Lythos SPWA — reference

Method notes

• Limit equilibrium: moment equilibrium about the toe (cantilever, simplified method) or the lowest anchor (free-earth). Internal forces are evaluated at the theoretical depth D_req; D_design = round-up(1.2·D_req) is the constructed length. For more than one anchor the LE distribution is approximate — the beam-spring results should govern.
• Seismic: Mononobe-Okabe with K_AE / K_PE (vertical wall); below the water table θ uses γ_sat/γ′ (restrained pore water); the Westergaard hydrodynamic pressure of the free water in front of the wall is applied as a driving load. Both corrections can be switched off.
• Beam-spring: p = clip(p_ref ± k_s·Δw, p_a, p_p) per node, at-rest start; anchors T = max(0, P₀·cos α/s + k_h·Δw); moment from the element curvature (EI·w″).
• Vertical check (indicative): ΣT_h·tan α against the skin friction ∫(p_a + p_p)·tan δ over the embedded length; no end bearing.

Inputs

Group	Fields
Geometry	retained height H, backfill slope β, dredge line slope α, wall friction δ
Loads and water	uniform surcharge; water levels on the active and passive sides, γw
Soil profile	per layer: thickness, γ, γsat, φ, cohesion, ks and its method (manual, Ménard-Bourdon, Schmitt), EM
Anchors	depth, angle, EA, free length, horizontal spacing, prestress
Section	manufacturer, section model (I and W from the database), steel grade
Safety	FSφ, FSc, bending FS, embedment increase factor (1.2), rounding increment
Seismic	on/off, kh, kv, submerged θ, hydrodynamic pressure
Beam-spring	on/off, staged, overdig, embedment (0 = Ddesign), water mode (final stage / as given)
Deflection criterion	FHWA H/120, H/100 or H/240

Project file (.spwa)

{
  "excavation_depth_H": 8.0, "surcharge_load": 15.0, "wall_friction_delta": 20.0,
  "water_level_active": 4.0, "water_level_passive": 7.0,
  "is_seismic": true, "kh": 0.1, "kv": 0.0,
  "selected_section_model": "NZ 26", "selected_steel_grade": "S355",
  "bs_enabled": true, "bs_staged": true, "bs_overdig": 0.5,
  "soil_profile": [
    {"name": "Sloped Sandy Gravel", "thickness": 25.0, "gamma": 19.5, "gamma_sat": 21.0,
     "phi": 38, "cohesion": 0, "k_s": 30000.0, "k_s_method": "manual"}
  ],
  "anchors": [
    {"depth": 1.5, "angle": 15.0, "EA": 117000.0, "free_length": 12.0, "spacing": 2.5, "prestress": 0.0},
    {"depth": 4.0, "angle": 15.0, "EA": 117000.0, "free_length": 12.0, "spacing": 2.5, "prestress": 0.0}
  ]
}

Modules

File	Content
analysis_engine.py	Free-earth support: Coulomb / Mononobe-Okabe pressures, embedment (brentq), anchor forces, diagrams at Dreq, stress / deflection / vertical checks
beam_spring.py	Winkler beam on elastoplastic springs with staged construction, tension-only inclined anchors, ks from Ménard-Bourdon or Schmitt
study.py, study_plots.py	Parametric (OAT / grid) and reliability (LHS / Monte Carlo) studies: optional Gaussian-copula correlation, parallel runner, sensitivities, Pf with 95 % CI and β
plotting.py, plot_style.py	Figures (schematic + diagrams, 4-panel beam-spring), theme-aware
report.py, pdf.py	Calculation report: PDF, HTML, DOCX
config.py, section_database.json	Defaults, theme, translations; I [m⁴/m] and W [m³/m] of sheet pile sections
web/	The local HTTP server, the session and the browser interface

Validation

106 tests: engine, beam-spring, report, study, forms, web and packaging. The analysis cores are checked against closed-form and published cases, the report in all three formats, the interface through its session and HTTP layer.

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