Geotechnical Engineering

Effective Stress & Seepage

Terzaghi's effective-stress principle, pore pressure, flow nets and the quick (boiling) condition — the backbone of all soil behaviour.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Terzaghi's principle states that soil strength and deformation are governed not by total stress but by effective stress

σ^{'} = σ - u

— the part carried by the soil skeleton. Below a static water table the pore pressure is

u = γ_{w} h_{w}

. Under seepage, flow nets give the discharge, and when the upward seepage gradient reaches the critical gradient the effective stress vanishes and the soil 'boils' (quick condition).

The Core Formula Matrix

Effective stress:

σ^{'} = σ - u

Saturated soil, WT at surface:

σ^{'} = γ^{'} z, γ^{'} = γ_{s a t} - γ_{w}

Seepage discharge (flow net):

q = k H \frac{N _{f}}{N _{d}}

Critical hydraulic gradient:

i_{c} = \frac{γ ^{'}}{γ _{w}} = \frac{G - 1}{1 + e}

The ‘IIT Traps’

⚠
Use head, not depth, for pore pressure under seepage. Hydrostatic $u = γ_{w} h_{w}$ only holds for no flow.
⚠
Submerged unit weight. Below the water table use $γ^{'} = γ_{s a t} - γ_{w}$ for effective stress, not $γ_{s a t}$ .
⚠
Quick condition is a gradient, not a stress. Boiling occurs when $i \to i_{c}$ , independent of particle size for the critical value.

📚 Standard references

Basic and Applied Soil Mechanics — Gopal Ranjan & A.S.R. Rao · Effective Stress & Seepage

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

A saturated sand (

γ_{s a t} = 20 kN/m^{3}

) has the water table at the surface. The effective vertical stress at

5 m

depth is _____ kPa.

Q2MEDIUM2 Marks · NAT

A soil has

G = 2.65

and void ratio

e = 0.65

. Its critical hydraulic gradient is _____.

Q3HARD2 Marks · NAT

A flow net beneath a dam has

4

flow channels and

12

potential drops; head loss

6 m

k = 2 \times 1 0^{- 5} m/s

. The seepage per metre length is _____ ×10⁻⁵ m³/s/m.