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Concrete Retaining Wall to AS4678's banner

Concrete Retaining Wall to AS4678

Verified by the CalcTree engineering team on September 27, 2024.

This calculator designs a concrete retaining wall to ensure it can withstand earth pressures, surcharge loads and environmental factors. It determines the design capacities of the retaining wall to meet stability, bearing, and structural design requirements.
This calculation has been written in accordance with AS4678:2002.
Design checks for a retaining wall are not explicitly stated in AS4678. The design methods presented below are based on Advanced Soil Mechanics by Braja M. Das and Module 6: Earthquake resistant retaining wall design published by the New Zealand Geotechnical Society.

Summary 
Design Check
Parameter
Utilisation
Status
Sliding
Sliding Force= 189.061759 kilonewton
0.60
🟢
Overturning
Overturning Moment= 519.659623 kilonewton * meter
1.37
🔴
Bearing Pressure
Bearing pressure= 85.698726 kilopascal
0.34
🟢

Calculation

Technical notes

Assumptions:
  1. Soil pressures on the retaining wall follow the Rankine method which is for non-cohesive soils (i.e.
    
    ) and assumes the soil is homogeneous, isotropic and frictionless at the wall. Active pressure will use the retained soil properties, and passive pressure will use the backfill soil properties.
  2. The retaining soil's height is equal to the height of the stem wall, as this is the critical condition for stability.
Exclusions:
  1. Only cantilever retaining concrete walls are considered. Gravity walls and secant pile walls are not considered.
  1. Currently, you can only input rectangular sections into the calculator. H-section and L-section retaining walls are not considered.
  1. As per Clause 3.2 of AS4678 there are six ultimate limit states, where sliding (limit mode U1) and rotation (limit mode U2) are the critical checks for a retaining wall. The other four limit state checks are excluded from this calculator: rupture of connections (limit state U3), pull-out of reinforcing elements (limit mode U4), global failure (limit mode U5) and bearing (limit state U6). The next revision of this calculation will include all checks for completeness.
  1. As per Clause 3.3 of AS4678 there are three serviceability limit states, where settlement (limit mode S3) is the critical check for a retaining wall. The other two limit state checks are excluded from this calculator: rotation (limit state S1) and translation (limit state S2). The next revision of this calculation will include all checks for completeness.
  2. Only dead loads (including backfill soil weight and imposed earth pressures) and live loads (including traffic surcharge) are considered. Wind loads and earthquake loads are not considered.

1. Properties

1.1 Classifications

1.1.1 Risk Classification

As per Table 1.1 of AS4678, the risk classifications are "A", "B" or "C" and are defined by:
  1. Class A: Where failure would result in minimal damage and loss of access
  2. Class B: Where failure would result in moderate damage and loss of services
  3. Class C: Where failure would result in significant damage or risk to life
The classification class has several impacts, including the level of site investigations required, the minimum live load and the structure classification design factor

used in the sliding and overturning check.


Risk Class
:B​


Table 1.1

1.1.2 Backfill Soil Condition

As per Clause 1.4.3 of AS4678, the soil condition is defined by one of four types:
  1. Controlled fill class I: "Soil rock or other inert material that has been placed at a site in a controlled fashion and under appropriate supervision to ensure the resultant material is consistent in character, placed and compacted to an average density equivalent to 98% (and no test result below 95%) of the maximum dry density (standard compaction effort) for the material when tested in accordance with AS 1289.5.1.1."
  1. Controlled fill class II: "Soil rock or other inert material that has been placed at a site in specified layers in a controlled fashion to ensure the resultant material is consistent in character, placed and compacted to an average density equivalent to 95% (and no test result below 95%) of the maximum dry density (standard compaction effort) for the material when tested in accordance with AS 1289.5.1.1."
  1. Uncontrolled fill
  2. In situ material: "Natural soil, weathered rock and rock materials."
The soil condition impacts the soil uncertainty factor

for soil shear strength, as per Clause 5.2.


Soil Condition
:Controlled fill class I​


Cl 1.4.3

1.1.3 Design Factors

The limit modes in AS 4678 (Earth-retaining structures) refer to the failure mechanisms that must be considered to ensure the structural integrity of retaining walls. These include:
  1. Serviceability limit state: addresses deformations like settlement or excessive deflections that affect wall functionality but not necessarily cause failure.
  2. Ultimate limit state (strength and stability): concerns overall failure, such as sliding, overturning, bearing capacity failure, or structural collapse under maximum design loads.
As per Clause 3.1.2, the design checks require calculating the design capacity

and design action

for each failure mode.

S=1.25G+1.5QϕsR≥ϕnSS = 1.25 G +1.5 Q \\ \phi_s R \ge \phi_n S
Where:
  1. 
    
    : Structure classification factor
  2. 
    
    : Stabilising reduction factor
  3. 
    
    : Permanent Loads, including retained soil weight, where 1.25 factor comes from Clause 4.1 a) iii)
  4. 
    
    : Live loads, where 1.5 factor comes from Clause 4.1 a) iii)
  5. 
    
    : Design Resistance effect
  6. 
    
    : Design Action effect


Φn
:1.00​


Table 5.2


Φs
:0.80​


Appendix J3


1.2 Materials

1.2.1 Soil

Retained soil:


gamma1
:18.0 kN / m^3​



phi1
:30.0 degrees​


Backfill soil:


Consider Passive Pressure
:No​



gamma2
:18.0 kN / m^3​



phi2
:30.0 degrees​


Ground base:


sigma_adm
:150.0 kPa​



friction_coefficient
:0.548​



1.2.2 Concrete



f'c
:40MPa​



concrete density
:25.0 kN / m^3​



1.3 Geometry

Stem wall:


hw
:3.00 m​



t1
:200 mm​



t2
:200 mm​



B
:1.00 m​

Base:


Lheel
:0.90 m​



Ltoe
:2.80 m​



hf
:400 mm​

Key:


Use key
:Yes​



hk
:300 mm​



Lk
:300 mm​



Xk
:3.60 m​

Soil:


beta
:0.0 degrees​



hs
:0.00 cm​

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2. Loads

2.1 Dead Loads

2.1.1 Soil Loads

Loads from the retained and backfill soil are both lateral loads (as it interacts with the retaining wall) and vertical loads (from it's self-weight).
Lateral soil loads are determined using the Rankine method for non-cohesive soils (i.e.

).
The Rankine method calculates lateral earth pressure for non-cohesive soils, assuming a linear failure criterion. It defines two pressure states: active (wall moves away) and passive (wall moves toward soil). The method assumes the soil is homogeneous, isotropic, and frictionless at the wall. Lateral pressure coefficients

and

depend on the soil's internal friction angle. The soil is divided into an elastic zone near the wall, where deformation occurs, and a plastic zone further away, where the soil reaches failure.
Rankine model

The active pressure coefficient

and the passive pressure coefficient

is given by:

Ka=cos⁡β−cos⁡2β−cos⁡2ϕ∗cos⁡β+cos⁡2β−cos⁡2ϕ∗Kp=1+sin⁡(ϕ∗)1−sin⁡(ϕ∗)K_a = \dfrac{\cos \beta - \sqrt{\cos^2 \beta - \cos^2 \phi^*}}{\cos \beta + \sqrt{\cos^2 \beta - \cos^2 \phi^*}} \quad K_p = \dfrac{1+\sin(\phi^*)}{1-\sin(\phi^*)}
Where:
  1. 
    
    is the angle between the top of the soil and top of the stem wall
  2. 
    
    is the design internal friction angle
  3. 
    
    is the partial design uncertainty factor for friction of the soils and backfill materials, as per Table 5.1(A)
  4. 
    
    is the internal friction angle of the retained soil


The active soil pressure

and the passive soil pressure

are then determined by:

pa=Kaγ1H1pp=Kpγ2H2p_a = K_a\gamma_1 H_1 \hspace{2cm}p_p = K_p\gamma_2 H_2
Where:
  1. 
    
    are the specific weight of the retained soil and backfill soil respectively
  2. 
    
    are the depths of the retained soil and backfill soil respectively
Then the equivalent active soil force

and passive soil force

is applied at the centroid of its corresponding triangular stress (which is 2/3rds of the triangle depth) given by:

Fa=paH1/2Fp=ppH2/2F_a = p_aH_1 /2\hspace{2cm} F_p = p_pH_2/2
Active and passive soil pressures on a retaining wall


Lateral forces:


Consider Passive Pressure
:No​



Φuφ
:0.95​


Table 5.1(A)


φ*1
:28.74 degrees​



φ*2
:0.50 rad​




Eq. 5.2(2)


Ka
:0.351​






Kp
:2.853​






pa
:21.45 kPa​





Fa
:36.47 kN​






pp
:35.95 kPa​






Fp
:0.00 N​




Vertical forces:


Retained soil area
:2.70 m^2​



Ws1
:48.60 kN​






Backfill soil area
:0.00 mm^2​



Ws2
:0.00 N​






2.1.2 Concrete Loads

To calculate the dead loads, the entire structure of the concrete retaining wall was considered, including the stem wall, toe slab, heel slab, and key. The total volume of concrete was determined by multiplying the cross-sectional area of the wall's profile by its width.


Retaining wall area
:2.25 m^2​



Wc
:56.25 kN​




2.2 External Loads

2.2.1 Surcharge

The active pressure from external (surcharge) loads is determined as an equivalent pressure with a uniform distribution along the height of the soil.
The equivalent active pressure

due to surcharge, and the equivalent force applied at

from the top of the retained soil is given by:

pa=KaSFa=paH1p_a = K_aS \hspace{1cm} F_a = p_aH_1
Where:
  1. 
    
    : Active pressure coefficient due to retained soil
  1. 
    
    : Surcharge load
  2. 
    
    : Total height of wall, including base thickness
Surcharge loads and the pressure distribution on a retaining wall



DL
:0.0 kPa​



LL
:3.0 kPa​




LL_min
:5.0 kPa​


Table 4.1
Lateral forces:


pa_DL
:0.00 kPa​






pa_LL
:1.75 kPa​






Fa_DL
:0.00 kN​






Fa_LL
:5.96 kN​




Vertical forces:


W_DL
:0.00 kN​






W_LL
:4.50 kN​






3. Design Checks

The below design checks follow the procedures outlined in Advanced Soil Mechanics by Braja M. Das.

3.1 Sliding Check

The sliding check is described in AS4678 as "Limit Mode U1" and refers to sliding failure within or at the base of the retaining structure. This occurs when the sliding forces on the wall exceed the resisting lateral forces, causing the wall to slide horizontally.
Sliding forces are caused by:
  1. active soil pressure due to retained soil
  2. active pressure from surcharge loads at top of the wall
Resisting (lateral) forces are caused by:
  1. passive resistance from the passive soil pressure of backfill soil, which can be enhanced by the addition of a key
  2. frictional resistance from the friction between the base of the wall and the founding soil
Sliding of a cantilevered wall

The design action for limit mode U1 (sliding)

is given by:

SU1=1.25Fa+1.25Fa,DL+1.5Fa,LLSU_1 = 1.25F_a + 1.25F_{a, DL}+ 1.5F_{a,LL}
Where:
  1. 
    
    : Active soil pressure force due to retained soil
  1. 
    
    : Active surcharge force due to additional dead and live loads, respectively
The design resistance for limit mode U1 (sliding)

is given by:

RU1=μV+FpRU_1 = \mu V + F_p
Where:
  1. 
    
    : Friction coefficient of base soil material
  2. 
    
    : Sum of vertical Forces, including the surcharge loads
    
    , self-weight of wall
    
    , self-weight of retained soil
    
    and self-weight of backfill soil
    
    
  3. 
    
    : Passive soil pressure force due to backfill soil, where the addition of a key on the retaining wall increases this resisting passive soil force
Sliding forces:


SU1
:54.53 kN​




Resisting (lateral) forces:


V
:109.35 kN​






RU1
:64.42 kN​






Sliding check
:ϕSU1 < RU1 🔴 Fail​






3.2 Rotation Check

The rotation check is described in AS4678 as "Limit Mode U2" and refers to the rotation of the retaining structure, where the wall tends to overturn around its toe due to lateral forces. This occurs when the overturning moments on the wall, exceed the restoring moments.
Overturning moments are caused by:
  1. active soil pressure due to retained soil
  2. active pressure from surcharge loads at top of the wall
  3. self-weight of backfill soil on the wall's toe
Restoring moments are provided by:
  1. self-weight of the wall
  1. self-weight of retained soil on the wall's heel
  1. passive soil pressure due to backfill soil
  2. vertical component of surcharge loads at top of the wall
Rotation of a cantilevered wall about it's base

The design action for limit mode U2 (rotation)

is given by:

SU2=1.25Ms,a+1.25Ms2,SW+1.25Ma,DL+1.5Ma,LL\small SU_2 = 1.25M_{s,a} + 1.25M_{s_2,SW} + 1.25M_{a,DL} + 1.5M_{a,LL}
Where:
  1. 
    
    : Overturning moment
    
    
  1. 
    
    : Active soil pressure moment from the retained soil, with a lever arm of
    
    from base of footing
  2. 
    
    : Active surcharge moment due to additional dead and live loads, respectively, with a lever arm of
    
    from base of footing
  1. 
    
    : Moment from the self-weight of the backfill soil, with a lever arm of
    
    from base of footing
The design resistance for limit mode U2 (rotation)

is given by:

RU2=Ms1,SW+MDL+MLL+Mp+Mw,SW\small RU_2 = M_{s_1,SW} + M_{DL} + M_{LL} + M_p + M_{w, SW}
Where:
  1. 
    
    : Restoring moment
    
    
  1. 
    
    : Moment from the self-weight of the retained soil, with a lever arm of
    
    from base of footing
  1. 
    
    : Moment from vertical component of surcharge loads, due to additional dead and live loads, respectively, with a lever arm of
    
    from base of footing
  1. 
    
    : Passive soil pressure moment from the backfill soil, with a lever arm of
    
    from base of footing
  1. 
    
    : Moment from the self-weight of the retaining wall, including the stem, toe and heel. The lever arm is calculated automatically using Python's library Shapely
Overturning moments:


Ms,a
:41.33 kN m​






Ms2,SW
:0.00 kN m​






Ma,DL
:0.00 kN m​






Ma,LL
:10.13 kN m​






SU2
:64.33 kN m​




Restoring moments:


Ms1,SW
:167.67 kN m​






M,DL
:0.00 kN m​






M,LL
:15.53 kN m​






Ms,p
:0.00 kN m​






Mw,SW
:127.99 kN m​






RU2
:311.18 kN m​






Overturning check
:ϕSU2 > RU2 🟢 Ok​






3.3 Settlement Check

The settlement check is described in AS4678 as "Limit Mode S3" and refers to the settlement of the structure, where the retaining wall sinks into the founding soil. This occurs when the vertical loads from the wall, backfill, and surcharge exceed the allowable bearing capacity of the foundation soil. When the applied pressure surpasses the soil's ability to support the load, the soil compresses, leading to differential or uniform settlement.
In Limit Mode S3, no reduction coefficient is applied for stability and resistance actions since it pertains to a serviceability check.
Settlement of a cantilevered wall

The design action for limit mode S3 (settlement) is given by the pressure applied to the soil beneath a retaining wall

due to serviceability actions:

SS3=σu=VAf+McISS3=\sigma_u = \dfrac{V}{A_f} + \dfrac{Mc}{I}
Where:
  1. 
    
    : Vertical serviceability actions
  2. 
    
    : Footing Area
  3. 
    
    : Flexural Moment due to serviceability actions
  4. 
    
    : Distance from the neutral axis to the most distanced fibre in compression/tension
  5. 
    
    : Footing inertia
Note,

accounts for the combined effect of the vertical forces and the pressure induced by the resultant flexural moment.
The design resistance for limit mode S3 (settlement) is given by:

RS3=σadmRS3 = \sigma_{adm}
Where:
  1. 
    
    : Allowable bearing pressure for supporting soil base which is a soil property defined in section 1.2 of this calculator


V
:109.35 kN​






Af
:3.90 m^2​






M
:259.72 kN m​






c
:1.95 m​






I
:4.94 m^4​






SS3
:130.49 kPa​






RS3
:150.00 kPa​






Settlement check
:SS3 > RS3 🟢 Ok​







Related Resources

  1. Concrete Slab-on-grade Designer to AS3600
  2. Rectangular Footing Design to AS3600
  3. Concrete Shear Wall to AS3600