5 - Consolidation

Question 1

To develop the 1D consolidation Theory, what 8 assumptions do we make?

Answer 1

1 - Soil is homgeneous and fully saturated.
2. Small strains
3. k and av are constant
4. Compression and flow are one-dimensional
5. Darcy’s Law is valid during the consolidation process
6. Settlement is due to change in voids ratio (i.e. the water and soil particles are incompressible)
7. The applied load causes an instantaneous increase in vertical total stress ∆σz (i.e. the total
stress remains constant during the consolidation process)
8. There is a unique linear relationship between ∆e and ∆σ
0
: ∆e = −av∆σ
0
, and av is constant
with time

Question 3

How do we derive Terzaghi’s 1D consolidation theory?

Answer 3

Question 4

Describe the step by step process of deriving Terzaghi’s 1D consolidation theory:

Answer 4

1 - Continuity equation , change in water pressure with time + change in q / distance = 0

2 - Darcy’s law, q = -k * hydraulic gradient

3 - Substiute darcy’s law into the continuity equation.

4 - Use the consolidation equation, strain = change in volume/V0 = change in e / 1+e0

5 - Final consolidation equation achieved, change in water pressure / time = Cv * d squared u / dx squared.

Question 5

What happens to the effective stress and water pressure immediately after loading?

Answer 5

Increases big time.

Question 6

What is the first stage of consolidation, when t<tc?

Answer 6

When the excess pore pressure at the impermeable boundary remains at the initial excess pore pressure while pore pressure in the rest of the soil starts to dissipate.

Question 7

What is the second stage of consolidation, when t > tc?

Answer 7

When the pore pressure at the impermeable boundary starts to reduce

Question 8

What are the 3 dimensionless parameters in Terzaghi’s equation?

Answer 8

The degree of consolidation, Uz

Time factor, Tv = cvt / Hd^2

Drainage path ratio, Z = z / Hd

Question 9

What is the drainage distance, Hd?

Answer 9

The drainage distance is the theoretical maximum distance water will have to travel in order to reach a drainage boundary.

Question 10

What is the Degree of consolidation, Uz?

Answer 10

Refers to the consolidation at a specific point in the consolidating layer, representing the extent to which that point has consolidated

Question 11

What is the average degree of consolidation?

Answer 11

Reflects how much each layer has consolidated

Question 12

Flashcard 3: Q: How is the Average Degree of Consolidation calculated?

Answer 12

Uavg = 1 - (integral of excess water pressure at a given time) / integral of excess pore pressure

Question 13

What is the significance of isochrones in the context of consolidation?

Answer 13

Isochrones represent lines of equal excess pore pressure at a given time, helping visualize the dissipation of pore pressure during consolidation.

Question 14

How does a hydraulic fill affect the excess pore pressure profile?

Answer 14

n hydraulic fill, due to the self-weight of the material, the stress increases with depth, creating a triangular excess pore pressure profile, with high pressure at the bottom and zero pressure at the top.

Question 15

What happens when a surface surcharge is applied to a layer?

Answer 15

A surface surcharge applied to a limited area can create a triangular excess pore pressure profile, with maximum pressure near the surface and decreasing with depth. The assumption of one-dimensional consolidation may introduce errors if the surcharge is not applied to the entire area of the soil layer.

Question 16

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Question 17

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Question 18

What is the relationship between strain and effective stress?

Answer 18

If we assume a linear relationship, then strain is equal to the pore pressure dissipation, and hence to the average degree of consolidation.

Question 19

How can the coefficient of consolidation be estimated?

Answer 19

can be estimated from the results of an oedometer test, using the relationship for permeability
𝑘
k and volume compressibility

Question 20

How can the time factor and average degree of consolidation be related?

Answer 20

Time factor can be correlated with time t, which is correlated with the average degree of consolidation, and long as the ultimate settlement is known.

Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

What methods are used to determine the correct point on the consolidation curve corresponding to a certain average degree of consolidation?

Answer 27

Two methods used are: Taylor's Root-Time Method Casagrande’s Log-Time Method

Question 28

How does Taylor’s Root-Time Method determine the time at which 90% of the consolidation settlement has occurred?

Answer 28

Plot the specimen settlement against the square root of time. Extend a line following the main linear part of the curve to time = 0, called "Point X." From Point X, draw a line with an inverse slope 1.15 times larger than the original line. The new line should intersect the experimental curve at a degree of consolidation of 90%, indicating time T90 ​ . To calculate the ultimate consolidation settlement, use the settlement occurring after Point X.

Question 29

Answer 29

Question 29

What are the main sources of errors in consolidation settlement predictions?

Answer 29

Differences between the soil profile used in analysis and the actual soil profile. Differences between the engineering properties of the soil samples and the average properties of the strata they represent. Errors introduced due to testing techniques in the laboratory.

Question 30

Answer 30

Question 31

What challenge is mentioned in relation to obtaining representative soil samples for consolidation testing?

Answer 31

One of the key challenges is obtaining representative and undisturbed samples from the site. Samples undergo significant changes in confining stress when being extracted from the site and placed into the oedometer.

Question 32

What did Kulhawy et al. (1991) report about the accuracy of Cc values from a single randomly obtained soil sample?

Answer 32

Kulhawy et al. (1991) reported that Cc values from a single randomly obtained soil sample have only a 30-56% probability of being within 20% of the true Cc value for the stratum.

Question 33

What is a major limitation in the mathematical models used for consolidation settlement predictions?

Answer 33

No real situation will be truly one-dimensional; the assumption of one-dimensional consolidation is an idealization that does not perfectly reflect actual conditions.

Question 34

What is the difference between Terzaghi’s Theory of Consolidation and real soil behavior in the field?

Answer 34

There are differences between Terzaghi’s Theory of Consolidation and the actual behavior of soils in the field, meaning the model may not fully capture all factors influencing consolidation.

Question 35

What typical error range can be expected in consolidation settlement predictions?

Answer 35

Even with careful sampling and testing, a typical error in consolidation settlement predictions can range from 25% to 50%.

Question 36

How do engineers typically handle prediction errors in consolidation settlement?

Answer 36

Engineers usually use conservative estimates when assessing settlement impacts on proposed construction to account for potential errors.

Question 37

What should be done when predicted settlements are large and conservative designs become expensive?

Answer 37

When predicted settlements are large, it's useful to monitor actual settlements in the field, compare them to the predictions, and modify the design accordingly.

Question 38

What can be done if the initial settlement prediction is too low?

Answer 38

If the initial prediction is too low, the prediction can be updated using initial settlement monitoring data to increase the predicted settlement.

Question 39

Why can updating consolidation settlement predictions be challenging?

Answer 39

t can be challenging because the updated predictions may vary depending on which input parameter (e.g., Cc or cv) is adjusted, making it difficult to pinpoint the exact cause of the error.

Question 40

How can monitoring pore pressures improve the accuracy of consolidation settlement predictions?

Answer 40

Monitoring pore pressures allows for determining the site’s coefficient of consolidation (cv), which helps obtain a more accurate final prediction of settlement