Vízügyi Közlemények, 1960 (42. évfolyam)

4. füzet - VI. Képek a Föld különböző részeinek vízépítési munkáiról

(41) occurring in a homogeneous space, the network of stream filaments and potential lines is determined therein. By the appropriate choice of the transformation function, all boundary conditions — i. e. in addition to the foundation profile constituting an impermeable boundary surface, also the lower limit of the pervious stratum — can be included in an exact manner. The only approximation is, in agreement with investigations of similar nature, the assumption of a homogeneous aquifer, by the introduction of which, all physical properties of the soil can be described by a single parameter viz. the permeability coefficient. This approximation is common to the other methods investigated (Figs. 1 and 2). The second computation method which can be supported theoretically rests on the assumption of a pervious substratum of infinite depth. In this method, the physical process of movement is as exactly followed as in the former, the only difference being the neglect of one of the boundary conditions, viz. the lower impermeable enclosure of the pervious aquifer, during the derivation of the relationships. However, for determining the flow the inclusion of the lower boundary is also required eventually. The approximation adopted for this purpose introduces a deviation with respect to the value of Pavtovsky, which latter may be regarded as theoretically correct (Fig. 4). Similarly to the first method, boundary conditions are allowed for in an exact manner in the third, yet the resulting relationship is less involved — at least as long as the foundation profile is not composed of several elements — since the physical process of movement is approximated by the introduction of simpler assumptions. For this reason this method is referred to as hydraulic approximation (Figs. 5, 6, 1). The experimental determination of flow constitutes the fourth method. From among the various experimental techniques, the one relying on electrical analogy is the simplest and therefore most frequently applied. As a result of this experiment the network of stream filaments and potential lines is determined graphically, and discharge is computed from this flow pattern. Naturally, this method is liable to all errors, which are common to such, where discharge is computed from a graphical flow pattern obtained in different ways (Fig. (•3). The empirical formula derived by the author earlier on the basis of results of field measurements is mentioned finally. Owing to its origin, no general validity and applicability to every conceivable foundation profile and set of characteristic dimensions can be claimed for this formula, its field being restricted to the narrow range, to which the underlying measurements belong. The aim followed in the preparation of the numerical examples was to characterize the reliability of the methods investigated. The examples were extended to include the full range of independent parameters, such as with of base, length and location of cutoff, and thickness of the pervious layer, which may be involved in practical problems. Results obtained by these examples have been summarized in tabulated form, and compared to the flow data determined by the transformation of Pavlovsky and regarded as theoretically correct (see the Tables). On the basis of these examples and of their results tabulated in the abovementioned manner it could be established, that none of the five methods can be regarded as a fast one of general validity and suitable for practical calculations. Owing to its limited applicability, the empirical relationship cannot be used generally in practice although the range of validity can be extended by determining the constants involved in the formula in a generalized form on the basis of further field measurements. Empirical constants determined by the author, when substituted properly into the computation, yield flow values which agree fairly well with the theoretical value in the entire range investigated for any combination of foundation slab and single cutoff wall. The error is in the majority of cases positive and does not exceed 10 per cent. Greater errors occur for extreme ratios of base dimensions to depth of pervious aquifer only. Therefore, relying on experiments and computations carried out so far, the following relationship is suggested for computing the seepage flow passing through