Lythos Settle — reference

Inputs

Group	Fields
Foundation	shape (rectangle, strip, circle), B (diameter of a circle), L, depth Df, gross bearing pressure q; optionally the excavated overburden is deducted (qnet = q − σv0(Df))
Embankment (shape “embankment”)	crest width, height H, left and right slope angles, unit weight of the fill γ; the load is γ·H under the crest, falling linearly to zero at the toes
Groundwater	depth of the water table, γw
Soil profile	from the surface down: thickness, granular or cohesive, γ, γsat, E, ν; for the clays Cc, Cr, e0, OCR, cv, Cα and single / double drainage. E is the drained modulus of a sand and the undrained modulus of a clay
Options	stress distribution, immediate-settlement method, flexible or rigid foundation, sublayer thickness, influence-depth ratio Δσ/σ′v0, design life, Schmertmann's creep factor
Criteria	allowable total settlement and angular distortion (1/x)

What it computes

Quantity	Method
Δσ under a rectangle	Newmark's integration of Boussinesq, superposed for any point
Δσ under a strip / circle	closed form / exact one-dimensional integral over the polar angle
Δσ under an embankment	exact: Flamant's line load integrated over the piecewise-linear (trapezoidal) load
Δσ, approximate	2:1 spread
Embankment, immediate	Steinbrenner in plane strain, the crest as one strip and each slope as 16 slices
Immediate settlement	Steinbrenner F1, F2 on each layer (layered elastic), or Schmertmann (1978) with C1, C2 and the L/B-interpolated influence diagram
Primary consolidation	Cr up to σ′p = OCR·σ′v0, Cc beyond it, sublayer by sublayer at each point
Secondary compression	Cα/(1+e0)·H·log(t/tp) from U = 95 % to the design life; Cα·Cr/Cc where the clay stays over-consolidated
Time	Terzaghi U(Tv), per clay layer, Hdr = H/2 or H
Rigid foundation	settlement of the characteristic point (0.74·B/2, 0.74·L/2; 0.845·R)
Angular distortion	(scentre − sedge) / (B/2)

Evaluation points

Loading	Points
Rectangle, strip, circle	centre · characteristic point · middle of the long edge · corner
Embankment	crest centre · crest edge · middle of the slope · toe

Project file (.settle)

JSON. Save writes the inputs and the study definition; missing entries keep their defaults.

{
  "shape": "rectangle", "B": 8.0, "L": 16.0, "Df": 1.5, "q": 100.0,
  "net_pressure": true, "water_depth": 2.0,
  "stress_method": "boussinesq", "immediate_method": "elastic", "rigidity": "flexible",
  "design_life": 50.0, "s_allow": 150.0, "distortion_allow": 500.0,
  "soil_profile": [
    {"name": "Soft clay", "thickness": 6.0, "behaviour": "cohesive", "gamma": 17.0,
     "gamma_sat": 17.5, "E": 6.0, "nu": 0.5, "Cc": 0.32, "Cr": 0.05, "e0": 1.05,
     "OCR": 1.3, "cv": 1.5, "Calpha": 0.01, "drainage": "double"}
  ]
}

Choices: stress_method ∈ {boussinesq, two_to_one}, immediate_method ∈ {elastic, schmertmann}, rigidity ∈ {flexible, rigid}, shape ∈ {rectangle, strip, circle, embankment}.

Modules

File	Content
stress.py	Boussinesq (rectangle, strip, circle), 2:1, Steinbrenner
consolidation.py	Terzaghi U(Tv) and its inverse, compression of clay, secondary compression
engine.py	The settlement analysis: profile, sublayers, points, checks, time curve
study.py, study_plots.py	Parametric (one at a time) and reliability (LHS / Monte Carlo) studies, P of exceedance, Spearman sensitivities, CSV / XLSX
plotting.py, render.py	Matplotlib figures, theme-aware
report.py, pdf.py	Calculation report as PDF (ReportLab), HTML or DOCX
forms.py, summary.py, i18n.py	Input schema, result cards, bilingual text
web/	The local HTTP server and the browser interface

Validation

The tests check the stress solutions against published values and brute-force integrals, the engine against closed-form cases (a square on an elastic half-space, a one-dimensional clay layer, Schmertmann by hand), the report in all three formats, the input schema and its file round-trips, and the interface (session and HTTP layer).

Limits

• Consolidation is one-dimensional (Terzaghi, uniform initial excess pore pressure). Each clay layer consolidates independently; interaction through a common drainage boundary is ignored. Vertical drains are not modelled.
• No Skempton–Bjerrum correction is applied; the one-dimensional value is conservative for over-consolidated clay under a narrow footing.
• Layered elastic immediate settlement is the difference of Steinbrenner brackets with each layer's own E and ν; in clay, with the undrained E and ν ≈ 0.5, it is the distortion settlement that precedes consolidation.
• Schmertmann is used in granular layers only; a strip is taken as a rectangle 200·B long, a circle as the square of the same area.
• Angular distortion is checked for a flexible foundation only; for a rigid one it is not checked.

Details: docs/theory.md.