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Design Guide: Concrete Footing to AS3600's banner
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Design Guide: Concrete Footing to AS3600

Embedded footings and slab-on-grade are structural elements which transfer load imposed by the superstructure to the soil underneath. They typically support columns, walls, or other vertical members. The geotechnical and structural engineer must work together to ensure the footing is adequate against bearing failure (geotechnical checks) and ultimate limit state (structural checks).
This design guide explains the principles behind the structural foundation design of reinforced spread footing and slab-on-grade as per AS3600-2018. The key difference between these two common footing types is that spread footings are embedded in soil whereas a slab-on-grade sits on top of the founding material. This guide explains the various checks that must be conducted to ensure that the foundations are adequate and stable to support nominated loads.

Geotechnical Checks

Bearing

Bearing failure is the most common failure mode for footings. The engineer must ensure that the bearing pressure of the foundation onto the soil from applied loading does not exceed the soil bearing capacity.

What is bearing capacity?

Bearing capacity is a variable which is specific to an individual foundation. A site cannot be classified as a particular bearing capacity, because it is dependent on numerous input parameters such as soil properties and the foundation size, geometry and depth.
Geotechnical engineers define the ultimate bearing capacity of a foundation as the pressure which would cause it to fail. Bearing failure means a foundation moves more than is acceptable. Check out our bearing capacity article for methods how to calculate the ultimate bearing capacity.
Bearing failure

The allowable bearing capacity is an additional term which describes the bearing pressure that should not be exceeded under working (unfactored) loads.
The relationship between these two definitions of bearing capacity is defined by a factor of safety (FoS). Different standards and codes recommended varying FoS values, generally greater than 1.5.

FoS=ultimate bearing capacityallowable bearing capacity≈1.5−3\text{FoS}=\dfrac{\text{ultimate bearing capacity}}{\text{allowable bearing capacity}} \approx1.5-3

How to define bearing pressure?

Distribution of the bearing pressure under the foundation depends on the eccentricity of the loads. A concentric load results in even distribution, while an eccentric load leads to a greater pressure on one side than the other. Eccentric loads lead to overturning moments, which are significantly more dangerous than concentric loads as they cause rotation and differential settlement.
The bearing pressure is assumed to vary linearly.
Concentric loading

Eccentric loading

When you have more then one eccentric column on a footing, or you have eccentric shear forces or applied moments, we can calculate the resultant eccentricity. This are the distances from the footing centroid where all the equivalent axial forces will act. See the below toggle for how it is calculated.

How to calculate the resultant eccentricity

Depending on the location of the resultant eccentricity, the base pressure causes the footing to be in full or partial compression. Full compression is when the entire soffit of the footing is in bearing against the soil, while partial compression is when there is loss of contact between the soil and footing. In practice, designers often size their footing to be in full compression because partial compression has a bearing distribution much more complex to calculate and requires additional checks for overturning.
The paper by Bellos & Bakas (2017) provides a method to calculate the linear pressure distribution under footings based on the location of your resultant eccentricity, which is a common approach used in practice. We summarise it here.
Bellos & Bakas (2017) show that a footing is deemed to be in full compression if the resultant eccentricity is within an area of the footing defined as the kern or the main core. The kern is shown in the green highlighted region in the image below, and is defined as having semi-diagonals within a sixth of its width/length from the centre.
Footing is in full compression if the resultant eccentricity is within the kern

When the eccentric load is within the highlighted zone, the maximum and minimum bearing pressure can be calculated as:

Pmax=ΣPArea[1+6(exL)]Pmin=ΣPArea[1−6(exL)]P_{max} = \frac{\Sigma P}{Area} [1 + 6(\frac{e_x}{L})] \\ P_{min} = \frac{\Sigma P}{Area} [1 - 6(\frac{e_x}{L})]
XX
Bearing corner pressures

Different cases of biaxial bearing pressure


Then the bearing check becomes:

Allowable bearing capacity≥max(P1,P2,P3,P4)\text{Allowable bearing capacity} \geq \text{max}(P_1,P_2,P_3,P_4)
Explore the toggles below for further information about eccentric loading.

Uniaxial vs biaxial eccentricity

Biaxial loading

Sliding


Ff = Frictional resistance=μ×vertical reaction=μ×(Wconcrete+Qsurcharge×BL−∑N∗)F∗ = Pushing force = applied shear in the direction being considered\small{F_f\ =\ \text{Frictional\ resistance}}=\mu \times \text{vertical reaction}\\\hspace{3.8cm}=\mu \times (W_{concrete}+Q_{surcharge}\times BL-\sum N^*) \\\small{F^*\ =\ \text{Pushing\ force}\ =\ \text{applied\ shear\ in\ the\ direction\ being\ considered}}

Overturning


ΣMo =Total overturning momentΣMr =Total resisting moment\small{ΣM_o}\ = \text{Total\ overturning\ moment}\\\small{ΣM_r\ =\text{Total\ resisting\ moment}}

Uplift

There are also other failure modes such as sliding and uplift but these are rare. Geotechnical investigations are conducted to ensure soil parameters (friction angle, cohesion, etc.) are adequate prior to construction and footings are almost always subject to compressive loads, hence no uplift.

Structural Checks

There are three ULS strength checks to be conducted for design of footings:
  1. One-way shear check (beam shear) - AS3600 Section 8.2
  2. Two-way shear check (punching shear) - AS3600 Section 9.3
  3. Flexural check (bending) - AS3600 Section 8.2
The section shear and flexural capacities,

and

, calculated as per the referenced AS3600 sections, must be greater than the imposed loads i.e.

V∗ < ϕVuM∗ < ϕMuV*\ <\ \phi{V_u}\\M*\ <\ \phi{M_u}
For a deep-dive into the section design procedures, check out CalcTree's Concrete Beam Design Calculator. Here we will explain how to calculate the design actions on footings. The design actions are derived by considering the critical sections for shear and bending of wide beams, as described in Design of Structural Elements by C. Arya.

One-way Shear

As per AS3600 Cl. 8.2.3.2, the maximum transverse shear near the support is taken at a distance dₒ away from the face of the support. Footings typically don't have shear reinforcement (also known as links or ligs) and so the design shear should be resisted by the concrete itself.
The critical one-way shear V* can be calculated by:

V∗ = q(x−do)where:x=L−Lc2  or  B−Bc2do=the distance from the extreme compressive fibre of a concrete member to the centroid of its tensile reinforcementV^*\ =\ q(x-d_o)\\\text{where:}\\x=L-\dfrac{L_c}{2}\text{\ \ or\ \ }B-\dfrac{B_c}{2}\\d_o=\text{the distance from the extreme compressive fibre }\\\text{of a concrete member\ to the centroid of its tensile reinforcement}
Critical shear plane in a footing


Two-Way (Punching Shear)

Punching shear failure is sudden and signs of failure cannot be observed (like flexural or shear cracks). Longitudinal reinforcement does not provide protection against punching shear, however it can be designed for by introducing shear reinforcement (also known as links or ligs) or local thickening of the concrete. Footings are typically designed thick enough as to avoid shear reinforcement.
AS3600-2018 deals with punching shear in the slabs section (section 9) of the code.
The punching shear design force can be calculated by:

V∗ = q (Atotal − Ashear)where:Atotal=L × BAshear=(Lc+dom)(Bc+dom)=area bound by shear perimeterdom=mean value of do considering tensile reinf in both directionsV^*\ =\ q\ (A_{total}\ -\ A_{shear})\\\text{where:}\\A_{total}=L\ \times\ B\\A_{shear}=(L_c+d_{om})(B_c+d_{om})=\text{area\ bound\ by\ shear\ perimeter}\\d_{om}=\text{mean\ value\ of}\ d_o\text{\ considering\ tensile\ reinf\ in\ both\ directions}
Punching shear perimeter in a footing


Flexure

The critical bending moment, M*, occurs at the column face. The calculators output the bending moment and capacity per meter strip of the footing in the direction considered:

M∗ = qx22where:x=L−Lc2  or  B−Bc2M^*\ =\ \dfrac{qx^2}{2}\\\text{where:}\\x=L-\dfrac{L_c}{2}\text{\ \ or\ \ }B-\dfrac{B_c}{2}
Critical section for bending in a footing


Other Considerations

Other than satisfying the limit state designs (strength checks) explained above, there are other factors which must be considered for the footing and slab-on-grade design:
  1. Soil condition - weaker soil tend to induce larger differential settlement and rotation in structure, reducing stability. This may require deeper embedment for a footing, or the use of engineering fill for a slab, or even a complete change of foundation structure. Chemical properties of the soil can affect the design of the footing and slab, hence geotechnical assessment is essential prior to design.
  2. Waterproofing - constant exposure to moisture causes hydrostatic pressure and continuous embedment in moist soil causes deterioration of the concrete surface. Typically, a waterproofing membrane is laid under the footing or slab to achieve watertightness. Ensure that there are sufficient drainage measures.
  3. Crack control and cover - minimum reinforcement must be met for serviceability design and to reduce cracking. Cover may need to be increased depending on how the footing or slab is cast (e.g. with formwork, against ground surface, pre-cast, etc.) and the soil classification.

References

  1. Australian Guidebook for Structural Engineers (2017) by Lonnie Pack
  2. Complete Analytical Solution for Linear Soil Pressure Distribution under Rigid Rectangular Spread Footings (2017) by J. Bellos and N. Bakas
  3. Design of Structural Elements by C. Arya.

Related Content

  1. Concrete Slab-on-Grade Designer to AS3600
  2. Rectangular Footing Designer to AS3600
  3. Foundation Bearing Failure Modes and Capacities
  4. Rectangular Spread Footing Design to ACI-384
  5. Concrete Slab-on-grade Calculator to ACI 360R-10
  6. Concrete Beam Design Calculator to AS3600

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