Simple gabion wall example.pdf

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GABION RETAINING WALL ANALYSIS AND DESIGN (BS8002:1994) TEDDS calculation version 1.1.03

10kN/m 2

71.6 0

3 - 1000 mm × 1000 mm 1000 3

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2 - 2000 mm × 1000 mm

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1 - 2000 mm × 1000 mm

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30.7kN/m 2 59.7kN/m 2

Wall geometry Width of gabion 1; 1;

w1 = 2000 mm 2000 mm

Height of gabion 1; 1;

h1 = 1000 mm 1000 mm

Width of gabion 2; 2;

w2 = 2000 mm 2000 mm

Height of gabion 2; 2;

h2 = 1000 mm 1000 mm

Step to front face between 1 and 2; 2;

s2 = 0 mm

Width of gabion 3; 3;

w3 = 1000 mm 1000 mm

Height of gabion 3; 3;

h3 = 1000 mm 1000 mm

Step to front face between 2 and 3; 3;

s3 = 1000 mm 1000 mm

Wall inclination; inclination;

ε = 0 deg

Wall fill Gabion fill unit weight; weight;

15 kN/m3 γ d = 15 kN/m

Centre of gravity Horizontal distance to centre of gravity gabion 1; 1;

xg1 = w1 / 2 = 1000 mm 1000 mm

Horizontal distance to centre of gravity gabion 2; 2;

xg2 = w2 / 2 + s2 = 1000 mm 1000 mm

Horizontal distance to centre of gravity gabion 3; 3;

xg3 = w3 / 2 + s2 + s3 = 1500 mm 1500 mm

Vertical distance to centre of gravity gabion 1; 1;

yg1 = h1 / 2 = 500  mm 500 mm

Vertical distance to centre of gravity gabion 2; 2;

yg2 = h2 / 2 + h1 = 1500 mm 1500 mm

Vertical distance to centre of gravity gabion 3; 3;

yg3 = h3 / 2 + h1 + h2 = 2500 mm 2500 mm

Weight of gabion 1; 1;

W g1 = γ d × w1 × h1 = 29.0 kN/m 29.0 kN/m

Weight of gabion 2; 2;

W g2 = γ d × w2 × h2 = 29.0 kN/m 29.0 kN/m

Weight of gabion 3; 3;

W g3 = γ d × w3 × h3 = 14.5 kN/m 14.5 kN/m

Weight of entire gabion; gabion;

W g = W g1 + W g2 + W g3 = 72.5 kN/m 72.5 kN/m

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Horiz distance to centre of gravity entire gabion;

xg = ((W g1 × xg1) + (W g2 × xg2) + (W g3 × xg3)) / W g = 1100 mm

Vert distance to centre of gravity entire gabion;

yg = ((W g1 × yg1) + (W g2 × yg2) + (W g3 × yg3)) / W g = 1300 mm

Correcting for wall inclination horiz dist;

Xg = xg × cos(ε) + yg × sin(ε) = 1100 mm

Vertical change in height due to wall inclination;

Hf = yg3 + h3 /2 - ((yg3 + h3 /2) × cos(ε) - (xg3 + w3 /2) × sin(ε)) = 0 mm

Calculate effective height of wall Effective height of wall; H = (y g3 + h3 / 2) + (w 1 × sin(ε)) - Hf + [cos (90 – α) × sin (β  + ε) × w3]/ sin [180 – (α + β )] = 3000 mm Height of wall from toe to front edge of top gabion; Hincl = ((yg3 + h3 / 2) × cos(ε) - (xg3 - (w3 / 2)) × sin(ε)) = 3000mm Calculate the angle of rear plane of wall

α =90 deg + ε = 90.0 deg

Effective angle of rear plane of wall; Calculate the effective face angle

θ = Atan [(yg3 + (h3 / 2)) / ((xg3 - (w3 / 2)))] - ε = 71.6 deg

Effective face angle; Soil parameters Slope of retained soil;

β = 0.0 deg

Mobilization factor;

M = 1.0

Internal angle of friction for retained soil; Saturated density of retained soil;

φ’ = 30.0 deg γ s = 20 kN/m3

Coefficient for wall friction;

K = 1.0

Wall friction; Design angle of base friction;

δ = φ’ × K = 30.0 deg δb = 30.0 deg

Bearing capacity of founding soil;

q = 75 kN/m2

Active Pressure using Coulomb Theory; Ka = (sin(α + φ’)2)/[(sin(α))2 × sin(α - δ) × (1+√[(sin(φ’ + δ) × sin(φ’ - β)) / (sin(α - δ) × sin(α + β ))])2] = 0.297 Loading Surcharge;

po = 10 kN/m2

Surcharge loading as equiv height of soil;

hs = po / γ s = 500 mm

Active thrust due to soil;

Pa,soil = 0.5 × Ka × γ s × H2 = 26.7 kN/m

Active thrust due to surcharge;

Pa,surch = po × Ka × H = 8.9 kN/m

Total active thrust;

Pa = Pa,soil + Pa,surch = 35.7 kN/m

Total thrust resolved horizontally;

Ph = Pa × cos(90 - α + δ) = 30.9 kN/m

Total thrust resolved vertically;

Pv = Pa × sin(90 - α + δ) = 17.8 kN/m

Height above toe thrust acts if α is 0;

dh,soil = H × (H + 3 × hs) / (3 × (H + 2 × hs)) = 1125 mm

Height above toe thrust acts;

dh = dh,soil – w1 × sin(ε) = 1125 mm

Horiz distance to where thrust acts;

bv = w1 × cos(ε) – (dh,soil / tan (α)) = 2000mm

Overturning stability – take moments about the toe Overturning moment;

Mo = Ph × dh = 34.7 kNm/m

Restoring moment;

MR = (Pv × bv) + (W g × Xg) = 115.4 kNm/m

Factor of safety for overturning;

Fo,M = MR / Mo = 3.32

Min allowable factor of safety for overturning;

Fo,M,min = 2.00

PASS - Design FOS for overturning exceeds min allowable FOS for overturning  Sliding stability – ignore any passive pressure infront of structure Total vertical force;

N = W g + Pv = 90.3 kN/m

Total horizontal force;

T = Ph = 30.9 kN/m

Sliding force;

Ff = T × cos (ε) – N × sin (ε) = 30.9 kN/m

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Resistance to sliding;

FR = (N × cos (ε) + T × sin (ε)) × tan (δb) = 52.2 kN/m

Factor of safety for sliding;

Fo,S = FR / Ff = 1.69

Min allowable factor of safety for sliding;

Fo,S,min = 1.50 PASS - Design FOS for sliding exceeds min allowable FOS for sliding 

Pressure at base Force normal to base;

Ns = (N × cos (ε) + T × sin (ε)) = 90.3 kN/m

Eccentricity;

e = (w1 / 2) – (MR – Mo) / Ns = 107 mm Reaction acts within middle third of base 

Pressure at toe; Pressure at heel;

σtoe = (Ns / w1) × (1 + (6 × e / w1)) = 59.7 kN/m2 σheel = (Ns / w1) × (1 - (6 × e / w1 )) = 30.7 kN/m2 PASS - Allowable bearing pressure exceeds max design pressure to base