Lythos Wall — reference

Units are kN, m and kPa (mm, mm², kNm and MPa in the concrete design); every force is per metre run of wall.

Earth pressure

The thrust acts on the virtual back, the vertical plane through the end of the heel; the soil between the stem and that plane moves with the wall and counts as its weight.

Method	Coefficient	Direction
Rankine	Ka = cos β·(cos β − √(cos²β − cos²φ))/(cos β + √(cos²β − cos²φ)); with the cohesion of the backfill, p = K·σ′v − 2c·√K ≥ 0	β
Coulomb	Coulomb's Ka with wall friction δ and backslope β	δ
At rest	K0 = (1 − sin φ)·√OCR·(1 + sin β) (EN 1997-1 eq. 9.2)	β
Trial wedge	the largest thrust over trial planes through the heel; reproduces Coulomb	δ

Passive resistance in front by Rankine or Coulomb (δ ≤ φ/2), down to the base or the bottom of the key; only the share entered is counted. Water pushes hydrostatically; uplift acts under the base.

Stability

sliding:       FS = [V·tan(kb·φ) + ka·c·B + share·Pp] / ΣH
overturning:   FS = M_R / M_O                      (about the toe)
eccentricity:  e = B/2 − (M_R − M_O)/V ≤ B/6 static, B/3 seismic
base pressure: q = V/B·(1 ± 6e/B),  or  2V/(3·(B/2 − e)) beyond the middle third
bearing:       B′ = B − 2e,  σv = ΣV/B′  against q_ult (Terzaghi, Meyerhof, Hansen, Vesić, EN 1997-1)

The live surcharge over the heel counts as a weight only for the bearing capacity. Global stability: slip circles passing under the footing and the key, by Bishop's simplified method and Fellenius', with k_h on every slice in an earthquake.

Earthquake — TBDY 2018

Quantity	Expression
Site coefficients	Fs, F1 from Tables 2.1 and 2.2, interpolated, site classes ZA–ZE
Design spectrum	SDS = Ss·Fs, SD1 = S1·F1; Sae(T)
Seismic coefficients	kh = βr·0.4·SDS (§16.12), kv = ratio·kh, up and down
Mononobe–Okabe	ΔP = (1 − kv)·KAE·(½γh² + q·h) − static thrust
Seed–Whitman	ΔKAE = ¾·kh
Wood	ΔP = kh·γ·h² (a wall that cannot move)
Inertia	kh·W of the wall and of the soil on the heel
Resistance factors	TBDY §16.7: sliding γRh = 1.1, bearing γRv = 1.4

Reinforced concrete — TS 500

Item	Rule
Combinations	TS 500: 1.4G + 1.6Q + 1.6H, 0.9G + 1.6H; TBDY 2018: G + Q + H + E, 0.9G + H + E, kv ±
Members	the stem under its own virtual back; the toe and the heel under the contact pressure; the key
Flexure	As from 0.85·fcd over k1·c; ρmin·b·h ≤ As; ρ ≤ min(0.85·ρb, 0.02)
Shear	Vd ≤ Vcr = 0.65·fctd·b·d
Spacing	s ≤ min(1.5h, 200 mm); 300 mm for distribution steel
Anchorage	lb = 0.12·fyd/fctd·φ ≥ 20φ
Curtailment	half the stem bars stop where Mr of the other half suffices, extended by max(d, 12φ), never below lb

Concrete C20–C50, steel B420C or B500C. The bars can be chosen or left to the program.

Inputs

Group	Fields
Geometry	H, stem thickness at the top and the base, the inclined face, toe, heel, footing thickness, soil over the toe, backslope β, slope in front; Suggest dimensions
Shear key	depth, width, distance from the front of the footing
Loads	permanent and live surcharges, a line load on the stem, a horizontal load at its top
Soils and water	backfill γ, γsat, φ′, c′; foundation soil γ, γsat, φ′, c′ (or cu); water behind and in front, or a water table below
Earth pressure	method, δ/φ, OCR; passive resistance, its method and share
Stability and bearing	base friction and adhesion, bearing method and factors, allowable pressure, slip circle search, required factors of safety (static and seismic)
Earthquake	Ss, S1, site class, βr (or kh directly), kv/kh, dynamic thrust method and height, share of the live load
Concrete	class, steel, unit weight, covers, main bars (or automatic), ρmin, front-face and distribution minimums, curtailment

Project files (.lwall) are JSON; missing entries keep their defaults.

Modules

File	Content
earth.py	Rankine, Coulomb, K0, trial wedge, Mononobe–Okabe, Seed–Whitman, Wood
tbdy.py	TBDY 2018 site coefficients, spectrum, kh, kv
factors.py, capacity.py	Bearing capacity factors and the general equation (from Lythos Bearing)
concrete.py	TS 500 materials, flexure, shear, development length, the choice of bars
geometry.py, engine.py	The wall's outline; pressures, forces, stability, bearing, earthquake, required heel
globalstab.py	Slip circles by Bishop and Fellenius, the grid search
design.py, drawing.py	Member forces, sections, curtailment, bars, schedule; the drawing and its DXF
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 earth pressure coefficients against their closed forms (the trial wedge against Coulomb, Mononobe–Okabe against Coulomb at k_h = 0), the TBDY coefficients and spectrum, the TS 500 strengths, steel, shear and anchorage against hand calculations, the wall's weights, thrust, sliding, overturning, base pressure and bearing by hand, the required heel as a boundary, the slip circles, the member moments, the bars, the schedule, the DXF, the report in all three formats and the interface.

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

Limits

Not included: settlement (use Lythos Settle), the drainage of the backfill, the hydrodynamic pressure of free water in an earthquake, and the joints and laps along the wall — check them separately.

Full derivations and sources: docs/theory.md.