Road Engineering Chapter 1-3 PDF

ROAD ENGINEERING-I-4 JIGJIGA UNIVERSITY JIGJIGA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING Lecturer : ADEN 2024 Reference: wright(1996) Highway Engineering  Course content 1. Introduction 2. Route selection 3. Geometric d...

ROAD ENGINEERING-I-4 JIGJIGA UNIVERSITY JIGJIGA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CIVIL ENGINEERING Lecturer : ADEN 2024 Reference: wright(1996) Highway Engineering  Course content 1. Introduction 2. Route selection 3. Geometric design 4. Earth work 5. Intersection design  CHAPTER 1: INTRODUCTION Check points The Environment of Highway Engineering The Highway Engineering Problem Economic Evaluation of Highways Effect of Highways on the Environment  Introduction ✓The route location problem ❖The route location problem is to establish, initially, a general location, or a narrow band, within which a more precise alignment would be finally designed.  Introduction ✓The design problem ❖Geometric Design ❖Drainage design ❖Pavement design  Introduction ✓Economic Evaluation of Highways ❖Quantifies the future benefits and costs of proposed highway. ❖ the economic evaluation of highways is generally done by computing the total transport cost which comprises of Construction cost Maintenance cost Road user cost Cost to the society  Introduction ▪ Road user cost is composed of – Vehicle operation cost – Travel time costs – Accident cost ▪ Cost of society includes ✓ Impact on the environment (noise pollution, air pollution, vibration) ✓ Changes in land values ✓ Land severance ✓ Loss of aesthetics  Introduction Effect of highway on the environment ❖The effect of highways and traffic on the environment will be of the following type: ✓Noise pollution ✓Air pollution ✓Visual intrusion and degrading the aesthetics ✓Community impact: relocation of individuals and families.  Introduction ✓The Environment of Highway Engineering The physical environment Technological environment The economic environment Social environment  2.HIGHWAY ALIGNMENT AND ROUTE LOCATION ✓Aim of route and alignment location ✓Guidelines/steps of route and alignment location ✓Reconnaissance survey and its importance ✓Preliminary location survey and its elements ✓Final location survey  Aim of route and alignment location ❖ In general, the aim of alignment selection process is to find a location for the new road that will result in the lowest total construction, land, traffic and environmental costs ❖ Data's needed for the prior to the location of the route Traffic data Future characteristics of the highway  Basic steps in route location ▪ Know the termini points of the scheme. ▪ From the study of a map of the area, identify and locate: – National parks – Existence of monasteries – Mining sites – Existing transport facilities – Other public facilities (electricity, water) – Location of construction materials ▪ Conduct preliminary and reconnaissance surveys and collect information on pertinent details of topography, climate, soil, vegetation, and any other factors.  Basic steps in route location… ▪ Based on the information collected in the previous two steps select a corridor. ▪ Identify a number of possible centerlines within the corridor. ▪ Make a preliminary design for the possible alternative alignments and plot on a base map. ▪ Examine each of the alternative alignment with respect to grades, volume of earthwork, drainage, crossing structures, etc to select the best alternative route. ▪ Make final design and location of the selected best alternative route.  Requirements of an ideal alignment ▪ Requirements of an ideal alignment between two terminals include: – Short ▪ A straight alignment would be the shortest, though there may be several practical considerations which would cause a devation from the shortest path – Easy ▪ Easy to construction ▪ Easy to maintain ▪ Easy for operation with easy grades and curves  Requirements of an ideal alignment – Economical ▪ Design should consider initial capital cost, maintenance cost, and operation cost – Safe ▪ Safe enough for construction and maintenance from the view point of stability of natural slopes, embankments, cut slopes, and foundations ▪ Safe for traffic operations with easy geometric features such as sharpness of curves, grades, side slopes and etc.  Factors Controlling Highway Alignment ▪ Obligatory Points – Points through which the alignment is to pass – Chosen Bridge Site, Intermediate town to be accessed between the termini, a mountain pass, etc. – Points which should be avoided – Areas requiring costly structures, highly developed expensive areas, marshes and low lying lands subject to flooding, hilly terrain where there is a possibility of land slides, etc.  Factors Controlling Highway Alignment ▪ Traffic – The alignment should suit the traffic requirements – Present and future travel patterns should be observed & forecasted ▪ Geometric Constraints – Design factors such as max. gradient, minimum radius of curve, minimum available sight distance, maximum allowable super-elevation, etc. should be within the limits of allowable design values which are governed by the expected traffic speed  Factors Controlling Highway Alignment ▪ Economy – Total transportation cost including initial construction cost, maintenance cost, and operation cost ▪ Example : – Deep cuttings, high embankments, no of bridges that need to be constructed, etc. increases the initial cost of construction. ▪ Other considerations – Drainage considerations – Hydrological factors – Political considerations – Monotony  Route Location Surveys ▪ In order to select the best road corridor, the following engineering surveys are usually carried out: ▪ Reconnaissance Surveys ▪ Preliminary Surveys ▪ Detailed (Location) Surveys  Reconnaissance Surveys ▪ 1st phase of Reconnaissance: Desk Study – Involves an examination of a relatively large area between terminal points for the purpose of determining a broad corridors through which a road alignment may pass – Usually such survey is made by the use of available maps and Aerial Photographs (stereoscopy) ▪ Probable Alignment is identified on the map by: – Avoiding valleys, ponds, etc.; – Avoiding river bends where bridges should not be located; – Keeping in view of geometric standards (e.g. avoiding steep topographies, etc)  Reconnaissance Surveys ▪ 2nd phase of Reconnaissance: Field Study – Involves inspection of each band (identified during the desk study) to determine the most feasible route based on some basic criteria – A survey party inspects a fairly broad stretch of land along the proposed routes identified on the map during the 1st phase and collects all relevant details not available on the map – Some of the details include: ▪ valley, ponds, lakes, marshy land, ridge, hills, permanent structures, & other obstructions; ▪ gradient, length of gradient, and radius of curves; ▪ number & types of cross-drainage structures, and maximum flood level; ▪ soil types from field identification; ▪ sources of construction materials, water and location stone quarries; ▪ geological formation, type of rock, depth of strata, seepage flow, etc to identify stable sides of a hill – A rapid field study of the area, especially, when it is vast and the terrain is difficult may be done by aerial survey  Criteria to evaluate the most feasible routes ▪ Design standards – Minimum design standards (max permissible gradient, etc ) are normally fixed prior to the survey and any one of the feasible routes that economically fits in these standards would be feasible ▪ Grading and Earthwork – Grading is a function if ruggedness of terrian and routes following contour is cheaper – The type of material encountered is another factor in the cost of earthwork. Excavation of Hard Rock might need blasting and thus expensive!! ▪ Foundation Conditions – Complete foundation study is not done during Reconnaissance, but the presence of Marshy and bogy areas are unsuitable ▪ Geological Conditions – Related to stability of side slopes, good quality and quantity of construction materials near site ▪ Drainage – Likely surface & sub-surface drainage problems, type and number of drainage structures  Criteria to evaluate the most feasible routes ▪ Right of Way – Acquisition of land for the location of a transportation system may cost much; shifting the alignment a little may reduce the cost considerably ▪ Effect on Population – Services offering the nearby population, its effect on the development of the community – schools, churches, public buildings, etc, undesirable effects such as pollution, etc ▪ Traffic Characteristics – how best will a route fit with traffic requirements of the area ▪ Maintenance Costs – An extraordinary maintenance cost (landslide,etc), and user costs from inconveniency due to closure of the facility due to maintenance problems After evaluating the alternative routes proposed, one or more routes will be recommended. If more than one routes passed the reconnaissance survey detail study is made to  Preliminary Surveys ▪ Consists of running an accurate traverse line along the routes already recommended as a result of reconnaissance survey in order to obtain sufficient data for final location ▪ Objectives – Survey and collect necessary data (topography, drainage, soil, etc.) on alternate alignments – To estimate quantity of earthwork, material, … of different alternatives – Compare alternate alignments – Finalize the best alignment from all considerations  Preliminary Surveys Cont.d ▪ The preliminary survey may be carried out by one of the following two methods: – Modern: Aerial Survey – using photo interpretation techniques, information on topography, soil, geology, etc. can be obtained – Conventional: a survey part carries out surveys using the require field equipment taking measurements, collecting topographical and other data and carrying out soil survey  Preliminary Surveys Cont.d ▪ Note After finishing the preliminary survey Select the most suitable alignment by conducting a comparative study considering economy, geometry, etc.  Final Location Survey Purpose to fix the centre line of the selected alignment and collect additional data for the design and preparation of working drawings. If extensive data is collected earlier the survey work here might be limited.  Tasks during Final Location Survey 1. Pegging the centre line: usually done at stations established at 30m intervals with reference to preliminary traverse/ base line (if used earlier) or a control survey (if aerial survey was used). 2. Centre-line Levelling: at the stations and at intermediate points between stations where there is a significant change in the slope to obtain the representative profile of the ground  Tasks during Final Location Survey Cont.d.. 3. Cross-section Levelling: at each station and at points with significant change in ground slope 4. Intersecting Roads: the directions of the centre line of all intersecting roads, profiles, and cross-sections for some distance on both sides 5. Ditches and Streams: horizontal alignment, profile, and cross section levelling of the banks of the stream/river  Drawings & Reports ▪ The data, after the necessary investigation and final location survey, is sent to the design office to be used for – geometric design, pavement design, and design of drainage and other structures, preparation of drawings, reports, and specifications ▪ A complete sets of drawings for a road design includs: – Site plan of proposed alignment – Detailed Plan & Profile – Cross-sections for Earth work – Typical Roadway sections at selected locations (e.g. junctions) – A mass-haul diagram – Construction details of structures like bridges, culverts, ….  Chapter -3 Geometric Design of Highways Design controls and criteria ✓ The elements of design are influenced by a wide variety of factors which includes the following: ▪ Functional classification of the roadway ▪ Projected traffic volume and composition ▪ Required design speed ▪ Topography of the surrounding land ▪ Capital costs for construction ▪ Human sensory capacities of roadway users ▪ Vehicle size and performance characteristics Geometric Design of Highways ▪ Traffic safety considerations ▪ Environmental considerations ▪ Right-of-way impacts and costs ✓ Note: Of all the factors that are considered in the design of a highway, the principal design criteria are traffic volume, design speed, sight distances, vehicle size, and vehicle mix.  Geometric Design of Highways Design Speed and Design Class ❖Design speed is the max safe speed selected for designing specific section of road considering the terrain, land use, classification of the road, etc. ❖The choice of design speed will depend primarily on the surrounding terrain and the functional class of the highway. ❖Other factors determining the selection of design speed include traffic volume, costs of right-of-way and construction, and aesthetic consideration. Geometric Design of Highways Note: It is therefore recommended that the basic parameters of road function, terrain type and traffic flow are defined initially. ✓ On the basis of these parameters, a design class is selected, while design speed is used only as an index which links design class to the design parameters of sight distance and curvature to ensure that a driver is presented with a reasonably consistent speed environment. Geometric Design of Highways ▪ Using road functional classification selection, terrain type and design traffic flow, a design class, or standard, is selected from Table 2-1, with reference to the design parameters associated with that class as given in Tables 2- 2 through 2-12.(see ERA geometric design manual) Road Hierarchy (The Ethiopian way) Roads linking centers of international importance and roads Trunk roads terminating at international boundaries and have a present AADT 1000 and as low as 100. Roads linking centers of national or international importance Link roads and have over 400 - 1000 first year AADT, although values can range between 50-10,000 AADT. Roads linking centers of provincial importance and their first Access roads year AADTs between 30-1,000. Roads linking locally important centers to each other, to a Collector roads more important center, or to higher class roads and their first year AADTs between 25-400. Any road link to a minor center such as market and local Feeder roads locations with first year AADT between 0-100. 40  Nature of Terrain ▪ The location and geometric design elements such as gradients, sight distance, cross-sections, radius of curvature, speeds, etc. of a highway are affected by topography, physical features, and land use. ▪ Transverse terrain properties are categorized into four classes as follows: ▪ FLAT: Flat or gently rolling country, which offers few obstacles to the construction of a road, having continuously unrestricted horizontal and vertical alignment (transverse terrain slope up to 5 percent).  Nature of Terrain ▪ ROLLING: Rolling, hilly or foothill country where the slopes generally rise and fall moderately and where occasional steep slopes are encountered, resulting in some restrictions in alignment (transverse terrain slope from 5 percent to 25 percent).  Nature of Terrain ▪ MOUNTAINOUS: Rocky, hilly and mountainous country and river gorges. This class of terrain imposes definite restrictions on the standard of alignment obtainable and often involves long steep grades and limited sight distance (transverse terrain slope from 25 percent to 50 percent).  Nature of Terrain ▪ ESCARPMENT: Escarpment include situations where switchback roadway sections are used or side hill transverse sections which cause considerable earthwork quantities, with transverse terrain slope in excess of 50 percent.  Traffic Volume and Composition ▪ Traffic data indicates the service for which the road is being planned and directly affects the geometric elements such as width, alignment, etc, – Traffic volume – AADT, ADT, PHV, DHV – Directional distribution – the percentage of traffic volume flowing in each direction – Traffic composition – the percentage of different types of vehicles in the traffic stream – different types of vehicles are converted into passenger car unit to design a road width – Traffic projection – using the design period of a road (5-20 years)a reliable traffic projection should be made considering the following elements  Traffic Volume and Composition – Traffic projection (cont’d.):– ▪ Current traffic – currently using the existing road ▪ Normal traffic growth – anticipated growth due to population growth or change in land use ▪ Diverted traffic – traffic that switches to a new facility from near by roads ▪ Converted traffic – traffic resulting from changes of mode ▪ Change of destination traffic – traffic that has changed to different destination due to new or improved transport and not changes in land use ▪ Development traffic – traffic due to improvement on adjacent land development that would have taken place had the new or improved road not been constructed ▪ Induced traffic – traffic that did not previously exist in a any form but results when new or improved transport facilities are provided  Speed ▪ Design speed is the max safe speed selected for designing specific section of road considering the terrain, land use, classification of the road, etc. Elements of Road Cross-section  Sight Distance ▪ Sight Distance is the distance visible to the driver of a vehicle. ▪ Stopping sight distance ▪ Passing sight distance ✓ For highway safety, the designer must provide sight distances of sufficient length so that drivers can control the operation of their vehicles. They must be able to avoid striking an unexpected object on the traveled way.  Stopping sight distance ▪ Stopping sight distance is the total distance traveled by a given vehicle before stopping during three time intervals ▪ the time to perceive the hazard ▪ the time to react ▪ the time to stop the vehicle ▪ During the first two intervals, the vehicle travels at full speed, during the third interval, its speed is reduced to zero, and must happen before hitting an object or vehicle ahead.  Stopping sight distance ✓ Reaction distance …….The distance before breaks are applied Dr = 0.278 Vt Where: – Dr = total reaction distance in m; – V = initial vehicle speed in Km/h – t = reaction time in sec…….taken as 2sec  Stopping sight distance ✓ Braking distance Where: Db = braking distance V2 Db = V = initial velocity when brakes are 254( f  G ) applied f = coefficient of friction G = grade (decimal)  Stopping sight distance V2 SSD = (0.278)(t )(V ) + 254( f  G ) SSD = Stopping Sight Distance (meter) = Dist. traveled during perception/reaction time + Braking Dist. t = Driver reaction time, generally taken to be 2.5 seconds V = Initial speed (km/h) f = Coefficient of friction between tires and roadway 53  Effect of Grade of SSD ▪ On grade, the braking distance formula is modified to V2 d= 254( f  G ) Where G=percent of grade divided by 100 Note: Safe SSD on upgrades is shorter than on downgrades Min. SD should be adjusted where steep grades and high speed occur in combination  Coefficient of friction, f Pavement condition Maximum Minimum Good, dry 1.00 0.80 Good, wet 0.90 0.60 Poor, dry 0.80 0.55 Poor, wet 0.60 0.30 Packed snow and Ice 0.25 0.10  Passing Sight Distance ▪ Minimum distance required to safely complete passing maneuver on 2-lane two-way highway ▪ Allows time for driver to avoid collision with approaching vehicle and not cut off passed vehicle when upon return to lane ▪ Assumes: – Vehicle that is passed travels at uniform speed – Speed of passing vehicle is reduced behind passed vehicle as it reaches passing section – Time elapses as driver reaches decision to pass – Passing vehicle accelerates during the passing maneuver and velocity of the passing vehicle is about 16km/hr greater than that of the passed vehicle – Enough distance is allowed between passing and oncoming vehicle when the passing vehicle returns to its lane  Passing Sight Distance ▪ The passing sight distances recommended for use by Overseas Road Note 6 are shown in table below ▪ Table: passing sight distance Design 50 60 70 85 100 120 speed (km/h) Psd(m) 140 180 240 320 430 590  Geometric Design Elements 1.Horizontal Alignment: ❖ Minimum curve radius (maximum degree of curvature); ❖ Minimum length of tangent between compound or reverse curves; ❖ Transition curve parameters; ❖ Minimum passing sight distance and stopping sight distance on horizontal curves.  Geometric Design Elements 2. Vertical Alignment: ❖ Maximum gradient; ❖ Length of maximum gradient; ❖ Minimum passing sight distance or stopping sight distance on summit (crest) curves; ❖ Length of sag curves.  Geometric Design Elements 3. Cross-section: ❖ Width of carriageway; ❖ Cross fall of carriageway; ❖ Rate of super elevation; ❖ Widening of bends; ❖ Width of shoulder; ❖ Cross fall of shoulder; ❖ Width of structures; ❖ Width of right-of-way; ❖ Sight distance; ❖ Cut and fill slopes and ditch cross-section.  Geometric Design Elements ✓ Note: Horizontal and vertical alignment should not be designed independently. They complement each other and proper combination of horizontal and vertical alignment, which increases road utility and safety, encourages uniform speed, and improves appearance, can almost always be obtained without additional costs.  Horizontal Alignment 1. Straights (Tangents ) ✓ The following guidelines may be applied concerning the length of straights: ❖Straights should not have lengths greater than (20 * V) meters, where V is the design speed in km/h. ❖Straights between circular curves turning in the same direction should have lengths greater than (6*V) meters, where V is the design speed in km/h. ❖Straights between the end and the beginning of un transitioned reverse circular curves should have lengths greater than two-thirds of the total super elevation run-off  Horizontal Alignment 2. Circular Curves Note: PC – point of curvature PI – point of intersection PT – point of tangency Δ – central angle R – radius of curve D – degree of curve that defines, Central angle which subtends 20m arc (arc definition), Central angle which subtends 20m chord (Chord definition) Figure 3.1: Parts of a Circular Curve  Horizontal Alignment Degree of Curvature Arc Definition 20 2R 1145.92 D = 360 D= R Chord Definition R = 10 / Sin (D/2) Relations T = R tan(  / 2) C = 2 R sin( / 2) L = R E = Rsec( / 2) − 1 M = R1 − cos( / 2) 65 Conti… Conti….  Exercise ▪ Check that E = R*(Sec (Δ/2) – 1 or E = T*tan (Δ/4) and Lc = 20* Δ/D or Lc = R*π* Δ/180  Successive curves ▪ There are three cases of successive curves Compound curves  Reverse curves Are adjacent curves that curve in opposite direction  Stability of a VEH To avoid overturning mV h / R  mgb  V h / R  gb 2 2 To avoid side slip mV / R  mg  V / R  g 2 2 mV 2 / R h F mg R’ b 72  Stability on Super-elevated Surface Forces & Equilibrium Resolving the Forces // and |to the road (// to the road) e Wv 2 1 F + WSin = Cos gR W (| to the road) Wv 2 Wv 2 F WCos + Sin = N gR gR  N Frictional force, F=N 73  Relations (cont.) Wv 2 N = Cos − WSin gR Wv 2  Wv 2  Sin + WCos  = Cos − WSin  gR  gR  v 2   v2  Sin  + 1 = Cos  −   gR   gR  v2 But the term v 2 has a very small value and − gR Tan = gR could be ignored for all practical purposes. v 2 Check using typical values like V=50km/hr; +1 gR =0.16; and R=100m. 74  Relations (cont.) v2 V=Km/hr Thus, Tan = − =e gR R=m v 2 (V 3.6) e=m/m 2 V2 e+ = = = =dimensionless gR 9.81R 127R 75  Super-elevation rate, e ▪ Is the raising of the outer edge of the road along a curve in-order to counteract the effect of radial centrifugal force in combination with the friction between the surface and tyres developed in the lateral direction ▪ Maximum value is controlled by: – Climatic conditions: frequency & amount of snow/icing – Terrain condition: flat vs. mountainous – Area type: rural vs. urban – Frequency of very slow moving vehicles ▪ 0.1m/m is a logical maximum super-elevation ▪ Minimum super-elevation rate is determined by drainage requirements ▪ UK emax: 0.07 (rural) & 0.05 (urban) 76 Maximum Degree of Curvature ▪ minimum radius for safety (veh. stability) ▪ Limiting value for a given design speed (given emax & max) V2 Rmin = 127(e +  ) ▪ The respective maximum Degree of Curvature is: D max = 1145.92 = 1145.92 = 143240(e +  ) Rmin V 2 127(e +  ) V2 ▪ Sharper Curve might justify use of e>emax or a higher dependence on tyre friction or both 77  Super elevation ▪ Asignment1 1: Show that e + f = V2 / (127*R) where: e = rate of super elevation (m per m) f = side friction factor (or coefficient of lateral friction) V = speed (Km/hr) R = radius of curvature (m) 2: define super elevation  Transition Curves spirals are curves which provide a gradual change in curvature from tangent to a circular path Advantages: Provides an easy-to-follow path so that centrifugal force increases and decreases gradually; lesser danger of overturning/ side-slipping Is convenient for the application of super-elevation Improved visual appearance, no “kinks” 79  Transition Curves - Geometry PI: Point of Intersection TS: Tangent to spiral SC: Spiral to Circle CS: Circle to Spiral ST: Spiral to tangent Ls: Total length of spiral Lc: Length of circular curve s: Central angle of spiral arc of length Ls ∆=total deflection angle of the curve Ys=tangent offset at SC Xs= K=abscissa of shifted PC with reference to TS 80  Important relations of spirals ▪ L = 2Rθ ▪ θ = (L / Ls)2 * θs ▪ θs = Ls / 2Rc (in radians) = 28.65Ls / Rc (in degrees) ▪ Ts = Ls /2 + (Rc + S)*tan(Δ/2) ▪ S = Ls2 / 24Rc ▪ Es = (Rc + S)*sec(Δ/2) - Rc  Length of Transition ▪ The length of transition should be determined from the following two conditions: ✓ The rate of change of centrifugal acceleration adopted in the design should not cause discomfort to the drivers. If C is the rate of change of acceleration, ❖ Ls = 0.0215V3 / (C*Rc) Where: V = speed (Km/hr) Rc = radius of the circular curve (m) ✓ The rate of change of super elevation (super elevation application ratio) should be such as not to cause higher gradients and unsightly appearances.  Widening of Highway Curves The widening required can be calculated from ▪ We = n *B2/ 2R + V / 10 Where: We = total widening B = wheel base R = radius of curve V = design speed (Km/hr) n = number of lanes  Vertical Alignment ▪ Consists of straight sections of the highway known as grades, or tangents, connected by vertical curves. ▪ The design involves the selection of suitable GRADES for the tangent sections and the design of the VERTICAL CURVES. ▪ The topography of the area through which the road traverses has a significant impact on the design of the vertical alignment. 84  GRADES ▪ Effect of grade is more pronounced on Heavy Vehicles than on Passenger Cars ▪ Maximum Grade on a highway should be carefully selected based on the design speed and design vehicle ▪ grades of 4 to 5 %  little or no effect on passenger cars, except for those with high weight/horsepower ratios, ▪ grade > 5% speed of passenger cars decrease on upgrades and increase on downgrades. ▪ truck speeds may increase up to 5 percent on downgrades and decrease by 7 percent on upgrades 85  Maximum Grade Design Speed Maximum Grade 110 kph 5% 50 kph 7-12% 60 to 100 kph Intermediate Very Important highways 7-8% Short grades less than 150m 1% steeper & one-way downgrades Low volume highways 2% steeper 86  Minimum Grade ▪ depend on the drainage conditions of the highway ▪ zero-percent grades may be used on uncurbed pavements with adequate cross slopes to laterally drain the surface water ▪ for curbed pavements, however, a longitudinal grade should be provided to facilitate the longitudinal flow of the surface water ▪ a minimum grade of 0.5% is usually used; it may reduced to 0.3% on high-type pavement constructed on suitably crowned, firm ground. 87  Critical Length of Grade ▪ indicates the maximum length of a designated upgrade on which a loaded truck can operate without an unreasonable reduction in speed ▪ For a given grade, lengths less than critical result in acceptable operation in the desired range of speeds. ▪ to maintain LOS on grades longer than critical – change in location to reduce grades – addition of extra lanes (climbing or crawler lanes): data for critical lengths of grade are used with other pertinent considerations (such as traffic volume in relation to capacity, % heavies) to determine where added lanes are warranted. ▪ To establish design values for critical lengths of grade data or assumptions are needed on the following: – Size and power of representative truck or truck combination to be used as a design vehicle – Speed at entrance to critical length grade – Minimum speed on the grade below which interference to following vehicles is considered unreasonable 88  Effect of Grade Speed-distance curves for a typical heavy truck of 180kg/kw for deceleration on upgrades 89  Vertical Curves ▪ are parabolic curves used to provide a gradual change from one tangent grade to another so that vehicles may run smoothly as they traverse the highway. ▪ Are of two types – Sag Vertical Curves – Crest Vertical Curves ▪ Design Criteria for vertical curves – Provision of minimum stopping sight distance – Adequate drainage – Comfortable in operation – Pleasant appearance The first criterion is the only criterion associated with crest vertical curves, whereas all four criteria are associated with sag vertical curves. 90 Types of Vertical Curves 91  Crest Vertical Curves ▪ Minimum length of the vertical curve (L) is determined by sight distance (SD) requirements ▪ That length is generally are satisfactory from the standpoint of safety, comfort, and appearance. ▪ Derivation is done for the two cases of: – SD > L – SD < L 92  Crest Vert. Curves minimum length when S>L Vehicle on the grade at C H1 height of the driver's eye at C H2 height of an object at D PN is line of sight, and S is the sight distance Note that the line of sight is not necessarily horizontal, but in calculating the sight distance, the horizontal projection is considered 93  Crest Vert. Curves Min. length – Derivation (S>L) From the properties of the parabola, X3 = L/2 The sight distance S is then given as S = X1 + L/2+ X2 X1 and X2 can be found in terms of the grades G1 and G2 and their algebraic difference A. The minimum length of the vertical curve for the required sight distance is obtained as L = 2S − ( 200 H 1 + H2 ) 2 A where, L = length of vertical curve, m S = sight distance, m A = algebraic difference in grades, % H1 = height of eye above roadway surface, m H2 = height of object above roadway surface, m 94 ▪ When the height of eye and the height of object are 1070 mm and 150 mm, respectively, as used for stopping sight distance, the length of the vertical curve is, 404 L = 2S − A  Crest Vert. Curves Min. length – Derivation (S L, L = 2 S − A AS 2 When S < L, L = 946 97  Sag Vertical Curves Design Criteria: 1. Headlight sight distance 2. Rider Comfort 3. Drainage Control 4. Aesthetics (rule of thumb) 98  Headlight Sight Distance, S Height of the headlight =600mm Upward divergence of the light beam = 1o (The upward spread of the light beam provides some additional visible length, but that is generally ignored.) 99  Length of curve with adequate SD When SL: 200(0.6 + S tan  ) 120 + 3.5S L = 2S − = 2S − A A L=length of curve (m), A=algebraic difference in grade (%), and S=headlight distance (m) 100  Length of Curve for comfort ▪ Considers that both the gravitational and centrifugal forces act in combination, resulting in a greater effect than on a crest vertical curve ▪ Comfort is affected by: – weight carried, body suspension of the vehicle, and tire flexibility – Measuring Comfort = Difficult! – Indicator = radial acceleration is not greater than 0.3 m/s3 ▪ The general expression for AV 2 such a criterion is: L= 395 V is the design speed, km/h. ▪ Usually this length is about 50 percent of that required to satisfy the headlight sight distance at various design speeds (for normal conditions). 101  Min. Length for Aesthetics ▪ Rule of thumb Lmin = 30 A ▪ Longer curves are necessary for high type of highways to improve appearance. 102  Max. Length of Curve for drainage Here the drainage criteria sets a limit on the MAXIMUM length of curve! ▪ Long curves would have a relatively flat portion near the bottom of curve ▪ A min. grade of 0.3% should be provided with in 15m of the level point of the curve ▪ Max length (drainage) is usually greater than min. length for other criteria up to 100kph and nearly equal to min length for other criteria up to 120kph 103  Cross section 1. Right- Of –Way ✓ The right-of-way should be adequate to accommodate all the elements that make up the cross-section of the highway and may reasonably provide for future development. 2. Road Width ✓ Road width should be minimized so as to reduce the costs of construction and maintenance, whilst being sufficient to carry the traffic loading efficiently and safely. The following factors need to be taken into account when selecting the width of a road: a. Classification of the road b. Traffic c. Vehicle dimension d. Vehicle speed  Cross section 3. Shoulders ✓ Shoulders provide for the accommodation of stopped vehicles ✓ Properly designed shoulders also provide an emergency outlet for motorists finding themselves on a collision course ✓ they also serve to provide lateral support to the carriageway 4. Cross-Fall ✓ According to Overseas Road Note 6 the normal cross-fall should be 3% on paved roads and 4 – 6% on unpaved roads.  Cross section ✓ To avoid the rutting developing into potholes a cross-fall of 5 – 6% should be reestablished during the routine and periodic maintenance works. 5. Side slopes ✓ Using these relatively steep slopes will result in minimization of earthworks, but steep slopes are, on the other hand, more liable to erosion than flatter slopes as plant and grass growth is hampered and surface water velocity will be higher.