Highway and Railroad Engineering: Lesson 4.2 PDF

HIGHWAY AND RAILROAD ENGINEERING: LESSON 4.2 GEOMETRIC DESIGN FOR HIGHWAY AND RAILWAYS HIGHWAY AND RAILWAY 1. Spiral Curves 2. Super Elevation ENGINEERING 3. Earthwork 4. Sight Distance  Th...

HIGHWAY AND RAILROAD ENGINEERING: LESSON 4.2 GEOMETRIC DESIGN FOR HIGHWAY AND RAILWAYS HIGHWAY AND RAILWAY 1. Spiral Curves 2. Super Elevation ENGINEERING 3. Earthwork 4. Sight Distance  The cross section of a typical highway has latitude of variables to consider such as: 1. The volume of traffic. 2. Character of the traffic. 3. Speed of the traffic. EARTHWORKS 4. Characteristics of motor vehicles and of the driver  A cross section design generally offers the expected level of service for safety and a recent study showed that: 1. A 7.20 meters wide pavement has l8% less accident compared with pavement narrower than 5.50 m. wide. 2. A 7.20 meters wide pavement has 4% fewer accidents than the 6.00 meters wide roadway. EARTHWORKS 3. Accident records showed no difference between the 6.60 meters and the 7.20 meters wide pavement. 4. For the 6.00 m., 6.60 m. and,7.20 meters wide pavement with 2.70 to 3.00 m. wide shoulder, recorded accident decreases by 30% compared to 0 to.60 m. wide shoulder. And 20% compared with a.90 to 1.20 meters wide shoulder.  FIGURE 2-1 CROSS SECTION OF TYPICAL TWO LANE HIGHWAYS EARTHWORKS FIGURE 2-2 MULTI-LANE HIGHWAYS AND FREEWAYS (HALF SECTION))  FIGURE 2-3 EARTHWORKS DIVIDED HIGHWAYS  FIGURE 2-4 EARTHWORKS UNDIVIDED HIGHWAYS  The method of plotting the existing cross section perpendicular to a particular line for the purpose of obtaining quantities such as volumes. The procedure involves staking the centerline then elevations are obtained at strategic points on the right angle to the centerline at intervals of full or half stations. Cross- sectional data is needed in estimating the amount of EARTHWORKS cut or fill needed for a given strip of roadway. Station Notes 𝑥𝐿 0 𝑥𝑅 𝑦𝐿 𝑦𝐶 𝑦𝑅 EARTHWORKS END – AREA METHOD 𝑳 𝑽𝑬 = [𝑨𝟏 + 𝑨 ] PRISMOIDAL FORMULA 2 𝑳 𝑽𝑷 = 𝟔 [𝑨𝟏 + 𝟒𝑨𝒎 + 𝑨𝟐] 𝑽 = 𝑽𝑷 − 𝑽𝑪 PRISMOIDAL CORRECTION 𝑳 𝑽𝑪 = (𝑪𝟏 - 𝑪 𝟐) (𝑫𝟏 - 𝑫 𝟐) 12  Example # 1: At Sta. 5+420 a rectangular trench is 4.8m wide by 1.8m deep and at Sta. 5+450 it was found to be 5.20m wide by 2.9m deep. Find the quantity of earthworks by Prismoidal formula. EARTHWORKS  Example # 2: The given cross-section notes of earthwork between A (20+200) and B (20+220) are shown below. Assume both stations have the same side slopes and base width. Left Center Right 20+200 6.60 0 4.80 EARTHWORKS +2.40 +2.00 +1.2 20+220 6.30 0 7.20 +2.20 y +2.80 A. Determine the width of the base. B. Determine the value of the Y at station B if it has an area of 16.82 m2. C. Find the volume EA between A and b with prismoidal correction.  Left Center Right 20+200 6.60 0 4.80 +2.40 +2.00 +1.2 20+220 6.30 0 7.20 +2.20 y +2.80 EARTHWORKS  Left Center Right 20+200 6.60 0 4.80 +2.40 +2.00 +1.2 20+220 6.30 0 7.20 +2.20 y +2.80 EARTHWORKS EARTHWORKS  Example # 3: From the given cross-section notes of an earthwork, it is required to determine the value x if the cross-sectional area is 13.1625 m2 with a side slope of 1.5:1 and road width of 6m. Left Center Right 1+000 6.45 0 4.5 +2.30 x +1.0 EARTHWORKS Example # 4: Given the following description of a 10m wide roadway having a side slope of 2.5:1. Find the prismoidal correction Left Center Right 5+000 30 0 12.5 +10 +5 +3 5+020 40 0 16.25 +14 +7 +4.5 SIGHT DISTANCE  Types of Sight Distances 1. Stopping or absolute minimum sight distance (SSD) Minimum sight distance available on a highway at any spot should be of sufficient length to stop a vehicle traveling at design speed, safely without collision with any other obstruction. It depends on SIGHT DISTANCE a. Feature of road ahead b. Height of driver’s eye above the road surface (1.2m) c. Height of the object above the road surface (0.15m) Criteria for measurement a. Height of driver’s eye above road surface (H) b. Height of object above road surface (h)  Factors affecting SSD Total reaction time of driver Speed of vehicle SIGHT DISTANCE Efficiency of brakes Frictional resistance between road and tire Gradient of road  Total reaction time of driver: It is the time taken from the instant the object is visible to the driver to the instant the brake is effectively applied. It is divided into types (a) Perception time It is the time from the instant the object comes SIGHT DISTANCE on the line of sight of the driver to the instant he realizes that the vehicle needs to be stopped. (b) Brake reaction time. The brake reaction also depends on several factor including the skill of the driver, the type of the problems and various other environment factor. Total reaction time of driver can be calculated by “PIEV” theory. PIEV Theory: P-perception, I-intellection, E-Emotion, V-Volition Theory  Analysis of SSD The stopping sight distance is the sum of lag distance and the braking distance 1. Lag Distance - The distance the vehicle travelled during the reaction time - If “V” is the design speed in m/s, ‘t’ is the total SIGHT DISTANCE reaction time of the driver in seconds lag distance = v ∙ t - If “V” is in kph, lag distance = 0.278 v ∙ t - AASHTO recommended reaction time is 2.5 seconds  2. Breaking Distance - Distance travelled by the vehicle after the application of brake. - For a level road, this is obtained by equating the work done in stopping the vehicle and the kinetic energy of the vehicle. - Work done against friction force in stopping the SIGHT DISTANCE vehicle is F∗L=f∙W∙L where W is the total weight of the vehicle - The kinetic energy at the design speed of v in m/s will be 1⁄2 m𝑣 2  2. Breaking Distance The stopping sight distance SIGHT DISTANCE Note that in this equation, v is in m/s, t is the reaction time, g is the gravity (9.81m/𝑠 2 ), f is the coefficient of longitudinal friction, G is the roadway grade.  Using typical units for velocity (kph) and considering the braking action of the driver, the stopping sight distance may also be written as where v is in kph and a is the braking action deceleration in m/𝑠 2 SIGHT DISTANCE Braking Action - Based on the driver’s ability to decelerate the vehicle while staying within the travel lane and maintaining steering control during the braking maneuver. A deceleration rate of 3.4 m/s2 is comfortable for 90% of the drivers.  Example : A vehicle is travelling at 35 kilometers per hour. Its driver is about to hit a 2-meter high wall 30 meters away if he did not react accordingly. Assuming the coefficient of friction between the road and tires is 0.35 and the driver steps on the brakes 2 seconds after seeing the obstruction, will he hit the wall? The road is perfectly horizontal. 𝑣2 𝑆𝑆𝐷 = 𝑣𝑡 + SIGHT DISTANCE Given: 2𝑔(𝑓 ± 𝐺) v = 35 kph = 9.72 m/s t = 2 seconds f = 0.35 G=0 Required: If SSD > 30, will the vehicle hit the wall?  SSD and Crest Vertical Curve Figure shows SSD and crest vertical curve (Image taken from ascelibrary.com) SIGHT DISTANCE The equations used in designing a crest vertical curve are as follows: Assuming SSD < L: where, Lm = minimum length of crest curve, in meters S = stopping sight distance, in meters H1 = driver’s eye level above roadway surface, in meters Assuming SSD > L H2 = height of obstruction above roadway surface, in meters A = absolute value of the difference in grades,  SSD and Sag Vertical Curve Figure shows SSD and sag vertical curve (Image taken from ascelibrary.com) SIGHT DISTANCE The equations used in designing a sag vertical curve are as follows: Assuming SSD < L: where, Lm = minimum length of sag curve, in meters S = stopping sight distance, in meters Assuming SSD > L H = height of headlight above roadway, in meters α = inclined angle of headlight beam, in degrees A = absolute value of the difference in grades, in percentage  EXAMPLE 1: Determine the length of the vertical curve with a stopping sight distance of 230 meters. Its initial and final grades are +1.75% and -2.05% respectively. The driver’s eye level above the roadway surface is 150 centimeters and the height of obstruction is 100 centimeters. SIGHT DISTANCE  EXAMPLE 2: A vertical curve is to be designed with a stopping sight distance of 310 m. Its initial and final grades are -3.2% and +2.1% respectively. The average height of the headlights of the vehicles that will pass through this road is 60 centimeters and α is set at 1°. Determine the length of the curve. SIGHT DISTANCE  2. Safe overtaking (OSD) or passing sight distance (PSD) - The minimum distance open to the vision of the driver of a vehicle intending to overtake slow vehicle ahead with safety against the traffic of opposite direction is known as the minimum overtaking sight distance (OSD) SIGHT DISTANCE or the safe passing sight distance - In limited 2-lane or 2-way highways, vehicles may overtake slower moving vehicles, and the passing maneuver must be accomplished on a lane used by opposing traffic  where 𝑑1 = initial maneuver distance (m) 𝑑2 = distance while passing SIGHT DISTANCE vehicle occupies left lane (m) 𝑑3 = clearance length (m) 𝑑4 = distance traversed by the opposing vehicle (m)  These values are determined using the AASHTO Policy on geometric design of highways and streets. SIGHT DISTANCE  For Rural Areas, the guideline considers the terrain in which road is being constructed. Table below shows the recommended values SIGHT DISTANCE  3. Safe sight distance for entering an intersection, Intersection Sight Distance - Driver entering an uncontrolled intersection (particularly unsignalized intersection) has sufficient visibility to enable him to take control of his vehicle and to avoid collision with another vehicle. - The corner sight distance available in intersection SIGHT DISTANCE quadrants that allows a driver approaching an intersection to observe the actions of vehicles on the crossing leg(s) - Evaluations involve establishing the needed sight triangle in each quadrant by determining the legs of the triangle on the two crossing roadways - Clear sight triangle must be free of sight obstructions such as buildings, parked or turning vehicles, trees, hedges, fences, retaining walls, and the actual ground line.  A car travelling at 105 kph applies a brake and stopped at a distance of 105 m. The coefficient of friction between the tires and the road is 0.5. If the reaction time is 1.5 seconds, what is the grade of the road? Find the minimum sight distance to avoid a head-on-collision of two cars approaching at 90 kph and 60 kph on an inclined road. The first car is moving uphill while the second is moving downhill. Given t=2.5 sec, f=0.7, G=-2% and a brake efficiency of 50% in either vehicles SIGHT DISTANCE Determine the minimum length of a crest vertical curve between a +0.5% grade and a -1.5% grade of a road with an 80 kph design speed. The vertical curve must provide a stopping sight distance of 180 m to meet with the required appearance criteria. Round up to the next greatest 20- m interval. Assume eye-height of 1.07 m and object height of 0.15 m. Compute the minimum length of vertical curve that will provide 130-m of stopping sight distance for a design speed for a design speed of 80 kph at the intersection of a +2.30% grade and a -4.80% grade. Assume eye-height of 1.30m and object height of 0.20 m. LECTURE 4.2