Road Design and Traffic Analysis: Ethiopian Road Project, Study notes of Earth science

Download Road Design and Traffic Analysis: Ethiopian Road Project and more Study notes Earth science in PDF only on Docsity! Contents CHAPTER ONE..............................................................................................................................4 1. INTRODUCTION.......................................................................................................................4 1.1 Objective of the project.......................................................................................................4 1.1.1 General objective.............................................................................................................4 1.1.2 Specific objective............................................................................................................4 1.2 Project location and description.........................................................................................5 CHAPTER TWO.............................................................................................................................5 2. ROUTE SURVEYING................................................................................................................5 2.1 Introduction..........................................................................................................................5 2.2 Types of route surveying.....................................................................................................7 2.2.1 Desk study.......................................................................................................................7 2.2.2 Reconnaissance survey....................................................................................................8 2.2.3 Preliminary survey..........................................................................................................8 2.2.4 Final location survey.......................................................................................................8 2.2.5 Drawings and reports.......................................................................................................9 2.3 Route Selection.....................................................................................................................9 CHAPTER THREE.......................................................................................................................10 3. TRAFFIC ANALYSIS AND LOADING.................................................................................10 3.1 Introduction........................................................................................................................11 3.3.2 Traffic Count.................................................................................................................11 3.4 Traffic Growth Rate (Traffic Forecast)...........................................................................12 3.4.1Types of traffic...............................................................................................................13 3.4.2 Design Period................................................................................................................14 3.4.3 Initial Traffic Volume (AADT).....................................................................................14 3.4.4 Vehicle Classification....................................................................................................14 3.4.5 Axle Load Survey............................................................................................................15 3.4.6 Truck Factor..................................................................................................................15 3.4.7 The Design vehicle........................................................................................................15 3.4.8 Design Traffic Loading.................................................................................................15 3.5 Road Functional Classification.......................................................................................16 3.6 Vehicle Classification.........................................................................................................17 3.7 Traffic Survey.....................................................................................................................17 3.8 Design of Traffic volume...................................................................................................24 Chapter four 4.Geometric designs................................................................................................29 4.2.1 Design Controls and Criteria.........................................................................................32 4.2.2 Terrain Type..................................................................................................................32 4.3 Road Functional Classification and Numbering.............................................................34 4.4 Geometric Design Standards.............................................................................................36 4.5 Geometric Design Elements..............................................................................................39 4.5.1 Cross Section Element...................................................................................................39 4.5.2. Lane Width...................................................................................................................39 4.5.3 Shoulder.........................................................................................................................40 4.5.6. Road side ditch.............................................................................................................41 4.5.7. Right of way.................................................................................................................41 4.5.8. Clear Zone....................................................................................................................42 4.6 Elements of Geometric Design..........................................................................................42 4.6.1 Horizontal alignment.....................................................................................................42 4.6.2 Design element of horizontal alignment.......................................................................43 4.6.3 Widening on curves and embankment..........................................................................46 4.6.4 Sight distance................................................................................................................47 4.6.5 Super elevation..............................................................................................................53 4.7 Vertical alignments............................................................................................................63 4.7.1 Crest Curves..................................................................................................................64 4.7.2 Sag Curves.....................................................................................................................67 4.7.3 Minimum Length of Vertical Curves............................................................................69 4.7.4 Gradient.........................................................................................................................69 4.7.8 Critical Length of Gradient...........................................................................................71 CHAPTER five..............................................................................................................................99 PAVEMENT DESIGN..................................................................................................................99 5.1 INTRODUCTION..............................................................................................................99 CHAPTER ONE 1. INTRODUCTION Transportation can be defined as movement of people and goods from one location to another. Transportation touches each one of us every day in all aspects of our lives. There are different modes of transportation systems such as Road transport, Air transport, Rail transport and Water transport and Highway transportation or road transportation. But in this document, we concern on road transportation, because it is important part of our life, the economy of the society as well as it is part of the infrastructure. Also it is important for the change location of humans, goods and information. The better of this structure is the faster, more effective and cheaper, can be the capacities of the society used. 1.1 Objective of the project 1.1.1 General objective The main objective of this project is to let students visualize conceptual ideas to quantifiable realities which could actually be implemented to the ground. And to help students apply the design parameters and design principles learned for the past 4 years. 1.1.2 Specific objective The specific objective of the project is applying technological and scientific principles to other planning, functional design and operation. To design safe and appropriate road for the fast growing traffic for the desired location  To provide access for the society to get social services (schools, health center…)  To develop problem solving ability on real life project  Exercise working manuals like ERA, AASHTO, etc...  To gain working experience and further knowledge on highway design  To know the principal designing criteria of high way  To develop integration and communication skills in a group project working. 1.2 Project location and description CHAPTER TWO 2. ROUTE SURVEYING 2.1 Introduction Any alignment of route surveying and design for the selected route is needed a detail route survey to understand the terrain, hydrology, and any other important parameters which affect the alignment of the route. For road alignment project highway surveying of the area is essential for best route selection, ease of design and to be economical. Road design, construction and maintenance require an approach depending on the terrain. The primary task in high way design is the selection of possible alignment from the available topographic map or data. This establishes the center line of the proposed road in plan on the ground. The selection of the best route is influenced by various factors. The shortest Road alignment is not necessarily the easiest, quickest or most economical option for construction and maintenance. In general, the aim of a highway route selection process is to find a location for the new road that will result in the lowest total construction, level, traffic and environmental costs. Requirements of ideal alignment:  Short  Easy(construction ,maintenance, vehicle operation)  Economical (initial coast, maintenance cost, operation cost)  Safe(low accident ,stable foundation) Before an attempt can be made at selecting a physical location for a highway design, data must be available regarding traffic desires and the planning intentions with in the area to be transverse. Factors controlling alignment are:  Obligatory points  Traffic  Geometric design,  Economics and  Other considerations Obligatory points: Those are points which tell us Points through which the alignment is to pass (Bridges sites, Intermediate town between terminals and Mountainous pass) and Points through which the alignment should not pass (Very costly structures, highly developed expensive land areas, cultural or religious places and Hospitals, schools). Traffic: The alignment should suit traffic demand and kept in view of the desire lines, flow patterns and future trend. Geometric design: This includes grades, radius of curves, sight distance then first determines standard of the road and then fix the geometric standards. Economy: Includes the initial cost, maintenance cost and operation cost that means if high embankment and deep cuts are avoided there would be a decrease in initial cost. Other considerations: That includes drainage consideration, guide the vertical alignment, hydrological factors, subsurface water level, seepage flow, high flood level and Political considerations. 2.2 Types of route surveying The purpose of the route survey is to fix the road alignment such as to position the central line of the road on the ground. The work of the highway location survey may include: design, and estimation of bill of quantities. A complete set of drawings for the highway may contain the following.  Site plan of the alignment  A detailed plan and profile  Cross sections for earth work at all necessary locations  Typical road sections at selected sections such as junctions  A mass-haul diagram showing the movement of earth work  Construction details of structures like culverts, bridges, retaining wall 2.3 Route Selection Route selection is a method of choosing the shortest and best alignment which connects two points. While selecting the best alignment there should be sufficient information about the locality either from well informed technical specialists, local leaders or existing programs on the project. Furthermore, information obtained from contour map of the locality, aerial photos and the like. Photogrammetric are most crucial aids to gather the information of the project area. But in this project study we have given the existing route and survey data and no need of route selection. Fig.3.1 existing route CHAPTER THREE 3. TRAFFIC ANALYSIS AND LOADING 3.1 Introduction Transport projects have to be planned carefully, keeping in view not only the present demand but also future requirements. This underlines the need for counting the present traffic and forecasting the future. The estimate made on the traffic will influence the design of the highway facility and economy of the project Traffic is the most important factor in cross sectional element of highway design, pavement design and stress analysis. Traffic constitutes the load imparted on the pavement causing the stresses, strains and deflections in the pavement layers and sub-grades. The structural parameters required evaluate traffic such as; traffic Volume, AADT are Select design period Estimate initial traffic volume (initial AAD To) per class of vehicle. Estimate traffic growth. Determine traffic volume AADT over the design period. Estimate cumulative AADT over the design period (in one direction). Select appropriate traffic class based on AADT. 3.3.2 Traffic Count Traffic count necessity: To assess the traffic carrying capacity of different types of roads, examine the distribution of traffic between the available traffic lanes. In the preparation of maintenance schedules for in- service roads. In the forecasting of expected t traffics on the proposed new road from traffic Studies on the surrounding road system. Traffic volume data determined from  Historical traffic data available in relevant authorities (ERA, 3 times a year)  By conducting classified traffic counts on the road to be designed- if the road is an Existing road and on other parallel routes and /or adjacent roads – for new roads.  Traffic volume data may vary daily, weekly and seasonally Hence to avoid error in traffic analysis and capture the average yearly trend Minimum seven days count recommended. ERA recommended procedure conduct seven days classified traffic count, 5 days For 12 hrs And Minimum 2 days for 24 hrs. 3.3.2.1 Average Annual Daily Traffic (AADT) It is the average of 24-hour counts collected every day of the year. AADTs are used in several traffic and transportation analyses for:  Estimation of highway user revenues  Computation of crash rates in terms of number of crashes per 100 million  Vehicle miles Establishment of traffic volume trends  Evaluation of the economic feasibility of highway projects  Development of freeway and major arterial street systems  Financial constraints.  Difficulty in forecasting traffic Table 3.2 design period 3.4.3 Initial Traffic Volume (AADT) Traffic volume studies are conducted to collect data on the number of vehicles and/or pedestrians that pass a point on a highway facility during a specified time period. This time period varies from as little as 15 minutes to as much as a year depending on the anticipated use of the data. The data collected also may be put into subclasses which may include directional movement, occupancy rates, vehicle classification, and pedestrian age. Traffic volume studies are usually conducted when certain volume characteristics are needed, some of which follow: 3.4.4 Vehicle Classification Small axle loads from private cars and other light vehicles do not cause significant pavement damage. Damage caused by heavier vehicles (commercial vehicles). Hence, it is important to distinguish the proportion of vehicles which cause pavement damage from total traffic. To do this, we need to have a vehicle classification system between commercial vehicles and small cars according to their type, size (loading), configuration, etc. 3.4.5 Axle Load Survey Axle load survey carried out together with the traffic count and each axle of the vehicles is weighed and EALF computed for each axle. 3.4.6 Truck Factor Track factor can be computed for each vehicle by summing up the number of ESAL per vehicle and average track factor can be computed for each vehicle category by summing up EASL of all Road Classification Design Period (years) Trunk road 20 Link road 20 Main access road 15 Other roads 10 the vehicles in each category and dividing by the number of vehicles (of that category) weighed. EALF= (Lx/8160)4.5 where; EALF= equivalent axle load factor Lx= load of each axle in KN 3.4.7 The Design vehicle Both the physical characteristics and turning capabilities of vehicles are controls in geometric design. The road elements affected include the selection of maximum gradient, lane width, horizontal curve widening, and junction design. 3.4.8 Design Traffic Loading The data and parameters obtained from the studies discussed in the preceding sections can now be used to estimate the design cumulative design traffic volume and loading. Adjust for lane and directional distribution of traffic-the AADT should be adjusted as follows; Lane distribution factor (L) It accounts for the proportion of commercial vehicles in the design lane. For two lane highways, the lane in each direction is the design lane, so the lane distribution factor is 100%. Directional distribution factor (D) Factors that accounts for any directional variation in total traffic volume or loading pattern. Calculating (AADT) (AADT) 1= (AADT) o (1+r) x (AADT) 2022= (AADT) 2018*(1+r) x According to IMF (International Money Fund) the growth rate of Ethiopia are 7% From our project we conclude the Traffic volume at midlife of 10 years based on the annual growth rate from GDP at 10 years of the growth rate 7% per annual up to 2022 years. After 2022 years it was assumed that the growth rate will be reduced to 6% taking into account the fact that the economy in the country shall stabilize and maintain a lower rate of growth. 3.5 Road Functional Classification Trunk Roads (Class I) Centers of international importance and roads terminating at international boundaries are linked with Addis Ababa by trunk roads. Trunk Road usually has a design AADT≥1000, although they can have volumes as low as 150 AADT. Link Roads (Class II) Centers of national or international importance, such as principal towns and urban centers must be linked between each other by link roads. A typical link road has over 300first years AADT, although values can range between75-10,000 AADT. Main Access Roads (Class III) Centers of provincial importance must be linked between each other by main access roads, First year AADT are typically between 150and 300 but can ranges from 25-1,000. Collector Roads (Class IV) Roads linking locally important centers to each other, to a more important center, or to higher class roads must be linked by a collector road. First year AADT ranges from 25-300. Feeder Roads (Class V) Any road link to a minor center such as market and local locations is served by a feeder road. First year AADTs are less than 150. 3.6 Vehicle Classification The types of vehicles are defined according to the breakdown adopted by ERA for traffic counts: cars; pick-ups and 4-wheel drive vehicles such as Land Rovers and Land Cruisers; small buses; medium and large size buses; small trucks; medium trucks; heavy trucks; and trucks and trailers. This breakdown is further simplified, for reporting purposes, and expressed in the five classes of vehicles (with vehicle codes 1 to 5). Table 2.1 Vehicle classification Vehicle Code Type of Vehicle Description Mon 12hrs day 243 71 133 8 6 5 9 7 482 Tue s 12 hrs day 296 131 176 10 16 7 18 6 660   12hrs night 79 21 56 1 2 1 0 0 160   24 hrs 375 152 132 11 18 8 18 6 820 Wed 12 hrs day 323 93 216 5 11 6 13 6 673 Thu r 12 hrs day 276 69 135 7 13 11 9 2 522 Frid 12 hrs day 261 126 111 6 7 4 7 3 525 Satu 12 hrs day 403 139 307 15 17 8 12 3 904   12 hrs night 83 46 63 2 3 0 0 0 197   24 hrs 486 185 370 17 20 8 12 3 1101 Sun 12 hrs day 173 78 106 6 5 4 6 2 380 Description Sm all Car 4W D Sm all Bus L/ Buses Sma ll Tru ck Mediu m Truck Hea vy Tru ck Truc k Trail er Seasonal Conversion Factor (SCF) 0 0.9 5 1.1 0.98 1.18 1.04 0.9 1 Night adjustment Factor:-The night factor was computed using the following relationship. Night Factor (NAF.) = Full of 24hrs count Count from 6hrs to 18hrs in 24hrs count Table 2.4 Computation of average night factor NAFYAD to SOLE TUE Day 321 126 182 12 12 6 12 7 678   NIGHT 71 33 47 2 3 0 0 0 156 24 hrs 392 159 229 14 15 6 12 7 834 NAF 1.2213 1.2619 1.2582 1.166 1.25 1 1 1 1.23 SATUR DAY 442 151 294 13 15 8 16 4 943 NIGHT 98 51 76 3 5 1 0 0 234 24 hrs 540 202 370 16 20 9 16 4 1177 NAF 1.2215 1.3377 1.2585 1.2307 1.333 1.125 1 1 9.5069 Avg 1.2215 1.2998 1.2584 1.1984 1.292 1.0625 1 1 5.3685 Table 2.5 Converting 12 hour count to 24 hour count NAFYAD to SOLE count hours Car 4WD S/ bus L/Bus L/Truck M/ Truck H/Truck T&T TOTA Mon 12hrs day 24hrs 251 307 82 107 141 178 11 14 9 12 4 5 10 10 8 8 516 638 Tue 12 hrs 126 182 12 12 6 12 7 678 s day 321 24hrs 393 164 230 15 16 7 12 7 841 Wed 12 hrs day 24hrs 342 418 98 128 201 253 7 9 10 13 8 9 15 15 5 5 686 848 Thu r 12 hrs day 24hrs 291 356 92 120 122 154 8 10 11 15 12 13 13 13 4 4 553 683 Frid 12 hrs day 24 hrs 233 285 137 179 128 162 2 3 8 11 6 7 5 5 2 2 521 650 Satu 12 hrs day 24hrs 442 540 151 197 294 370 13 16 15 20 8 9 16 16 4 4 943 1170 Sun 12 hrs day 24 hrs 162 198 73 95 112 141 5 6 4 6 3 4 5 5 1 1 365 455 TOTAL ADT1 357 141 213 10 13 8 11 5 755 ADT2 349 126 214 10 13 7 11 5 732 SCF 0 0.95 1.1 0.98 1.18 1.04 0.9 1.04 1.02 AADT0 0 134 234 10 16 9 10 6 419 AADT0 0 120 236 10 16 8 10 6 406 Summation (AADT0) 0 254 470 20 32 17 20 12 825 3.8 Design of Traffic volume A further factor influencing the development of road design standards and in particular the design speed is the volume and composition of traffic. The design of a road should be based in part on actual traffic volumes. Traffic indicates the need for improvement and directly affects features of design such as width, alignment and gradients. Traffic data for a road or section of a road including traffic trends is generally available in terms of annual average daily traffic (AADT). In order to determine the cumulative number of vehicles over the design period of the road, the procedure should be followed: 1. Determine the initial traffic volume, AADT (m1), of each traffic class (m) using the results of the traffic survey and any other recent traffic count information that is available. 2. Estimate the annual growth rate “i” expressed as a decimal fraction, and the anticipated number of years “n” between the traffic survey and the opening of the road. 3. For each vehicle class, estimate the traffic in the first year that the road is opened to traffic. For normal traffic this is given by AADT (m) 1 = AADT (m) 0 (1+i)n Equation 2.1 4. For each vehicle class, add the estimate for diverted traffic and for generated traffic if any are anticipated. For structural pavement design the cumulative traffic loading of each of the motorized vehicle classes over the design life of the road in one direction is required. For a given class, m, this is given by the following equation: T (m) = 0.9x0.5 x 365 x AADT (m) 0 [(1+i/100) N – 1]/(i/100) Equation 2.2 Where T(m) = the cumulative traffic of traffic class m AADT (m) 1 = The AADT of traffic class m in the first year N = the design period in years i = the annual growth rate of traffic in percent Table 2.7Estimation of Growth Rate (i) Macroeconomic Indicators % Change GDP (2011-2020) 2011 11.8 2012 8.65 2013 10.58 2014 10.26 2015 10.39 2016 9.43 2017 9.56 2018 6.82 2019 8.36 Average growth rate(i) 9.54 Normal traffic Normal traffic volume in both directions on the year of the road opening Sample Calculation @ year 2024: AADT (4WD) = AADT (1+i) n Where i= 9.54% n=3 =254(1+0.0954)3=295 Table 2.8 Normal traffic volume in both directions on the year of the road opening (m1) values of 2024 has been used for the traffic volume projection up to year 2044 (i.e., 20years after 3 year construction period) has been used in the design of pavement. This is the AADT at the midlife of the project. AADT (2034) = 1357.This value of AADT is important to determine the design standard for geometric design of the road. Based on the traffic projections as per ERA Design manual-2013 the design standard of the Road is taken as DC-6, our project is link road. Table 4-6 ERA road classification, AADT, carriageway widths and design speed. Based on this our Design standard should be DC6. Chapter four 4.Geometric designs 4.1. Introduction Geometric design is the process whereby the layout of the road through the terrain is designed to meet the needs of the road users. The principal geometric features are the road cross-section , Horizontal alignment and vertical alignment. Geometric design has been carried out with aid of Eagle point design software. The Categories of geometric design Cross section Width of carriage way Width of shoulders Right of way Cross fall, camber and super elevation Horizontal alignment Minimum radius of curve Minimum stopping sight distance Minimum passing sight distance Vertical alignment Maximum gradient Minimum stopping sight distance on vertical curves Length of vertical curve A total 10 horizontal curves are provided ranging from 50m radius to maximum 300m radius. Spiral transitions curves are provided for both flat and rolling terrain with speed of 85 km/hr and 70km/hr respectively according to ERA manual. A total 11 vertical curves gradients are needed and the minimum gradient is 0.38 % whereas the maximum gradient is 9.3%. The minimum curve length is 46m while the maximum curve length is 357m. The k factors which provide sight distances are provided with a minimum value of 8 and a maximum value of 30 for crest and 8& 30 for sag curves. 4.2 Design Vehicle The physical characteristics of vehicles and the proportions of variously sized vehicles using the highway are positive controls in geometric design. Therefore it is necessary to examine all vehicle types, select general class groupings, and establish representatively sized vehicles within each class for design use. The selection of the appropriate design vehicle is a key element in deciding lane width and providing minimum turning paths at the intersections. a) Establishing Design vehicle Design vehicles are selected motor vehicles with the representative weight, dimensions, and operating characteristics, used to establish highway design controls for accommodating vehicles of designated classes. For purposes of geometric design, each design vehicle has larger physical dimensions and a larger minimum turning radius than most vehicles in its class. Based on ERA there are four design vehicles in Ethiopia those are:  Utility vehicle DV1  Single unit truck DV2  Single unit bus DV3  Semi-trailer combination DV4 Table 5-4: Design Vehicle Dimensions and Characteristics Design Vehicle Code Height (m) Width (m) Length (m) Front Overhang (m) Rear Overhan g (m Wheel base(m) Minimum turning radius(m) 4×4 utility DV1 1.3 2.1 5.8 0.9 1.5 3.4 7.3 Single unit truck DV2 4.1 2.6 11 1.5 3 6.5 12.8 Single unit bus DV3 4.1 2.6 12.1 2.1 2.4 7.6 12.8 Truck semi- trailer DV4 4.1 2.6 15.2 1.2 1.8 13.2 13.7 The Largest vehicle size allowed to rover in the country’s road as detailed in “Vehicle Size and Weight (Amendment) Council of Ministers Regulations No.11/1990.”  Total outside width 2.50m  Total length of truck tractor and semi-trailer , including front and rear bumpers 17.00m 1+000 to 2+000 3.45 Rolling 2+000 to 3+000 22.9 Rolling 3+000 to 4+000 12.12 Rolling 4+000 to 5+000 1.42 flat 5+000 to 5+590.79 6.87 Rolling The detailed traverse cross slope computation for the project road is presented in Annex 5.1- of the report. 4.3 Road Functional Classification and Numbering The functional classification in Ethiopia includes five functional classes. The following are the functional classes with their description. Table 16-Functional classification of road Type of class Numbering First Year AADT Accommodations Function Class I Trunk Road A >1000, although has as low as 100 Connecting centers of international importance with capital city Class II Link road B 400-1000, although values can vary from (50- 10000) Connecting towns of international or national importance with urban centers Class-III Main Access Roads C 30-1000 Connecting centers of provisional importance with each other Class IV Collector Roads D 25-400 Link locally important centers to each other Class V Feeder Roads E 0-100 Link any road to a minor center According to the Ethiopian Road Authority Geometric Design Manual, centers of provisional importance must be connected each other by Link access roads that have over 50- 10000 first year AADT. Therefore, the Nafiyad II to sole road is Link access road. 4.3.1 Design Speed The design speed is used as an index which links traffic flow and terrain to the design parameters of sight distance and curvature to ensure that a driver is presented with a reasonably consistent speed environment. In practice, most roads will only be constrained to minimum parameter values over short section or on specific geometric elements. ERA defines Design Speed as the maximum safe speed that can be maintained over a specified section of a road, Design speed is defined as the speed which is used to determine the various geometric design features of the roadway, such as horizontal curve radius, maximum gradient, super-elevation, curtailed sight distance and so on. During selection of design speed factors such as  Functional classification  Topography  Adjacent land use,  Anticipated operating speeds are considered. For the road project from Nafiyad II to sole, the design speed chosen depends on the Design Standard chosen; in this case DS-6. The design speed varies according to the terrain classification and these are presented in table 5-5 below with others geometric design standard 4.3.2 Design standards The design standard of a road is selected based on the design traffic flow (AADT) as shown in the following table 4.4 according to ERA Geometric Design Manual. Table 18- Design Standards vs. Road Classification and AADT 4.4 Geometric Design Standards The geometric design standards provide the link between the cost of constructing the road and the costs of the road users. Geometric standards are not more than a first approximation to design needs, since it is now accepted that design must be site-specific. The optimal design for a given traffic flow will depend on terrain and other characteristics. For the Detailed Engineering Design of the project at hand, we have paid due consideration to the use ERA standards. The Geometric Designs Standards for the project is based on the above basic factors are summarized and presented in the tables below elevation Crest Vertical Curve k 100 55 30 17 10 Sag Vertical Curve k 25 18 12 9 7 Normal Cross fall % 2.5 2.5 2.5 2.5 2.5 Shoulder Cross fall % 4 4 4 4 4 Right of Way m 50 50 50 50 30 From Design Standards vs. Road Classification and AADT table of ERA for DS6, AADT=1000 – 3000 vehicle/day Surface type = paved Carriageway =7m Shoulder width =1.5m for flat and rolling Design speed = 85km/hr for rolling and 100km/hr for flat 4.5 Geometric Design Elements 4.5.1 Cross Section Element Cross section element will normally consists carriage way, shoulder or curb, drainage features and earth work profile.  Carriage way  Roadway  Earth work profile 4.5.2. Lane Width The width of the running surface and shoulder of the road largely define its cost, other thing being equal, hence defining width standard that are acceptable both to the highway authority and to the travelling public is vital. 4.5.3 Shoulder Shoulder is portion of the road way continuous to the carriageway for the accommodation of stopped vehicle; traditional and intermediate non-motorized traffic, animal, and pedestrian; emergency use On paved road shoulder vary from a minimum of 0.5m up to 3m on the terrain and design classification on where the carriage way is paved, the shoulder should also be sealed with surface treatment. Table 19- Minimum requirement of shoulder for DC6 Design standar d Rural Terrain/Shoulder width(m) Town section width (m) Flat Rolling Mountain Escarpmen t Parkin g lane Foo t way Media n DC6 1.5 1.5 0.5 0.5 3.5 2.5 N/ A This has several advantages. Prevent edge reveling and the maintenance problem associated with Parking on an unpaved shoulder Control increase of moister into the upper pavement layer Provide paved space for vehicle parking outside of traffic flow Provide better surface for vehicle experiencing emergency repair carts for the heavy pedestrian traffic observed in the village, traffic that would otherwise use the roadway. 4.5.4. Normal Cross Fall Normal cross fall should be sufficient to provide adequate surface drainage while not being so great as to make steering difficulty. The normal cross fall should be 3% on paved road. Shoulders having the same surface as roadway should have the same normal cross fall. Unpaved shoulder on paved road should be 1.5% steeper than the cross fall off the roadway. 4.5.5. Side slope and Back slope Side slope should be designed to ensure the stability of the road way and to provide reasonable opportunity for recovery of an out of control vehicle. Three regions of roadside are important when evaluating the safety aspect: Top of the slope (hinge point) Side slope, and Toe of the slope (intersection of the fore-slope with level ground or with a back slope, forming a ditch). Research has found that the rounding at the hinge point can sufficiently reduce the hazard potentially. Similarly, reducing at toe of the slope also beneficial. 4.5.6. Road side ditch Road side ditches should be low enough to drain the water from the pavement. When using a V-ditch configuration minimum depth of ditch should be 0.6m in mountainous and escarpment terrain, and 1m elsewhere. 4.5.7. Right of way Right of ways are provided in order to accommodate road width and to depend on the cross The curve which is single arc of circle, it is tangent to both the straights when vehicles negotiate a circular curve; a sideways frictional force is developed between the tires and road surface. This inertial force must be balanced by centripetal forces derived from the applied super elevation. The relationship between the radius, speed and frictional forces required to keep the vehicle in its path are given by: R= V 2 127(e+f ) Where:  R is the radius of curve (m);  V the speed of vehicle (km/h);  e the cross fall of road (per cent) (e is negative for adverse cross fall)  fs the coefficient of side (radial) friction force developed between the tires and road pavement Elements of simple circular curve Figure 5.1 element of simple circular curve  Deflection angle the angle formed by two tangents intersecting (Δ)  Radius of curve by arc definition (R)  tangent distance (T) , T = R× tan ∆ 2  External distance , E = R× (sec ∆ 2 -1)  curve length, L= ∆ × R ×2 π 360 = ∆ × R × π 180  Midlevel ordinate M= R ×(1-cos ∆ 2 )  Chord form pc to pt C=2×R×sin ∆ 2  paint of curvature (pc) station, PC=PI-T  Point of tangency (pt) station, PT = PC+L 2.Transition curves Transition curve is that having constantly changing radius. They may be inserted between tangents & circulars to reduce the abrupt introduction of lateral acceleration. They may also be used between two circular curves. For lower classification road no requirement of transition curves. For Ethiopian roads transition curves are requirement for trunk and link road segments having a design speed of equal to or greater than 80 km/hr The provision of transition curves between tangents and circular curves has the Following benefits:  Transition curves provide a natural easy-to-follow path for drivers, such that the centripetal force increases and decreases gradually as a vehicle enters and leaves a circular curve.  The transition between the normal cross-slope and the fully super elevated section on the curve can be effected along the length of transition curve in a manner closely fitting the speed–radius relationship for the vehicle.  Where the pavement is to be widened around a sharp circular curve, the widening can conveniently be applied over the transition curve length.  The appearance of the road is enhanced by the application of transition curves Table 5.1Transition curve requirements Design speed(Km/hr) Transition required if radius of curve is less than 80 380 85 428 90 480 100 590 110 720 120 850 Figure 5.2 Transition curve  Radius of curve (R)  Deflection angle of the tangents (Δ) TS= PI – TS  Length of spiral (Ls)  Shift distance (s)  Tangent to spiral (Ts)  Spiral deflection (Δs) A brake reaction time of 2.5 s is considered adequate for conditions that are more complex than the simple conditions used in laboratory and road tests, but it is not adequate for the most complex conditions encountered in actual driving. ERA states the following formula for determining break reaction distance as D1 = 0.278× t × V Braking distance the distance needed to stop the vehicle from the instant brake application begins D2= V 2 [254+ g 100 ] Therefore stopping sight distance is given by the following formula D=0.278×t×V V 2 [254+ g 100 ] + Where: d = distance (meters) t = driver reaction time, generally taken to be 2.5 seconds V = initial speed (km/h) f = coefficient of friction between tires and roadway g = gradient of road as a percentage (downhill is negative) Stopping Sight Distance for curve 2 SSD= Break reaction (D1) +Breaking (D2)  Break reaction distance (D1) = 0.278×t× V  Breaking distance (D2) = Vd ² 254( f +g) d=0.278×t×V+ Vd ² 254( f +g) Where t=2.5sec, v=85km/hrs., f=0.295 and g=0.05 d=0.278×2.5sec×85km/hr.+ 85 ² 254(254+0.05) d=154.345m But ERA provides 155m for design speed 85km/hr. Therefore, SSD min for design speed of 85km/hr. 155m Criteria for Measuring Sight Distance Sight distance is the distance along a roadway throughout which an object of specified height is continuously visible to the driver. This distance is dependent on the height of the driver’s eye above the road surface, the specified object height above the road surface, and the height and lateral position of sight obstructions within the driver’s line of sight. • Driver's eye height: 1.07 meters • Object height for stopping sight distance: 0.15 meters • Object height for passing sight distance: 1.30 meters Figure 5.3 stopping sight distance at crest curve Figure 5-4: Stopping Sight Distance at Sag Passing Sight Distance Passing Sight Distance is the minimum sight distance on two-way single roadway roads that must be available to enable the driver of one vehicle to pass another vehicle safely without interfering with the speed of an oncoming vehicle traveling at the design speed. Assumptions about driver behavior.  The overtaken vehicle travels at uniform speed.  The passing vehicle has reduced speed and trails the overtaken vehicle as it enters a passing section.  When the passing section is reached, the passing driver needs a short period of time to perceive the clear passing section and to react to start his or her maneuver.  Passing is accomplished under what may be termed a delayed start and a hurried return in the face of opposing traffic. The passing vehicle accelerates during the maneuver, and its average speed during the occupancy of the left lane is 15 km/h [10 mph] higher than that of the overtaken vehicle.  When the passing vehicle returns to its lane, there is a suitable clearance length between it and an oncoming vehicle in the other lane The minimum passing sight distance for two-lane highways is determined as the sum of the following four distances, Figure 5.5passing sight distance 4.6.5 Super elevation Super elevation is an integral part of the design of horizontal curvature that allows a vehicle to safely and comfortably navigate through curves at higher speed. When a vehicle travels on a horizontal curve, it is forced radially outward by centrifugal force. This is counterbalanced by roadway super elevation and remaining part by the friction between the vehicle tires and surfacing. Figure 5.6 Super elevation plan Super elevation parameter BS= Begin of super elevation PX= Crown removed PY= Reverse crown BMS= Begging of maximum super elevation EMS= End of maximum super elevation TR= Tangent run out length, distance from BS to PC for non-spiraled curve, distance from BS to TS for spiraled curve X= Distance from BS to PX Y= Distance from BS to PY SR= Super elevation run off distance from PX to BMS MSE= Cross slop at maximum super elevation Supper elevation design  Super elevation Runoff distance  SR= Vd 3 28× R For Vd<50Km/hr  SR=w×e×Mrs. For Vd>50Km/hr  Distance from BS to PX  X= SR ×C e  Distance from BS to PY  Y = 2×X  Tangent run out length, Distance from BS to PC for non-spiraled curve, Distance from BS to TS for Spiraled curve  TR = X + SE + SR ……. For Non-spiraled curves  TR = X ……. For spiraled curves Where:  X = Distance from the beginning of super elevation to where adverse crown is removed  Y = Distance from the beginning of Super elevation to where the outside lane Achieves reverse crown  SR = Super elevation Runoff distance  C = Pavement Cross-slope  e = Computed super elevation rate  SE = Percentage of super elevation that is applied before the circular curve Supper elevation design calculation for curve 1  C =2.5% (Pavement Cross-slope)  e = 7.9%  w = 3.5m (Horizontal lane width)  Curve type ------ Transition curve  SR = 47…... From ERA Table 8-5 using R=400 and Super Elevation Rates e=8 Distance from BS to PX  X= SR ×C e  X= 47 ×2.5 7.9  X=14.68m Distance from BS to PY  Y = 2×X  Y = 2×14.68  Y = 29.37m Tangent run out length, Distance from BS to TS for Spiral curve  TR = X ……. For spiral curves TR = 14.68m Table 5.4 Summary of super elevation PI STATION Design Speed (DC6) MSE e SR X Y TR R SL 1 0+590.79 85 8 7.9 47 14.68 29.37 14.68 410 - 2 1+126.01 100 8 2.4 56 56.3 116.6 56.3 175 56 Sample calculation for circular curve Rmin=393.7m ‘Rmin’ is recommended to be 395m (ERA geometric design manual 2013) R provided =410m > 395m Since R provided< 428m so need of Transition curve Degree of curvature at 10m standard arc (Da) Da= 360 ×10 2× π × R Da= 360 ×10 2× 3.14 × 410 Da=1.39 Maximum Length of spiral curve  Lmax = √ (24 ×𝑅)  Lmax = √ (24 ×410)  Lmax = 99.19m Length of spiral curve for comfort  𝐿s= 0.0215× Vd ³ CR Where:  rate of change of centrifugal force is within the range of 0.3 to 0.6, Take C=0.6  Ls= 0.0215× Vd ³ CR  Ls= 0.0215× 100 ³ 0.6 × 410  Ls=87<Lmax=99.19  So take Ls=87m Shift distance  S = Ls 2 R × 24  S= 87.42 410 ×24  S=0.776m Total tangent length  Ts= Ls 2 +(Rc+S) tan (Δ /2)  Ts= 87.4 2 +(410+0.776)tan(60.44/2)  Ts=282.96m Spiral deflection  ΔS =28.65× Ls Rc  ΔS =28.65× 87.4 410  ΔS = 6.1m Circular curve deflection  Δc= Δ-2× ΔS  Δc=60.44-2×6.1  Δc=48.24m Length of circular curve  Lc=Rc×Δc  Lc = 410×6.1× π 180  Lc = 43.6m Tangent length of circular curve  T=R×tan× Δc 2  T=410×tan ( 6.1 2 )  T = 21.85m External Distance  E = R× (sec Δc 2 – 1)  E = 410× (sec ( 6.1 2 ) – 1)  E = 0.58m Chord from P.C to P.T  C= 2×R×sin( Δc 2 )  C = 2×410×sin ( 6.1 2 )  C = 43.63m Middle Ordinate  M = R×(1- cos( Δc 2 ))  M = 400×(1-cos ( 6.1 2 ))  M = 0.58m Station PI= 1+126.01 Station TS= PI-TS=1+126.01– 183.57= 0+942.44 Station SC= PC+LS=0+942.44 +87.4=1+029.84 Station CS=SC+LC=1+029.84 +345.02 = 1+374.86 Station ST=CS+LS=1+374.86 +87.4=1+462.26 Curve setting out by deflection angle method There are different techniques of setting out a horizontal curve on the ground. The methods of setting a curve on the field depend on the type of the curve. For this particular project, since all the circular curves are provided with transition, there are two options to set the curves on the fields:  Offset Method  deflection angle Method 180 π ×Dx 1+029.84 0 0 0 0 1+O33.8 3.95 0.0048 0.276 3.95 1+196.4 22.689 0.02836 1.62498 22.686 1+374.86 43.6 0.053 3.048 43.6 4.7 Vertical alignments Vertical alignment is the combination of parabolic vertical curves and tangent sections of a particular slope. The selection of rates of grade and lengths of vertical curve is based on assumptions about characteristics of the driver, the vehicle and the roadway. Thus the two major aspects of vertical alignment are vertical curvature, which is governed by sight distance criteria, and gradient, which is related to vehicle performance and level of service. Vertical curves are required to provide smooth transition between two consecutive gradients. Equations relating the various aspects of the vertical curve are as follows: Y(X)= r× X 2 200 + X × g 1 100 +YBVC r= (g 2−g 1) L Where: BVC=Begging of Vertical curve EVC=End of the vertical curve Y(X)=Elevations of point on curve(m) X=Horizontal distance from the (BVC)(m) G1=Starting Gradient (%) G2=Ending Gradient (%) r= Rate of change of grade per section L=Length of curve (horizontal curve(horizontal distance) in meters,  G=(g2-g1)(%)  K=L/G=Horizontal distance to achieve a 1% change in grade(meters)  Equation of tangent g1 is Y(X)=Y (0 )+ g1 × X 100  Equations of tangent g2=Y ( L )+ g 2×( X−L) 100  The y ordinate of the EVC is Y(L)=Y (0 )+ (g 1+g2 ) × L 200 According to the topography (position of gradient) vertical curves are of two types. Those are crest and sag curves 4.7.1 Crest Curves If the offsets of curve are below the tangent line (grade) the curve is called crest curve. This curve occurred if there is a change in gradient from large positive to small positive). Crest vertical curves are those that have a tangent slope at the end of the curve that is lower than that of the beginning of the curve. When driving on a crest curve, the road appears as a hill, with the vehicle first going uphill before reaching the top of the curve and continuing downhill.  Positive to small positive.  If there is a change in gradient from positive to negative.  If there is a change in gradient small negative to large negative. Figure 5-4: Crest Curve Table 5.9Minimum value of k for crest vertical curves Design speed(Km/h) K for stopping sight distance K for passing Sight distanceh2 h2 h2 20 2 1 1 10 25 3 1 1 30 30 4 2 1 50 40 10 5 3 90 50 20 10 7 130 60 35 17 11 180 70 60 30 20 245 80 95 45 30 315 85 115 55 35 350 90 140 67 45 390 100 205 100 67 480 110 285 140 95 580 120 385 185 125 680 Design length of crest curves In determining the length of the curve the following points are taken in to account  Sight distance (both stopping and passing)  Class of highway (DC5)  Terrain type 4) Length of sag curve required for passenger’s comfort Lc = 30×G The maximum of the above values is taken as design length for the curve. But if the Computed curve length for the above requirements is less than the minimum curve length recommended by ERA then the recommended value is taken as a curve length. Length of curve= max {calculated length, minimum curve length of recommended by ERA} Where:-  G = the algebraic difference of the two gradient  K = rate of vertical curvature  SSD = minimum stopping sight distance  h = the height from the ground to the eye of the driver, for sag curve, h = 0.6m  Vd =deign speed α= angle between the ray from the observer’s eye to the object for sag Curve, α= 1O Figure 5-4: Sag Curve Table 5.10 Minimum value of k for sag vertical curves Design speed(Km/h) K for driver comfort 20 1.0 25 1.5 30 2.5 40 4 50 6.5 60 9 70 12 80 16 85 18 90 20 100 25 110 30 120 36 4.7.3 Minimum Length of Vertical Curves If the vertical alignment is allowed to contain many curves of short length, the result can be a “hidden dip” profile, and/or a “roller coaster” type profile, where the algebraic difference in gradient is less than 0.5 percent, a minimum curve length is recommended for purely aesthetic reasons. The minimum length should not be less than twice the design speed in km/h and, for preference, should be 400 meters or longer, except in mountainous or escarpment terrain. 4.7.4 Gradient The grades are selected based on:  The amount of earthwork (cut/fill) should be as minimum as possible to reduce cost.  Design speed and topographic factors  Vehicle operating cost  Minimum grade of 0.5% should be provided for drainage purpose.  Grades are selected as much as possible not to cause high fill. Maximum Gradient Vehicle operations on gradients are complex and depend on a number of factors:  severity and length of gradient:  volume and composition of traffic; and  The number of overtaking opportunities on the gradient and its vicinity. For very low levels of traffic of only a few four-wheel drive vehicles, various reference advocates a maximum traversable gradient of up to 18 percent, small commercial vehicles can usually negotiate 18 percent gradient, whilst two-wheel drive trucks can successfully manage gradients of 15-16 percent except when heavily laden. Maximum “absolute” gradient and maximum “desirable’ gradients are therefore extremely important criteria that greatly affect both the serviceability and cost of the road. When the gradients of 7 percent or greater are reached consideration should be given to paving the steep sections to enable sufficient traction to be achieved as well as to minimize maintenance requirement. Table: 5.11. Maximum Gradient for Paved road Topography Maximum Gradient(%),for paved section DC8,DC7,DC6 DC5,DC4 DC3,DC2 DC1 Base access D A D A D A D A D A Flat 3 5 4 6 6 8 6 10 NA NARolling 4,5 7 6 8 7 9 7 10 Mountainous 6,7 9 8 10 10 12 10 12 Escarpment 6,7 9 8 10 10 12 10 12 Urban 6 8 7 9 7 9 7 9  For our case since the since the project road is classified under standard of DC5 and rolling topography the desirable and the absolute values of gradient are 6 and 8 respectively. We take SSD=121.48 Lsd¿214.24m>SSD Length of crest curve required for aesthetic value  La = Vd 2× G 395  La = 702× 9.4 395  La =116.6m Length of crest curve required for passenger’s comfort  Lc=30×G  Lc=30×9.4  Lc=282m Therefore, the length the curve should be maximum of the above calculation: Lmax=max(188, 214.24, 116.6, 282) =282m L provided=282m  Station of BVC =Station of PVI- L 2 = 0+620- 282 2 =0+479  Elevation of BVC=elevation of PVI-g1× L 2 =3127.08-(0.0403)×141 =3121.39m  Station of EVC=station of PVI + L 2 = 0+620 +141 =0+761 Elevation of PVT = EPVI + G2*(L/2) Elevation of PVT = 3127.08+ (-5.37/100)*(282/2) Elevation of PVT = 3119.5365m Curve setting out The general equation of the parabola is Curve elevation = Y + X*G1 EPVC = Y(X) = 𝐺∗𝑋2 /200 + 1 /100 + YPVC ∗𝐿 𝑋∗𝑔 Y = 𝐺∗𝑋2 /200∗𝐿 Where:  y = vertical distance from the tangent to the curve (m)  x = horizontal distance from the start of the vertical curve (m)  G = algebraic difference in gradients (%)  L = length of vertical curve Table 5.13Setting out for crest vertical curve Station X Y= 𝐺∗𝑋2 /200∗𝐿 1 /100 +𝑋∗𝑔 YPVC Curve elevation BVC 0+479 0 0 3121.39 3121.39 0+480 1 1.67×10-4 3121.4303 3121.430467 0+500 21 0.0735 3122.2363 3122.3098 0+520 41 0.280166 3123.0423 3123.322446 0+540 61 0.620166 3123.8483 3124.468466 0+560 81 1.0935 3124.6543 3125.7478 0+580 101 1.700166 3125.4603 3127.160466 0+600 121 2.44016 3126.2663 3128.70646 PVI 0+620 141 3.3135 3127.08 3130.3935 0+640 161 4.320166 3127.8783 3123.558134 0+660 181 5.460166 3128.6843 3123.224134 0+680 201 6.7335 3129.4903 3122.7568 0+700 221 8.140166 3130.2963 3122.156134 0+720 241 9.680166 3131.1023 3121.422134 0+740 261 11.3535 3131.9083 3120.5548 0+760 281 13.160166 3132.7143 3119.554134 EVC 0+761 282 13.254 3132.7546 3119.5006 CURVE 2  Vd= 70km/hr.  Topography=Rolling  Maximum gradient desirable= 6%  Maximum gradient absolute= 8%  Departed gradient ---- G1=-5.37% and G2=7.56%  Curve type=Sag  Coefficient of friction= 0.315  h1=1.05 (derivers eye height)  h2= 0.6 (object height for stopping sight distance)  Minimum allowable "K" value = 12 (from ERA geometric design manual 2013) Curve data computation Algebraic difference in grade (G) =7.56-(-5.37) = 12.93% Station of PVI is 0+654.879 Elevation of PVI=3103.7 Curve length required for minimum curvature, k L=GK, where K is rate of vertical curvature. L=12.93×12 BOC 0+460.88 0 0 3114.138 3114.138 0+470 9.12 0.013858 3113.648256 3113.662114 0+490 29.12 0.141292886 3112.574256 3112.715548 0+510 49.12 0.402026122 3111.500256 3111.902282 0+530 69.12 0.79695855 3110.426256 3111.223214 0+550 89.12 1.3233902 3109.352256 3110.675646 0+570 109.12 1.984021 3108.278256 3110.262277 0+590 129.12 2.777951 3107.204256 3109.982207 0+610 149.12 3.705180298 3106.130256 3109.835436 0+630 169.12 4.765708733 3105.056256 3109.821964 0+650 189.12 5.959536368 3103.982256 3109.941792 PVI 0+654.879 193.999 6.270996214 3103.720253 3109.991249 0+675 213.999 7.630641389 3102.646253 3110.276894 0+695 233.999 9.123585764 3101.572253 3110.696338 0+715 253.999 10.74982933 3100.498253 3111.248082 0+735 273.999 12.50937211 3099.424253 3111.933625 0+755 293.999 14.40221408 3098.350253 3112.752467 0+775 313.999 16.42835526 3097.276253 3113.704608 0+795 333.999 18.58779563 3096.202253 3114.790048 0+815 353.999 20.88053521 3095.128253 3116.008788 0+835 373.999 23.30657398 3094.054253 3117.360826 EVC 0+848.88 388 25.08424345 3093.3024 3118.386 Curve 3 Elevation PVI =3148.45  V= 70km/hr  Topography= Rolling  Maximum gradient desirable= 6%  Maximum gradient absolute= 8%  Departed gradient ---- g1 =7.52% and g2 =1.75%  Curve type=crest  Coefficient of friction= 0.315  h1=1.05 (derivers eye height)  h2= 0.6 (object height for stopping sight distance)  Minimum allowable "K" value = 20m (from ERA geometric design manual 2013) Curve data computation Algebraic difference in grade (G) =g1–g2=7.52-(1.75)= 5.81 % Curve length required for minimum curvature, k L=GK, where K is rate of vertical curvature L=5.81×20=116.2m Length required for safe stopping site distance When SSD <L Lsd ¿ G × S2 100×(√ 2 h1+√ 2 h2)2  SSD =0.278 ×t ×Vd+ Vd ² 254 (f −g) SSD =(0.278×2.5×70)+ 70² 254(0.315−0.0756) SSD=129.23<121.48(min. SSD provided in ERA, by interpolation for g=7.52% we take SSD=130.24 Lsd ¿152.2m>SSD Length of crest curve required for aesthetic value  La = Vd 2× G 395  La = 702×5.81 395  La =72.07m Length of crest curve required for passenger’s comfort  Lc=30×G  Lc=30×5.81  Lc=174.3m Therefore, the length the curve should be maximum of the above calculation: Lmax=max(116.2m, 152.2 , 72.07m,174.3m) =174.3m L provided=175m  Station of BVC =Station of PVI- L 2 = 1+246.389- 175 2 =1+158.889  Elevation of BVC=elevation of PVI-g1× L 2 =3127.08-(0.0756)×87.5 =3141.835m  Station of EVC=station of PVI + L 2 = 1+246,389 +87.5 =1+333.889 SSD =(0.278×2.5×70)+ 70² 254(0.315−0.0499) SSD=129.23<174.98(min. SSD provided in ERA, by interpolation for g=4.99% we take SSD=174.98 Lsd ¿152.89<SSD SSD>L L=2×S- 200× (h 1−h 2 ) 2 G L=2×174.98- 200× (1.05−0.6 )2 3.24 L=345.74 Length of crest curve required for aesthetic value  La = Vd 2× G 395  La = 85 2× 3.24 395  La =59.26 m Length of crest curve required for passenger’s comfort  Lc=30×G  Lc=30×3.24  Lc=97.2m Therefore, the length the curve should be maximum of the above calculation: Lmax=max(113.4, 345.74, 59.26,97.2) =345.74 L provided=346 m  Station of BVC =Station of PVI- L 2 = 2+844.599- 346 2 =2+671.599  Elevation of BVC=elevation of PVI-g1× L 2 =3127.08-(0.0175)×173 =3173.3725m  Station of EVC=station of PVI + L 2 = 2+844.599+175 =3+017.599 Elevation of PVT = EPVI + G2*(L/2) Elevation of PVT = 3127.08+ (0.0175)*(175) Elevation of PVT = 3185.0327m Curve setting out The general equation of the parabola is Curve elevation = Y + X*G1 EPVC = Y(X) = 𝐺∗𝑋2 /200 + 1 /100 + YPVC ∗𝐿 𝑋∗𝑔 Y = 𝐺∗𝑋2 /200∗𝐿 Where:  y = vertical distance from the tangent to the curve (m)  x = horizontal distance from the start of the vertical curve (m)  G = algebraic difference in gradients (%)  L = length of vertical curve Table 5.15 Setting out for crest vertical curve Station X G*X^2/200*L X*g1/100 +YPVC Curve elevation BOC 2+671.59 9 0 0 3173.373 3173.373 2+680 8.401 0.003304 3173.52 3173.523 2+700 28.401 0.037766 3173.87 3173.908 2+720 48.401 0.109685 3174.22 3174.33 2+740 68.401 0.21906 3174.57 3174.789 2+760 88.401 0.365892 3174.92 3175.286 2+780 108.40 1 0.550181 3175.27 3175.82 2+800 128.40 1 0.771926 3175.62 3176.392 2+820 148.40 1 1.031128 3175.97 3177.001 2+840 168.40 1 1.327786 3176.32 3177.648 PVI 2+844.59 9 173 1.4013 3176.401 3177.802 2+850 178.40 1 1.490162 3176.495 3177.985 2+870 198.40 1 1.843005 3176.845 3178.688 2+890 218.40 1 2.233306 3177.195 3179.428 2+910 238.40 1 2.661062 3177.545 3180.206 2+930 258.40 1 3.126276 3177.895 3181.021 2+950 278.40 1 3.628946 3178.245 3181.874 2+970 298.40 1 4.169073 3178.595 3182.764 2+990 318.40 1 4.746656 3178.945 3183.692 3+010 338.40 1 5.361696 3179.295 3184.657 =3+469 Elevation of PVT = EPVI + G2*(L/2) Elevation of PVT = 399.62+ (0.0174)*(158) Elevation of PVT = 3196.8534m Curve setting out The general equation of the parabola is Curve elevation = Y + X*G1 EPVC = Y(X) = 𝐺∗𝑋2 /200 + 1 /100 + YPVC ∗𝐿 𝑋∗𝑔 Y = 𝐺∗𝑋2 /200∗𝐿 Where:  y = vertical distance from the tangent to the curve (m)  x = horizontal distance from the start of the vertical curve (m)  G = algebraic difference in gradients (%) ,L = length of vertical curve Table 5.16 Setting out for crest vertical curve Station X G*X^2/200*L X*g1/100 +YPVC Curve elevation BOC 3+151 0 0 3191.686 3191.686 3+160 9 0.008571 3192.135 3192.144 3+180 29 0.088993 3193.133 3193.222 3+200 49 0.254068 3194.131 3194.385 3+220 69 0.503798 3195.129 3195.633 3+240 89 0.838181 3196.127 3196.965 3+260 109 1.257219 3197.125 3198.382 3+280 129 1.760911 3198.123 3199.884 3+300 149 2.349257 3199.121 3201.47 PVI 3+310 159 2.675175 3199.62 3202.295 3+330 179 3.390502 3200.618 3197.228 3+350 199 4.190483 3201.616 3197.426 3+370 219 5.075118 3202.614 3197.539 3+390 239 6.044408 3203.612 3197.568 3+410 259 7.098351 3204.61 3197.512 3+430 279 8.236949 3205.608 3197.371 3+450 299 9.4602 3206.606 3197.146 EVI 3+469 318 10.7007 3207.554 3196.854 Curve 6  Vd= 70km/hr.  Topography=Rolling  Maximum gradient desirable= 6%  Maximum gradient absolute= 8%  Departed gradient ---- G1=-1.74% and G2=2.51%  Curve type=Sag  Coefficient of friction= 0.315  h1=1.05 (derivers eye height)  h2= 0.6 (object height for stopping sight distance)  Minimum allowable "K" value = 12 (from ERA geometric design manual 2013) Curve data computation Algebraic difference in grade (G) =2.51-(-1.74) = 4.25% Curve length required for minimum curvature, k L=GK, where K is rate of vertical curvature. L=4.25×12 L=51m Length required for safe stopping site distance When SSD <L Lsd¿ G × S2 100×(√ 2 h1+√ 2 h2)2  SSD =0.278 ×t ×Vd+ Vd ² 254 (f −g) SSD =(0.278×2.5×70)+ 70² 254(0.315−0.0251) SSD=115.2>115.02(min. SSD provided in ERA, by interpolation for g=2.51% We takeSSD= 115.2m Lsd¿86.83<SSD SSD>L L=2×S- 200× (h 1−h 2 ) 2 G L=2×115.2- 200× (1.05−0.6 )2 4.25 L=227.096 m Length of crest curve required for aesthetic value  La = Vd 2× G 395  La = 702 × 4.25 395  La =52.72 m Length of crest curve required for passenger’s comfort  Lc=30×G  Lc=30×4.25  Lc=127.5 m Therefore, the length the curve should be maximum of the above calculation: Lmax=max(51, 227.096, 52.72, 127.5) =228m L provided=228m  Station of BVC =Station of PVI- L 2 = 3+700- 228 2 =3+586  Elevation of BVC=elevation of PVI-g1× L 2 Algebraic difference in grade (G) =g1–g2=2.51-(-3.97)= 6.48 % Curve length required for minimum curvature, k L=GK, where K is rate of vertical curvature L=6.48×20=129.6m Length required for safe stopping site distance When SSD <L Lsd ¿ G × S2 100×(√ 2 h1+√ 2 h2)2  SSD =0.278 ×t ×Vd+ Vd ² 254 (f −g) SSD =(0.278×2.5×70)+ 70² 254(0.315+0.0397) SSD=118.72<117.94(min. SSD provided in ERA, by interpolation for g=3.97% we take SSD=118.72 m Lsd ¿141.055 m>SSD Length of crest curve required for aesthetic value  La = Vd 2× G 395  La = 702×6.48 395  La =80.38 m Length of crest curve required for passenger’s comfort  Lc=30×G  Lc=30×6.48  Lc=194.4 m Therefore, the length the curve should be maximum of the above calculation: Lmax=max(129.6, 141.055, 80.38,194.4) =195 m L provided=195m  Station of BVC =Station of PVI- L 2 = 4+119.2- 195 2 =4+021.789  Elevation of BVC=elevation of PVI-g1× L 2 =3203.35-(0.0251)×97.5 =3200.90275m  Station of EVC=station of PVI + L 2 = 4+119.2+97.5 =4+216.789 Elevation of PVT = EPVI + G2*(L/2) Elevation of PVT = 3203.35+ (-0.0397)×(97.5) Elevation of PVT = 3199.47925m Curve setting out The general equation of the parabola is Curve elevation = Y + X*G1 EPVC = Y(X) = 𝐺∗𝑋2 /200 + 1 /100 + YPVC ∗𝐿 𝑋∗𝑔 Y = 𝐺∗𝑋2 /200∗𝐿 Where:  y = vertical distance from the tangent to the curve (m)  x = horizontal distance from the start of the vertical curve (m)  G = algebraic difference in gradients (%)  L = length of vertical curve Table 5.18 Setting out for crest vertical curve Station X G*X^2/200*L X*g1/100 +YPVC Curve elevation BOC 4+021.78 9 0 0 3200.903 3200.903 4+030 8.211 0.011202 3201.109 3201.12 4+050 28.211 0.132235 3201.611 3201.743 4+070 48.211 0.386191 3202.113 3202.499 4+090 68.211 0.773071 3202.615 3203.388 4+110 88.211 1.292873 3203.117 3204.41 PVI 4+119.2 97.411 1.576618 3203.348 3204.925 4+120 98.211 1.60262 3203.368 3201.765 4+140 118.21 1 2.321807 3203.87 3201.548 4+160 138.21 1 3.173917 3204.372 3201.198 4+180 158.21 1 4.15895 3204.874 3200.715 4+200 178.21 1 5.276907 3205.376 3200.099 EVI 4+216.78 9 195 6.318 3205.798 3199.48 Curve 8  Vd= 70km/hr.  Topography=Rolling  Maximum gradient desirable= 6%  Maximum gradient absolute= 8%  Departed gradient ---- G1=-3.97% and G2=2.21%