Critical State of Soil

This is a relatively new (in comparison to many decades old of soil mechanics theories) but very useful concept in soil mechanics. It is a topic that is analysed in advanced soil mechanics courses only, in masters level classes, but it doesn’t prevent us from at least describing it, as it is good to know what it is.

In previous sections, we have seen shear strength and volume relations of soil separately, such as the

  • τ – σ’ graph, such as in figures soil strength 9a, 11, 12, when we talked about shear stress,


  • e vs. log σ’ graph such as in figures soil strength 23a, b, when talking about consolidation and volume change.

Critical state theory goes one step further than each of these two separately and unifies both of these relations. It provides a unified model of soil behaviour, where stress and volume states in soil are related to each other.

So it is as if combining these two separate graphs in 3D.

For example, to the τ – σ’ graph, which is of course a 2D graph, think about adding a third dimension in perpendicular, making it 3D, and naming that third dimension for volume. This is how critical state theory relates all these basically.

We can see a typical critical state graph below:

Soil strength 27

The new graph’s three axes can also be  called as p’,q’ and v for convenience of drawing easier, which are parameters directly derived from the τ – σ’ and e vs. log σ’ relations, that we already know about.

The critical state is a unique characteristic of material, in other words, it doesn’t depend on the degree of saturation or current state of compaction of soil. Previously we mentioned that the void ratio after critical state is reached, is called critical void ratio and it is a characteristic, in other words, unique property of that material. For example the same soil loose or dense with different void ratios, will always try to get towards its critical state void ratio (as was shown in figure soil strength 9b before). The 3D critical state graph has similar logic to this. There is only one critical state graph (which is a curved line in 3D space) for a certain material, if you were to draw a 3D graph with these three axes of p,q,v, which are directly derived from τ, σ’ and v, the ones we saw before. That curved 3D line is a unique characteristic, in other words, a fingerprint of that soil. The same soil, if too loose or too dense, will always ultimately try to approach towards that line. The critical state may shift however, depending on a material is whether normally consolidated or overconsolidated. As we said under the section for consolidation, overconsolidated soils behave differently than normally consolidated soils. The discussion of why this is so, is way beyond this book’s scope.

And with this, we conclude the longest and the most fundamental two sections of this book, structural basics and soil strength…. A non-engineer who read up to here attentively, should have gained a lot of insight, into the most fundamental and most widely used concepts of civil engineering. Yes we still have not talked about transportation, water resources and construction management, but these concepts are applicable to more things than any other topics in civil engineering. These were basically the ABC of civil engineering. And we hope that for our engineer readers, who know very well what we mean by this, even up to this point, there was still a lot of useful details or at least refresher information.

Now let’s move on to other topics in soil mechanics first, and then we will keep introducing other subjects in civil engineering….   

In the next post of this series, we will discuss “Subsurface Investigation” Go back to Index Page

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