Chapter 3 - Leveling Methods PDF

Chapter 3: Leveling Methods General Surveying 1: Measurement of Vertical Distances Frank Stephen Balbanera Geodetic Engineer | Instructor Differential Leveling. The process of determining the difference in elevation between two or more points some distance. apart...

Chapter 3: Leveling Methods General Surveying 1: Measurement of Vertical Distances Frank Stephen Balbanera Geodetic Engineer | Instructor Differential Leveling. The process of determining the difference in elevation between two or more points some distance. apart - It requires a series of set ups of the instrument along a general route and, for each setup, a rod reading back to the point of known elevation and forward to a point of unknown elevation are taken. - The basic equipment used includes a graduated leveling rod, and a leveling instruments such as a dumpy level, automatic level, or an engineer’s transit. Benchmark (BM). a fixed point of reference whose elevation is either known or assumed. Granite tile of BGT-11 at the Mount Pulag summit  Benchmark (BM). a fixed point of reference whose elevation is either known or assumed. Benchmark at the side of the Freedom Park near City Coliseum Backsight (BS). It is a reading taken on a rod held on a point of known or assumed elevation. - It is the measure of the vertical distance from the established line of sight to the point sighted, and is always the first rod reading taken after the instrument has been set up and leveled. Foresight. It is a reading taken on a rod held on a point whose elevation is to be determined. - It is represented as a vertical distance from the line of sight of the instrument to the point observed. Backsight Distance (BSD). Measured from the center of the instrument to the rod on which a backsight is taken. Foresight Distance (FSD). Horizontal distance from the center of the instrument to the rod on which a foresight is taken. Its length is usually made nearly equal to its corresponding backsight distance. Turning Point (TP). The intervening point between two bench marks upon which point foresight and backsight rod readings are taken to enable a leveling operation to continue from a new instrument position. Height of Instrument or the height of collimation is the elevation of the line of sight of an instrument above or below a selected reference datum. Procedure (see Fig 17-1) There should be at least two persons to undertake differential leveling; the rodman who carries and holds the rod, and the instrumentman who sets up the level and determines the required rod readings. However, it still depends if bigger leveling party could be formed. The leveling instrument is set up at any convenient location along the level route.  Backsight is taken on a leveling rod held vertically on BMa. The backsight reading added to the known or assumed elevation of the initial bench mark gives the height of instrument (HI) above datum or HI = Elev BMa + BS The rodman moves forward along the general direction of BMb­and holds the rod at a convenient turning point (TP1). The instrumentman takes a foresight on the rod. This foresight reading subtracted from the height of instrument gives the elevation above datum of the turning point or Elev TP1 = HI – FS  The level is then transferred and set up at another convenient location beyond TP1, but still in the general direction of BMb. The exact location at which the level is set up is of little importance. A backsight is then taken on TP1 to establish a new height of insturment (HI2). The rodman finally moves forward to the location of BMb and a foresight is taken on the rod held on it. Since the new HI has already been determined, the elevation of BMb is ­ computed by subtracting the foresight reading from the height of instrument.  However, if terminal point (BMB) is still some distance away such that more turning points have to be established before it could be foresighted, repeat the procedure until the elevation of BMb is finally obtained. You may also see this link to know how to use the dumpy level. https://www.wikihow.com/Use-a-Dumpy-Level LEVELING NOTES Dumpy Level Leveling Rod/Staff Illustrative Problem 1. Differential Leveling. Complete the differential level notes shown below and perform the customary arithmetic check. Level Notes from BM1 to BM4: STATION BS HI FS ELEV BM1 1.256 127.133 m TP1 1.116 1.886 TP2 1.228 1.527 BM2 1.189 2.246 BM3 1.070 2.017 TP3 1.831 2.656 BM4 2.765 A. Computation of HI’s and Elevation of Stations: 127.133 (Elev BM1) 125.074 (Elev BM2) + 1.256 (BS on BM1) + 1.189 (BS on BM2) 128.389 (HI) 126.263 (HI4) - 1.886 (FS on TP1) - 2.017 (FS on BM3) 126.503 (Elev TP1) 124.246 (Elev BM3) + 1.116 (BS on TP1) + 1.070 (BS on TP1) 127.619 (HI2) 125.316 (HI5) - 1.527 (FS on TP2) - 2.656 (FS on TP3) 126.092 (Elev TP2) 122.660 (Elev TP3) + 1.228 (BS on TP2) + 1.831 (BS on TP3) 127.320 (HI3) 124.491 (HI6) - 2.246 (FS on BM2) - 2.765 (FS on BM4) 125.074 (Elev on BM2) 121.726 (Elev on BM4) B. Determining Backsight and Foresight Sums: Σ BS = 1.256 + 1.116 + 1.228 + 1.189 + 1.070 + 1.831 = +7.690 Σ FS = - (1.886 + 1.527 + 2.246 + 2.017 + 2.656 + 2.765) = -13.097 C. Tabulated Solution STATION BS HI FS ELEV BM1 1.256 128.389 127.133 m TP1 1.116 127.619 1.886 126.503 TP2 1.228 127.320 1.527 126.092 BM2 1.189 126.263 2.246 125.074 BM3 1.070 125.316 2.017 124.246 TP3 1.831 124.491 2.656 122.660 BM4 2.765 121.726 (Σ BS) = +7.690 (Σ FS) = -13.097 D. Arithmetic Check 127.133 m (Elevation of BM1) + 7.690 m (Σ BS) Sum 134.823 m (Σ FS) - 13.097 m 121.726 m (Checks with Elevation of BM4) Assignment Differential Leveling. Prepare and complete the differential level notes for the table shown below. Level Notes from BM1 to BM2: STATION BS HI FS ELEV BMA 0.68 126.130 125.45 m TP1 0.98 123.360 3.75 122.338 TP2 3.73 123.57 3.52 119.840 TP3 3.90 125.830 1.64 121.930 BM2 0.35 125.480  Computation of HI’s and Elevation of Stations  Show tabulated solution  Arithmetic Check Double-Rodded Leveling. A method of determining differences in elevation between points by employing two level routes simultaneously. - This method differs from conventional differential leveling in that two turning points are established such that at each setup of the leveling instrument, two sets of independent backsights and foresights are taken. Double-Rodded Leveling. A method of determining differences in elevation between points by employing two level routes simultaneously. Illustrative Problem 2. Double-Rodded Leveling. Complete the differential level notes for a double-rodded line from BM1 to BM2. Show the customary arithmetic check. STATION BS HI FS ELEV BM1 1.964 1.964 205.549 m TP1 H 2.187 1.104 TP1 L 2.629 1.549 TP2 H 1.393 1.794 TP2 L 1.780 2.202 TP3 H 0.317 2.991 TP3 L 0.741 3.415 BM2 2.634 2.634 Illustrative Problem 2. Double-Rodded Leveling. Complete the differential level notes for a double-rodded line from BM1 to BM2. Show the customary arithmetic check. STATION BS HI FS ELEV BM1 1.964 207.513 1.964 205.549 m 207.513 TP1 H 2.187 1.104 2.629 208.596 1.549 206.409 TP1 L 208.593 205.964 TP2 H 1.393 1.794 TP2 L 1.780 208.195 2.202 206.802 208.171 206.391 TP3 H 0.317 2.991 TP3 L 0.741 205.521 3.415 205.204 205.497 204.756 BM2 2.634 2.634 202.887 202.863 (Σ BS) = +12.975 (Σ FS) = -18.323 Solution: Mean Elevation of BM2 = ½ (202.887 + 202.863) = 202.875 Σ BS = 1.964 + 1.964 + 2.187 + 2.629 + 1.393 + 1.780 Σ BS = 12.975 m Σ FS = - (1.104 + 1.549 + 1.794 + 2.202 + 2.991 + 3.415 + 2.634 + 2.634) Σ FS = - 18.323 m Arithmetic Check: Get the sum of the summation of backsight and foresight: SUM = Σ BS + Σ FS Mean Elev. BM2 = Ave + Elev. BM1 = 12.975 m – 18.323m Mean Elev. BM2 = -2.674 + 205.549 Mean Elev. BM2 = -202.875 m = -5.348 m AVE = -5.348 m / 2 = -2.674 m D. Arithmetic Check 127.133 m (Elevation of BM1) + 7.690 m (Σ BS) Sum 134.823 m (Σ FS) - 13.097 m 121.726 m (Checks with Elevation of BM4) Three-Wire Leveling. A more precise method of differential leveling wherein three horizontal hairs (or threads) are read and recorded rather than from a horizontal hair. - This method is employed for high precision work thus, it requires only precise leveling rods. Where a = upper stadia hair reading b = lower stadia hair reading c = horizontal cross-hair reading or rod reading on P s = stadia intercept or the difference between the upper stadia hair reading and lower stadia hair reading m = mean of three-hair readings HD = horizontal distance from the level to the rod held at P K = stadia interval factor C = instrument constant HI = height of the line of sight above datum or mean sea level Elev. of P = unknown elevation of station P The following equations are used in three-wire leveling: s=a-b s, stadia intercept Provides an indirect measure of the distance from the center of the leveling instrument to the rod sighted m = ( a + b + c) / 3 mean reading Average of the three stadia hair readings HD = Ks + C Horizontal distance, K = stadia interval factor, and C = instrument constant For most leveling instrument, K is usually equal to 100 & C is zero. Procedures: BACKSIGHT FORESIGHT Elevati Station Hair Mean HI Hair Mean S S on Rdgs Rdgs Rdgs Rdgs 2.85 A 2.46 2.06 5.01 B 4.61 4.20 Illustrative Problem 3. Three Wire Leveling. Complete the differential level notes shown below and perform the customary arithmetic check. BACKSIGHT FORESIGHT Station Hair Mean HI Hair Mean Elevation S S Rdgs Rdgs Rdgs Rdgs 1.152 BM1 0.935 0.718 TP1 2.784 1.117 2.420 0.899 2.057 0.682 TP2 1.713 1.900 1.440 1.537 1.166 1.172 TP3 2.591 1.450 2.094 1.177 1.599 0.904 0.913 2.210 TP4 0.730 1.714 0.547 1.218 BM2 1.593 1.410 1.227 Illustrative Problem 3. Three Wire Leveling. Complete the differential level notes shown below and perform the customary arithmetic check. BACKSIGHT FORESIGHT Station Hair Mean HI Hair Mean Elevation S S Rdgs Rdgs Rdgs Rdgs 1.152 BM1 0.935 0.935 0.434 445.177 444.242 0.718 TP1 2.784 1.117 2.420 2.420 0.727 446.698 0.899 0.899 0.435 444.278 2.057 0.682 TP2 1.713 1.900 1.440 1.440 0.547 446.602 1.537 1.536 0.728 445.162 1.166 1.172 TP3 2.591 1.450 2.094 2.095 0.992 447.502 1.177 1.177 0.546 445.425 1.599 0.904 0.913 2.210 TP4 0.730 1.714 0.547 0.730 0.366 446.536 1.218 1.714 0.992 445.806 BM2 1.593 1.410 1.227 1.410 0.366 445.126 D. Arithmetic Check 444.242 m (Elevation of BM1) + 7.620 m (Σ BS) Sum 451.862 m (Σ FS) - 6.736 m 445.126 m (Checks with Elevation of BM4)