Laterally loaded piles (p-y)
The COM624P p-y finite-difference method — pile inputs, every soil model and parameter, head conditions, and how to read the response.
A laterally loaded pile resists horizontal load by mobilizing the soil around it. The p-y method models that interaction as a beam — the pile — supported by a bed of independent, nonlinear springs — the soil. PileCalc solves it with the COM624P finite-difference formulation (Wang & Reese, FHWA-SA-91-048), the same engine that underlies LPILE and RSPile. This page explains the method and every input on the lateral tool.
The p-y method
The pile is governed by the beam-column equation on a nonlinear (Winkler) foundation. At every depth x, the soil pushes back with a reaction p (force per unit length) that depends on the local deflection y through a p-y curve:
Here EI is the pile's flexural rigidity, Pₓ the axial load (the P-Δ term), and E_py the secant modulus of the p-y curve at the current deflection. Because the springs soften as they load, E_py changes with y — which is what makes the response nonlinear: doubling the load more than doubles the deflection.
Each soil model defines the shape of its p-y curve from the soil's strength and stiffness. A defining feature for clays is the deflection that mobilizes half the ultimate resistance:
where b is the pile diameter and ε₅₀ the strain at half the failure stress in a triaxial test. The smaller ε₅₀, the stiffer the soil's response near the surface.
The finite-difference solver
The pile is divided into a number of equal segments — the increments — and the governing differential equation is replaced by a finite-difference approximation at each node. Because the soil springs are nonlinear, the solver iterates: it assumes a stiffness, solves the linear system, reads new secant moduli off the p-y curves at the resulting deflections, and repeats until the deflections stop changing.
Two diagnostics tell you the solution is trustworthy. Convergence means the iteration settled. The equilibrium residual — the applied load minus the integrated soil reaction — should be essentially zero; a large residual means the model did not balance and the result should not be used.
Direct vs. Georgiadis layering
Pile inputs
The pile is modeled as an elastic beam. For a uniform pile you provide its geometry and bending stiffness directly.
The length of the pile below the head, in contact with soil.
Why it matters. Beyond a critical length the head response stops changing — the pile behaves as “long” and added length does nothing. Too short and the tip itself translates and rotates, changing the entire profile. Length is usually set by axial capacity and the depth to a competent bearing layer.
The pile width or diameter, b.
Why it matters. Diameter appears throughout the p-y curves — ultimate resistance scales with b, and y₅₀ = 2.5·ε₅₀·b — and in the section's bending stiffness. A larger pile attracts more soil resistance and is stiffer. Typical driven/bored piles are 0.3–2 m.
The bending stiffness EI = E · I — modulus times moment of inertia of the section.
Why it matters. EI governs how much the pile bends. A stiffer pile spreads load deeper and deflects less, but it can attract more bending moment. For sections that crack or yield, use moment–curvature to get an effective EI. A 0.6 m solid concrete pile is on the order of 1.9×10⁵ kN·m².
The length of pile standing above the ground surface, between the head and the soil — the depth of the ground surface below the pile head.
Why it matters. Models a pile that projects above grade — a pier column, or a pile exposed by scour. The free length acts as a cantilever and adds substantial deflection. Set it to 0 when the head is at the ground surface.
Soil models
Each soil layer is assigned a p-y model calibrated to its material. Picking the right family matters more than fine-tuning a parameter — the models produce genuinely different resistance shapes. Choose the model in each layer's editor; the parameters that appear adapt to your choice.
| Model | Use for | Key parameters |
|---|---|---|
| Soft clay — Matlock (1970) | Soft to medium clay, submerged | c, ε₅₀, J |
| Stiff clay above water — Welch & Reese | Stiff clay, no free water | c, ε₅₀, J |
| Stiff clay below water — Reese | Stiff clay, submerged (cyclic-sensitive) | c, ε₅₀, k |
| Sand — Reese (1974) | Sand, wedge + flow model | φ, k |
| Sand — API / O'Neill–Murchison | Sand, the API tanh form | φ, k |
| Weak rock — Reese (1997) | Weathered / weak rock | qu, Eir, RQD, k_rm |
| Elastic (Winkler) subgrade | Linear springs, back-analysis | E_py |
For clays, the soft-clay and stiff-clay families differ in how resistance is mobilized and how cyclic loading degrades it. For sands, the Reese model builds an explicit passive wedge while the API model uses a calibrated hyperbolic-tangent curve; the two agree closely for typical sands. The elastic model is a linear spring p = E_py·y for back-calculation or code checks.
Soil parameters
Below is every parameter the soil models use, with what it is and why it changes the result. Each layer also carries its top and bottom depth, which must tile the profile without gaps.
The unit weight used to build the effective vertical stress profile that drives p-y resistance with depth.
Why it matters. Higher effective stress means stronger soil and a stiffer response. Use total unit weight above the water table and buoyant (effective) unit weight below it. Typical total ~18–20 kN/m³; buoyant ~8–10 kN/m³.
The undrained shear strength of the clay — the cohesion that resists pile movement.
Why it matters. It scales the ultimate soil resistance pu directly: stronger clay carries more lateral load before the soil yields. Guide values — soft 12–25, medium 25–50, stiff 50–100 kPa.
Source: Matlock (1970)
The strain at one-half the maximum stress difference in an undrained triaxial test.
Why it matters. It sets y₅₀ = 2.5·ε₅₀·b, the deflection that mobilizes half of pu — so it controls how soft or stiff the clay p-y curve is near the surface. Soft clay ≈ 0.02, medium ≈ 0.01, stiff ≈ 0.005–0.007.
Source: Matlock (1970)
An empirical factor in the depth term of the soft-clay ultimate resistance.
Why it matters. It sets how quickly pu grows with depth in the shallow wedge zone. 0.5 is standard; 0.25 suits stiffer, more brittle clays.
Source: Matlock (1970)
The initial modulus of subgrade reaction — the starting slope of the p-y curve, increasing with depth.
Why it matters. Governs near-surface stiffness for sand and below-water stiff clay. This is one of the few inherently unit-dependent inputs — match it to your unit system (see Units). Loose sand ~5,400, medium ~16,300, dense ~34,000 kN/m³; lower below water.
Source: Reese, Cox & Koop (1974)
The drained angle of internal friction of the sand.
Why it matters. Controls the passive-wedge size and the ultimate resistance pu — a few degrees materially change capacity and deflection. Loose 28–30, medium 32–36, dense 38–42°.
Source: API / O'Neill & Murchison (1983)
The uniaxial (unconfined) compressive strength of the intact rock.
Why it matters. Sets the ultimate side resistance of the weak-rock p-y curve. Weak rock is roughly 0.5–5 MPa.
Source: Reese (1997)
The initial modulus of the rock mass.
Why it matters. Sets the initial stiffness of the weak-rock p-y curve before yielding. Often on the order of 100–500× qu for weak rock.
Source: Reese (1997)
The percentage of an intact rock core recovered in pieces ≥ 100 mm — a fracturing index.
Why it matters. Reduces the rock-mass strength via aᵣ = 1 − ⅔(RQD/100); lower RQD means more fractured, weaker rock. Weak / fractured rock is often 25–75%.
Source: Reese & Nyman (1978)
A constant relating the rock-mass modulus to the deflection at which resistance mobilizes.
Why it matters. Larger k_rm softens the rock p-y curve. Reese suggests a narrow band, 0.0005 to 0.00005; use the lower end for stiffer rock.
Source: Reese (1997)
For the elastic (Winkler) model, the linear spring modulus p = E_py·y, specified at the top and bottom of the layer.
Why it matters. Defines a linear, deflection-independent spring. Set the top value to 0 and the bottom to n_h · depth for a modulus that increases linearly with depth. Back-calculate it from a known stiffness.
Source: Terzaghi subgrade reaction
Head boundary conditions
The pile head needs two prescribed quantities. Which two you set is the boundary condition, and it has a first-order effect on the answer: a free head deflects most, while fixing rotation cuts deflection and shifts the peak moment up to the head.
The horizontal load applied at the pile head — the primary demand.
Why it matters. Deflection and bending moment grow with it, nonlinearly, because the soil softens as it loads. Present in every head condition.
The bending moment applied at the pile head.
Why it matters. An eccentric load or a partially fixed cap applies head moment, increasing near-surface bending and deflection. Use 0 for a free, concentrically loaded head.
The prescribed rotation dy/dx of the pile head.
Why it matters. Set 0 to model a head fully fixed against rotation — for example, embedded in a rigid cap — which markedly reduces deflection.
The rotational restraint provided by a partially fixed connection.
Why it matters. Bridges the free and fixed extremes — a stiffer connection rotates less and sheds more moment into the pile. Large → fixed, 0 → free.
A prescribed lateral displacement of the pile head (paired with a head moment).
Why it matters. Use when the head movement is known — a serviceability target, say — and you want the force and moment that develop to produce it.
Loading & options
Whether the p-y curves are built for static (monotonic) or cyclic (repeated) loading.
Why it matters. Cyclic loading degrades soil resistance — especially in clay — giving larger deflections and moments for the same load. Use static for one-off loads; cyclic for wind, wave, or traffic.
How layered soil is handled. Direct builds each layer's curve at its true depth (original COM624P). Georgiadis shifts lower layers to an equivalent depth that accounts for the resistance of the soil above.
Why it matters. Georgiadis is what LPILE and RSPile use for layered profiles and generally improves agreement; choose it for multi-layer soils. Direct reproduces the original COM624P behavior.
Source: Georgiadis (1983)
The number of finite-difference segments the pile is divided into.
Why it matters. More increments improve accuracy but cost a little compute. About 100 is plenty for typical piles; 100–200 is a good range.
Axial load carried down the pile (compression positive), included as a second-order term.
Why it matters. Axial load acting through the lateral deflection adds P-Δ moment, which increases deflection — important for slender piles with significant axial load. Set 0 to ignore it.
Reading the results
The tool reports four summary quantities and four response profiles.
Summary quantities
- Head deflection — the lateral movement at the top of the pile, compared against the structure's allowable displacement. Usually the governing serviceability check.
- Max moment and its depth — drives the structural (reinforcement / section) design of the pile.
- Max shear — checked against the section's shear capacity.
- Equilibrium residual — applied load minus integrated soil reaction; ≈ 0 for a good solution, large if the model failed to balance.
Response profiles
Deflection, bending moment, shear, and soil reaction are plotted against depth, drawn with depth increasing downward. These shapes are what engineers reason about: where the pile crosses zero deflection, where the moment peaks, how deep the soil reaction develops. The Data tab gives the node-by-node table for export.
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