Pile Load Test: 2D Section

What a static load test shows

A jack pushes the pile head against a reaction beam held by anchor piles while dial gauges record how far the head moves. The load-settlement curve tells how much of the load goes into the soil along the shaft and how much into the tip, and where the pile is considered to have failed. Both views use the same load-transfer model, so every number matches.

Load transfer along the pile

Axial equilibrium and elasticity give dP/dz = −π D τ(z) and dw/dz = P/(E A) (settlement grows upward as the pile shortens). The shaft shear is a nonlinear spring: τ = τmax f((w − ssoil)/D) with an API-style t-z curve (30 % of τ_max at 0.16 % D, 75 % at 0.57 % D, 100 % at 1 % D, then a residual 80 % in clay). The tip follows a q-z curve (25 % of the base capacity at 0.2 % D, 75 % at 4.2 % D, 100 % at 10 % D). The model picks a tip settlement wb, sets Pb = Qp q(wb) and marches up the pile; sweeping wb gives the whole curve with no iteration (shooting method, 80 segments).

Soil resistance

Clay (alpha method): τmax = α cu with α = 0.5 (cu/σ′v)−0.5 (exponent −0.25 above 1), clipped to 0.2-1.0, and base qb = 9 cu. Sand and gravel (beta method): τmax = K tanδ σ′v with K = 0.8, δ = φ − 5°, capped at 100-130 kPa, and base qb = Nq σ′v limited by an API-style table (N_q 8-40, q_lim 1.9-9.6 MPa). The effective stress is σ′v = ∑γ h − γw(z − zw) with the water table you set.

Reading the failure load

Davisson: the load where the curve meets the line w = PL/(EA) + 4 mm + D/120. 10 % D: the load at a head settlement of 0.1 D. Chin-Kondner: the late curve is nearly hyperbolic, w/P = C1 w + C2, so Qu = 1/C1. The criteria give different answers (the readouts show all three), which is why codes say which one they use.

Negative skin friction

When the soft clay is still settling under a fill, the soil moves down faster than the pile. The shear then reverses, τ < 0, and adds drag load. The axial force peaks at the neutral plane where pile and soil settle equally (w = ssoil), not at the head. The clay settlement is assumed to fall linearly from the surface value to zero at the base of the clay.

Pile groups

Converse-Labarre efficiency η = 1 − θ [(m−1)n + (n−1)m] / (90 m n) with θ = atan(D/s), and a Vesic-type group settlement Sg = S1 √(Bg/D). These are empirical rules of thumb, shown as readouts and as the movement of the ghost piles; the test itself is on one pile.

Honest simplifications

Homogeneous layers, no soil-plug or installation effects, no creep or set-up with time, no hysteresis on unloading (the same curve is retraced), a solid circular concrete section with E = 4700 sqrt(fc), constant sand strength parameters, and a hand-coded API-style curve set rather than a site calibration. Numbers are textbook-scale, not for design.