Stavros Yannopoulos

Water Distribution System Reliability Based on Minimum Cut – Set Approach and the Hydraulic Availability

Reliability analysis of water distribution systems is a complex task, as it requires both definition and calculation of several reliability measures. In this paper, a methodology for evaluating water distribution system reliability is developed and demonstrated on a simple water distribution network based on the minimum cut-set approach. In general, the definition of the minimum cut-set can arise either from the mechanical reliability or from the concept of hydraulic reliability. In the case of mechanical reliability, a new method based on graph theory is developed, in order to determine the minimum cut-set. This method is based on the counting of paths between nodes. Furthermore, the general concept of reliability is proposed, to include apart from the mechanical reliability, more generally, the pressure availability at nodes as a main hydraulic property. Based on the pressure availability, the sense of hydraulic availability can be expressed as a fuzzy set, while the combination of the water unavailability of the nodes can be achieved by using fuzzy averaging aggregator. Finally, an overall reliability index is proposed based on both the hydraulic and the mechanical reliability. An illustrative example is developed to indicate the methodology.

Sensitivity analysis of closed-form analytical hydraulic conductivity models

The three parameters α, n and m in the Van Genuchten analytical soil-moisture characteristic curve are considered to be independent in this paper. The three-parameter fitting problem that arises is reduced to a one-dimensional minimization search, through a suitable transformation. The resulting unidimensional algorithm is amenable to analysis. Its qualitative characteristics are derived and the existence of a minimum is established. The values of the parameters thus obtained are introduced as starting estimates in a three-parameter minimization process of the Newton-Raphson type. As a continuation of this, a sensitivity analysis is formulated of the unsaturated hydraulic conductivity with respect to the residual (θr) and the saturated (θs) water content. The entire analysis is applied to the retention data of five selected soils of different hydraulic properties. In all cases considered, the very good fit offered by the unidimensional algorithm is demonstrated. Also, the sensitivity of the hydraulic conductivity shows a drastic increase in the range of lower water contents, and the sensitivity with respect to θs maintains nonnegligible values over the whole water content range.

Simplified determination and sensitivity analysis of soil-moisture retention curves and hydraulic conductivity

Abstract A simple algorithm is presented that estimates the parameters contained in the Van Genuchten analytical soil-moisture characteristic curves. No graphical estimations are involved and convergence is rapid. The values obtained from the simple algorithm are introduced as starting values in a Newton-Raphson minimization procedure which yields more accurate evaluations of the parameters. The very good approximation offered by the simple algorithm is responsible for the small number of subsequent Newton-Raphson iterations. Based on the final results of the minimization scheme an analytical sensitivity analysis is carried out with respect to changes induced in the basic parameter “residual water content”. Soils with a wide range of hydraulic properties were subjected to the above analysis. It is demonstrated that for lower water contents the sensitivity of the hydraulic conductivity becomes by 2–5 orders of magnitude larger than it is for higher ones.

A comparative study of closed-form hydraulic conductivity prediction models

Abstract The Mualem and the Burdine hydraulic conductivity prediction models are considered in combination with the van Genuchten analytical retention curve, as well as the Brooks and Corey prediction model. An equivalence is presented between the retention curves of these models. A comparative study follows between hydraulic conductivities that are based on equivalent retention curves. A unified presentation of prediction models provides a framework for the whole analysis. The treatment of the equivalence problem consists in a minimization procedure characterized by uncoupling of the parameters and analytical evaluation of the objective function. Exact analytical equivalence relations are given for significant parts of the parameter ranges, and, for the remaining parts, analytical approximations are proposed. The comparisons between hydraulic conductivities are carried out via an inequality analysis. It is shown that the hydraulic conductivity of the Burdine model is less than that of the other models for extended ranges of equivalent parameters.

Transient Flow Through Soil Into Open Ditches With Constant Recharge

An analytical solution of the linearized Boussinesq equation is presented, which is used to predict the temporal and spatial variations of the groundwater table in a free unconfined aquifer based upon impermeable layer. The variations are caused by the sudden rise of the water table in an adjacent ditch, and the simultaneous constant rainfall or irrigation, uniformly distributed over the soil surface. The results of the presented solution are in very close agreement with those obtained from the numerical solution of the linerarized Boussinesq equation and at time t-»oo, approach those of the nonlinear problem.