner point grids is currently the standard grid representation for use in reservoir simulation. The cell faces in corner point grids are traditionally represented as bilinear surfaces where the edges between the corner points all are straight lines. This representation has the disadvantage that along faults with varying dip the cell faces on either side will not precisely match, giving overlapping cells or gaps between cells. We propose an alternative representation for the cell faces. The four vertical cell faces are still represented as bilinear surfaces, but instead of having linear edges between the cell corners along the top and bottom faces, we propose a representation of the vertical cell faces where any horizontal intersection will give a straight line, giving column faces whose shape is independent of the corner point locations of the individual grid cells. This ensures that the grid columns match up and that there are no gaps or overlapping volumes between grid cells. This representation gives a local parameterization for the whole grid column, and the top and bottom grid cell surfaces are modeled as bilinear using this parameterization. A set of local coordinates for the grid cell permits all the common grid operations like volume calculation, area calculation for cell faces, and blocking of well traces.     

Numerical study for production of space charge within the stratiform cloud

One dimensional numerical model has been developed to predict the production of space charge and variations in other electrical parameters within the low level stratiform type of cloud having very weak vertical motion. Non-linear coupled differential equations which govern ion concentrations, charged and neutral droplet concentrations and electric field were used. Symmetry has been observed in all the electrical parameters within the cloud. The magnitude of average positive ion concentrations was observed to be high as compared to the negative ion concentrations, which is due to low scavenging rate of positive ions than the negative ions, highly attributed to their mobilities. The rate of scavenging of ions affects the concentration of charged droplets, which eventually influence the electric field and thus the space charge density within the cloud. Maximum electric field (E _max) was observed at middle of the cloud whereas minimum was observed at both the edges of the cloud. Minimum electric field (E _min) was found to be equal and constant (∼27 Vm⁻¹) for any drop concentration. Net positive and negative space charges were observed at the top and bottom of the cloud, respectively. The simulated results show some discrepancies to the natural condition, which are due to simulations made under some basic assumptions and limitations and that will be incorporated in the future studies for natural cloud condition.     

Impact of biochar,bentonite, and compost on physical and chemical characteristics of a sandy soil

In this study, bentonite (Ben), compost (Com), and biochar (Bio) were used as soil amendments to enhance sandy soil physical properties. A soil column experiment was conducted in a laboratory. Application rates were 3% (weight/weight) of Bio (T₁), Ben (T₂), and Com (T₃). Furthermore, mixtures 1.5% and 1.5% of Bio and Ben (T₄), Ben and Com (T₅), and Bio and Com (T₆), and a mixture 1%, 1%, and 1% of Bio, Ben, and Com (T₇) in addition to control treatment were adopted. The mixtures of amendments and sandy soil were concentrated at the top 10 cm of columns. Results revealed that the cumulative evaporation was reduced by 2.3% and 5.7% as a result of using T₃ and T₅, respectively. However, the remaining treatments enhanced the cumulative evaporation. The application of amendments increased the capacity of the soil to maintain water by 35.4%, 24.4%, 13.3%, and 10.2%, for soils treated with T₅, T₃, T₇, and T₄, respectively. The water content at field capacity had the highest increase in the top 10 cm when treatment T₃ was used. Although T₃ (compost) was the most efficient for enhancing soil physical properties, this study recommends T₅ and T₇ to improve hydraulic properties of sandy soils. This is due to the fact that biochar and bentonite remain in the soil for a longer period and resist biodegradation while compost overcomes the negative impact of soil chemical properties as a result of biochar and bentonite additions.     

Geometry of isograds in metamorphic terrains

A simple mathematical relation among the dip of isograd surface (θ), dip of isotherm surface (α), temperature gradient (T_g), pressure gradient (P_g) and δT/gdP of reaction is given by:

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P_g is taken to be constant at 0.3 kb/km. Four major theoretical models for shapes and orientations of isograds are formulated on the basis of the parameters α, T_g and δT/δP. This offers a rational basis for studying the geometry of isograds, normal/reverse metamorphism and determination of temperature gradient. Two examples have been studied in the light of these models; in one case the domed shape of the isograd is best explained by a downwardly directed T_g; in the other case, reverse metamorphism is best explained as the result of a horizontal T_g of 18°C/km.     

Assessing probability of surface manifestation of liquefaction at a given site in a given exposure time using CPTU

This paper is a follow-up to a previous paper on the subject of liquefaction potential index (LPI), a parameter that is often used to characterize the potential for surface manifestation of liquefaction at a given site subjected to a given shaking level (represented by a pair of peak ground surface acceleration a_max and moment magnitude M_w). In the previous paper by Juang and his coworkers, the LPI was re-calibrated for a piezocone penetration test (CPTU) model, and a simplified model based on LPI was created for computing the conditional probability of surface manifestation of liquefaction (P_G). In this paper, the model for this conditional probability P_G is extended into a complete framework for assessing the probability of surface manifestation of liquefaction in a given exposure time at a given site subjected to all possible ground motions at all seismic hazard levels. This new framework is formulated and demonstrated with an example site in 10 different seismic regions in the United States.     

桂林盘龙洞岩溶表层带土壤CO2浓度的季节变化研究

以桂林盘龙洞岩溶实验场为例,选择岩溶洼地里的坡地和洼地2个样地,通过长期定时监测土壤CO2浓度变化,表明:(1)土壤CO2浓度具有明显的季节性变化特征,夏季(6-8月)土壤CO2浓度是其它时期的2～3倍,并显示与气温、降水和生物活动密切相关;(2)洼地地段土壤CO2浓度比坡地地段要高,尤其夏季时洼地比坡地高近1000mg/m2;(3)在垂直剖面上,大多数的情况下土壤CO2浓度随土壤深度的递增而升高,但在雨季时坡地(-50cm与-80cm处)和洼地(-80cm与-100cm处)的土壤CO2浓度随深度的增加而降低。      

Quantitative Parameters for Rock Joint Surface Roughness

Summary The morphologies of two artificial granite joints (sanded and hammered surfaces), one artificial regularly undulated joint and one natural schist joint, were studied. The sanded and hammered granite joints underwent 5 cycles of direct shear under 3 normal stress levels ranging between 0.3–4 MPa. The regularly undulated joint underwent 10 cycles of shear under 6 normal stress levels ranging between 0.5–5 MPa and the natural schist replicas underwent a monotonous shear under 5 normal stress levels ranging between 0.4–2.4 MPa. In order to characterize the morphology of the sheared joints, a laser sensor profilometer was used to perform surface data measurements prior to and after each shear test. Rather than describing the morphology of the joints from the single profiles, our characterization is based on a simultaneous analysis of all the surface profiles. Roughness was viewed as a combination of a primary roughness and a secondary roughness. The surface angularity was quantified by defining its three-dimensional mean angle, θ_s, and the parameter Z2_s. The surface anisotropy and the secondary roughness were respectively quantified by the degree of apparent anisotropy, k _a, and the surface relative roughness coefficient, R _s. The surface sinuosity was quantified by the surface tortuosity coefficient, T _s.  Comparison between the means of the classical linear parameters and those proposed shows that linear parameters underestimate the morphological characteristics of the joint surfaces. As a result, the proposed bi-dimensional and tri-dimensional parameters better describe the evolution of the joints initial roughness during the course of shearing.     

Evaluation of brightness temperature from a forward model of ground-based microwave radiometer

Ground-based microwave radiometers are getting great attention in recent years due to their capability to profile the temperature and humidity at high temporal and vertical resolution in the lower troposphere. The process of retrieving these parameters from the measurements of radiometric brightness temperature (T _B ) includes the inversion algorithm, which uses the back ground information from a forward model. In the present study, an algorithm development and evaluation of this forward model for a ground-based microwave radiometer, being developed by Society for Applied Microwave Electronics Engineering and Research (SAMEER) of India, is presented. Initially, the analysis of absorption coefficient and weighting function at different frequencies was made to select the channels. Further the range of variation of T _B for these selected channels for the year 2011, over the two stations Mumbai and Delhi is discussed. Finally the comparison between forward-model simulated T _B s and radiometer measured T _B s at Mahabaleshwar (73.66 ^°E and 17.93^°N) is done to evaluate the model. There is good agreement between model simulations and radiometer observations, which suggests that these forward model simulations can be used as background for inversion models for retrieving the temperature and humidity profiles.     

Correlations Developed for Estimation of Hydraulic Parameters of Rough Fractures Through the Simulation of JRC Flow Channels

The hydro-mechanical response of fractured rock masses is complex, due partly to the presence of fractures at different scales. Surface morphology has a significant influence on fluid flow behaviour of a fracture. Different empirical correlations and statistical models have been proposed to estimate the equivalent hydraulic aperture and determine the pressure drop along a fracture. However, the existing models suffer from not being adequately generalised to be applicable to a wide range of real fracture surfaces. To incorporate the effect of profile roughness in the hydro-mechanical behaviour of fractured rock masses, the joint roughness coefficient (JRC) is the most widely used empirical approach. However, the average JRC of two fracture walls in fluid flow analysis, as is a common practice, appears to be inappropriate. It will be shown how different combinations of pairs of JRCs could lead to a similar JRC value. Also, changing the position of the top and bottom walls of a fracture can significantly change the hydraulic response of the fracture while the average JRC is identical in both cases. In this paper, correlations are developed which are based on the simulation of JRCs using estimated fluid flow parameters of 2D fractures can be estimated. In order to widen the application range of the correlations, JRC flow channels were generated: these are 2D channels with their top and bottom walls being made from two of the JRC profiles. To estimate the JRC of linear profiles, a correlation developed between JRC and a newly developed Riemannian roughness parameter, D _R1, is proposed. Considering ten JRC profiles, a total of 100 JRC flow channels were generated. In order to only investigate the effect of surface roughness on fluid flow, the minimum closure between the top and bottom walls of JRC flow channels were considered to be constant. Three cases with minimum closures of 0.01, 0.05 and 0.10 cm were considered in this study. All JRC flow channels were subjected to fluid analysis using FLUENT software. Based on these results, correlations were developed between the geometrical and hydraulic properties of flow channels. Analysis of several real fractures demonstrated the applicability of these correlations.     

Thermal diffusivity of garnets at high temperature

Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca₃(Fe,Al)₂Si₃O₁₂ and (Mg,Fe,Ca)₃Al₂Si₃O₁₂] and varying amounts of OH^- were examined. Cation substitution or hydroxyl incorporation lowers D from end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (T _sat) of ~1,100 to 1,500 K. From ~290 K to T _sat, the measurements are best represented by 1/D=A+BT+CT ² where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only when T _sat is low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T ²×10⁻⁶+6.0168T ³×10⁻¹⁰(1/D in s/mm²; T in K). The mean free path (λ, computed from D and sound velocities) is slightly larger than the lattice parameter above T _sat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior with T and chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/D goes as T ⁿ where n is between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderate T, but is constant above T _sat. The predicted and observed temperature response of 1/D mimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.