5 - Consolidation Flashcards
To develop the 1D consolidation Theory, what 8 assumptions do we make?
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
How do we derive Terzaghi’s 1D consolidation theory?
Describe the step by step process of deriving Terzaghi’s 1D consolidation theory:
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.
What happens to the effective stress and water pressure immediately after loading?
Increases big time.
What is the first stage of consolidation, when t<tc?
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.
What is the second stage of consolidation, when t > tc?
When the pore pressure at the impermeable boundary starts to reduce
What are the 3 dimensionless parameters in Terzaghi’s equation?
The degree of consolidation, Uz
Time factor, Tv = cvt / Hd^2
Drainage path ratio, Z = z / Hd
What is the drainage distance, Hd?
The drainage distance is the theoretical maximum distance water will have to travel in order to reach a drainage boundary.
What is the Degree of consolidation, Uz?
Refers to the consolidation at a specific point in the consolidating layer, representing the extent to which that point has consolidated
What is the average degree of consolidation?
Reflects how much each layer has consolidated
Flashcard 3: Q: How is the Average Degree of Consolidation calculated?
Uavg = 1 - (integral of excess water pressure at a given time) / integral of excess pore pressure
What is the significance of isochrones in the context of consolidation?
Isochrones represent lines of equal excess pore pressure at a given time, helping visualize the dissipation of pore pressure during consolidation.
How does a hydraulic fill affect the excess pore pressure profile?
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.
What happens when a surface surcharge is applied to a layer?
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.
What is the relationship between strain and effective stress?
If we assume a linear relationship, then strain is equal to the pore pressure dissipation, and hence to the average degree of consolidation.
How can the coefficient of consolidation be estimated?
can be estimated from the results of an oedometer test, using the relationship for permeability
𝑘
k and volume compressibility
How can the time factor and average degree of consolidation be related?
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.
What methods are used to determine the correct point on the consolidation curve corresponding to a certain average degree of consolidation?
Two methods used are:
Taylor’s Root-Time Method
Casagrande’s Log-Time Method
How does Taylor’s Root-Time Method determine the time at which 90% of the consolidation settlement has occurred?
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.
What are the main sources of errors in consolidation settlement predictions?
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.
What challenge is mentioned in relation to obtaining representative soil samples for consolidation testing?
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.
What did Kulhawy et al. (1991) report about the accuracy of Cc values from a single randomly obtained soil sample?
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.
What is a major limitation in the mathematical models used for consolidation settlement predictions?
No real situation will be truly one-dimensional; the assumption of one-dimensional consolidation is an idealization that does not perfectly reflect actual conditions.
What is the difference between Terzaghi’s Theory of Consolidation and real soil behavior in the field?
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.
What typical error range can be expected in consolidation settlement predictions?
Even with careful sampling and testing, a typical error in consolidation settlement predictions can range from 25% to 50%.
How do engineers typically handle prediction errors in consolidation settlement?
Engineers usually use conservative estimates when assessing settlement impacts on proposed construction to account for potential errors.
What should be done when predicted settlements are large and conservative designs become expensive?
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.
What can be done if the initial settlement prediction is too low?
If the initial prediction is too low, the prediction can be updated using initial settlement monitoring data to increase the predicted settlement.
Why can updating consolidation settlement predictions be challenging?
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.
How can monitoring pore pressures improve the accuracy of consolidation settlement predictions?
Monitoring pore pressures allows for determining the site’s coefficient of consolidation (cv), which helps obtain a more accurate final prediction of settlement
