SlipSurface Pile — examples
Every output is from a real run. The starter project: a 3 × 3 group of bored piles in layered ground.
| Input | Value |
|---|---|
| Pile | circular, D = 0.80 m, L = 20 m, head at 1.5 m, bored / CFA, γp = 25 kN/m³ |
| Group | 3 × 3 at 2.40 m (3D), Q = 10 000 kN, Converse–Labarre, block failure on |
| Water table | 2.5 m |
| Profile | 2 m fill / 6 m soft clay (cu = 35) / 7 m medium dense sand (φ′ = 32°) / 5 m stiff clay (cu = 120) / 12 m dense sand (φ′ = 36°, N60 = 40) |
| Seismic case | V = 8 000 kN, MB = 16 000 kN·m; FS 1.5 in compression, 2.0 in uplift |
| Criteria | FS = 2.5, allowable settlement 40 mm |
1. A pile group
slipsurface-pile example -o group.pile
slipsurface-pile run group.pilePILE CAPACITY RESULTS
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Pile: Circular, D = 0.80 m, L = 20.00 m, head at 1.50 m, tip at 21.50 m; Bored / CFA
Base area Ab = 0.5027 m², perimeter p = 2.513 m
Group: 3 × 3 = 9 piles at 2.40 × 2.40 m; Q = 10,000 kN, 1,111 kN per pile
Water table at 2.50 m
Critical depth zc = 12.00 m (15·D)
In sand: K/K0 = 1.00, δ/φ' = 0.75
BASE RESISTANCE
Tip in 'Dense sand' (Granular) at 21.50 m, σ'v0 = 228.6 kPa
Meyerhof * Nq* = 168.0 6,184 kPa 3,108 kN
Vesić Nq* = 114.9 14,970 kPa 7,525 kN
Janbu Nq* = 37.8 4,919 kPa 2,473 kN
SPT — Meyerhof 3,040 kPa 1,528 kN
SHAFT FRICTION
Layer Depth (m) Qs (kN)
Fill 1.50–2.00 8 kN
Soft clay 2.00–8.00 357 kN
Medium dense sand 8.00–15.00 437 kN
Stiff clay 15.00–20.00 939 kN
Dense sand 20.00–21.50 103 kN
Shaft friction by clay method:
α — API RP 2A * 1,844 kN
α — Kulhawy & Phoon 1,704 kN
α — Sladen 1,560 kN
β — Burland 1,962 kN
λ — Vijayvergiya & Focht 1,776 kN
SPT — Meyerhof 1,815 kN
CAPACITY OF A SINGLE PILE
Qs = 1,844 kN + Qb = 3,108 kN = Qult = 4,952 kN
Pile weight W = 158 kN (subtracted: yes)
Qult,net = 4,794 kN, FS = 2.50, Qall = 1,918 kN
PILE GROUP
Converse–Labarre * η = 0.727
Los Angeles Group η = 0.792
Seiler–Keeney η = 0.887
Feld η = 0.722
η = 1 η = 1.000
η = 0.727: η·n·Qult = 0.727 · 9 · Qult = 32,396 kN
Block 5.60 × 5.60 m: shaft 26,227 kN + base 193,925 kN = 220,151 kN
Qg,ult = 32,396 kN (efficiency), Qg,ult − n·W = 30,978 kN, Qg,all = 12,391 kN
SETTLEMENT
Single pile (Vesić): s1 = 1.20 + s2 = 12.27 + s3 = 0.74 = 14.20 mm
Equivalent raft at 14.84 m, q = 318.9 kPa: consolidation 19.6 + elastic 12.2 + pile shortening 1.0 = 32.8 mm
Vesić: s·√(Bg/D) = s·√(5.60/0.80) = 37.6 mm
Meyerhof SPT: N60 = 40, I = 0.55, q = 318.9 kPa, sg = 10.0 mm
SEISMIC LOAD CASE
V = 8,000 kN, M_B = 16,000 kN·m, M_L = 0 kN·m: pile loads from -222 to 2,000 kN
Compression: Qult,net / FS = 4,794 / 1.50 = 3,196 kN against Pmax = 2,000 kN
Uplift: λt = 0.75 (sand), 1.00 (clay), ζ = 1.00; Qs,t = 1,707 kN, W = 158 kN, Tall = Qs,t / 2.00 + W = 1,011 kN
Largest tension T = 222 kN, 3 piles in tension
CHECKS
Single pile: FS = 4.31 (required 2.50) — OK
Group: FS = 3.10 (required 2.50) — OK
Settlement: 32.8 mm (allowed 40.0 mm) — OK
Seismic compression: FS = 2.40 (required 1.50) — OK
Seismic uplift: FS on Qs,t = 26.43 (required 2.00) — OK
Required length: L = 18.50 m (tip at 20.00 m)
SOIL PROFILE
Layer Depth (m) γ (kN/m³) φ' (°) cu (kPa) N60 σ'v0 (kPa)
Fill 0.0–2.0 18.0 28.0 — 8 18.0
Soft clay 2.0–8.0 17.0 22.0 35.0 — 65.0
Medium dense sand 8.0–15.0 19.0 32.0 — 20 125.2
Stiff clay 15.0–20.0 19.5 26.0 120.0 — 186.3
Dense sand 20.0–32.0 20.0 36.0 — 40 279.0
Warnings
• Meyerhof's limit governs the base: qb = 0.5·pa·Nq*·tan φ' = 6,184 kPa.
• Meyerhof's SPT rule was derived for driven piles; for a bored pile it is shown for comparison only.
• Below the critical depth zc = 12.00 m the shaft friction and the base resistance in sand no longer grow with depth.
• In the seismic case 3 piles are in tension, the largest pull T = 222 kN: the reinforcement must carry it down the pile and into the cap.
• The stresses under the equivalent raft still matter at the foot of the profile (32.00 m); layers below it would settle too.Reading the output. The base methods differ by more than a factor of three (Janbu 2 473 kN – Vesić 7 525 kN); Meyerhof's limiting value governs. In the group, the efficiency (0.727) matters far more than block failure. Under the seismic moment the edge row carries 2 000 kN and the opposite row is pulled up by 222 kN — well inside what its shaft friction in tension allows. The Warnings are among the program's most valuable output: they say where each assumption is being stretched.
2. A length sweep
from slipsurface.pile import forms
from slipsurface.pile.web.session import Session
session = Session(lang="en")
values = forms.defaults() # 3 × 3 bored group, D = 0.8 m, Q = 10 000 kN
for L in (16.0, 18.0, 20.0, 22.0):
values["L"] = L
r = session.analyse(values)
print(f"L = {L:4.1f} m Qult,net = {r['Q_ult_net']:7.0f} kN FS = {r['FS']:.2f}")L = 16.0 m Qult,net = 1671 kN FS = 1.50
L = 18.0 m Qult,net = 2041 kN FS = 1.84
L = 20.0 m Qult,net = 4794 kN FS = 4.31
L = 22.0 m Qult,net = 4917 kN FS = 4.43With the head at 1.5 m, at L = 18.5 m the tip reaches 20 m — the dense sand — and the capacity jumps there. The required length (r["required_length"] = 18.5 m) is the search that finds that jump; the capacity–length curve is stepped for the same reason.
3. Group efficiency methods
efficiency selects which efficiency the group capacity uses: converse_labarre, los_angeles, seiler_keeney, feld or unity (η = 1, the group as n single piles). The report always lists them all; the chosen one is starred. Closer spacing than 2.4 m (3D) lowers the efficiencies and brings block failure forward — sweep sx and sy with a study.
4. A rock socket
The starter project also carries a rock socket: D = 1.0 m, head at 1 m, rock at 12 m, a 4 m socket, Q = 9 000 kN, qu = 20 MPa.
slipsurface-pile socket group.pileROCK-SOCKETED PILE
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D = 1.00 m, head at 1.00 m, rock at 12.00 m (overburden 11.00 m), socket Ls = 4.00 m, Q = 9,000 kN
qu = 20.0 MPa (side shear with 20.0 MPa, f'c = 30.0 MPa), Em = 5,940 MPa, Em/Ei = 0.297, αE = 0.698
Hoek–Brown: GSI = 60, mi = 10.0, mb = 2.397, s = 1.17e-02
UNIT SIDE SHEAR AND SOCKET LENGTH
Correlation fs (kPa) Ls needed (m) Qall at Ls (kN)
Rosenberg & Journeaux (1976) 1,754 2.67 11,922
Horvath & Kenney (1979) 939 5.01 7,826
Meigh & Wolski (1979) 1,328 3.53 9,778
Williams et al. (1980) 1,294 3.62 9,608
Reynolds & Kaderabek (1980) † 6,000 0.78 33,264
Gupton & Logan (1984) † 4,000 1.17 23,211
Rowe & Armitage (1987) 2,012 2.32 13,221
Carter & Kulhawy (1988) 894 5.26 7,601
Toh et al. (1989) † 5,000 0.93 28,238
Zhang & Einstein (1998) 1,789 2.62 12,097
O'Neill & Reese (1999) / AASHTO 646 7.32 6,350
Kulhawy et al. (2005) 1,424 3.29 10,260
9 correlations in range: mean 1,342, median 1,328, 646 – 2,012 kPa
† fitted to weak rock; out of range above qu = 5.0 MPa
UNIT BASE RESISTANCE
Coates (1967) 3·qu 60.00 MPa
Rowe & Armitage (1987) 2.7·qu 54.00 MPa
Carter & Kulhawy (1988), Hoek–Brown [√s + √(m√s + s)]·qu 12.59 MPa
Zhang & Einstein (1998) 4.83·qu^0.51 22.26 MPa
AASHTO / O'Neill & Reese 2.5·qu 50.00 MPa
CFEM (Ladanyi & Roy) 3·Ksp·d·qu 45.85 MPa
DESIGN
fs = 1,342 kPa, qb = 12.59 MPa, FSside = 2.50, FSbase = 3.00
Socket length needed 3.49 m, minimum 1.00 m → design Ls = 3.49 m
At Ls = 4.00 m: Qs = 16,866, Qb = 9,886, W = 191, Qall = 9,851 kN against Q = 9,000 kN (Q/Qall = 0.91) — OK
ELASTIC SETTLEMENT AT Ls = 4.00 m
Shortening through the overburden: 4.20 mm
Randolph & Wroth, side and base: 5.00 mm (10 % through the base)
Randolph & Wroth, side only: 5.03 mm
Vesić: 6.01 mmReading the output. For the same rock the twelve correlations give between 646 and 6 000 kPa of side shear. The three fitted to weak rock (†) are left out of the statistics above qu = 5 MPa. The design side shear is the mean of the remaining nine (design = "mean"); the base uses the smallest (base_design = "min"). The lengths needed range from 2.3 to 7.3 m — again, knowing which correlation the specification asks for is what decides.
5. A seismic load case
New in 0.2.0. The rigid cap shares the seismic vertical load and the overturning moments among the piles; the most loaded pile is checked in compression, the piles in tension against their shaft friction in tension plus their own weight, and the group against being lifted as one block. Doubling the moment of the starter project:
# in group.pile: "seismic": { "enabled": true, "V": 8000, "M_B": 32000, ... }
slipsurface-pile run group.pileSEISMIC LOAD CASE
V = 8,000 kN, M_B = 32,000 kN·m, M_L = 0 kN·m: pile loads from -1,333 to 3,111 kN
Compression: Qult,net / FS = 4,794 / 1.50 = 3,196 kN against Pmax = 3,111 kN
Uplift: λt = 0.75 (sand), 1.00 (clay), ζ = 1.00; Qs,t = 1,707 kN, W = 158 kN, Tall = Qs,t / 2.00 + W = 1,011 kN
Largest tension T = 1,333 kN, 3 piles in tension
CHECKS
Single pile: FS = 4.31 (required 2.50) — OK
Group: FS = 3.10 (required 2.50) — OK
Settlement: 32.8 mm (allowed 40.0 mm) — OK
Seismic compression: FS = 1.54 (required 1.50) — OK
Seismic uplift: FS on Qs,t = 1.45 (required 2.00) — NOT OK
Required length: L = 29.75 m (tip at 31.25 m)Reading the output. Compression still passes, just, but the uplift check fails: the piles on the tension side are pulled with 1 333 kN against an allowable 1 011 kN. The required length now comes from the seismic uplift, not from the static checks, and jumps from 18.5 m to 29.75 m. Shaft friction in tension is reduced by λt (0.75 in sand, 1.0 in clay) and by the cyclic factor ζ.