---
title: "Direct shear on loose and dense sand graphs"
subject: "Soil Mechanics"
chapter: 10
key: "semester_4/soil_mechanics:direct-shear-sand-graphs"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/direct-shear-sand-graphs
site: BCT Engineering
---

# Direct shear on loose and dense sand graphs

Soil Mechanics · Chapter 10: Shear Strength of Soil

- Asked in: 2074 Bhadra, 2 marks
- Video: [Direct Shear Test | Elementary Engineering](https://www.youtube.com/watch?v=1Cwyuu7ve90) — Elementary Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/direct-shear-sand-graphs
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-10

## Question

If a direct shear test is conducted for loose and dense sands, then plot the graphs of shear stress and change in height of specimen versus shear displacement.

## Short answer

Dense sand shows a peak shear stress then drops to residual, and dilates (height increases). Loose sand shows a gradual rise to a constant strength and contracts (height decreases). Both reach the same ultimate strength at large strains.

## Answer

In a drained direct shear test on sand under a constant normal stress:

- **Dense sand** shows a distinct peak shear stress at small displacement, then drops to a lower (residual or ultimate) value. It first contracts slightly and then **dilates** (expands), so the height of the specimen increases.
- **Loose sand** shows shear stress rising gradually to a maximum without a peak, and then staying nearly constant. It **contracts** continuously, so the specimen height decreases.

```text
 Shear stress
 tau
  |      ,-.
  |    ,'   `--.__  dense (peak, then drops)
  |   /     .-----------  loose (gradual rise)
  |  / ..-''
  | /.'
  +-------------------- shear displacement
              Both reach about the same
              ultimate value (same phi_cv)

 Change in height (expansion up)
  dH
  |            ___ dense (dilates)
  |         ,-'
  |  ___.--'
  +----`.__----------- shear displacement
  |       `-.__ loose (contracts)
  |
```

The peak friction angle of dense sand is greater than that of loose sand, but both reach the same ultimate (critical state) strength at large strains.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does shear stress behave for dense sand in direct shear?
   A. Gradual rise to a maximum with no peak
   B. Continuous decrease from the start
   C. Constant from the start
   D. A distinct peak at small displacement, then a drop to a lower ultimate value
   Answer: D. Interlocking in dense sand gives a peak that falls to the ultimate strength as the sand dilates. (Key point: Dense sand stress)

2. What volume change happens in loose vs dense sand during shear?
   A. Loose sand dilates; dense sand contracts
   B. Both dilate continuously
   C. Loose sand contracts; dense sand contracts slightly then dilates
   D. Neither changes volume
   Answer: C. Loose sand compacts (height decreases); dense sand dilates (height increases) after a small initial contraction. (Key point: Volume change)

3. At large strains how do the two sands compare?
   A. Dense sand stays much stronger
   B. Both reach about the same ultimate (critical state) strength
   C. Loose sand is stronger
   D. Both drop to zero strength
   Answer: B. Peak friction angle is higher for dense sand, but at large strain both reach the same phi_cv. (Key point: Ultimate strength)

## Related in Soil Mechanics

- [Limitations of direct shear test](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adirect-shear-limitations) — Soil Mechanics, chapter 10
- [Two-layer sand, plot stresses (bulk 18)](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Atwo-layer-sand-stress-plot) — Soil Mechanics, chapter 6
- [Shear tests; direct shear calculation](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Ashear-tests-direct-shear-strength-calc) — Soil Mechanics, chapter 10
- [Triaxial advantage over direct shear](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Atriaxial-advantages-over-direct-shear) — Soil Mechanics, chapter 10
- [Draw UCS and direct shear results](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aucs-direct-shear-results-plot) — Soil Mechanics, chapter 10
- [Shear strength of sand, WT rises](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asand-shear-strength-water-rise) — Soil Mechanics, chapter 10

## Related in other subjects

- [Stress on oblique section with direct and shear stress](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aoblique-section-stress-derive) — Strength of Materials, chapter 4
- [Shear stress, displacement thickness, drag on plate](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aflat-plate-shear-displacement-drag) — Fluid Mechanics, chapter 8
- [SPT corrected N-value, dense sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aspt-dilatancy-20m) — Foundation Engineering, chapter 2
- [Tensile test numerical, 40 mm specimen](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Anumerical-tensile-test-40mm) — Civil Engineering Materials, chapter 1