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Modulus of Subgrade Reaction | Representative of Soil

We need familiar with the concept of modulus of subgrade reaction, which is used to measure the soil’s stiffness or resistance against deformation due to applied loads. This article aims to provide an in-depth exploration of the concept of modulus of subgrade reaction, with a particular focus on its application in civil engineering.

Through this article, we will better understand the factors that affect the modulus of subgrade reaction and the benefits of including this knowledge in civil engineering solutions.

What is the Modulus of the Subgrade Reaction

It is the parameter used to represent the soil in geotechnical modeling and analysis. The soil stiffness is represented by the form of values related to each soil condition.

Further, subgrade reaction can also be considered as the representation of the soil-bearing capacity.

There are many methods to calculate the modulus of the subgrade reaction of the soil. Relationships with the soil bearing capacity, standard penetration value (SPT), cone penetration values (CPT), etc. can be correlated to find the modulus.

In addition, there is a testing method that can be used to calculate the modulus. The most common test is the plate load test.

plate load test

The following equation is the basic equation to represent the modulus of the subgrade reaction.

Subgrade Reaction = Soil Pressure / Soil Settlement

ks = q / s

The empirical equation proposed by the different researchers is also available.

The following table indicates some of the empirical methods used to calculate the subgrade reaction.

Modulus of subgrade reaction.png

There are other simple empirical relationships also to calculate the subgrade reaction.

According to the book Bowels Foundation Analysis and Design Book, we can use the following method.

ks = 40 x [Factor] [Allowable Bearing Capacity]


  • Factor – safety factor used to calculate the allowable bearing capacity. In this calculation, consider the factor in the range of 2-3.
  • The number “40” is for 25mm settlement [1000/25 = 40 – with the unit conversion]. When the settlement is higher, this value can be adjusted accordingly.

Example: Soil allowable bearing capacity 150 kN/m2

Subgrade reaction = 40 x 3 x 150 = 18,000 kN/m2 /m

Factors Affecting Modulus of Subgrade Reaction

One of the main factors that affect the subgrade reaction is the soil type. Different soils have different stiffnesses, which will in turn affect the subgrade modulus.

For example, clay soils are generally much stiffer than sandy soils. This is because clay particles are much smaller than sand particles, and thus can resist deformation better. Another important factor is the compaction of the soil. More densely packed soils will have a higher subgrade reaction than less densely packed soils. This is because there is less space for the soil to deform when under load.

The benefits of understanding the modulus of subgrade reaction are many.

First, it can be used to design foundations that are better able to resist settlement.

Second, a better understanding of the subgrade reaction can help engineers to better predict the behavior of soils under load, and to design accordingly.

Finally, by understanding the subgrade modulus, civil engineers can develop better models to simulate the behavior of soils and to test proposed solutions before they are implemented.

In conclusion, the modulus of subgrade reaction is an important concept for civil engineers to understand, as it can have a significant impact on the design of the foundation and the prediction of soil behavior.

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