Vízügyi Közlemények, 1937 (19. évfolyam)

3-4. szám - Szakirodalom

23 VIIÍ. MASS CONSISTING OF EQUAL SPHERES. Ну L. FILEP. (Pages : 128—144.) The structure of gravel and sand soils may be studied by considering them as a mass of spherical grains. Besides it may be assumed that no friction or adhesion exists between the grains. In order to perform the physical examination in view, we have to study the mass of spheres geometrically. A mass of spheres may be defined as a multitude of spheres which do not intersect one another. Three main groups may be distinguished : incoherent, coherent-compressible, and incompressible masses. The properties of the latter are similar to those of gravel and sand soils. These properties can best be studied in those masses where all the grains have the same mutual situation throughout the whole mass. These are called uniform masses and may be characterised by a numerical value, which indicates the number of grains which are in contact with individual grain in the mass. This numerical value is called the contact number. The contact number of an incoherent mass may, as a matter of course, be zero, but is at most 9 ; that of a coherent compressible mass at least 2, and at most 11 ; and that of an incompressible mass at least 4, and at most 12. A larger contact number than 12 does not exist. Incompressible uniform mass may be composed of strata by placing the centres of spheres in the points of a plane assigned according to a certain rule. In this way each strata are formed in the mass ; then the strata are put into contact so that the spheres of the different strata touch one another. Table I gives the characteristic properties of such masses consisting of uniform equal spheres ; columns 3 and 5 of this table show how the spheres of the mass are arranged. Column 4 gives the contact number of the mass. The density of an incompressible uniform mass with a certain contact number is not necessarily constant, but may vary between certain limits. The upper limit is always 07405 ; the lower limit can be taken from column 3 of Table II. From this it can be stated that the density of a mass with the contact number 6 may vary between 0.3702 and 0.7405 ; with the contact number 4 it varies between 0-2819 and 0.7405 ; while the density of a mass with a contact number 12 is always constant and can be stated as 0.7405. The density of masses of higher contact number varies between higher limits. Natural deposits and settlements cannot produce all sorts of arrangements of grains. We exclude from our further examinations those masses the grains of which are so arranged that their order could have been produced only by accumulation of chance events. In so doing we assume that in nature the grains of gravel and sand layers have settled without any necessary accumulation of chances. In selecting from our tables the masses arranged in this way, we can ascertain that the density of gravel and sand masses occurring in nature also varies between