CIEN 3164 Route Surveying AND Earthworks PDF

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College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: pup.eduPOLYTECHNIC UNIVERSITY OF THE PHILIPPINESOffice of the Vice President for Academic AffairsCOLLEGE OF ENGINEERINGCivil Engineering DepartmentROUTE SURVEYING AND EARTHWORKSOverview:This course covers the funda...

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Republic of the Philippines

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department ROUTE SURVEYING AND EARTHWORKS

Overview: This course covers the fundamental principles of curves as utilized in roads and highways, and earthworks. The elements of circular curves, parabolic curves and spiral curves will be studied and passing sight distance in vertical and horizontal curves are also covered. Volume of cut and volume of fill, volume by end-area method, volume by parallel cross-section method, and haul and mass diagram will also be covered. Watch: Simple Curves: https://youtu.be/OEwdW_hAQPA Compound Curves: https://youtu.be/-tIlfrlI43Q Reversed Curves: https://youtu.be/7zDtK3auYwM Vertical Curves: https://youtu.be/0kbowiwLjQ4 Unsymmetrical Parabolic Curves: https://youtu.be/nx0JadEp1lc Passing Sight Distance: https://youtu.be/0xwPILJUqsI Spiral Curves: https://youtu.be/CCpi0eNks94 Earthworks: https://youtu.be/mJH3_ewE6rY Haul and Mass Diagram: https://youtu.be/Zw7vZfvgefE

Module 1: Simple Curve

Learning Objectives: At the end of this lesson, the learner will be able to: • Explain highway curves • Relate highway curves to circular arcs • Define simple curve • Identify the elements of a simple curve • Apply trigonometry in calculating for the elements of a simple curve • Compute the necessary data for laying-out simple curves Course Materials: ROUTE SURVEYING is a survey which supplies data necessary to determine the alignment, grades, and earthworks quantities necessary for the location and construction of engineering projects. This includes highways, drainage, canal, pipelines, railways, transmission lines, and other civil engineering projects that do not close upon the point of beginning.

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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Republic of the Philippines

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department SIMPLE CURVE

An arc of a circle that joins two tangents together. Most commonly used for highways and railroad construction. Circular arc, extending from one tangent to the next.

Elements of A Simple Curve ◼ Vertex (P.I. , V) – point of intersection of the tangents ◼ Radius (R) – radius of the slope curve ◼ Angle of intersection of the Tangent/ Central Angle of the Simple Curve (I) ◼ Tangent Distance (T) – distance from the PC to vertex ◼ Point of Curvature (PC) – from the vertex to the PT ◼ Point of Tangency (PT) ◼ External Distance (E) – distance from midpoint of the curve connecting PC to PT ◼ Middle ordinate (M) – distance from midpoint of the curve to midpoint of the chord connecting PC and PT ◼ Long chord (LC) – length of chord from the PC to PT ◼ Length of curve (Lcu) – length of the circular arc ◼ Degree of curve (D) ◼ Arc basis College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department ◼ In highway practice wherein the radius is small and distance are usually measured along arcs, the degree of curve is the angle subtended by an arc equal to 1 full station or 20m. A) Arc Basis

2. ENGLISH 1. SI

B) Chord Basis The degree of the curve is the angle subtended by a chord of 20m (SI) or 100’ (English)

1. SI

2. ENGLISH

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department Tangent distance (T) Tan I/2 = T/R T=R Tan I/2

External distance (E) Cos I/2 = R/(R+E) (R+E) CosI/2 = R R+E = RSec I/2 E=RsecI/2-R E= R(SecI/2-1)

Middle ordinate (M) CosI/2 = (R-M)/R RCos I/2 = R-M M = R-RCos I/2 M = R(1-Cos I/2)

Length of chord (LC) Sin I/2 = LC/2 /R LC = 2RSin I/2

Length of curve (LCu) LCu/I = 20/D LCu = 20I/D SUMMARY OF FORMULAS T = R tan I/2 → Tangent Distance E = R (sec I/2 -1) → External Distance M = R (1 – cos I/2) → Middle Ordinate LC = 2R sin I/2 → Long Chord Lcu = RI (π/180) → Length of Curve/Arc Methods of Laying Out Simple Curves In The Field 1. Circular curve deflection / Deflection angle 2. Offset from the tangent method Method of Deflection Angles ▪ The most common method of laying out simple curves in the field ▪ Typically, the theodolite is set upped at the PC and the deflection triangles are drawn from the tangent line Deflection Angle = (Arc Length/Lcu) x I/2

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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COLLEGE OF ENGINEERING Civil Engineering Department Activities/Assessments: 1. The tangent distance of a 3˚ simple curve is ½ of its radius. Determine:  Angle of intersection (I)  LC  Area of the fillet of the curve Solution: D=3˚, T=1/2R T=RTanI/2 1/2R=RTanI/2 TanI/2=0.5 I/2=tan 0.5 I=53.13˚

LC=20I/D LC=20(53.13)/3˚ LC=354.2m

A=T(R)- R²  /360˚ A=(190.99)(381.97)R=1145.916/D R=381.97 sq.m.

2.

(381.97) (53.13)/360˚ A=5305.89sqm

Given: I, R & station of V (see figure) Deflection Angle = Arc Length/Lcu x I/2 @ 0+200 subchord = 2(400) sin 0⁰14’01” = 3.262m even stations: subchord = 2(400) sin 1⁰25’57” = 19.999 ≈ 20m @ last stations: subchord = 2(400) sin 0⁰27’42” = 6.446 ≈ 7m

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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Republic of the Philippines

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department 3. A simple curve connects two tangents AB and BC with bearings N85°30’E and S68°30’E respectively. If the vertex is at Sta. 4+360.2 and the PC is at Sta. 4+288.4, solve for the following: a. Radius of the connecting simple curve b. External Distance c. Middle Ordinate d. Length of the Long Chord e. Length of the entire circular arc f. Stationing of PT

Solution: I = 180- 85°30’- 68°30’ = 26° Sta. PC = Sta V – T 𝐼

𝑇 = 𝑅𝑡𝑎𝑛 2 𝐼

𝑀 = 𝑅(1 − 𝑐𝑜𝑠 2) 𝐿𝑐𝑢 = 𝑅𝐼(

𝜋

180

)

4288.4 = 4360.2 -T

T = 71.8m 𝐼

R = 311.0m

𝐸 = 𝑅(𝑠𝑒𝑐 − 1) 2

M = 7.97m

𝐿𝐶 = 2𝑅(𝑠𝑖𝑛 ) 2

𝐼

Lcu = 141.13m

Sta. PT = Sta. PC + Lcu

Sta. PT = 4288.4+141.13

Sta. PT = 4 + 429.53

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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E = 8.18m LC = 139.92m

Republic of the Philippines

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department Module 2: Compound Curves

Learning Objectives: At the end of this lesson, the learner will be able to: • Classify the similarities and differences of a simple and compound curve • Define compound curve • Identify the elements of a compound curve • Apply trigonometry in calculating for the elements of a compound curve • Compute the necessary data for laying-out compound curves Course Materials: Composed of two or more consecutive simple curve having different radii but whose center lie on the same side of the curve. Any two consecutive curves must have a common tangent on their meeting PT. Elements of a Compound Curve 1. V 2. R, R₂ 3. PC 4. PT 5. Long Chord (Lc) 6. Common Tangent 7. Lcu 8. Point of compound curvature (PCC) ▪ Point along the common tangent line in w/c the two curves PCC Point of Compound Curvature (PCC) - the point on the common tangent line through which the two simple curves meet.

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department

Activities/Assessments: EXAMPLE: The long chord from the PC to the PT of a compound curve is 300m long and the angle that it makes the longer and shorter tangents are 12˚ and 15˚ respectively. If the common tangent is parallel to the long chord. Required: ❑ R1 ❑ R2 ❑ Station PT if PC is at sta 10+204.30

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department

SOLUTION: sine law: 300m/sin166˚30’=LC1/sin7˚30’=LC2/sin6˚ LC1=167.74mLC2=134.33m LC=2RsinI/2 LC1=2R1sinI1/2 R1=802.36m

167.74m=2(R1)sin6˚/2

LC2=2R2sinI2/2 R2=514.57m

134.33m=2(R2)sin7˚30’/2

LCu1=R1I1( π/180˚) LCu1=168.05m

LCu1=802.36n(6˚)( ‼/180˚)

LCu2=R2I2( π/180˚) LCu2=134.71m

LCu2=514.57m(7˚30’)( π/180˚)

sta PT=staPC+LCu1+LCu2 Sta PT=10+507.06

sta PT=10+204.30+168.05+134.71

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department Module 3: Reversed Curve

Learning Objectives: At the end of this lesson, the learner will be able to: • Recall the fundamental concepts the horizontal curves • Define reversed curve • Classify the elements of a reversed curve • Apply trigonometry in calculating for the elements of a reversed curve • Compute the necessary data for laying-out reversed curves

Course Materials: Reversed Curves ⚫ Composed of two consecutive circular simple curves having a common tangent, but which centers lie on the opposite side of the curve. PRC ⚫ Point of the reversed curvature. ⚫ The point along the common tangent to which the curve reversed in its direction.

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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COLLEGE OF ENGINEERING Civil Engineering Department Four Types of Reversed Curves

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department Activities/Assessments: EXAMPLE: The parallel tangent of a reversal curve is 10m apart the long chord from the PC to the PT is equal to 120m determine the following: ⚫ Radius of the curve ⚫ Length of the common tangent ⚫ Sta. PRC if V1 is at 3+420

I=9˚33’ T=RtanI/2 30.14=Rtan(9˚33’/2) R=360.82m

sinI/2=10/120 sinI=10/2T 2T=60.27m T=30.14m Common tangent = V1V2 = 2T = 60.27m 𝐿𝑐𝑢 = 𝑅𝐼(

𝜋

180

)

Lcu = 60.1m

Sta. PRC = Sta. V1 – T+ Lcu Sta. PRC = 3+450

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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COLLEGE OF ENGINEERING Civil Engineering Department Module 4: Symmetrical Parabolic Curve

Learning Objectives: At the end of this lesson, the learner will be able to: • • • •

Define the fundamental concepts about vertical curves Identify symmetrical parabolic curve Identify the elements of a symmetrical parabolic curve Apply trigonometry and geometry in calculating the elements of a parabolic curve

Course Materials: VERTICAL PARABOLIC CURVES • A curve used to connect two intersecting grade lines • A curve tangent to two intersecting grade lines TYPES OF VERTICAL PARABOLIC CURVES • SYMMETRICAL PARABOLIC CURVES A parabolic curve wherein the horizontal length of the curve from the PC to the vertex is equal to the horizontal length from the vertex to the PT.

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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COLLEGE OF ENGINEERING Civil Engineering Department ELEMENTS OF A SYMMETRICALPARABOLIC CURVE • VERTEX (PI) • PC • PT • BACKWARD TANGENT • FORWARD TANGENT • g1 and g2 (GRADES) GUIDING PRICIPLES FOR SYMMETRICAL PARABOLIC CURVES 1. A given grade or slope (in %) is numerically the rate at which an elevation changes in a horizontal distance.

e.g. g=5% 2. The vertical offset from the tangent to the curve is proportional to the squares of the distances from the point of tangency. (Squared Property of a Parabola) •

y1 / x12 = H / (L/2)2 = y2 / (x2)²

3. The curve bisects the distance between the vertex and the midpoint of the long chord. •

BF / (L/2)² = CD / (L)²

4. For the algebraic difference of slopes: g1 - g2 is + = “summit” curve g1 - g2 is - = “sag” curve 5. The number of stations to the left of the vertex is equal to the number of stations to the right. 6. The slope of the parabola varies uniformly along the curve. r = g2 - g1 / L (for the entire length of curve) r = g2 - g1 / n (for n number of stations) 7. Vertical offset, H 𝑯=

𝑳

𝟖

(𝒈𝟏 − 𝒈𝟐)

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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COLLEGE OF ENGINEERING Civil Engineering Department 8. LOCATION OF THE HIGHEST OR LOWEST POINT OF THE CURVE FROM PC

𝒈𝟏𝑳

𝑺𝟏 = 𝒈𝟏−𝒈𝟐

FROM PT 𝑺𝟐 =

𝒈𝟐𝑳 𝒈𝟐−𝒈𝟏

Activities/Assessments: EXAMPLE: 1. A grade descending at a rate of -4% intersects another grade ascending at a rate of +8% at Sta. 2+000, elev. 100m. A vertical symmetrical curve is to connect the two grades such that it will clear a boulder located at 1+960. The elev. of the tip of the boulder is 101.8m. Required: a. Length of the curve b. Location of the sewer to be laid out c. Elevation of the curve at the location of the sewer SOLUTION:

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COLLEGE OF ENGINEERING Civil Engineering Department elev. 101.8 = elev. V + a + y 101.8 = 100 + 1.6 + y

a = 40*g1 = 40(0.04) = 1.6m y = 0.20m

Using the squared property of a parabola (spp), 𝒚

𝑳 {(𝟐)−𝟒𝟎}𝟐

=

𝑳

𝑯 (𝑳/𝟐)𝟐 𝟎.𝟐𝟎

Therefore:

𝑳

but 𝑯 = 𝟖 (𝒈𝟏 − 𝒈𝟐) = (𝟎. 𝟎𝟒 − (−𝟎. 𝟎𝟖)) = 0.015L 𝟖

𝑳 {(𝟐)−𝟒𝟎}𝟐

=

𝟎.𝟎𝟏𝟓𝑳

(𝑳/𝟐)𝟐

L = 120.0m

H = 1.8m

For sewer location (lowest point of the curve) 𝒈𝟏𝑳

𝑺𝟏 = 𝒈𝟏−𝒈𝟐 = 𝑺𝟐 =

𝒈𝟐𝑳

𝒈𝟐−𝒈𝟏

=

𝟎.𝟎𝟒(𝟏𝟐𝟎) = 𝟎.𝟏𝟐 𝟎.𝟎𝟖(𝟏𝟐𝟎) 𝟎.𝟏𝟐

40.0m (from the PC)

𝑳

( ) − 𝑺𝟏 = 20.0 m 𝟐

= 80.0m (from the PT)

note that S1 + S2 = L (for symmetrical curves) 𝐿

Sta. sewer = Sta. V - ( ) − 𝑆1 = 2000 – 20 = 1+980 2 Elevation of the curve at sewer location (elevation of the lowest point of the curve/ vertical curve transition point): Elev. Lowest Point (LP) = Elev. V + a1 + y1

𝐿

a1 = {( ) − 𝑆1} 𝑔1 = 20.0*0.04 = 0.8m 2

Using the squared property of a parabola (spp), 𝒚𝟏

{𝑺𝟏}𝟐

=

𝑯 (𝑳/𝟐)𝟐

𝒚𝟏

= {𝟒𝟎}𝟐 =

𝟏.𝟖 (𝟔𝟎)𝟐

y1 = 0.8m

Elev. Lowest Point (LP) = Elev. V + a1 + y1 = 100+0.8+0.8 Elev. Lowest Point (LP) = 101.6m

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department Module 5: Unsymmetrical Parabolic Curve

Learning Objectives: At the end of this lesson, the learner will be able to: • • • •

Identify unsymmetrical parabolic curve Identify the similarities and differences of unsymmetrical and symmetrical parabolic curves Identify the elements of an unsymmetrical parabolic curve Apply trigonometry and geometry in calculating the elements of an unsymmetrical parabolic curve.

Course Materials: UNSYMMETRICAL PARABOLIC CURVES •

Consist of a symmetrical parabolic curve from PC to V and another symmetrical parabolic curve from V to PT

•

Used in provide a smooth and continues curve transition from PC to PT

College of Engineering PUP A. Mabini Campus Anonas Street, Sta. Mesa, Manila website: www.pup.edu.ph

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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES Office of the Vice President for Academic Affairs

COLLEGE OF ENGINEERING Civil Engineering Department Useful Formulas •

Using similar triangles 2H/L1= (g1-g2)L2/(L1+L2) H = (g1-g2) L1 L2 2(L1+L2)

•

From the squared property of a parabola (SPP) h1/(L1/2)²=H/L1²

•

h1=H/4

•

h2=H/4

•

Y1/X1²=H1/L1²

•

Y2/X22=H/L2²

LOCATION OF THE HIGHEST POINT OR LOWEST POINT ON THE CURVE 1. From PC when g1L1/2H

S2=g2L2²/2...