Posted in Soil Mechanics

Sorting Out the Coarse Fraction Using Pie Charts, and a Unified Classification Example

In the process of classifying soils using the Unified System, one of the parts which some students find tricky is the business of the “proportion of the coarse fraction,” i.e., the way we decide if a mostly coarse-grained soil sample is sand or gravel. This is an attempt to illustrate this using a pie chart.

First, for purposes of the Unified System of soil classification, for particle distribution size by weight/mass all soils can be broken down into three parts:

  1. Gravel, the portion of the sample retained on the #4 sieve
  2. Silt and Clay/Fine-grained portion, the portion which passes the #200 sieve (or, put a little eccentrically, retained on the pan)
  3. Sand, what’s left over from the first two portions

Let’s start with an example, the Soil “A” from the course example, which has a fine fraction of 10% and a gravel portion of 11%. Conventionally, we would say that the coarse fraction is 90% of the weight, and that the gravel portion of the coarse fraction is 11%/0.9 = 12.1%. Since the sand portion is 100% – 12.1% = 87.9%, the sand portion is greater, and thus the soil is a sand. This is correct but confusing to beginners.

If we were to graph the three portions in a pie chart, it would look like this:

We break out the fine grained (silt and clay) portion and see immediately that the sand fraction is larger than the gravel. Since the combination of the two are most of the soil (overwhelmingly in this case) the soil is a) coarse-grained and b) a sand.

Let’s look at something a little more challenging: a soil which is only slightly predominantly course grained:

The soil is split 51/49 coarse-grained, so it’s classified as coarse grained (S or G.) We could go through the math like we did earlier, but the pie chart, be it ever so closely, shows that the gravel portion is slightly (26 vs. 25) larger than the sand portion. So this would classify as a gravel, GM or GC depending upon the Atterberg limits.

Here’s another example, this time with the fine fraction reduced. Here the sand is slightly larger than the gravel (32 vs. 28) and so the soil will classify as a sand, SM or SC.

For our last example, let’s do an entire soil classification. The gradation chart looks like this:

From this, we can construct our pie chart as follows:

From the pie chart we see two things:

  1. The silt and clay fraction is only 3.4%; this is obviously a coarse-grained soil, and given the low portion of fines a clean one.
  2. The gravel portion is obviously larger than the sand, thus this is a gravel, “G” classification.

Since the fines are so low, it is either a GW or GP. We can determine which by looking at the coefficients of uniformity and curvature. Using the method shown in the Soils and Foundations Manual, these are as follows: D_{60} = 17.11,\,D_{30} = 2.84,\,D_{10} = 0.16 , from which C_u = 107,55\,C_c =  2.97 . In the Unified System this is a well graded soil, hence the classification is GW.

We can see from this that the pie chart visualisation is a useful tool when attempting to understand whether a coarse-grained soil is predominantly sand or gravel. It also helps us to see that the “hard” distinctions of the Unified System are not necessarily the whole story of a soil sample, which is why experience is so important in geotechnical engineering.

Posted in Civil Engineering

Construction Begins on an Interstate Highway in California — Transportation History

September 25, 1967 In Southern California, a groundbreaking ceremony was held at El Cajon Boulevard and Boundary Street in San Diego for Interstate 805 (I-805). Planning for that route dated back to 1956, the same year in which the Interstate Highway System itself first came into existence. After the groundbreaking ceremony, I-805 was constructed in phases. It […]

Construction Begins on an Interstate Highway in California — Transportation History
Posted in Geotechnical Engineering, Soil Mechanics

Folds, Dip and Strike

Soil Mechanics courses tend to do a cursory treatment of engineering geology, and mine is no exception. This is due to time and curriculum limitations. This is a nice presentation on this subject, describing the various kinds of folds and how they relate to the strike and dip on geologic maps.

A salutary note at the end of Rutherford Aris’ Mathematical Modelling Techniques: When a model is being used as a simulation an obvious comparison can be made between its predictions and the results of the experiment. We are favourably impressed with the model if the agreement is good and if it has not been purchased […]

Don’t Try to Predict Physics (or Much of Anything Else) Without a Model — Chet Aero Marine

Don’t Try to Predict Physics (or Much of Anything Else) Without a Model — Chet Aero Marine

Posted in Academic Issues

A Salutary Reminder About the Limitations of Data and Statistics

In a culture that imputes statistical studies with authority they don’t deserve, this warning, from Numerical Recipes in FORTRAN 77, is very salutary:

Data consist of numbers, of course. But these numbers are fed into the computer, not produced by it. These are numbers to be treated with considerable respect, neither to be tampered with, nor subjected to a numerical process whose character you do not completely understand. You are well advised to acquire a reverence for data that is rather different from the “sporty” attitude that is sometimes allowable, or even commendable, in other numerical tasks.

The analysis of data inevitably involves some trafficking with the field of statistics, that grey area which is not quite a branch of mathematics —and just as surely not quite a branch of science. In the following sections, you will repeatedly encounter the following paradigm:

  • apply some formula to the data to compute “a statistic”
  • compute where the value of that statistic falls in a probability distribution
    that is computed on the basis of some “null hypothesis”
  • if it falls in a very unlikely spot, way out on a tail of the distribution,
    conclude that the null hypothesis is false for your data set

If a statistic falls in a reasonable part of the distribution, you must not make the mistake of concluding that the null hypothesis is “verified” or “proved.” That is the curse of statistics, that it can never prove things, only disprove them! At best, you can substantiate a hypothesis by ruling out, statistically, a whole long list of competing hypotheses, every one that has ever been proposed. After a while your adversaries and competitors will give up trying to think of alternative hypotheses, or else they will grow old and die, and then your hypothesis will become accepted. Sounds crazy, we know, but that’s how science works!