GEOGUIDE 1 GUIDE TO RETAINING WALL ... - HKU Libraries

63where OCR = overconsolidation ratio of the soilK 0?oc = (1 - sin 0')OCR a5 ........ (6.4)For soils which have undergone complex stress histories, the distribution of the earthpressure at rest with depth should be carefully assessed (Burland et al, 1979). At shallowdepths in a heavily overconsolidated clay, KO ?OC may approach the passive earth pressurecoefficient, K p .It should be noted that for walls retaining insitu ground, the initial stress conditionsin the ground can be modified by the processes of wall installation and bulk excavation infront of the wall (see Section 6.2.2).6,5 ACTIVE EARTH PRESSURES6.5.1 Rankine Earth Pressure TheoryFor a soil modelled as a c f = 0 (i.e. cohesionless) material, Rankine theory gives thecomplete state of stress in the soil mass, which is assumed to have expanded or compressedto a state of plastic equilibrium. The pore water pressure is assumed to be zero everywherewithin the soil mass.The Rankine active earth pressure is most conveniently calculated on a vertical plane,which is often referred to as the Virtual back 1 of the retaining wall. The stress conditionsrequire that the earth pressure on the vertical plane acts in a direction parallel to the groundsurface and that it is directly proportional to the depth below the surface, i.e. the pressuredistribution is triangular. Rankine 1 s equation for active earth pressure is given inFigure 15(a).For a retaining wall with an inclined rear face, the active force P a and its angle ofinclination i a may be obtained by Mohr circle construction, or alternatively may simply beevaluated by the resolution of forces, as illustrated in Figure 15(b).Rankine theory assumes sufficient movement can take place for the soil to reach astate of plastic equilibrium. However, there are some modes of movement which willinvalidate the Rankine stress conditions. For example, for a retaining wall restrained at itstop, the triangular Rankine earth pressure cannot develop (see Figure 13(c)).Depending on the wall friction mobilised as a result of wall movement, the actual lineof thrust acting on a retaining wall at failure may not coincide with the direction of the activeforce given by Rankine theory. However, because the Rankine stress field is such that allsoil elements within the soil mass satisfy equilibrium and that the Mohr circles of stress areall limiting (i.e. the yield condition is not violated anywhere), the retaining wall will be 'safe 1provided that it can support Rankine active force and any associated shear force acting onthe back of the wall.Rankine theory should not be applfed where ^, the angle which tiie Rankine activeforce makes with tfee normal to the back of the retaking wall, exceeds the angle of wall