Single Pile Analysis — Verification

Single Pile Analysis is checked against two kinds of anchor. The first is a worked example: the source's own numerical example is reproduced end to end and the two answers are compared. The second is a field load test: the computed response is compared with the measured load-movement curve of a real pile.

The two answer different questions. A worked example shows that the published method is implemented correctly; if it deviates, the cause is identifiable. A field test shows how well the method predicts reality, and it carries the scatter of the ground with it.

The field tests below have no connection to StructuralMind. Each was carried out, reported and published years ago by the institution that ran it. What we did is enter that test's pile and soil profile and see what the calculation says.

Worked examples

In every row below the comparison is against a number the source itself published.

What was checked	Source	Result
Sand p-y coefficients $C_1$ , $C_2$ , $C_3$	Fenske (1981) Table 3.11	Identical to the table's five digits ( $\varphi$ = 25–40°)
The same coefficients in closed form	API RP 2A's independent closed form	Within 12 %
Deep asymptotes	Values given on the FHWA/RD-85/106 figures	Within 2 %
Elastic Winkler solution	Hetenyi closed form	Deflection and rotation within 0.1 %
Side resistance in clay ( $\alpha$ method)	GEC 10 Example 13-2	Nominal side resistance within 0.2 %
Settlement by load transfer	O'Neill & Reese Example C-3	Total developed resistance within 0.2 %

Fenske Table 3.11 — sand p-y coefficients

The source separately tabulates the bearing coefficients of the sand p-y curves for each friction angle.

The table names the coefficients $S_1$ , $S_2$ , $S_3$ under a different normalisation; the identity with our $C_1$ , $C_2$ , $C_3$ is $S_1 = C_2$ , $S_2 = C_1$ , $S_3 = C_3$ . Three rows from the table:

$\varphi$	$S_1$	$S_2$	$S_3$	$x_t/b$
25°	2.05805	1.21808	15.68459	11.18690
32°	2.94733	2.28134	36.81400	14.84507
40°	4.38147	4.62396	104.14818	21.57604

The calculation reproduces every digit of these. So does $x_t/b$ , the transition depth where the shallow and deep mechanisms cross.

GEC 10 Example 13-2 — side resistance in clay

The source works through the side resistance of a 1.52 m drilled shaft in overconsolidated clay step by step. Side friction is neglected over the top 1.52 m and the undrained shear strength is averaged over the remaining 13.72 m. Every intermediate step can be compared:

Step	Source's value	Calculation
$s_u$ below the excluded zone	1,802 psf (86.3 kPa)	Same (within 0.2 %)
Average $s_u$ over the effective depth	2,395 psf (114.7 kPa)	Same (within 0.1 %)
$s_u/p_a$	1.13	Same
Adhesion factor $\alpha$	0.55	0.55
Unit side friction $f$	1,317 psf (63.1 kPa)	Same (within 0.2 %)
Nominal side resistance $R_s$	930.9 kips (4,141 kN)	Same (within 0.2 %)

Every intermediate step agrees.

O'Neill & Reese Example C-3 — settlement by load transfer

The source asks for the settlement of a 1.22 m diameter, 18.3 m drilled shaft under 2.00 MN. Ultimate side resistance is given as 3.56 MN and ultimate base resistance as 1.11 MN, and the source's own answer is about 1.9 mm.

Quantity	Source's value	Calculation
Mobilised side resistance ratio	0.54	0.54
Mobilised base resistance ratio	0.035	0.027
Total developed resistance	1,960 kN	1,964 kN
Head settlement	1.9 mm	Within 5 %

The difference in the base ratio does not carry into the answer, because at these movements end bearing is only 1.5 % of the total.

Field load tests

Five tests are used: three lateral, two axial. Each section below gives that test's pile, its soil, every measured and computed value, and the assumptions we had to make.

Test	Soil / pile	Direction	Loaded to failure
Sabine River	Soft clay, steel pipe	Lateral	Yes
Mustang Island	Sand, steel pipe	Lateral	Yes
Houston	Stiff clay above the water table, drilled shaft	Lateral	Yes
Kentucky Lake TPK-1	Sand, driven pipe	Axial compression	No
Port of Oakland TP6-17NCI	Clay, driven pipe	Compression and uplift	No

What a test that never failed can prove. The two axial cases cannot be read without this distinction; it is the most commonly misread part of a load test:

Situation	What follows
Computed capacity below the maximum applied load	The calculation is on the safe side. The pile carried more than the method says it can — a measurable finding.
Computed capacity above the maximum applied load	Neither confirmed nor refuted. The test says only "at least this much".
Movement at a given load	Directly comparable. This is where a load-transfer method is actually tested.

Sabine River — soft clay

The test Matlock's (1970) soft-clay p-y curve was derived from.

Pile: 324 mm steel pipe, 12.80 m embedded, $EI$ = 31,300 kN·m², free head, lateral load 305 mm above the mudline. Soil: submerged soft clay, $s_u$ = 14.4 kPa, $\gamma'$ = 5.5 kN/m³, $\varepsilon_{50}$ = 0.007 (site-measured).

Lateral load	Measured deflection	Computed	Deviation
17.8 kN	5.6 mm	5.2 mm	−7 %
34.7 kN	18.3 mm	17.2 mm	−6 %
51.6 kN	35.1 mm	35.1 mm	+0.2 %
69.8 kN	57.1 mm	61.7 mm	+8 %
78.7 kN	72.4 mm	79.5 mm	+10 %

Mean absolute deviation is 6.3 % and the largest is 10 %. The sign turns as the load grows: at small loads the calculation gives less deflection than measured, at large loads more. The maximum moment was compared separately and falls on FHWA's own computed curve.

Mustang Island — sand

The test Reese, Cox and Koop's (1974) sand p-y curve was derived from.

Pile: 610 mm steel pipe, 21.03 m embedded, $EI$ = 167,168 kN·m², free head, lateral load 305 mm above the ground surface. Soil: submerged sand, $\varphi$ = 39°, $\gamma'$ = 10.4 kN/m³.

Lateral load	Measured deflection	Computed	Deviation
22.2 kN	0.8 mm	1.0 mm	+35 %
44.5 kN	2.3 mm	2.1 mm	−9 %
64.5 kN	3.6 mm	3.2 mm	−9 %
89.0 kN	5.6 mm	5.3 mm	−6 %
133.4 kN	10.2 mm	10.2 mm	+0.3 %
177.9 kN	16.0 mm	16.1 mm	+0.6 %
222.4 kN	22.9 mm	22.6 mm	−1 %
264.7 kN	30.0 mm	29.3 mm	−2 %

Mean absolute deviation is 7.8 %, and 3.9 % with the sub-millimetre first reading left out. Above 133 kN the deviation drops below 3 %.

Houston — stiff clay above the water table

The first field check of Welch and Reese's (1975) above-water stiff-clay curve.

Pile: 762 mm drilled shaft, 12.80 m embedded, $EI$ = 422,000 kN·m² (field-measured), free head, lateral load at the ground surface. Soil: stiff clay, $s_u$ = 105 kPa, $\varepsilon_{50}$ = 0.005, $\gamma$ = 18.9 kN/m³, water table at 5.5 m.

The laterally active zone reaches about 5 diameters, or 3.8 m, which places it entirely above the water table, so the above-water branch governs.

Lateral load	Measured deflection	Computed	Deviation
191.3 kN	1.8 mm	2.7 mm	+54 %
275.8 kN	5.1 mm	6.0 mm	+18 %
360.3 kN	11.4 mm	10.6 mm	−7 %
431.5 kN	22.9 mm	15.5 mm	−32 %

Over the working range (276–360 kN) the deviation is 7–18 %. The +54 % at the bottom occurs at a movement of about a millimetre, and the −32 % at the top comes from the measured curve softening quickly as the pile approaches failure while the calculation does not soften with it.

⚠️ A single $s_u$ = 105 kPa was chosen even though the source states that the shear strength "varies widely" over the top 6 m. The match should be read knowing it rests on that choice.

Kentucky Lake TPK-1 — driven pipe in sand

From the FHWA Deep Foundation Load Test Database (Terracon 2014 report).

Pile: 1,219 mm OD open-ended steel pipe, 38.1 mm wall, 41.76 m embedded, $EA$ = 2.83·10⁷ kN, driven. A constrictor plate sits 29.9 m above the tip, so the toe is taken as plugged. Soil: 6.6 m of soft clay ( $s_u$ = 47.9 kPa) over sand layers with $\varphi$ between 32° and 36°. The water table is at the ground surface.

Capacity. The computed ultimate capacity is 23,594 kN (11,919 kN shaft + 11,675 kN toe). In the test the pile carried 26,800 kN without failing. Because the calculation stays below a load the pile demonstrably carried, it is conservative by at least 12 %.

Settlement.

Load	Measured settlement	Computed	Ratio
3,737 kN	2.12 mm	4.97 mm	2.3×
6,579 kN	5.69 mm	8.74 mm	1.5×
9,065 kN	10.21 mm	12.04 mm	1.2×
11,888 kN	13.13 mm	15.79 mm	1.2×
14,088 kN	15.34 mm	20.47 mm	1.3×
16,370 kN	19.35 mm	27.72 mm	1.4×
18,977 kN	22.96 mm	52.20 mm	2.3×
21,719 kN	25.94 mm	100.0 mm	3.9×
24,133 kN	31.02 mm	computed curve has ended	—
26,801 kN	35.88 mm	computed curve has ended	—

Over the first half of the loading (to about 14,000 kN) the agreement is 1.2–1.5× and in the right direction: the calculation gives more settlement than measured. Above that it departs quickly, because the computed capacity runs out at 23,528 kN and the curve ends there. The last two rows have no computed settlement: the calculation says the pile has already failed at the load it actually carried. That is what "conservative by at least 12 %" looks like on the settlement side.

⚠️ The boring stops at 34.66 m while the pile reaches 41.76 m. The deepest layer was extended down to the toe. That is our assumption, not the source's data.

Port of Oakland TP6-17NCI — driven pipe in clay

From the same database (Turner & Swanson 1995, Caltrans). The same pile was tested in both compression and uplift, so both directions can be compared.

Pile: 1,067 mm OD open-ended steel pipe, 19.05 mm wall, 30.79 m embedded, $EA$ = 1.25·10⁷ kN, driven, toe plugged. Soil: 14 layers of interbedded Bay Mud and dense granular material; water table at 1.22 m.

Compression. The computed ultimate capacity is 5,733 kN (4,968 kN shaft + 764 kN toe). The pile was loaded to 4,612 kN without failing, and the calculation sits above that, so the capacity is neither confirmed nor refuted.

Load	Measured settlement	Computed	Ratio
441 kN	0.41 mm	1.21 mm	3.0×
933 kN	0.89 mm	2.55 mm	2.9×
1,565 kN	2.07 mm	4.29 mm	2.1×
1,914 kN	2.84 mm	5.24 mm	1.8×
2,369 kN	3.65 mm	6.48 mm	1.8×
2,808 kN	4.76 mm	7.69 mm	1.6×
3,377 kN	5.96 mm	9.24 mm	1.6×
3,792 kN	7.57 mm	10.93 mm	1.4×
4,386 kN	9.53 mm	13.71 mm	1.4×
4,612 kN	13.41 mm	14.77 mm	1.1×

The calculation gives more settlement than measured at every load level, so it stays on the conservative side for a serviceability answer; the gap narrows from 3× at small loads to 1.1× by the end of the test.

The cause is the mobilisation displacement. The API t-z curve takes side friction to mobilise over a movement of 1 % of the diameter, which is 10.7 mm on this pile. A driven pile that has gained capacity with time mobilises faster than that. RP 2GEO states its own uncertainty for that value as 0.25 %–2 % of D, so the difference sits inside the method's declared range, and it is an input that can be set per layer.

Uplift. The same pile was pulled to 4,028 kN, again without failing. End bearing does not count in uplift; the capacity comes from side friction and the pile's own weight alone. The computed capacity is 4,968 kN.

Load	Measured movement	Computed	Ratio
584 kN	0.58 mm	1.63 mm	2.8×
1,336 kN	1.62 mm	3.73 mm	2.3×
1,858 kN	4.16 mm	5.19 mm	1.2×
2,296 kN	5.19 mm	6.41 mm	1.2×
2,609 kN	6.46 mm	7.28 mm	1.1×
3,047 kN	7.85 mm	8.51 mm	1.1×
3,465 kN	9.35 mm	10.14 mm	1.1×
3,820 kN	11.78 mm	11.79 mm	1.0×
4,028 kN	18.01 mm	12.76 mm	0.7×

Through the middle of the range the agreement is within 15 %. ⚠️ On the last row the direction reverses: the calculation is stiffer than the pile (12.8 mm against a measured 18.0 mm). As the pile approaches failure the measured curve runs away, and a monotonic computed curve does not reproduce that.

⚠️ Six of the fourteen layers carry only an SPT blow count in the database; the friction angle was taken from Peck, Hanson and Thornburn's bands. That is our input, not a measurement.

What this calculation covers

What the results above cover, with the direction each omission works in.

The results are read at working-load level. At the top of Houston, above 16,000 kN at Kentucky Lake and on the last point of the Oakland uplift, the measured curve softens quickly as failure approaches and a monotonic computed curve does not soften with it. Behaviour close to the failure load needs its own experimental basis.

⚠️ The soil parameters govern the result far more than the default tables do. The Sabine River match holds with the site-measured $\varepsilon_{50} = 0.007$ ; with the normally consolidated default of 0.020, which the $s_u < 48$ kPa band would select automatically, the deflection comes out roughly 55 % higher. For comparison, the model's largest mean deviation from a measured curve is 6.3 %. The Houston match likewise rests on a single $s_u = 105$ kPa chosen from a strength the source describes as varying widely over the top 20 ft. Entering site-measured parameters makes more difference than the choice of p-y curve.

Curve shape in a layered profile. All three lateral field cases are a single uniform layer; the layered case the Georgiadis equivalent-depth correction addresses is checked against closed form.

Section shape and loading type. The square section is checked against closed-form geometry and the cyclic p-y branch against the source's equations; all five field tests are circular sections under static load.

The axial field cases are driven piles. Both axial cases verify the driven (API) path; the bored path is checked against the sources' worked examples (GEC 10 Example 13-2 and O'Neill & Reese Example C-3).

Worked examples#

Fenske Table 3.11 — sand p-y coefficients#

GEC 10 Example 13-2 — side resistance in clay#

O'Neill & Reese Example C-3 — settlement by load transfer#

Field load tests#

Sabine River — soft clay#

Mustang Island — sand#

Houston — stiff clay above the water table#

Kentucky Lake TPK-1 — driven pipe in sand#

Port of Oakland TP6-17NCI — driven pipe in clay#

What this calculation covers#

Sources