The Matlock (1970) soft clay p-y model

The Matlock soft clay p-y model (Matlock, 1970) defines the lateral resistance–deflection response of soft to medium clay below the water table. Ultimate resistance is pᵤ = min[(3 + γ′z/c + J·z/b)·c·b, 9·c·b], and the curve is the cubic parabola p = 0.5·pᵤ·(y/y₅₀)^(1/3) with y₅₀ = 2.5·ε₅₀·b. It remains the default soft-clay criterion in COM624P, LPILE, RSPile, and PileCalc.

Where the model comes from

Matlock developed the criteria from static and cyclic lateral load tests on an instrumented 324 mm (12.75 in) steel pipe pile driven into soft clay at the Sabine River site in Texas, with companion tests at Lake Austin. The work was motivated by offshore platform design, where piles in soft marine clay see large, repeated wave loads. He published it as Correlations for Design of Laterally Loaded Piles in Soft Clay, Offshore Technology Conference paper OTC 1204 (1970). The paper reduced the measured bending-moment and deflection profiles to a family of nondimensional p-y curves — soil resistance p (force per unit length of pile) versus lateral deflection y at a given depth — that could be regenerated from routine soil data. If p-y curves are new to you, start with what a p-y curve is and come back.

When the model applies

Matlock's criteria are intended for soft to medium clay in the presence of free water — in practice, clay below the water table with undrained shear strength up to roughly 50 kPa (soft: 12–25 kPa; medium: 25–50 kPa). The presence of free water matters because the cyclic degradation Matlock observed is driven partly by water working into the gap that opens between pile and soil and scouring softened clay out of it. For stiff clay the profession switches models: above the water table, use the Welch & Reese (1972) criteria; below it, the brittle Reese, Cox & Koop (1975) criteria.

Ultimate resistance and the critical depth

The ultimate soil resistance pᵤ is the lesser of two failure mechanisms. Near the surface a passive wedge of soil can heave upward and outward; at depth the clay flows around the pile instead. With undrained strength c, effective unit weight γ′, depth z, and pile diameter b:

pᵤ = (3 + γ′·z/c + J·z/b) · c · b     (shallow wedge)
pᵤ = 9 · c · b                        (deep flow-around)
pᵤ = min of the two

J is an empirical factor Matlock fitted to the field tests: 0.5 for soft clay (the Sabine River value), 0.25 for somewhat stiffer clay. The two expressions cross at the critical depth

xᵣ = 6·c·b / (γ′·b + J·c)

Above xᵣ the wedge governs and pᵤ grows with depth; below it, pᵤ is constant at 9cb. The same depth reappears in the cyclic criteria as the reduced resistance depth. Note that γ′ here is the effective (buoyant) unit weight — the model assumes submerged conditions, and using total unit weight below the water table overstates the wedge term.

The static p-y curve

The static backbone is a single cubic parabola, normalized by the deflection y₅₀ at which half the ultimate resistance is mobilized:

p = 0.5 · pᵤ · (y/y₅₀)^(1/3),   with  y₅₀ = 2.5 · ε₅₀ · b

ε₅₀ is the strain at one-half the maximum principal stress difference in an undrained triaxial test on the clay — the one parameter beyond strength that shapes the curve. The curve reaches pᵤ at y = 8·y₅₀ and stays flat beyond it: soft clay is ductile, with no post-peak loss under static (monotonic) load. Because of the one-third exponent the initial tangent stiffness is theoretically infinite; in a numerical solver this is harmless because the curve is only ever sampled at finite deflections.

Cyclic loading

Cyclic curves are where Matlock's field data earn their keep. Up to y = 3·y₅₀ the cyclic curve follows the static cubic parabola, reaching 0.72·pᵤ (that number is simply 0.5·3^(1/3)). What happens next depends on depth relative to xᵣ:

At or below xᵣ — the curve simply stays flat at 0.72·pᵤ. Confinement is high enough that repeated cycles do not degrade the resistance further.
Above xᵣ — resistance degrades linearly between y = 3·y₅₀ and y = 15·y₅₀, dropping from 0.72·pᵤ to a residual of 0.72·pᵤ·(x/xᵣ). At the ground surface (x = 0) the cyclic residual is zero — the gap opens, water enters, and the softened clay offers nothing.

The degradation is an envelope for a large number of cycles, not a per-cycle count: unlike the Welch & Reese stiff-clay criteria, the Matlock cyclic curve has no N parameter.

Choosing the parameters

The model needs three soil inputs — c, ε₅₀, and J — plus the effective unit weight profile. Where triaxial data are unavailable, Matlock's recommendations tied to consistency are standard practice:

Clay consistency	c (kPa)	ε₅₀	J
Soft	12–25	0.02	0.5
Medium	25–50	0.01	0.5
Stiff (upper limit of the model)	50–100	0.005–0.007	0.25

ε₅₀ deserves respect: it scales y₅₀ directly, so halving it stiffens the whole near-surface response. Measure it when the deflection prediction matters.

Worked example

Take a 0.6 m pile in soft clay with c = 25 kPa, γ′ = 8 kN/m³, ε₅₀ = 0.02, J = 0.5, at a depth of z = 3 m:

wedge:  pᵤ = (3 + 8·3/25 + 0.5·3/0.6) · 25 · 0.6
           = (3 + 0.96 + 2.50) · 15 = 96.9 kN/m
flow:   pᵤ = 9 · 25 · 0.6 = 135 kN/m
→ pᵤ = 96.9 kN/m  (wedge governs; xᵣ = 6·25·0.6/(8·0.6 + 0.5·25) = 5.2 m)

y₅₀ = 2.5 · 0.02 · 0.6 = 0.030 m = 30 mm
at y = 10 mm:  p = 0.5 · 96.9 · (10/30)^(1/3) = 33.6 kN/m

The full 96.9 kN/m is not mobilized until y = 8·y₅₀ = 240 mm — soft clay p-y curves are long and gentle, which is why deflection, not soil failure, usually controls design in these profiles. This is exactly the calculation PileCalc's engine performs at every node of the finite-difference lateral pile solution, and the implementation is checked term-by-term against the published equations (see how we validate).

Limitations

Wrong model for stiff clay. Above ~50 kPa the response becomes brittle and the Reese-family criteria apply; Matlock's ductile curve can be unconservative on deflection shape for stiff submerged clay.
Assumes free water. The cyclic degradation mechanism presumes a submerged gap. For stiff clay above the water table the cyclic behavior is different in kind, not just degree.
ε₅₀ sensitivity. The deflection prediction scales with an often-estimated lab parameter. Bracket it (e.g. 0.01–0.02) when data are thin.
Calibration base. The criteria come from one pile size at two Texas sites, extrapolated by dimensional reasoning. Fifty years of successful use back the extrapolation, but very large diameters and unusual clays warrant judgment.
Envelope cyclic curve. No cycle count, load asymmetry, or reconsolidation between storms — the cyclic curve is a lower-bound envelope.

Common questions

What is the J factor in the Matlock p-y model?

J is an empirical coefficient in the shallow-wedge term of the ultimate resistance, pᵤ = (3 + γ′z/c + J·z/b)·c·b. Matlock fitted J = 0.5 to the Sabine River tests in soft clay and suggested 0.25 for stiffer clays. It controls how quickly resistance grows with depth in the wedge zone; most software, PileCalc included, defaults to 0.5.

What is y₅₀ and why is ε₅₀ in it?

y₅₀ = 2.5·ε₅₀·b is the pile deflection at which half the ultimate resistance is mobilized. ε₅₀ — the triaxial strain at half the maximum stress difference — converts a soil stress-strain property into a pile-scale deflection, with the 2.5 factor and the diameter b coming from Matlock's correlation. Softer clay has larger ε₅₀, hence a softer p-y curve.

How do static and cyclic Matlock curves differ?

Both follow p = 0.5·pᵤ·(y/y₅₀)^(1/3) initially. The static curve caps at pᵤ from y = 8·y₅₀ with no post-peak loss. The cyclic curve caps at 0.72·pᵤ, and above the critical depth xᵣ it degrades further — linearly between 3·y₅₀ and 15·y₅₀ — down to a residual of 0.72·pᵤ·(x/xᵣ), which is zero at the ground surface.

Is the Matlock model conservative?

For its intended range — soft to medium submerged clay — it is a well-calibrated best estimate, not a deliberate lower bound, though the cyclic envelope is conservative for small cycle counts. Outside its range it can err either way: applied to stiff fissured clay it misses brittle post-peak loss entirely, which is why the Reese criteria exist.

The fastest way to build intuition is to plot the curves: the free p-y curve generator draws Matlock static and cyclic curves at any depth from your c, ε₅₀, and J — the same engine PileCalc uses for full lateral pile analysis.