Lythos MSEW — reference

What it computes

Quantity	Method
Ka	Coulomb (AASHTO 3.11.5.3), θ = 90 + ω from a 10° batter on; δ = β behind the block, δ = 0 inside it
Forces	V1 = γr·H·L, the slope wedge over the block, F1 = ½·Ka·γ·h² and F2 = Ka·q·h at β, h = H + L·tan β
Sliding	the weakest of tan φr, tan φf + c·L and Cds·tan φr; the live load over the block left out
Overturning, eccentricity	moments about the toe; e ≤ L/6 (ASD), L/3 (LRFD), L/4 (seismic ASD)
Bearing	B′ = L − 2e, σv = ΣV/B′ against qult by Terzaghi, Meyerhof, Hansen, Vesić, EN 1997-1
Tmax	Kr·σv·Sv, σv = γr·Z + σ2 + q + Δσv (2:1 strip load), Kr/Ka 1.7 → 1.2 over 6 m for strips
Active zone	Rankine 45 + φ/2 (extensible), bilinear 0.3·H1 (inextensible)
Pullout	Pr = F*·α·σ′v·Le·C·Rc, C = 2, no live load; F* = Ci·tan φ, or F*0 → tan φ over 6 m
Strength	Tult/(RFID·RFCR·RFD)·Rc; Fy·b·Ec/Sh with Ec after zinc and steel corrosion
LRFD	EV 1.00/1.35, EH 1.50, ES 0.75/1.50, LS 1.75; φ as entered
Earthquake	Am = (1.45 − A)·A; PAE = 0.375·Am·γ·H² (M–O with a backslope) at 0.6·H, ½PAE + PIR; Pi = Am·Wa by Le
Required length	bisection on a uniform L until every external and pullout check holds

Inputs

Group	Fields
Wall	design height H, embedment d, face batter ω, backslope β, slope in front of the toe, facing thickness
Surcharges	permanent and live (traffic) uniform surcharges; a strip load (P, width, offset from the face, permanent or live)
Soils	reinforced fill (γ, φ′), retained fill (γ, φ′), foundation soil (γ, γsat, φ′, c′ — or φ = 0 and cu), the water table below the base
Reinforcement types (a table)	name, kind (steel strip, polymer strip, geogrid, geotextile); geosynthetics: Tult, RFID, RFCR, RFD, Rc, Ci; steel strips: b, t, Fy, Sh, F*0 at the top; all: scale correction α and connection strength ratio CR
Layers (a table)	height above the levelling pad z, length L, type — or the layout generator: first layer, Sv, L = ratio·H (never below a shortest length) or a fixed L
Corrosion	design life, galvanising thickness, carbon steel loss rate
Design method	ASD (FS for sliding, overturning, eccentricity, bearing, tensile, pullout, connection; 0.55·Fy for steel) or LRFD (φ); the minimum length beyond the active zone
Bearing capacity	the factor set; embedment and load inclination on or off; the direct sliding coefficient Cds of a geosynthetic
Earthquake	A, the reduction of F* under seismic loading
Height study	the range and the step

Project file (.msew)

JSON with every input, the tables included. A layer list and type table:

{
  "H": 6.0, "embedment": 0.6, "q_live": 10.0,
  "gamma_r": 19.0, "phi_r": 34.0, "phi_b": 30.0, "phi_f": 30.0, "c_f": 5.0,
  "layout_z1": 0.375, "layout_Sv": 0.75, "layout_rule": "ratio", "layout_ratio": 0.9,
  "design": "asd", "bearing_method": "vesic", "design_life": 75.0,
  "reinforcement_types": [
    {"name": "Geogrid 80", "kind": "geogrid", "Tult": 80.0, "RFID": 1.1, "RFCR": 1.6,
     "RFD": 1.1, "Rc": 1.0, "Ci": 0.67, "alpha": 0.8, "CR": 0.8}
  ],
  "layers": [{"z": 0.375, "L": 5.4, "type": "Geogrid 80"}]
}

Modules

File	Content
earth.py	Coulomb, Rankine, Mononobe–Okabe, Am
reinforcement.py	Corrosion, long-term strength, Kr/Ka, F*, pullout
catalog.py	Typical market reinforcement
factors.py, capacity.py	Bearing capacity factors and the general equation (from Lythos Bearing)
engine.py	The wall: forces, external checks, bearing, internal checks, earthquake, required length, layout generator
heights.py, height_plots.py	The height study, its figures, CSV / XLSX
report.py, pdf.py, web/	Report and interface

Validation

The tests check the earth pressure coefficients against their closed forms; the corrosion and the strengths, the forces, the external checks, the bearing capacity, and the tension and pullout of a layer against hand calculations; the LRFD factors, the seismic forces, the required length as a boundary, the refusals and warnings, the report in all three formats and the interface.

Not included

Global and compound stability, settlement and drainage. Details: docs/theory.md.