One - dimensional consolidation

Question 1

When a saturated soil is loaded, why can’t the soil particles immediately rearrange?

Answer 1

Because the water surrounding them is incompressible, preventing particle rearrangement until water can escape.

Question 2

True or False: In fully drained conditions, the pore water pressure (u) increases.

Answer 2

False

Question 3

Fill in the Gap: In fully drained conditions, Δσ = _______ and Δu = _______.

Answer 3

Δσ = Δσ´ and Δu = 0

Question 4

In undrained conditions for clay soils, the initial increment of total stress is carried by:

Answer 4

Pore water

Question 5

Formula: Effective Stress

Answer 5

σ´ = σ - u

Question 6

What happens to soil volume during consolidation?

Answer 6

Soil volume reduces as particles reorient and inter-particle forces increase.

Question 7

Fill in the Gap: In the consolidation analogy, the spring represents the _______ and the water represents the _______.

Answer 7

Spring = compressible soil skeleton, Water = pore water

Question 8

True or False: When the valve is closed and a load is applied, the system behaves under drained conditions.

Answer 8

False

Question 9

Opening the valve and allowing water to escape simulates:

Answer 9

Consolidation process

Question 10

In a clay layer under an embankment, where is the excess pore water pressure maximum?

Answer 10

At the mid-depth of the clay layer.

Question 11

Formula: Effective Stress Increase

Answer 11

Δσ´ = Δσ - Δu

Question 12

What is the purpose of the oedometer test?

Answer 12

To determine consolidation settlement and the rate of consolidation.

Question 13

True or False: In an oedometer test, the sample is allowed to expand laterally during compression.

Answer 13

False

Question 14

Fill in the Gap: In the oedometer test, porous stones are placed at the _______ and _______ of the soil specimen.

Answer 14

Top and bottom

Question 15

How is vertical strain typically expressed in oedometer results?

Answer 15

As Δh/H₀

Question 16

In oedometer tests, what happens to compressibility with increasing stress level?

Answer 16

Decreases

Question 17

Formula: Coefficient of Volume Compressibility (mv)

Answer 17

mv = Δe / (1 + e₀)Δσ’ or mv = ΔH / H₀Δσ’

Question 18

What is the formula for settlement ρ∞ under 1-D conditions?

Answer 18

ρ∞ = mv × Δσ’ × H

Question 19

Formula: Void Ratio from Water Content

Answer 19

e₀ = w₀ × Gs

Question 20

Which material had the lowest compressibility in the oedometer tests with lentils, oats, and foam?

Answer 20

Lentils

Question 21

Fill in the Gap: The plasticity index (PI) is defined as PI = _______ - _______.

Answer 21

PI = Liquid Limit (LL) - Plastic Limit (PL)

Question 22

What does the speed at which water can flow to escape depend on?

Answer 22

Permeability of soil

Question 23

Δσ = Force/ ____

Answer 23

Piston area

Question 24

Components of an oedometer?

Answer 24

• Rigid top cap
• Load
• Confining ring
• Soil specimen
• Container
• Porous stones
• Dial gauge for measuring displacement
• Smooth surface to avoid friction

Question 25

What are the steps in the oedometer test?

Answer 25

1. Initial pressure usually roughly equal to in-situ effective stress 2. A series of loads applied daily, each double the previous 3. For each load, the compression of the sample is measured at suitable time intervals 4. Dissipation of excess pore water pressures assumed to be complete after 24 hours

Question 26

What happens to stiffness when compressibility reduces?

Answer 26

Increases

Question 27

How are oedometer test results usually plotted?

Answer 27

e vs σ'

Question 28

What might have unloading taken place?

Answer 28

- Melting ice sheets - Erosion of upper layers - Rise in ground water table

Question 29

What is the formula for ΔH?

Answer 29

ΔH = H₀* Δe/1+e₀

Question 30

What is the formula for C_c (compression index)?

Answer 30

C_c = e₀ -e_1/logσ'1-logσ'0

Question 31

What is the purpose of the theory of one-dimensional consolidation?

Answer 31

Provides a method for determining the rate and time of consolidation.

Question 32

List three assumptions made in the theory of one-dimensional consolidation.

Answer 32

Soil is homogeneous, fully saturated, and solid particles & water are incompressible.

Question 33

State Darcy's law used in consolidation theory.

Answer 33

Flow Q = k_z * ∂i/∂z * ∂x∂y∂z where i = ∂h/∂z.

Question 34

Express i in terms of u and γw.

Answer 34

i = ∂(u/γw)/∂z.

Question 35

What does mv represent in consolidation?

Answer 35

Coefficient of volume compressibility.

Question 36

What is Terzaghi's one-dimensional consolidation equation?

Answer 36

∂u/∂t = cv ∂²u/∂z².

Question 37

Define coefficient of consolidation, cv.

Answer 37

cv = k / (γw * mv).

Question 38

What is the dimensionless time factor Tv?

Answer 38

Tv = (cv * t) / H².

Question 39

Difference between 1-way and 2-way drainage path lengths?

Answer 39

1-way: length = 2H; 2-way: length = H.

Question 40

What are isochrones in consolidation?

Answer 40

Curves showing excess pore pressure distribution at different times.

Question 41

Define average degree of consolidation U.

Answer 41

U = compression at time t / compression at t∞.

Question 42

Formula for U using isochrone areas?

Answer 42

U = 1 - Area(3)/Area(1).

Question 43

Expression of U in terms of effective stresses?

Answer 43

U = (σ' - σ0') / (σ1' - σ0').

Question 44

Expression of U in terms of excess pore pressures?

Answer 44

U = 1 - (ue/ui).

Question 45

Typical values of cv for stiff clays?

Answer 45

0.5 to 5 m²/year.

Question 46

Typical values of cv for soft clays?

Answer 46

5 to 25 m²/year.

Question 47

Typical values of cv for silty clays?

Answer 47

>25 m²/year.

Question 48

How is cv determined from oedometer tests?

Answer 48

By plotting ΔH against √time and analyzing primary consolidation portion.

Question 49

What part of the consolidation curve represents primary consolidation?

Answer 49

Part BC, where excess pore pressure reduces to negligible levels.

Question 50

What is secondary consolidation?

Answer 50

Volume changes independent of excess pore water pressures, often in organic soils.

Question 51

Formula for U vs Tv for early consolidation stages?

Answer 51

U = (2/π)√Tv.

Question 52

Formula relating Tv to drainage path and time?

Answer 52

Tv = (cv * t) / d². where d is the half mean thickness of sample for stress increment being considered

Question 53

When does secondary consolidation (creep) usually start?

Answer 53

After U = 90%.

Question 54

At U = 90%, what is √Tv approximately?

Answer 54

√Tv = 0.798 (empirical) or 0.921 (theory).