**1. Introduction**

The Design of Experiments theory DOE is detailed and covered in many fundamental books [1–3]; its application to machining studies is discussed by various researches [4–7]. However, they have yet to make any inroads in engineering geology except for environmental engineering areas. In fact, geological and geotechnical engineering researchers, especially those who never heard about it and continue to use different inefficient methods and techniques. Moreover, in DOE there are many commercial software packages as, for example, Design-Expert by Stat-Ease, Minitab by Minitab, R Packages powered by R foundation for Statistical Computing, S-Plus by Mathsoft. A great literature and online sources combined are readily available as commercial software packages that apparently make DOE almost effortless.

Though, the simplicity of DOE is really pseudo-simplicity or masked complexity.

That is, in the first stage of DOE requires the formulation of clear objectives study on the swelling pressure of clayey soils as mentioned in this paper. The statistical model selected in DOE requires the quantitative formulation of the objective(s). A response is considered as objective, which is the result of the process under study presented in **Figure 1**. In satisfying these constraints, the software allowed us to establish minimum criteria for the response variables, then view both feasible and unfeasible regions of specific portions of the design space. The process under study may be characterized by several important output parameters but only one of them should be selected as the response. The response must satisfy certain requirements. It should be the effective output in terms of desirable final aim of the study, also easily measurable, preferably quantitatively and a single-valued function of the chosen parameters (dry unit weight ( ) <sup>3</sup> <sup>d</sup> γ *kN* / m , water content w %( ) , Clay fraction Cf (%), plasticity index I %p ( ) , Limite of liquidity (%), Saturation degree (%), the preconsolidation pressure Pc (*kPa*) and the swelling pressure Ps (kPa) as the output parameter).

Basically, swelling soil experiments is one or a series of tests in which purposeful changes are made to dependent or independent input factors or variables of a system, so we may observe and identify the reasons for changes observed in the output response.

Expansive soil has extensively been found in all over the world and cover especially arid and semi-arid regions, literatures and studies investigate deeply the swelling soils behavior and assume that physical properties, geological facies, mechanical and mineralogical characteristics present the main governs parameters dependency [8–13]. Swelling pressure parameter (Ps) or potential was presented in enormous conducted studies as the indicator of phenomenon that can be used in infrastructure sustainable and geotechnical design [14–19]. The output parameter (Ps) is defined in many ways and depend on the testing procedure, to assess the degree of swell, many procedures including laboratory methods determining swell pressure have been developed by geotechnical researchers and engineers [20–22]. Though swelling pressure methods have been developed by

**Figure 1.** *Visualization of DOE intent.*

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

various researchers, only three methods are standardized and also popularly used as documented in the literature.

The swelling is a complicated phenomenon and the different parameters effects cannot be predictable, used methods for estimating the swelling pressure of clayey soil can be direct or indirect. Direct methods are based on tests, experiences and the basic soil mechanics parameters and provide quick and useful identification, various authors in literature present some empirical relationships with indirect methods [23, 24].

The Tebessa area (Algeria) is the case study of the present work, in point, the weathered geological facies in this arid region has primarily created cover soils in a large basin with very plastic behavior. However, expansive soils exist and well identified litigation and reports high difficulties to infrastructure stability.

In the present research the concept of design of experiments (DOE) has been introduced to study the swelling behavior of the clayey soils with about 121 samples collected and tested in soil mechanics laboratory identification (LTPE).

In various engineering branch, the DOE method is largely used especially in manufacturing and chemical research, it is a powerful approach in experimentations; it seeks to determine the factors affecting a process in relationships with an output of our choice. This research aims to study the swelling pressure as an output parameter affected by several of physical and mechanical parameters as dependent or independent input parameters. Sequential application of DOE plan is used to find the optimal parameter and propose mathematical models to predict the swell pressure generated by clayey soil in Tebessa area and provide recommendations in the quality control measures.
