Linear (Subgrade)

For applications where a linear treatment of the p-y relationship is appropriate, the soil resistance per unit length is proportional to the displacement. The constant slope is the coefficient of subgrade reaction multiplied by the pile diameter:

$$\tag{1} p = kby$$

where,

$p$ = horizontal soil resistance per unit length $k$ = coefficient of subgrade reaction (force per length cubed), entered as the Subgrade Modulus of the layer $b$ = pile diameter $y$ = horizontal displacement

There is no ultimate resistance. OpenBrIM generates the curve up to a displacement of 6 in; the spring is linear within that range. This is the classical Winkler subgrade-reaction idealization rather than a model derived from load tests, so no article is associated with it.