Geotechnical Engineering Circular No. 9 Design, Analysis, and Testing of Laterally Loaded Deep Foundations that Support Transportation Facilities

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Figure 7-3: Illustration of the p-multiplier concept for rows of deep foundation elements in a group
(from Hannigan et al. 2006).

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7.2.2.1
Development of p-Multipliers
Brown et al. (1988), Ruesta and Townsend (1997), and Brown et al. (2001) conducted lateral loading tests on full-scale pile groups in loose to dense sands. McVay et al. (1995) performed centrifuge tests on a single pile and a series of pile groups in sand. Meimon et al. (1986), Brown et al. (1987), Rollins et al.
(1998), and Rollins et al. (2006) conducted full-scale lateral load tests on pile groups in clay. Cox (1984),
Rao et al. (1998), and Ilyas et al. (2004) performed model tests to examine the behavior of laterally loaded pile groups in clay. Based on these and similar test programs, it is apparent that pile spacing, group arrangement, and group size have the most significant effect on group efficiency. Group efficiency decreases with an increase in group size (number of pile/shaft elements, as well as a decrease in pile/shaft spacing. The leading row develops the greatest soil resistance (attracting the largest lateral load demand) with decreasing contributions from each subsequent row, with the last rows) developing the lowest soil resistance (and attracting the least lateral load demand i.e., the leading rows have the highest p-multipliers and the last trailing row has the lowest p-multiplier. The most significant reduction in p-multiplier values occurs between the leading row and the trailing row immediately following the leading row. The reductions between subsequent trailing rows (i.e., between the second and third rows, or third and fourth rows) is relatively small compared to the reduction between the leading row (first row) and second row. In some cases, the outer (side) elements appear to take more load than the interior elements. However, some experiments have observed approximately equal load distribution along a row of elements positioned perpendicular to the applied load. For analysis, p-multipliers are generally taken as the same for each row i.e., equal load distribution along a row is generally assumed. Pile group efficiency and p-multipliers decrease significantly when foundation element spacing decreases. In general, side by side interaction effects are not significant at a center-to-center spacing of B or more for sands or B or more for clays, where Bis the width or diameter of the foundation element. Sand density and clay strengths also have some effect on the p-multiplier values. McVay et al. (1995) compared the results from lateral load tests on a 3 × 3 pile group at a spacing of Bin sand, and found that the load distribution was different for piles in dense sands compared to loose sands. In dense sands, a higher share of the load was taken by the leading row of piles compared to the trailing row, whereas in loose sands, the load share among the rows was more evenly distributed. Ilyas et al. (2004) found that interactions among piles in a group in normally consolidated clay are more significant than similar pile groups in stiff over-consolidated clay. However, overall, the effects of the soil type, density, and/or strength have a much less significant effect on the value of the p-multiplier values than the pile/shaft size, spacing, and layout relative to the applied load. Inmost cases, the type of soil and strength are not considered in the selection of p-multipliers for design, rather the p-multipliers are based on the size and layout of the foundation elements.
P-multipliers are somewhat dependent on pile deflection, but they are relatively constant at large pile head deflections, generally above about ¾ inch, as shown in Figure 7-4 (Rollins et al. 1998). This is consistent with results of a testing program reported by Caltrans (2003), which indicated that p-multipliers vary for displacements up to about 0.5 to 1.0 inches, but were generally constant for larger deflections up to 3 to 4 inches.

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