6_asurvey_leveling Part 2_other Leveling Methods_1730672714.pdf

Double-Rodded Leveling

Double-Rodded Leveling A

method of determining the differences in elevation between points by employing two level routes simultaneously  Two turning points are established such that at each set up of the leveling instrument, two sets of independent backsights and foresights are taken

Double-Rodded Leveling  Advantage: provide a continuous check on the

process of determining ground elevations while the work is in progress  Useful when there is an urgent need to undertake differential leveling in a short period of time where no established benchmarks are available for checking results.

Illustrative Problem  Complete the following differential level notes for a double-

rodded line from BM1 to BM2. Show the customary arithmetic check. STA

BS

HI

FS

BM1

1.86 1.86

TP1 H L

2.15 2.52

1.10 1.58

TP2 H L

1.40 1.76

1.79 2.27

TP3 H L

0.33 0.74

2.99 3.41

BM2

ELEV 205.60m

2.63 2.63

Illustrative Problem  Arithmetic Check  1st Method • Mean Elev BM2 =

• DE1 = (ΣBS-ΣFS)/2

• DE2 = BM1 – Mean Elev BM2

 2nd Method

• Mean Elev BM2 = BM1 + [(ΣBS-ΣFS)/2]

Three-Wire Leveling

Three-Wire Leveling  More precise method  Method of determining the differences in elevation

wherein three horizontal hairs are read and recorded rather than from a single horizontal hair  Any level equipped with three horizontal cross hairs can be used for three-wire leveling

Three-Wire Leveling s = a-b m = (a+b+c)/3 HD = Ks + C Elev = HI - m a = upper stadia hair reading b = lower stadia hair reading c = horizontal cross hair reading s = stadia intercept - difference between the upper and lower stadia hair reading m = mean of the three-hair readings HD = horizontal distance from the level to the rod K = stadia interval factor (100) C = instrument constant (0)

Illustrative Problem BACKSIGHT

STA

HAIR RDGS

MEAN RDG

FORESIGHT S

HI

HAIR RDGS

BM1

1.15 0.95 0.72

TP1

2.79 2.42 2.06

1.11 0.89 0.68

TP2

1.70 1.44 1.18

1.90 1.54 1.17

TP3

2.59 2.10 1.59

1.45 1.18 0.95

BM2

MEAN RDG

S

ELEV

445.20

1.60 1.35 1.25

Illustrative Problem  Arithmetic Check  1st Method • DE1 = (ΣBSm-ΣFSm)/2

• DE2 = Elev BM1 – Elev BM2

 2nd Method

• Elev BM2 = BM1 + ΣBS - ΣFS

Profile Leveling

Profile Leveling  The process of determining differences in elevation

along a fixed line at designated short measured intervals  Design and construction of roads, railroads, canals,

culverts, bridges, sewer lines (horizontal structures)  Usually taken along the centerline with the level set up

a convenient distance away from it so that sights of more uniform lengths can be obtained

Profile Leveling  Any number of foresights can be taken

 Intermediate foresights are taken where necessary to

portray accurately the existing ground surface along the route surveyed

Profile Leveling  Profile  A curved line which graphically portrays the intersection of a vertical plane with the surface of the earth  Represent the ground elevations of selected critical points along a surveyed line and the horizontal distances between these points  Stationing  A numerical designation given in terms of horizontal distance any point along a profile line is away from the starting point

Profile Leveling  Intermediate foresights (ground rod readings)  Taken along the centerline of the proposed project to provide an accurate representation of the ground surface

 Full stations  Points which are established along the profile level route at uniformly measured distances  Plus stations  Points established along a profile level route which is not designated as a full station  Points taken at breaks in the ground surface slope and at critical points (location of culverts, bridges)

Illustrative Problem  A schematic arrangement of a profile level route from BM3 to BM4

are shown below. The values indicated represent backsight, foresight, and intermediate foresight readings taken on stations along the route. Prepare and complete profile level notes for the portrayed information. Show the customary arithmetic check and plot the profile. 2+00 HI 1+00

2

3+00 0+00

BM4 TP1

HI1 4+50

BM3 Elev 300.50m

5+50

6+70 6+00

Illustrative Problem STA

BM3

BS

HI

FS

IFS

2.4

300.50m

0+00

1.5

1+00

2.0

2+00

1.3

3+00

0.7

TP1

2.55

3.2

4+50

2.8

5+50

3.5

6+00

4.5

6+70

3.95

BM4

ELEV

3.3

Illustrative Problem 303

ELEVATION (m)

302

301

300

299

298

0+00

1+00

2+00 STATIONINGS

3+00

4+00

Illustrative Problem  Arithmetic Check • Elev BM4 = BM3 + ΣBS - ΣFS

Reciprocal Leveling

Reciprocal Leveling  Employed to determine the difference in elevation

between two points when it is difficult or impossible to keep backsights and foresights short and equal  Such conditions are running a line of levels across wide rivers, lakes, and rugged terrain (deep canyons)  Two sets of rod readings are observed (Method of Reversion)  One set taken with the instrument set up close to one

point and another instrument on the other

Reciprocal Leveling  Errors due to refraction by the atmosphere,

curvature of the earth and faulty adjustment of the instrument are significantly reduced if not eliminated

Reciprocal Leveling

DE1 a  b DE2  a'b' Instrumental errors and the effect of curvature and refraction DE1 ≠ DE2, » »

DE1 DE2 (a  b)  (a'b' ) TDE   2 2 *Note:

If TDE is negative, A is higher than B; If TDE is positive, B is higher than A.

Illustrative Problem  In leveling across a deep and wide river, reciprocal level

readings were taken between two points, X and Y as follows: a. With instrument set up near X, the rod readings on X are 1.27 and 1.265 meters; on the distant point Y, the rod readings are 2.50, 2.52, 2.55, and 2.49 meters. b. With instrument set up near Y, the rod readings on Y are 3.48 and 3.47 meters; on the distant point X, the rod readings are 2.13, 2.14, and 2.145 meters. Determine the true difference in elevation between the two points and the elevation of Y if the known elevation of X is 289.90meters.

Illustrative Problem Elev=289.90m

Instrument Set up near X STA

BS

X

1.27

FS

Instrument Set up near Y STA

BS

X’

2.13

1.265

Y

2.14

2.50 2.52

2.145 Y’

2.55 2.49 SUM

MEAN

FS

3.48

3.47 SUM MEAN

Trigonometric Leveling

Trigonometric Leveling  “Indirect Leveling”  Determine the difference in elevation from

observed vertical angle and either horizontal or inclined distances  Used extensively when undertaking topographic surveys over rugged or rolling terrain since it provides a rapid means of determining vertical distances and elevation of points

Trigonometric Leveling

V  dTan

DEab  dTan  HI  RR

V  sSin

DEab  sSin  HI  RR

ElevB  ElevA  DEab

Trigonometric Leveling  For horizontal distance is greater than 300 meters,

effects of the earth’s curvature and refraction must be considered in the calculation of the vertical distances. d 2 DEab  dTan  HI  RR  0.0675( ) 1000 d 2 DEab  sSin  HI  RR  0.0675( ) 1000

Illustrative Problem  A vertical angle of +13°45’ is read to a target

1.23m above point B. the measured inclined distance, s, is 823.29m and the elevation of A is 123.65m above datum. If the HI at A is 1.35m, determine the difference in elevation between A and B and the elevation of B, considering the effects of curvature and atmospheric refraction.

Illustrative Problem

Cross-Section Leveling

CROSS-SECTION LEVELING  Short profiles taken perpendicular to the centerline

of projects such as a highway, railroad, irrigation canal, or sewer line  They may also be taken for borrow pits and excavations required for buildings, structures, and quarries. Roadway Cross-Sections Borrow-Pit Cross Sections

ROADWAY CROSS-SECTION  This type of cross-section is

required for most route projects such as roads and railroads.  Elevations of ground points

along the section are taken at regular intervals on either side. Where significant changes occur in ground features, ground elevations are also taken.

BORROW-PIT CROSS-SECTION  Employed in the construction of structures and buildings,

and in the excavation of borrow pits.  Borrow pit is an open area which is usually adjacent to a construction project where suitable fill material is excavated. The base line from which the GL are referred should be established outside the immediate project area so that reference stakes and other markers will not be obliterated or disturbed during the process of excavation. Similarly, any reference bench mark should also be located outside the work area.