1. Continuum Mechanics for Hillslopes: Part II
Focus on fluids today.
Strain and deformation next week.
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2. Pore Water, Hydraulic Head and Pore-Water Pressure
Hydraulic head (h):
a measure of the energy in a fluid filled, porous medium
Pore-water potential, per unit weight of fluid (negligable kenitic energy)
ψ : Gravitational potential
Pressure potential (p is gage pressure relative to atmos., isotropic: ‘pore water pressure’)
f( depth below water table, proportion of soil weight carried by contacts between grains)
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3. Elevated PWP decreases soil strength
Pore water pressure (PWP) is hydrostatic if just due to weight of water above.
Hydrodynamic conditions allow PWP to be > or < hydrostatic due to compaction or dilation
Elevated PWP decreases soil strength
Liquefaction is when the fluid supports the weight of the grains
Capillary/electrostatic forces strengthen unsaturated soils (more so for fine-grained soils)
0 = pA y p
Negative pore water pressures
due to tensional capillary forces
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4. Effective Stress
(note that normal stresses are negative in compression and pore-fluid pressure is positive in compression.)
Total state of stress is a function of :
-stresses that act on the skeleton of solid material
-pressure of the pore fluid
are the effective stresses acting on the solid skeleton the total stresses acting on the porous medium the pore-fluid pressure
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5. Effective Stress
Note regarding the first diagram: through the image shows all the effective
stresses as equal, they are in reality all different as the total stress is not
uniformly distributed throughout the granular matrix. Some grains bear
more of the total stress than others. The term for the effective stress,
is a mean value for the continuum.
As the second image shows, stress in granular solids is partitioned along
‘chains’ of non-uniformly high stress that support loads.
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6. Terzaghi’s 1943 experiment demonstrating effective stress
clay
clay
clay
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7. Terzaghi’s 1943 experiment demonstrating effective stress
Results:
an increase in total stress does not produce consolidation!
-Adding water increases both the total stress and the pore pressure equally, not changing the effective stress
-Increases pore pressure throughout the clay and at its surface
-Increasing the depth of fluid produces no consolidation
-Same is true for compression of clay with impermeable plunger.
clay
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Remember: Total Stress = effective stress + pore pressure

8. Terzaghi’s 1943 experiment demonstrating effective stress
Results:
an increase in total stress does not produce consolidation!
-Shot is partially supported by buoyancy and clay grain framework
-Over time, pore pressure increases above hydrostatic ,but water is expelled upward through permeable layer and the clay is consolidated and takes the weight of the lead.
-Lead increased total stress without increasing pore pressure, thus effective stress increased.
clay
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9. Effective stress Remember: In porus media,
the measureable effects from changes in stress
(such as volume change or distortion)
are due exclusively to changes in effective stress
If there is no change in effective stress, there is not change in the material.
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10. Consolidation of a saturated sediment slurry
Saturated, stable soil.
Hydrostatic fluid pressure
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11. Consolidation of a saturated sediment slurry
Saturated, stable soil.
Total Stress (- in compression):
(n = porosity)
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12. Consolidation of a saturated sediment slurry
Saturated, stable soil.
Total Stress (after substitution):
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13. Consolidation of a saturated sediment slurry
Now add more saturated sediment to the top of the deposit.
Pore water pressure increases as particles adjust.
(excess
water
pressure)
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14. Consolidation of a saturated sediment slurry
(Fluid pressure
exceeding hydrostatic)
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15. Consolidation of a saturated sediment slurry
Effective
intergranular
stress
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16. Consolidation of a saturated sediment slurry
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