Learning Objectives:

• Define effective stress and understand its importance in describing the mechanical behavior of soils.
• Recognize the difference between total stress and effective stress and how they influence soil strength, consolidation, and permeability.
• Understand Terzaghi's principle of effective stress, which states that the effective stress governs soil behavior and controls the strength and volume change characteristics of soils.
• Apply Terzaghi's principle to analyze soil stability, settlement, and seepage problems.

• Effective stress is an imaginary parameter which is sum of the contact force divided by the gross area.
• This is the reason why effective stress is not measured, hence it is not a physical parameter.
• Effective stress is a function of normal force acting at the contact points of grains and pore pressure.

Solved Example: 9075-01

Effective stress on soil:

A. Increases voids ratio and decreases permeability

B. Increases both voids ratio and permeability

C. Decreases both voids ratio and permeability

D. Decreases void ratio and increases permeability

Correct Answer: C

Solved Example: 9075-02

Contact pressure for flexible footing on any type of soil is:

A. Uniform

B. Varies with maximum at center

C. Varies with maximum edges

D. NO specific trend of variation

Correct Answer: A

Solved Example: 9075-03

Due to rise in water table, the effective stress in soil:

A. Increases

B. Decreases

C. Does not change

D. May increase or decrease

Correct Answer: B

Solved Example: 9075-04

What is the effective stress at a depth of 10 m below the ground level, when water table is 3 m below ground level, saturated density is 20 kN/m$^3$ and bulk density is 18 kN/m$^3$?

A. 124 KN/m$^2$

B. 116 KN/m$^2$

C. 264 KN/m$^2$

D. 194 KN/m$^2$

Effective stress \begin{align*} &= \gamma_b \times 3 + \gamma_{\mathrm{sub}} \times 7\\ &= 18 \times 3 + (20 - 10) \times 7\\ &= 124\ \mathrm{kN/m}^3 \end{align*}

Correct Answer: A

Solved Example: 9075-05

The Pore water pressure in a capillary zone is:

A. Zero

B. Positive

C. Negative

D. Very low

Correct Answer: C

Solved Example: 9075-06

A flownet is drawn to obtain:

A. Seepage, coefficient of permeability and uplift pressure

B. Coefficient of permeability, uplift pressure and exit gradient

C. Exit gradient, uplift pressure and seepage quantity

D. Exit gradient, seepage, and coefficient of permeability

Correct Answer: C

Solved Example: 9075-07

In which one of the following pairs of soil types would you anticipate negative pore pressure when subjected to shearing?

A. Normally consolidated clay and dense sand

B. Overconsolidated clay and loose sand

C. Less consolidated clay and overconsolidated clay

D. Dense sand and overconsolidated clay

Correct Answer: D

Solved Example: 9075-08

A uniform collapsible sand stratum, 2.5 m thick, has specific gravity of its sand as 2.65, with a natural void ratio of 0.65. The hydraulic head required to cause quick collapsible sand condition is:

A. 2.50 m

B. 2.75 m

C. 3.25 m

D. 3.50 m

\begin{align*} i_{cr} &= \dfrac{G - 1}{1 + e}\\ &= \dfrac{2.65 - 1}{1 + 0.65}\\ &= 1 \end{align*} Also, \begin{align*} i_{cr} &= \dfrac{\mathrm{head\ loss}}{\mathrm{total\ head}}\\ 1 &= \dfrac{h}{2.5}\\ h &= 2.5\ \mathrm{m} \end{align*}

Correct Answer: A

Solved Example: 9075-09

The pore water pressure in the soil sample of consolidometer test is:

A. Maximum at bottom

B. Maximum at centre

C. Maximum at top

D. Minimum at centre

Correct Answer: B

Solved Example: 9075-10

A lake 5 m deep consist of sand bed with saturated unit weight of 20 kN/m$^3$, Determine the effective vertical stress at 5 m below the bed of the river. (take unit weight of water as 9.81 kN/m$^3$)

A. 65 KN/m$^2$

B. 51 KN/m$^2$

C. 149 KN/m$^2$

D. 100 KN/m$^2$

Total stress, \begin{align*} s &= \gamma_{sat} \times h \\ 20 \times 5 &=100\ \mathrm{kN/m}^2 \end{align*} Pore water pressure, \begin{align*} u &= \gamma_w \times h\\ &=9.81 \times 5 = 49.05\ \mathrm{kN/m}^2 \end{align*} Effective stress, \begin{align*} \sigma &= s - u = 100 - 49.05\\ &= 51\ \mathrm{kN/m}^2 \end{align*}

Correct Answer: B