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  • INTRODUCTION OF SURVEYING
    • INTRODUCTION
    • REFERENCE ELLIPSOID
    • BASIC MEASUREMENTS
    • The geoid
    • PROTECTION AND REFERENCING
    • CONTROL NETWORKS
    • The ellipsoid
    • BASIC SETTING-OUT PROCEDURES USING COORDINATES
    • LOCATING POSITION
    • COORDINATE SYSTEMS
    • USE OF GRIDS
    • PLOTTING DETAIL
    • Geodetic coordinates
    • SETTING OUT BUILDINGS
    • Computer-aided design (CAD)
    • Cartesian coordinates
    • Error and uncertainty
    • Plane rectangular coordinates
    • SIGNIFICANT FIGURES
    • Height
    • ERRORS IN MEASUREMENT
    • WEIGHT MATRIX
    • LOCAL SYSTEMS
    • Probability
    • ERROR ANALYSIS
    • Deviation of the vertical
    • INDICES OF PRECISION
    • VARIANCE-COVARIANCE MATRIX OF THE PARAMETERS
    • COMPUTATION ON THE ELLIPSOID
    • COMBINATION OF ERRORS
    • Uncertainty of addition or subtraction
    • Eigenvalues, eigenvectors and error ellipses
    • BLUNDER DETECTION
    • RELIABILITY OF THE OBSERVATIONS
    • PRACTICAL CONSIDERATIONS
    • ESTIMATION IN THREE DIMENSIONS

  • LEVELLING
    • LEVELLING
    • OPTICAL METHODS
    • CURVATURE AND REFRACTION
    • MECHANICAL METHODS
    • EQUIPMENT
    • Weiss quadrilateral
    • INSTRUMENT ADJUSTMENT
    • PARAMETER VECTOR
    • Single wires in two shafts
    • Automatic level
    • DESIGN MATRIX AND OBSERVATIONS VECTOR
    • GYRO-THEODOLITE
    • PRINCIPLE OF LEVELLING
    • Plan network
    • SOURCES OF ERROR
    • Distance equation
    • LEVELLING APPLICATIONS
    • Direction & Angle equation
    • Direct and Indirect contouring
    • Controlling earthworks
    • RECIPROCAL LEVELLING
    • PRECISE LEVELLING
    • Parallel plate micrometer
    • ERROR ELLIPSES
    • Field procedure
    • Booking and computing
    • DIGITAL LEVELLING
    • Factors affecting the measuring procedure
    • TRIGONOMETRICAL LEVELLING

  • CONTOURING
    • TAPES
    • Introduction of Satellite positioning
    • FIELD WORK
    • GPS SEGMENTS
    • Measuring in catenary
    • GPS
    • DISTANCE ADJUSTMENT
    • SATELLITE ORBITS
    • Sag
    • BASIC PRINCIPLE OF POSITION FIXING
    • ERRORS IN TAPING
    • DIFFERENCING DATA
    • Tension,Sag and Slope
    • GPS OBSERVING METHODS
    • ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM)
    • Kinematic positioning
    • ERROR SOURCES
    • Global datums
    • GPS SYSTEM FUTURE
    • DATUM TRANSFORMATIONS
    • GALILEO
    • ORTHOMORPHIC PROJECTION
    • APPLICATIONS
    • ORDNANCE SURVEY NATIONAL GRID
    • (t – T) correction
    • PRACTICAL APPLICATIONS
    • Contouring
    • HEIGHTING WITH GPS

  • Theodolite Surveying
    • PLANE RECTANGULAR COORDINATES
    • PRINCIPLE OF LEAST SQUARES
    • PRINCIPLE OF LEAST SQUARES
    • TRAVERSING
    • LINEARIZATION
    • LEAST SQUARES APPLIED TO SURVEYING
    • Reconnaissance
    • NETWORKS
    • LINEARIZATION
    • Sources of error
    • Traverse computation
    • TRIANGULATION
    • Resection and intersection
    • Resection
    • NETWORKS
    • INSTRUMENT ADJUSTMENT
    • FIELD PROCEDURE
    • Setting up using the optical plumb-bob
    • MEASURING ANGLES
    • Measurement by directions
    • SOURCES OF ERROR

  • Simple Curves
    • CIRCULAR CURVES
    • Plotted areas
    • RESPONSIBILITY ON SITE
    • PHOTOGRAMMETRY
    • SETTING OUT CURVES
    • PARTITION OF LAND
    • COMPOUND AND REVERSE CURVES
    • CROSS-SECTIONS
    • SHORT AND/OR SMALL-RADIUS CURVES
    • VOLUMES
    • TRANSITION CURVES
    • Effect of curvature on volumes
    • Centrifugal ratio
    • MASS-HAUL DIAGRAMS
    • CONTROLLING VERTICALITY
    • The equation of motion
    • Coefficient of friction
    • CONTROLLING GRADING EXCAVATION
    • Sources of error
    • SETTING-OUT DATA
    • ROUTE LOCATION
    • LINE AND LEVEL
    • Highway transition curve tables (metric)
    • THE OSCULATING CIRCLE
    • Transitions joining arcs of different radii (compound curves)
    • Coordinates on the transition spiral
    • VERTICAL CURVES
    • Vertical curve design
    • Sight distances
    • Permissible approximations in vertical curve computation

Branch : Civil Engineering
Subject : Surveying-I
Unit : Simple Curves

LINE AND LEVEL


Line:


The line of the tunnel, having been established by wire survey or gyro observations, must be fixed in physical form in the tunnel. For instance, in the case of a Weisbach triangle  the bearing WuW1 can be computed; then, knowing the design bearing of the tunnel, the angle θ can be computed and

 

Plan view

(a) Section, and (b) plan

 

 

turned off to give the design bearing, offset from the true by the distance XWu. This latter distance is easily obtained from right-angled triangle W1XWu. The line may then be physically established by carefully lining in three plugs in the roof from which weighted strings may be suspended as shown in Figure The third string serves to check the other two.

 

 

These strings may be advanced by eye for short distances but must always be checked by theodolite as soon as possible. The gradient of the tunnel may be controlled by inverted boning rods suspended from the roof and established by normal levelling techniques. In addition to the above, ‘square marks’ are fixed in the tunnel by taping equilateral triangles from the centre-line or, where dimensions of the tunnel permit, turning off 90◦ with a theodolite .

 

 

Measurements from these marks enable the amount of lead in the rings to be detected. For instance, if D1 > D2 then the difference is the amount of left-hand lead of the rings. The gap between the rings is termed creep. In the vertical plane, if the top of the ring is ahead of the bottom this is termed overhang, and the reverse is look-up. All this information is necessary to reduce to a minimum the amount of ‘wriggle’ in the tunnel alignment.

 

 


With a total station using conventional survey instrument and target mounts may be permanently attached to the wall of the tunnel to ensure forced centring. If that is the case then if all the mounts are on the same side of the tunnel then either it will not be possible to see round the bend if the curvature is to the same side as the mounts or there may be systematic horizontal refraction effects. Therefore where possible target and instrument mounts should be on alternate sides of the tunnel.

 

 

Level:
In addition to transferring bearing down the shaft, height must also be transferred. One particular method is to measure down the shaft using a 30-m standardized steel band. The zero of the tape is correlated to the surface BM as shown in Figure 13.23, and the other end of the tape is precisely located using a bracket fixed to the side of the shaft. This process is continued down the shaft until a level reading can be obtained on the last tape length at B. The standard tension is applied to the bottom of the

Transfer height down a shaft

 

tape and tape temperature recorded for each bay. A further correction is made for elongation of the tape under its own weight using:


Elongation (m) = WL/2AE
where E = modulus of elasticity of steel (N/mm2)
L = length of tape (m)
A = cross-sectional area of tape (mm2)
W = mass of tape (N)
Then the corrected distance AB is used to establish the value of the underground BM relative to the
surface BM.

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