civl235-slope stake overheads

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    May 9, 2003 Civil 235 - Plane Surveying 1

    Route SurveyingRoute SurveyingRoute SurveyingRoute Surveying - ---Slope StakesSlope StakesSlope StakesSlope Stakes

    Instructor: A. Shahkarami

    Civil 235 Plane Surveying

    The University of British ColumbiaDepartments of Civil Engineering

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    May 9, 2003 Civil 235 - Plane Surveying 2

    Introduction

    Picture taken from http://www.tpub.com/engbas/14-31.htm

    Centre-line layout is one of the firststeps in constructing a road.

    The road is broken into stations.

    At each station, the location of thecentre-line, shoulders and slopestakes are identified.

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    May 9, 2003 Civil 235 - Plane Surveying 3

    H.I.H.I.H.I.H.I.

    Ground RodGround RodGround RodGround Rod

    Grade RodGrade RodGrade RodGrade Rod

    FillFillFillFill

    Introduction

    TerminologyTerminologyTerminologyTerminologyGrade

    Centre-lineShoulder

    Side-slopeSlope stake

    Side-hill section

    Grade Rod = H.I. elevation of the grade

    Ground Rod = reading of the rod at any point

    Cut/fill = Grade Rod Ground Rod

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    May 9, 2003 Civil 235 - Plane Surveying 4

    Cut/Fill

    1. Cut section1. Cut section1. Cut section1. Cut section

    Ground rod > 0Ground rod > 0Ground rod > 0Ground rod > 0Grade rod > 0Grade rod > 0Grade rod > 0Grade rod > 0

    2. Fill section2. Fill section2. Fill section2. Fill section

    H.I. > Grade Elev.H.I. > Grade Elev.H.I. > Grade Elev.H.I. > Grade Elev.

    Ground rod > 0Ground rod > 0Ground rod > 0Ground rod > 0Grade rod > 0Grade rod > 0Grade rod > 0Grade rod > 0

    H.I. > Grade Elev.H.I. > Grade Elev.H.I. > Grade Elev.H.I. > Grade Elev.

    Ground rod > 0Ground rod > 0Ground rod > 0Ground rod > 0Grade rod < 0Grade rod < 0Grade rod < 0Grade rod < 0

    H.I. < Grade Elev.H.I. < Grade Elev.H.I. < Grade Elev.H.I. < Grade Elev.

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    May 9, 2003 Civil 235 - Plane Surveying 5

    Cut-Fill Transition

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    May 9, 2003 Civil 235 - Plane Surveying 6

    w/2w/2w/2w/2 dddd

    ssss

    1111

    Slope StakeSlope StakeSlope StakeSlope Stake

    Shoulder StakeShoulder StakeShoulder StakeShoulder StakeCenterline StakeCenterline StakeCenterline StakeCenterline Stake

    Natural GroundNatural GroundNatural GroundNatural Ground

    Road GradeRoad GradeRoad GradeRoad Grade

    Slope Stakes(Side-hill section is where cross-section passes from cut to fill)

    csw

    d +=2

    fsw

    d +=2

    Cut SectionCut SectionCut SectionCut Section Fill SectionFill SectionFill SectionFill Section

    f ff f

    cccc

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    May 9, 2003 Civil 235 - Plane Surveying 7

    Example Slope Stake

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    May 9, 2003 Civil 235 - Plane Surveying 8

    Example Slope Stake

    H.I. = 241.90 m , grade elevation = 240.36 mrod reading on centerline = 2.65 m centerline elevation = 239.25 m

    grade rod = H.I. grade elevation = 241.90 240.36 = 1.54 m

    first trial at point 1:ground rod = 3.23 f 1 = grade rod ground rod = 1.54 3.23 = -1.69 m

    (the negative sign indicates a fill)

    Slope stake distance from the centre-line, d 1 : 3.5 + (1.69)(2) = 6.88 m

    measured d 1 = 6.2 m

    The rod must be moved farther from the centerline

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    May 9, 2003 Civil 235 - Plane Surveying 9

    second trial at point 2:ground rod = 3.62 m f 2 = 1.54 3.62 = -2.08 m

    d 2 = 3.5 + (2.08)(2) = 7.66 m

    measured distanced

    2 = 8.2 m

    The rod is out too far

    Eventually, by trial, the rod is held at 3:

    ground rod = 3.40 f r = 1.54-3.40 = -1.86 md r = 3.5 + (1.86)(2) = 7.22 m

    This distance agrees with the measured distance d r ; hence, point 3 is the

    correct location for the slope stake.

    The notes for this slope stake will be:

    Example Slope Stake

    22.7

    86.1 f

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    May 9, 2003 Civil 235 - Plane Surveying 10

    Volume of Earthwork

    w/2w/2w/2w/2wwww

    A1 A1 A1 A1 A2 A2 A2 A2 A3 A3 A3 A3 A4 A4 A4 A4

    Cross-sectional area iscalculated from the cut/fill data.

    = i A A1. Average End Area Method

    (exact for A 1 =A 2 )l A AV +=

    2

    21

    2. Prismoidal Method ( )21 46 A A Al V m ++=

    ( A m obtained by averaging the linear dimensions of the end section)

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    May 9, 2003 Civil 235 - Plane Surveying 11

    Example Volume CalculationFor the following two stations, calculate the volume of earthwork using the Average End Area method and the Prismoidal method.width of the road-bed is 20 m and side-slope ratio is 1.5 to 1.

    StationStationStationStation1+101+101+101+10

    StationStationStationStation1+001+001+001+00

    R.R.R.R.C.L.C.L.C.L.C.L.L.L.L.L.

    CrossCrossCrossCross- ---sectionsectionsectionsectionStationStationStationStation

    0.16

    0.4c

    0

    0.6c

    0.28

    0.12c

    0.13

    0.2c0

    0.3c0.22

    0.8c 4 m4 m4 m4 m

    12 m12 m12 m12 m6 m6 m6 m6 m

    16 m16 m16 m16 m 28 m28 m28 m28 m

    2122

    121828

    2

    126

    2

    6416

    2

    461

    =

    +

    +

    +

    = A

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    May 9, 2003 Civil 235 - Plane Surveying 12

    1575157515751575

    Vol.Vol.Vol.Vol. A.E.A. A.E.A. A.E.A. A.E.A.

    154154154154MidsectionMidsectionMidsectionMidsection

    103103103103StationStationStationStation

    1+101+101+101+10

    1551.71551.71551.71551.7

    212212212212StationStationStationStation1+001+001+001+00

    R.R.R.R.C.L.C.L.C.L.C.L.L.L.L.L.Vol.Vol.Vol.Vol.

    Prism.Prism.Prism.Prism. Area Area Area AreaCrossCrossCrossCross- ---sectionsectionsectionsectionStationStationStationStation

    0.16

    0.4c0

    0.6c0.28

    0.12c

    0.13

    0.2c

    0

    0.3c

    5.14

    0.3c0

    5.4c0.22

    0.8c

    0.25

    0.10c

    Similarly, for station 1+10: 1032 = A

    Volume from the Average End Area method:

    1575102

    103212=

    +=V

    m 2

    m 3

    Example Volume Calculation

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    May 9, 2003 Civil 235 - Plane Surveying 13

    600+80.0083.2283.43600+70.00

    GradeGround

    RightSlope S.

    RightShoulder S.

    C.L.Stake

    LeftShoulder S.

    LeftSlope S.

    ElevationStation

    56.6

    37.2c0.3

    07.1c0

    21.0c0.3

    85.0 f 50.4

    0.1 f

    3.00 m3.00 m3.00 m3.00 m 3.00 m3.00 m3.00 m3.00 m

    1.51.51.51.5

    1111

    83.22 m83.22 m83.22 m83.22 m 1.07 m1.07 m1.07 m1.07 m

    2.37 m2.37 m2.37 m2.37 m

    0.85 m0.85 m0.85 m0.85 m 1.0 m1.0 m1.0 m1.0 m

    3.56 m3.56 m3.56 m3.56 m 1.50 m1.50 m1.50 m1.50 m

    Cross-Section Data