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Rock mass plasticity

Rock mass plasticity is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Rock mass plasticity rather than just read about it. In short: In geotechnical engineering, rock mass plasticity is the study of the response of rocks to loads beyond the elastic limit. Historically, conventional wisdom has it that rock is brittle and fails by fracture, while plasticity (irreversible deformation without fracture) is identified with ductile materials such as metals.

Rock mass plasticity — main illustration
Rock mass plasticity — illustration

Key takeaways

  • Rock mass plasticity belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Rock mass plasticity to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Rock mass plasticity from memory before moving on to harder problems.

Reference excerpt

In geotechnical engineering, rock mass plasticity is the study of the response of rocks to loads beyond the elastic limit. Historically, conventional wisdom has it that rock is brittle and fails by fracture, while plasticity (irreversible deformation without fracture) is identified with ductile materials such as metals. In field-scale rock masses, structural discontinuities exist in the rock indicating that failure has taken place. Since the rock has not fallen apart, contrary to expectation of brittle behavior, clearly elasticity theory is not the last word. Theoretically, the concept of rock plasticity is based on soil plasticity which is different from metal plasticity. In metal plasticity, for example in steel, the size of a dislocation is sub-grain size while for soil it is the relative movement of microscopic grains. The theory of soil plasticity was developed in the 1960s at Rice University to provide for inelastic effects not observed in metals. Typical behaviors observed in rocks include strain softening, perfect plasticity, and work hardening. Application of continuum theory is possible in jointed rocks because of the continuity of tractions across joints even through displacements may be discontinuous. The difference between an aggregate with joints and a continuous solid is in the type of constitutive law and the values of constitutive parameters.

Experimental evidence Experiments are usually carried out with the intention of characterizing the mechanical behavior of rock in terms of rock strength. The strength is the limit to elastic behavior and delineates the regions where plasticity theory is applicable. Laboratory tests for characterizing rock plasticity fall into four overlapping categories: confining pressure tests, pore pressure or effective stress tests, temperature-dependent tests, and strain rate-dependent tests. Plastic behavior has been observed in rocks using all these techniques since the early 1900s. The Boudinage experiments show that localized plasticity is observed in certain rock specimens that have failed in shear. Other examples of rock displaying plasticity can be seen in the work of Cheatham and Gnirk. Test using compression and tension show necking of rock specimens while tests using wedge penetration show lip formation. The tests carried out by Robertson show plasticity occurring at high confining pressures. Similar results are observable in the experimental work carried out by Handin and Hager, Paterson, and Mogi. From these results it appears that the transition from elastic to plastic behavior may also indicate the transition from softening to hardening. More evidence is presented by Robinson and Schwartz. It is observed that the higher the confining pressure, the greater the ductility observed. However, the strain to rupture remains roughly the same at around 1. The effect of temperature on rock plasticity has been explored by several teams of researchers. It is observed that the peak stress decreases with temperature. Extension tests (with confining pressure greater than the compressive stress) show that the intermediate principal stress as well as the strain rate has an effect on the strength. The experiments on the effect of strain rate by Serdengecti and Boozer show that increasing the strain rate makes rock stronger but also makes it appear more brittle. Thus dynamic loading may actually cause the strength of the rock to increase substantially. Increase in temperature appears to increase the rate effect in the plastic behavior of rocks. After these early explorations in the plastic behavior of rocks, a significant amount of research has been carried out on the subject, primarily by the petroleum industry. From the accumulated evidence, it is clear that rock does exhibit remarkable plasticity under certain conditions and the application of a plasticity theory to rock is appropriate.

Governing equations The equations that govern the deformation of jointed rocks are the same as those used to describe the motion of a continuum:

… excerpt ends here. Continue reading the full article.

Illustrations

Rock mass plasticity: Boudinaged quartz vein (with strain fringe) showing sinistral shear sense, Starlight Pit, Fortnum Gold Mine, Western Australia
Boudinaged quartz vein (with strain fringe) showing sinistral shear sense, Starlight Pit, Fortnum Gold Mine, Western Australia
Rock mass plasticity: Stress-strain curve showing typical plastic behavior of rocks in uniaxial compression. The strain can be decomposed into a recoverable elastic strain ( ε e {\displaystyle \varepsilon _{e}} ) and an inelastic strain ( ε p {\displaystyle \varepsilon _{p}} ). The stress at initial yield is σ 0 {\displaystyle \sigma _{0}} . For strain hardening rocks (as shown in the figure) the yield stress increases with increasing plastic deformation to a value of σ y {\displaystyle \sigma _{y}} .
Stress-strain curve showing typical plastic behavior of rocks in uniaxial compression. The strain can be decomposed into a recoverable elastic strain ( ε e {\displaystyle \varepsilon _{e}} ) and an inelastic strain ( ε p {\displaystyle \varepsilon _{p}} ). The stress at initial yield is σ 0 {\displaystyle \sigma _{0}} . For strain hardening rocks (as shown in the figure) the yield stress increases with increasing plastic deformation to a value of σ y {\displaystyle \sigma _{y}} .
Rock mass plasticity: View of Mohr–Coulomb failure surface in 3D space of principal stresses for c = 2 , ϕ = − 20 ∘ {\displaystyle c=2,\phi =-20^{\circ }}
View of Mohr–Coulomb failure surface in 3D space of principal stresses for c = 2 , ϕ = − 20 ∘ {\displaystyle c=2,\phi =-20^{\circ }}
Rock mass plasticity: View of Drucker–Prager yield surface in 3D space of principal stresses for c = 2 , ϕ = − 20 ∘ {\displaystyle c=2,\phi =-20^{\circ }}
View of Drucker–Prager yield surface in 3D space of principal stresses for c = 2 , ϕ = − 20 ∘ {\displaystyle c=2,\phi =-20^{\circ }}

Worked examples

Example 1 — a first encounter with Rock mass plasticity

Start with the simplest possible case. Write down what Rock mass plasticity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rock mass plasticity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rock mass plasticity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rock mass plasticity

In research
Rock mass plasticity appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Rock mass plasticity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Rock mass plasticity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Continuum mechanics, Plasticity (physics), Rock mechanics, so understanding it makes those chapters shorter.
In everyday life
Look for Rock mass plasticity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Rock mass plasticity in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Rock mass plasticity means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Rock mass plasticity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rock mass plasticity in simple terms?

In geotechnical engineering, rock mass plasticity is the study of the response of rocks to loads beyond the elastic limit. Historically, conventional wisdom has it that rock is brittle and fails by fracture, while plasticity (irreversible deformation without fracture) is identified with ductile mat…

Why does Rock mass plasticity matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rock mass plasticity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rock mass plasticity.

Tags

  • Continuum mechanics
  • Plasticity (physics)
  • Rock mechanics

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