Effective Stress, Pore Pressure and Stress Profiles

NCEES FE Civil spec: Geotechnical Engineering, D. Effective stress. FE Reference Handbook: Civil Engineering chapter, Geotechnical section (Vertical Stress Profiles).

What the FE Civil Spec Covers

Effective stress is the foundation of nearly every geotechnical calculation on the exam: settlement, shear strength, bearing capacity and earth pressure all use it. Section D problems typically give a layered soil profile with a water table and ask for total stress, pore pressure or effective stress at some depth, sometimes with a surface surcharge or seepage.

Key Concepts

Total vertical stress is the weight of everything above the point: soil, water and surcharge.
Pore water pressure under hydrostatic conditions is the unit weight of water times the depth below the water table.
Effective stress is the difference. It is the stress carried by the soil skeleton.
Above the water table use the moist unit weight. Below it use the saturated unit weight for total stress.
A uniform surface surcharge that covers a wide area adds its full value to total and effective stress at every depth.

Core Formulas

σ^{'} = σ - u

σ = q + \sum γ_{i} H_{i} u = γ_{w} z_{w}

Below the water table you can also add submerged unit weights directly:

σ^{'} = q + above WT \sum γ_{i} H_{i} + below WT \sum (γ_{s a t, i} - γ_{w}) H_{i}

With vertical seepage at gradient i through a depth z, the seepage force changes the effective stress:

σ^{'} = γ^{'} z \mp i γ_{w} z i_{cr} = \frac{γ ^{'}}{γ _{w}}

Upward flow reduces effective stress (minus sign); downward flow increases it (plus sign).

Seepage and the quick condition

For a sand with $γ_{s a t} = 20$ kN/m³, the submerged unit weight is 20 minus 9.81 = 10.19 kN/m³, so the critical gradient is 10.19 / 9.81 = 1.04. If upward seepage under a cofferdam or sheet pile approaches that gradient, the sand boils. The factor of safety against heave is the critical gradient divided by the actual exit gradient.

Artesian pressure and capillary rise

In a confined aquifer, the piezometric level can sit above the ground surface. Pore pressure at the top of the aquifer is then larger than the depth below the ground water table would suggest, and effective stress in the overlying clay drops. In the capillary zone just above the water table, pore pressure is negative, which slightly increases effective stress. The FE rarely asks for capillary effects, but you should recognize both situations.

Where It Is in the FE Reference Handbook

Search the Civil Engineering chapter, Geotechnical section, for Vertical Stress Profiles and Vertical Stress Profiles with Surcharge. Those diagrams lay out total stress, pore pressure and effective stress for a two-layer profile, which matches most exam questions. Effective stress and the seepage factor of safety are also defined near the phase relationships.

Worked Example

A site has 3 m of sand ( $γ = 17$ kN/m³) above the water table, underlain by 5 m of clay ( $γ_{s a t} = 19$ kN/m³). The water table is at the top of the clay. Find the effective stress at the middle and at the bottom of the clay.

Middle of clay (depth 5.5 m, 2.5 m below water table):

σ = (17) (3) + (19) (2.5) = 51.0 + 47.5 = 98.5 kPa

u = (9.81) (2.5) = 24.5 kPa

σ^{'} = 98.5 - 24.5 = 74.0 kPa

Bottom of clay (depth 8 m, 5 m below water table):

σ = 51.0 + (19) (5) = 146.0 kPa u = (9.81) (5) = 49.05 kPa

σ^{'} = 146.0 - 49.05 = 96.95 \approx 97.0 kPa

Check with submerged unit weight at mid-clay: 51.0 + (19 minus 9.81)(2.5) = 51.0 + 23.0 = 74.0 kPa. The mid-depth value is the one you would use for a consolidation settlement estimate of this layer.

Common Mistakes

Measuring pore pressure depth from the ground surface instead of from the water table.
Using the saturated unit weight above the water table, or the moist unit weight below it.
Subtracting pore pressure twice by using submerged unit weight and then also subtracting u.
Forgetting that a raised water table lowers effective stress and therefore lowers bearing capacity and slope stability.
Ignoring a surcharge, or applying a small footing load as if it were an infinite surcharge.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

Uniform saturated soil has γ_sat = 20 kN/m³ with the water table at the ground surface. Assuming hydrostatic conditions and no surcharge, what is the vertical effective stress at 5 m depth? Use γ_w = 9.81 kN/m³. See the worked solution or practice the Soil Mechanics deck
A saturated soil has G_s = 2.68 and void ratio e = 0.70. Taking γ_w = 9.81 kN/m³, its saturated unit weight is most nearly: See the worked solution or practice the Soil Mechanics deck
For a footing on granular soil, a rise in the groundwater table to near the footing generally causes the bearing capacity to: See the worked solution or practice the Soils & Foundations deck
With all else constant, increasing pore-water pressure in a soil slope generally causes its factor of safety to: See the worked solution or practice the Soil Mechanics deck

Related Calculators and Examples

Frequently Asked Questions

Why does effective stress control soil behavior?

Water carries no shear, so only the stress transmitted through grain to grain contacts mobilizes friction and causes compression. Strength and settlement therefore depend on effective stress, not total stress.

What happens to effective stress when the water table drops?

Pore pressure decreases, so effective stress increases even though the soil weight barely changes. This is why lowering the water table can cause settlement of soft clay layers.

What is a quick condition?

Under strong upward seepage, the effective stress in a cohesionless soil can drop to zero and the soil loses all strength. This happens when the hydraulic gradient reaches the critical gradient, which equals the submerged unit weight divided by the unit weight of water, roughly 1.0 for most soils.

Does a surcharge change the pore water pressure?

Under long-term drained conditions, no. A wide surcharge adds its full value to total and effective stress while hydrostatic pore pressure stays the same. In a saturated clay loaded quickly, the surcharge is first carried by excess pore pressure, which then dissipates during consolidation.

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