Posted in Uncategorized

In Memoriam: GZA Founder Donald T. Goldberg —

His contributions and legacy are reflected in the values of the company he built and the leadership he provided to the industry he loved. President and CEO Patrick Sheehan reflects on Don’s legacy. “It would be […]

In Memoriam: GZA Founder Donald T. Goldberg —

Since 2004 this site has hosted Goldberg’s classic document Lateral Support Systems and Underpinning.

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 Geotechnical Engineering

An Overview of Compaction Equipment, from DM 7

Below are some charts for selecting compaction equipment for a given project and soil condition, from NAVFAC DM 7.02

You can order NAVFAC DM 7.02–and 7.01–for this and more valuable information by clicking here.

Posted in Academic Issues, Civil Engineering

Yes, Civil Engineers, Things Move —

A salutary reminder from Y. Ryabov’s An Elementary Survey of Celestial Mechanics: There is of course no sense in asking why the planets rotate or why they have motion in general. Everything in the universe, from the smallest dust particle to colossal cosmic bodies, is in constant motion. There is no such thing as matter […]

Yes, Civil Engineers, Things Move —