Soil nail Manual

Σ F N = 0 : E1(1-L1W/l1)Sin δ 1 - T ′N1Sin(α+θ1) - W 1Cosθ1 + C′l3Cosθ1 + R 31Sin(Φ′-θ1) + R 1CosΦ′ = 0 ----------(6) Σ FT = 0 : - E1Cosδ 1 + T  ′N1Cos(α+θ1) - W 1Sinθ1 + C′l1 + C′l3Sinθ1 + R 31Cos(Φ′-θ1) + R 1SinΦ′ = 0

----------(7)

From : R 1 = [(W1-C′l3)Cosθ1/CosΦ′] + [(B1-A1)/CosΦ′] - [R 31Sin(Φ′-θ1)/CosΦ′]

----------(8)

R 1 = [(W1-C′l3)Sinθ1/SinΦ′] - [C′l1/SinΦ′] + [(A11-B11)/SinΦ′] - [R 31Cos(Φ′-θ1)/SinΦ′]--(9) (8) = (9) => R 31[(Cos(Φ′-θ1)) - (Sin(Φ′-θ1)Tan Φ′)] = (A11-B11) + (W1-C′l3)Sinθ1 - (C′l1) [(B1-A1) + (W1-C′l3)Cosθ1]Tan Φ′ Rearranging and reducing to a simpler form ; R 31 = {(A11-B11) + (W1-C′l3)Sinθ1 - (C′l1) - [(B1-A1) + (W1-C′l3)Cosθ1]Tan Φ′}/(Cos(Φ′ - θ1) - Sin(Φ′-θ1)TanΦ′) ----------(10) Set 5) = 10) & remember that : 1 l A1 = E1(1-L1W/l1)Sin δ 1

B1 = T  ′N1Sin(α+θ1)

A11 = E1Cosδ 1

B11 = T  ′N1Cos(α+θ1)

A2

= E2(1-L2W/l2)Sin δ 2

B2 = T  ′N2Sin(α+θ2)

A22 = E2Cosδ 2

B22= T  ′N2Cos(α+θ2)

R 32 = {(E2Cosδ 2-T ′N2Cos(α+θ2)) + (W2+C′l3)Sinθ2 - (C′l2) - [(T  ′N2Sin(α+θ2) - E 2(1 L2W/l2)Sin δ 2) + (W2+C′l3)Cosθ2]Tan Φ′) / [(Cos(2Φ′ -θ2))/CosΦ′] ----------(11) R 31 = {(E1 Cosδ 1 -T ′N1 Cos(α+θ1)) + (W1-C′l3)Sinθ1 - (C′l1 ) - [(T  ′N1Sin(α+θ1 )-E1 (1 L1W/l1 )Sin δ 1 ) + (W1 -C′l3)Cosθ1]TanΦ′}/[(Cos(2Φ′-θ1))/CosΦ′] ----------(12) Iterate on F until |R 32 - R 31| / [ |R 32 | + |R 31| ] ≤ 0.01

PASSIVE CASE

For passive case, the following assumption are made:

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