Route Surveying PDF

ROUTE SURVEYING INTRODUCTION Planning the Route Alignment Route surveying is applied to the surveys required to establish the horizontal and vertical alignment for transportation facilities. Transportation facilities comprise a network that includes...

ROUTE SURVEYING INTRODUCTION Planning the Route Alignment Route surveying is applied to the surveys required to establish the horizontal and vertical alignment for transportation facilities. Transportation facilities comprise a network that includes highways, railways, rapid transit guide ways, canals, pipelines, and transmission lines. Surveys of some type are required for practically all phases of route alignment planning, design, and construction work. For small projects involving widening or minor improvement of an existing facility, the survey may be relatively simple and may include only the obtaining of sufficient information for the design engineer to prepare plans and specifications defining the work to be done. For more complex projects involving multiline highways on new locations, the survey may require a myriad of details including data from specialist in related fields to determine the location; to prepare plans, specifications, and estimates for construction; and to prepare deed descriptions and maps for appraisal and acquisition of the necessary rights of way. The function of the survey or project engineer is to plan the surveys and gather all survey data that may be needed to execute the design of a route alignment for a particular project. This process includes obtaining the necessary information regarding terrain and land use, making surveys to determine detailed topography, and establishing horizontal and vertical control required for construction layout. To acquire these data, the survey engineer must be familiar with: 1. The geometry of horizontal and vertical curves and how they are used in the route alignment procedure. 2. The methods of acquiring terrain data utilized in the route design procedure. 3. The procedures followed in processing terrain data to obtain earthwork volumes, and 4. The earthwork distribution processes. Steps To Be Undertaken In Route Surveys: 1. Reconnaissance survey - It is a rapid survey without the use of ordinary instruments in surveying that will serve as a guide in selecting the route to be taken. 2. Preliminary survey - is a survey made with the ordinary surveying instruments. The purpose of which is to fix and mark on the ground the first trial route and to collect data upon which the final location may be made. 3. Location or Final Survey - this is the survey for the construction of the project a. Construction survey - a survey used in the implementation and inspection of the project. Route Curves for Horizontal and Vertical Alignments In highway, railway, canal, and pipeline location, the horizontal curves employed at points of change in direction are arcs of circles. The straight lines connecting these circular curves are tangent to them and are therefore called tangents. For the completed line, the transitions from tangent to circular curve and from circular curve to tangent may be accomplished gradually by means of a segment in the form of a spiral. 1  Vertical curves are usually arcs of parabolas. Horizontal parabolic curves are occasionally employed in route surveying and in landscaping. Curves Curves are defined as arcs, with some finite radius, provided between intersecting straights to gradually negotiate a change in direction. For example, when two straights of a highway or a railway are at some angle to each other, a curve is introduced between them to avoid abrupt change in direction and to make the vehicle move safely, smoothly and comfortably. This change in direction of the straights may be in a horizontal or a vertical plane, resulting in a provision of a horizontal and vertical curve, respectively. Curves are basically classified as horizontal or vertical curve, the former being in the horizontal plane and the latter in the vertical plane. a. Horizontal Curve 1. Simple Circular Curve A curve connecting two intersecting straights having a constant radius all throughout. It is tangential to the two straights at the joining ends. 2. Compound Curve When two or more simple curves, of different radii, turning in the same direction join two intersecting straights, the resulting curve is known as a compound curve. 2  3. Reverse Curve When two circular curves, of equal or different radii, having opposite direction of curvature join together, the resultant curve is a reverse curve. 4. Transition or Spiral Curve It is a curve introduced between a simple circular curve and a straight, or between two simple curves. It is also known as an easement curve. A transition curve has radius, gradually changing from a finite to infinite value or vice versa. It is widely used on highways and railroads, since its radius increases or decreases in a very gradual manner. b. Vertical or Parabolic Curve 1. Summit Curve 2. Sag Curve Sharpness of Curvature The sharpness of curvature may be expressed in any of three ways: a. Radius The curvature is defined by stating the length of radius. This method is often employed in subdivision surveys and sometimes in highway work. The radius is usually taken as a multiple of 100 ft. or 20 m. b. Arc basis The curvature is expressed by stating the “degree of curve”, D which is defined as the angle subtended at the center of the curve by an arc 100 ft. in the English System or 20 m in the metric system. English System: D 360 5729.578  or D  100 2 R R 3  Metric System D 360 1145.916  or D  20 2 R R c. Chord Basis The degree of curve is defined as the angle subtended by a chord having a length of one full station. English System D 50 50 sin  or R  2 R D sin 2 Metric System 4 Stationing One of the basic tasks of a survey crew is to layout or stake centerline and vertical alignments. One of the tools available to make this job easier is centerline stationing. Stationing is the assignment of a value representing the distance from some arbitrary starting point. Where the stationing begins is not generally too important, but any point along the alignment can be related to any other point on the same alignment by using the stationing. A station is a linear distance of 100 feet (20 m) along some described alignment. Without a described alignment, the station has no direction and therefore is rather meaningless. Stationing is usually expressed as number of stations or 100 foot units (1 km units) plus the number of feet (meter) less than 100 (20 m) and any decimal feet (meter). This value is preceded by an alphanumeric alignment designation. A point on an alignment called B3 and 1345.29 feet from the beginning of the stationing would be designated as “B3 13+45.29”. To perform math with stationing, the “+” can be dropped and the distance treated as feet (meter). 5  SIMPLE CURVES Elements of a Simple Curve A simple curve is a circular arc, extending from one tangent to the next. a. Point of Curve or Point of Curvature (PC) - The point where the circular curve begins or the point where the circular curve leaves the first tangent. b. Point of Tangent or Point of Tangency (PT) - The point where the curve ends or the point where the curve joins the second tangent. c. Point of Intersection (PI) or Vertex (V) - The point where the two tangents intersect. d. Tangent Distance (T) - The distance from the vertex to the PC or PT. e. External Distance (E) - The distance from the vertex to the curve measured towards the center. f. Middle Ordinate (M) - The line joining the middle of the chord, C, with the middle of the curve subtended by this chord. g. Radius (R) - The radius of the curve. h. Intersection Angle (I) - The angle of deflection between the tangents. i. Long Chord (C) - The straight line joining the PC and the PT. j. Degree of Curve (D) - The angle subtended at the center of the curve by an arc 100 ft. or 20 m long. 6 Curve Formulas I T  R tan 2  I  E  R  sec  1  2  I I C  2 R sin  2T cos 2 2  I C I M  R  1  cos   tan  2 2 4 I  Lc  20   metric system D I  Lc  100   english system D Methods of Laying Out a Curve: 1. By the deflection angle method: Deflection angle is the angle subtended by the tangent and the chord drawn from the PC to the arbitrary point, P on the curve. Assume the chord/curve to begin and end with a sub-chord: Let d represents the central angle of the sub-chord whose length is less than 20 m D represents the central angle of the full chord whose length is equal to 20 m Solve for the deflection angles,  d d DD D 1  1 3  1  2  2 2 2 d D D d  D  d 2 I 2  1  1  n  1  2 2 2 2 7 Tabulated Data of Results for the lay-out of the simple curve by deflection angle method: Station Stationin Station Central Occupie g Chord Deflection Angle Observed Angle d PC 0 + 000 0 0 d 1 C1 d1 1  1 2 d D D 2 C2 D 2  1  1  2 2 d DD D 3  1  2  3 C3 D 2 2 d  D  d 2 I Up to PT C d2 n  1  2 2 2. By offset from tangents: xp cos  or x p  c p cos  cp yp sin   or y p  c p sin  cp The tabulation of data for this method should be as follows: Points on the Total deflection Chord distance Station xp yp curve angle from PC PC 1 2 3 Up to PT 8 3. By Middle Ordinates or Offset from Long Chord: Points on Total Angle from Chord the Deflection Long Chord, distance Xp yp Station Curve Angle  From PC PC 1 2 3 Up to PT 9  COMPOUND CURVE Introduction A compound curve consists of two or more consecutive simple curves having a common tangent at their meeting point but having different radius. The centers of the curves lie on the same side of the common tangent. The point of the common tangent where the two curves join is called the point of compound curvature (P.C.C.) Elements of a Compound Curve  PC = point of curvature  PT = point of tangency  PI = point of intersection  PCC = point of compound curve  T1 = length of tangent of the first curve  T2 = length of tangent of the second curve  V1 = vertex of the first curve  V2 = vertex of the second curve  I1 = central angle of the first curve  I2 = central angle of the second curve  I = angle of intersection = I1 + I2  Lc1 = length of first curve  Lc2 = length of second curve  L1 = length of first chord 10  L2 = length of second chord  L = length of long chord from PC to PT  T1 + T2 = length of common tangent measured from V1 to V2  θ = 180° – I  x and y can be found from triangle V1-V2-PI.  L can be found from triangle PC-PCC-PT I1 T1  R1 tan 2 I T2  R2 tan 2 2 11  REVERSED CURVE Introduction A reversed curve is formed by two circular simple curves having a common tangent but lies on opposite side. At the point where the curve reversed in its direction is called the Point of Reversed Curvature (P.R.C.). After this point has been laid out from the P.C., the instrument is then transferred to this point (P.R.C.). With transit at P.R.C., and a reading equal to the total deflection angle from the P.C. to the P.R.C., the P.C. is backsighted. If the line of sight is rotated about the vertical axis until horizontal reading becomes zero, this line of sight falls on the common tangent. The next simple curve could be laid out on the opposite side of this tangent by deflection angle method. Elements of Reversed Curve  PC = point of curvature  PT = point of tangency  PRC = point of reversed curvature  T1 = length of tangent of the first curve  T2 = length of tangent of the second curve  V1 = vertex of the first curve  V2 = vertex of the second curve  I1 = central angle of the first curve  I2 = central angle of the second curve  Lc1 = length of first curve  Lc2 = length of second curve  Lc = length of reversed curvature  Lc  Lc 1 2  C1 = length of first chord  C2 = length of second chord  T1 + T2 = length of common tangent measured from V1 to V2  R1 and R2 = radii of curvature  D1 and D2 = degrees of curves   = angle between converging tangents = I2 – I1  P.C. = point of curvature  P = distance between parallel tangents 12 Types of a Reversed Curve Problem 1. Reversed curve with nonparallel tangents 2. Reversed curve with parallel tangents 13