A methodology for validating numerical ground water models

Ground water validation is one of the most challenging issues facing modelers and hydrogeologists. Increased complexity in ground water models has created a gap between model predictions and the ability to validate or build confidence in predictions. Specific procedures and tests that can be easily adapted and applied to determine the validity of site-specific ground water models do not exist. This is true for both deterministic and stochastic models, with stochastic models posing the more difficult validation problem. The objective of this paper is to propose a general validation approach that addresses important issues recognized in previous validation studies, conferences, and symposia. The proposed method links the processes for building, calibrating, evaluating, and validating models in an iterative loop. The approach focuses on using collected validation data to reduce uncertainty in the model and narrow the range of possible outcomes. This method is designed for stochastic numerical models utilizing Monte Carlo simulation approaches, but it can be easily adapted for deterministic models. The proposed methodology relies on the premise that absolute validity is not theoretically possible, nor is it a regulatory requirement. Rather, the proposed methodology highlights the importance of testing various aspects of the model and using diverse statistical tools for rigorous checking and confidence building in the model and its predictions. It is this confidence that will encourage regulators and the public to accept decisions based on the model predictions. This validation approach will be applied to a model, described in this paper, dealing with an underground nuclear test site in rural Nevada.     

A discussion on models of thermals

For a thermal starting from rest, the scales of motion consistent with the initial conditions are given. An alternative time scale based on the motion of the thermal is derived. The anticipated similarity solutions for thermals are summarised and possible qualitative differences between solutions are given. Within this consistent framework previously published laboratory and numerical models of thermals are discussed. Reasons why numerical models have not rigorously demonstrated the existence of a self-similarity solution are considered. Comparisons of all available results show that a single similarity solution valid for all thermals does not exist.     

Analytic element modeling of embedded multiaquifer domains

An analytic element approach is presented for the modeling of multiaquifer domains embedded in a single-aquifer model. The inside of each domain may consist of an arbitrary number of aquifers separated by leaky layers. The analytic element solution is obtained through a combination of existing single-aquifer and multiaquifer analytic elements and allows for the analytic computation of head and leakage at any point in the aquifer. Along the boundary of an embedded multiaquifer domain, the normal flux is continuous everywhere; continuity of head across the boundary is met exactly at collocations points and approximately, but very accurately, in between. The analytic element solution compares well with an existing exact solution. A hypothetical example with a river intersecting two embedded domains illustrates the practical application of the proposed approach.     

A re-evaluation of equivalent linear models for simple yielding systems

Commonly used equivalent linear models for simple yielding systems subjected to harmonic and earthquake excitations are re-evaluated. It is shown that with respect to damping, these models contain the same basic information. Reported differences in the literature are simply due to scaling: since the product of the equivalent stiffness and equivalent damping is a constant, smaller damping values would be obtained by the use of the small amplitude equivalent stiffnesses. It is argued that for harmonic excitation, the secant stiffness is an appropriate representation of equivalent stiffness, leading to large equivalent damping values that increase with ductility. For earthquake excitation the Iwan proposal is shown to be the preferred model leading to larger damping values than previously reported. A comparison of the models for harmonic and earthquake excitations shows that, in general, and at comparable ductilities, damping values due to harmonic excitation are about five times those due to earthquake excitation, and the period changes due to harmonic excitation are about twice those due to earthquake excitation.     

A note on benchmarking of numerical models for density dependent flow in porous media

Verification of numerical models for density dependent flow in porous media (DDFPM) by the means of appropriate benchmark problems is a very important step in developing and using these models. Recently, Infinite Horizontal Box (IHB) problem was suggested as a possible benchmark problem for verification of DDFPM codes. IHB is based on Horton–Rogers–Lapwood (HRL) problem. Suitability of this problem for the benchmarking purpose has been investigated in this paper. It is shown that the wavelength of instabilities fails to be a proper criterion to be considered for this problem. However, the threshold of instability formation has been found to be appropriate for benchmarking purpose.     

Evaluation of numerical earthquake forecasting models

Evaluation of numerical earthquake forecasting models needs to consider two issues of equal importance: the application scenario of the simulation, and the complexity of the model. Criterion of the evaluation-based model selection faces some interesting problems in need of discussion.     

The development of new analytic elements for transient flow and multiaquifer flow

We deal in this paper with an ongoing development of the analytic element method. We present in outline new analytic line elements that are suitable to model general flow fields, i.e., flow fields that possess a continuously varying areal inflow or outflow. These elements are constructed specifically to model the leakage through leaky layers that separate aquifers in leaky systems and to model transient effects. The leakage or release from storage underneath linear features is modeled precisely by the new elements; the singularity in leakage is matched exactly by the approximate solution. Applications are given for a problem involving leakage and for a case of transient flow. We note that the analytic elements can be used also to reproduce the effect of continuously varying aquifer properties, e.g., the hydraulic conductivity or the elevation of the base of the aquifer. In the latter case, the elements would reproduce the rotation of the flow field caused by the variation in properties, rather than the divergence as for the case of leakage.     

A comparison of two numerical models for the prediction of vibrations from underground railway traffic

Two prediction models for calculating vibration from underground railways are developed: the pipe-in-pipe model and the coupled periodic finite element–boundary element (FE–BE) model.The pipe-in-pipe model is a semi-analytical three-dimensional model that accounts for the dynamic interaction between the track, the tunnel and the soil. The continuum theory of elasticity in cylindrical coordinates is used to model two concentric pipes: an inner pipe to represent the tunnel wall and an outer pipe to represent the surrounding soil. The tunnel and soil are coupled accounting for equilibrium of stresses and compatibility of displacements at the tunnel–soil interface. This method assumes that the tunnel is invariant in the longitudinal direction and the problem is formulated in the frequency–wavenumber domain using a Fourier transformation. A track, formulated as an Euler–Bernoulli beam, is then coupled to this model. Results are transformed to the space domain using the inverse Fourier transform.The coupled periodic FE–BE model is based on a subdomain formulation, where a boundary element method is used for the soil and a finite element method for the tunnel. The Craig–Bampton substructuring technique is used to efficiently incorporate the track in the tunnel. The periodicity of the tunnel is exploited using the Floquet transformation to formulate the track–tunnel–soil interaction problem in the frequency–wavenumber domain and to compute the wave field radiated into the soil.An invariant concrete tunnel, embedded in a homogeneous full space is analyzed using both approaches. The pipe-in-pipe model offers an exact solution to this problem, which is used to validate the coupled periodic FE–BE model. The free field response due to a harmonic load in the tunnel is predicted and results obtained with both models are compared. The advantages and limitations of both models are highlighted. The coupled periodic FE–BE model has a greater potential as it can account for the complex periodic geometry of the tunnel and the layering in a soil medium. The effect of coupling a floating slab to the tunnel–soil system is also studied with both models by calculating the insertion gain.     

A numerical study on response factors for steel wall–frame systems

A numerical investigation was undertaken to evaluate the response of dual structural systems that consisting of steel plate shear walls and moment‐resisting frames. The primary objective of the study was to investigate the influence of elastic base shear distribution between the wall and the frame on the global system response. A total of 10 walls and 30 wall–frame systems, ranging from 3 to 15 stories, were selected for numerical assessment. These systems represent cases in which the elastic base shear resisted by the frame has a share of 10, 25, or 50% of the total base shear resisted by the dual system. The numerical study consisted of 1600 time history analyses employing three‐dimensional finite elements. All 40 structures were separately analyzed for elastic and inelastic response by subjecting them to the selected suite of earthquake records. Interstory drifts, top story drift, base shears resisted by the wall, and the frame were collected during each analysis. Based on the analysis results, important response quantities, such as the strength reduction, the overstrength, and the displacement amplification factors, are evaluated herein. Results are presented in terms of displacement measures, such as the interstory drift ratio and the top story drift ratio. Analysis results revealed that the increase in the strength reduction factor with the amount of load share is insignificant. Furthermore, there is an inverse relationship between the ductility reduction and the overtsrength. Copyright © 2010 John Wiley & Sons, Ltd.     

恢复力模型中求突变折点的一种新方法

在结构弹塑性动力计算中,恢复力曲线是一个重要问题。简化的折线型恢复力模型虽然应用简单,计算工作量小,但是有个突出缺点,即存在很多刚度突变点,即折点,这给计算带来麻烦。本文针对这一问题,提出了一种折点处理新方法。利用结构动力学方程和线性加速度法等推导出求解折线型恢复力模型中加载点和卸载点两类折点的计算公式。该公式基于结构动力学方程推导而来,逻辑严密,结果可信,精度有保证。此外,计算突变折点出现时刻,仅涉及结构动力特性等几个已知量,计算简单,不需迭代,计算工作量小。而且加载点与卸载点两类折点的计算公式形式简单又统一,方便编程。     

Improving stability of regional numerical ocean models

An operational limited-area ocean modelling system was developed to supply forecasts of ocean state out to 3 days. This system is designed to allow non-specialist users to locate the model domain anywhere within the Australasian region with minimum user input. The model is required to produce a stable simulation every time it is invoked. This paper outlines the methodology used to ensure the model remains stable over the wide range of circumstances it might encounter. Central to the model configuration is an alternative approach to implementing open boundary conditions in a one-way nesting environment. Approximately 170 simulations were performed on limited areas in the Australasian region to assess the model stability; of these, 130 ran successfully with a static model parameterisation allowing a statistical estimate of the model’s approach toward instability to be determined. Based on this, when the model was deemed to be approaching instability a strategy of adaptive intervention in the form of constraint on velocity and elevation was invoked to maintain stability.     

Effective ambient vibration testing for validating numerical models of concrete dams

Ambient vibration tests were conducted on a 56 metre high concrete gravity dam to measure its modal properties for validating a finite element model of the dam–reservoir–foundation system. Excitation was provided by wind, by reservoir water cascading down the spillweir, and by the force of water released through outlet-pipes. Vibrations of the dam were measured using accelerometers, and 3-hour data records were acquired from each location. Data were processed by testing for stationarity and rejecting non-stationary portions before Fourier analysis. Power spectra with low variance were generated from which natural frequencies of the dam were identified clearly and modal damping factors estimated. Modal analysis of the frequency response spectra yielded mode shapes for the six lowest lateral modes of vibration of the dam. The finite element model for the dam was analysed using EACD-3D, and the computed mode shapes and natural frequencies compared well with the measured results. The study demonstrates that ambient vibration testing can offer a viable alternative to forced vibration testing when only the modal properties of a dam are required. Copyright © 1999 John Wiley & Sons, Ltd.     

Equivalent fixed-base models for soil-structure interaction systems

To simplify the consideration of the soil-structure interaction (SSI) effects, a single degree-of-freedom (SDOF) replacement oscillator has been successfully utilized to represent an SSI system with SDOF structural model. In the present paper, this approximation is first extended to an equivalent fixed-base model with modified system parameters. Based on this generalization, a methodology is then proposed to determine the equivalent fixed-base models of a general multi degree-of-freedom SSI system using simple system identification techniques in the frequency domain. Various fixed-base models are formulated and their accuracy is compared for a five-story shear building resting on soft soil. It is shown that the actual SSI system can be accurately represented with an appropriate fixed-base model.     

Comparative analyses of current three-dimensional numerical solar wind models

We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories:(I) theoretical, empirical and numerically based models and(II) self-consistent multi-dimensional numerical magnetohydrodynamic(MHD) models. The models of Category I are used to separately describe the solar wind solution in two plasma flows regions: transonic/trans-Alfvénic and supersonic/super-Alfvénic, respectively. Models of Category II construct a complete, single, numerical solar wind solution through subsonic/sub-Alfvénic region into supersonic/super-Alfvénic region. The Wang-Sheeley-Arge(WSA)/ENLIL in CISM is the most successful space weather model that belongs to Category I, and the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme(BATS-R-US) code in SWMF(Space Weather Modeling Framework) and the solar-interplanetary conservative element solution element MHD(SIP-CESE MHD) model in SWIM(Space Weather Integrated Model) are the most commonly-used models that belong to Category II. We review the structures of their frameworks, the main results for solar wind background studies that are essential for solar transient event studies, and discuss the common features and differences between these two categories of solar wind models. Finally, we conclude that the transition of these two categories of models to operational use depends on the availability of computational resources at reasonable cost and point out that the models' prediction capabilities may be improved by employing finer computational grids, incorporating more observational data and by adding more physical constraints to the models.     

An exact numerical time integration of scalar equations for undamped structural systems

An exact numerical time integration of scalar equations for undamped structural systems is presented. Typical numerical examples are included to illustrate the use of the proposed procedure.     

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba,Canada

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m²/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.     

Flood-plain mapping: a critical discussion of deterministic and probabilistic approaches

Abstract

Different methodologies for flood-plain mapping are analysed and discussed by comparing deterministic and probabilistic approaches using hydrodynamic numerical solutions. In order to facilitate the critical discussion, state-of-art techniques in the field of flood inundation modelling are applied to a specific test site (River Dee, UK). Specifically, different flood-plain maps are derived for this test site. A first map is built by applying an advanced deterministic approach: use of a fully two-dimensional finite element model (TELEMAC-2D), calibrated against a historical flood extent, to derive a 1-in-100 year flood inundation map. A second map is derived by using a probabilistic approach: use of a simple raster-based inundation model (LISFLOOD-FP) to derive an uncertain flood extent map predicting the 1-in-100 year event conditioned on the extent of the 2006 flood. The flood-plain maps are then compared and the advantages and disadvantages of the two different approaches are critically discussed.

Citation Di Baldassarre, G., Schumann, G., Bates, P. D., Freer, J. E. & Beven, K. J. (2010) Flood-plain mapping: a critical discussion of deterministic and probabilistic approaches. Hydrol. Sci. J. 55(3), 364–376.