G1-Lecture19-Variability-of-Soils

G1-Lecture19-Variability-of-Soils - United States Military...

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United States Military Academy Mathematics Seminar Professor L. Prieto-Portar PhD, PE MA-206: Statistics in Construction: Compaction
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The Variability of Soils for Compaction. The complexity of the soils that support transportation pavements (highways, railroad embankments, airport runways, etc) require powerful tools for predicting their behavior, despite their variability and uncertainty. Their variability is handled with statistics . Their uncertainty is handled with probability . These notes are an attempt to show how they are used in a common daily task, such as the compaction of roads. Two road contractors A and B are given a ten kilometer stretch of highway to build. Their compaction efforts need to be evaluated. These notes represent an attempt to study their skills and quality control.
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How can you quantify the compaction of a soil when it varies greatly from point to point? A conventional approach has been to use an “average” value, and assume that the soil has that same average homogeneity for design purposes. This single value of the soil parameter then receives a factor of safety to prepare a design. This method is called the deterministic approach, which is still very popular because of its simplicity, albeit unrealistic representation of nature. It forms the basis of analysis for the elastic theories of steel and concrete structures. The quality assurance from a road contractor however, requires an assessment of the soil’s variability . Instead of factors of safety applied to a simple deterministic model, it is replaced by the concept of a probability of failure . Also, recall the distinction between the accuracy of the tested compaction versus the precision of the results. Instruments may give very precise measurements, but they may be meaningless if they are not accurate. For example, suppose the real (accurate) pore pressure at a point under a dam is u = 3.2 kN/m 2 . It would be meaningless that a very precise instrument show u = 3.9568 kN/m 2 .
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In general, the true value of any soil parameter can never be known, and is only estimated from a number of measurements, all of which have varying degrees of errors such as: 1. From the soil’s intrinsic variability, 2. from sampling errors, and 3. from testing errors. Each of these errors possesses both bias and random errors. They are random when they are from unknown sources, or systematic (also called bias ) when they come from the way or method of testing. Testing a soil using the
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G1-Lecture19-Variability-of-Soils - United States Military...

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