Shape factors of cylindrical piezometers

Abstract

This Paper describes a liquid electric analogue model and a finite difference model used to establish reliable values for the shape factors of cylindrical piezometers with length/diameter ratios of up to 15. For piezometers with length/diameter ratios greater than 4, it was found that the shape factor is given with negligible error by the relationship: F = 7d + 1·651. An examination of the effect on the shape factor of piezometer proximity to the watertable showed this to be negligible for practical purposes, except where the piezometer is within a few piezometer lengths of the water-table. Shape factors were also established for cylindrical piezometers embedded in cylindrical soil specimens subjected to all five possible boundary conditions. The measured shape factors were higher or lower than the infinite values depending upon the boundary conditions and the proximity of the boundaries to the piezometer. These data give some guidance to theperformance of pore pressure probes used in laboratory specimens, and they are useful in the analysis of steady state flow conditions and for the assessment of response studies of piezometer systems. Cet Article décrit un modèle analogique électrique fluide et un modèle à différence finie servant à établir des valeurs fiables pour les coefficients de forme de piézométres cyhndriques dont les rapports longueur/diamètre peuvent atteindre 15. Pour les piézomètres dont le rapport longueur/daimétre est supérieur à 4, on a trouvé que le coefficient de forme était donné, avec une erreur négligeable, par la relation F = 7d + 1·65. L'influence sur le coefficient de forme de la proximité de la nappc phréatique est pratiquement négligeable sauf lorsque le piézomètre était à quelques longueurs de piézomètre de la nappe phréatique. Les coefficients de forme ont également été établis pour des piézomètres cylindriques enfoncés dans des échantillons de sols cylindriques soumis aux cinq conditions aux limites possibles. Les coefficients de forme mesurés étaient supérieurs ou inférieurs aux valeurs infinies dependant des conditions aux hmites, et de la proximité des limites par rapport au piézomètre. Ces données permettent de se faire une certaine idée de la performance de sondes de pression interstitielle utilisées dans des échantillons de laboratoire et sont utiles pour l'analyse des conditions d'icoulement stationnaire ainsi que pour I'évaluation des réponses des piézomètres.

A constant-head pumping test method using direct-push equipment for in situ hydraulic conductivity measurements T. KOBAYASHI, N. ONOUE, S. OBA, N. YASUFUKU and K. OMINE (2012). Géotechnique 62, No. 3, 253–262, http:dx.doi.org/10.1680/geot.9.P.150

“…17, along with the regression equations (5) and (7) and the solutions by Brand & Premchitt (1980), which showed good agreement with equation (1) of Kobayashi et al (2012). It is evident from the figure that, when L/D , 1, equation (5) is in better agreement with the finite-element method solutions than equation (6).…”

“…999 for equation (5) (6); in other words, Fig. 18 shows the ratio of the intake factors of equation (5) and those proposed by other researchers (Hvorslev, 1951;Wilkinson, 1968;Brand & Premchitt, 1980;Chapuis, 1989;Ratnam et al, 2001) to equation (6). This figure indicates that equation (7) by Ratnam et al (2001) gives a slightly smaller F compared to equation (6) and that the difference is within a range of 10% throughout the full range of aspect ratio, whereas the differences between equation (6) and the other solutions become significant when L/D is less than 1.…”

An assessment of the piezometer method for measuring the hydraulic conductivity of a Cladium mariscus—Phragmites australis root mat in a Norfolk (UK) fen

“…F for closed-bottom cylindrical intakes such as that used here can be calculated using the empirical formula of Hvorslev (1951) as modified by Brand and Premchitt (1980;see also Brand and Premchitt (1982)):…”

Evaluating the quality of hydraulic conductivity estimates from piezometer slug tests in peat

“…F for closed-bottom cylindrical intakes, such as those used in this study (see below), can be calculated using the empirical formula of Hvorslev (1951) as modified by Brand and Premchitt (1980) (see also Brand and Premchitt, 1982).…”