THEORY

Karl Terzaghi (1925) proposed the differential equation that explained the one-dimensional equation of consolidation as follows:

(Eq. 1)

The solution of (Eq. 1) can be written in series solution:

(Eq. 2)

where

(Eq. 3)

The solution in Eq.2 can be plotted as shown below

APPLICATION

Although the theory looks complicated, applying time-dependent consolidation is much simpler.

The degree of consolidation is defined as

(Eq. 4)

The following steps are used for computing consolidation at time *t.*

For a given time

*t*, compute Tv from Eq. 3 for each soil layerFrom chart 3-3, find U from Tv

Multiply U by the final settlement (Eq.4) for each soil layer

The total settlement is the sum of settlement from each soil layer

EXAMPLE

(Coming Soon)

Q: HOW TO DETERMINE COEFFICIENT OF CONSOLIDATION (*Cv*)?

Two standard methods to compute the value of Cv are

- Logarithm of time method (t50)

- Square root of time method (t90)

By concept, the value of *Cv* is constant with time. Both methods use consolidation test data and graphical methods to find the value of *Cv *at* *a specific time *t*. The log of time method uses *t* to complete 50% of consolidation (t50), while the square root of time method uses *t* to complete 90% (t90) to obtain the *Cv *value.

REFERENCES