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One of those “things” in geotechnical engineering that looks like “settled science” but may not be is the whole business of lateral earth pressures for braced cuts. (An example of one is shown at the right.) Textbooks of all kinds (including Soils in Construction) show pressure profiles and solution techniques that are “definitive.” Or are they? This article is more about asking questions than delivering another round of “definitive” answers, but hopefully it will at least spark some thought and perhaps make practitioners more careful in their application of these methods.

The Basic Problem

Based on experience, first in Berlin and later in Chicago, Terzaghi (and later also Ralph Peck) developed a set of pressure distributions as shown at the left. These are at variance with those usually associated with retaining walls in general and sheet pile walls in particular. The theory behind these (certainly for the clays) had its genesis in Rankine theory adapted for cohesive soils, but the distribution is rather different. These distributions have been reproduced in many textbooks and reference books, including Soils in Construction and Sheet Pile Design by Pile Buck.

It’s worth noting that there are other pressure distributions that have been formulated other than the ones shown above, as outlined by Boone and Westland (2005).

Along with the distributions came the method of using them: the “hinged method” of analysing the sheet pile wall. Strictly speaking the sheet pile wall is a continuous beam with multiple supports. Since there are usually more than two struts and supports, to use a continuous beam requires a statically indeterminate beam. Applying hinges (as shown at the right) can make the beam statically determinate. Although methods for solving statically indeterminate beams existed in Terzaghi’s day (remember it was geotechnical methods which then and now lag the rest of civil engineering in advancement,) converting the problem to a statically determinate one was convenient for computational purposes.

But then comes the kicker: as generally presented, if the distributions above are used, they must be used with the hinged method, even when analysing a braced cut wall using a braced cut method with a continuous beam is nearly trivial now. Why is this?

How It Came About

Like so many things in civil engineering, the investigation of pressures on braced cuts came about as a result of tragedy. As noted by Rogers (2013):

On the evening of December 1, 1938 Terzaghi delivered a terse lecture titled “The danger of excavating subways in soft clays beneath large cities.” The lecture focused on his recent experiences with construction of the Berlin Subway, which was hampered by a high water table in running sands. These conditions had contributed to the sudden failure of a shored excavation which killed 20 workers in August 1935. He made a convincing case for proper geotechnical oversight during construction if similar tragedies were to be avoided in Chicago.

The lecture with its graphic images of the dead bodies beneath the collapsed bulkhead along the Hermann Goring Strasse succeeded in scaring his audience to death, and promptly found the State Street Property Owners’ Association and City of Chicago bidding for Terzaghi’s services. The City wanted him to advise them on how best to monitor progress of excavations and ground settlement, differentiating what structural or architectural damage was caused by subway construction.

Both Terzaghi and Ralph Peck ended up doing the monitoring. The soils in Chicago were predominantly soft clays, so the earth pressures were different. Much of the theory and application behind this is documented in Peck (1943). (Interesting side note: one of the lines of the subway ran past the site of Vulcan’s old Milwaukee Avenue plant where the first Warrington-Vulcan steam hammers were designed and built.)

One might ask, “How did they come up with the earth pressure distributions?” They did so–and this is the key to the problem–by measuring the reactions on the braces. They did this in the face of the fact that, as is usual with braced cuts, the braces were put in successively with excavations, and that much of the movement of the wall–and thus the mobilisation of the earth pressures–was in place before the braces were installed. (It is easy to forget the importance of that mobilisation, but both Terzaghi and Peck were well aware of it and its effects.) To translate the loads on the braces into a pressure distribution, they adopted Terzaghi’s procedure from the Berlin subway as follows (Peck (1943)):

The vertical members of the sheeting are assumed to be hinged at each strut except the uppermost one, and a hinge is assumed to exist at the bottom of the cut. The abscissas of the pressure diagram “A” represent the intensity of horizontal pressure required to produce the measured strut loads. A study of such diagrams for all of the measured profiles disclosed that the maximum abscissa never exceeded the value K_A Y_a H. Every measured set of strut loads resulted in a different pressure diagram “A,” all of which were found to lie within the boundaries of the trapezoid indicated by the dotted lines. Thus, if strut loads are computed on the basis of this trapezoid, they will most probably be on the safe side.

This, therefore, is the origin of the requirement to use a hinged wall where there were no actual hinges. At the time it was a reasonable solution. As noted earlier, solutions for continuous beams existed but back-figuring the pressures using them would have been a formidable “inverse problem” given the computing power of the day. Doing this, however, raises as many questions as it answers, such as the following:

• If a continuous beam had been used, would the pressure distribution have been different?
• What is the relationship between the pressure distribution computed by Terzaghi’s method and what is actually experienced by the wall? Put another way, did Terzaghi’s simplification of the structural situation compromise his distribution? (No doubt some conservatism in the pressure distributions offset that problem.)
• If the pressure distributions are right for engineering purposes, is it still necessary to use a hinged solution? Especially with beam software, a continuous beam is much simpler to analyse and structurally more representative of the actual sheeting and bracing.

Peck himself was well aware of the limitations of the method; he made the following admission:

It is apparent, therefore, that it is useless to attempt to compute the real distribution of lateral pressure over the sheeting. Of far greater practical importance is the statistical investigation of the variation in strut loads actually measured, in order to determine the maximum loads that may be expected under ordinary construction procedures.

This too raises another question: in developing distributions primarily to determine brace/strut loads, do we compromise the accuracy of determining the maximum moment in the sheeting itself?

Moving Forward

It’s difficult to really know how to answer many of the questions this problem raises. Some suggestions are as follows:

• It is hoped that there is enough conservatism in these earth pressure distributions to accommodate either method. That’s likely, as inspection of some of Peck (1943) curves will attest. That likeliness is buttressed by the fact that these methods came out of a deadly accident.
• More comparisons of hinged and continuous beam models are needed. There is one in Sheet Pile Design by Pile Buck and another in the post on this site A Simple Example of Braced Cut Analysis. These are simply not enough to establish a trend one way or another, although the results are interesting and hold promise.
• A “hand” solution based on parametric studies using FEA or another numerical method would move things forward considerably. Obviously these are limited by the accuracy of the soil modelling but they can be applied to a wider variety of cases.
• Field tests should include measurement of actual lateral earth pressures on the sheeting at various points. The use of strut loads, although easier to measure with the technology of the 1930’s and 1940’s, is still indirect. Another interesting approach is to use an inverse method and a continuous beam with existing data, although this is not as satisfactory as direct measurement of earth pressures.

References

• Boone, S.J. & Westland, J. (2005) “Design of excavation support using apparent earth pressure diagrams: consistent design or consistent problem?” Fifth International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, International Conference on Soil Mechanics and Geotechnical Engineering, 809 – 816.
• Peck, R.B. (1943) “Earth-Pressure Measurements In Open Cuts, Chicago (Ill.) Subway.” Transactions of the American Society of Civil Engineers, Vol 108, pp 1008-1036.
• Rogers, D.A. (2013) “Ralph Peck’s Circuitous Path to Professor of Foundation Engineering (1930-48)” Presented at the Seventh International Conference on Case Histories in Geotechnical Engineering.