Calculations

Calculations

• Rain results in inches and cubic feet per second

  Depths and flows from the rain solver converted from meters for a feet project.

  inches = meters × 39.3700787; ft³/s = m³/s ÷ 0.028316846592

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
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• Pad level set by an assistant

  A pad's level and, for a tilted pad, its corner elevations, as stored in the project.

  z stored = r3(level); corner z = r3(level + gx·(x − cx) + gy·(y − cy))

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Alignment from route points

  The PIs of an alignment made by an assistant from route points, with curve radii.

  r = min(R, min(l₁, l₂) ÷ (2·tan(Δ/2))), stored to 3 decimals

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
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• Orifice sized by an assistant

  The orifice diameter found for an allowed outflow, as used for the reported run.

  diameter = r3(d ÷ L)

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
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• Arc from two points and a bulge

  The center, radius, start angle, sweep and length of the arc between two vertices.

  k = (1 − b²) ÷ (4b); center = chord middle + k·(−Δy, Δx); r = c·(1 + b²) ÷ (4|b|); sweep = 4·atan(b); L = r·|sweep|

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Bulge of an arc through three points

  The bulge of the arc drawn from a start, through a middle point, to an end.

  sweep = 2·(π − angle at the middle point); bulge = sign × tan(sweep ÷ 4)

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Bulge for a typed radius

  The bulge of the shorter arc of a given radius between two vertices.

  Δ = 2·asin(c ÷ 2r); bulge = ±tan(Δ ÷ 4)

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Point and direction along a segment

  The plan point and travel direction at a fraction of a straight or arc segment.

  arc: p = c + r·(cos θ, sin θ), θ = a₀ + sweep × u

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Segment lengths and grades

  Each segment's plan length, chord, 3D length, rise and grade.

  length = chord or r·|sweep|; 3D length = √(L² + Δz²); grade = Δz ÷ L

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Stations along a feature line

  The plan distance from the start to each vertex.

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Elevation from a grade

  The far vertex of a segment moved to the elevation a typed grade gives.

  z₂ = z₁ + grade × length

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• One grade between two vertices

  The vertices between two chosen ones placed on a single grade.

  z = z₀ + (z₁ − z₀) × (s − s₀) ÷ L

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Stepped offset

  A copy of the line moved sideways with mitred corners and raised by a height or a cross slope.

  corner shift = bisector × d ÷ cos(half angle); z + Δz, or z + |d| × slope

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Straight segment against an alignment element

  Where a straight feature line segment crosses a line or arc of the alignment, with the station.

  line: 2×2 solve by cross products; arc: A·t² + B·t + C = 0, t = (−B ± √(B² − 4AC)) ÷ 2A

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Arc segment against an alignment element

  Where an arc of a feature line crosses a line or arc of the alignment.

  two circles: along = (r₁² − r₂² + d²) ÷ 2d; h = √(r₁² − along²)

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Feature line read from a file

  The vertices kept when a feature line is read from a project file or a drawing.

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
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• Elevations of a newly drawn line

  The elevation each vertex of a new feature line gets.

  Feature line grades, arcs, offsets and crossings features-ui.js

  • CivilCraft
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• Elevation and grade boxes

  A typed vertex elevation or segment grade applied to the line.

  grade = typed percent ÷ 100

  Feature line grades, arcs, offsets and crossings features-ui.js

  • CivilCraft
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• Offset distance and amount

  The typed offset distance and height or slope passed to the stepped offset.

  slope = typed percent ÷ 100

  Feature line grades, arcs, offsets and crossings features-ui.js

  • CivilCraft
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• Number of pieces for an arc

  How many straight pieces draw an arc within the tolerance.

  step = min(2·acos(1 − tol ÷ r), 5°); pieces = ⌈|sweep| ÷ step⌉, from 1 to 720

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
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• Line as straight pieces

  The feature line with every arc replaced by vertices on the arc.

  p = c + r·(cos θ, sin θ), θ = a₀ + sweep × s ÷ k; z = z_a + (z_b − z_a) × s ÷ k

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Closed design line as a grading item

  The outline and the single elevation a closed design feature line passes to grading.

  z = Σ vertex z ÷ number of vertices

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Feature line written to DWG or DXF

  The 3D polyline and the extended data that records which runs of pieces were arcs.

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Feature line read back from DWG or DXF

  The feature line rebuilt from a polyline and its extended data.

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Crossings with an alignment

  Every place a feature line crosses the centerline, with its station and elevation.

  z = z_a + t × Δz

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Stretches running beside an alignment

  The parts of a feature line within a given distance of the centerline, as station and elevation for a profile view.

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Project units to meters

  The factor that takes a project length to meters for every engine in this file.

  feet: 0.3048; meters: 1

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

  • CivilCraft
  64-bit

• Soil profile along a section

  The borings in meters, the layers between them, and the layer stack at evenly spaced stations.

  stations = max(2, round(length ÷ step)), default step = max(length ÷ 40, 0.5 m)

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

  • CivilCraft
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• 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
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• 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
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• 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
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• 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
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• 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

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• 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
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• 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
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• 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
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• 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
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• 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

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• Elevation of a line at a position

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

  Slope stability geotech.js

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• 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

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• 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
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• 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

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• 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
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• 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