Calculations

Calculations

• Design plane

  The design elevation at a point for a level and two grades.

  z = z₀ + gx·(x − cx) + gy·(y − cy)

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Free-haul moment

  The volume moved times the distance between the centroid of cut and the centroid of fill.

  moment = min(cut × factor, fill) × |centroid(cut) − centroid(fill)|

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Best tilt

  The level and tilt, within the grade limit, that balance with the least haul moment.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Blocks of cut and fill

  Cells grouped into blocks, each with its volume and its volume-weighted center.

  center = Σ (p × v) ÷ Σ v

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Minimum-cost transport

  How much goes from each block of cut to each block of fill at the least total volume times distance.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Haul plan totals

  Volume moved on site, total haul, average haul distance, and what is left to take away or bring in.

  haul = Σ volume × distance; average = haul ÷ moved

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Earthwork balancer run

  The volumes at the pad's present level, the balanced level, the tilt and the haul plan for one pad.

  factor = 1 + percent ÷ 100; cell area = cell²

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

  • CivilCraft
  64-bit

• Balanced level written to the pad

  The pad's level, and its corner elevations when it tilts, as stored in the project.

  z stored = Number(z.toFixed(3))

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

  • CivilCraft
  64-bit

• Haul plan CSV

  The haul flows exported as a CSV file.

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

  • CivilCraft
  64-bit

• Alignment from a found route

  The PIs of a new alignment from the route's points, with a curve radius at each bend.

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

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

  • CivilCraft
  64-bit

• Route ends picked in the plan

  The start and end of a route search as taken from two picked points.

  x, y = Number(v.toFixed(3))

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

  • CivilCraft
  64-bit

• Sized orifice written to the pond

  The orifice diameter found for the target outflow, as stored in the pond.

  diameter stored = Number((d ÷ L).toFixed(3))

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

  • CivilCraft
  64-bit

• Pond hydrograph CSV

  Inflow, outflow and stage against time exported as a CSV file.

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

  • CivilCraft
  64-bit

• Survey points for progress checks

  Ground points read from a LAS, LAZ, CSV or text file and turned into a surface.

  LAS thinning cell = max(0.5, √(extent area ÷ 400 000)) unless a spacing is given

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

  • CivilCraft
  64-bit

• Three-decimal rounding of tool results

  The rounding applied to nearly every number a tool returns to an assistant or script.

  r3(v) = round(v × 1000) ÷ 1000

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

  • CivilCraft
  64-bit

• Volumes in report units

  Volumes converted to cubic yards or cubic meters for a tool's answer.

  cubic yards = cubic feet ÷ 27; from cubic meters: ÷ 0.028316846592 ÷ 27

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

  • CivilCraft
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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

• 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