**2.1. Definition of the input variables and the output responses**

In this study, the effects of input parameters (dry unit weight ( / ) **<sup>3</sup>** γ **<sup>d</sup> kN m** , water content **w** (%) , plasticity index **Ip** (%) Liquidity limits **Wl** (%) Saturation degree **Sr**(%) , the preconsolidation pressure **P kPa <sup>c</sup>** ( ) and the clay fraction **Cf** (%)) on the output response the swelling pressure **P kPa <sup>s</sup>** ( ) . The levels for each factor are tabulated in **Table 1**.

Significant factors are identified using two-level factors as the first technique permit to compare the obtained results in full factorial design, where lower numbers of runs are required in this identification.

Results of the full factorial design are then compared to the results of two-level fractional factorial design, in which much lower number of runs are required to identify the significant factors. Explicitly, the half-fraction design can be also compared to the two-level factorial design.


#### **Figure 2.**

*Definition of different parameters as numeric factors in design-expert, and the dialog box for definition replication points and "alpha" parameter.*

*Swelling Clay Parameters Investigation Using Design of Experiments (A Case Study) DOI: http://dx.doi.org/10.5772/intechopen.95443*

## **2.2. DOE and response data implementation**

The two sides unit's length of the cube rang between −1 to +1. "Alpha" is the distance out of cube area measured in levels of coded factors, statistically it is always been a point of discussion view. A variety of Alpha options is presented in the Design-Expert software (**Figure 2**).
