Quantitative precipitation forecasting over Narmada Catchment

Quantitative precipitation forecasting (QPF) has been attempted over the Narmada Catchment following a statistical approach. The catchment has been divided into five sub-regions for the development of QPF models with a maximum lead-time of 24 hours. For this purpose the data of daily rainfall from 56 raingauge stations, twice daily observations on different surface meteorological parameters from 28 meteorological observatories and upper air data from 11 aerological stations for the nine monsoon seasons of 1972–1980 have been utilized. The horizontal divergence, relative vorticity, vertical velocity and moisture divergence are computed using the kinematic method at different pressure levels and used as independent variables along with the rainfall and surface meteorological parameters. Multiple linear regression equations have been developed using the stepwise procedure separately with actual and square root and log-transformed rainfall using 8-year data (1972–1979). When these equations were verified with an independent data for the monsoon season of 1980, it was found that the transformed rainfall equations fared much better compared to the actual rainfall equations. The performance of the forecasts of QPF model compared to the climatological and persistence forecasts has been assessed by computing the verification scores using the forecasts for the monsoon season of 1980.     

Comparison between neuro-fuzzy and fractal models for permeability prediction

We have used different techniques for permeability prediction using porosity core data from one well at the Maracaibo Lake, Venezuela. One of these techniques is statistical and uses neuro-fuzzy concepts. Another has been developed by Pape et al. (Geophysics 64(5):1447–1460, 1999), based on fractal theory and the Kozeny–Carman equations. We have also calculated permeability values using the empirical model obtained in 1949 by Tixier and a simple linear regression between the logarithms of permeability and porosity. We have used 100% of the permeability–porosity data to obtain the predictor equations in each case. The best fit, in terms of the root mean-square error, was obtained with the statistical approach. The results obtained from the fractal model, the Tixier equation or the linear approach do not improve the neuro-fuzzy results. We have also randomly taken 25% of the porosity data to obtain the predictor equations. The increase of the input data density for the neuro-fuzzy approach improves the results, as is expected for a statistical analysis. On the contrary, for the physical model based on the fractal theory, the decrease in the data density could allow reaching the ideal theoretical Kozeny–Carman model, on which are based the fractal equations, and hence, the permeability prediction using these expressions is improved.     

Numerical simulation of secondary consolidation of soil: Finite element application

A rheological model has been developed for simulating the secondary consolidation of soils. Numerical procedures have been incorporated into a coupled consolidation program using results from a representative oedometer test. A solution of a two-dimensional problem has also been performed. The technique is numerically stable and has provided satisfactory predictions for the consolidation settlements and the dissipation of pore water pressure within soils.     

Microstructural deformation mechanisms of unsaturated granular soils

A discrete model for unsaturated granular soils has been developed. Three discrete entities have been defined: particles, water menisci and pores. Local interaction forces and water transfer mechanisms have been integrated into a model through the appropriate equilibrium and balance equations. The results of several numerical tests using this model have been described and discussed. Simulations include wetting and drying under load tests, the application of suction cycles and the effect of a deviatoric stress ratio on wetting‐induced collapse. The model reacts just as true granular soil samples behave in laboratory tests. The model provides a new insight into the internal mechanisms leading to large‐scale features of behaviour such as wetting‐induced collapse or the increase in soil strength provided by suction. The paper also stresses that matric suction changes acting on a granular structure are capable of explaining most of the macroscopic features of stress–strain behaviour. Copyright © 2002 John Wiley & Sons, Ltd.     

Data Assimilation (4D-VAR) for Shallow-Water Flow: The Case of the Chicoutimi River

This is a web presentation of the work presented at the 10th Annual Conference of the CFD Society of Canada, “CFD 2002”, at the University of Windsor on June 9-11, 2002. This discussion paper presents the four-dimensional variational data assimilation (4D-VAR) technique as a tool to forecast floods. This discussion will be limited to hydrological forecast. We assume that the weather, here a large rainstorm, had already been forecasted by the meteorological services. In the 4D-VAR technique, we need to minimize, in the sense of Lagrange, a cost function which measures the difference between the forecast and the observations. The physical equations acts as a set of constraints. Here, the model is the shallow-water equations modified to include sediment transport. The minimum was found by using the steepest descent algorithm. This is made possible because the gradient of the cost function can be calculated analytically by using the adjoint equations of the model. To illustrate the 4D-VAR technique, the bypass of a simple theoretical dam as well as the more complex overflowing of the Chicoutimi River at the Chute-Garneau dam (during the 1996 flood) are investigated.     

Analysis of beams on tensionless reinforced granular fill‐soil system

In this paper, a beam subjected to end concentrated loads has been modeled and analyzed to estimate its flexural response. The beam has been assumed to rest on reinforced earth beds with reinforcing elements having some finite bending stiffness. The reinforcing elements have been idealized as beams with smooth surface characteristics. The foundation system has been assumed to react only in compression (tensionless foundation), i.e. the separation between the upper beam and the ground surface has been taken into consideration. Winkler springs of different stiffnesses have been used to idealize the upper dense and lower poor soils. As the analysis considers the separation between the upper beam and the soil, the weight of the upper beam has been taken into account. The governing differential equations have been derived and presented in a non‐dimensional form. These equations have been solved using finite difference method with the help of appropriate boundary and continuity conditions. The response of the foundation system has been compared with the case when the beam is in perfect contact with the ground surface. The parametric study shows that the response of the model is greatly affected by the length ratio of beams, ratio of stiffness of upper and lower soil layers, ratio of flexural rigidity of upper and lower beams and weight of the upper foundation beam. Copyright © 2008 John Wiley & Sons, Ltd.     

Developing constitutive models from EPR‐based self‐learning finite element analysis

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.     

应用二阶完全非线性Boussinesq方程模拟破碎波浪

建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Boussinesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽中(强)非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证,通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎,利用物理模型实验数据,分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究,数值结果同实验数据吻合良好,验证了模型的有效性。     

A comparative study of slip velocity models for the prediction of performance of floatex density separator

The separation features of the floatex density separator (FDS) are investigated through experimental and computational approaches. It has been shown that the performance of the FDS can be predicted reasonably well using a slip velocity model and steady-state mass balance equations. The approach for the formulation of the slip velocity model makes a difference in the prediction of FDS performance. The computed data from four different slip velocity models have been compared and contrasted with the experimental observations. It has been shown that a slip velocity model based on the modified Richardson and Zaki equation, in which the dissipative pressure gradient is considered to be the primary driving force for separation, predicts the performance more accurately than the other three. A deslimed feed is recommended for better performance of the FDS.     

Response of an anisotropic liquid-saturated porous medium due to two dimensional sources

Eigenvalue approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field equations in an anisotropic liquid-saturated porous medium, in the transformed domain. The results of isotropic liquid-saturated porous medium can be derived as a special case. A numerical inversion technique has been applied to get the solutions in the physical domain. To illustrate the utility of the approach, an application of infinite space with impulsive force at the origin has been considered. The results in the form of displacement and stress components have been obtained and discussed graphically for a particular model.     

Mathematical analysis of gravity anomalies due to an infinite sheet-like structure

Gravity anomalies caused by a thin infinite sheet are interpreted quantitatively based on an integral transform approach which is elegant and simple. The proposed technique depends on the modified Hilbert transform which is called “Sundararajan transform.” The amplitudes of the well-known Hilbert transform and Sundararajan transform are exactly the same but with a phase difference of 270° between them. The interpretation of gravity anomalies due to a thin infinite sheet has been implemented using the Sundararajan transform rather than the well-known Hilbert transform, yielding a straightforward solution. Parameters such as the depth to the top of the sheet (z), the inclination angle (θ), and the amplitude coefficient (K) have been analytically determined using simple mathematical equations. The origin of the causative target can be determined by the intersection point between Hilbert and Sundararajan transforms as well as the intersection point of the amplitudes of the analytic signal of the two transforms. The proposed technique has been first applied to synthetic data where the procedures are clearly illustrated. The effect of noise on the interpretation procedures of the proposed technique has been investigated, showing in general satisfactory results especially depth estimation. However, the most sensitive parameter to noise is the dipping angle, which can be misleading in high level of noise, whereas the least sensitive parameter is the depth. Strictly speaking, the noise does not significantly distort the depth estimation obtained with this proposed technique. Finally, the interpretation of the gravity anomaly across the Mobrun ore body, Noranda, Quebec, Canada, has been carried out using the proposed technique where the parameters are estimated and compared to the results that have been published in literatures using different techniques.     

滑坡发生时间预报分析

系统论述了滑坡监测资料的整理方法：滤波和等时化。讨论了滑坡运动响应的主要组成成分。重点阐述了滑坡发生时间预报的理论基础，此基础不同于一般物理方程建立的思路，而是直接来源于观察和经验总结，并抽象为一定的数学模型。单次滑坡发生的整个过程包括孕育、如速、减速、停止等4个阶段，滑坡发生时间则指加速向减速转换的特征时间点，此点是滑坡爆发的峰值点，也是需要预报的特征时间。能够反映滑坡如此运动过程的典型数学函数是Pearl曲线，本质上此S型曲线与系统有阻尼的自由振动微分方程是一致的，也与生物群体演化的虫口方程一致，它们都共同反映了物质运动的一般规律，因此可以用来预测滑坡运动过程。直接运用一般力学报分方程描述滑坡运动过程的困难在于缺乏对滑体系统力学参数的精确把握，直接运用Logistic虫口微分方程则存在模型参数识别的困难，作者还发现某些误用灰色系统理论对Verbulst非线性方程，参数进行辩识。文末，为展示方法而不强调结果，以拥有10a监测资料的某滑坡为例，分析预报了滑坡活动过程，并进行了预测结果的数学检验。     

The performance of the empirical models on industrial hydrocyclone design

Many empirical models have been used widely for designing hydrocyclones in industry. These empirical models consist of a set of design equations. Most of the design equations are based on the correlations obtained experimentally, using dimensionless similarity numbers. These equations have their limitations due to the specific systems used for model development. Therefore, in many cases, they cannot be used with confidence to predict the design of an individual separator, or the overall plant configuration that is required to meet different user requirements. A modified version of the existing design equations presented by previous researchers was developed. The design equations, describing four fundamental parameters: pressure drop, flow recovery to underflow, corrected cut size and classification function, were modified by fitting with set of experimental data to obtain the system-specific constant parameters. These modified design equations were then called, the fine-tuned design equations. Four sets of fine-tuned design equations describing all the fundamental parameters were constructed and used to predict the separation performance of many hydrocyclone operational systems at the Dow Chemical Company, Texas, USA. The performance of these equations is evaluated, and the limitations of their use are discussed, thus providing useful insights into hydrocyclone design.     

Linear coupled analysis of desiccation shrinkage in a double‐layer partially saturated medium: semi‐explicit solutions

Solutions are presented for the problem of isothermal dessiccation shrinkage in a double‐layer porous partially saturated medium. The rheological model taken into account is linear poroelastic. Hence the analysis is mainly focused on hydromechanical coupling effects and contrasts of mechanical and hydraulic properties between two materials: a low thickness skin comprised between the outer boundary and the reference porous material. Three one‐dimensional ideal structures are taken into account: a wall of finite thickness (cartesian geometry), a thick cylinder and a thick sphere. The solution of the time‐dependent problem is arrived at by applying Laplace transforms to the field variables. Exact solutions are obtained in Laplace transform space using Mathematica^© to solve the field equations whilst taking into account the continuity equations at the interface and the boundary conditions. The Talbot's modified algorithm has been performed to invert the Laplace transform solutions. A bibliographical and numerical study shows that this method is remarkably precise, stable and close to the analytical inversion. Results are presented using poroelastic data representative of a concrete material and involve a strong coupling effect between hydraulical and mechanical behaviours. A first approach elastic modelling of degradation process have been presented using a thin outer layer. Apart from emphasising the semi‐explicit solution utility due to accurate speed calculation, this paper deals with more complex problems than those which can be solved using purely analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

Advanced programming methods and data structures for computational modelling using edge‐based finite volume methods

The generation of a numerical model must consider the separate issues of the governing equations, the numerical representation of those equations, the data structure that describes the model, the choice of programming language and finally the implementation and code management issues. These issues are considered as a whole in this paper and as a consequence, 10 golden rules for numerical modelling are proposed. By way of application, a saturated–unsaturated flow problem is modelled using the Richards equation and an innovative edge‐based finite volume method. The implementation uses a novel data structure. This is shown to have over 91% code re‐use and hence code written in this way is highly flexible and applicable to many different problems. By way of example, a compacted core earth filled dam problem has been solved. Finally, we conclude that this advanced programming method can significantly reduce code development time. Copyright © 2004 John Wiley & Sons, Ltd.     

A numerical method for laterally loaded piles

A numerical model for a laterally loaded pile in an elastic continuum is presented. The governing differential equations for vertical piles in a homogeneous and a layered soil are obtained by using variational calculus. Two parameters, k and t, are used in this approach to represent the elastic foundation, and an iterative technique is adopted to obtain a consistent energy solution. Both free and fixed headed piles have been considered. Two kinds of boundary conditions of practical interest at the pile tip, floating tip and clamped tip, are also considered. The proposed method has been validated by comparison of the results with those obtained by other available methods. Typical solutions are presented and recommendations are given for their use in design problems.     

Discretization of flow contain nitrate in porous media by finite volume technique

One of the most important pollutants of groudwaters is nitrate. Different human activities including the application of chemical fertilizers in agriculture, causes the emission of nitrate into groudwaters. In this paper, the dynamic effect of soil moisture on carbon and nitrogen cycles has been analyzed by presenting a connection between soil moisture sample and nonlinear differential equations. At present, wide researches are carried out on modeling soil moisture control in solution flows contain nitrate. In order to do so, separation of energy conservation law equations is carried out by a particular method. The mathematical model governing the nitrate containing current in non-isotropic environment has been presented in the form of combined equations. Equation for distribution in multiple environments and Darcy rule has been considered in this model. Then, using finite volume method, separation of flows contain nitrate in porous media is carried out. The current flux is obtained from central difference approximations or upwind approximation. Mashad plain has been considered for case study at this research. Carrying out calibration operation, the measured results have been contrasted with numerical results of finite volume method. After testing the model, it is possible to foresee the way of nitrate changes in other nodes of calculation network. Using these forecasts, the quality of drinking water for several next years is determined. Carrying out numerical modeling by finite volume method, it is found out that the quality of drinking water of Mashad plain would be suitable for the next ten years.