The city with a metropolitan population of over 20 million is sinking at a rate of almost 50 centimeters (20 inches) per year — and this isn’t stopping anytime soon.
At first glance, you’d be inclined to attribute this to the strong earthquakes that sometimes strike Mexico City. But while earthquakes can cause their own damage, they’re not the main culprit here. Instead, it’s something much more inconspicuous: subsidence.
You can read it all here. Put into geotechnical terms, the bed of old Lake Texcoco has some very high void ratio soils, and as a large city puts pressure on them the void ratio decreases as the voids between the soil grains shrink. Thus the entire city has severe settlement, total and differential.
There are some things in geotechnical engineering that don’t get really good (if any) coverage in many textbooks, which means that those who go on into that part of civil engineering are blindsided by their appearance. One of these is the “line of optimums” approach for compaction evaluation. The only formal textbook I know of that covers it is Soils in Construction, for which I must credit my co-author, Lee Schroeder. It also appears in the Soils and Foundations Reference Manual.
The line of optimums approach seeks to answer a key question in compaction: how much compactive energy is necessary to effect a given compaction? We have the Standard Proctor and the Modified Proctor test, but when we’re trying to determine a specific compactive effort for a particular soil and project, we need more flexibility.
Lines 1, 2, 3 and 4 represent compaction curves for a soil, but with a different number of blows (25, 50, 100 and 150, as shown in the chart.) The energy variation is explained in my video. In any case with the increase in compactive energy is a closer packing of the soil particles. The peak dry density/unit weight also increases with compactive energy, although the water content decreases (which makes sense as the void ratio decreases with greater compaction.) Line 6 through the peaks in the compaction curve is referred to as the “line of optimums.” Once we establish this line we can make a determination of the compactive effort we will need based on the result we are looking for, taking into consideration the degree of relative compaction we are prepared to allow for.
Line 5 is the zero air voids curve.
The line of optimums method is a good one for compaction evaluation, and we hope that this little presentation helps you to understand it.
Rebrik, B.M (1966) Vibrotekhnika v burenii (Vibro-technology for Drilling.) Moscow, Russia: Nedra.
In the course of teaching my Soil Mechanics class, I’ve tried numerous different charts and methods for teaching the Unified system of soil classification. Probably the most success I’ve had is with the one from NAVFAC DM 7, and it’s below. (I’ve included the plasticity chart for completeness.)