Category: TAMWAVE

Getting ready for another semester of Foundations comes with a minor update to the TAMWAVE driven pile analyser, which includes axial and lateral settlement analysis and wave equation analysis of pile driving. The last major revision was in 2017 and details about that are here. The revisions this time are as follows:

• Initial pile length reduced to 50′, and initial phreatic surface depth reduced to 25′.
• H-Piles excluded from toe plugging.
• Strain softening coefficient for soil shear modulus increased for more realistic values.
• Toe quake for cohesive soils set to more conventional values, as Tomlinson’s method was used to compute N_q.
• Added Davisson’s Method line for evaluation of virtual pile load test, and flipped the graph to more realistically simulate actual load-settlement curves. (See above for the new format.)
• Marked the target SRD value differently to make it easier to see.

This will probably be the last update to the routine, which first went online in 2005. We hope that you find it useful.

One of the things that was attempted in the TAMWAVE project is the use of cavity expansion theory to estimate soil set-up in cohesive soils.  Doing this, however, brought some complications that need some explanation.

Cavity expansion theory is basically the study of what happens when one body expands inside of another.  When this takes places, additional radial stresses (most analyses center around a cylinder or sphere) are generated.  In the case of driven piles, these additional stresses add to the pile’s resistance to load.  It can be argued that cavity expansion is one of the key advantages of driven piles.  In the case of drilled piles such as drilled shafts or auger-cast piles, this does not take place, as the soil is removed either before or during the actual pile installation.  The result of this is that driven piles, for the same length and diameter as a corresponding drilled pile, a driven pile will have a greater resistance to load (ultimate capacity.)

Applying cavity expansion theory to piles has a long history and is detailed in documents such as Randolph, Carter and Wroth (1979) and Yu and Houlsby (1991).  Our particular interest is with clays because, in addition to the changes in the soil from cavity expansion, the pore water pressure increases.  This is the primary (but not the only) reason why the SRD (soil resistance to driving) in cohesive soils is significantly less than the ultimate capacity; this fact inevitably complicates drivability studies.

The increase in pore water pressure is a dynamic phenomenon; it experiences a sudden increase during driving and then gradually dissipates after installation.  How gradually the latter takes place depends on many factors such as the permeability of the soil.  Study of this phenomenon is well represented in the literature; however, for the TAMWAVE project it is not really of interest.  The primary interest here is the value of SRD after the immediate increase of pore water pressures during driving.

Both cavity expansion theory and practice show that excess pore water pressures can easily exceed the effective stresses.  In principle, considering that we have established the beta (effective-stress dependent) method for both cohesionless and cohesive soils, this can mean a complete loss of SRD.  Although dramatic drops in SRD are not unknown, for most piles this is unrealistic.  The reason for this is that, like the dissipation, the build-up of pore water pressures is a dynamic phenomenon, albeit in a much smaller time frame.  Dissipation, hindered as it is by the low permeability of cohesive soils, begins immediately.  Pore water pressures (along with any other stresses induced by cavity expansion) also vary with the distance from the pile.

The result of all this is that prediction of both the increase of pore water pressure and its effect on the SRD of the pile during driving is a complicated phenomenon that is not completely represented by closed-form cavity expansion based solutions.  For a project such as this, what we need is something that will give a reasonable representation of soil set-up for cohesive soils.  To accomplish this, we stick with computing the excess pore water pressure, but with a different methodology.  We assume the following:

1. The basic validity of our effective-stress based beta methods of shaft friction calculation.
2. All of the decrease from static ultimate capacity to SRD takes place due to pore water pressure increase.
3. The excess pore water pressure increases affect the effective stress used to compute the shaft friction.
4. Only those pile segments under the water table are subject to this analysis.

Assuming all that, for a soil set-up factor (from this source, loosely adapted) , the excess pore water pressures that affect the effective stress (which in turn determine the shaft friction) are computed by the equation

This gives identical results to those when the are applied directly.

In practice this phenomenon is still subject to investigation.  Some of the research involves use of numerical methods (such as finite element methods) to simulate cavity expansion effects.  This is doubtless an advance over the closed-form solutions of the past, and a necessity given the complexity of the physics of the problem.  Empirical methods are also still being developed, such as are documented by Wang, Verma and Steward (2009).

The completely revised TAMWAVE program is now available.  The goal of this project is to produce a free, online set of routines which analyse driven piles for axial and lateral load-deflection characteristics and drivability by the wave equation. The program is not intended for commercial use but for educational purposes, to introduce students to both the wave equation and methods for estimating load-deflection characteristics of piles in both axial and lateral loading.

We have a series of posts which detail the theory behind and workings of the program:

• TAMWAVE: Pile Toe Resistance, and Some More on Pile Shaft Resistance
• TAMWAVE 1: Entering Basic Soil and Pile Properties
• TAMWAVE 2: Modifying the Soil Properties
• TAMWAVE 3: Basic Results of Pile Capacity Analysis
• TAMWAVE 4: Shaft Resistance Profile, ALP and CLM2
• TAMWAVE 5: Wave Equation Analysis, Overview and Initial Entry
• TAMWAVE 6: Results of Wave Equation Analysis
• TAMWAVE 7: Analysis for a Cohesive Soil

This program replaces the original routine which was originally written in 2005 and updated in 2010. The documentation for that effort is here.

With the data entered for the wave equation analysis, we can now see the results.  There’s a lot of tabular data here but you need to read the notes between it to understand what the program is putting out.  If you are not familiar at all with the wave equation for piles, you need to review this as well.

For those familiar with the wave equation, there are few surprises.  Some explanation of the parameters can be found with the documentation for the TTI program.

A detailed output of the parameters for each segment/element.  TAMWAVE no longer uses the simplifications used in the past for resistance distribution along the shaft, i.e., uniform, triangular, etc., but constructs one based on the soil properties.  Much of this data is repeated from the static analysis.

This table shows the end results of the run for the “target” SRD of the pile.  “SRD” is “soil resistance to driving,” and in TAMWAVE for cohesionless soils, SRD and the ultimate capacity are the same.  That’s not the case with cohesive soils, as we will see.  In any case TAMWAVE always does a “bearing graph” analysis, which proportionally varies the SRD and obtains different results for the blow count, maximum tensile and compressive stresses.  The bearing graph method isn’t perfect but it’s probably the best way we have to account for varying site conditions and to make judgments about the effect of those on our hammer selection.

The adoption of “Smith-type” damping was originally done for comparison purposes but for bearing graph analysis has one important advantages: it varies the soil radiation damping with the SRD, which is more realistic than just assuming fixed damping.

The table above only appears if the target SRD is actually achieved during bearing graph analysis.  If it doesn’t come up, the bearing graph analysis could not achieve net pile penetration at the target SRD, which means you need to revisit your hammer selection.

Here we see the second graphical output: the force-time history at the target SRD.  There are actually two histories: the actual pile head force (blue) and the pile head velocity multiplied by the impedance (red.)  For semi-infinite piles, the two should be the same; they will differ for actual finite piles, as is easily seen.  Although a “semi-infinite pile” may seem a very theoretical concept, the relationship of the two plots is very important in the field application of pile dynamics.

The final results are shown here.  In this case, at the target SRD, no permanent set of the pile is recorded.  It will be necessary to vary the size of the hammer, being mindful of the stresses (whose allowable values are described here.)

At this point the analysis of this pile is complete.  The program gives you the choice of simply trying another hammer or starting over.  The latter is what we will do next with a sample case for cohesive soils.