Lythos Bearing — reference

The general equation

q_ult = c·Nc·sc·dc·ic·bc·gc·Fc  +  q·Nq·sq·dq·iq·bq·gq·Fq  +  ½·γ·B′·Nγ·sγ·dγ·iγ·bγ·gγ·Fγ

s, d, i, b, g and F are the shape, depth, load-inclination, base-tilt, ground-slope and compressibility corrections. Each method brings its own factors and its own corrections; a correction the method does not define is 1 and is reported as 1.

Method	Nq	Nc	Nγ	Corrections
Terzaghi (1943)	e(3π/2 − φ)tan φ / (2 cos²(45 + φ/2))	(Nq − 1)cot φ; 5.7 at φ = 0	Bowles's fit 2(Nq + 1)tan φ / (1 + 0.4 sin 4φ)	shape only
Meyerhof (1963)	eπ tan φ·tan²(45 + φ/2)	(Nq − 1)cot φ; π + 2 at φ = 0	(Nq − 1)tan(1.4φ)	s, d, i
Brinch Hansen (1970)	as Meyerhof	as Meyerhof	1.5(Nq − 1)tan φ	s, d, i, b, g
Vesić (1973)	as Meyerhof	as Meyerhof	2(Nq + 1)tan φ	s, d, i, b, g, F
EN 1997-1 Annex D	as Meyerhof	as Meyerhof	2(Nq − 1)tan φ	s, i, b (d, g borrowed on request)
Skempton (1951)	—	5(1 + 0.2B/L)(1 + 0.2D/B) ≤ 7.5(1 + 0.2B/L)	—	inside Nc

Inputs

Group	Fields
Foundation	shape (rectangle, square, strip, circle), B (diameter of a circle), L, depth Df, base tilt η, ground slope β
Actions at the base	V, horizontal loads along B and L, moments about both axes, the variable share of the actions (for the Eurocode's partial factors)
Groundwater	depth of the water table, γw
Soil profile	from the surface down, one row per layer: thickness, granular or cohesive, γ, γsat, c′, φ′, cu, E, ν
Method	the factor set; drained / undrained / whichever governs; general or local shear; each correction and the effective area on or off
Layered ground	averaging over the failure zone (with a depth factor), or the two-layer punching (Ks, ca/c1) or load-spread (angle) check
Earthquake	kh, kv, soil inertia on or off
In-situ test	SPT N60, CPT qc, or pressuremeter pl, p0 and soil category; the tolerable settlement of the SPT / CPT rules
Rock	σci, GSI, mi, D and the rock mass unit weight; or discontinuity spacing and aperture
Verification	factor of safety, or EN 1997-1 DA1 / DA2 / DA3; required FS against sliding; allowable eccentricity; base friction δ/φ′

What it computes

Quantity	Method
Nc, Nq, Nγ	Terzaghi, Meyerhof, Hansen, Vesić, EN 1997-1 Annex D; Skempton's undrained Nc
Shape, depth, inclination factors	each method's own; EN 1997-1 borrows Hansen's depth factors on request
Base tilt, ground slope	Hansen, Vesić, EN 1997-1 (base)
Compressibility	Vesić's rigidity index Ir against Ir,cr
Undrained, Hansen	the additive 5.14·cu·(1 + s′c + d′c − i′c − b′c − g′c) + q
Eccentricity	Meyerhof's effective area; Vesić's equivalent rectangle for a circle
Contact pressure	trapezoid in the middle third, triangle outside it
Layered profile	strength averaged over the Prandtl zone, (B′/2)·cos φ/cos(45 + φ/2)·e(π/4 + φ/2)tan φ
Strong over weak layer	Meyerhof & Hanna punching; load spread onto the weak layer
Earthquake	kh·V added to H, V(1 − kv); Paolucci & Pecker's (1 − kh/tan φ)0.35
SPT / CPT / PMT	Meyerhof (as revised by Bowles), Meyerhof, Ménard
Rock	Hoek–Brown 2002 equivalent c′, φ′; CFEM Ksp
Checks	FS on the net capacity; sliding; e/B; EN 1997-1 DA1 / DA2 / DA3
Required width	bisection on B until the check is met; a rectangle keeps L/B

Checks and EN 1997-1

• Bearing: FS = q_net,ult / q_net with q_net = V/A′ − q; q_all = q_net,ult/FS + q.
• Sliding: R = V·tan δ + A′·c_a (drained), R = A′·c_u (undrained); FS = R/H.
• Eccentricity: e/B against the chosen limit (B/6 by default).
• EN 1997-1 Annex A recommended values:

Set	γG	γQ	γφ′	γc′	γcu	γR;v	γR;h
A1	1.35	1.50
A2	1.00	1.30
M1			1.00	1.00	1.00
M2			1.25	1.25	1.40
R1 / R2 / R3						1.0 / 1.4 / 1.0	1.0 / 1.1 / 1.0

DA1 checks A1+M1+R1 and A2+M2+R1, DA2 A1+M1+R2, DA3 A1+M2+R3.

Project file (.bearing)

JSON. Save writes the inputs and the study definition; Open… reads them back. Missing entries keep their defaults. The keys are those of forms.defaults():

{
  "shape": "rectangle", "B": 2.5, "L": 4.0, "Df": 1.5,
  "V": 1700.0, "Hb": 150.0, "Mb": 300.0,
  "water_depth": 2.0, "method": "vesic", "analysis": "both",
  "approach": "fs", "FS": 3.0,
  "soil_profile": [
    {"name": "Fill", "thickness": 1.5, "behaviour": "granular", "gamma": 18.0,
     "gamma_sat": 19.5, "c": 0.0, "phi": 30.0, "cu": 0.0, "E": 15.0, "nu": 0.3}
  ]
}

Modules

File	Content
factors.py	Bearing capacity factors and every correction, per method
capacity.py	The general equation, effective area, contact pressure, failure zone, sliding
layered.py	Two-layer punching and load spread
seismic.py	Pseudo-static loads and soil-inertia factors
insitu.py, rock.py	SPT / CPT / pressuremeter rules; Hoek–Brown and Ksp
engine.py	The analysis: profile, strength over the zone, all methods, checks, Eurocode, width
study.py, study_plots.py	Parametric and reliability studies
report.py, pdf.py	Calculation report: one HTML assembly, exported as PDF / HTML / DOCX
web/	The local HTTP server, the session and the browser interface

Validation

The tests check the factors against the published tables, the equation against hand calculations (Prandtl's 5.14·c_u, a Vesić square footing term by term, the contact pressure trapezoid and triangle), each auxiliary method against its expression, the engine's checks and refusals, the report in all three formats, and the interface (session and HTTP layer).

pip install -e ".[dev]"
pytest -q

Limits

• Shallow foundations: the equations lose meaning much beyond D/B ≈ 2–4.
• The failure zone average is a simplification for a layered profile; where a strong layer of limited thickness overlies a weak one, use the two-layer check.
• Settlement is not checked beyond the SPT/CPT rules — see Lythos Settle.
• Terzaghi's N_γ is a fit (about 10 % low at φ′ = 20°), K_s defaults to a conservative estimate, and the rock methods are empirical: each is flagged where it is used.

Full derivations and sources: docs/theory.md.