Mohr-Coulomb Failure Criterion

The Mohr-Coulomb Failure Criterion is a model that predicts when soil or rock will fail in shear based on normal stress, cohesion, and friction angle. In Intro to Civil Engineering, it shows up in soil mechanics for slopes, foundations, and earth pressure.

What is the Mohr-Coulomb Failure Criterion?

The Mohr-Coulomb Failure Criterion is the soil and rock strength model you use when you want to know when a material will start to fail by sliding along a surface in Intro to Civil Engineering. It says shear failure happens when the shear stress on a plane reaches a limit set by the normal stress, the material's cohesion, and its angle of internal friction.

A simple way to picture it is this: the more a soil sample is squeezed, the more shear force it can resist, but only up to a point. That relationship is often written as $\tau = c + \sigma' \tan \phi$, where $\tau$ is shear strength, $c$ is cohesion, $\sigma'$ is effective normal stress, and $\phi$ is the friction angle. The use of effective stress matters because water pressure in the pores can reduce the stress carried by the soil skeleton, which lowers shear strength.

On a graph, the criterion is shown as a straight failure envelope in shear stress versus normal stress space. Stress states below the line are safe, while stress states on the line are at failure. If a load pushes the soil state above that envelope, the material cannot keep resisting and failure occurs, often along a slip surface.

The model combines two real sources of resistance. Cohesion is the part of strength that does not depend much on normal stress, while friction is the part that increases as particles are pressed together. That is why dense sands, clays, and fractured rock can all be described with the same framework, even though the parameter values are very different.

In practice, civil engineering problems rarely use the criterion by itself. You pair it with stress calculations, effective stress ideas, and a factor of safety check to judge whether a slope, retaining wall, or foundation soil is likely to fail. The model is popular because it is simple enough for hand calculations, but still tied to real geotechnical behavior.

Why the Mohr-Coulomb Failure Criterion matters in Intro to Civil Engineering

This criterion sits right in the middle of soil mechanics because it turns raw stress data into a yes-or-no stability check. When you are looking at a slope, a footing, or a retaining wall, the big question is not just how much stress is in the ground, but whether that stress is enough to trigger shear failure.

It also connects several topics you see elsewhere in Intro to Civil Engineering. Effective stress tells you what part of the load is actually carried by the soil grains. Shear strength tells you how much resistance the soil has. Mohr-Coulomb gives you the line that separates those two from failure, so you can connect theory to a design decision.

A lot of class problems use this model in a very practical way. You might be given cohesion and friction angle, then asked to estimate whether a soil sample will fail under a certain normal stress. Or you may need to compare dry and saturated conditions and explain why added pore water pressure makes failure more likely. That makes it a useful bridge between formulas and real ground behavior.

It also shows up in design thinking. If the calculated stress state is close to the failure envelope, the soil needs more margin, better drainage, a flatter slope, or a different foundation approach. So even though the model is simplified, it is one of the main tools for turning geotechnical data into safer civil engineering choices.

How the Mohr-Coulomb Failure Criterion connects across the course

Shear Strength

Mohr-Coulomb is one way to describe shear strength, but shear strength is the broader idea. In soil mechanics, you use the criterion to estimate how much shear stress the ground can take before it slips. That lets you move from a general property of the soil to a specific failure check for a slope, footing, or retaining structure.

Effective Stress Principle

Effective stress is the stress that actually matters for frictional resistance in soil. If pore water pressure rises, effective normal stress drops, and the Mohr-Coulomb strength drops with it. That connection is why wet soils can become much less stable than the same soil under drained conditions.

Cohesion

Cohesion is the intercept in the Mohr-Coulomb equation, so it sets the shear strength when normal stress is low or zero. Some soils have real cohesion, while others seem cohesive because of moisture or structure. In class problems, separating cohesion from friction angle helps you see which part of strength comes from bonding and which comes from confinement.

Factor of Safety

Factor of Safety compares available strength to applied stress, so Mohr-Coulomb gives you the strength side of that ratio. If the stress state is too close to the failure envelope, the factor of safety shrinks. Civil engineering design often aims to keep the soil comfortably below failure, not just barely below it.

Is the Mohr-Coulomb Failure Criterion on the Intro to Civil Engineering exam?

A quiz question may give you cohesion, friction angle, and normal stress, then ask whether the soil fails or what its shear strength is. The move is to plug the values into the Mohr-Coulomb equation and compare the applied shear stress to the failure value. If the course gives you a stress plot, you may need to identify whether the point is below, on, or above the failure envelope. In short-answer questions, explain that higher effective normal stress increases shear resistance, while higher pore water pressure lowers it. On problem sets, this often shows up in slope stability or foundation checks where you decide whether the soil has enough strength for the load.

The Mohr-Coulomb Failure Criterion vs Effective Stress Principle

These are related, but they are not the same. The effective stress principle tells you how much stress the soil skeleton actually carries, while Mohr-Coulomb tells you how much shear stress the soil can resist before failing. You usually need effective stress first, then Mohr-Coulomb to judge failure.

Key things to remember about the Mohr-Coulomb Failure Criterion

• Mohr-Coulomb Failure Criterion predicts shear failure in soil and rock using normal stress, cohesion, and friction angle.

• The criterion is usually written as $\tau = c + \sigma' \tan \phi$, which means strength increases as effective normal stress increases.

• A failure envelope graph shows the boundary between safe stress states and failure.

• Water pressure matters because it lowers effective stress and can reduce shear strength even when total stress stays the same.

• In civil engineering, you use this model to judge slope stability, footing behavior, and other geotechnical problems.

Frequently asked questions about the Mohr-Coulomb Failure Criterion

What is Mohr-Coulomb Failure Criterion in Intro to Civil Engineering?

It is a soil and rock failure model that predicts when a material will fail in shear. The model links shear strength to effective normal stress, cohesion, and internal friction angle. In Intro to Civil Engineering, it usually appears in soil mechanics problems about stability.

How do you use the Mohr-Coulomb equation?

You use the soil parameters, usually cohesion and friction angle, along with the effective normal stress to find the shear strength. Then you compare that strength to the shear stress acting on the soil. If applied shear stress reaches the limit, failure is expected.

Is Mohr-Coulomb the same as shear strength?

Not exactly. Shear strength is the general resistance a material has against sliding, while Mohr-Coulomb is a specific model for estimating that resistance. The criterion is one common way civil engineers describe shear strength in soils and rocks.

Why does water change Mohr-Coulomb failure?

Water raises pore water pressure, which lowers effective stress. Since Mohr-Coulomb strength depends on effective normal stress, more pore pressure usually means less shear resistance. That is why saturated slopes and soils can fail more easily.