One-layer Case Research Articles

Bearing Capacity Evaluation of Shallow Foundations on Stabilized Layered Soil using ABAQUS

Abstract In this paper, the finite element method (FEM) is applied to calculate the bearing capacity of two footings having the aspect ratio L/B (where L and B are the length and width of the footing, respectively) equal to 1, 2 resting on one-layer and two-layer soil. Soil profile contains two soil types including sand and clay. The soil strip is 500mm × 500mm × 350mm; however, only a quarter of the model (250mm × 250mm × 350mm) is examined in the study. Two primary situations are investigated in this study. In the first situation, the one-layer system is supposed to be sandy soil with footing overlays on medium-dense sand. The soft clay/stabilized clayey layer is supposed to be on top of the sandy soil in the second condition, with the footing resting on top of the soft clay/stabilized clay. The influence of layer thickness, aspect ratio, and material property on the bearing capacity value and footing failure mechanism is studied for eight different combinations of layered soil. The bearing capacity for a one-layer case is also estimated, and it agrees well with Vesic (1973), Hansen (1970), and Terzaghi's (1943) equations. The bearing capacity of footings is observed to decline when the height of unstabilized clayey soil increases, and it increases when clayey soil is stabilized with molasses, waste foundry sand, and lime alone and in combination with each other.

Numerical Simulations of a Dispersive Model Approximating Free-Surface Euler Equations

In some configurations, dispersion effects must be taken into account to improve the simulation of complex fluid flows. A family of free-surface dispersive models has been derived in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018). The hierarchy of models is based on a Galerkin approach and parameterised by the number of discrete layers along the vertical axis. In this paper we propose some numerical schemes designed for these models in a 1D open channel. The cornerstone of this family of models is the Serre – Green-Naghdi model which has been extensively studied in the literature from both theoretical and numerical points of view. More precisely, the goal is to propose a numerical method for the LDNH_2 model that is based on a projection method extended from the one-layer case to any number of layers. To do so, the one-layer case is addressed by means of a projection-correction method applied to a non-standard differential operator. A special attention is paid to boundary conditions. This case is extended to several layers thanks to an original relabelling of the unknowns. In the numerical tests we show the convergence of the method and its accuracy compared to the LDNH_0 model.

Analysis of heat transfer characteristics in textiles and factors affecting thermal properties by modeling

The heat transmission through a fabric during the measurement of thermal resistance was simulated by a novel heterogeneous model that was constructed according to the structure of ThermolabII Tester KES-F7. In this model, the heat transmissions along the longitudinal and transverse directions of yarn were treated independently. The material constants of fabrics, such as mass density, specific heat, thermal conductivity and thickness, were used as parameters for simulation in this fabric model. The validity of this model was then confirmed by the high consistency between the heat flux obtained from experiment and simulation, with the average difference ratio lower than 5%. The simulation results suggested that the guard area could effectively reduce the horizontal heat leakage from the test plate when the experimental fabric was thin. Only less than 8% of heat leaked in the one-layer case, while the leakage was significantly aggravated when more layers of fabric were stacked, resulting in the considerably lower thermal insulation achieved in both experiment and simulation compared with that in real fabrics. The temperature distribution in the model also implied that the longitudinal and transverse thermal conductivity of yarn exerted great effect on the heat leakage during the measurement. Moreover, for multilayers consisting of different fabrics, the laying sequence could obviously influence the heat leakage and, consequently, change the obtained thermal resistance.

Semi-implicit staggered mesh scheme for the multi-layer shallow water system

We present a semi-implicit scheme for a two-dimensional multilayer shallow water system with density stratification, formulated on general staggered meshes. The main result of the present note concerns the control of the mechanical energy at the discrete level, principally based on advective fluxes implying a diffusion term expressed in terms of the gradient pressure. The scheme is also designed to capture the dynamics of low-Froude-number regimes and offers interesting positivity and well-balancing results. A numerical test is proposed to highlight the scheme's efficiency in the one-layer case.

Dislocation Nucleation in Nickel-Graphene Nanocomposites Under Mode I Loading

Graphene has superior mechanical properties, and previous studies have shown that it can be used as a fiber laminate in metal-graphene nanocomposites. Our research outlines the advantages and disadvantages of different Ni-graphene nanocomposite laminates. Using molecular dynamics, Ni-graphene nanocomposites are studied under mode I loading normal to the graphene laminate plane. The stress intensity factor (\(K_{\text{I}}\)) is predicted for the nanocomposite at varying distances between a simulated crack and the graphene sheet(s) in the Ni-matrix. We find that \(K_{\text{I}}\) of the Ni-matrix is reduced with the addition of graphene sheet. However, for a single graphene sheet in the Ni-matrix, \(K_{\text{I}}\) increases with increased spacing between the crack and the graphene sheet. This is due to the change in the crack-generated stress field in the region between the Ni-matrix containing the crack and the graphene sheet, which leads to the lower stress values at which dislocation nucleation occurs compared to single-crystal Ni. For multiple layers of graphene sheets in the Ni-matrix, we find that failure occurs exclusively by delamination at a lower stress than the one-layer case. This research concludes that fabricated Ni-graphene nanocomposites can be tuned for optimal fracture strength by the structural arrangement of graphene sheets within the Ni-matrix.

Barotropic, baroclinic, and inertial instabilities of the easterly Gaussian jet on the equatorial β-plane in rotating shallow water model

A detailed linear stability analysis of an easterly barotropic Gaussian jet centered at the equator is performed in the long-wave sector in the framework of one- and two-layer shallow-water models on the equatorial β-plane. It is shown that the dominant instability of the jet is due to phase-locking and resonance between Yanai waves, although the standard barotropic and baroclinic instabilities due to the resonance between Rossby waves are also present. In the one-layer case, this dominant instability has non-zero growth rate at zero wavenumber for high enough Rossby and low enough Burger numbers, thus reproducing the classical symmetric inertial instability. Yet its asymmetric counterpart has the highest growth rate. In the two-layer case, the dominant instability may be barotropic or baroclinic, the latter being stronger, with the maximum of the growth rate shifting towards smaller downstream wavenumbers as Rossby number increases at fixed Burger number, and given thickness and density ratios. At large enough Rossby numbers this instability has a non-zero growth rate limit at zero wavenumber, giving the baroclinic symmetric inertial instability. Again, the maximal growth rate is achieved at small but non-zero wavenumbers, corresponding to the asymmetric inertial instability. At high enough Rossby number and low enough Burger number not only the baroclinic, but also the barotropic symmetric instability appears, as well as higher meridional modes of the baroclinic symmetric instability. Still, all of them are dominated by their asymmetric counterparts. Direct numerical simulations of the saturation of the leading instabilities are performed, showing that the barotropic species of the instability saturates by forming a double vortex street subject to nonlinear oscillations, while the baroclinic, the most vigorous one, saturates by producing strong vertical shears and related dissipation and mixing.

Shallow water asymptotic models for the propagation of internal waves

We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidirectional models of Camassa-Holm type, are shown to descend from a broad Green-Naghdi model, that we introduce and justify in the sense of consistency. Contrarily to earlier works, our Green-Naghdi model allows a non-flat topography, and horizontal dimension $d=2$. Its derivation follows directly from classical results concerning the one-layer case, and we believe such strategy may be used to construct interesting models in different regimes than the shallow-water/shallow-water studied in the present work.

Possible High-Temperature Superconductivity in Multilayer Graphane: Can the Cuprates be Beaten?

We analyze a possible superconductivity in the hole-doped system of layered hydrogenized graphene by taking into account thermal fluctuations of the order parameter. In particular, we demonstrate that in the one-layer case the values of the high mean-field (MF) critical temperature $T_{\mathrm{\mathrm{c}}}^{\mathrm{MF}}\sim 80$ –90 K, predicted recently by Savini et al (Phys. Rev. Lett. 105:037002, 2010), do not alter significantly due to the fluctuations, and the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the vortex superconductivity is almost the same as the MF temperature at doping 0.01–0.1. We show that in the case of multilayer system, when the coupling between the layers stabilizes the superconducting phase in the form of fluxon superconductivity, the critical temperature T c can increase dramatically to the values ∼150 K, higher than the corresponding values in cuprates under ambient pressure.

Microwave Properties of Ferromagnetic Nanowires and Applications to Tunable Devices

Microwave devices as circulators or tunable filters demand nowadays small size and broad bandwidth. Ferromagnetic nanowired membranes are ideal candidates for this purpose. This paper focuses on the dielectric properties of such substrates, as influenced by the ferromagnetic nature of nanowires and their filling factor. Two particular cases are considered: a membrane filled up to its top with nanowires, forming a one-layer substrate, and a membrane filled up to a certain percentage of its height with nanowires, forming a two-layer substrate. The models proposed in this paper for each case take the inductive and gyromagnetic effects in the wires into account. They predict for the one-layer case a magnetodielectric behavior which is tunable by applying an external magnetic field. The effect is no longer visible for the two-layer topology corresponding to microwave circuit applications.

Conditioned Simulations of Random Velocity Fields

In petroleum exploration and production, it is essential to have good estimations of the uncertainties on the reserves. Uncertainties on the velocity model used during the data processing are of major importance in this estimation. The generation of several velocity fields gives access to a quantified estimation of the uncertainties due to the velocity model inversion. The use of statistical methods helps in generating several important, equiprobable velocity fields, matching all the available velocity information. This paper presents an efficient simulation algorithm to generate instantaneous velocity fields, constrained by the distribution of values measured at the wells, and calibrated by the stacking velocities, taken as root-mean-square velocities. The simulations also match the covariance model given for the instantaneous velocity fields. The method is developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is shown, using data provided by ENI–Agip Division, and the efficiency of the proposed simulation method is discussed.

Statistical Characterization of a Random Velocity Field Using Stacking Velocity Profiles

In petroleum exploration and production, it is important to have good estimations of the uncertainties on the reserves. Uncertainties in the velocity model used during the data processing are of major importance in this estimation. The use of geo-statistical tools can help in dealing with these uncertainties. Up to now, a strong limitation has been the inability to properly merge velocity functions measured in the wells with seismic velocity data. This was due to the different “supports” among the two, i.e. the well velocity may be regarded as a direct measurement of the instantaneous velocity field, while the seismic velocities correspond to an “average along the travelled paths” of this field. The problem is that, apart from the well positions, the instantaneous velocity field is out of reach. Luckily, for many practical applications, it is enough to know just its covariance model. However, no algorithmic method is available in the literature to yield the covariance model, and geologists are forced to use arbitrary distributions. The present paper proposes an original method to obtain a good estimate of this covariance model, using widely available information, mainly seismic stacking velocities. This method was first developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is performed, which highlights the robustness of the resulting estimation.

The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems

This paper deals with the numerical difficulties related to the appearance of the so-called wet/dry fronts that may occur during the simulation of free-surface waves in shallow fluids and internal waves in stratified fluids composed by two shallow layers of immiscible liquids. In the one-layer case, the fluid is supposed to be governed by the shallow water equations. In the case of two layers, the system to solve is formulated under the form of two-coupled system of shallow water equations. In both cases, the discretization of the equations are performed by means of the Q-schemes of Roe upwinding the source term developed in [1,2] for the one-layer system, and [3] for the two-layer system. These schemes satisfy the so-called C-property: they solve exactly steady solutions corresponding to water at rest. In order to handle properly with wet/dry fronts, a numerical scheme has to verify also an extended C-property: it has to solve exactly steady solutions corresponding to water at rest including wet/dry transitions. In [4-6] , some numerical schemes satisfying this property has been obtained. In this paper, we propose an improvement of these schemes and its extension to two-layer systems. We present some numerical results: for one-layer fluids, we compare the numerical results with some measurements corresponding to a physical model. For two-layer systems, we use the numerical scheme to perform a lock-exchange experiment, and we verify its validity by comparing the steady state reached with an approximate solution obtained by Armi and Farmer in [7,8] by using a simplified model.

The accuracy of surface elevations in forward global barotropic and baroclinic tide models

Abstract This paper examines the accuracy of surface elevations in a forward global numerical model of 10 tidal constituents. Both one-layer and two-layer simulations are performed. As far as the authors are aware, the two-layer simulations and the simulations in a companion paper (Deep-Sea Research II, 51 (2004) 3043) represent the first published global numerical solutions for baroclinic tides. Self-consistent forward solutions for the global tide are achieved with a convergent iteration procedure for the self-attraction and loading term. Energies are too large, and elevation accuracies are poor, unless substantial abyssal drag is present. Reasonably accurate tidal elevations can be obtained with a spatially uniform bulk drag c d or horizontal viscosity K H , but only if these are inordinately large. More plausible schemes concentrate drag over rough topography. The topographic drag scheme used here is based on an exact analytical solution for arbitrary small-amplitude terrain, and supplemented by dimensional analysis to account for drag due to flow-splitting and low-level turbulence as well as that due to breaking of radiating waves. The scheme is augmented by a multiplicative factor tuned to minimize elevation discrepancies with respect to the TOPEX/POSEIDON (T/P)-constrained GOT99.2 model. The multiplicative factor may account for undersampled small spatial scales in bathymetric datasets. An optimally tuned multi-constituent one-layer simulation has an RMS elevation discrepancy of 9.54 cm with respect to GOT99.2, in waters deeper than 1000 m and over latitudes covered by T/P (66 ∘ N to 66 ∘ S). The surface elevation discrepancy decreases to 8.90 cm (92 percent of the height variance captured) in the optimally tuned two-layer solution. The improvement in accuracy is not due to the direct surface elevation signature of internal tides, which is of small amplitude, but to a shift in the barotropic tide induced by baroclinicity. Elevations are also more accurate in the two-layer model when pelagic tide gauges are used as the benchmark, and when the T/P-constrained TPXO6.2 model is used as a benchmark in deep waters south of 66 ∘ S. For Antarctic diurnal tides, the improvement in forward model elevation accuracy with baroclinicity is substantial. The optimal multiplicative factor in the two-layer case is nearly the same as in the one-layer case, against initial expectations that the explicit resolution of low-mode conversion would allow less parameterized drag. In the optimally tuned two-layer M 2 solution, local values of the ratio of temporally averaged squared upper layer speed to squared lower layer speed often exceed 10.

Two-layer hydraulic falls over an obstacle

Motions in a forced channel flow of two contiguous homogeneous fluids of different constant densities and different thicknesses are considered. The total depth is finite and the upper surface is constrained to be planar (rigid lid approximation). The forcing is due to a bottom obstruction. The existence of a critical thickness ratio, obtained when the square of the thickness ratio is equal to the density ratio, leads to major differences with the one-layer case. The present study concentrates on this critical case. Moreover it is restricted to hydraulic falls, which are steady flows over an obstacle providing a transition between a subcritical and a supercritical flow. A weakly nonlinear analysis is performed. At leading order the problem reduces to a forced modified Korteweg–de Vries equation which can be integrated exactly. The weakly nonlinear results are validated by comparison with a numerical integration of the full governing equations. The numerical method is based on boundary integral equation techniques. The differences with the one-layer case are the existence of a second family of subcritical hydraulic falls when the thickness ratio is below critical, and the existence of supercritical hydraulic falls described by four parameters instead of three for all thickness ratios.

Gravity currents in rotating channels. Part 1. Steady-state theory

A theory is developed for the speed and structure of steady-state non-dissipative gravity currents in rotating channels. The theory is an extension of that of Benjamin (1968) for non-rotating gravity currents, and in a similar way makes use of the steady-state and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes the existence of a hydrostatic ‘control point’ in the current some distance away from the nose. The model allows for fully non-hydrostatic and ageostrophic motion in a control volume V ahead of the control point, with the solution being determined by the requirements, consistent with the perfect-fluid approximation, of energy and momentum conservation in V, as expressed by Bernoulli's theorem and a generalized flow-force balance. The governing parameter in the problem, which expresses the strength of the background rotation, is the ratio W = B/R, where B is the channel width and R = (g′H)1/2/f is the internal Rossby radius of deformation based on the total depth of the ambient fluid H. Analytic solutions are determined for the particular case of zero front-relative flow within the gravity current. For each value of W there is a unique non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the wall-depth h0. In the two-layer case, the non-dimensional propagation speed c = cf(g′H)−1/2 increases smoothly from the non-rotating value of 0.5 as W increases, asymptoting to unity for W → ∞. The gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter has decreasing width. The depth of the current at the right-hand wall, h0, increases, reaching the full depth at W = 1.90, after which point the interface outcrops on both the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the one-layer case, the wall-depth based propagation speed Froude number c0 = cf(g′h0)−1/2 = 21/2, as in the non-rotating one-layer case. The current separates from the left-hand wall of the channel at W0 ≡ B/R0 = 2−1/2, and thereafter has width 2−1/2R0, where R0 = (g′h0)1/2/f is the wall-depth based deformation radius.

The effusivity model for multi-layer walls

The effusivity model for describing the time response of walls to changes in heat flux is extended to two-layer walls using an integral method. Based on a simple integral method, shown to obtain results close to the ones of the effusivity method for the one-layer case, a simple correction of the expressions for temperature variation due to a step change in the heat flux is obtained. The results are shown to be in good agreement with the exact solution. It is shown that, depending on the ratio of the effusivities of the two layers, significant deviations from the results obtained using the effusivity of the outer layer can be expected.

A nonlinear numerical model for the interaction of surface and internal waves with very large floating or submerged flexible platforms

The interaction of both surface and internal water waves with floatinglsubmerged platforms was studied by considering the nonlinear properties of the fluid motion and the flexibility of the oscillating plates. First a set of nonlinear governing equations for the interaction between a multi-layer fluid system and floating/submerged elastic thin plates was obtained. In each fluid layer, the Lagrangian was integrated vertically by taking the nonlinear boundary conditions on the interfaces into account. Then the variational principle was applied to yield a set of time-dependent, horizontally twodimensional, fully nonlinear equations. Secondly, using this model, several numerical computations were carried out for the surfacelinternal long waves and the oscillations of horizontally very large platforms. The resonated pressure beneath the plate floating on the sea surface in the two-layer system was compared with that in the one-layer case. The surface/internal waves generated by the trembling of the floatinglsubmerged elastic plates were also simulated.

On the Number of Conserved Quantities for the Two‐Layer Shallow‐Water Equations

The shallow‐water equations for two‐layer inviscid flow with a free surface overlying a rigid horizontal bottom subject to gravitational forcing only are examined to determine the possible forms of conservation laws that the equations permit. In the case of a single layer with flow in only one horizontal direction, it is known that there are an infinite number of associated equations in conservation form, where the conserved quantity is a multinomial in the layer variables. The method used to determine this result is generalized to show that in the two‐layer case, the result does not generalize, and it is discovered that only a finite number of conservation equations exist when the density difference between the layers is nonzero. The subsequent conservation equations are given explicitly, and a systematic method for deriving conservation laws from an arbitrary first‐order system is described. For the case when the flow is in both horizontal dimensions, the method of analysis is straightforward in the one‐layer case, and the finite number of conservation equations are derived. The two‐layer case is similar, and the finite number of generalized conserved quantities are stated, although the question of whether or not there are only a finite number is posed as an open question.

Tracking Atmospheric Instabilities with the Kalman Filter. Part II: Two-Layer Results

Abstract Sequential data assimilation schemes approaching true optimality for sizable atmospheric models are becoming a reality. The behavior of the Kalman filter (KF) under difficult conditions needs therefore to be understood. In this two-part paper the authors implemented a KF for a two-dimensional shallow-water model with one or two layers. The model is linearized about a basic flow that depends on latitude; this permits the one-layer (1-L) case to be barotropically unstable. Constant vertical shear in the two-layer (2-L) case induces baroclinic instability. The stable and unstable 1-L cases were studied in Part I. In the unstable case, even a very small number of observations can keep the forecast and analysis errors from the exponential growth induced by the flow's instability. In Part II, the authors now consider the 2-L, baroclinically stable and unstable cases. Simple experiments show that both cases are, quite similar to their barotropic counterparts. Once again, the KF is shown to keep the esti...

Low frequency surface acoustic waves propagating in a system of n anisotropic layers on an anisotropic substrate

Propagation of surface acoustic waves in a system of n anisotropic layers on a semi-infinite anisotropic substrate is considered. In the limit when the wavelength is large compared to the total thickness of the layers, the dispersion relation for surface waves is derived. The dispersion relation agrees with the one-layer case and the case of isotropic media studied elsewhere. Possible applications of the results obtained are discussed.