CIVL2410 Chap.10 Total stress, pore water pressure and effective stress
Total stress, pore water pressure and effective stress
Stress controls deformation, strength and stability, but which stress? A saturated soil element carries load in two parallel systems: the pore water, which can push but cannot resist shear, and the grain skeleton, which does both. Only the second responds to load in any way an engineer cares about.
This chapter separates them, which is the single idea the second half of the unit is built on, and it is where most Module 3 questions begin.
What this chapter covers
- 01
Total vertical stress as a sum over layers, plus any surcharge
- 02
Choosing the bulk or the saturated unit weight for each layer
- 03
Splitting a layer that straddles the water table
- 04
Hydrostatic pore pressure below a static water table
- 05
Pore pressure under seepage, taken from a flow net
- 06
Terzaghi's effective stress principle, and why it applies on every plane
- 07
Why pore water subtracts equally from all normal stresses and leaves shear untouched
- 08
The partially saturated form, and why this unit works saturated
- 09
Zero effective stress: quicksand, piping and liquefaction as one limit
- 10
Capillary rise, negative pore pressure and why damp sand stands up
- 11
Drained and undrained loading, and the two things that decide which applies
Building a stress profile at two depths
- +1At 4.0 m the point lies 1.5 m into the saturated sand, so the total stress is 2.5 x 17.5 + 1.5 x 20.2 = 43.75 + 30.3 = 74.1 kPa.
- +1It sits 1.5 m below the water table, so u = 1.5 x 9.81 = 14.7 kPa, and the effective stress is 59.4 kPa.
- +2At 9.0 m add the rest of the sand and 3.0 m of clay: 43.75 + 3.5 x 20.2 + 3.0 x 18.6 = 170.3 kPa.
- +1The point is 6.5 m below the water table, so u = 6.5 x 9.81 = 63.8 kPa, giving an effective stress of 106.5 kPa.
- +1Check by the submerged route: 43.75 + 3.5 x 10.39 + 3.0 x 8.79 = 106.5 kPa, which agrees.
Key terms
- Total stress
- The weight per unit area of everything above a point, solids and pore water together, plus any surcharge applied at the surface.
- Pore water pressure
- The pressure in the water filling the void space. It is hydrostatic below a static water table and comes from a flow net when water is moving.
- Effective stress principle
- Terzaghi's statement that compression, distortion and changes in shearing resistance are due exclusively to changes in effective stress, which is total stress minus pore water pressure.
- Capillary rise
- Water drawn above the water table by surface tension, held in tension so that the pore pressure is negative and the effective stress is raised above the total stress.
- Undrained loading
- Loading applied faster than water can leave, so the pore pressure carries the increment and the effective stress barely changes while the loading lasts.
Total stress, pore water pressure and effective stress FAQ
Why can effective stress not simply be measured?
Because there is no plane inside a soil on which it acts as a physical traction, and no instrument reads it. What can be measured is the total stress from the overburden and the pore pressure from a piezometer, and the effective stress is defined as the difference between them.
It earns its place because soil behaviour correlates with it and not with either measurement alone: two elements at the same total stress but different pore pressures behave differently, while two at the same effective stress behave the same however they arrived there.
What happens if the effective stress reaches zero?
The grains stop being pressed together, the soil has no frictional strength, and it behaves as a heavy liquid. That single condition is quicksand, it is what occurs at the exit face when piping begins, and it is the essence of liquefaction during an earthquake.
All three are the same equation reaching the same limit by different routes: rising pore pressure from upward seepage in one case, and from rapid cyclic loading of a loose saturated sand in another.
Why does lowering a water table cause settlement?
Because it raises the effective stress without anything being built. If the soil above the falling table stays saturated, the total stress hardly changes while the pore pressure falls by the weight of the water column removed, so the difference between them grows.
That increment compresses the ground exactly as a surface load would, which is why groundwater lowering is a recognised cause of regional settlement and why dewatering near existing structures is controlled.
Exam move
Draw the section for every question in this module: ground surface, water table, layer boundaries and the point of interest, with each depth written on it. Almost every error here is a depth measured from the wrong reference rather than a misunderstanding, and the sketch removes that class of error for the cost of a minute.
Write the effective stress definition at the top of the page and check every line against it, since the most expensive mistake in the second half of the unit is analysing behaviour in total stress. Finally, learn drained and undrained as a statement about a particular loading at a particular rate on a soil of a particular permeability, not as a label attached to a soil type.
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