The Brinch Hansen bearing capacity equation is the most commonly applied method of calculating the allowable bearing capacity of soil in Europe. The Hansen bearing capacity equation is an extension of the Terzaghi method which includes foundations on slopes and other conditions not considered in the Terzaghi method.
The Brinch Hansen bearing capacity equation is included in the CivilWeb Soil Bearing Capacity Calculation Excel Suite which includes a total of 6 different analytical methods. This spreadsheet suite can be purchased at the bottom of this page for only £20. Alternatively the full Foundation Design Suite including all 12 foundation design spreadsheets can be purchased for just £50.
Brinch Hansen Bearing Capacity Equation
Brinch Hansen extended the work of Meyerhof to include for any tilting of the base of the foundation and a new formula for foundations on slopes. Hansen also derived a new formula for the bearing capacity factor Nγ.
The Brinch Hansen bearing capacity equations are presented below. These take the same form as the Terzaghi or Meyerhof equations but the equation for the bearing capacity factor Nγ is different and additional factors are present. Further information on the Terzaghi method can be found in our Terzaghi Bearing Capacity article. The Terzaghi method is also included in the CivilWeb Soil Bearing Capacity Calculation Excel Suite.
Brinch Hansen Bearing Capacity Factors
As with other bearing capacity analysis methods, the bearing capacity factors have been converted to graphs and tables to assist with the calculations. Some examples are included below.
Hansen Bearing Capacity Equation - Smooth Foundation Bases
Brinch Hansen also included analysis of the bearing capacity factors for smooth foundations which limit the friction between the base of the foundation and the underlying soils. This is not a common condition as foundations poured insitu will have a rough base. However this can be required in some cases such as where pre-cast concrete foundations are used for example in cold climates where the foundations cannot be poured insitu.
The below graph shows the Brinch Hansen bearing capacity factor Nγ in relation to the soil angle of internal friction and the friction between the base and the soil.
Brinch Hansen Bearing Capacity Equation - Modification Factors
Like other bearing capacity analysis methods the Brinch Hansen method uses a number of modification factors to adjust the results to suit certain design conditions. In the Hansen bearing capacity equation these modification factors are;
Shape Factor – To modify for different foundation shapes
Depth Factor – To modify for foundation depth
Inclination Factor – To modify for inclined loads
Slope Factor – To modify for foundations on slopes
Tilted Base Factor – To modify for tilted or non-horizontal bases
The modification factors are presented below with a diagram on the following page.
The Hansen bearing capacity equation therefore expands on the Meyerhof method to include for conditions where the base of the foundation is not horizontal and where the foundation is on a slope. This increases the usefulness of this method. Further information on the Meyerhof method can be found in our Meyerhof Bearing Capacity article. The Meyerhof method is also included in the CivilWeb Soil Bearing Capacity Calculation Excel Suite.
Hansen uses a value for α1 and α2 as 5 which is conservative.
Hansen Bearing Capacity Equation -Discussion
The Brinch Hansen bearing capacity equation has been used for many years. In Europe the Brinch Hansen method has been generally preferred to the Meyerhof method which has been preferred in North America. However the recommendations in the latest Eurocode do deviate from the Brinch Hansen bearing capacity equation, particularly with regard to the calculation of the bearing capacity factor Nγ with the Eurocode following the higher values commonly used in German practice. The Eurocode also removes the depth modification factors as these have been found to be unreliable. Further details of the Eurocode 7 method can be found in our Eurocode 7 Bearing Capacity article. The Eurocode7 method is also included in the CivilWeb Soil Bearing Capacity Calculation Excel Suite.
CivilWeb Soil Bearing Capacity Calculation Excel Suite
The CivilWeb Soil Bearing Capacity Calculation Excel Suite includes a spreadsheet which can be used to complete a full Hansen bearing capacity equation analysis. The spreadsheet also includes unique comparison tools allowing the designer to instantly see the results from 5 other methods for comparison with the Brinch Hansen bearing capacity equation. This will save the designer hours of work on every bearing capacity analysis and ensure that the most appropriate result is used every time.
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