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

72
P-y curves are largely empirical, having been primarily developed based on the performance of instrumented lateral load tests on deep foundations indifferent soil and rock conditions. The p-y curves therefore are based on specific loading conditions, subsurface conditions, and pile type and geometry. These p-y curves are often used for project conditions that differ from the original experiment conditions. It is therefore important that the designer understand the experimental basis for the p-y curves that are used in analysis as well as the limitations of the p-y curves so that inherent risks are appreciated.
P-y curves fora single deep foundation element typically consist of three portions, as shown in Figure
6-6: (i) an initial linear portion (origin to point a, representing the almost linear elastic response of soil for small displacements (ii) a nonlinear transition portion (ab), representing soil nonlinear stress-strain behavior and (iii) a horizontal portion (bc), representing the soil ultimate resistance, p
ult
Figure 6-6: Typical p-y curve fora single deep foundation element.
As indicated in Figure 6-5, the soil response to an applied horizontal load, P
t
, or moment, M
t
, can be represented by a series of discrete nonlinear soil springs located at various distances below the head of the foundation element. The soil modulus, E
py
,
(or spring constant) in Equation 6-5 is the secant modulus of the p-y curve, which represents the reaction modulus of soil. The maximum value of the soil modulus,
E
py-max
, occurs for y = 0 and is proportional to the soil elastic modulus, E
s
(Reese and Van Impe 2001). As displacement of the foundation element increases, the secant modulus of the p-y curve decreases nonlinearly. In general, each soil-spring has a particular p-y curve representing the soil-pile interaction at that location. If the soil conditions are relatively uniform, then the shape of the p-y curve is similar for all soil springs along the depth of the foundation element. However, the ultimate resistance of the p-y curve,
p
ult
(i.e., segment bc and beyond in Figure 6-6) tends to increase with depth, as suggested in the lower part of Figure 6-5. Several factors affect p-y curves including soil properties, foundation material and geometric properties, spring location, and loading characteristics. These factors affect the initial, ultimate, and transition portions of the p-y curves. The initial portion of p-y curves represents the elastic response of soil to small pile/shaft deflections and is typically characterized by K, which coincides with the maximum reaction modulus E
py max
. The parameter
K
has units of force per square length (FL) and is not a soil property (Terzaghi 1955). In general, K depends on

73 i. geomaterial properties, such as strength, stiffness parameters, modulus of subgrade reaction, etc. ii. depth of the equivalent spring iii. deep foundation element section properties such as diameter, moment of inertia, etc. iv. subsurface conditions, such as soil above or under the groundwater surface, etc. Based on work by Skempton (1951), Terzaghi (1955), and McClelland and Focht (1958), Reese et al.
(1974) developed the following empirical equation for estimating K in sands Equation 6-6) where k is a proportionality coefficient with units of F/L
3
and z is the depth below ground. The coefficient k
and the conventional subgrade reaction modulus can be related although these parameters are numerically different. While the subgrade reaction modulus is related to the loading of a rectangular plate resting on an elastic horizontal surface, k is related to along beam (i.e., pile/shaft) loaded with a horizontal load and exhibiting a different failure mode. Correlations are available for estimating k, and many modern computer programs can estimate k based on soil parameters inputs. Reese (1997) proposed the following empirical equation for estimating K in a rock mass Equation 6-7) Where E
m
= modulus of the rock mass and k
i
= dimensionless constant that depends on the drilled shaft diameter and the depth below ground (Turner, 2006).
𝐾𝐾 = 𝑘𝑘𝑘𝑘

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