Active Earth Pressure Acting on Retaining Walls on Cut Slopes

1. Introduction

If the original ground behind the retaining wall is cut off, the earth pressure acting on the retaining wall may be different from the earth pressure acting on the embankment retaining wall due to the influence of the boundary surface. However, if the destruction plane of the soil wedge passes through the backfilling soil, the earth pressure can be obtained in the same way as the embankment retaining wall.

2. Precautions while calculating the active earth pressure

If the ground behind the retaining wall is cut,

• The slope of the natural ground is 45° or more,

• The horizontal distance between the heel of the retaining wall and the bottom of the original ground is 1.0m or less, as shown in the figure below,

The earth pressure on a retaining wall is affected by the cut surface and should be treated differently than the earth pressure on a typical retaining wall.

If the stability of the original ground can be confirmed, certain precautions should be taken when calculating the earth pressure for a cut retaining wall. These include:

• The location of the retaining wall and its face,

• The slope of the original ground,

• The roughness of the surface

Depending on these factors, the earth pressure will vary, and it is important to note that active earth pressure acting on retaining walls with cut slopes may be greater than the earth pressure acting on a typical retaining wall.

(a) j > ψ	(b) 45° < j < ψ	(c) Non-uniform slope

The angle of friction (δ') with the backfill depends on the geology and surface condition of the original ground, but it can be applied as (2/3 ~ 1.0)Ф in general.

• If the original ground is better than partially weathered rock and is a relatively uniform surface: (2/3)Ф

• If the original ground layer has a rough surface: (1.0)Ф

The friction angle (δ') has a large effect on the earth pressure magnitude, so δ' should be determined carefully.

3. Active earth pressure acting on retaining wall with cut slopes 

If the failure surface of the earth wedge is close to or intersects the stable slope (cut surface), the soil pressure acting on the retaining wall should be calculated by considering the influence of the stable slope (cut surface).

(1) When the failure surface of the wedge and the cut slope occur at the same point

Let's take a look at the case where the failure surface of the wedge is close to the stable slope (ω ≒ θ).

1) If the angle of failure of the wedge is the same as the slope angle of the stable slope (cut surface)

Where,

α: The angle between the back of the retaining wall and the perpendicular plane (°)

β: Back slope angle (°)

Ф: Internal friction angle of the soil (°)

δ: Friction angle between backfill and wall (°)

θ: angle of cut surface (°)

δ': Friction angle at the stable slope (cut surface) (°)

ω: Failure angle of wedge (°)

W: Weight of soil wedge (kN/m)

H: Backfill height considered for soil pressure (m)

Since ω = θ, the earth wedge is △ABC.

The method of calculating the soil pressure is similar to that of Coulomb's wedge method, but note that the friction angle at the failure surface of the earth wedge is δ' instead of Ф.

2) If the failure angle of the wedge is greater than the slope angle of cut surface

Where,

α: The angle between the back of the retaining wall and the perpendicular plane (°)

β: Back slope angle (°)

Ф: Internal friction angle of the soil (°)

δ: Friction angle between backfill and wall (°)

θ: angle of cut surface (°)

δ': Friction angle at the stable slope (cut surface) (°)

ω: Failure angle of wedge (°)

W: Weight of soil wedge (kN/m)

H: Backfill height considered for soil pressure (m)

Since ω > θ, the earth wedge is △ABC'.

This can be calculated by the method of calculating the soil pressure in Coulomb's wedge method.

(2) The failure surface of the wedge intersects with the cut surface, and from that point, it is failed along the cut surface

1) When the failure angle of the wedge is less than ∠DAF

Where,

α : The angle between the back of the retaining wall and the perpendicular plane (°)

β: Back slope angle (°)

Ф: Internal friction angle of the soil (°)

δ: Friction angle between backfill and wall (°)

θ: angle of cut surface (°)

δ': Friction angle at the stable slope (cut surface) (°)

ω: Failure angle of wedge (°)

W1: Weight of the triangle △ECD (kN/m)

W2: Weight of □ABCE (kN/m)

hv: Height of backfill from the failure surface of the wedge to the stable slope (m)

H: Backfill height considered for soil pressure (m)

δx : Friction angle at part of hv (°)

d : distance from the bottom of the retaining wall to the bottom of the stable slope (m)

① Find the internal force X as the force equilibrium on the wedge △ECD.

② Calculate Pa using the internal force X as the force equilibrium in ABCE.

At the above force equilibrium, Pa can be found using ∑Fx=0, ∑Fy=0.

2) If the failure angle of the wedge is greater than or equal to ∠DAF

Where,

α : The angle between the back of the retaining wall and the perpendicular plane (°)

β: Back slope angle (°)

Ф: Internal friction angle of the soil (°)

δ: Friction angle between backfill and wall (°)

θ: angle of cut surface (°)

δ': Friction angle at the stable slope (cut surface) (°)

ω: Failure angle of wedge (°)

W: Weight of wedge (kN/m)

H: Backfill height considered for soil pressure (m)

d : distance from the bottom of the retaining wall to the bottom of the stable slope (m)

Since ω > θ, the earth wedge is △ABC.

The soil pressure can be calculated by Coulomb's wedge method.

4. Active Earth Pressure Acting on the Retaining Wall

(1) Example of calculating the active earth pressure acting on a retaining wall

where,

α: The angle between the back of the retaining wall and the perpendicular plane (10°)

β: Back slope angle (20°)

Ф: Internal friction angle of the soil (30°)

δ: Friction angle between backfill and wall (20°)

θ: angle of cut surface (60°)

δ': Friction angle at the stable slope (cut surface) (20°)

ω: Failure angle of the earth wedge (variable, °)

H: Backfill height considered for soil pressure (5.0m)

δx : Friction angle at part of hv (20°)

γ: Unit weight of backfill (19kN/m3)

d: Distance from the bottom of the retaining wall to the bottom of the stable slope (1.0m)

Active earth pressure = 138.494 kN/m

(2) Example of calculating the active earth pressure acting on an embankment retaining wall

The design conditions are similar to the cut retaining wall.

α: Angle between the back surface of the retaining wall and the perpendicular surface (10°)

β: Back slope angle (20°)

Ф: Internal friction angle of the backfill (30°)

δ: Friction angle between backfill and wall (20°)

ω: Failure angle of the wedge (°)

H: Height of backfill considering soil pressure (5.0m)

γ: Unit weight of backfill (19kN/m3)

Failure angle of the wedge = 50°.

Active earth pressure in the embankment = 128.321 kN/m

To calculate the active earth pressure of the retaining wall with cut slopes and the embankment wall with the same assumed conditions.

Active earth pressure in the retaining wall with cut slopes = 138.494 kN/m

Active earth pressure in the embankment = 128.321 kN/m

The active earth pressure in the retaining wall with cut slopes is greater than the active earth pressure in the embankment.

It is important to note that in some cases, the active earth pressure of the retaining wall with a cut slope is greater than the active earth pressure of the embankment.

5. Conclusion

In this context, we have discussed the active earth pressure on a retaining wall with cut slopes.

Although it seems that the active earth pressure acting on the retaining wall with a cut slope is smaller than the earth pressure acting on the embankment, there are cases where the active earth pressure acting on the retaining wall with a cut slope is larger.

Even if the original ground is considered to be stable, The earth pressure varies depending on the location of the retaining wall and its face, the slope of the ground, and the roughness of its surface, and may be larger than the earth pressure acting on a typical retaining wall. Therefore it is important to consider.

Topic

# Soil pressure in retaining wall with cut slopes

# Stable slope

# Active earth pressure

# Wedge method

# Excavation in retaining wall

About the Editor

4Newbie

Structural Engineer Over 20 years of experiences

Currently I am working as an structural engineer in South Korea.

Mainly involved in bridge and underground structure design projects.

For the analysis programs, I mainly work with MIDAS Civil.

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