Patent ID: 7896582

Claim:
A retaining wall, comprising: a vertical stem wall section; a base section positioned below the vertical stem wall section, wherein the base section includes a heel portion that extends horizontally outwards from the stem wall section and wherein the heel portion has an outer vertical edge at an end of the heel portion and a top surface and a bevel at a top, outer edge thereof, wherein the bevel has a first edge that meets the outer vertical edge of the heel and a second edge on the top surface positioned between the outer vertical edge and the vertical stem wall section; and wherein the bevel has an angle, β, selected such that when the base has zero deflection, the bevel angle β satisfies the relations: K 0 ″ = ( cos 2 ⁢ β + K 0 ⁢ r ⁢ sin 2 ⁢ β ) ⁡ [ 1 + cot ⁢ ⁢ β ⁡ ( tan ⁢ ⁢ δ - tan ⁢ ⁢ β ⁡ ( 1 - K 0 ⁢ r ) 1 + K 0 ⁢ r ⁢ tan 2 ⁢ β ) ] K b ⁢ ⁢ 0 = ( cos 2 ⁢ β + K 0 ⁢ r ⁢ sin 2 ⁢ β ) ⁡ [ - cot ⁢ ⁢ β + tan ⁢ ⁢ δ - tan ⁢ ⁢ β ⁡ ( 1 - K 0 ⁢ r ) 1 + K 0 ⁢ r ⁢ tan 2 ⁢ β ] K 0 ⁢ r = cos 2 ⁢ ϕ z 0 2 - z m 2 ⁡ [ A 1 ⁡ ( 1 - z m 2 ) - 4 ⁢ A 2 ⁡ ( 1 - z m ) + 2 ⁢ ln ⁢ ⁢ z 0 - 2 ⁢ A 3 ⁢ ln ⁢ ⁢ z m ] where, A 1 =[1+tan(φ−ε)tan φ] 2 A 2 =tan φ tan(φ−ε)[1+tan(φ−ε)tan φ] A 3 =tan 2 φ tan 2 (φ−ε) z 0 =1+sin φ√{square root over (1−cot φ tan ε)} z m =sin φ√{square root over (1−cot φ tan ε)} K″ 0 =At rest pressure coefficient at bevel at heel; K b0 =Vertical at rest pressure coefficient at bevel at heel; K 0r =At rest coefficient for a sloped backfill; β=180−β′=bevel angle; α=local slip surface at the bevel; δ=concrete friction angle with soil at the bevel; φ=internal friction angle of the soil; and ε=is the angle of the backfill behind the retaining wall.