Calculations

Calculations

• Slope cross section for stability

  The ground line, layer tops, water level, surcharges and floor that the slope stability engine reads.

  81 samples along the section; layer top = min(layer top, ground)

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Slope stability run

  The factor of safety of a given circle, or the critical circle from a search.

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Settlement run

  Settlement under a footing at a boring, and the time for 50 % and 90 % consolidation.

  layer top = (z − from) × k; drainage path = clay thickness ÷ 2

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Traverse run

  A traverse closed by the compass rule from legs typed as distance and azimuth in degrees.

  azimuth in radians = degrees × π ÷ 180

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Radio link run

  Path length, terrain profile, line of sight, link budget and mast height for a link between two points.

  distance in km = √(Δx² + Δy²) ÷ 1000

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Coverage run

  Received power over a grid round a transmitter and the farthest covered cell.

  farthest = max over covered cells of √(Δx² + Δy²) ÷ k

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Open pit run

  The block model in meters, block values, the ultimate pit and its phases.

  slope in radians = degrees × π ÷ 180; phase factors from 0.4 to 1 in equal steps

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Layers made end to end

  The depth limits of a boring's layers after gaps and overlaps are removed.

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Layer elevations

  The top and bottom elevation and the thickness of each layer of a boring.

  top = z − from; bottom = z − to; thickness = to − from

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• SPT blow count corrections

  N60 and (N1)60 from a field blow count.

  N60 = N × ER ÷ 60 × CB × CS × CR; CN = min(1.7, √(101.325 ÷ σ′v)); (N1)60 = CN × N60

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Boring projected onto the section line

  The station along the section and the offset from it of a boring.

  t = ((p − a)·(b − a)) ÷ |b − a|², clamped to 0…1; station = length so far + t·|b − a|

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Soil profile between borings

  The polygon of each soil unit between neighboring borings, the ground line and the water line.

  pinch-out point = ((s₁ + s₂) ÷ 2, (top + bottom) ÷ 2)

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Layer stack at a station

  The top and bottom of every soil unit at one station of the profile.

  z = z_a + (s − s_a) ÷ (s_c − s_a) × (z_c − z_a)

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Unit weight of water

  The constant behind every pore pressure and every submerged unit weight in this file.

  γw = 9.81 kN/m³

  Slope stability geotech.js

  • CivilCraft
  64-bit

• Elevation of a line at a position

  The ground, a layer top or the water table at a horizontal position.

  Slope stability geotech.js

  • CivilCraft
  64-bit

• Where a circle meets the ground

  The positions where the lower arc of a trial circle crosses the ground line.

  f(x) = ground(x) − (zc − √(R² − (x − xc)²))

  Slope stability geotech.js

  • CivilCraft
  64-bit

• Slices of the sliding mass

  Each slice's width, weight, base angle, strength and pore pressure.

  W = Σ layers γ × thickness × b; sin α = −(x − xc) ÷ R; u = γw × (zw − zb), or ru × W ÷ b

  Slope stability geotech.js

  • CivilCraft
  64-bit

• Factor of safety

  The factor of safety of one circle by the ordinary method or by Bishop's simplified method.

  Bishop: FS = Σ[(c·b + (W − u·b)·tan φ) ÷ (cos α + sin α·tan φ ÷ FS)] ÷ Σ W·sin α

  Slope stability geotech.js

  • CivilCraft
  64-bit

• Critical circle search

  The circle with the lowest factor of safety among those tried.

  Slope stability geotech.js

  • CivilCraft
  64-bit

• Stress influence factor under a corner

  The share of the surface load felt at a depth under the corner of a loaded rectangle.

  m = a ÷ z, n = b ÷ z, v = m² + n² + 1; I = [2mn√v ÷ (v + m²n²) × (v + 1) ÷ v + atan2(2mn√v, v − m²n²)] ÷ 4π

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Stress under a footing

  The vertical stress increase under the center or a corner of a rectangular footing.

  center: Δσ = 4·q·I(B ÷ 2, L ÷ 2, z); corner: Δσ = q·I(B, L, z)

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• Stress by the 2:1 spread

  The average stress increase at a depth by the quick 2:1 rule.

  Δσ = q·B·L ÷ ((B + z)·(L + z))

  Foundation settlement geotech.js

  • CivilCraft
  64-bit

• 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