Vertical Alignment

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Vertical Alignment

Mainly 2 componentsGradientRulingExceptionalLimitingVertical CurvesSummit CurvesValley Curves

Effects of GradientResistance to the vehiclesGrade resistanceGrade CompensationAccording to IRC(30+R)/R %Maximum Compensation = 75/R %Not required on flat gradients i.e., < 4%

Vertical Curves Summit Curve

Shape of Summit CurveCircular Equal Sight distance at all pointsMost IdealParabolaGood riding comfortCalculation of ordinatesLaying out on groundMost preferredFor small deviation angles above shapes doesnt make substantial difference

Design Parameters for LengthSight DistanceStopping Sight DistanceOvertaking Sight DistanceCentrifugal ForceActs UpwardsCounteracted by weight of vehicle

Summit Curve S < L

Y = ax a = N/2L h1 = aS12 h2 = aS22S1 = h1/aS1 = h2/aS = h1+h2L = NS2/2(h1+h2)2

Summit Curve = S > L

Valley CurvesConvexity DownwardsDifferent types like summit curves

Valley curves - types

Design ParametersDaytime No ProblemSD reduces at nightSSD under head lightsCF acts downwardsW acts downwardsFrom the aboveImpact free movement of vehiclesAvailability of SSDTransition curves for safely introducing C.F (P)Cubic Parabola shape is preferred

Length2 transition curves of equal lengthY = bX3 b= 2N/3L2Allowable rate of change of acceleration = 0.6m/s2Adequate sight distance

Length - Based on C.F AccelerationC = ((v2 /R) 0) /t t = Ls/vFrom the aboveLs = v3 / cR But for Cubic Parabola,R = Ls/NHence, Ls = (Nv3 /c)Required L = 2Ls N deviation angle in radian, c = c.f acceleration, v = m/s

Based on SD = SD L

Length - SD > LBeginning and Ending Points of the curveSD Varies in both CasesSD calculated assuming vehicle is at beginning of the curve.

GATE 2015 QuestionsA vehicle is moving in a circular curve and it has a super elevation of e when it does not slide inwards. When friction factor is f (A) e f (B) e f (C) e f = (D) Cannot be determined Which of these statements is false?Plumb line is along direction of gravityMean Sea Level in reference surface for establishing horizontal control Mean Sea Level is simplification of geoidGeoid is an equi potential surface of gravity

For a portion of highway descending gradient 1 in 25 meets an ascending gradient 1 in 20. A valley curve needs to be designed at a velocity of 90 kmph based on (i) Head light sight distance equal to stopping sight distance of a level terrain. Consider length of curve > SSD (ii) Comfort condition if rate of change of acceleration is 3 0.5 m / s Reaction time = 2.5 sec, coefficient of longitudinal friction = 0.35. Height of head light = 0.75 m, and beam angle o = 1 48. What is the length of valley curve as per headlight sight distance?What is the length of valley curve (in meter) based on comfort condition?Ans: 308, 106

While designing a hill road with a ruling gradient of 6%, if a sharp horizontal curve of 50m radius is encountered, the compensated gradient at the curve as per the Indian Roads Congress specifications should be (A) 4.4% (B) 4.75% (C) 5.0% (D) 5.25%A road is provided with a horizontal circular curve having deflection angle 550 and centre line radius of 250m. A transition curve is to be provided at each end of the circular curve of such a length that the rate of gain of radial acceleration is 0.3m/s3 at a curve required at each of the ends is (A) 2.57m (B) 33.33m (C) 35.73m (D) 1666.67m

A horizontal circular curve with a centre line radius of 200m is provided on a 2-lane, 2- way SH section. The width of the 2-lane road is 7.0m. Design speed for this section is 80 km per hour. The brake reaction time is 2.4s, and the coefficients of friction in longitudinal and lateral directions are 0.355 and 0.15, respectively. The safe stopping sight distance on the section is (A) 221m (B) 195m (C) 125m (D) 65m The set-back distance from the centre line of the inner lane is (A) 7.93m (B) 8.10m (C) 9.60m (D) 9.77m

GATE PREVIOUS QUESTIONSA rest vertical curve joins two gradients of +3% and -2% for a design speed of 80km/h and the corresponding stopping sight distance of 120m. The height of drivers eye and the object above the road surface are 1.20m and 0.15m respectively. The curve length (which is less than stopping sight distance) to be provided is(A) 120m (B) 152m (C) 163m (D) 240m

The length of Summit Curve on a two lane two way highway depends upon (A) Allowable rate of change of centrifugal acceleration (B) Coefficient of lateral friction (C) Required Stopping Sight Distance (D) Required Overtaking Sight Distance

1. A valley curve is formed by descending gradient n1= 1 in 25 and ascending gradient n2= 1 in 30. Design the length of the valley curve for V =80kmph. (Hint: c=0.6 m/cm3) 2. A vertical summit curve is formed by n1 = +3.0% and n2 = 5.0%. Design the length of the summit curve for V=80 kmph. 3. n1 = +1/50 and n2 = 1/80, SSD=180m, OSD=640m. Due to site constraints, L is limited to 500m. Calculate the length of summit curve to meet SSD, ISD and OSD. Discuss results.1. c=0.6 m/cm3 , SSD=127.3m), L=max(73.1,199.5)2. SSD=128m), L = 298m3. L for SSD=240m, okay, L for OSD=1387m, > 500m not ok, L for ISD=439m ok

Pavement MaterialsObjectivesUnderstanding Different types of materials for different types of pavementsDifferent parameters for selecting the materialProperties of Soil used for pavement designTesting and Evaluation of Pavement materials

Pavement Vertical Cross-SectionEmbankmentSubgradeSubbaseBaseWearing Course + Shoulders

Pavement MaterialsVariety of materialsSoilAggregatesBitumenConcreteBindersGeotextilesEtcMaterials, Properties and Interaction b/w them decides properties of pavement.Durability and Stability are affected

Pavement materialsSoilDeposit of earth material formed by disintegration of rocks etc.Used in Embankment, SubgradeAggregates used in sub base and baseBindersBituminous mixes aggregates+ Bitumen + bindersIn concrete pavements Cement + reinforcement etcRecycled materials

Why Study?Understand the behaviour individually and in combinationCharacterizeClassify/GradeFor design purposeStudy the condition of existing pavementQuality controlTests are conducted to ensure quality during pre and post construction phases.Lab tests on representative samplesField testsEstimation

Parameters considered for characterizationLoadsStationary/ MovingHeavy/LightApplication modeClimatic conditionsTemperature, Rainfall, MoistureWeathering ActionBehaviour under cyclic nature Wetting/Drying, Chemical Action, Freezing etc

SoilUsed in Embankment, Subgrade, ShouldersNatural form or stabilized formClassified based on the particle size distribution and index propertiesIS Soil ClassificationCourse Grained 50% > 0.075mm sieveFine Grained - ViceversaGravel 80 to 4.75 mmSand 4.75 to 0.075mmSilt and Clay < 0.075mm

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