弾性床上のハリとしての地すべり抑止グイの式 分布荷重が働く場合

Abstract

Discussed herein are formulae for designing landslide-restraint piles with the horizontal subgrade reactions in consideration. With the intensity of the subgrade reaction p assumed to be lineally proportional to the horizontal displacement of pile axis y, that is, p=kh⋅δ⋅ywhere δ is the pile diameter and kh is the coefficient of horizontal subgrade reaction, there are still three different approaches: the first one assumes the force of landsliding H as acting only along the slip surface and the pile length as being infinite both upwards and downwards from the slip surface; the second one assumes, with the loading condition as the same, the pile length as being infinite downwards only; and the third one assumes H as distributing all along the pile above the slip surface while the root part of the pile being infinite.Observations in large-scale shearing tests in situ and excavations of yielded piles in situ present us three markedly different curves of pile deflection as illustrated in Fig. 5. Any of piling formulae are to explain the differences between these three.Fig. 1 shows a case in which the pile was so constructed as to yield only to the shearing force but actually ran to rupture by bending moment. Landsliderestraint piles are recommended to be due tested against the rupture by bending moment.§1 presents the general solution to the elastically supported elastic pile under distributed load; §2.1 the solution particular for the case with additional lateral force H0 and bending moment M0 at the head; §2.2 that for the free-head pile and §2.3 that for the pile only under H0 and M0. §2.4 deals with pile of finite lengths both above and below the slip surface. As is seen in Fig. 6 or in Fig. 11 the point of y2=0 is likely to deepen far below the slip surface with the value βh decreased: the finite-length-pile formula presented in §2.4 will be warranted. Fig. 10 is the chart for easy calculation of Mmax and based on exps. (11), (6), (7) and (8), the parameter being n, the fourth root of the ratio of kh values. Fig. 11 gives values for calculating resultant subgrade reaction and necessary length of pile below the slip surface. The meanings of symbols are:EI: rigidity of pile, δ: diameter of pilekh: coefficient of horizontal subgrade reactiony: displacement of pile axis, Es=kh·δ·y and β=4√Es/4EI: for the landsliding mass, Es, and β for the part below the slip surfacen=β/η, h: depth to the slip surfaceK=η/Es H: resultant force of landslidingη: load conversion factor=2H/h2 for hydrostatically distributed loadi: deflection angle, M: bending moment, S: sheare, ν and ν: dimensionless factors of deflection, bending moment and shear, respectively.ρ and λ0: dimensionless factors of rusultant subgrade reaction and root length of pile, respectively.Note: Suffix 0, 1 and 2 or head bar denote pile head, sliding mass and the root part of the pile, respectively. Numbers with asterisk refer to those in the literature.