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Direct shear on loose and dense sand graphs

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.

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.

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.
 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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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