Lateral Pile Analysis (p-y Method)

What it calculates

This free online lateral pile analysis calculator solves a single pile under lateral load by the p-y method - the nonlinear beam-on-soil-springs model that is standard practice for laterally loaded piles and drilled shafts. It returns lateral deflection, bending moment, shear force and mobilised soil reaction at every depth down the pile, for a layered soil profile you define. Everything runs in your browser: no login, no download, no queue.

The pile is modelled as a beam column and the soil as a set of independent nonlinear springs, one per station. Each spring follows a published p-y curve chosen per layer, so a profile of sand over soft clay over stiff clay uses three different soil models in one analysis. Because the springs are nonlinear, the solution is iterative - the calculator reports how many iterations it took and whether it converged.

What you enter

Pile section

Steel pipe, solid circular, square or a custom second moment of area

Diameter or width

The dimension the soil bears against (m)

Total pile length

Head to tip, including any free-standing length (m)

Head above ground

Free-standing stickup, or negative for a head below ground (m)

Stiffness

Young's modulus E (GPa) and second moment of area I (m4), derived automatically for a pipe

Head loading

Lateral shear (kN), applied moment (kNm) and axial thrust (kN) for the P-delta effect

Head condition

Free head, fixed head, an elastic rotational spring, or a prescribed displacement

Soil layers

Depth range, soil description and a p-y model per layer

Soil strength

From SPT blow counts, CPT cone resistance, laboratory data, or the soil description

Water table

Depth below ground - it sets the effective unit weight below that level (m)

Loading type

Static (monotonic) or cyclic, which degrades several of the curves

What you get back

Four diagrams against depth, drawn to a shared depth axis beside the soil profile, plus the summary quantities below. Each is named here because these are the outputs engineers search for individually.

Pile head deflection

The lateral movement of the pile head, which is usually what governs the design - a laterally loaded pile is far more often limited by serviceability deflection than by structural capacity. Where the pile stands above ground the calculator reports the groundline deflection separately, because the free-standing length adds cantilever movement that the soil never sees, and published load tests report the groundline value.

Maximum bending moment and its depth

The peak moment in the pile, and how far below the head it occurs. For a free-headed pile in reasonably uniform soil this typically falls a few diameters down, where the soil reaction has finished reversing the shear. This is the value you carry into a structural section check - for a prestressed concrete pile, into the P-M interaction check.

Shear force and soil reaction against depth

Shear starts at the applied head load and reverses as the soil pushes back; the calculator reports the largest shear below the head, which is the design value rather than the load you typed in. The mobilised soil reaction shows how much of each layer is actually working - a layer carrying almost no reaction is telling you the pile is longer than it needs to be, and a layer at its ultimate resistance is telling you it has yielded.

Head rotation

The rotation of the pile head in milliradians. It matters when the pile supports a structure sensitive to tilt, and when several piles share a cap - the cap enforces a common rotation, which is what the fixed-head condition models.

Soil models available

Each layer picks its own published p-y formulation. The choice matters: a soft clay and a stiff clay of the same strength mobilise resistance at very different deflections.

Soft clay (Matlock)

Matlock (1970), OTC 1204. The standard soft-clay curve, cubic backbone with a cyclic degradation branch

Stiff clay with free water (Reese)

Reese, Cox & Koop (1975), OTC 2312. Includes the falling branch caused by scour around the pile

Stiff clay without free water

Reese & Welch (1975). Stiffer fourth-root backbone, no scour

Sand (Reese)

Reese, Cox & Koop (1974), OTC 2080. Four-segment curve built from the published A and B coefficients

Sand (API RP 2A)

The offshore hyperbolic-tangent form, smooth and less sensitive to chart digitisation

Elastic subgrade

Linear springs - useful for a first estimate and for checking against closed-form solutions

Building the soil profile from SPT, CPT or lab data

A p-y model needs undrained shear strength, friction angle, unit weight, the strain factor and the modulus of subgrade reaction. Most projects do not have all of those measured, so each layer picks an entry mode and the calculator derives what is missing from published correlations: SPT blow counts (with the energy and overburden corrections), CPT cone resistance, laboratory strengths, or the soil description alone.

Every derived value is shown, marked as derived, and editable - clicking a value overrides it, and an overridden value is never recomputed. Each one carries the correlation that produced it, so a reviewer can see that a friction angle of 34 degrees came from Peck, Hanson and Thornburn rather than from nowhere. These correlations carry real scatter, which is exactly why they are shown rather than hidden.

Head conditions - free, fixed and everything between

A free-headed pile carries the applied moment and is free to rotate; a fixed-headed pile is held against rotation by a cap or a rigid connection. The difference is large. In the worked example below, fixing the head cuts the deflection from 6.15 mm to 2.20 mm but moves the peak moment to the head and increases it to 213.3 kNm - the moment has to go somewhere, and restraining the rotation puts it in the connection.

Real pile caps are neither perfectly free nor perfectly rigid, so the calculator also accepts an elastic rotational spring, and prescribed displacement conditions for back-analysing a load test.

Piles that stand above ground

Jetty piles, bridge piers, sign posts and pile bents have a free-standing length between the load and the ground. That length carries no soil resistance at all, so it behaves as a cantilever and adds a lever arm to everything below it. Setting the head above ground models this directly: the soil layers stay referenced to ground level, so a profile taken from a borehole log does not need re-entering when the free length changes.

The effect is much larger on the head than on the soil. Raising the head 5 m above ground in the example below multiplies the head deflection by about 21 while the groundline deflection grows only about 5 times, because only the extra moment reaches the soil.

Worked example

The calculator opens with this case: a 0.6 m outside diameter steel pipe pile, 16 mm wall, 20 m long, carrying 150 kN of lateral load at a free head. The profile is medium dense sand from 0 to 4 m over soft clay to 10 m over stiff clay to 20 m, with the water table 2 m down. Soil strengths are derived from SPT blow counts of 15, 4 and 20.

Second moment of area, I

1.2524e-3 m4

Bending stiffness, EI

2.5048e5 kNm2

Derived sand friction angle (0-4 m)

34.4 degrees from N = 15

Derived soft clay strength (4-10 m)

cu = 18 kPa from N = 4

Derived stiff clay strength (10-20 m)

cu = 90 kPa from N = 20

Head deflection

6.15 mm

Head rotation

2.586 mrad

Maximum bending moment

185.6 kNm at 2.00 m depth

Maximum shear below the head

149.4 kN

Ultimate soil resistance at 2 m

116.9 kN/m (Reese sand)

Ultimate soil resistance at 6 m

97.2 kN/m (Matlock soft clay)

Same case, fixed head

2.20 mm deflection, 213.3 kNm at the head

Same case, cyclic loading

6.92 mm deflection, 202.2 kNm

Note what cyclic loading does: the deflection grows from 6.15 mm to 6.92 mm and the moment from 185.6 to 202.2 kNm, because the cyclic curves degrade the soil resistance. That direction is the check - a cyclic analysis that predicts less movement than a static one is wrong.

Formula reference

The governing equation is a beam column on a nonlinear elastic foundation, solved by central finite differences. The soil term p is not a constant stiffness but a function of the local deflection, which is what makes the solution iterative.

Governing equation

$EI\dfrac{d^{4y}}{dz^{4}} + P\dfrac{d^{2y}}{dz^{2}} - p(y,z) = 0$

Soft clay ultimate resistance (Matlock)

$p_u = \min\left[\left(3 + \dfrac{\gamma' z}{c_u} + \dfrac{Jz}{D}\right)c_u D,\; 9c_u D\right]$

Transition depth

$z_r = \dfrac{6D}{\gamma' D / c_u + J}$

Clay reference deflection

$y_{50} = 2.5\,\varepsilon_{50}\,D$

Soft clay backbone

$\dfrac{p}{p_u} = 0.5\left(\dfrac{y}{y_{50}}\right)^{1/3}$

Stiff clay backbone (no free water)

$\dfrac{p}{p_u} = 0.5\left(\dfrac{y}{y_{50}}\right)^{1/4}$

API sand curve

$p = A\,p_u \tanh\!\left(\dfrac{k z y}{A\,p_u}\right)$

Initial soil modulus

$E_{s} = k\,z$

Assumptions and limits

The p-y method treats the soil as independent springs, so it carries no shear between layers and no continuum behaviour. That simplification is what makes it tractable and it is the basis of standard practice, but it means the model is only as good as the curves feeding it.

The published curves were calibrated on driven piles roughly 300 to 1200 mm in diameter. Applying them to a very large diameter monopile is extrapolation, and the profession has developed separate formulations for that case. Group effects are not included - a pile in a closely spaced group attracts less resistance than an isolated one, which is normally handled with p-multipliers.

The calculator models a single pile with a constant section, static or cyclic loading, and no soil movement imposed from outside. Liquefaction, lateral spreading, downdrag and sloping ground are outside its scope. Correlated soil parameters are a starting point for preliminary work - laboratory or in-situ strength testing should govern a final design.

Questions engineers ask about this calculator