**4. Research course**

86 Multivariate Analysis in Management, Engineering and the Sciences

angular displacement of the dam with the foundation [10].

the contact of concrete and rock, joints and faults and other sub-horizontal discontinuities in the foundation. This approach was used at the Itaipu Dam, where different points of foundation mass were instrumented, specially the geological discontinuities. Figure 4 shows a typical geological profile of the foundation mass of the Itaipu Dam part, which has no tunnel in its right-side, where primary geological discontinuities can be found (contacts, joints, and gaps) of that specific site. In blocks where there is a transversal gallery access to the shaft, the installation of downstream-upstream extensometers can help in the measurement of the

**Figure 4.** Schematic geological profile of the foundation of Itaipu (ITAIPU BINACIONAL, 1995, *apud* [8]).

The measurement of the horizontal displacement of the ridge is a relevant parameter which is affected by deflections of the concrete structure, by the rotation of the base of the structure (due to the deformability of the foundation), and by thermal and environmental influences. These displacements are affected by the characteristics of the concrete or by the proprieties of the foundation rock mass, resulting in important information for the auscultation of the behavior of the dam and of its foundation. The horizontal displacements of the ridge can be measured by a direct pendulum, usually installed at the end of the construction process. The

measurements are done on the stages of reservoir spillway and of dam operation [10].

The stability of the structure in terms of sliding, overturning or floating is directly affected by the level of the piezometric pressures in the concrete-rock interface and in the sub horizontal discontinuities of low resistance that exists in the foundation. The measurements of low pressures on the concrete dam foundation are important for the monitoring of its safety conditions. The drainage is one of the most efficient ways to ensure adequate safety coefficients. The measurements of low pressure are performed by the piezometer [10].

### **4.1. Itaipu Binacional**

The Itaipu Binacional, the largest energy producer of the world, had its construction started in 1973 at a river stretch of Rio Paraná known as Itaipu, which in Tupi language means "the singing boulder", located in the heart of Latin America, on the border of Brazil and Paraguay [12]. The construction of the dam ended in 1982 and the last generator unit was completed in 2008.

Nowadays, the Itaipu Dam has 20 generator units of 700 MW (megawatts) each, generating a total potential of 14.000 MW. Itaipu Binacional (Bi-national Itaipu) reached its record in producing energy in 2000, generating over 93,4 billions kilowatts-hour (KWh). It is responsible for supplying 95% of the energy consumed in Paraguay and 24% of all the Brazilian consumption.

The Itaipu Dam has 7.919m of extension and a maximum high of 196m; these dimensions made of the Itaipu construction a reference in concrete, and dam safety studies. Itaipu dam is made of two stretches of earth dam, one stretch of rock-fill dams and concrete stretches, and these forms the higher structures of it. Figure 5 illustrates the whole structure of the Itaipu dam, and table 1 shows the main characteristics of the stretches pointed on figure 5.

**Figure 5.** Whole structure of the Itaipu Complex [12].

It is possible to find in all the Itaipu extension an amount of 2.218 instruments (1.362 in the concrete, and 865 in the foundations and earthen embankments) and from this amount 270 of them are automated, to monitor the performance of the concrete structures and foundations. Furthermore, there are 5.239 drains (949 in the concrete and 4.290 in the foundations). The readings of these instruments occur in different frequencies, they can be, for example, daily, weekly, fortnightly, and monthly, depending on the type of instrument. These readings have been stored for over 30 years.

Even though, every stretch of the dam is instrumented and monitored, one of the stretches, called *Barragem principal* (main dam) (Denominated stretch F and identified as number "5"

on Figure 5), should be highlighted in a deeper study. The turbines for generating energy can be found in stretch F. In addition, this stretch is the most high water column and the most instrumented one. This stretch is made of many blocks, and each of them has instruments in the concrete structures and in the foundation that provides data about its physical behavior. This study was developed based on the data collected in this stretch of the dam.

Itaipu Hydroelectric Power Plant Structural Geotechnical Instrumentation

Temporal Data Under the Application of Multivariate Analysis – Grouping and Ranking Techniques 89

In the fourth phase, the Factor Analysis and the Clustering Analysis were applied at the same time. The Factor Analysis was also applied within each cluster formed through

The methodology used for the analysis was applied to the data of 30 extensometers located in different blocks of stretch F of the dam, which having one or two point rods, totalizes 72 displacement measures. These measurements are identified as follow: equip4\_1, meaning

The data used in this study are monthly stored and they correspond to the period of January/1995 to December/2004, totalizing 120 readings. This period was chosen as a suggestion of the engineer team of Itaipu because it is subsequent the construction of the dam and prior to the system of automatic acquisition of data. During the period of system implementation, some instruments ended up having no manual readings, in addition, a total of 11 automated instruments (totalizing 24 rods) went through modifications that might have influenced the subsequent readings; there was an exchange on the instrument head for a 70 cm longer one. In this way, the referred 120 readings were immune to these

During the period of pre-processing the data, it was identified that most of the instruments readings are monthly, but some of them showed more than one reading per month, so for this cases, the monthly average was considered. Moreover, some instruments had missing readings, in these cases; interpolations were performed through temporal series, meaning that, an adequate model was established from the Box & Jenkins methodology, using the Statgraphics [13]. In this way, it was possible to assure that all the 120 instruments had 120 readings (10 years). See [14] for more information about the interpolation techniques with

In this way, the Matrix of entrance of structural geotechnical instrumentation data (Matrix *Q*) *is of order a* x *b,* where *a* is the number of patterns and *b* is the number of attributes. For the structural geotechnical instrumentation data of Itaipu, a = 72 (number of patterns) and

During the period of the Multivariate Analysis was applied and the patterns were grouped through the Ward's hierarchical clustering method. The grouping was performed in order to find out similar groups of instruments, and the aim of doing it was to establish the technical justifications for its formation. In addition, the Factor Analysis was applied to the referred data. The Factor Analysis was used to rank the rods of the extensometers through a balanced average of factor scores. Next, the Factor Analysis was applied within each group formed by the clustering analysis. Once having groups that have the instrumentations with a similar behavior, a raking of these instruments was performed within each group, in order to indicate the most relevant instruments, which would be chosen, for example, in cases of

Clustering Analysis.

**5. Method used** 

irregularities.

temporal series.

b = 120 (number of attributes).

intensifying the reading.

rod 1 of the extensometer 4, and so on.


**Table 1.** Characteristics of the stretches of Itaipu.

In the stretch F it is possible to find extensometers, piezometers, triothogonal meter, water level gauge and foundation instrumentation (seepage flow meter). Among these instruments, the multiple point rod extensometers, that are installed in boreholes, were selected for the analysis. This type of instrument is considered one of the most important because they are responsible for measuring the vertical displacement. That is one of the most important observations while monitoring the behavior of the dam structure. There are 30 extensometers located in stretch F.

The procedure for the methodology used for the analysis of the problem of *Itaipu* is the following:

In the first phase, the data were selected and it was decided that the methodology would be applied only to the extensometers located in stretch F.

In the second phase, the data given by *Itaipu* were converted into spreadsheets, from which the necessary data used for developing this study were extracted.

In the third phase, the data were standardized in order to receive the subsequent application of the clustering methods.

In the fourth phase, the Factor Analysis and the Clustering Analysis were applied at the same time. The Factor Analysis was also applied within each cluster formed through Clustering Analysis.
