The bearing capacity of soil is its ability to resist shear failure and excessive settlement under bearing pressures from foundations.

The bearing capacity of shallow foundations on soil is mainly dependent on the following factors:

• Width of bearing area (B)
• Length of bearing area (L)
• Soil cohesion (c’)
• Soil internal friction angle (φ)
• Soil unit weight (γ)
• Load inclination or moments applied to structure
• Inclination of base or of ground
• Water table presence

A foundation is the structural element that transfers the load of a building or structure to the ground, ensuring stability and preventing excessive settlement, tilting, or collapse.

Foundations can be broadly categorized into shallow and deep types, depending on the depth at which they are placed relative to the ground surface and the method of load transfer. You can read about different types of foundations in this post.

The bearing capacity theory discussed on this page is particularly for shallow foundations. According to Terzaghi, shallow foundations are those where the depth beneath the soil surface of the footing is less than or equal to its width. Other investigations have suggested that foundations with a depth of 3 to 4 times the width of the foundation may also be considered to be shallow (DAS).

The ultimate bearing capacity of soil is the bearing pressure it can withstand before failure without the consideration of any factors of safety.

Over the years several different methods have been developed for calculating bearing capacity. These methods are based on testing and as time has passed more parameters have been added to the general bearing capacity equation to account for effects that may reduce or increase the bearing capacity of a foundation.

Since these are all estimation methods of a soil bearing capacity none is necessarily right or wrong and they are all useful to review in bearing capacity calculations. In instances where there are load inclinations or inclinations in the base of the structure, it may be more suitable to use a method that can account for reductions due to these effects.

The most common bearing capacity methods that can be used to estimate the bearing capacity are:

• Terzaghi
• Meyerhoff
• Hansen
• Vesic

Finite element analysis can also be an appropriate tool to estimate the bearing capacity of soil however constructing such a model often requires a lot of additional parameters such as the soil Young's Modulus and Poisson's Ratio and requires a lot of time to analyze compared to analytical methods.

To compare the different methods and their sensitivity to a certain parameter we can conduct a sensitivity analysis. For example in the graph below the bearing capacity is compared for different friction values so that we can see how sensitive each method is to the parameter. Based on the graph we can then choose which value is most appropriate for the ultimate bearing capacity.

The Terzaghi Bearing Capacity theory was the first comprehensive theory for calculating the bearing capacity of shallow foundations and is still widely used today.

Terzaghi’s formula calculates the ultimate bearing capacity (qu) of a foundation, incorporating soil strength parameters such as cohesion, unit weight, and the angle of internal friction. The general equation for a strip footing is:

• q_u=c N_c+q N_q+0.5 γ B N_γ

where:

• c is the cohesion of the soil,
• q is the overburden pressure or surcharge at the foundation level,
• γ is the unit weight of the soil,
• B is the width of the foundation,
• N_c, N_q, and N_γ are the bearing capacity factors that depend on the soil’s friction angle (ϕ).

Using Terzaghi’s theory let us consider the following foundation details:

• Foundation width is 0.5 m
• Soil base is sand with a cohesion of 0 kPa, friction angle of 30 degrees and unit weight of 18 kN/m3
• Foundation depth is 0 m

First, we can look up a table to get Terzaghi’s bearing capacity factors for an internal friction angle of 30 degrees. From this, we get that Nc = 37.16, Nq = 22.46 and Nγ = 19.13.

We can then plug our values into the bearing capacity equation

qu=0 * 37.16 + 0 * 22.46 +0.5 * 18 * 0.5 * 19.13 = 86 kPa

We can perform this calculation a lot faster with the SkyCiv Bearing Capacity Calculator since we won't have to look up any values from tables or combine the values ourselves. This is more true with the other methods for bearing capacity such as the Meyerhof bearing capacity which has additional parameters.

One of the easiest ways to increase the bearing capacity of a footing is the increase the base dimensions to better distribute loading.

Doubling a footing width can double the bearing capacity but at the same time also means that any point load is spread over a larger area, thereby decreasing the bearing pressure exerted by the structure. So increasing a footing width by a factor of 2 can result in a 4x utilization benefit.

Other common methods to increase the bearing capacity can involve:

• Removing unsuitable material from the foundation and placing engineered fill (can increase material properties and reduce uncertainty in material parameters)
• Setting footing lower into the ground (weight of adjacent soil helps resist bearing failure)
• Leveling ground if uneven (can remove reduction factors required for uneven ground)
• Using a roller to compact material beneath a foundation (can increase material properties)

Another appropriate solution could be to use the SkyCiv Bearing Capacity Calculator which does not take a conservative approach in calculations but rather calculates the bearing capacity with a high accuracy. By allowing users to assess different bearing capacity methods and design methods the designer can choose the least conservative appropriate method.

The ultimate bearing capacity should be reduced to account for variability in the soil strength. Depending on the standard this reduction may be applied by either using a single geotechnical reduction factor (AS 5100, Eurocode 7 DA2) or by reducing different soil factors separately and using these to calculate the bearing capacity (AS 4678, Eurocode 7 DA1-2, DA3). This is the design bearing capacity.

Loads are then factored in accordance with design standards to be compared with the design bearing capacity.

The design bearing capacity is used in limit state design (LSD) or load and resistance factor design (LRFD).

The calculations for the design bearing capacity are dependent on the standard being used.

Where material reduction factors are used (AS 4678, Eurocode 7 DA1-2, DA3) these are applied to the soil parameters first before any other calculations have taken place. The design bearing capacity can then be calculated with methods such as Terzaghi's bearing capacity calculations.

Alternatively, if material reduction factors are 1 and we have a single factor to reduce our bearing capacity by we can simply calculate the ultimate bearing capacity and multiply it by our geotechnical reduction factor (AS 5100) or divide it by our partial factor of safety (EC7 DA2).

Let us take the unfactored properties from our previous example with a c' = 0 kPa, φ' = 30 degrees and γ = 18 kN/m3 and calculate the design bearing capacity based on the following partial safety factors as defined by M2 of EC7:

• γ_φ' = 1.25
• γ_c' = 1.40
• γ_γ = 1.00

We can calculate our design soil properties as c' = 0 kPa, φ' = 30 degrees and γ = 18 kN/m3

• φ' = tan-1( tan(30) / 1.25) = 24.8 degrees
• c' = 0 * 1.40 = 0 kPa
• γ = 1.00 * 18 = 18 kN/m3

We can then look up Terzaghi’s bearing capacity factors for an internal friction angle of 24.8 degrees. From this we get that Nc = 24.75, Nq = 12.43 and Nγ = 9.46.

We can then plug our values into the bearing capacity equation

• q_d = 0 * 24.75 + 0 * 12.43 +0.5 * 18 * 0.5 * 9.46 = 42.6 kPa

If we instead had no material reduction factors but rather a single factor to reduce our bearing capacity we would calculate the ultimate bearing capacity of 86 kPa first as we did previously.

For the AS 5100.3 calculation, we could then multiply by our geotechnical reduction factor φg . For example, if we had a geotechnical reduction factor of 0.5 we would get a design bearing capacity as:

• q_d = φ_g * q_u = 0.5 * 86 = 43 kPa

For the EC7 DA2 calculation, we would take our ultimate bearing capacity and divide it by our partial reduction factor γRv. If we take the R2 partial factor of 1.4 our calculation would become:

• q_d = q_u / γ_Rv = 86 / 1.4 = 61.4 kPa

The design bearing capacities would all need to be compared to the design load combination bearing pressure for the respective load combinations required by the standard. We can not tell which of these design methods is more critical purely based on the design bearing capacity since we have not yet considered our load factors.

The allowable bearing capacity refers to the ultimate bearing capacity reduced by some factor of safety when using an ASD (allowable stress design) approach rather than an LRFD approach.

The allowable bearing capacity is specified about serviceability or working loads rather than factored loads. Since it is accounting for both the variability of loading as well as the variability of material strength it will typically be lower than the design bearing capacity produced by LRFD design methods.

For example, a footing with a working pressure of 100 kPa will have sufficient bearing capacity if the soil has an allowable bearing capacity not less than 100 kPa.

To calculate the allowable bearing capacity we simply reduce the ultimate bearing capacity by our factor of safety. This factor of safety is variable in different standards and guidelines but generally ranges from a value of 2 to 3.

If we take the previous ultimate bearing capacity of 86 kPa that we calculated and also consider a factor of safety of 2 then our allowable bearing capacity would be 86 / 2 = 43 kPa. This is assuming that we do not need to factor down our material properties. In Eurocode 7 for design approach 2 for example we would not need to factor down material strengths and we would reduce the ultimate bearing capacity by a factor of 1.4.

• ACI Strip Footing Design
• ACI Spread Footing Design

• SkyCiv Foundation Design Software
• SkyCiv Isolated Footings Introduction

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