Lythos Bearing — examples
Every command and script on this page was run and its output is quoted as it came. They all start from the same starter project: a 2.5 × 4.0 m rectangular footing on layered ground.
| Input | Value |
|---|---|
| Footing | rectangle, B = 2.5 m, L = 4.0 m, Df = 1.5 m |
| Actions | V = 1700 kN, HB = 150 kN, MB = 300 kNm |
| Water table | 2.0 m deep |
| Soil | 1.5 m fill (φ′ = 30°) / 5.0 m stiff clay (c′ = 5 kPa, φ′ = 24°, cu = 90 kPa) / 8.0 m dense sand (φ′ = 38°) |
| Criteria | FS ≥ 3.0 (bearing), ≥ 1.5 (sliding), e ≤ B/6 |
1. Running the starter project
lythos-bearing example -o project.bearing
lythos-bearing run project.bearingBEARING CAPACITY RESULTS
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Foundation: Rectangle, B = 2.50 m, L = 4.00 m, Df = 1.50 m
Actions: V = 1700.0 kN, H = 150.0 kN (5.0° from vertical)
Eccentricity: e_B = 0.176 m, e_L = 0.000 m → B' = 2.147 m, L' = 4.000 m, A' = 8.59 m²
Contact pressure: q_max = 242.0 kPa, q_min = 98.0 kPa (within the middle third)
Surcharge at the base: σv0 = 27.0 kPa, u = 0.0 kPa, σ'v0 = 27.0 kPa
Failure zone: 2.80 m below the base (Stiff clay)
Design strength: c' = 5.0 kPa, φ' = 24.0°, cu = 90.0 kPa, γ = 9.69 kN/m³
Bearing capacity by method
Method Analysis q_ult q_net,ult Nc Nq Nγ
Terzaghi (1943) drained 516.8 489.8 23.36 11.40 7.90
Meyerhof (1963) drained 466.0 439.0 19.32 9.60 5.72
Brinch Hansen (1970) drained 474.2 447.2 19.32 9.60 5.75
Vesić (1973) * drained 533.5 506.5 19.32 9.60 9.44
EN 1997-1 Annex D drained 517.3 490.3 19.32 9.60 7.66
Skempton (1951), undrain undrained 594.9 567.9 6.31 1.00 0.00
The three terms of the governing method
cohesion: 133.2 kPa (25 %)
surcharge: 339.1 kPa (64 %)
self weight: 61.2 kPa (11 %)
Checks
Bearing: FS = 2.96 ≥ 3.00 — NOT OK
Sliding: FS = 5.33 ≥ 1.50 — OK
Eccentricity: e/B = 0.071 ≤ 0.167 — OK
The bearing check is satisfied from B = 2.51 mReading the output. The water table is 0.5 m below the base, so the effective unit weight in the failure zone drops to 9.69 kN/m³. Strength is averaged over the Prandtl zone reaching 2.80 m below the base, which stays entirely in the stiff clay. The moment moves the resultant 0.176 m along B and the effective width becomes 2.147 m. 64 % of the capacity comes from the surcharge term: the founding depth is the key parameter of this footing.
Add -o report.pdf (or .html, .docx) for a report; --lang tr gives the whole output in Turkish.
2. A width sweep from Python
from lythosbearing import forms
from lythosbearing.web.session import Session
session = Session(lang="en")
values = forms.defaults() # the starter project: 2.5 × 4.0 m footing
for B in (2.0, 2.5, 3.0, 3.5):
values["B"] = B
r = session.analyse(values)
print(f"B = {B:.1f} m q_ult = {r['q_ult']:6.1f} kPa FS = {r['FS']:.2f}")B = 2.0 m q_ult = 522.7 kPa FS = 2.15
B = 2.5 m q_ult = 533.5 kPa FS = 2.96
B = 3.0 m q_ult = 550.4 kPa FS = 3.92
B = 3.5 m q_ult = 569.7 kPa FS = 5.02qult grows slowly with the width (the Nγ term), but most of the gain comes from the drop in the applied pressure; the factor of safety therefore rises quickly.
3. Reading the methods as a table
The interface's table is result["table"]:
r = Session(lang="en").analyse(forms.defaults())
for row in r["table"]["rows"]:
method, analysis, q_ult, q_net, q_all, fs = row["cells"]
print(f"{method:28s} {analysis:10s} q_ult = {q_ult:>7s} kPa FS = {fs}")Terzaghi (1943) drained q_ult = 516.8 kPa FS = 2.87
Meyerhof (1963) drained q_ult = 466.0 kPa FS = 2.57
Brinch Hansen (1970) drained q_ult = 474.2 kPa FS = 2.62
Vesić (1973) drained q_ult = 533.5 kPa FS = 2.96
EN 1997-1 Annex D drained q_ult = 517.3 kPa FS = 2.87
Skempton (1951), undrained undrained q_ult = 594.9 kPa FS = 3.32The methods differ by 14 % for the same footing (Meyerhof 2.57 – Vesić 2.96). Knowing which method the specification asks for matters more than “which number is right”.
4. EN 1997-1 design approaches
To verify with partial factors instead of a factor of safety, change approach:
values = forms.defaults()
for approach in ("fs", "da1", "da2", "da3"):
values["approach"] = approach
r = session.analyse(values)
print(f"{approach:4s} B ≥ {r['required_width']:.2f} m")fs B ≥ 2.51 m
da1 B ≥ 2.08 m
da2 B ≥ 2.13 m
da3 B ≥ 2.34 mWith DA1 selected the report adds both combinations:
EN 1997-1 verification (EN 1997-1, Design Approach 1)
DA1-1 (A1 + M1 + R1): Ed = 2372 kN ≤ Rd = 4570 kN, Λ = 0.52 — OK
sliding: Hd = 209 kN ≤ Rd = 1099 kN — OK
DA1-2 (A2 + M2 + R1): Ed = 1853 kN ≤ Rd = 2733 kN, Λ = 0.68 — OK
sliding: Hd = 163 kN ≤ Rd = 694 kN — OKFor this footing the FS = 3.0 criterion is more conservative than any of the three Eurocode approaches. variable_fraction (0.3 by default) is the variable share of the actions and sets the A1/A2 factors.
5. Earthquake
With B = 2.6 m chosen, the effect of the pseudo-static horizontal coefficient:
values = forms.defaults()
values["B"] = 2.6
for kh in (0.0, 0.1, 0.2):
values["seismic_enabled"] = kh > 0
values["kh"] = kh
r = session.analyse(values)
print(f"kh = {kh:.1f} q_ult = {r['q_ult']:6.1f} kPa FS = {r['FS']:.2f}")kh = 0.0 q_ult = 536.6 kPa FS = 3.14
kh = 0.1 q_ult = 497.9 kPa FS = 2.90
kh = 0.2 q_ult = 452.1 kPa FS = 2.62kh·V is added to the horizontal load (the load inclination grows) and, with soil_inertia on, Paolucci & Pecker's (1 − kh/tan φ)0.35 reduction is applied.
6. A reliability study
The project written by example carries two study variables: V (lognormal, CoV = 0.15) and the stiff clay's φ′ (normal, CoV = 0.12). 300 Latin hypercube samples:
lythos-bearing study project.bearing -o samples.csvSTUDY RESULTS
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Method: Latin hypercube; samples: 300; successful: 300
Statistics of the outputs
n mean std P5 P50 P95
Ultimate capacity (kPa) 300 519.3 111.7 322.8 531.9 642.1
Factor of safety 300 2.916 0.7192 1.768 2.942 4.112
Factor of safety, sliding 300 5.014 0.7633 3.717 5.118 6.266
Probability of failure
Bearing capacity: 158 of 300, P = 0.527 (95 % CI 0.47 – 0.582), β = -0.07
Sliding: 0 of 300, P = 0 (95 % CI 8.67e-19 – 0.0126), β = > 2.71
Eccentricity: 0 of 300, P = 0 (95 % CI 8.67e-19 – 0.0126), β = > 2.71
Sensitivity of the factor of safety (Spearman ρ)
Stiff clay · phi +0.851
Actions · V -0.287Here “failure” means FS < 3.0; for a design whose mean sits at the threshold a probability near 0.5 is expected. The real information is in the sensitivity: the clay's φ′ drives the result, not the load (ρ = +0.85). A little more site investigation could be worth more than a wider footing.
Setting up a study in the interface
In the 2 · Study tab add any input to the list, choose a range or a distribution, and run. Results are drawn as tornado, histogram and scatter plots; the samples export to CSV/XLSX and become a section of the report.
7. An in-situ test (SPT)
With insitu_enabled, Meyerhof's SPT rule (as revised by Bowles, 25 mm tolerable settlement) is added to the “other methods”:
values = forms.defaults()
values.update(insitu_enabled=True, test="spt", N60=20.0, settlement=25.0)Other methods
SPT (Meyerhof), settlement … — — 355.6The SPT rule is a settlement criterion: 355.6 kPa is the net pressure that keeps the footing's settlement within 25 mm, not a failure load.