# FE EXAM – SOIL SHEAR STRENGTH

NCEES FE Civil Exam – 12. Geotechnical Engineering – F. Shear Strength

The strength of a material is the greatest stress it can sustain. If the stress exceeds the strength of the material, failure occurs. But we know not all materials behave the same, some materials will fail in tension (steel), some fail in compression (concrete), and some fail in shear (soils!).

This post is intended to help you understand what is meant by the shear strength of soils, factors that affect the shear strength, and ultimately provide you with the general concept needed to answer any NCEES FE Exam question related to soil shear strength.

### Engineering Applications

So what real-life engineering scenarios depend on the shear strength of soils? There are many!

• Earth Slopes
• Structural foundations
• Retaining Walls
• Tunnel linings
• Highway pavements

On top of that list, can you think of more?

Let’s look at how earth slopes and structural foundations fail due to insufficient shear strength supplied inherent in the underlying soil.

#### Earth Slopes

Typically an earth slope or “embankment” is inclined. The inclined surface produces a gravitational weight force that produces geostatic stresses in the soil. If these stresses exceed the shear strength of the underlying soil, a landslide failure will occur.

#### Structural Foundations

A foundation serves the purposes of taking loads from a building and transmits these loads to the ground. After the loads are transferred to the soil, compressive and shear stresses are induced into the soil.

If these shear stresses exceed the shear strength of the soil, shear failure is said to occur. This is also known as bearing capacity failure and can cause the structure to collapse.

### What gives soils shear strength?

So what factors create soil shear strength that ultimately allows soil particle to hold together?

Soil shear strength primarily depends on interactions between the particles, not their internal strength. This interaction can be divided into frictional strength and cohesive strength.

#### Frictional Strength

Frictional strength is similar to sliding friction developed usually expressed as $$\mu$$ in classical mechanics. But geotechnical engineers prefer to use the effective friction angle  $$\left(\phi^{\prime}\right)$$ instead of $$\mu$$.

The angle of Internal Friction can be determined in the laboratory by the Direct Shear Test.

#### Cohesive strength

Cohesive strength depends on “cohesion”. Cohesion is defined as the tendency of two particles to stick together. This sticking action depends on the surface area of the particles and is influenced by the amount of water present.

What soils have high, low, or no cohesion?

Typically for engineering design, we are working with inorganic soil. Inorganic soils will consist of:

• stones
• gravels
• sands
• silts
• clays

Cohesive soil and consists of clay and silt – these will have a $$c$$ values.

Cohesionless soil and consists of sand, gravel and stone – these will have no $$c$$ values ($$c$$ = 0).

### Mohr-Coulomb Failure Criteria

The failure criterion called the “Mohr-Coulomb Failure Envelope” accounts for the factors discussed above that make up the soil shear strength. Namely, the shear strength will consist of two components: frictional strength and cohesive strength. A similar figure is presented on page. 262 in FE Handbook 10.0.1

As shown by the failure envelope above, the shear stress at failure is given by the following equation,

$$\tau_{F}=c+\sigma_{N} \tan \phi$$ (pg. 263 FE Handbook 10.0.1.)

where,

$\begin{array}{l}c=\text { cohesion } \\\phi=\text { angle of internal friction }\end{array}$

$$\begin{array}{l} \sigma_{N}=\text { normal stress at failure } \end{array}$$

From the equation, we can conclude that $$c$$ and $$\phi$$ are the measures of soil shear strength. The higher the values, the higher the shear strength.

Let’s finish off by looking at how a soil element x is expected to fail due to induced stresses transferred to the ground through a structural foundation.

Based on the figure below, we can conclude that the soil element x under the foundation does not fail if the Mohr circle is contained within the envelope. Initially, the Mohr circle starts at $$\sigma_{\mathrm{c}}$$. As the loading progresses, the Mohr circle becomes larger. And finally, failure occurs when the Mohr circle touches the failure envelope line.

The following post is taken from our Civil FE Exam course for the afternoon topics. You can learn more about the course by following the link below.