Analytical moment–rotation curves for rigid foundations based on a Winkler model

Analytical equations for the moment–rotation response of a rigid foundation on a Winkler soil model are presented. An equation is derived for the uplift-yield condition and is combined with equations for uplift- and yield-only conditions to enable the definition of the entire static moment–rotation response. The results obtained from the developed model show that the inverse of the factor of safety, χ, has a significant effect on the moment–rotation curve. The value of χ=0.5 not only determines whether uplift or yield occurs first but also defines the condition of the maximum moment–rotation response of the footing. A Winkler model is developed based on the derived equations and is used to analyze the TRISEE experiments. The computed moment–rotation response agrees well with the experimental results when the subgrade modulus is estimated using the unload–reload stiffness from static plate load–deformation tests. A comparison with the recommended NEHRP guidelines based on the FEMA 273/274 documents shows that the choice of value of the effective shear modulus significantly affected the comparison.     

Beach water table fluctuations due to spring–neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection–diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring–neap tides (a bichromatic tidal system with the fundamental frequencies ω₁andω₂) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency ω₁−ω₂, i.e., the spring–neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations.     

ELF propagation parameters for uniform models of the Earth–ionosphere waveguide

Uniform models for the Earth–ionosphere cavity are considered with particular attention to the physical properties of the ionosphere for the extremely low frequency (ELF) range. Two consistent features have long been recognized for the range: the presence of two distinct altitude layers of maximum energy dissipation within the lower ionosphere, and a “knee”-like change in the vertical conductivity profile representing a transition in dominance from ion-dominated to electron-dominated conductivity. A simplified two-exponential version of the Greifinger and Greifinger (1978) technique widely used in ELF work identifies two slopes in the conductivity profile and, providing accurate results in the ELF communication band (45–75 Hz), simulates too flat a frequency dependence of the quality factor within the Schumann resonance frequency range (5–40 Hz). The problem is traced to the upward migration, with frequency increasing, of the lower dissipation layer through the “knee” region resulting in a pronounced decrease of the effective scale height for conductivity. To overcome this shortcoming of the two-exponential approximation and still retain valuable model analyticity, a more general approach (but still based on the Greifinger and Greifinger formalism) is presented in the form of a “knee” model whose predictions for the modal frequencies, the wave phase velocities and the quality factors reasonably represent observations in the Schumann resonance frequency range.     

Behavior of stratified sand–silt–gravel composites under seismic liquefaction conditions

Laboratory seismic liquefaction studies have generally dealt with homogeneous soil conditions only, although stratified soils exist for various soil deposits. The main objective of this research project was to compare the behavior of stratified and homogeneous sand–silt–gravel composites during seismic liquefaction conditions for various silt and gravel contents. An experimental program was undertaken in which a total of eighty stress-controlled undrained cyclic triaxial tests were performed. Two methods of sample preparation were used for each soil type. These methods included moist tamping (representing homogeneous soil conditions) and sedimentation (representing layered soil conditions). The silt contents ranged from 0 to 50%, and soils with 10 and 30% gravel contents were tested. The confining pressure in all test series was 100 kPa. The results indicate that the liquefaction resistances of layered and uniform soils are not significantly different, despite the fact that the soil fabric produced by the two methods of sample preparation is totally different. This finding justifies applying the laboratory tests results to the field conditions for the range of variable studied.     

U–Th dating of carbonate nodules from methane seeps off Joetsu, Eastern Margin of Japan Sea

We performed U–Th radioactive disequilibrium analyses of carbonate nodules and sediment samples recovered from methane seep sites off Joetsu, of the eastern margin of Japan Sea, to decipher the active period of the methane seep. The carbonates contain ²³⁰Th, part of which is located in detritus such as silicate and organics, at the time of precipitation. The initial ²³⁰Th renders accurate dating with U–Th radioactive disequilibrium method difficult. We assessed the feasibility of correction using radioactive disequilibrium data of ambient sediment to overcome this difficulty. A (²³⁰Th/²³²Th)–(²³⁴U/²³²Th) isochron drawn by three chips divided from a carbonate nodule (PC05-04-50) passed through data points of local sediments. We conclude that the problem of initial ²³⁰Th can be resolved by measurements of local sediments. Results show that carbonate nodules include local sediment as impurities. Furthermore, the results of trace element analyses such as Rb, Zr, Nb, REE, Pb, and Th also support the idea.In all, 18 carbonate samples were dated with correction of initial ²³⁰Th using the mean value of local sediment in this study. The U–Th correction ages show 12–35ka with an isochron age of 26 ± 3ka. Results indicate that during the time interval of U–Th ages, from 12ka to 35ka, environmental conditions must have been favorable for enhanced methane flux through sediment. The extensive methane flow period at 20ka accords with the lowest-stand sea level during the last glacial age. Results of this study also suggest that U–Th ages of carbonate are useful as a reliable chronometer with regard to methane seep activation. In order to acquire U–Th ages of carbonate at methane seep sites, however, it is important to evaluate the amount of initial ²³⁰Th accurately using the value of sediment.     

Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: Shaking in the direction perpendicular to ground flow

The 1995 Kobe earthquake seriously damaged numerous buildings with pile foundations adjacent to quay walls. The seismic behavior of a pile group is affected by movement of quay walls, pile foundations, and liquefied backfill soil. For such cases, a three-dimensional (3-D) soil–water coupled dynamic analysis is a promising tool to predict overall behavior. We report predictions of large shake table test results to validate 3-D soil–water coupled dynamic analyses, and we discuss liquefaction-induced earth pressure on a pile group during the shaking in the direction perpendicular to ground flow. Numerical analyses predicted the peak displacement of footing and peak bending moment of the group pile. The earth pressure on the pile in the crustal layer is most important for the evaluation of the peak bending moment along the piles. In addition, the larger curvatures in the bending moment distribution along the piles at the water side in the liquefied ground were measured and predicted.     

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.     

Numerical simulation of dynamic soil–structure interaction in shaking table testing

This paper provides an insight into the numerical simulation of soil–structure interaction (SSI) phenomena studied in a shaking table facility. The shaking table test is purposely designed to confirm the ability of the numerical substructure technique to simulate the SSI phenomenon. A model foundation–structure system with strong SSI potential is embedded in a dry bed of sand deposited within a purpose designed shaking-table soil container. The experimental system is subjected to a strong ground motion. The numerical simulation of the complete soil–foundation–structure system is conducted in the linear viscoelastic domain using the substructure approach. The matching of the experimental and numerical responses in both frequency and in time domain is satisfying. Many important aspects of SSI that are apparent in the experiment are captured by the numerical simulation. Furthermore, the numerical modelling is shown to be adequate for practical engineering design purposes.     

Validity limits for the van Genuchten–Mualem model and implications for parameter estimation and numerical simulation

The calculation of the relative hydraulic conductivity function based on water retention data is an attractive and widely used approach, since direct measurements of unsaturated conductivities are difficult. We show theoretically under which conditions an air-entry value for water retention data is definitely required when using the statistical approach of Mualem. Moreover we rigorously specify the conditions for which the classical van Genuchten–Mualem model leads to wrong predictions of relative hydraulic conductivity and, hence, an alternative formulation including an air-entry value should be used. Significant consequences are demonstrated for the inverse parameter estimation based on multistep outflow experiments. Furthermore it is shown that the use of a physically correct formulation of the water retention curve including an air-entry value and the derived hydraulic conductivity function influences not only the stability of numerical simulations but also their final results. This is especially grave as simulations with van Genuchten–Mualem parameters are frequently used to compare experiments and simulations and to draw conclusions on the correctness of Richards’ equation.     

Seismic analysis of lock–soil–fluid systems by hybrid BEM–FEM

A study of soil–structure–fluid interaction (SSFI) of a lock system subjected to harmonic seismic excitation is presented. The water contained lock is embedded in layered soils supported by a half-space bedrock. The ground excitation is prescribed at the soil–bedrock interface. The response is numerically obtained through a hybrid boundary element (BEM) finite element method (FEM) formulation. The semi-infinite soil and the fluid are modeled by the BEM and the lock is modeled by the FEM. The equilibrium equation for the lock system is obtained by enforcing compatibility and equilibrium conditions at the fluid–structure, soil–structure and soil–layer interfaces under conditions of plane strain. To the authors’ knowledge this is the first study of a lock system that considers the effects of dynamic soil–fluid–structure interaction through a BEM–FEM methodology. A numerical example and parametric studies are presented to examine the effects of the presence of water, lock stiffness, and lock embedment on the response.     

Treatment of Domestic Sewage in an Anaerobic–Aerobic Fixed‐bed Reactor with Recirculation of the Liquid Phase

This study reports the performance of a combined anaerobic–aerobic packed‐bed reactor that can be used to treat domestic sewage. Initially, a bench‐scale reactor was operated in three experimental phases. In the first phase, the anaerobic reactor was operated with an average organic matter removal efficiency of 77% for a hydraulic retention time (HRT) of 10 h. In the second phase, the reactor was operated with an anaerobic stage followed by an aerobic zone, resulting in a mean value of 91% efficiency. In the third and final phase, the anaerobic–aerobic reactor was operated with recirculation of the effluent of the reactor through the anaerobic zone. The system yielded mean total nitrogen removal percentages of 65 and 75% for recycle ratios (r) of 0.5 and 1.5, respectively, and the chemical oxygen demand (COD) removal efficiencies were higher than 90%. When the pilot‐scale reactor was operated with an HRT of 12 h and r values of 1.5 and 3.0, its performance was similar to that observed in the bench‐scale unit (92% COD removal for r = 3.0). However, the nitrogen removal was lower (55% N removal for r = 3.0) due to problems with the hydrodynamics in the aerobic zone. The anaerobic–aerobic fixed‐bed reactor with recirculation of the liquid phase allows for concomitant carbon and nitrogen removal without adding an exogenous source of electron donors and without requiring any additional alkalinity supplementation.     

Modelling the long‐term sediment trap efficiency of small ponds

A numerical model (sediment trap efficiency for small ponds—STEP) is developed to simulate sediment deposition in small ponds (i.e. <1 ha) and to calculate the sediment trap efficiency (STE). The algorithms are kept simple to allow the model to simulate larger time periods (i.e. several years). Eight runs with an experimental pond were executed to test the model. The STEP model produces reasonable predictions of STE as well as the shape and magnitude of the effluent sediment concentration graph. The model efficiency of STEP for the prediction of STE equals 0·38 and the root mean square error equals 4·7%. Similar models, such as DEPOSITS and CSTRS, were inefficient in predicting the experimental results. The STEP model was used to simulate the long‐term (33 years) STE of small retention ponds in central Belgium using 10‐min rainfall data. For a typical pond (1000 m²) with a catchment area of 25 ha, annual STE can vary from 58 to 100%, with a long‐term STE of only 68%. Copyright © 2001 John Wiley & Sons, Ltd.     

Feed forward neural network and interpolation function models to predict the soil and subsurface sediments distribution in Bam,Iran

An application of the artificial neural network (ANN) approach for predicting mean grain size using electric resistivity data from Bam city is presented. A feed forward back propagation network was developed employing 45 sets of input data. The input variables in the ANN model are the electrical resistivity, water table as a Boolean value and depth; the output is the mean grain size. To demonstrate the authenticity of this approach, the network predictions are compared with those from interpolation methods and the same data. This comparison shows that the ANN approach performs better results. The predicted and observed mean grain size values were compared and show high correlation coefficients. The ANN approach maps show a high degree of correlation with well data based grain size maps and can therefore be used conservatively to better understand the influence of input parameters on sedimentological predictions.     

Morphology and composition of spinel in Pu’u ’O’o lava (1996–1998), Kilauea volcano, Hawaii

The morphology and composition of spinel in rapidly quenched Pu’u ’O’o vent and lava tube samples are described. These samples contain glass, olivine phenocrysts (3–5 vol.%) and microphenocrysts of spinel (0.05 vol.%). The spinel surrounded by glass occurs as idiomorphic octahedra 5–50 μm in diameter and as chains of octahedra that are oriented with respect to each other. Spinel enclosed by olivine phenocrysts is sometimes rounded and does not generally form chains. The temperature before quenching was calculated from the MgO content of the glass and ranges from 1150°C to 1180°C. The oxygen fugacity before quenching was calculated by two independent methods and the log f_O2 ranged from −9.2 to −9.9 (delta QFM=−1). The spinel in the Pu’u ’O’o samples has a narrow range in composition with Cr/(Cr+Al)=0.61 to 0.73 and Fe²⁺/(Fe²⁺+Mg)=0.46 to 0.56. The lower the calculated temperature for the samples, the higher the average Fe²⁺/(Fe²⁺+Mg), Fe³⁺ and Ti in the spinel. Most zoned spinel crystals decrease in Cr/(Cr+Al) from core to rim and, in the chains, the Cr/(Cr+Al) is greater in the core of larger crystals than in the core of smaller crystals. The occurrence of chains and hopper crystals and the presence of Cr/(Cr+Al) zoning from core to rim of the spinel suggest diffusion-controlled growth of the crystals. Some of the spinel crystals may have grown rapidly under the turbulent conditions of the summit reservoir and in the flowing lava, and the crystals may have remained in suspension for a considerable period. The rapid growth may have caused very local (μm) gradients of Cr in the melt ahead of the spinel crystal faces. The crystals seem to have retained the Cr/(Cr+Al) ratio that developed during the original growth of the crystal, but the Fe²⁺/(Fe²⁺+Mg) ratio may have equilibrated fairly rapidly with the changing melt composition due to olivine crystallization. Six of the samples were collected on the same day at various locations along a 10-km lava tube and the calculated pre-collection temperatures of the samples show a 5°C drop with distance from the vent. The average Fe²⁺/(Fe²⁺+Mg) of the spinel in these samples shows a weak positive correlation with decreasing MgO in the glass of these samples. The range in Cr₂O₃ (0.041–0.045 wt.%) of the glass for these six samples is too small to distinguish a consistent change along the lava tube. The spinel in the Pu’u ’O’o samples shows a zoning trend in a Cr–Al–Fe³⁺ diagram almost directly away from the Cr apex. This compares with a zoning trend in rapidly quenched MORB samples away from Cr coupled with decreasing Fe³⁺. The trend away from Cr displayed by spinel in rapidly quenched samples is in marked contrast to the trend of increasing Fe³⁺ shown by spinel in slowly cooled lava.     

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m ² s ^–2 (±2.5 mm).     

A model of the wave and current boundary‐layer structure

A model of the wave and current boundary‐layer structure was developed using the k–ε turbulent closure model. The finite‐difference method was used to solve the governing equations. Vertical logarithmic grids and equal time steps were adopted. The following modelled simulations were obtained: (1) vertical profiles of wave velocity amplitude, eddy viscosity coefficient and turbulent kinetic energy with waves only; (2) vertical profiles of wave velocity amplitude, mean current velocity, eddy viscosity coefficient and turbulent kinetic energy with waves having a following current. To test the validity and the rationality of the present model, vertical profiles of modelled wave velocity amplitude and mean velocity were compared with corresponding experimental results available in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model

The parallel physically-based surface–subsurface model PARFLOW was used to investigate the spatial patterns and temporal dynamics of river–aquifer exchange in a heterogeneous alluvial river–aquifer system with deep water table. Aquifer heterogeneity at two scales was incorporated into the model. The architecture of the alluvial hydrofacies was represented based on conditioned geostatistical indicator simulations. Subscale variability of hydraulic conductivities (K) within hydrofacies bodies was created with a parallel Gaussian simulation. The effects of subscale heterogeneity were investigated in a Monte Carlo framework. Dynamics and patterns of river–aquifer exchange were simulated for a 30-day flow event. Simulation results show the rapid formation of saturated connections between the river channel and the deep water table at preferential flow zones that are characterized by high conductivity hydrofacies. Where the river intersects low conductivity hydrofacies shallow perched saturated zones immediately below the river form, but seepage to the deep water table remains unsaturated and seepage rates are low. Preferential flow zones, although only taking up around 50% of the river channel, account for more than 98% of total seepage. Groundwater recharge is most efficiently realized through these zones. Subscale variability of K_sat slightly increased seepage volumes, but did not change the general seepage patterns (preferential flow zones versus perched zones). Overall it is concluded that typical alluvial heterogeneity (hydrofacies architecture) is an important control of river–aquifer exchange in rivers overlying deep water tables. Simulated patterns and dynamics are in line with field observations and results from previous modeling studies using simpler models. Alluvial heterogeneity results in distinct patterns and dynamics of river–aquifer exchange with implications for groundwater recharge and the management of riparian zones (e.g. river channel-floodplain connectivity via saturated zones).     

The period of the free core nutation: towards a dynamical basis for an ‘extra-flattening’ of the core-mantle boundary

Indirect observations and theoretical predictions for the period of the free core nutation (FCN) differ by anywhere from 15 to 30 days, and various effects have been invoked in attempts to explain this difference. The favored explanation remains as much as 5% departure in the flattening of the core-mantle boundary (CMB) from that of its hydrostatic reference figure. This 5% ‘extra-flattening’ of the CMB is not seen at the Earth's surface, where the difference is only about 0.5%. In contrast to the a posteriori model adjustments used to determine this up to 5% value, and the kinematic results available from viscous flow modeling using the seismically determined lateral heterogeneity in density data, we consider this problem from the perspective of a forward-modeling dynamical study. More specifically, we investigate the related problem of flow-induced surface and CMB topography, arising from convection in the mantle. As such, we have completed a comparative and systematic study of relative surface and CMB topography resulting from numerical models of mantle convection. When effects resulting from boundary curvature are isolated, it appears that the magnitude of CMB topography produced is insufficient in producing a significant extra-flattening of the CMB. However, results concerning effects solely resulting from a depth-dependent mantle viscosity profile, indicate that this factor may indeed lead to enhanced topography at the CMB of the magnitude required to produce the extra-flattening there.     

Atmospheric nitrogen inputs into the North Sea: effect on productivity

The ANICE (Atmospheric Nitrogen Inputs into the Coastal Ecosystem) project addressed the atmospheric deposition of nitrogen to the North Sea, with emphasis on coastal effects. ANICE focused on quantifying the deposition of inorganic nitrogen compounds to the North Sea and the governing processes. An overview of the results from modelling and experimental efforts is presented. They serve to identify the role of the atmosphere as a source of biologically essential chemical species to the marine biota. Data from the Weybourne Atmospheric Observatory (UK) are used to evaluate the effect of short episodes with very high atmospheric nitrogen concentrations. One such episode resulted in an average deposition of 0.8 mmol N m⁻² day⁻¹, which has the potential to promote primary productivity of 5.3 mmol C m⁻² day⁻¹. This value is compared to long-term effects determined from model results. The total calculated atmospheric deposition to the North Sea in 1999 is 948 kg N km⁻¹, i.e. 0.19 mmol N m⁻² day⁻¹ which has the potential to promote primary productivity of 1.2 mmol C m⁻² day⁻¹. Detailed results for August 1999 show strong gradients across the North Sea due to adjacent areas where emissions of NO_x and NH₃ are among the highest in Europe. The average atmospheric deposition to the southern part of the North Sea in August 1999 could potentially promote primary production of 2.0 mmol C m⁻² day⁻¹, i.e. 5.5% of the total production at this time of the year in this area of the North Sea. For the entire study area the atmospheric contribution to the primary production per m² is about two-third of this value. Most of the deposition occurs during short periods with high atmospheric concentrations. This atmospheric nitrogen is almost entirely anthropogenic in origin and thus represents a human-induced perturbation of the ecosystem.