Strain gages are one of the most fundamental types of transducers for experimental data. In fact, since force cannot be measured directly (yes that sounds odd, but it’s true!), strain gages form the basis of many other transducer types, including load cells, torque meters, piezometers, etc. Interpreting strain gage data should be straightforward, as anyone who has completed a mechanics or materials course will attest. Strain times modulus equals stress, and stress times area equals force. No big deal, right?
Unfortunately, like real life, real world engineering is never quite that simple. To begin with, deep foundation elements are a composite of two materials (concrete and steel) whose properties are an order of magnitude different. Second, concrete itself is a material with properties which are heterogeneous. It varies widely with mix recipes and placement techniques and its stress-strain curve is non-linear under any significant applied load. Lastly, the Young’s modulus for concrete is typically derived from the ACI formula, which itself is a best-fit through a scatterplot, with the potential for significant uncertainty. All these factors combine to make estimating the Young’s modulus using standard methods to the precision required to accurately interpret embedded strain gage data quite tricky.
A top-down static load test usually overcomes this difficulty by embedding one set of strain gages near the head of the pile, above the ground or mudline elevation. These gages are subject to the full force of the applied load as in a free-standing column, and the pile’s stiffness (modulus times area) can be back-calculated as applied load divided by the average strain measured in this top level of gages.
For bi-directional tests with embedded jacks this technique is not an option. This is because strain gages have to be located at least two pile diameters away from the load assembly for uniform plane strain to develop. But over this length, load is shed via skin friction. In other words, even the closest strain gages to the jack will not be subject to the full applied load, but rather a reduced load. How much load is shed is a function of the load computed from the strain gage, so that cannot be used (directly) to compute the pile stiffness because it becomes a circular calculation.
Fortunately, the Tangent Stiffness analysis method derived by Dr. Bengt Fellenius helps solve this problem. The method allows for an indirect analysis of pile stiffness by plotting the change in strain divided the change in applied load vs. total load, then integrating the resulting linear regression fit. A further refinement in Nonlinear Pile Stiffness analysis was introduced by Jon Sinnreich to explicitly document the need for incremental load calculation when dealing with variable pile stiffness. While these two papers explain the material in a straightforward manner, perusing them should convince most readers that interpreting strain gage data in deep foundation testing is far from trivial.
LTC is committed to giving our clients the full benefit of our combined years of experience dealing with exactly these types of issues.