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The differential equation derived by Childs for groundwater flow over a sloping bed, the streamlines being assumed to be parallel to the slope, is integrated for the case of ditches and uniform rainfall. Expressions are obtained for the maximum vertical water table height, the location of this maximum and of the watershed, and the water table shape. Calculated water table heights are in much better agreement with previously published experimental data than those calculated from an earlier theory based on the assumption that streamlines are horizontal. Thus Childs' revised assumption is confirmed. An approximate solution for the form of the water table under small rainfall rates is also derived.Childs [1971] pointed out that in applying the Dupuit-Forchheimer approximations to groundwater flow over sloping impermeable beds to transverse ditch drains in the presence of uniform rainfall, Werner [1957] and Schmid and Luthin [1964] had incorrectly assumed that the equipotentials were vertical rather than perpendicular to the sloping bed, Childs presented a revised analysis leading to a differential equation for the groundwater flow incorporating the necessary modifications but indicated that there were no analytical solutions available except in a few special cases considered by Wooding and Chapman [1966], and he therefore proceeded by numerical methods. However, it is possible to obtain analytical solutions, which are moreover very similar in form to those given by Schmid and Luthin, and these are presented in this paper. THEORYThe particular problem considered is that of the drainage of groundwater in equilibrium with rainfall flowing down a sloping bed by equidistant parallel ditches traversing the slope and penetrating to the impermeable bed. It is assumed that the water levels in the drains are maintained at bed level. The

The influence of pore-water suction on the strength of a porous material is that it contributes a compressive load which increases the shear strength. When the material is unsaturated, the normal load or effective stress is due, in part to the continuous water at measured suction in unemptied pores, and in part to isolated bodies in nominally emptied pores at suctions approximating to the suction at emptying.When the material is draining from saturation, the effective stress u iswhere S is the fraction of saturation, (Y is the fraction of the initial water content drained at the maximum suction, DSd is the prevailing pore water suction, and sd is a suction passed through in reaching p s d at which the reduction of s is dS.When the material is rewetting, the relationship becomes where psw is now the prevailing suction during wetting and f is a distribution function of the degree of saturation such that 6 s = f&w 8Sd 6 s is the fractional saturation removed i n the suction range 6sd at sd and regained in the suction range as, at s,. ,& is the maximum suction attained.The effective stress is revealed experimentally by unconfined compression tests on samples with imposed pore water suctions, and the dependence on this suction confirms reasonably that which is predicted by the theoretical formulas.

Measurements of unconfined shear strengths were made over a range of moisture contents on seven remoulded agricultural soils which covered a range of textures, and these were used to calibrate the Swedish fall-cone device. It was found that the calibration factor, usually regarded as constant in engineering literature, was dependent on soil texture, but constant over a range of moisture contents for a given soil texture.From the assumption that the liquid and plastic limits correspond to two fixed specified strengths, it is shown that one can use the fall-cone device to determine these limits by making measurements uf cone penetrations over a range of moisture contents. It is suggested that a modified plasticitychart, which can be obtained very simply from measurements of cone penetrations made over a restricted range of moisture contents, may be used for characterizing soil behaviour.

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