Engineering Survey

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This section defines engineering survey, distinguishes the preliminary, feasibility and construction stages, and covers objectives, scope, methodology, and the establishment of horizontal and vertical control.

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Definition and Objectives Engineering survey is the surveying carried out for the planning, design, construction, operation and maintenance of engineering works — roads, railways, canals, tunnels, bridges, dams, buildings and utility networks.

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Unlike a purely mapping survey, it is two-directional: it both takes information from the ground (mapping, profiles, quantities) and puts the design back onto the ground (setting out). • Objectives: to provide a reliable control framework; to supply topographic data for design; to transfer the designed position, level, line and grade to the ground; to measure quantities for payment; to record the as-built work; and to monitor deformation during and after construction. • Scope: reconnaissance and route location; topographic and detail survey; profile and cross-section levelling; hydrographic and geotechnical support surveys; setting out of centre lines, foundations, curves and levels; quantity and volume computation; as-built surveys; and deformation monitoring.

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Stages of an Engineering Survey Stage Purpose and typical work Accuracy Reconnaissance Rapid field and map/imagery study of alternatives; no or very coarse measurement; identifies obligatory points and obstacles Low — sketch level Preliminary survey Traverse or GNSS along the selected corridors, topographic strip mapping, provisional profiles; compares alternative alignments Moderate Feasibility / detailed survey Detailed topographic survey, longitudinal profile and cross-sections, geotechnical and hydrological data; produces the design drawings, quantities and cost estimate for the decision to proceed High Construction (location/setting-out) survey Transfer of the design to the ground — centre line, curves, offsets, grade, formation levels, foundations; continuous checking Highest As-built and monitoring Records what was actually built; deformation and convergence monitoring during and after construction High, repeatable • The three terms used in the syllabus map onto this sequence: preliminary (comparison of alternatives), feasibility (the detailed survey on which the technical and financial decision rests) and construction (setting out and control of the work).

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Cost and effort rise sharply, and the acceptable tolerance falls sharply, from left to right.

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Methodology • Sequence: collect existing maps, imagery and records → reconnaissance → establish horizontal and vertical control → detail/topographic survey → office computation and plotting (now a digital terrain model in GIS/CAD) → design → setting out → checking and as-built. • Governing principles: work from the whole to the part (control first, detail afterwards, so errors do not accumulate); provide independent checks on every measurement; fix a point by at least two independent measurements; and match the accuracy to the purpose. • Instruments: total station and robotic total station, GNSS (static, RTK and network RTK), digital and automatic levels, laser levels and pipe lasers, gyro-theodolite, UAV photogrammetry and terrestrial laser scanning; all with recorded calibration.

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Horizontal Control • Horizontal control is a framework of points of known plane coordinates covering the project, from which all detail and setting out is derived.

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It may be a traverse (the usual method for a linear project — closed-loop or closed-link, never open), a triangulation/trilateration network, or a GNSS network connected to the national framework. • Requirements: points must be intervisible in pairs (for total-station work), permanent, stable and safe from construction traffic, sited on firm ground clear of the works but close enough for setting out, and monumented (concrete pillar with a centre mark) and referenced by witness marks so they can be re-established. • Accuracy is expressed as a closing error and relative precision (e.g.

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1:10,000 for ordinary work, 1:25,000 or better for major structures and tunnels); angular misclosure is commonly limited to c·√n seconds.

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Adjustment is by least squares, or by the Bowditch (compass) rule for simple traverses. • Work must be tied to the national datum — in Nepal the Modified UTM projection on Everest 1830, or WGS84/UTM for GNSS work — and a project may also use a local grid with a scale factor of unity at project height to avoid projection and height corrections in setting out.

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Vertical Control • Vertical control is a set of benchmarks of known reduced level, established by differential (spirit) levelling from a national benchmark, or by trigonometric levelling or GNSS with a geoid model over long distances. • Benchmarks should be stable, numerous (at intervals of 200-500 m along a route), outside the zone of construction disturbance and outside the influence of settlement, with at least two independent benchmarks near every structure so that movement can be detected. • Levelling is run as a closed loop or a link between two known benchmarks; the permissible misclosure is of the form C·√K mm with K in kilometres — commonly 12√K mm for ordinary and 4-6√K mm for precise work.

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Errors are reduced by balancing backsight and foresight distances (which eliminates collimation and largely removes curvature and refraction), keeping sights short, and using a stable, well-supported staff. • In Nepal, levels are referred to mean sea level at the Indian datum through the national benchmark network; on a project a temporary benchmark (TBM) is established and checked daily against the permanent network.

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This section covers hydrographic surveying and depth measurement, discharge measurement, river profiles and cross-sections, bridge survey, gauge stations, and the survey requirements of the components of a hydropower or irrigation project.

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Introduction, Objectives and Scope • Hydrographic surveying is the survey of bodies of water — rivers, lakes, reservoirs, canals, harbours — to determine the configuration of the bed, the depth of water, the position of the shoreline and the direction and quantity of flow. • Objectives: to map the bed (bathymetry); to fix the shoreline and high-flood line; to obtain river cross-sections and the longitudinal profile; to measure discharge and velocity; to estimate sediment transport and scour; to determine reservoir capacity and sedimentation; and to provide data for navigation, bridge, intake, weir and canal design. • Scope in a hydropower or irrigation project: site selection and layout, catchment and reservoir survey, headworks and intake, alignment of the conveyance system, surge tank and penstock, powerhouse and tailrace, together with the hydrological gauging that fixes the design discharge. • Methodology: establish shore-based horizontal and vertical control → fix the boat's position continuously (today by RTK GNSS, formerly by range-azimuth with a theodolite, two-angle intersection, range-range or by sextant three-point resection) → run sounding lines normal to the shore or the channel with cross-check lines → reduce all soundings to a common datum (chart datum, or MSL for inland work) using simultaneous tide/gauge readings → plot the depths and draw depth contours (isobaths).

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Depth Measurement Equipment and Working Principle Equipment Working principle and remarks Sounding rod / pole Graduated pole pushed to the bed; depths up to about 5-6 m in still, shallow water Lead line (sounding line) Weighted graduated line lowered to the bed; simple, slow, affected by current drift; used to check echo sounders Single-beam echo sounder Transmits an acoustic pulse and measures the two-way travel time t: depth = v·t/2, with v the speed of sound in water (about 1,500 m/s, calibrated by a bar check or a velocity profiler).

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Gives a single line of depths under the boat Multi-beam echo sounder A fan of beams gives full-coverage swath bathymetry; needs motion (heave, pitch, roll) and heading sensors and sound-velocity profiles Side-scan sonar Images the bed texture and objects; gives shape rather than accurate depth ADCP Acoustic Doppler Current Profiler — Doppler shift of backscatter from moving particles gives a profile of velocity, and hence discharge, as well as depth Airborne lidar bathymetry / UAV photogrammetry Green laser penetrates clear shallow water; photogrammetry maps banks and dry-season beds • Corrections to soundings: sound-velocity (bar check or CTD profile), transducer draft and squat, heave/pitch/roll, and reduction to datum using the water-level record at a nearby gauge.

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The frequency chosen is a trade-off — high frequency gives better resolution and shallow-water accuracy, low frequency penetrates deeper and into soft mud.

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Discharge Measurement • Discharge Q = A × V (area of flow × mean velocity).

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The area-velocity (velocity-area) method divides the cross-section into vertical segments, measures depth and velocity in each, and sums Q = Σ ai vi (mid-section or mean-section method). • Velocity in the vertical: the mean velocity is taken at 0.6 of the depth below the surface for shallow water (one-point method), or as the average of the readings at 0.2 and 0.8 depth (two-point method); three-point and five-point methods are used for precise work. • Instruments and methods: current meter (cup-type/price or propeller — revolutions per second converted by the rating equation v = a·N + b), ADCP (a moving-boat transect gives the whole discharge directly), float method (surface float velocity × a coefficient of about 0.85 — a rough method), dilution/salt-tracer gauging (suited to turbulent mountain streams where a current meter cannot be used), and structures — weirs, flumes (Parshall, Venturi) and notches with an established head-discharge relation. • Slope-area method using Manning's equation V = (1/n)·R2/3·S1/2 is used for flood estimation from high-water marks, where R is the hydraulic radius, S the energy slope and n the roughness coefficient.

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River Profile and Cross-Section • The longitudinal profile runs along the channel — usually along the thalweg (line of greatest depth) or the centre line — and plots the bed level, water surface and bank levels against chainage, with the vertical scale exaggerated (commonly 10:1) to show the gradient. • Cross-sections are taken perpendicular to the flow at regular chainages (typically 20-50 m in the project reach, closer at structures and bends), extending beyond the high-flood level on both banks.

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They give the area of flow, the storage, the scour depth and the quantities for excavation and protection works. • Dry parts are surveyed by total station, GNSS or UAV; wet parts by sounding.

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The two must be reduced to one common vertical datum, and the survey should record the water level and date/time of every section.

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Bridge Survey • Purpose: to fix the crossing site and the bridge axis; to provide the topography for the approaches; to determine the span, waterway and vertical clearance from the high-flood level and design discharge; to locate piers and abutments; and to establish control for setting them out. • Site selection criteria: a straight, stable, narrow reach with firm banks and good foundation, flow perpendicular to the axis, no sharp bend immediately upstream or downstream, adequate approach alignment and economical span. • Survey work: a control traverse or GNSS network on both banks with at least two intervisible points on each side; a topographic survey of the site; cross-sections at, upstream and downstream of the axis; determination of the HFL by gauge records and flood marks; sounding for bed profile and scour; and the measurement of the span across the river by triangulation/trilateration or EDM, since a tape cannot be used. • Setting out of piers in water is done by intersection from two or more shore baselines or by RTK GNSS, always with an independent check; pier centres are referenced to permanent marks on both banks.

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Gauge Station • A gauge (gauging) station is a permanent installation for measuring water level, and from it discharge.

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Types of gauge: staff gauge (vertical or inclined graduated plate), wire-weight gauge, float-operated automatic recorder in a stilling well, pressure transducer/bubbler, ultrasonic/radar non-contact sensor, and today telemetered stations. • Siting: a straight, stable reach with a well-defined channel and permanent control section, free from backwater and weed growth, accessible in flood, with the full range of stage readable and the gauge zero below the lowest expected water level. • The gauge must be connected by levelling to a permanent benchmark and re-checked periodically.

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The stage-discharge (rating) curve is built by simultaneous gauge readings and current-meter discharge measurements, usually of the form Q = a(H − H0)n, and is extrapolated with care for floods and re-established after any change in the channel. • In Nepal these stations are operated by the Department of Hydrology and Meteorology (DHM), and their records give the design discharges (Qdesign, Q100) used for hydropower, irrigation and bridge design.

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Project Components and Their Survey Requirements Component Function and survey requirement Reservoir Stores water.

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Needs catchment and reservoir-area survey, elevation-area-capacity curves from contours, submergence and resettlement mapping, and periodic sedimentation surveys Dam / weir Raises the water level (a dam stores, a weir merely diverts).

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Needs detailed foundation topography, the axis set out precisely, cross-sections, and post-construction deformation monitoring Intake Draws water into the system — side intake, trench or Tyrolean type, usually with a gravel trap and settling basin.

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Needs accurate levels to set the sill and to exclude sediment Conveyance system Headrace canal, tunnel or pipe carrying water to the forebay/surge tank; requires a precise longitudinal profile because the gradient is very flat and fixed; alignment set out with offsets and grade stakes Forebay / surge tank Provides storage and absorbs pressure surge at the transition from the low-pressure conveyance to the penstock Penstock Steep pressure pipe delivering water to the turbines; the gross head is the surveyed level difference between forebay water level and turbine centre line, so its levelling must be of high precision — an error in head is an error in power Powerhouse Houses turbines and generators; needs precise setting out of foundations, machine axes and anchor bolts, and as-built verification Tailrace Returns water to the river; its level fixes the net head and must clear the flood level of the receiving river • Power output is P = ρ·g·Q·H·η (watts), with ρ = 1000 kg/m³, g = 9.81 m/s², Q the discharge in m³/s, H the net head in metres and η the overall efficiency — which is why the survey quantities Q (from gauging) and H (from levelling) are the two that determine the viability of a scheme. • Irrigation projects use the same chain — headworks/weir, intake, main canal with branch and tertiary canals, cross-drainage works (aqueduct, siphon, culvert) and the command-area survey — where the canal gradient and the command area contours govern the whole design.

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This section covers the objectives, scope and methodology of underground survey, its equipment and terminology, the connection of surface and underground surveys, tunnel survey and setting out, convergence monitoring and instrumentation, and an introduction to geophysical survey and electrical resistivity tomography.

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Introduction, Objectives and Scope • Underground surveying is the survey carried out in tunnels, mines, shafts, caverns and underground powerhouses.

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Its distinguishing difficulties are no GNSS signal, no natural light, confined space, dust, water and fumes, a very narrow and elongated geometry (so traverses are weak in azimuth), heavy refraction along the tunnel axis and continuous interference from construction traffic. • Objectives: to transfer position, direction and level from the surface to underground; to set out the tunnel axis, grade and excavation profile; to control the direction of driving so that headings from opposite ends meet within tolerance (the breakthrough); to measure the excavated volume for payment; to record the as-built alignment; and to monitor deformation. • Scope: mine and tunnel surveys, shaft plumbing, underground powerhouse and cavern layout, hydropower headrace and tailrace tunnels, metro and highway tunnels, and monitoring of surface settlement above the works.

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Terminology Term Meaning Portal The entrance of a tunnel at the surface Heading and bench The upper part driven first and the lower part excavated afterwards Face The advancing end of the excavation Invert / crown (soffit) / springing The bottom, top and the level where the arch begins Adit A nearly horizontal access driven into a hillside Shaft / winze / raise A vertical opening from the surface / sunk downward / driven upward from below Overbreak and underbreak Excavation beyond, and short of, the designed profile — the basis of payment disputes Breakthrough (holing through) The meeting of two headings; the misalignment there is the ultimate test of the survey Chainage / grade / gradient Distance along the axis / designed level / designed slope Convergence The closing-in of the tunnel walls and crown after excavation Spad, roof station, wall station Survey marks fixed in the roof or wall, since the floor is constantly disturbed Underground Survey Equipment • Total station with reflectorless measurement and vertical/steep-sight capability; often mounted on wall or roof brackets rather than tripods to keep it clear of traffic.

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Instruments and targets must be illuminated, and prisms are commonly left in place as permanent references. • Gyro-theodolite (gyroscopic attachment) — determines true (astronomic) north independently of the surface network and without GNSS, by observing the oscillation of a suspended spinning gyro; it is the key instrument for controlling the azimuth of a long tunnel traverse, which would otherwise drift, and is used to check azimuth transferred down a shaft. • Precise/digital level with short sights and invar staff for grade; laser (tunnel) guidance systems and pipe lasers giving a visible reference line and grade for the excavation machine; plumb bobs and optical/laser plummets for shaft transfer; terrestrial laser scanner for as-built profile, overbreak/underbreak and volume; and automated total stations for monitoring. • Tunnel Boring Machine (TBM) guidance uses an automatic total station sighting a target on the machine, with a laser reference and inclinometers, updating the machine's position and attitude continuously.

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Connecting Surface and Underground Survey • The problem is to carry coordinates, azimuth and level from the surface framework into the tunnel so that both ends work on one system. • Through an adit or portal (the easy case): the traverse is simply continued from surface control into the tunnel, with the azimuth checked periodically by gyro-theodolite. • Down a shaft (the difficult case).

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Transfer of position and azimuth: hang two heavy plumb wires in the shaft as far apart as possible, immersed in oil or water to damp the swing; coordinate them at the surface and then set up underground to connect to them.

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Because the wires are close together, the transferred azimuth is weak — hence the classical Weisbach triangle, in which the underground instrument is set very nearly on the line of the two wires so that the small angle at the instrument can be measured accurately and the azimuth computed with minimum error.

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Alternatives are the Weiss quadrilateral, the coplaning method, and modern optical/laser plumbing and gyro-theodolite orientation, which avoids wires altogether. • Transfer of level down a shaft: a steel tape (or invar wire) suspended in the shaft is read simultaneously against levels set at the top and bottom, applying corrections for temperature, tension, the weight of the tape itself and standardisation; or an EDM measures vertically down to a target on the floor. • Every transfer must be repeated independently — commonly the whole procedure is done twice on different days and the results compared, since an undetected error at this stage misaligns the entire tunnel.

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Tunnel Survey and Setting Out • Surface work first: a strong, well-conditioned control network linking the two portals (or the shaft and the portal), observed by GNSS and/or precise traverse and adjusted by least squares.

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The accuracy of this surface network largely determines the breakthrough error, so it is normally designed for a specific breakthrough tolerance. • Underground control: a traverse of the longest practicable legs along the tunnel, with roof/wall stations, forced-centring and repeated angle sets; the azimuth is checked by gyro-theodolite at intervals because a narrow traverse has almost no geometric strength in direction.

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Levels are carried forward by precise levelling and checked by running back. • Setting out at the face: the tunnel axis is marked by points in the roof or by a laser beam aligned to the design line; the grade is fixed from a spad or from the laser; the excavation profile is marked from the axis, usually today by a total station with tunnel-profile software or by projecting the profile with a laser.

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Drill patterns for blasting are set out from the marked axis. • Breakthrough error is resolved into lateral (transverse), longitudinal and vertical components; the lateral component is the critical one and is governed chiefly by azimuth error, which is why gyro observations matter.

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Typical specifications require a lateral misclosure of a few centimetres over kilometres. • As-built survey: laser scanning of the excavated profile gives the overbreak/underbreak volume, the lining thickness check and the pay quantity.

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Tunnel Convergence Monitoring and Instrumentation • Convergence is the reduction in the distance between points on the tunnel periphery as the rock relaxes after excavation.

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It is the primary indicator of rock-mass behaviour and the adequacy of the support, and is central to the New Austrian Tunnelling Method (NATM), in which support is adjusted according to the measured deformation. • Convergence measurement: traditionally a tape extensometer (convergence tape) stretched at constant tension between fixed pins in the wall and crown, reading to ±0.01-0.1 mm; today optical 3-D monitoring with an automatic total station and reflective/bireflex targets installed in each section, giving absolute displacement rather than only relative closure. • Other instrumentation: extensometers (single- and multi-point borehole, measuring movement into the rock mass), convergence bolts and pins, load cells on rock bolts and steel ribs, pressure cells in the lining, strain gauges, inclinometers in boreholes, piezometers for pore pressure, and precise levelling arrays at the surface for settlement above shallow tunnels. • Interpretation: displacement is plotted against time and against distance from the face; convergence that decelerates and stabilises indicates equilibrium, while accelerating or non-converging displacement signals distress and triggers additional support.

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Readings must begin as soon as possible after excavation because a large part of the deformation occurs before the first reading is taken.

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Geophysical Survey and Electrical Resistivity Tomography • Geophysical survey investigates the subsurface by measuring a physical property from the surface (or in boreholes), without excavation.

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The main methods are seismic refraction and reflection (velocity, rockhead, rippability), electrical resistivity, ground-penetrating radar (shallow, high resolution, utilities and voids), gravity (density contrast, cavities), magnetic (ferrous objects, dykes) and electromagnetic methods.

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They are indirect and non-unique, so they are always calibrated against boreholes. • Electrical Resistivity Tomography (ERT) injects a direct current into the ground through a pair of current electrodes (A, B) and measures the resulting potential difference across a pair of potential electrodes (M, N).

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From Ohm's law the apparent resistivity ρa = K·(ΔV/I), where K is the geometric factor determined by the electrode configuration. • A multi-electrode cable with an automatic switching unit takes hundreds of readings at increasing spacings; greater electrode separation senses greater depth.

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The measured pseudo-section is then processed by inversion to produce a 2-D or 3-D model of true resistivity against depth. • Common arrays:

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Wenner (good vertical resolution and signal strength), Schlumberger (good depth sounding), dipole-dipole (good lateral resolution, weaker signal) and pole-dipole. • Interpretation: resistivity is low in clay, saline water and weathered, fractured, saturated rock, and high in dry, massive, unweathered rock, dry sand and gravel, and voids filled with air.

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Applications in engineering: locating the rockhead and depth of weathering along a tunnel or dam axis, detecting fracture and shear zones and groundwater, cavity and karst detection, landslide slip-surface mapping, leakage through a dam, and groundwater exploration — all standard preliminary investigations for tunnels and hydropower in Nepal's geology.

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This section covers the survey of linear projects — transmission lines, sewers, pipelines, roads, railways and cable cars — and the geometry and setting out of simple circular, transition and vertical curves, together with superelevation.

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Introduction, Objectives and Methodology • Route surveying is the survey for any linear project.

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Its objectives are to select the most economical and safe alignment consistent with the design standards, to provide topographic data along the corridor, to design the horizontal and vertical geometry, to set it out, and to compute earthwork quantities and land requirements. • General methodology: map and imagery study → reconnaissance of alternative corridors → preliminary survey (strip topographic survey along the chosen corridors) → selection of the alignment → detailed survey: centre-line traverse with chainage, longitudinal profile and cross-sections at regular intervals → design of horizontal curves, gradients and vertical curves → setting out → construction control and as-built. • Controls on alignment: obligatory points that the route must pass through (a bridge site, a pass, a town, a mine) or avoid (a settlement, a shrine, a protected forest, unstable slope), permissible gradient and curvature, geology and drainage, land acquisition cost, and, in Nepal's hills, slope stability and the risk of landslide and debris flow.

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Project Particular survey requirements Transmission line Straight sections between angle points; survey of tower/pylon positions with ground profile between them, because the sag of the conductor and the ground clearance govern tower height and spacing; crossings of rivers, roads and other lines surveyed in detail; a profile-and-plan drawing with a sag template Sewer Gravity flow, so the invert level and a continuous, very precise falling gradient are everything; deep, accurate longitudinal profile; manholes set at changes of direction and grade; setting out by sight rails and boning rods, or a pipe laser Water pipeline Can rise and fall (pressure flow), but needs the hydraulic grade line profiled to site air valves at summits and washouts at low points; crossings and anchor blocks set out precisely Road Balanced horizontal and vertical geometry to a design speed; cross-sections for earthwork; drainage, structures and intersections; superelevation and sight distance Railway Much flatter gradients and larger radii than a road; transition curves and cant essential; very tight tolerance on the as-built track geometry Cable car / ropeway Straight span between terminals and tower positions; the critical survey data are the ground profile and clearance beneath the rope, tower heights and the level difference between terminals; anchor and foundation setting out on steep, often inaccessible ground Curves:

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Types and Terms • Horizontal curves: simple circular (a single arc), compound (two or more arcs of different radii curving the same way, meeting at a point of compound curvature), reverse (two arcs curving in opposite directions, meeting at a point of reverse curvature — avoided on high-speed roads without an intervening straight), and transition/spiral curves.

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Vertical curves are summit (crest) or sag (valley), normally parabolic. • Terms of a simple circular curve:

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PI or V the point of intersection of the two tangents; Δ (or φ) the deflection angle between them;

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T1/PC/BC the point of curve (tangent to curve) and T2/PT/EC the point of tangency (curve to tangent);

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T the tangent length;

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L the length of curve;

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E the apex (external) distance;

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M the mid-ordinate (versine).

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Element Formula Tangent length T = R · tan(Δ/2) Length of curve L = πRΔ/180 = R·Δrad Element Formula Long chord C = 2R · sin(Δ/2) External (apex) distance E = R[sec(Δ/2) − 1] = R[1/cos(Δ/2) − 1] Mid-ordinate (versine) M = R[1 − cos(Δ/2)] Degree of curve (30 m arc) D = 1718.87 / R (for a 20 m arc, D = 1145.92/R) Chainage relations Chainage of T1 = chainage of PI − T; chainage of T2 = chainage of T1 + L (note: not PI + T) Deflection angle for a chord c δ = 1718.87 · c / R minutes = (c/2R) radians Setting Out a Simple Circular Curve • Linear (chain-and-tape) methods, used where no angular instrument is available or the curve is short: offsets from the long chord (Ox = √(R² − x²) − (R − M)), perpendicular offsets from the tangent (Ox = R − √(R² − x²), or approximately x²/2R), offsets from the chords produced (successive bisection) with the first offset c₁²/2R and subsequent offsets c(c₁ + c₂)/2R, and radial offsets. • Angular (instrumental) methods:

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Rankine's method of deflection angles — the standard method.

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The instrument is set at T1, sighted on the PI with zero reading, and successive points are fixed by turning the cumulative deflection angle Δn = δ₁ + δ₂ + … + δn and laying off the chord from the previous point; the check is that the final cumulative deflection equals Δ/2 and the last point falls on T2.

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Other methods are two-theodolite intersection (no linear measurement — ideal over water or rough ground) and tacheometric setting out. • Total station / coordinate method — now universal: the coordinates of each curve point are computed in the project grid and set out by polar (bearing and distance) from any control point, or by GNSS RTK from a stake-out file.

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It needs no intervisibility along the curve and is the only practical method on hill roads. • Sub-chords: the first and last chords are normally sub-chords so that the intermediate points fall on round chainages (peg interval of 10, 20 or 30 m, shorter on sharp curves).

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Transition Curves • A transition (easement) curve is introduced between a straight and a circular arc so that the radius decreases gradually from infinity to R and the centrifugal force and the superelevation are introduced gradually.

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The ideal curve is the clothoid (spiral), in which curvature varies linearly with length:

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R·L = constant = Ls·R; the cubic parabola and lemniscate are approximations. • Purposes: passenger comfort, gradual application of superelevation and of the extra widening on curves, reduction of side thrust and wear, and a safe, pleasing alignment. • Length of transition is taken as the greatest of:

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(a) the rate of change of centrifugal acceleration, Ls = V³/(C·R) with V in m/s and C usually 0.3-0.8 m/s³ (in the common highway form Ls = 0.0215 V³/(C·R) with V in km/h);

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(b) the rate of introduction of superelevation, Ls = (e·N)·(W) from the permissible gradient of the outer edge (1 in 150 for plain and rolling terrain, 1 in 60 for hills); and (c) an empirical minimum such as 2.7 V²/R. • Shift S = Ls²/(24R) — the circular curve is shifted inward by S so that the transitions can be fitted; the total tangent length becomes T = (R + S)·tan(Δ/2) + Ls/2.

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The spiral angle is θs = Ls/(2R) radians, and half the transition lies on either side of the shifted circular curve.

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Superelevation (Cant) • Superelevation is the transverse slope given to the carriageway (or the cant given to a railway track) at a curve, raising the outer edge so that a component of the vehicle's weight balances the centrifugal force. • The basic relation is e + f = V² / (127 R), with V in km/h, R in metres, e the superelevation as a ratio and f the coefficient of lateral friction (commonly taken as 0.15 for highways).

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For a railway, cant e = G·V²/(127 R) with G the gauge. • Design practice (IRC-type, also followed in Nepal Road Standard): superelevation is first computed for 75 % of the design speed ignoring friction, e = V²/(225 R); if this exceeds the permissible maximum (7 % in plain/rolling terrain, 10 % in hilly terrain without snow, 4 % in urban areas) it is limited to that maximum and the remaining force is checked against the allowable friction; the minimum superelevation equals the camber, for drainage. • Attainment: the crown is eliminated and the pavement rotated about the centre line or about the inner edge over the length of the transition, so that full superelevation is reached at the beginning of the circular curve.

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Related curve provisions are extra widening (mechanical plus psychological) and the check on sight distance, the set-back from obstructions on the inside of the curve.

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Vertical Curves • A vertical curve joins two gradients, providing a gradual change of grade for comfort and sight distance.

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It is normally a simple parabola, because the parabola gives a constant rate of change of grade and equal horizontal intervals give elevations easily computed. • Let the gradients be g₁ and g₂ (as percentages, upgrade positive, downgrade negative) and A = g₁ − g₂ the algebraic grade difference.

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A curve with A positive is a summit (crest) curve and with A negative a sag (valley) curve.

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The length L = K·A, where K is the rate of vertical curvature (length per 1 % change of grade) taken from the design standard for the design speed. • Elevation at a distance x from the start (BVC): y = yBVC + g₁x + [(g₂ − g₁)/(2L)]·x².

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The highest or lowest point occurs where the grade is zero, at x = g₁L/(g₁ − g₂) from the BVC.

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The mid-ordinate (offset at the vertex) is AL/800 with A in per cent and L in metres. • Length governed by sight distance: for a summit curve, when L > S, L = A·S²/[√(2h₁) + √(2h₂)]² (driver eye height h₁ = 1.2 m, object height h₂ = 0.15 m for stopping sight distance); for a sag curve the criterion is headlight sight distance, comfort, and clearance under overhead structures.

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Sag curves generally need to be longer than summit curves for the same speed at night. • Setting out is by computing the reduced level of the curve at every peg chainage and transferring it with a level, or by a total station in 3-D stake-out mode.

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This section gives a general introduction to the principal civil engineering structures — buildings, bridges, dams, weirs, tunnels and roads — and covers stakeout: its meaning, principles and survey techniques.

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Buildings • Components: the substructure (foundation and plinth, transferring the load to the ground) and the superstructure (columns, beams, walls, slabs, staircase, roof, doors and windows, finishes). • Foundations: shallow — isolated/spread footing, combined footing, strip footing, raft/mat; deep — pile, pier and well/caisson foundation, used where the bearing stratum is deep or the load is heavy.

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Selection depends on the safe bearing capacity, the depth of good ground, the water table and the loading. • Structural systems: load-bearing masonry (brick or stone walls carrying the load — common in Nepali housing), RCC framed structures (columns, beams and slabs), and steel or composite frames.

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Loads are dead, live (imposed), wind, seismic, snow and temperature effects. • Seismic design matters in Nepal: the Nepal National Building Code (NBC) and the Building Act govern design, with mandatory rules of thumb for ordinary houses; symmetry, continuity, adequate ductile detailing and good construction quality determine performance.

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Setting out requires precise right angles and diagonals, level plinths and plumb columns. • Survey inputs: site topographic survey and levels, setting out of the grid of column centres, foundation and plinth levels, verticality checks of columns and lift shafts, floor levels, and settlement monitoring of large buildings.

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Bridges • Components: superstructure (deck, girders, trusses, cables, bearings) and substructure (piers, abutments, wing walls, foundations), plus approaches, river training and protection works. • Types: beam/girder (RCC, steel, prestressed), slab and box girder; arch; truss; cantilever; cable-stayed; suspension — the last being the characteristic type for long spans and for Nepal's many trail and suspension footbridges; and culverts for very small spans. • Terms: span (clear and effective), waterway, afflux, freeboard, vertical clearance above HFL, scour depth and skew angle. • Survey inputs: site selection and the bridge axis, cross-sections and HFL, sounding and scour survey, setting out of piers and abutments by intersection, precise levels for bearings and deck, and post-construction monitoring of piers.

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Dams and Weirs • Dam — a barrier across a river creating a reservoir for storage.

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Types by material: earthfill and rockfill embankment dams (the commonest, flexible, needing a wide base and spillway away from the body), concrete gravity (resists by weight), arch (transfers thrust to the abutments in a narrow gorge), buttress; and by purpose: storage, diversion, detention. • Appurtenances: spillway (passes flood safely — the single most critical safety element), energy dissipator/stilling basin, outlet works and sluices, gallery, cut-off and grout curtain against seepage, and instrumentation. • Weir — a low barrier that raises and diverts water without significant storage, used at the headworks of irrigation and run-of-river hydropower schemes; a barrage is a gated structure giving fuller control of levels.

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Nepal's hydropower is predominantly run-of-river with a weir and side intake. • Survey inputs: catchment and reservoir survey with elevation-area-capacity curves, detailed foundation topography, precise setting out of the axis and of the spillway crest level, borrow-area and quantity survey, and deformation monitoring (levelling arrays, plumb lines, geodetic networks, extensometers and piezometers) throughout the dam's life.

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Tunnels and Roads • Tunnels are classified by purpose (traffic, water conveyance, sewer, mining) and by method: drill and blast (the usual method in the hard rock of Nepal), road-header and mechanical excavation, TBM, cut-and-cover for shallow depths, and immersed tube under water.

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Support is by rock bolts, shotcrete, steel ribs and a concrete lining, adjusted by the observed convergence (NATM) — see 9.3. • Roads: the cross-section comprises the carriageway, shoulders, camber, kerbs, side drains, cut and fill slopes, formation (subgrade) and the pavement layers — subgrade, sub-base, base course and surface course.

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Pavements are flexible (bituminous, distributing load through the layers) or rigid (cement concrete slab, acting in flexure). • Geometric design elements are the design speed, horizontal and vertical alignment, gradient (ruling, limiting and exceptional), camber, superelevation, extra widening, sight distance and the right of way.

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In Nepal these follow the Nepal Road Standard and the Department of Roads' design guidelines, with hill roads designed to much tighter radii and steeper gradients than plains roads. • Survey inputs: centre-line survey and chainage, longitudinal profile and cross-sections at 20-50 m (closer in hills and at structures), setting out of curves, formation levels by grade stakes and sight rails, cross-slope checks and earthwork quantities.

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Introduction • Stakeout (setting out, layout) is the reverse of surveying: instead of determining the position of existing features, it marks on the ground the position, line, level and grade of a designed feature so that construction can follow it.

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The marks are pegs, stakes, nails, profile boards or paint, referenced to the control framework. • Principles: always set out from established control, never from another setting-out point; work from the whole to the part; check every point independently by a different method or from a different station; record everything; and protect and periodically re-check the reference marks, which are frequently disturbed on a construction site. • Tolerances are specified by the contract and are far tighter than mapping accuracies — millimetres for steel structures and machine foundations, a few millimetres to a centimetre for concrete work, centimetres for earthwork.

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Stakeout Survey Techniques Technique Description and use Polar (bearing and distance) The standard total-station method: compute the bearing and distance from a control point to the design point and set it out directly; most instruments do this from uploaded coordinates Coordinate stake-out by total station or GNSS RTK Design coordinates uploaded and the instrument guides the rodman to the point; fast, needs no intervisibility along the works for GNSS Intersection (angular) Two or more theodolites/total stations intersect the point — used where distance cannot be measured, as for bridge piers in water Offsets from a baseline / centre line Simple tape method for buildings, roads and pipelines; right angles by the 3-4-5 rule, optical square or cross staff Profile boards, batter boards and sight rails with boning rods Wooden rails set at a known level outside the excavation; the required invert or formation level is obtained by sighting across successive rails with a traveller (boning rod) — the classic method for trenches and pipelines Grade stakes and slope (batter) stakes Mark the formation level and the point where the design side slope meets the natural ground (the catch point) in earthwork Laser level / pipe laser / rotating laser Provides a continuous reference plane or line and grade; widely used for floors, drainage and pipe laying Machine guidance (3-D) GNSS or total-station control of the blade or bucket of excavators and graders directly from the design model • Setting out a building: establish the baseline from the boundary or control, set out the main grid of column/wall centre lines, check the diagonals of every rectangle (the standard check that corners are square), transfer the lines to profile boards clear of the excavation, and mark the levels of foundation and plinth from a TBM. • Setting out a road or pipeline: peg the centre line at regular chainages and at curve points, place reference pegs offset from the centre line so that they survive excavation, set slope stakes at the catch points, and control the formation with grade stakes or sight rails. • Common errors: using an unchecked or disturbed reference mark, mixing datums or grids, transcription errors in coordinates or levels, neglecting the scale factor between grid and ground distance, and failing to check independently — the last being the cause of most serious setting-out failures.

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This section covers construction materials, the purpose and types of estimate, the methods of computing areas and volumes, the methodology of quantity estimation, and the mass haul diagram with its properties.

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Construction Materials Material Notes relevant to estimation Cement OPC/PPC;

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1 bag = 50 kg ≈ 0.035 m³; density about 1,440 kg/m³ Sand (fine aggregate) River or crushed; graded by zone; bulking of damp sand must be allowed for Aggregate (coarse) Crushed stone or gravel, 10-40 mm; the nominal maximum size depends on the member Bricks Nepal standard brick about 240 × 115 × 57 mm with 10 mm mortar joint; roughly 500 bricks per m³ of brickwork Stone Rubble and dressed stone masonry — the traditional material of hill construction Steel Reinforcement bars of 8-32 mm; unit weight = d²/162 kg/m with d in mm; structural steel sections Timber, bamboo Formwork, scaffolding, doors, windows and roofing Concrete Nominal mixes 1:1.5:3 (M20), 1:2:4 (M15), 1:3:6 (M10); dry volume = about 1.54 × wet volume Bitumen, cement blocks, CGI sheet, tiles, glass, paint, PVC/GI pipe Finishing, roofing and services items • Mortar and concrete quantities are computed by the dry-volume method: multiply the wet volume by about 1.54 for concrete (1.30-1.33 for mortar) and divide in the ratio of the mix.

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For 1 m³ of 1:2:4 concrete, cement = 1.54 × 1/7 = 0.22 m³ ≈ 6.3 bags, sand = 0.44 m³ and aggregate = 0.88 m³. • Rates are built up from material + labour + equipment + overheads and profit, using the official District Rate and the Department of Urban Development / Department of Roads norms for labour and material coefficients in Nepal.

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Purpose and Types Type of estimate Basis and use Preliminary / approximate (rough cost) Plinth-area, cubical-content, unit (per bed, per km, per kW) or service-unit rate — for administrative approval and budgeting Plinth area estimate Plinth area × the prevailing rate per m² Cube rate / cubical content Plinth area × height × rate per m³ — more reliable than plinth area Detailed estimate Item-by-item measurement of every quantity from the drawings, priced at analysed rates — the basis of the tender and of the bill of quantities Revised estimate Prepared when the sanctioned estimate is exceeded by more than the permitted margin, or the scope changes Supplementary estimate For additional work not in the original scope Annual repair / maintenance estimate For routine upkeep Complete estimate Includes all ancillary costs — land, contingencies, supervision, escalation • Methods of detailed measurement: the long wall and short wall method (centre-to-centre lengths corrected to out-to-out for the long walls and in-to-in for the short walls) and the centre line method (total centre-line length × breadth × depth, with a deduction of half the breadth of the junction for each cross wall) — the latter is quicker for symmetrical plans. • Contingencies of about 3-5 %, work charge establishment, VAT and price escalation are added to the measured cost; quantities are measured to the standard method of measurement so that deductions for openings, laps and so on are consistent.

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Area Calculation • From a plan: by division into triangles, rectangles and trapezia; by planimeter; by digital area computation in CAD/GIS; or by counting squares. • From coordinates — the shoelace (cross-multiplication) rule:

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A = ½ |Σ (xi·yi+1 − xi+1·yi)|, the standard method in a total-station or GIS computation; the double longitude/meridian distance methods are its traverse equivalents. • From offsets along a base line, with n intervals of constant width d and offsets O: • Trapezoidal rule:

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A = d·[ (O₀ + On)/2 + O₁ + O₂ + … + On−1 ] — assumes straight boundaries between offsets; works for any number of offsets. • Simpson's rule (one-third rule):

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A = (d/3)·[ O₀ + On + 4(odd offsets) + 2(even offsets) ] — assumes a parabolic boundary and is more accurate, but requires an even number of intervals, i.e. an odd number of offsets.

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If the number is not suitable, the last strip is treated separately by the trapezoidal rule. • For a curved boundary Simpson's rule gives a greater area than the trapezoidal rule when the boundary is convex outwards, and a smaller area when it is concave.

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Volume Calculation • From cross-sections (the usual method for roads, canals and embankments) — compute the area of cut and of fill at each cross-section (level, two-level, three-level or irregular sections), then combine: • Average end-area (trapezoidal) formula:

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V = (L/2)·(A₁ + A₂) for two consecutive sections at spacing L, or for n sections V = L·[ (A₁ + An)/2 + A₂ + … + An−1 ].

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It is simple but overestimates the volume when the section areas change non-linearly. • Prismoidal formula:

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V = (L/6)·(A₁ + 4Am + A₂), where Am is the area of the mid-section (computed from the mean dimensions, not the mean of the two end areas).

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Applied to n sections at spacing d with an odd number of sections it becomes V = (d/3)·[A₁ + An + 4(odd) + 2(even)] — the volume form of Simpson's rule.

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It is the more accurate formula, and the difference average end-area − prismoidal is the prismoidal correction, which is always deducted. • From spot levels / grid method (for excavation of a site or a tank): divide the area into squares or rectangles and take V = (A/4)·(Σh₁ + 2Σh₂ + 3Σh₃ + 4Σh₄), where h₁, h₂, h₃ and h₄ are heights at corners common to one, two, three and four squares respectively (for triangles the divisor is 3). • From contours: the area enclosed by each contour is measured and the volume between successive contours found by the average-end-area or prismoidal formula with L = the contour interval — the standard way of obtaining reservoir capacity. • From a DTM: the difference between the existing and design surfaces is integrated over the site, in a TIN facet by facet or in a grid cell by cell (see 8.4).

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Methodology of Quantity Estimation for Earthwork • Take the longitudinal profile and cross-sections at regular chainages → superimpose the design formation level and side slopes → compute the cut and fill areas at each section → apply the end-area or prismoidal formula between sections → tabulate cut and fill separately by chainage → apply the shrinkage and bulking factors → compute the cumulative volumes → draw the mass haul diagram. • Bulking (swell): excavated soil occupies more volume loose than in situ (commonly + 10-30 %, and much more for rock).

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Shrinkage: fill compacted in the embankment occupies less volume than the same material in situ (commonly − 10-25 %).

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Quantities must therefore be converted to a common basis, normally the in-situ (bank) measure, before cut and fill are compared.

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Mass Haul Diagram • A mass haul diagram is a plot of the cumulative (algebraic) volume of earthwork against chainage, drawn below the longitudinal profile, with cut taken as positive and fill as negative (after applying the shrinkage factor).

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It is used to plan the economical movement of earth — how much to move, how far and in which direction — and to decide on borrow and waste (spoil).

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Property Meaning Rising curve The section is in cut (volume accumulating) Falling curve The section is in fill Maximum (peak) Change from cut to fill — the ground passes through the formation level Minimum (trough) Change from fill to cut Any horizontal line (balancing line) Cuts the curve at two points between which the cut exactly balances the fill; the length intercepted is the balancing distance and the area between the line and the curve is proportional to the haul Curve above the balancing line Haul is from left to right (forward) Curve below the balancing line Haul is from right to left (backward) Vertical distance between a maximum and the following minimum The volume of earth moved in that loop Area between the curve and the balancing line Haul = volume × distance (in station-metres or m³-km); dividing by the volume gives the average haul distance Free haul / overhaul Free-haul distance is the distance within which transport is included in the excavation rate; volume moved beyond it is overhaul and is paid separately Curve ending above the start Surplus material to be wasted; ending below means borrow is required • The engineer chooses the balancing line(s) that minimise the total haul (the area between curve and line) while respecting the free-haul distance and the limit of economical haul — the distance beyond which it is cheaper to borrow and waste than to haul.

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Short balancing lines with small loops mean cheap, local earth movement; long loops mean expensive haulage.