Recent Advances in the Design of Axially-Loaded Piles in Sandy Soils

M. Prezzi
Assist. Prof., School of Civil Engineering, Purdue Univ., W. Lafayette, IN, 47907, USA
R. Salgado
Prof., School of Civil Engineering, Purdue Univ., W. Lafayette, IN, 47907, USA
D. Basu
Ph.D. Student, School of Civil Engineering, Purdue Univ., W. Lafayette, IN, 47907, USA
K. Paik
Assoc. Prof., Dept. of Civil Engineering, Kwandong Univ., Kangwon-do, South Korea
J. Lee
Assist. Prof., School of Civil Engineering, Yonsei Univ., Seoul, South Korea

Piles are classified into displacement (driven) and non-displacement (bored) piles, depending on their methods of installation. The installation method (driving or boring) has a significant effect on the pile static capacity for the level of settlements we allow in design. The state of the soil (density and stress state) is changed significantly when a pile is driven into the ground (Lee et al. 2003). Thus, design of non-displacement piles (e.g. drilled shafts) can be based on the original (before pile installation) in-situ states of soils, but the design of displacement piles (e.g. open- and closed-ended pipe piles, H-piles) must account for the changed soil states. The matter is further complicated for open-ended pipe piles, which often show responses that are in between those of non-displacement and full displacement piles.

During the driving of open-ended pipe piles, some amount of soil will initially enter into the hollow pipe. Depending on the soil state (dense or loose) and type (fine-grained or coarsegrained), diameter and length of pile, and the driving technique, the soil inside the pile may or may not allow further entry of soil into the pipe. If soil enters the pipe throughout the driving process, driving is said to take place in a fully coring mode and the behavior is more like that of a non-displacement pile. However, if the soil forms a plug at the pile base that does not allow further entry of soil, then driving is said to be done in a fully plugged mode. If a pile were driven in the plugged mode during all of the driving, its load response would approach that of a displacement pile. In real field conditions, the behavior is generally in between the fully plugged and coring modes. Further, depending on whether a pipe is jacked or driven into the ground, the behavior is different (Paik and Salgado 2004).

The research carried out at Purdue University on the analysis and design of drilled shafts and open- and closed-ended piles was reviewed. Both numerical analysis and experiments (field and calibration chamber tests) were done to assess the behavior of these piles, taking into account the role of the different soil properties and the loading processes associated with the different installation methods. The resulting unit base and shaft resistances were found to depend on relative density and horizontal stress for drilled shafts and closed-ended piles, and also on IFR for open-ended piles.

The base resistance of a displacement pile is more than that of a geometrically identical drilled shaft. Moreover, the capacity of a closed-ended driven pile is more than that of an openended pile of same outer diameter. Further, the normalized shaft resistances are less in magnitude compared to the corresponding base resistances.

The strongest effect on normalized unit base resistance is that of the relative density; the normalized resistance decreases as relative density increases. The shaft resistance, on the other hand, shows a larger scatter when plotted against relative density. Since the results are presented by taking into account the various effects of soil state and the loading process, these can be readily used for design. However, the values of base resistances for closed-ended displacement piles, extrapolated from the non-displacement pile analysis by considering values available in the literature, should be used with caution because of the large amount of variability involved in the values.

This paper, thus, proposes that pile design for axial loads be done in terms of unit resistances, normalized with respect to cone resistances, for given settlement levels for vertically loaded piles. The research done at Purdue University in the past decade offers some guidance on what these values should be. 

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Advanced Modeling Tools for the Analysis of Axially Loaded Piles

Hoyoung Seo 
Purdue University, Civil Engineering Building, 550 Stadium Mall Drive, West Lafayette, IN 47907-2051, USA 
Rodrigo Salgado
Purdue University, Civil Engineering Building, 550 Stadium Mall Drive, West Lafayette, IN 47907-2051, USA
Monica Prezzi
Purdue University, Civil Engineering Building, 550 Stadium Mall Drive, West Lafayette, IN 47907-2051, USA. Tel.: +1 765 494 5034; fax: +1 765 496 1364. E-mail addresses: mprezzi@ecn.purdue.edu (Corresponding author)

Pile foundations have been used in construction for thousands of years but only in the last few decades has there been significant progress in the technology of pile installation. This progress has not been matched by progress in the analysis and design of these foundation elements. This is in large part due to considerable difficulties in analyzing both pile installation and the response of piles to various types of loadings rigorously. Given these difficulties, the profession has in general used relatively crude design approaches. This is likely to change due to pressures from different directions, particularly the progress in code design (the push towards load and resistance factor design in geotechnical engineering requires a much better grip on all the factors that need to be considered in calculating pile resistances and what the uncertainties in quantities and analyses are, requiring sounder analytical frameworks) and economics (materials costs have started to rise, a trend that, if continued, would make it more economically interesting to have optimal designs).

If pile resistance is determined using sound mechanics from a soil model that captures the essence of soil load response without reliance on empiricism or direct correlations, the fundamental basis for rigorous analysis of pile load response is in place. We have shown this to be true for non-displacement piles.

For non-displacement piles installed in sand, the limit base resistance can be calculated with good accuracy using a cavity expansion-based analysis. We have shown using finite element analysis that the ratio of ultimate to limit base resistance is in the 0.13 (for dense sand) to 0.2 (for loose sand) range. The shaft resistance of non-displacement piles in sand is the product of a lateral stress ratio K by the vertical effective stress and the tangent of the critical-state friction angle. We have shown that K lies between just under K₀ for loose sands to about twice K₀ for dense sands.

For non-displacement piles installed in clay, numerical analyses (both finite element and limit analysis) have established accurate bounds on the values of limit unit base resistance. The ratio of net limit unit base resistance to undrained shear strength has been shown convincingly to be in the 10 to 13.5 range. The same ratio for ultimate instead of limit resistance would be less than that; some authors suggest numbers just under 10. The shaft resistance is most frequently calculated using the α method. We have shown that the value of α can be determined analytically if the critical-state and residual friction angles, as well as the relationship between the residual friction angle and the normal effective stress on the shearing plane, are known. The analysis can also be used to determine α for soils containing clay contents greater than 25%.

In part because of the absence of realistic analysis allowing calculation of settlement given an axial load on the pile, design has relied on calculations of ultimate resistances reduced by factors of safety that would indirectly prevent settlement-based limit states. However, recent work suggests realistic analyses of pile settlement will soon be available, facilitating cost-effective pile design. Explicit analytical solutions for a vertically loaded pile subjected to compressive or tensile loadings and embedded in a multi-layered elastic soil were presented. The solutions satisfy the boundary conditions of the problem. The governing differential equations are derived based on the principle of minimum potential energy and calculus of variations. The integration constants are determined using Cramer’s rule and a recurrence formula. The solutions allow calculation of the vertical pile displacement as a function of depth, the load transferred to the pile shaft at any depth, and the vertical soil displacement as a function of the radial direction at any depth if the following is known: radius, length and Young’s modulus of the pile, Poisson’s ratio and Young’s modulus of the soil in each layer, thickness of each soil layer, number of soil layers, and applied load. The use of the analysis was illustrated by obtaining load-transfer and load-settlement curves for a case discussed in the literature for which pile load test results are available. 

Read more: Monica Prezzi