Posted in Geotechnical Engineering, Soil Mechanics

Mexico City’s surprising crisis: the city is sinking

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.

A diagram, from the Swedish geotechnical engineer and academic Bengt Broms, showing how we consider the volume and mass/weight relationships in soil. The particulate matter of the soil means that the soil mass has three components: solid (particles,) water (in the voids) and gas/air (also in the voids.) That simplification is shown above, along with the definition of void ratio.
A diagram, again from Bengt Broms, illustrating the problem in Mexico City and whenever what we call consolidation settlement takes place. The soil particles have been combined into one mass (hatched area.) As pressure is applied, the particles come closer to each other and the volume of the voids decreases, thus we have settlement.
A photo from Mexico City showing the effects of subsidence many years ago. The top of the pole was originally the ground surface before structures were built on it and subsidence started. The photo and an explanation can be found in the textbook Soils in Construction. Needless to say, it’s only gotten worse in the intervening years. Photo courtesy of J.R. Bell.

My own lecture on the subject of settlement and consolidation is here.

Posted in Academic Issues, Soil Mechanics

The “Line of Optimums” Approach for Compaction

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.

I discuss this in my class video for Soil Mechanics: Compaction and Soil Improvement, but let’s consider an example, in this case from Rebrik (1966).

Compaction Chart with Multiple Compactive Energies and Line of Optimums, from Rebrik (1966)

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.
Posted in Academic Issues, Geotechnical Engineering, Soil Mechanics

Unified Soil Classification, from NAVFAC DM 7

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.)

An example of how this works is here.

NAVFAC DM 7 remains a popular reference book for geotechnical engineers, and ordering information is here.