Square Root Time Graph Calculations

SUMMARY

This document will describe how the T90 calculations are achieved.  The T50 and Cv calculations will also be discussed. 

All auto generated tangent lines should be reviewed and modified as necessary.

Note:  Cv is not calculated for the CU or CD test modules.

SOLUTION

Graph Construction

The NEXT Square Root of Time graph has a single construction line that is either automatically determined by software or is drawn by the user, this is the 0% construction line.

The software will then automatically computer a second construction line with the tail being 15% greater, this is the 15% construction line.  For calculation purposes we need one point of this line, the tail, we will call this point Tail151.

From the 15% construction line the software will compute where this line intersects the Settlement vs. Square Root Time curve, this intersection point will be called IntPnt1.

Calculations

t90 = IntPnt1.X ^ 2

d0 = Tail151.Y

d90 = IntPnt1.Y

d100 = (10 / 9) * (d90 - d0) + d0

d50 = (d0 + d100) / 2

Cv = (0.848 * (Height - d50)  / Drainage) ^ 2 / t50

0.848 = Constant, a dimensionless time factor defined in the standard.

Height = Sample Height

Drainage = 1 (some tests support the option of double sided drainage, if this is the case this value will be 2).

* Cv units are based on specimen height units and the x and y graph units.

** Cv is then calculated per user specified units in the Summary tab of the consolidation test.