Calculations

Calculations

• Elastic settlement under a corner

  The settlement of the corner of a flexible loaded rectangle on an elastic half-space.

  w = q·(1 − ν²) ÷ (π·E) × [a·ln((b + d) ÷ a) + b·ln((a + d) ÷ b)], d = √(a² + b²)

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Settlement of a layered soil

  Consolidation and immediate settlement under a footing, sub-layer by sub-layer.

  clay: s = Cc·Δz ÷ (1 + e₀) × log₁₀(σ′f ÷ σ′₀), with Cs below σ′c; sand: s = Δσ ÷ Es × Δz

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Degree of consolidation

  The share of the final consolidation settlement reached at a time factor.

  U = 1 − Σ (2 ÷ M²)·exp(−M²·Tv), M = π·(2m + 1) ÷ 2

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Time factor for a degree of consolidation

  The time factor at which a given share of the settlement is reached.

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Time to reach a degree of consolidation

  The time for a share of the consolidation settlement.

  t = Tv·Hdr² ÷ cv

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Settlement against time

  The settlement curve from zero to a chosen time.

  s(t) = s_final × U(cv·t ÷ Hdr²)

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Secondary compression

  Settlement from secondary compression between two times.

  S = Cα·H ÷ (1 + ep) × log₁₀(t₂ ÷ t₁)

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Elevation grid from a surface

  The elevation at the center of every grid cell, row by row from the north.

  x₀ = ⌊minX ÷ cell⌋·cell; y₀ = ⌈maxY ÷ cell⌉·cell; center = (x₀ + (c + 0.5)·cell, y₀ − (r + 0.5)·cell)

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  32-bit in part

• Elevations written to the file

  The tiles or strips of elevation values as they go into the TIFF.

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  32-bit in part

• Grid origin and cell size in the file

  The pixel scale and the tie point that place the grid.

  pixel scale = (cell, cell, 0); tie point = pixel (0, 0) at (x₀, y₀)

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  64-bit

• Default cell size

  The mean plan length of the surface's triangle edges, offered as the cell size.

  Σ |edge| ÷ number of edges

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  64-bit

• Signed area of a ring

  The area of a ring, positive when it runs counter-clockwise.

  area = Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ) ÷ 2

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Point inside a ring

  Whether a point lies inside a ring.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Rings sorted into polygons and holes

  Which rings are outlines and which are holes, and which outline each hole belongs to.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Coordinates through a conversion

  Every vertex of a geometry passed through a function of x and y, keeping z.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Elevations through a conversion

  The z of every vertex passed through a function, for unit conversion.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Layers moved to a new coordinate system

  Every GIS layer's coordinates converted when the project's system changes.

  project → grid of the old system → grid of the new system → project

  GIS feature geometry gis-layers.js

  • CivilCraft
  64-bit

• Attribute value as a label

  The text drawn on the plan for a feature's attribute value.

  number shown = +v.toFixed(3)

  GIS feature geometry gis-layers.js

  • CivilCraft
  64-bit

• Label point of a polygon

  The centroid of a polygon's largest ring, where its label is placed.

  cx = Σ (xᵢ + xᵢ₊₁)·cᵢ ÷ (3·Σ cᵢ), cᵢ = xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ

  GIS feature geometry gis-layers.js

  • CivilCraft
  64-bit

• Pad elevation and area

  The ELEV and AREA attributes of an exported pad.

  AREA = |shoelace area of the pad's corners|

  Project objects exported as GIS layers gis-export.js

  • CivilCraft
  64-bit

• Alignment line and length

  An alignment's exported linework and its LENGTH, STA_START and STA_END attributes.

  chords of at most π ÷ 360 (0.5°) of turn

  Project objects exported as GIS layers gis-export.js

  • CivilCraft
  64-bit

• Pipe attributes

  A pipe's exported inverts, slope in percent and length.

  SLOPE = slope × 100; LENGTH = checked length, else √(Δx² + Δy²)

  Project objects exported as GIS layers gis-export.js

  • CivilCraft
  64-bit

• Surface edge as polygons with holes

  The surface's outline loops arranged as outer rings and holes for the boundary export.

  Project objects exported as GIS layers gis-export.js

  • CivilCraft
  64-bit

• Features in grid coordinates

  Every exported feature's coordinates passed through the project's grid transform, with the N and E attributes of survey points set to match.

  Project objects exported as GIS layers gis-export.js

  • CivilCraft
  64-bit

• Elevations to meters for GeoJSON and KML

  The factor applied to elevations when the export is in longitude and latitude.

  z in meters = z × meters per project unit

  Project objects exported as GIS layers gis-export.js

  • CivilCraft
  64-bit

• Number box

  The text of a property box turned into the value handed to the model.

  typed sum of lengths → Number(value.toFixed(9))

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• PI coordinates box

  The easting and northing of an alignment's point of intersection as shown and as stored from the box.

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• First design profile from the ground

  The two profile points a new design profile starts with, at the ends of the ground profile.

  z stored = Number(z.toFixed(2))

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Profile point added by a click

  The station and elevation of a profile point placed in the profile view.

  station = Number(sta.toFixed(2)), clamped to the alignment; z = Number(z.toFixed(2))

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Profile point moved by dragging

  The station and elevation of a profile point while it is dragged, as stored when released.

  station and z = Number(v.toFixed(2)); station kept 0.01 inside its neighbors

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Elevation of a newly drawn pad

  The elevation a new pad starts at.

  z = Number(ground(mean of corners).toFixed(1))

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Default curve radius at a new PI

  The radius given to each bend of a newly drawn alignment.

  r = min(R, ⌊half the shorter leg ÷ tan(Δ ÷ 2)⌋)

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Ground elevation at a station

  The existing ground elevation read out at the cursor's station in the profile view.

  z = z_a + (z_b − z_a) × (s − s_a) ÷ (s_b − s_a)

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Project units per file unit

  The factor that turns a spacing typed in project units into the file's own units.

  k = |f(c + d) − f(c)| ÷ d, c = middle of the file

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• Default thinning spacing

  The spacing the dialog proposes so the import stays under the point limit.

  grid: cell × ⌈√(n ÷ (0.98 × cap))⌉; LiDAR: max(1.5 × √(area ÷ points), 1.1 × √(area ÷ cap)) rounded to a 1-2-5 step

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• Points a grid import will make

  The number of cells read and of points or triangles made, shown before the import runs.

  count = ⌈columns ÷ step⌉ × ⌈rows ÷ step⌉; triangles = 2 × (⌈columns ÷ step⌉ − 1) × (⌈rows ÷ step⌉ − 1)

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• LiDAR point into project coordinates

  Each kept LiDAR point's position and elevation as stored in the project.

  (x, y) → f(x, y); z → z × z factor

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• Default GeoTIFF cell size

  The cell size proposed when a surface is exported as an elevation grid.

  cell = average triangle edge ÷ 2.5, rounded to a 1-2-5 step

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• GeoTIFF grid size estimate

  The number of columns and rows the dialog says the export will have.

  nx = ⌈width ÷ cell⌉ + 1; ny = ⌈height ÷ cell⌉ + 1

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• One slope line to the ground

  The point where a cut or fill slope leaving the pad edge meets the surface.

  f(d) = z + g·d − ground(p₀ + u·d); g = rate ÷ cut or −rate ÷ fill; find d with f(d) = 0

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Rays round the pad

  The start, direction and climb rate of every slope line: square to each edge, fanned at convex corners, along the bisector at concave corners.

  turn = atan2(n₁ × n₂, n₁ · n₂); concave rate = cos(|turn| ÷ 2); wall mitre = thickness ÷ max(0.25, cos(|turn| ÷ 2))

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Rays trimmed at a concave corner

  Drops edge rays that would reach past the line where two slopes meet in an inside corner.

  side(x, y) = b_x·(y − v_y) − b_y·(x − v_x); drop when the ray's ends have opposite signs

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Pad, slopes and daylight line as breaklines

  The lines that go into the proposed surface for one pad: its edge, its daylight line and every slope line longer than 1e-6.

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Proposed surface from ground and graded items

  Removes ground points and breaklines inside each graded region, adds the item's own, and triangulates again.

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Do two segments cross

  The yes-or-no test used for self-crossing pads, self-crossing daylight lines and breaklines that cross a region.

  o(p, q, r) = (q − p) × (r − p); cross when both pairs of signs are opposite

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Distance from a point to a polygon edge

  Whether a ground point lies on a daylight line.

  t = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); distance = |p − a − t·(b − a)|

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Cut, fill and net volume

  The volumes reported between the existing and the proposed surface.

  fill = Σ (z₁ − z₀)·c² where z₁ > z₀; cut = Σ (z₀ − z₁)·c² otherwise; net = fill − cut; area = cells × c²

  Cut and fill volumes by the grid method grading.js

  • CivilCraft
  64-bit

• Default cell size

  Rounds the automatic cell size to 1, 2, 5 or 10 times a power of ten.

  p = 10^⌊log₁₀ v⌋; cell = {1, 2, 5, 10} × p

  Cut and fill volumes by the grid method grading.js

  • CivilCraft
  64-bit

• Elevation of a contour line

  The one elevation a line carries: its own z, or the z all its vertices share.

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Elevations by picking lines in order

  Gives the k-th picked line the elevation start + k × interval.

  z_k = start + k × interval

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit