# Stress and strain relationship in rocks

### Stress and Strain - Rock Deformation

Request PDF on ResearchGate | The stress-strain behaviour of rock material describes the relationship between the macro deformation of rock. PDF | The post-peak mechanical characteristic of rock mass plays a leading role in stability of geotechnical engineering. Based on Hoek-Brown. This page provides an introduction to stress-strain relationships. They form the foundation for several rock properties such as elastic moduli.

General stress can be decomposed into normal and tangential components Fig. We usually refer to balanced stresses because, under quasi-static conditions, they produce no net acceleration. In earth sciences and engineering, compressive stresses are usually considered positive, whereas most material sciences consider tensional stress positive. More details on the influence of stresses and the stress tensor can be found in Jeager and Cook [2] and Nye.

The stresses must be balanced so that there is no acceleration of the body. Standard stress conditions Several standard stress conditions are either assumed for analysis or modeling, or applied in the laboratory: Hydrostatic stress - all confining stresses are equal Uniaxial stress - one stress applied along a single axis other stresses are zero or held constant during an experiment Biaxial stress - two nonequal stresses applied third direction is equal to one of the others Triaxial stress - while this really represents three independent principal stresses, it is commonly used to represent separate vertical and two equal horizontal stresses e.

In contrast, increasing the pore pressure Pp tends to increase rock volume. Pp counteracts the effects of Pc. Thus, rock properties are controlled largely by the difference between Pc and Pp, or the differential pressure Pd. A more exact form will account for the interaction of the fluid pressure with the pore space and minerals and result in an effective stress Pe law Deformation, strain and modulus Application of a single vertical stress is one typical experiment run to measure material mechanical properties Fig.

If this stress continues to increase, eventually the material will fail when the uniaxial compressive strength is reached see Rock failure relationships. They also may have difficulty imagining the forces necessary to fold or fault rocks or comprehending that the seemingly constant Earth can change dramatically over time.

This is especially true of students who live in tectonically stable areas.

Stress Vs. Strain Diagram for Ductile Materials - Design of Machine

If students are to understand the basics of stress and strain, they must overcome this barrier since it will be difficult to examine the causes and conditions of deformation if students cannot comprehend deformation. It is often helpful to have students create analog models of the structures present in rock photos or hand samples. Here is a picture of a structure known as boudinage named after the French word for blood sausage - note the sausage-like structure.

What kind of rate of strain is necessary to produce something similar do you get the same result if you pull it apart quickly or more slowly? All of these conditions can be translated to rocks - rate at which it is strained, temperature, type of material, scale - and affect the types of structures that show up in the rock record.

In order to show students that rocks deform, pictures and hand samples of real faulted and folded rocks at a variety of scales can be used. Stress causes strain, strain results in structures Many geologists consider it important for introductory students to understand that visible structures are a record of the stress and physical conditions in the Earth.

As a result, the differences between stress, strain and structures formed during strain become key concepts. Hide Stress is a force acting on a rock per unit area.

### Seismology and Earthquakes

It has the same units as pressure, but also has a direction i. There are three types of stress: Stress can cause strain, if it is sufficient to overcome the strength of the object that is under stress.

Strain is a change in shape or size resulting from applied forces deformation.

Rocks only strain when placed under stress. Any rock can be strained. Strain can be elastic, brittle, or ductile. Ductile deformation is also called plastic deformation. Structures in geology are deformation features that result from permanent brittle or ductile strain.

Examples include folds and faults. Geologists use these features to identify the type of stress a rock experienced, as well as the conditions of stress it suffered or enjoyed, depending on your point of view. Students can experiment with types of stress and rates of strain necessary to make analogs break or bend.

Alternatively, they can use structures in the analog to infer stresses and strain rates after the "structure" is created.

## Stress and Strain

See Rocks deform above for an example of having students create boudins. Stress, strain and structure start with the same three letters, yet mean very different things. These words are also used differently in geology than in common usage in English, which can cause confusion. However, here are some tricks that I use to remember: Stress is the same as pressure.

When you are under pressure, you are stressed! Stress can happen with out strain, but strain cannot happen without stress. Look at this rock I am squeezing in my hand.

• Seismology and Earthquakes
• Stress strain relationships in rocks
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Yes, it is under pressure. No, it hasn't changed shape. Now look at this rock with a fold in it. Is it under stress?

No, it is not under pressure. No, it isn't currently changing shape. Does it have structure? Yes, there is a fold. Analogs, however, are difficult to scale appropriately both in time and space to the gigantic scale on which geologic structures form.

Students may still have difficulty understanding the tremendous scale of forces needed to bend or break rock and the long time scales involved to generate structures. Make sure that you make it clear to your students that these pitfalls exist. More detailed ideas for analogs are available at Teaching Structural Geology analog materials web page.

Once students have mastered the connections among stress, strain and structure, I develop a 3 x 2 table of different structures that form under differing stress and strain conditions. I then proceed to fill out the table with students' help.

Let's look at what features are found under different stress conditions and with different styles of strain. We'll do this by making a table. What are the three types of stress?

Compression, tension, and shearing. Now, what are the 2 types of permanent deformation? Let's make a table that is three columns by two rows and fill it in with appropriate structures!