Lythos 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) |
| Criteria | FS = 2.5, allowable settlement 40 mm |
1. A pile group
lythos-pile example -o group.pile
lythos-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
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
Required length: L = 18.50 m (tip at 20.00 m)
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.
• 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. The Warnings are among the program's most valuable output: they say where each assumption is being stretched.
2. A length sweep
from lythospile import forms
from lythospile.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.
lythos-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.