Travis M. Gerber1, M. ASCE, P.E., and Kyle M. Rollins2, M. ASCE
1Assist. Prof., Dept. of Civil & Environmental Engineering, Brigham Young University, 368 CB,Provo, UT 84602; [email protected]., Dept. of Civil & Environmental Engineering, Brigham Young University, 368 CB, Provo, UT84602; [email protected].
ABSTRACT: A lateral load test was performed on a full-scale steel pipe pileinstalled in a soil profile consisting of cohesive, fine-grained soils with occasionalsand layers. The pile was loaded in nine increments from 0 to 89 mm ofdisplacement, with 15 loading cycles applied for each increment. P-y curvesrepresenting static monotonic and cyclic loading conditions were derived from straingauge data using a moving cubic polynomial technique. The results of push-overanalyses using the derived p-y curves as input agreed well with the measured load-displacement response. It was observed that the cyclic p-y curves exhibited a sharpconcave-up shape which contrasted with the broader concave-down shape of thestatic p-y curves. The cyclic p-y curves also exhibited lower peak resistances relativeto the static p-y curves. The initial portion of the cyclic p-y curves is relatively flatwith near-zero resistance which represents gapping of the soil. The displacement atwhich the soil reaction component of the cyclic p-y curves begins to dramaticallyincrease is a function of the maximum displacement during previous loading cycles.It was also observed that the effects of cyclic loading were more pronounced inshallower soils.
INTRODUCTION
The soil-structure interaction problem of a laterally loaded deep foundation is oftentreated as a beam interacting with a set of discrete, non-linear springs. P-y curvesused to describe the load-displacement response of these soil springs have generallybeen developed from monotonic lateral load tests conducted on instrumented full-scale deep foundations. While such curves are helpful in conducting static pushoveranalyses, the curves do not accurately describe soil-structure behavior when theloading is cyclic in nature. For example, during cyclic loading, the soil surrounding astructure may develop gaps and experience strength loss. The engineering modulusof the soil also changes as the load path varies from loading to unloading to reloading.Few cyclic p-y curves have been developed and published, with curves for soft clay
by Matlock (1970), curves for stiff clay by Reese et al. (1975), and curves for sand byReese et al. (1974) being the most prominent. These curves are based on “intuitionand judgment,” (Matlock, 1970) coupled with theoretical mechanics adjusted to fitlimited empirical data. To augment and further substantiate the few p-y curves thatare available, the authors have tested a single full-scale pile and used the resultingdata to derive cyclic p-y curves.
TESTING PROGRAM
Site Conditions
Testing of the full-scale pile, as well as two nearby pile groups, is reported inJohnson (2003) and Rollins et al. (2005a, 2005b). Because multiple research projectshave been conducted at the site, subsurface conditions are relatively well known.Prior to testing, 1.5 m of imported sandy gravel fill was excavated to expose theoriginal ground surface. A generalized profile of the remaining soil strata is shown inFig. 1 together with data from a cone penetration test (CPT) performed within 10 mof the pile location. The soil profile consists of multiple silt and clay strata and twosandy strata 1 to 2 m in thickness. Also shown in Fig. 1 is a profile of undrainedshear strength as derived in the work of Johnson (2003) and Rollins et al. (2005a,2005b) based on laboratory unconsolidated undrained triaxial compression tests (UU)
and field tests (vane shear (VST), torvane, and pressuremeter (PMT)). During testingof the pile, the water table was located at a depth of approximately 0.4 m.
Test Components and Testing Procedure
The test pile, consisting of ASTM A252 Grade 3 (i.e., 310 MPa minimum yieldstrength) steel pipe, had an outside diameter and wall thickness of 324 and 9.5 mm,respectively. To protect externally mounted strain gauges from damage duringdriving, small continuous steel angles were welded on opposing sides of the pile. Ascaled cross-section of the composite pile is shown in Fig. 2. The moment of inertiaof the pile section was approximately 1.43 x 108 mm4. Pairs of strain gauges werespaced along the pile at 457-mm intervals, beginning at a distance of 2.13 m from thetop end of the pile and ending at 7.62 m, followed by additional pairs of gaugesspaced at 914-mm intervals, extending to 12.19 m. One additional pair of gauges wasplaced near the bottom of the pile at 13.44 m, for a total of 19 pairs of gauges. Afterinstallation of the pile, the uppermost pair of gauges was located approximately at theground surface.
Strain Gauges
324 mm OD Pipe Pile
Protective Angles
FIG. 2. Cross-section of test pile.
The pile was laterally loaded at a height of 0.48 m above the ground surface using a1.34-MN hydraulic jack reacting against an adjacent pile group. Swivel plates andpinned-connections were used to prevent eccentric loading and provide a free pile-head condition. A string potentiometer was used to measure displacement of the pile-head relative to an independent reference frame. Load, displacement, and strain datawas measured at a frequency of 2 Hz.
The pile was loaded in one direction using manual displacement control. After asingle, initial displacement of 4 mm to verify functionality of the equipment, nineseries of fifteen loading cycles each were applied. The target displacement of eachseries was progressively increased from 6.4 to 13, 19, 25, 38, 51, 64, 76, and 89 mm,as measured at the pile-head. During a typical cycle, load was applied at a rate ofapproximately 3 to 6 kN/s until the target displacement level was reached, after whichthe load was removed. In the case of the first loading cycle of a series, the peak
displacement was held constant for five minutes before unloading. A continuous plotof the measured load-displacement response of the pile is shown in Fig. 3.
FIG. 3. Continuous plot of the measured load-displacement response of the pile.
ANALYSIS AND INTERPRETATION
Development of P-Y Curves
As part of the process of developing p-y curves, profiles of both pile curvature andbending moment were generated. Curvature was determined by dividing the straindifference between the two sides of the pile by the distance between those gauges.Since peak strains were less than the elastic limit, bending moment was taken as theproduct of curvature and the flexural stiffness, EI, of pile cross-section.Representative bending moment profiles are presented later. To mitigate the effectsof gaps and errors in the strain data resulting from the attrition of gauges duringinstallation and testing, missing and errant data was estimated using a quadraticLagrangian interpolation polynomial based on adjacent measured values.
To determine the displacement component, y, of the p-y curves, the curvature-areamethod from beam mechanics was used, providing a bottom-to-top piecewise doubleintegration of the curvature profile which relies on the fixity of the pile at its toe todefine boundary conditions. Because the determination of soil pressure, p, (expressedas a reaction force per unit length of foundation) is significantly more problematicthan the determination of displacement, y, due to the double differentiation requiredand the accompanying magnification of experimental errors, the cubic polynomialapproach proposed by Matlock and Ripperger (1958) and later modified by Gerber(2003) was used. In this approach, cubic polynomials are fit to successive sets of fivedata points along the bending moment profile. These polynomials are then twicedifferentiated and evaluate at their mid-points. The resulting values are then averagedusing a planar gradient method to develop the soil pressure profile. Corresponding pand y values were then paired to form p-y curves. The continuous p-y curve
generated for a depth of 0.46 m below the ground surface (bgs) [which corresponds to0.94 m below the load point (blp) on the pile] is shown in Fig. 4.
0 10 20 3 0 4 0 50 6 0Displacement, y (mm)
0
25
50
75
100
Soil
Rea
ctio
n,p
(kN
/m)
FIG. 4. Continuous p-y curve for a depth of 0.46 m below the ground surface(0.94 m blp).
Two types of discrete p-y curves were produced from the continuous p-y curvedata. The first type of p-y curves are ‘static backbone’ curves. These curves werecreated by fitting a curve along the peak soil reaction value at the end of the firstloading cycle for each displacement series. These curves represent what the soilresponse would be under a static, monotonic loading. The second type of p-y curvesare cyclic curves generated by isolating the load path for each cycle within eachdisplacement series and fitting a curve to the path. Some judgment was requiredduring both fitting processes due to artifacts of the soil pressure computation process.The static p-y curves developed for the six gauge depths from 0.46 to 2.74 m belowground surface, z, are shown in Fig. 5. A depth of 2.74 m corresponds to 8.5 pilediameters, a depth above which soils are commonly assumed to have the greatestinfluence on the load-displacement response of a free-headed pile. Cyclic p-y curvesfor the same depths from the second loading cycles of the 25- and 76-mmdisplacement series are also shown in Fig. 5.
Discussion of P-Y Curves
As seen in Fig. 5, the cyclic p-y curves exhibit a sharp concave-up shape whichcontrasts with the broader concave-down shape of the static p-y curves. Also evidentis the generally lower peak value of the cyclic p-y curves relative to the static p-ycurves. Both of these characteristics are mirrored in the load-displacement responseof the pile-head shown previously in Fig. 3. The vastly different shapes of the staticmonotonic and cyclic p-y curves indicate that the loading-unloading-reloading ofthese soils cannot be described by constitutive models based on Masing-type rules.
FIG. 5. Comparison of monotonic or static backbone p-y curves (dashed line)and second cycle p-y curves from the 25-and 76-mm displacement series (solidlines, left and right, respectively).
The static curves shown in Fig. 5 depict different types of response. For example,the first curve at a depth of 0.46 m below the ground surface (bgs) exhibits greaterresistance to load than the curves immediately below it. This is consistent with thiscurve being almost above the water table and within a more overconsolidated crustwhile the deeper curves are well beneath the water table. The three curves from 0.91to 1.83 m bgs exhibit the same the general shape, consistent with their being withinthe same silty stratum. Although one might typically expect that resistance shouldincrease with depth, the presence of near-surface overconsolidation produces a profileof strength which decreases with increasing depth. The last two curves from 2.28 and2.74 m bgs coincide with the lean clay stratum. These curves exhibit greaterresistance, consistent with the greater depth and overburden pressure present.
For the second cycle p-y curves, the displacement corresponding to the greatestchange in the rate of reaction (i.e., the point where soil reaction begins to rise sharplyfrom near-zero values) appears to be a function of the maximum displacement duringprevious loadings. It can also be observed that, in general, the reloading stiffnessafter this transition point is at least as great as the initial loading stiffness of the staticp-y curves. In the case of the 25-mm displacement series, the transition pointbetween near-zero and significant soil reaction occurs essentially at the beginning ofthe curves, indicating that the pile/soil interface experienced a permanentdisplacement with minimal gapping or “slotting” at depth during the previous 6.4- to
19-mm displacement series. In contrast, the shallower curves from the 76-mmdisplacement series exhibit a significant amount of displacement before the transitionpoint is encountered, indicating that significant permanent gapping of the soil haddeveloped during the previous displacement series. (This gapping was visible duringthe pile load test and was determined by probing to extend to a depth exceeding 1 m).At greater depths, the extent of gapping is less evident in the p-y curves.
One can conclude that at large displacement levels, the effects of cyclic loading aremore pronounced in shallow soils than in deeper soils. The reason for this occurrenceis that, during the first loading cycle, the shallower soils quickly mobilize their fullstrength in response to pile displacement due to their relatively low ultimateresistance, whereas deeper soils usually have a ‘reserve’ capacity due to acombination of greater ultimate resistance and smaller pile displacement. During asecond or subsequent loading cycle, the effective resistance of the soils has beenreduced due to gapping and inherent strength degradation (the latter of which isexhibited in the curves by the lower-than-static peak strengths for a givendisplacement). Consequently, a similarly loaded pile must, upon its next loading,displace a greater amount to mobilize the same total amount of resistance. Sinceadditional resistance is not available in the shallower soils, the pile continues todisplace, forming gaps, until pile displacements in the deeper soils mobilize enoughof the soils’ remaining capacity to satisfy force equilibrium. This mechanism is alsomanifest as progressively larger pile bending moments occurring at depth duringcyclic loading.
Oft times, quasi-cyclic p-y curves are constructed by connecting the peaks ofreaction-displacement loops after a specified number of loading cycles or at a steady-state of load-displacement response. These types of p-y curves can be seen as“degraded” static backbone curves which illustrate how peak soil resistance reduceswith cyclic loading. In Fig. 5, comparisons between the peak soil resistances for thecyclic p-y curves and the static backbone curves indicate that peak soil resistance isreduced by 5 to 40% for the second loading cycle relative to the first, but a clear trendof loss with respect to displacement level is not readily discerned.
Validation of P-Y Curves
The computer program LPILE (1997) was used to help verify the correctness of thestatic and cyclic p-y curves derived from the pile load test. Using measured pile-headloads and the derived p-y curves as inputs, pile displacement and bending momentswere calculated. In the case of the cyclic loadings, the initial displacement offsets inthe p-y curves were removed when the curves were input into LPILE. This was doneso that the program’s method of defining p-y curves only using the first quadrantwould produce appropriate results when calculating displacements and reactions inthe third quadrant. The removed displacements are afterward added back to thecalculated pile displacement profile to obtain the pile displacements that would haveoccurred had the original p-y curves been used. This procedure for addressing non-zero displacements when the pile-head load is zero must also be used for pile bending
moments; non-zero bending moments existing before load is applied to the pile-headmust be accounted for in the LPILE analysis by adding the initial moments back tothe calculated results.
Fig. 6 presents a comparison of the measured and calculated load-displacementcurves for the static monotonic p-y curves as well as for the second cycle p-y curvesfrom the 25- and 76-mm displacements series. (Recall that in the case of the staticmonotonic data, the measured values are based on the peak values obtained from thefirst cycle of loading at each displacement level rather than from a single continuousloading) It can be seen that there is good agreement between the two sets of curves,indicating that the derived static and cycle p-y curves are reasonable representationsof the actual load-displacement response of the soil.
FIG. 6. Comparison of measured (markers) and calculated (solid line) pile headload-displacement response.
An additional validation of the second cycle p-y curves from the 76-mmdisplacements series is provided in Fig. 7. Figs. 7a through 7c show very goodagreement between the measured and calculated bending moment profiles for pile-head loads of 1.1 (the start of the loading cycle), 50.2 (the middle of the loadingcycle), and 113.4 kN (the peak load and end of the loading cycle). (Field test datapoints created from the Lagrangian interpolation polynomial to replace errant ormissing bending moment data are indicated by the hollow markers). Fig. 7a exhibitssmall amounts of residual displacement and bending moment from previous loadingcycles which were used to adjust the p-y curves in the LPILE validation analyses asdiscussed previously. In addition to the very good agreement in bending moment,Fig. 7 also shows similar agreement between calculated pile displacement profilesand measured pile head displacements.
FIG. 7. Comparison of pile bending moment and displacement profiles based onfield test data (markers) and p-y curves (lines) for the second cycle p-y curvesfrom the 76-mm displacements series.
CONCLUSION
Based on the results of the pile load test and subsequent analysis of the test data, bothstatic monotonic and cyclic p-y curves have been developed which accuratelydescribe the load-displacement response of the test pile. Based on these curves, thefollowing conclusions are drawn.
1. Cyclic p-y curves exhibit a sharp concave-up shape which contrasts with thebroader concave-down shape of the static p-y curves.
2. Cyclic p-y curves exhibit lower peak resistances relative to the static p-y curves.3. After experiencing a previous load cycle, the initial portion of the cyclic p-y
curves becomes relatively flat with near-zero resistance; this behavior representsgapping of the soil.
4. The displacement at which the soil reaction component of a cyclic p-y curvebegins to increase dramatically is a function of the maximum displacement duringprevious loading cycles.
5. The effects of cyclic loading are more pronounced in shallower soils.6. Cyclic loading reduces peak soil resistance, but a clear trend of loss with respect
Support for the pile testing program was provided by the National ScienceFoundation through grant number CMS-0100363. This support is gratefullyacknowledged. The conclusions in this paper do not necessarily reflect the views ofthe sponsor.
REFERENCES
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