Fundamentals of Surveying PDF

SUBJECT DETAILS Course No.: Eng Surv Description: FUNDAMENTALS OF SURVEYING Units: 5 Time: 7:30-10:30AM; 11:00AM-12:30PM Tues & Fri GRADING SYSTEM REQUIREMENTS PRELIMS: 25% CLASS STANDING MIDTERMS: 25% Attendance & Recitation FINALS: 50%...

SUBJECT DETAILS Course No.: Eng Surv Description: FUNDAMENTALS OF SURVEYING Units: 5 Time: 7:30-10:30AM; 11:00AM-12:30PM Tues & Fri GRADING SYSTEM REQUIREMENTS PRELIMS: 25% CLASS STANDING MIDTERMS: 25% Attendance & Recitation FINALS: 50% Assignments/ Seatwork 100% Field Activity Quizzes Exams  COURSE OUTLINE I. ELEMENTARY SURVEYING II. HIGHER SURVEYING III. ROUTE AND RAILWAY SURVEYING a. Approximating Distance by a. Tachometry a. Simple Curve Pacing b. Earth's Curvature and b. Compound Curve b. Tape Correction Refraction c. Reverse Curve c. Orienting Engineer's Transit c. Topographic Surveying d. Spiral Curve d. Open and Close Traverse d. Mapping e. Calculation of Area of Close e. Vertical Curve e. Hydrographic Surveying f. Symmetrical Parabolic Curve Traverse i. DPD i. Discharge Calculation g. Unsymmetrical Parabolic Curve ii. DMD ii. Volume Calculation h. Earthworks – Volume Calculation iii.Coordinate f. Differential Leveling g. Profile Leveling What do we do in Surveying? Measuring distances, angles, and positions, on or near the surface of the earth. There are two basic methods used in linear measurement: - Direct: using of tape, chain - Indirect: using of transit or theodolite and stadia, and GPS  Why do we need Surveying? PROJECT CONSTRUCTION - First thing to do on site is measuring and mapping the land. - The primary measurements are used by architects/engineers to understand and make the most of the area when designing. - Structural Engineers create structural design ensuring it will be suitable within the lot area and able to construct. A B C D Example of a Foundation Layout SURVEYING IN CONSTRUCTION Internet Photos MISTAKES DUE TO INCORRECT SURVEY Internet Photos  SURVEYING Surveying is the technique of determining the relative position of different features on, above or beneath the surface of the earth by means of direct or indirect measurements and representing them as plan or map.  HISTORY of SURVEYING The earliest known use of surveying practices is in 1400 BC by the Egyptians. Land along the Nile River was divided for taxation, divisions were washed away by floods. Rope-stretches method was created by the Egyptian surveyors to relocate the land divisions (measurements were made with ropes having knots at unit distances).  TYPES of SURVEYING 1. Depending on the METHOD OF SURVEY: a) Aerial Survey is a form of collection of geographical information using airborne vehicles. The collection of information can be made using different technologies such as aerial photography, radar, laser, satellite or from remote sensing imagery using other bands of the electromagnetic spectrum, such as infrared, gamma, or ultraviolet. b) Ground Survey is the kind of survey that takes place on the surface of the earth. In this type of surveying, the features to be surveyed are directly measured by physically touching them.  TYPES of SURVEYING 2. GROUND SURVEYING can be divided into 2 major areas based on the area to be surveyed: a) Plane Survey deals with small areas on the surface of the earth assuming the surface of the land to be plane. Thus, curvature of the earth is neglected. It is assumed that the plane surveying method can be applied to an area up to 250. b) Geodetic Survey deals with large areas such as the surveys of countries. Curvature has to be considered. It is a highly accurate type of survey which usually the scale of the resulting map is small (1:100,000 or smaller)  TYPES of SURVEYING 3. Based on PURPOSE OF SURVEYING, plane surveying can be divided into the following types: a) TOPOGRAPHIC SURVEY – it determines the position and shape of natural and man-made features over an area, usually for the purpose of producing a map of an area.  TYPES of SURVEYING 3. Based on PURPOSE OF SURVEYING, plane surveying can be divided into the following types: b) HYDROGRAPHIC SURVEY – preliminary surveys that are used to tie underwater features to surface control points. It defines shorelines and depth of lakes, streams, oceans, reservoirs, and other bodies of water.  TYPES of SURVEYING 3. Based on PURPOSE OF SURVEYING, plane surveying can be divided into the following types: c) ROUTE SURVEY – preliminary, layout, and control surveys that range over a narrow but long strip of land. Typical projects that require route surveys are highways, railroads, electric transmission, etc.  TYPES of SURVEYING 3. Based on PURPOSE OF SURVEYING, plane surveying can be divided into the following types: d) CADASTRAL SURVEY – preliminary, layout, and control surveys that are involved in determining boundary locations or in setting out new property boundaries.  TYPES of SURVEYING 3. Based on PURPOSE OF SURVEYING, plane surveying can be divided into the following types: e) CONSTRUCTION SURVEY – layout surveys for engineering works (e.g. line, grade, elevations, and dimensions). They also secure essential data for computing quantities.  SURVEYING INSTRUMENT STEEL TAPE: measure horizontal and slope distances. Level and rod: measure differences in elevations. Theodolite: measure horizontal and vertical angles. Total Station: measure horizontal and vertical angles, and horizontal and slope distances. GPS (global positioning system) receivers.  SCALE in SURVEY Scale is defined as the ratio of the distance between two points on the map to horizontal distance between the same points on the ground. For example: if 1m in reality is drawn on a map as 1cm, then the scale is 1:100 (meaning 1cm on the map is equivalent to 100cm in reality). UNIT OF MEASUREMENTS  ACCURACY and PRECISION ACCURACY - refers to how closely a measurement or observation comes to measuring a "true value," since measurements and observations are always subject to error. PRECISION - refers to how closely repeated measurements or observations come to duplicating measured or observed values.  TYPES OF DISTANCE DISTANCE is generally regarded as the most fundamental of all surveying observations. It can be categorized into: horizontal, vertical, and slope distances. Horizontal Distance B Vertical Distance A  DISTANCE MEASUREMENT If the angle Ø is determined, the horizontal distance between Points A and B can be computed, B A  METHODS 1. PACING (approximate method) 2. ODOMETER (approximate method) 3. TAPING 4. CHAINING 5. ELECTRONIC DISTANCE MEASUREMENT (EDM) *Others  PACING It consists of counting the number of steps, or paces, in a required distance. This is best done by walking with natural step/pace. A pace is defined as a single step A stride is considered two steps NOTE: - Only used as an approximate result - It is used widely during reconnaissance survey for preparation of military plans and approximate checking distances. - The results varies with uphill, downhill, height and age. PACING  FIELD ACTIVITY NO. 1: PACING 1. DETERMINING PACE FACTOR: a) Select a straight and level course and on both ends establish markers at least 70 meters apart. Designate these end points as A and B. b) Walk over the course at a natural pace starting with either heel or toe over point A and count the number of paces to reach point B. c) For succeeding trials, walk from B to A, then A to B, until 5 trials are completed, and the number of paces recorded accordingly. d) Tabulate e) To compute for the pace factor, divide the taped length of course AB to the average of the number of paces.  FIELD ACTIVITY NO. 1 : PACING Table 1.1. Pace Factor TAPED MEAN PACE NUMBER TRIAL LINE DISTANCE NUMBER FACTOR OF PACES (m) OF PACES (m/ pace) 1 AB 2 BA 3 AB 4 BA 5 AB  FIELD ACTIVITY NO. 1 : PACING 2. MEASURING DISTANCE BY PACING a) Define or establish the end points of another level course whose length is to be determined by pacing. Designate these end points as C and D. b) For the first trial, walk over the course from C to D at a natural pace and record the number of paces. Then, walk from D to C and again record the number of paces. c) Repeat the above procedure until all five trials are completed. d) After the field data is recorded, make an actual taping of the course CD to determine the taped distance. e) Tabulate f) To compute for the paced distance, get the mean of the number of paces for the five trials performed on course CD and multiply this to the pace factor. g) To get the relative precision, determine the difference between the taped and paced distance of line CD. Then, divide it by the taped distance.  FIELD ACTIVITY NO. 1: PACING Table 1.2. Measuring Distance by Pacing MEAN NUMBER PACED TAPED RELATIVE TRIAL LINE NUMBER OF PACES DISTANCE DISTANCE ERROR OF PACES 1 CD 2 DC 3 CD 4 DC 5 CD SAMPLE PROBLEM 1 A student paces a 25-meter length four times, recording the following results: 29, 28.5, 28, and 28.75 paces. Determine the number of paces he must take to establish a distance of 320 meters on level ground. SAMPLE PROBLEM 2 A surveyor recorded the following repeated paces of a given line: 456, 448, 462, 447, 452, 455. If his pace factor is 0.628 m/pace. a. What is the approximate length of line in meters? b. If the taped length of the line is 455 meters, does the calculated length from pacing meet the standard relative error? Evaluate the accuracy of the pacing method.  ODOMETER A device or tool that measures the distance traveled along a specific path or route. It's often used to measure distances walked or traveled by a surveyor during fieldwork. The odometer records the cumulative distance as the surveyor moves along the terrain, providing an estimate of the distances between different survey points.  TAPING The most common and easiest method of measuring horizontal distances. This is the process of measuring the length of a line or course with a surveyor’s tape. Tapes come in a variety of lengths and materials. For engineering work, the lengths are generally 10m, 30m, 50m and 100m. Tapping Accessories  Taping Conditions 1. When the length is less than the tape: measurements are carried out by laying the tape along the straight line between the points.  Taping Conditions 2. When the length of a the line between two points exceeds that of the tape: some form of alignment is necessary to ensure that the tape is positioned along the straight line required. This is known as ranging and is achieved using range poles or pins.  Plumb Bob (Plumbing)  CHAINING The method used in determining or laying off linear measurement for construction surveys, triangular base lines, and traverse distances. The chain traditionally used in chaining is made up of metal links, and it's laid out along the ground between two points to measure the distance between them.  ELECTRONIC DISTANCE MEASUREMENT A technology used in surveying and geodesy to measure distances between points with high accuracy. It replaces traditional methods like tape measurements and is widely used in construction. EDM technology utilizes electromagnetic waves or signals to determine the distance between two points. Distance can be measured easily, quickly and with great accuracy, regardless of terrain conditions.  ELECTRONIC DISTANCE MEASUREMENT To use an EDM system, the instrument is set over at one end of the line to be measured and some form of reflector is set over the other end such that of sight between the instrument and reflector is unobstructed. An electromagnetic wave is transmitted from the instrument towards the reflector where part of it is returned to the instrument.  TYPES OF ERRORS 1. Random/ Accidental 3. Natural - not predictable - Factors in the environment - tend to be small and will usually that can cause error are cancel themselves curvature and refraction - best controlled by repeating - Must use correction values measurements 2. Systematic / Instrumental 4. Personal - Usually caused by damaged - Commonly called as blunders instrument - arises principally from - Error tends to multiply (occur limitations of the human for each measurement) senses of touch and sight - Best control is calibration of an instrument 1. Most Probable Value ( ) 2. Residual/ Deviation (v) or ( ) - used to determine how much each - represents the nearest observation deviates from the MPV. approximation of actual Smaller residuals indicate that an measurement based on multiple observation is closer to the MPV, observations or measurements. suggesting higher accuracy, while larger residuals suggest the presence of errors where: - Summation of all of observations - number of observations 3. Standard Deviation (of any 4. Standard error of the mean, ( ̅ ) single measurement), ( 𝒙 ) - used to assess the precision of - it provides an approximation of multiple measurements of the how much the individual same quantity. It helps in measurements differ from the mean understanding how close the (or average) of the dataset. average of these repeated measurements is likely to be to the true value. ̅ 5. Probable Error (PE) 6. Relative Precision (RP) - a measure of how precise a set of - Used to estimate the range within measurements is in relation to which the true value of a the size of the measurements measured quantity is likely to fall. themselves. It expresses the It represents the value below consistency of measurements as a which the absolute errors of half proportion of the measured the measurements are expected value. to lie. ̅ Example 1: A surveying instructor tasked her 40 students with measuring the distance between two points marked on the roadway. The students, working in groups of four, provided ten different measurements as follows: 10.5, 11.8, 11.15, 10.55, 10.8, 11.25, 11.60, 10.95, 11.35, and 10.85 meters. Assume that these measurements are equally reliable and that any variations are due solely to accidental errors. a. Compute the most probable value. b. Determine the probable error of the mean measurement. c. Calculate the relative precision of the mean. Example 2: The table below shows the data in measuring the distance of a certain line. Frequency Distance 6 38.20 2 38.55 5 38.37 3 38.28 a. Determine the MPV of the measurements. b. Calculate the standard deviation of any single observation. c. Calculate the standard error of the mean. d. Calculate the probable error of any single observation. e. Calculate the relative precision of the mean. TAPE CORRECTION  CAUSES of ERRORS in TAPING 1. INCORRECT TAPE LENGTH, - too long or too short 2. TEMPERATURE, - to be added or subtracted 3. PULL, - to be added or subtracted 4. SAG, - to be subtracted only 5. SLOPE, - to be subtracted only 6. NORMAL PULL / TENSION - The required pull/ tension to eliminate effect of sag Example 1: The measured distance from B to C was 318m. The steel tape used has a standard length at 20°C with a coefficient of the thermal expansion of 0.0000116/°C. The corrected distance B to C is 318.103m. Find the temperature during the measurement. Example 2: The measured distance from A to B was 318m using tape having a cross-sectional area of 0.05 has been standardized at a tension of 5.5kg. If the modulus of elasticity E = , determine the pull applied if the corrected distance A to B is 318.012m. Example 3: A 30m tape is supported only at its ends and under a steady pull of 8kg. If the tape weighs 0.91kg. Determine the following: a. The sag correction b. Correct distance between the ends of the tape Example 4: A line was determined to be 2395.25m when measured with a 30m steel tape supported throughout its length under a pull of 4kg at a mean temperature of 350C. Tape used is of standard length at 200C under a pull of 5kg. Cross sectional area of the tape is 0.03sq.cm. Coefficient of thermal expansion is 0.0000116/0C. Modulus of elasticity of tape is 2x106 kg/sq.cm. a. Determine the error of the tape due to temperature change. b. Determine the error due to tension c. Determine the corrected length of the line. Example 5: Slope distances AB and BC measure 330.49m and 660.97m, respectively. The difference in elevation is 10.85m for B and C, and 12.22m for A and B. Using the slope correction formula, determine the horizontal length of line ABC. Assume the line AB has a rising slope and BC a falling slope. Example 6: Under a standard pull of 8kg, the steel tape is 40m long. A normal tension of 18kg makes the elongation of the tape offset the effect of sag. If the tape weighs 0.025kg/m, and E= kg/c , determine its cross sectional area in sq.cm.  PROBLEM SET 1. A 30m tape was standardized and was found to be 0.0025m too long than the standard length at an observed temperature of 28C and a pull of 15kg. The same tape was used to measure a certain distance and was recorded to be 354.12m long at an observed temperature of 28C and a pull of 15kg. Determine the true length of the line. Coefficient of thermal expansion = 0.0000116/C.  PROBLEM SET 2. A 50m steel tape is of standard length under a pull of 5.50kg and a temperature of 20°C when supported throughout its entire length. The tape weighs 0.05kg/m, has a cross-sectional area of 0.04c and a modulus of elasticity of kg/c this tape was used in the field to measure the distance that was determined to be 458.65m. At the time the measurement was made, the constant pull applied was 8kg with the tape supported only at endpoints. During measurement the temperature was observed to be an average of 18°C. Determine the correction due to pull, temperature and sag, and calculate the correct length of the line. 3. A chaining party measures a distance of AB along a slope with a 100m tape which is known to be too long by 0.04. The distance from A at the base of the slope to B at the summit is recorded as 416.85m. Levels runs from A to B established a difference in elevation of 24.50m. Compute the true horizontal distance from A to B. 4. Distance AB on the ground was measured five times. Results are of different values but of same degrees of reliability. Difference in measurement is due to accidental errors. If the results are 320.15m, 319.95m, 320.45m, 320.32m and 319.98m, determine the most probable value of distance AB. Compute for the standard deviation (by single and mean measurements) and probable error (by single and mean measurements).