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A wide range of p-y curves are available in PileLAT and PileGroup programs for modelling behaviour of soils and rocks under lateral loading. This blog presents and discusses API models for cohesive and cohesionless soils under lateral loading.

API model for soft clay

Soft clay can be modeled by the method recommended in API RP2A 21st Edition (2000), where the ultimate resistance (Pu) of soft clay is determined in the same way as Matlock (1970).

Pu = Cu . D . (3 + Gamma' . X / Cu + J . X / D) for X <= XR

Pu = 9 . Cu. D for X > =XR

where:

Pu is ultimate soil resistance per unit length

Cu is undrained shear strength

Gamma' is effective soil unit weight

D is pile diameter

J is dimensionless empirical constant (0.5 for soft clays and 0.25 for medium clay). in PileLAT 2, the default value of 0.24 is adopted

X is depth below soil surface

XR is transition depth when both equations produce the same value

The only difference between API model and Matlock (1970)'s model is that the piece-wise curves are used as shown in the figures below for both static and cyclic loading conditions.

Figure 1 P-Y curve for soft clay (API) model under static loading condition

Figure 2 P-Y curve for soft clay (API) model under cyclic loading condition

The reference displacement Yc is calculated by the equation below:

Yc = 2.5 x E50 X D

where E50 is the strain at one-half the maximum stress for an undrained tri-axial compression test and is based on the recommendations in the following table.

The following figure shows the default P-Y parameter input for soft clay (API) model in PileLAT 2.

Figure 3 P-Y parameter input dialog for soft clay (API) model in PileLAT 2

Figure 4 Examples of P-Y curves for soft clay (API) model in PileLAT 2

API model for sand - API (2000)

For API sand model (API 2000), the ultimate lateral bearing capacity for sand at shallow depth is calculated as:

Pus = (C1 . X + C2 . D) . Gamma' . X

The ultimate lateral bearing capacity for sand at deep depth is calculated as:

Pud = C3 . D . Gamma' . X

where

Gamma' is effective soil unit weight

X is depth

C1, C2 and C3 are coefficients determined from Figure A.6-2 of the API RP2A 21st Edition

D is pile diameter

P-Y curves for API Sand under both static and cyclic loading conditions are shown in the figure below.

Figure 5 P-Y curve for API Sand model under both static and cyclic loading condition

The lateral soil resistance - deflection (p-y) relationship is described by the following equation:

P = A . Pu . tanh [(K . D . y) / (A . Pu)]

where

P is actual lateral resistance