Neither the institution I teach at nor the FHWA have any interest in this topic. So funding is unlikely.

The sudden shift to online instruction has forced me to focus my attention on getting all of my content online, done for my Fluid Mechanics Laboratory course, currently in progress with my Foundations course but also probably with my Soil Mechanics Course.

As was the case with the original wave equation program and the inverse effort, to get to a better solution is going to require a major, sustained effort, and given the current tendency for research to be piecemeal, that’s unlikely in this country for the foreseeable future.

Some observations:

This project was never intended to be the “end-all” of this topic, although it’s probably the last time that a 3D model is developed “from scratch” for this problem. It was intended to inspire others with better numerical and programming skills to take this to a higher level.

My plans are to concentrate on my online educational activities, and also topics that are more pile driving equipment related. Putting my course lectures on YouTube is a big part of that. The TAMWAVE project needs a revision to incorporate some of the improvements suggested by my research into STADYN. Stay tuned.

I think that, sooner or later, this problem will be solved, and pile dynamics will be performed with a model using the same basic concept as STADYN. I doubt, however, that this model will first be developed and made practical in the U.S.. There are just too many obstacles, some regulatory, others simply reflecting the state of deep foundations here, that mitigate against that. That is a tragedy, but sad to say it’s one that will be repeated in other fields with growing frequency.

This is a new paper on the STADYN project. You can download it here. The abstract is as follows:

Methods of estimating the capacity of driven piles from dynamic pile top data have been well established for many years. The STADYN program uses a finite element methodology that is different from those currently in use. In this paper this program is applied to a well documented pile scenario of concrete piles driven into predominantly cohesionless soils. The pile top force-time and velocity-time history is applied to the model and the results compared with both dynamic tests using conventional methods and static load test results. The results are mixed; the dynamic results compare well with CAPWAP but other factors suggest that more work needs to be done on the STADYN model.

The conference that this was scheduled to be presented at was cancelled in view of COVID-19, so I created a “voice over PowerPoint” presentation. You can listen to it here:

While looking through some files, I found these from the original STADYN project, from the comparison case with GRLWEAP. I’m passing these along to give you an idea of the graphical output of this program. My thanks to Jonathan Tremmier of Pile Hammer Equipment for allowing me to use this copy of GRLWEAP.

It’s been a while since the last post on this subject; this has slowed things down. But in the course of getting started again a little “side trip” shows a good illustration of how sometimes determining the engineering properties of a structural element–in this case a driven concrete pile–can be challenging.

The test case for this is the FHWA’s A Laboratory and Field Study of Composite Piles for Bridge Substructures. All of the information in this piece comes from that report. The report dates back to 2006 and the actual field work earlier in the decade. One of the test cases involves a bridge replacement in Hampton, VA, as shown above.

The study involved the installation and testing of three different types of piles, as shown below. We’ll concentrate on the prestressed concrete pile on the left.

The prestressed concrete pile was a 610 mm square solid pile. This means that the cross-sectional area is . The pile was 18 m long, as shown below.

Stress-strain curves were developed for the three materials, and these are shown below.

From the stress-strain curve for the concrete alone (and we usually assume that the concrete governs the pile elastic properties for compression at least) the curve would indicate that the modulus of elasticity is somewhere around . The diagram below, however, indicates that those involved in the project determined the modulus of elasticity to be around .

The interest from the STADYN standpoint is to obtain a force-time and velocity-time curve from the Pile Driving Analyzer, and this is certainly forthcoming:

The value of was probably determined from the two force peaks. The first force peak is the impact of the hammer on the pile and the second is the reflection of that impact from the toe. Both are compressive and the second is strong, which indicates a high level of toe resistance.

As is typical with PDA output, the force and the velocity (multiplied by the impedance) are plotted together. Unfortunately the document does not give the impedance for this case, so it’s necessary to back compute the impedance. Since we have a reasonably good idea of from the PDA, and the impedance Z is

we can determine the impedance. Solving for c from ,

We need to pause at this point and note that other values of acoustic speed are implied in the data. For example, the following table states an acoustic or wave speed of 3800 m/sec.

Before and after the test, PIT (Pile Integrity Tests) were run on the pile. The results are below.

Converted to SI units, the acoustic or wave speed becomes 4037 m/sec, which is fairly close to the PDA tests. The PDA results will be used for the remainder of this piece.

In any case, using the EA values from the earliest part of the test, the impedance is

The data was extracted from the PDA results. The force values could be used “as is.” The velocities were in reality the product of the velocity and the impedance, so the dashed line values were divided by the impedance just obtained to yield a velocity. Unfortunately, when this was put into STADYN, the velocities that resulted–even in the early stages of impact, where semi-infinite pile conditions predominate–the velocities of the program varied from the velocities extracted from the data by a factor of two. Checks in the program did not show any change in the way the program executed the algorithm from earlier runs, but the impedance values the program was yielding were considerably different from the one above.

In an attempt to sort things out, it is good to start by noting that the acoustic speed is computed by the equation

The report states that the pile was poured to normal Virginia DOT specifications. A fair assumption is that the density or unit weight of the concrete is close to normal, or . That being the case, the computed acoustic speed from the values of Young’s modulus E (which is necessary to put into Pa for unit consistency) and the density assumed yields

Something is clearly wrong here, and the most probable culprit is the modulus of elasticity of the concrete. A common way to estimate the modulus of elasticity of concrete in MPa is to use the formula

where is the 28-day compressive strength of the concrete. The report gives this to us at the time of the load tests as 55 MPa, which yields a modulus of elasticity of

This is considerably higher than the earlier data would indicate. It’s worth noting the the specifications for the pile set a minimum value for as 35 MPa; this indicates that the values of Young’s Modulus for concrete in piles can vary widely.

Another–and given the data probably a stronger–approach to compute the value of Young’s Modulus is to back compute it from the acoustic speed (which is known within reasonable values) and the density (see assumption above.) Solving the basic equation for acoustic speed for Young’s Modulus yields

Substituting our values yields

The impedance from this would be

Applying values along this line and recomputing the velocities, the results of the STADYN program and the actual PDA results were much closer.

Conclusions

The reason for the discrepancy in Young’s Modulus–and thus the pile impedance–is unclear. It may be due to rate effects on the elastic response to concrete, or it may be due to other factors.

Wave equation analysis are typically run according to “standard” material properties. Those who run these should be aware that, with concrete and wood, those properties may not reflect the properties of what actually gets driven into the ground.

Any force- and velocity-time data such as are produced by the PDA should have their axes labelled properly (with both force and velocity) or with the impedance reported.

Even with controlled research projects, discrepancies can arise in the data which can impede (pun somewhat intentional) the use of the data, and careful analysis is necessary to avoid problems such as was seen in this situation.

Abstract: The STADYN program was developed for the analysis of driven piles both during installation and in axial loading. Up until now the test cases used were in predominantly cohesive soils. In this paper, the expansion of the program’s use into predominantly cohesionless stratigraphies has required consideration of two important factors. The first is the difference between strain-softening in clays as opposed to sands, and additionally static vs. dynamic strain effects. This requires a review of the whole concept of the “magical radius” for pile elasticity. The second is the effect of dilatancy on the response of the pile to axial loading. Both of these are discussed in this paper, and test cases are presented to illustrate the application of the program to actual driven piles.