Solution of 1D Consolidation

Submitted to

Professor Myoung Soo Won

By

Sanchari Halder

The solution of variation of excess pore water pressure with depth and time can be obtained for various initial conditions.

Terzaghi’s one dimensional consolidation equation:

Mathematical Solutions:

The solution of consolidation equation consists of the following three variables

1. The depth z2. The excess pore water pressure u3. The time (t) after application of loading

……….. (1)

Graphical solution of 1D consolidation equation:

v

v

The variables are expressed in the form of the following non-dimensional terms as,

The graphical solution of the equation is an illustration in which the lines of equal time factor are known as Isochrones.

Layer of Clay

2Hdr

These lines represent the degrees of consolidation at particular times and at particular locations throughout the thickness of the consolidating layer. For example, at point P at a time corresponding to a time factor Tv of 0.4 the pore pressure (excess hydrostatic) has dissipated to 40% of the initial value which is the same as saying that the degree of consolidation is 0.6.

PHdr

For a soil layer that is drained at both the upper and lower boundaries the value of H must be made equal to one half of the total layer thickness. The isochrones in the Figure would apply to the upper half of the layer and their mirror images would apply to the lower half.

Degree of Consolidation (Uz):

Mathematical Example 1:

From practical point of view, the average degree of consolidation over the entire depth at any given time is desirable.

Average Degree of Consolidation (U):

Thus,

Mathematical Example 2:

50%

Thank you all………