Two-dimensional Finite-difference Analysis Research Articles

Numerical evaluation of liquefaction-induced lateral spreading with an advanced plasticity model for liquefiable sand

Two different approaches are employed to predict the magnitude of lateral spreading induced by liquefaction using a two-dimensional finite difference analysis with an advanced plasticity constitutive model for the liquefiable sand. One approach uses the advanced plasticity model to directly predict lateral spreading. The other approach is a hybrid approach that first uses the advanced plasticity model to calculate the time to triggering of liquefaction and then uses a Newmark-type displacement analysis to predict the magnitude of lateral spreading. To evaluate the accuracy of these methods for predicting lateral spreading displacements, both approaches were applied to five well-documented case histories of lateral spreading. Comparison of the calculated and reported displacements shows that the hybrid approach that calculates lateral spreading with a Newmark analysis that employs the free field ground surface motions starting from the time at which liquefaction is triggered was, on the average, the most accurate approach. The two-dimensional finite difference analysis gave generally conservative results, yielding larger displacement than the reported value. While the uncertainty associated with both methods is very high, based upon the five case histories analyzed herein it appears that the two-dimensional finite difference analysis can be used with good confidence to predict a conservative value for the magnitude of liquefaction-induced lateral spreading if the parameters that govern lateral spreading are well known.

Approximation of transient redox boundary conditions: its application to numerical analysis of iron plume migration near landfills

An efficient scheme is presented that attempts to implement the moving boundary conditions in a two-dimensional finite difference analysis model that simulates reductive dissolution and subsequent precipitation of iron species in surficial aquifer exposed to time-dependent redox boundary conditions near landfills. A mathematical and numerical model for simulating the vertical flux of oxygen through the variably saturated vadose zone and resulting hydrochemical response of groundwater system is developed and subsequently used to study dissolved iron plume migration phenomena from substrates beneath landfills. The proposed modeling scheme of the boundary condition is then applied to the groundwater system near an in-service landfill site located in state of Florida to produce an approximate solution to highly nonlinear boundary-value problems in hydrochemical systems subjected to various site geometries and soil conditions. As a result of the 12 years of consecutive runs with annually updated boundary conditions, a steady-state distribution of iron concentration is obtained and well compared with historical in situ data of groundwater iron concentrations depending on the desired degrees of accuracy.

Liquefaction and Deformation Analyses Using a Total Stress Approach

Estimating deformations due to seismically induced liquefaction is often accomplished with a series of simplified uncoupled analyses. An alternative approach is presented in this paper that builds upon this common practice while making significant improvements to the modeling quality. A two-dimensional finite-difference analysis is performed in the time domain using a simple plasticity-based constitutive model. The triggering of liquefaction is assessed in each element by continuously weighting the cyclic shear stress history. Liquefaction is initially predicted in the most susceptible elements and then progressively spreads as the earthquake continues. The properties of liquefied elements are adjusted at the instant of liquefaction to reflect the anticipated loss of strength and stiffness. Dynamic equilibrium is always maintained so that computed deformations are rationally affected by the structural response, progressing liquefaction, and gravity forces. The method is demonstrated through application to the Upper San Fernando Dam and its response to the San Fernando earthquake of 1971. The objective of this approach is to achieve a practical balance between a rigorous numerical and theoretical analysis and currently accepted practice.

Heat transfer in symmetric U-shaped microreactors for thin film calorimetry

We describe the results of two-dimensional finite difference analysis of the thermal profile, in both transient and steady state, of a symmetric U-shape designed high-sensitive nanocalorimeter. The thin film calorimeter, with a heat capacity of 100 nJ K−1 at room temperature, consists of a 180 nm thick freestanding silicon-rich nitride membrane on which thin film heaters and sensors are deposited. Simulated temperature profiles are in good agreement with in situ experimental data obtained at the heater and sensor locations. The first-order solid-to-liquid transition of indium films, from a few Å to hundreds of nm thick, was used as an experimental reference of the thermal profiles obtained from the 2D modeling. Temperature differences inside the sample region induced by the symmetric U-shape design of the Pt heaters limit the use of the nanocalorimeter to two different heating rate regimes. At low heating rates, β < 10 K s−1, especially with a thermal layer, the temperature profile is reasonably flat so that small samples can be characterized in power compensation mode. At heating rates faster than 4 × 104 K s−1 the nanocalorimeter works in adiabatic mode and measures transitions occurring in the sample directly loaded underneath the heater.

Practical applications of a nonlinear approach to analysis of earthquake-induced liquefaction and deformation of earth structures

Seismic stability, liquefaction, and deformation of earth structures are critical issues in geotechnical earthquake engineering practice. At present, the equivalent linear approach is considered the ‘state of practice’ in common use. More recently, dynamic analyses incorporating nonlinear, effective-stress-based soil models have been used more frequently in engineering applications. This paper describes a bounding surface hypoplasticity model for sand [Wang ZL. Bounding surface hypoplasticity model for granular soils and its applications. PhD Dissertation for the University of California at Davis, U.M.I. Dissertation Information Service, Order No. 9110679; 1990; Wang ZL, Dafalias YF, Shen CK. Bounding surface hypoplasticity model for sand. ASCE, J Eng Mech 1990;116(5):983–1001; Wang ZL, Makdisi FI. Implementing a bounding surface hypoplasticity model for sand into the FLAC program. In: Proceedings of the international symposium on numerical modeling in geomechanics. Minnesota, USA; 1999. p. 483–90] incorporated into a two-dimensional finite difference analysis program [Itasca Consulting Group, Inc. FLAC (Fast Lagrangian Analysis of Continua), Version 4. Minneapolis, MN; 2000] to perform nonlinear, effective-stress analyses of soil structures. The soil properties needed to support such analyses are generally similar to those currently used for equivalent linear and approximate effective-stress analyses. The advantages of using a nonlinear approach are illustrated by comparison with results from the equivalent linear approach for a rockfill dam. The earthquake performance of a waterfront slope and an earth dam were evaluated to demonstrate the model's ability to simulate pore-pressure generation and liquefaction in cohesionless soils.

Meander-type wavelength demultiplexer with weighted coupling

An experimental and theoretical investigation of meander-type wavelength demultiplexers with weighted coupling is reported. Numerical simulations have been performed combining a two-dimensional finite difference analysis and a suitably developed coupling mode method. Devices have been realized based on rib waveguides in GaInAsP/InP with filter center wavelengths around 1.3 μm. With weighted coupling the sinc2(λ)-type transmission characteristics of standard meander couplers change and the sidelobes of the latter devices are efficiently suppressed. We further show the determination of optimum weighted coupling for wavelength filters meeting given requirements with respect to channel separation, maximum allowable crosstalk, and total device length.

Subthreshold current in undoped AlGaAs/GaAs MODFET structures

The subthreshold current in undoped AlGaAs/GaAs MODFET structures can have a negative gradient with respect to the gate voltage, whereas in doped structures it has normally either a positive gradient or is constant. A two-dimensional finite-difference analysis is used to clarify this difference. It is shown that the behavior of the threshold current in an undoped structure is due to the effect of gate bias on the leakage between the drain and the gate. This leakage occurs near the top surface of the AlGaAs layer, and is strongly affected by the lateral straggle of the n/sup +/ implants and by the surface states in AlGaAs. The charge-control model, which is conventionally applied to the doped case, does not describe the behavior of the subthreshold current in the undoped case because it neglects leakage currents.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The importance of contact injection in undoped AlGaAs/GaAs heterostructures

A two-dimensional finite-difference analysis is used to simulate the current flow and charge distribution in undoped AlGaAs/GaAs MODFET structures called heterostructure insulated-gate field-effect transistors (HIGFETs). How an electron channel can be induced at the AlGaAs/GaAs interface when there is no doped supply layer is studied. The origins of the charge in this channel are studied by comparing its behavior in equilibrium with that when a current flows. By considering the different geometries of a Schottky gate and implanted source and drain contacts, the interrelationship between gate control and electron injection from the doped contact regions is shown and a graphic view of the origins of the interfacial charge in a HIGFET is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two-dimensional finite difference analysis of shape instabilities in plates

A two-dimensional finite difference analysis is applied to surface diffusion-controlled instabilities of plates. Plates can evolve into “cylinders,” or if the plates have longitudinal internal boundaries, they may split into two segments. The evolution process of plates containing internal boundaries into equilibrium shapes depends on both the initial plate aspect ratio (plate width to thickness) and the ratio of the internal boundary energy to the plate-matrix interface energy. When the internal boundary energy is relatively low or the initial plate aspect ratio is relatively small, the transverse equilibrium cross-sectional area shape is composed of two circular segments, with an appropriate dihedral angle dictated by the ratio of the interface energy terms. As either the internal boundary energy or the initial aspect ratio increases, plate splitting, rather than cylinderization, becomes the dominant instability mode. The results of this work are compared to a recent theory of Courtney and Malzahn Kampe (CMK) on shape instability diagrams.[1] The complicated interactive effects between cylinderization and boundary splitting were not considered in the analytical CMK approach; thus, when they are minimal, the results of this finite difference calculation are in reasonable accord with the CMK results, as far as predicting instability times are concerned. However, when the interaction is significant, cylinderization and/or splitting times are markedly changed. The present accurate calculations allow refinement of the CMK plate instability diagrams.

Numerical solutions for surface electric field distributions in avalanching p-i-n power diodes

The results of a two-dimensional finite-difference analysis of the electric field distribution near the surface of reverse-biased p-i-n power diodes are presented. The boundary conditions encountered in fully passivated and encapsulated devices have been modelled as closely as possible, thereby enabling the effects of device polarity, electrode overhang and dielectric coating to be investigated. Our calculations show that the peak field near the surface is less than the peak bulk field for all positive bevel angles, whereas with negative bevel angles it is significantly less than the peak bulk field only for shallow bevel angles of 10° or less. Metal overhang and shallow doping profiles have been shown to reduce the field near the surface. It is concluded that a 50° positive bevel angle with metal overhang and shallow doping profile represents the optimum design. Experimental devices made to this design using two deep diffusions gave higher breakdown voltages with harder and more stable characteristics than devices with steeper doping profile, or with steeper bevel angle or with metal underhang.

Melting of a Vertical Ice Wall by Free Convection into Fresh Water

A steady-state two-dimensional finite difference analysis is presented for the heat and momentum transfer resulting when the leading portion of a semi-infinite vertical ice sheet at 0°C melts into fresh water by natural convection. Fluid properties are assumed to be constant and are evaluated beyond the edges of the boundary layers with the exception of fluid density which varies with the local temperature. Results of the analysis are presented for free stream temperatures from 0 to 24.0°C. They include streamlines, velocity profiles, melt velocities, and average Nusselt numbers for the leading 0.7632 m portion of a semi-infinite ice sheet. Overall, the results show three distinct flow regimes: steady upward flow for T∞ ≤ 4.50°C, steady downward flow for T∞ ≥ 6.0°C and steady dual or bi-directional flow for 5.70 ≤ T∞ ≤ 6.0°C. In the range 4.50°C &lt; T∞ &lt; 5.70°C the solution failed to converge and since the method is capable of accounting for local recirculations, it is suggested that this flow regime may be transitory in nature.