Broadly, civil Engineering curriculum covers structural, geotechnical, transportation, water resources, and environmental engineering related subjects. In most of these subjects, it is necessary to deal with the physical, mathematical, and simulation models and representative field data. When dealing with the models one has to deal with the experimental data. In many of these branches field data are collected to analyze and model the real life phenomenon and there are lot of uncertainties involved related to this data. Some of them are briefly described in the following paragraphs.

Concrete is the major building material and various grades of concrete are available for various applications. Compressive strength of a particular grade of concrete is determined based on the strength of a few sample cubes made from it. It is necessary to test a minimum number of cubes to have certain confidence on the characteristic strength of a particular grade of concrete. In this case, the test on a particular cube made from a particular grade of concrete is an experiment and when similar experiments are conducted on many samples the resulting strength may take different values. Though a particular gradation of materials is used in making these cubes, there is going to be some variability in the gradation of materials and there is no control on this variability. When huge quantity of concrete is mixed at once, it is difficult to control the variability in the gradation. This variability leads to different values of compressive strength (Figure 1.2). Other graphical representations of the same data are shown in Figures 1.3 to 1.5. Exact utility of these figures is discussed in the coming lectures.

Figure 1.2: Compressive strength data of a particular grade of concrete

 

Figure 1.3: Frequency histogram of the compressive strength data

The mean compressive of strength of a representative sample cubes is taken as the characteristic strength of a particular grade of concrete. Strength of not more than 5% of cubes is expected to fall below the characteristic strength. The strength of the cubes made from a particular grade of concrete is a variable and hence the mean strength of a sample cubes is also a variable under repeated sampling. To understand this variability and its implications it is necessary to have minimum knowledge of probability methods and statistics.