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.

The finite difference solutions presented for the fundamental process of pore pressure equalization in a soil piezometer system are the first of their kind to be published for cyhndrical piezometers. The response-time relationships established for cylindrical piezometers (of radius a and length b) are of the same general form as those for spherical piezomelers, the exact shape of a particular relationship being a function of the ratio a/b, the soil compressibility m and the flexibility of the piezometer measuring system V. The soil-pierometer system characteristics can be best represented by a control parameter λ = 47πbm/V. The value of this parameter characterizes the shape of the response-time curve, for which there is a unique time ratio t90/t50 and time factor ratio T90/T50. On this basis, the cylindrical equalization chart is constructed, which provides a direct means for the analysis of equalization tests in cylindrical piezometers. Interpretation of laboratory tests on piezometers embedded in clay triaxial specimens shows that equalization tests can provide reliable in situ measurement of soil permeability and good estimations of coefficients of consolidation. Les solutions de différences finies présentiées relativement au processus fondamental de l'égalisation de la pression interstitielle dans un système sol-piézomètre sont les premières de ce type à être publiées en ce qui concerne les piézométres cylindriques. Les relations réponse-temps établises pour les piézomètres cylindriques (de rayon a et de longueur b) sont de la même forme générale que celles qui correspondent aux piézroméres sphériques, la forme exacte d'une relation donnéé étant fonction du rapport a/b, de la compressibilité du sol m et de la souplesse du système de mesure du piézomètre V. La meilleure façon de représenter les caractéristiques du système sol-piézomètre est de faire appel à un paramètre de contrôle λ = 4π2bm/V. La valeur de ce paramètre caractérise la forme de la courbe réponse-temps pour ladquelle il existe un rapport unique de temps t90/t50 et un rapport de facteur de temps T90/T50. L'abaque d'égalisation cylindrique est établi à partir de ces données; cetabaque permet d'analyser directement les essais d'égalisation dans le cas de piézomètres cylindriques. L'interprétation des résultats des essais en laboratoire de piézomètres fichés dans des échantillons triaxiaux d'argle montre que les essais d'égalisation sent capables de fournir des mesures in situ fables de la perméabilité du sol ainsi que de bonnes évaluations de coefficients de consolidation.

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A numerical technique for modeling a multiaquifer system is developed on the basis of a quasi threedimensional flow model. The model consists of many horizontal aquifers interconnected by leakage flux from aquitards. The direct flow across aquitards and yield from aquitard storage are taken into account in leakage flux terms in the form of convolution integrals. Mathematical formulation results in flow functions which diminish with time and can be approximated by few exponential terms. They have been proved to be very convenient in a numerical solution scheme involving the convolution integrals. The approach reduces the dimensionality of the problem and uncouples the equations corresponding to each of the aquifers. The technique is flexible and can be used for any basin geometry with an arbitrary pumping scheme. The validity of the technique is demonstrated by comparing the model results with available analytical solutions. In general, it appears that this technique is more economical than the full three-dimensional model or even the quasi three-dimensional models that use one-dimensional elements to represent the aquitards. Figueroa V. [1969]. Herrera and his co-workers [Herrera, 1970; 1974; Herrera and Rodarte, 1973; Herrera and Yates, 1977] formulated the problem of a multiaquifer system in the form of integrodifferential equations in which the influences of adjacent aquitards and aquifers are expressed by means of 'memory' and 'influence' functions. In the latest paper, Herrera and Yates [1977] suggested that the associated functions can be approximated by a few terms of the exponential series and then they can be readily employed in a step-by-step finite element model. The 'memory function' g vanishes at large values of time, and it can be approximated roughly by a truncated exponential series and a residual in the form of Dirac's delta function. Herrera and Yates mentioned that there are difficulties in finding a satisfactory approximating function for the 'influence function' h, which is zero at the initial val. ue of time and is unity at large values of time. The difficulties remain unsolved. In their work, rigorous integrodifferential equations were elegently derived, and the formulation was presented with clarity. However, practical approximating functions were not given for model application, the formulation has not been verified with analytical formulae (derived by Neuman and Witherspoon [1969]), and it is not yet employed in practical field situations.In this paper the method used to formulate the multiaquifer model that was developed in connection with the Bangkok land subsidence study [Premchitt, , 1979 is described. An integrodifferential equation is used in the formulation of a -PREMCHITT: MULTIAQUIFER SYSTEMS 163 s s 1 (t•) ,(.'••.• s ' (t')

A severe rainfall event occurs once every two years in Hong Kong, causing widespread landslides which result in human casualties and much damage. It has recently been established that these landslides are caused largely by short-period, high-intensity rainfall, with nearly all failures occurring within a few hours of peak intensity. The failures are therefore attributable mainly to rapid transient variations in groundwater conditions. These findings are in contradiction to previously accepted theories on failure mechanisms, and it is therefore necessary for these to be reconsidered.A new theoretical model is now being examined in Hong Kong to explain the rapid landslide response following high-intensity rainfall. This is based on well-defined hillslope hydrological theories. Of particular significance in this context are thought to be subsurface erosion pipes and tunnels which have been found to exist in some of Hong Kong's hiilslopes, especially those carpeted with colluvium.