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API REPORT 13 Document Information:
Title
Cyclic Lateral Loading of Piles; Analysis of Centrifuge Tests
American Petroleum Institute
Publication Date:
Jun 4, 1979
Scope:
Summary of Previous Work
In two previous reports (6,7) results were given of a number of cyclic lateral load tests on model piles loaded in a centrifuge. The tests results were obtained in the form of loads and deflections at the top of the pile and readings from strain gauges distributed down the pile; the latter are interpreted in the form of moments. In contrast to field tests, the centrifuge pile experiments are carried out in an extremely uniform medium consisting, in the tests discussed, of dry and wet sand in two test series. The result of this soil uniformity is that moment readings can be represented by a smooth and continuous curve. Erratic data due to alternately dense and loose soil layers are avoided. In the second report (7) the fitting of curves to this data was discussed briefly with reference to the use of a fifth-order spline function. The advantage of the technique is that the curve passes through all the data points in contrast with least squares or linear regression fits. In the latter , general curves are obtained representative of the pile deflections in some way which pass near but not necessarily through the data points. Errors in the data are inherently accepted in this method.
In addition, the spline fit can be adapted to the boundary conditions at both ends of the pile so that these requirements can be met exactly by the functions selected. For example at the point of lateral load application to the pile top, the moment is zero. However, the derivative of the moment is the lateral load in the pile, and this value is known at the pile top during the experiment. Also, the second derivative is the soil reaction on the pile, and, in sand, this must be zero a t the pile top, The smoothness of the spline fit to the moment data is good enough to suggest the possibility of carrying out double integrations and double differentiations of the moment (with a multiplicative constant, EI) in order to get information on the pile deflections and pressure acting on the pile as a function of depth. Curves of deflection and pressure were presented in the second report, although no interpretation of the data at that stage of the investigation had been attempted.
No a priori assumptions regarding soil-pile interaction pressure either as a function of pile deflection or with depth are involved in the spline-fitting approach. In other pile studies (2) carried out on prototype piles in natural soil deposits, some scatter in strain-gauge (moment) data were inevitable and led to fitting difficulties. In consequence, a model for pile-soil behavior was adduced in that investigation, and the fitting method consisted of finding for that model those soil properties which gave smooth moment curves best representing the data observed. Such an approach does not inform the investigator of the real soil-pile behavior developed. For example, since, in all soils, a lateral load applied to the pile at ground surface will develop a moment curve which resembles a damped sine wave, it would be possible to use the well-known Winkler foundation solution for a laterally-loaded pile imbedded in a medium of constant spring property k, where the pile moment M is given by the equation
It is the purpose of this report to take the centrifuge data analysis to a further stage to examine the interaction between pile and soil as a function of manipulation of the test results and the fitting techniques, with the fewest assumptions.
Problems With Fitting Technique
In the second report it is apparent that the spline functions give smooth curves fitting the moment data extremely well and to some extent confirming that the data are a reliable indication of the pile response in a uniform soil. When the spline functions are differentiated once, the resulting curve gives the distribution of shear force in the pile. One of the requirements made in the fitting process was that the shear force at the top of the pile should equal the known applied load. Consequently, a fair degree of confidence can be placed in the shear force versus depth curves since they are correct at the extreme vaue at the top of the pile.
Similarly when the moment curves are divided by the product EI and integrated once, the result is the slope of the pile as a function of depth. A further integration of the slope gives the displacement at the pile top. Since the displacement was measured in the course of the test, the second integral curve can be checked at the extreme point again, that is, at ground surface. When this was done, it was found that the ground surface deflections obtained from the two integrations were very close to the deflections actually measured at different loads in the test. Consequently it seems likely that the deflection data as a function of depth obtained by two integrations are also reliable. It is of course well-known that integrations of even poor quality data can lead to reasonably reliable results. Differentiation is another matter, however.
Although there is control over the first differentiation of the moment curves, the identification of the pressure acting on the pile from the soil surrounding it depends on a second differentiation. It would be anticipated that this might give rise to problems, and, in fact, there has been discussion in the literature of the possible introduction of errors by such double differentiation (2 ,5 ). However in field tests on instrumented piles, there has been no control over the nature of the soil, which, in general, has been a relatively nonuniform or layered material, In consequence, the moment data recorded in field tests exhibits a fair degree of scatter and the application of spline fitting methods to such scattered points would not be expected to be reliable. In consequence either hand fitting or regression techniques of curve fitting must be applied to such field data. The greater uniformity of the centrifuge test soil and the smoothness of the original spline fitting technique give some hope that the second derivative of the present data may not be subjected to as great errors as in former field test fitting processes.
With the fifth-order spline the second derivative curves are of course smooth and continuous; the question i s whether they can be believed to be numerically accurate for the purpose of further interpretation of the soil behavior. In Figure 1 are shown the pressure distribution curves for the first cycle of loading and unloading in the tests carried out on the pile in dry and wet sand, respectively. These curves represent the derived distribution of the interaction between the pile and the soil as a function of depth. Although they are referred to as pressure curves, some care must be taken in understanding the meaning of this phrase. As a portion of the pile below the surface deflects horizontally under the surface loading, the soil in front of the pile will be compressed and displaced, exerting some pressure in the process on the front surface of the pile. The soil along the side of the pile will be largely subjected to more or less simple shearing behavior and will interact with the pile through shearing stresses. On the rear surface of the pile, the pile is moving away from the soil and the lateral soil pressures developed during pile driving will be reduced as the pile retreats. The curves shown in Figure 1 represent the cumulative effect on the pile of all these mechanisms of behavior. Are they reasonable in appearance?
At the ground surface the pile is displaced laterally with a deflection which decreases rapidly with depth. It is expected that the soil interaction resistance increases with depth from zero at the surface because of the increasing confining pressure in the cohesionless soil of the test. The combination of increasing soil resistance and decreasing pile deflection with depth should cause the soil pressure t o reach some maximum value below which it decreases. At some depth below the surface the pile deflection is zero and consequently the pressure distribution should go through zero at this point. Below this the pile has a retro-grade motion. Consequently in this region it is expected that the net soil pressure would be in the opposite direction. This is referred to here as negative pressure, compared to the positive pressure in the upper section of the pile.
It is apparent from Figure i that neither of the two derived pressure distributions for the pile response in the dry or the wet soil corresponds to this logical model. In both cases to a depth of something like 8 or 9 inches below ground surface it can be seen that small pressures, both negative and positive, occur. The pressures during the first loading phase only begin to increase consistently at depths below this level. An indication of negative pressure in the soil in the top eight inches therefore represents an error in the manipulation of the data. It might develop either as a consequence of cumulative errors in the strain gauge readouts and calibration, or in digitization and processing of the data. Alternatively, if small errors can be accepted in these aspects of the analysis the difference between the interpreted and the logical or correct distribution of pressures may be due to the spline fitting process. Since a check of the cumulative calibration and digitizing errors indicated that they were fairly small, it was decided to make the assumption that the moment data could be accepted, and that better distributions of the pressure acting on the pile could be derived by manipulating the spline function or by other methods of fitting the data, This is discussed subsequently.
Further Investigations
Several different approaches were taken to the fitting problem and are described in subsequent sections of this report. Initially attempts involved other forms of function. After devoting a small amount of time to this, it was decided that it was not a fruitful way to proceed in view of the good fits achieved with the spline function. Consequently attention was paid to manipulating the spline-fitting technique to give more rational results in the top section of the pile.
One of these involved omitting the top data point (moment) and utilizing only the moments at the five other locations as well as the top and bottom boundary conditions in the pile. This, as will be shown subsequently, gave rise to pressure distributions which were obviously incorrect and considerably worse than the ones which had been obtained before.
After careful study of the method by which the tests had been conducted in the centrifuge, it was concluded that the soil level was not necessarily accurately located with respect to the application of the load. In the tests, it was intended to have the filament applying the load act exactly at ground surface. This implies the identification of ground surface quite accurately for the following reason. The tests were conducted at 100g on a 1/100 scale model pile. All linear dimensions in the experiment, therefore, including deflections, were 1/100 of those of the prototype pile. Consequently, if the point of attachment of the lateral load to the pile top was in error with respect to the soil level by 1/100 of an inch, it means that the prototype pile was loaded at a point one inch different from that intended. With prototype loads of 30 or 40 Kips, the moment at the point interpreted to be ground surface could be different from zero by a substantial amount. It is difficult in the model to measure the attachment point initially to this level of accuracy, and during the cyclic loading tests, the soil level changes by an unknown amount. Accordingly it was decided to move the zero moment point on the pile up or down by small amounts in the analysis in order to examine the effect on the spline-fitting technique. The consequences are discussed in detail in the following sections.
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