Design Steps of Retaining Wall – Cantilever

Given Data:

Height of wall = ________ m

Angle of inclination of backfill (δ) = _____ degree

Unit weight of backfill soil = ______ kN/m²

Angle of internal friction (ɸ) = _____ degree

Exposure Condition = ___________

Safe bearing capacity of soil (q_u) = _______ kN/m²

Coefficient of friction (μ) = ______ (unitless)

Step 1: Computation of Initial Dimensions of the Wall

Depth of foundation

D_f =

q₀(1 - sinɸ)² γₛ(1 + sinɸ)

Overall depth of retaining wall = D_f + wall height = ______ m = H

Select the initial sizes

Width of footing = B = 0.5H to 0.7H = ______ m
Width of heel = 0.5B = ______ m
Thickness of base slab = F/12 = ______ mm
Adopt top thickness of stem = ______ mm
Height of stem = overall depth of retaining wall − thickness of base slab

Step 2: Calculate the forces and moments acting on the wall

Sr. No.	Notation	Item
1	W₁	Footing Rectangular
2	W₂	Portion of wall Triangular
3	W₃	Portion of wall
4	W₄	Soil on heel
5	W₅	Soil in inclined slope

Force Calculation (kN)

W₁ = B × "thickness of base slab" × concrete density (25 kN/m³)
W₂ = "width of rectangular portion of wall" × ("overall depth of wall" - B) × 25
W₃ = (B - "width of rectangular portion of wall") × ("overall depth of wall" - B) × 25/2
W₄ = ("overall depth of wall" - B) × "heel width" × γₛ / 2
W₅ = "width of heel" × "height of slope (backfill)" × γₛ / 2

Distance from Heel (m)

W₁ = "Width of footing" / 2
W₂ = "width of footing" / 2 + "top width of wall" / 2
W₃ = "width of footing" / 2 + "top width of wall" + "width of rectangular portion" / 2
W₄ = "Width of footing" / 2
W₅ = "Width of backfill slope" / 3

Step 3: Calculation of Earth Pressure (kN)

When the surface is inclined

Active Earth Pressure:

P_a = K_aγₛ

H² 2

= _______ kN

Where:

K_a =

cosδ - √(cos²δ - cos²ɸ) cosδ + √(cos²δ - cos²ɸ)

H = "overall height of wall" + "height of inclined portion"

∴ Height of inclined portion = width of heel × tan δ

Passive Earth Pressure:

P_p = K_pγₛ

H² 2

Where:

K_p =

cosδ + √(cos²δ - cos²ɸ) cosδ - √(cos²δ - cos²ɸ)

H = "overall height of wall" + "height of inclined portion"

Height of inclined portion = width of heel × tan δ

When the surface is flat

Passive Pressure:

P_p = K_pγₛ

H² 2

K_p =

1 + sinɸ 1 - sinɸ

= tan²(45° + ɸ/2)

Active Pressure (Flat Surface):

P_a = K_aγₛ

H² 2

K_a =

1 - sinɸ 1 + sinɸ

= tan²(45° - ɸ/2)

H = "overall height of wall" + "height of inclined portion"

Height of inclined portion = width of heel × tan δ

Vertical force component : P_a·sinδ

Horizontal force component : P_a·cosδ

Step 4: Check for Stability

Overturning Moment = M_o = P_acosδ ·

H' 3

Distance of resultant vertical force from heel: x =

ΣM ΣW

= ________ m

Stabilizing moment about toe: M_r = ΣW(B - x) = _______ kNm

Factor of Safety: FOS_overturning =

0.9M_r M_o

> 1.4

Step 5: Soil Pressure Below Footing

x₁ =

ΣM + M_o ΣW

= __________ m

e = x₁ -

B 2

B 6

= _________ m

(Required: resultant must lie in middle third of base)

q_max =

ΣW B

(1 +

6e B

) = ___________ kN/mm²

q_min =

ΣW B

(1 -

6e B

) = ___________ kN/mm²

q_min > 0 ⇒ No tension in soil.

Step 6: Check for Stability Against Sliding

Sliding force =

P_acosδ (inclined)
P_a (flat)

Resisting force:

F = μΣW = ________ kN

FOS_sliding =

0.9F P_acosδ

> 1.4

(If < 1.4 → provide shear key)

Step 7: Design of Shear Key

Width of key = 300 mm

Depth = ______ mm

Distance from toe = ______ m

For computing the passive earth pressure below the toe, top overburden of ____ mm (width of key) neglected.

η₁ = "depth from top of road surface" - a

b = "distance from toe" × tanɸ

P_p =

1 2

γₛ K_p (η₁ + a + b)² = _______ kN

Factor of safety against sliding: FOS_Sliding =

0.9(P_p + F) P_acosδ

= _______ > 1.4

Step 8: Design of Toe Slab

Pressure due to self-weight of toe slab: 25 × B = ______ kN/m²

Clear cover = ______ mm

Effective depth: d = D - CC -

ɸ 2

= ______ N/mm²

Design shear force: V_u = 1.5 ×

x 2(B + d)

× (e - d) = _____ kN

Bending moment: M_u = 1.5(M_rect + M_tri) = ______ kNm

Nominal shear stress: τ_v =

V_u bd

= _______ N/mm²

τ_c = (τ_c as per IS 456:2000 (Cl. 40.2 & Table 19))

τ_v < τ_c

Calculation of steel:

A_st = 0.5f_ck (1 - √(1 -

4.6M_u f_ckbd²

))

b f_y

= _______ mm²

Spacing =

A_ɸ × 1000 A_st

= _______ mm

Distribution steel: A_st,min = 0.12% bD = _______ mm²

Development length: Ld = 47ɸ = ______ mm

Step 9: Design of Heel Slab

Loads:

Due to soil: γₛ ("height of stem" +

"height of triangular soil" 2

) = ______ kN/m²

Due to self-weight: 25 × "thickness of base slab" = ______ kN/m²

Shear: V_u = 1.5(

bl 2(B + e)

× e) = _______ kN/m²

Moment: M_u = 1.5(x + (W₂ - W₁) × b ×

x² 2

) = _______ kN/m²

Shear stress: τ_v =

V_u bd

= ______ N/mm²

τ_c = (τ_c as per IS 456:2000 (Cl. 40.2 & Table 19))

τ_v < τ_c

Step 10: Design of Vertical Stem

Height of stem = ______ m

Clear cover = ______ mm

Bar dia = ______ mm

Effective depth: d = "thickness at base" - CC -

ɸ 2

= __________ mm

Earth pressure: P_a = K_aγₛ

H² 2

= _________ kN

Horizontal component: P_h = P_acosδ = ______ kN

Moment: M_u = 1.5P_h

H' 2

= _________ kNm

Steel:

A_st = 0.5

f_ck f_y

(1 - √(1 -

4.6M_u f_ckbd²

))bd = ________ mm²

Spacing =

A_bar × 1000 A_st

= ________ mm

Anchorage: Ld = 47ɸ = ________ mm

Shear stress: τ_v =

V_u bd

= ________ N/mm²

Curtailment:

A_st,y =

y³d h³

= _________ mm²

Temperature steel:

A_st = 0.12% bD = _______ mm²

Spacing =

A_bar × 1000 A_st

= ________ mm

Disclaimer

This design guide is generated by AI for educational purposes only. The formulas and procedures presented here are based on standard structural engineering principles, but actual design should be performed by qualified engineers following local building codes and regulations. Use this information at your own responsibility.