Vízügyi Közlemények, 1935 (17. évfolyam)

Kivonatok, mellékletek - Kivonat a 3. számhoz

24 Statically the only acceptable and correct solution is Rankings theory, in which «, the inclination angle of the sliding plane is determined by equation 7. A special case of this is the original Coulomb'

s solution, when the surface of terrain is horizontal (e=0). In Rankine'

s theory the direction of earth pressure is parallel to the slope of terrain, and the only hypothesis is that the continuum of infinitive extent is identical with a half continuum replaced by a wall on the one side, because Coulomb's other assumptions, such as sliding plane and maximum earth pressure, are unnecessary. In the course of later investigations Rankine'

s theory, though quite perfect mathematically, came into conflict with reality, because, as MuellerBreslau ascertained by means of tests performed with instruments of precision, the direction of earth pressure is not at all parallel to the slope of terrain, being rather almost independent of it. MuellerBreslau also explained that the real cause of all trouble is the hypothesis of-a sliding plane, because by assuming a curved sliding slope, all conditions of the equilibrium of forces, and the larger values of earth pressure found by experiments, can easily be complied with. He proves by photographs that the lower portion of the sliding slope is not a plane, but a smoothly curved surface. Examinations of plasticity opened by Prof. Prandtl in 1920 drew the attention of investigators to the importance of the curved sliding slope, and in the post-war years many investigators have searched for a solution of the problem on this basis. a) Investigations based on curved sliding slope may be divided into two groups. Group I., the Swedish and German school, assumes the sliding slope to be a circle, and attempts to find approximate solutions for practical purposes. Here the investigations of W. Fellenius, Dr. Terzaghi and Dr. Krey may be mentioned, who search for the site of a dangerous slope of sliding by employing a graphically interpolating method. This school, as has been stated, does not attempt to find mathematically correct solutions, and among the conditions of equilibrium only that of _Jilf=0 is-fulfilled, while those of 2' V=0, and 2 H=0 are not satisfied, or only partly so. These draftings, as is usual with all graphical methods, are easy to glance over, but they require much work, so that the solving of one problem may take several days. Group II., the theoretical school, try to solve the problem in an absolute mathematico-mechanical way, not forming any presumption as to the sliding slope, but trying to find it by satisfying all conditions of equilibrium. The first master of this school is Fr. Kötter, who derived the differential equation No. 9 that relates to q resultant stress acting in the surface of sliding. But the problem is not yet solved by this, because it is only serviceable for computing stress, if the form of the sliding slope is known in advance. Kötter'

s equation undoubtedly belongs to a perfect solution of the problem, but deals with only a fragment of it. Prof. Reissner pointed out the very important fact that the sliding slope may consist of several tangential surfaces, i. e. is not a continuous curve ; Prof. Kármán II. Earth Pressure with Curved Sliding Slope.