Vízügyi Közlemények, 1956 (38. évfolyam)

2. füzet - VII. Kisebb közlemények

(5) distributed on the surface of rupture, and their resultant can thus be simply located. (The reaction is tangent to a circle drawn with radius R sin Ф around the centre ; the cohesion force is parallel to the chord of the curve of rupture). Simplest is the application of Jdky's vector-polygonal method (Fig. 7.), in which the magnitude of cohesion necessary for securing stability is determined on the basis of the closed vector triangle of weight G of the earth mass, of cohesion force К and of reaction Q of the surface of rupture. The further development of this method according to Fig. 9. for the determination of the critical circle is not reasonable ; moreover, all three conditions of equilibrium are not satisfied. 2. The degree of mobilization of shearing strength denoted with e (the author suggests the determination of the value of r on the basis of the proportional section of the shearing deformation curve according to Fig. 12.), the conditions of equilibrium of the forces acting in the case of the surface of rupture assumed in the still stable bank, can be written on the basis of Fig. 11. in the form of equations (4) and (5). Values of shearing strength are considered reduced by factor v. Relationships under (6) subsist between pertaining components of the reaction of the surface of rupture. With the moment condition considered, all force components are determinable, if an assumption is made as to the distribution of normal stresses. Conventional eases are shown in Fig. 14. [15 ]. The arm of the resultant of slide stresses (equation 9.) can thus be obtained from the diagram (Fig. 13.). On the basis of (4), (5) and ((j) equation (7) may thus be written, afterwards using (8) and (9) the final result, equation (10) is obtained in which only factor с is unknown, which can thus be calculated. The solution leads to a cubic equation. The method satisfies all three conditions of equilibrium, and the safety margin is referred to the total shearing strength. •Í. Effects affecting the stability of slopes 3.1. Earthquake effect is taken account of by applying a horizontal mass force (II — n

g G) at the centre of gravity [20 ]. It is advisable to consider that in the case of tremors the angle of friction radically decreases (Fig. lő.). 3.2. Heavy revetment transmits normal loading to the slope and makes it more stable in case of a bottom point surface of rupture (Fig. 16.). 3.3. Effect о/ weder on slopes 3.31. Water has no lubricating effect ; it reduces shearing strength by pore pressure, dynamic pressure head or loosening due to swelling. 3.32. Shrinkage caused by drying produces cracks ; if the latter are filled with water the stability of the slope diminishes very much ( Fig. 18.). Volume change caused the longitudinal cracks of the flood protection levee of Fig. 19. The soil of the levee had been soaked by capillary action under the effect of water pressure and dried later. The depth of soaking was such that the soil very much subject to volume change ( Fig. 20.) suffered cracks of the order of magnitude of decimeters under the effect of alternate soaking and drying caused by flood waves. 3.33. After sudden drawdown of the water piezometric pressure is upheld in the bank, and the shearing stress decreases according to equation (1.3). Safety against slide is calculable by equation (14a) (Fig. 24.). Incase of slow drawdown of water (Fig. 23.) the safety margin hardly decreases. 3.34. Water flow produces seepage pressure in the slope. The force of seepage is approximately calculable after Ohde or Terzaghi-Peck (equations 15 and 15.a, Fig. 25. and 26.). Dam failures shown in pictures 5. and 6. were caused by effect of rainstorms and water flow. Seepage pressure acts similarly upon the slope of cuts made below the groundwater level, li' the drawdown curve cuts the slope the lower part of the bank is washed out, because in this case the slope of the bank can be only after equation (16) according to Bernatzik [18 j. Protection can be attained (Fig. 28.) either by successive lowering of the water table or by laying a mat (apron) of sand (Fig. 30.). Equation (17) gives after Fröhlich [15] the approximate value of the safety margin (Fig. 31.).