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CVG4150-Final-Exam-Formula-Sheet-Final-Version

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Flexible Pavement Design
Structural Design Procedure to determine D1, D2 and D3
1. Determine the total ESAL for the design period
2. Determine the design serviceability loss (βˆ†π‘ƒπ‘†πΌ = 𝑝𝑖 − 𝑝𝑑 )
3. Determine the effective Mr for each segment AND find a1,a2,a3
4. Determine the drainage coefficient (m2 and m3)
5. Select the reliability design level (R) and overall standard deviation (So)
6. Use monograph to find Structural Number – SN
7. Determine Layer Thickness
Flexible Pavement Design
1) Pavement Performance → βˆ†π‘ƒπ‘†πΌ = 𝑝𝑖 − 𝑝𝑑
PSI=Present Serviceability Index (0-5, 5 is best) – quantifies pavement
performance
pi= Initial serviceability Index (4.2-4.5)
pt=Terminal serviceability Index (2.5-3.0 for major highway), (2.0 - lower class.)
2) Traffic (ESAL)
𝐸𝑆𝐴𝐿𝑖 = 𝑓𝑑 ∗ πΊπ‘Ÿπ‘› ∗ 𝐴𝐴𝐷𝑇𝑖 ∗ 365 ∗ 𝑁𝑖 ∗ 𝐹𝐸𝑖 , πΊπ‘Ÿπ‘› =
[(1+π‘Ÿ)𝑛 −1]
π‘Ÿ
r=i/100 and is not zero, if annual growth is zero, growth factor=design period
i=growth rate, n= design life (years)
ESALi=equivalent accumulated 18kip (80kN) single axle load for axle category i
fd=design lane factor
Grn=growth factor for a given growth rate t and design period n
AADTi=first year annual average daily traffic for axle category i
Ni=number of axles on each vehicle category i
FEi=load equivalency factor for axle category i
3) Road Soils (Subgrade), → π‘€π‘Ÿ
Expressed in terms of CBR (California Bearing Ratio) or R-value (Resistance and
Resilient Modulus (Mr). if only CBR or R are known:
πΉπ‘œπ‘Ÿ
𝑙𝑏
𝑖𝑛2
𝐾𝑁
To Determine Design ESAL:
ESALi = fd ∗ Grn ∗ AADTi ∗ 365 ∗ Ni ∗ FEi , ESAL = ∑ ESALi
fd=design lane factor – From Table 2 using # of Lanes – in % - as decimal
Grn=growth factor – From Table 3 using design period & annual growth rate
AADT = Average Daily Traffic (Given) , 365 = # of days/year,
Ni=number of axles on each vehicle category i
FEi=load equivalency factor for axle category I – From Table 1 – using load.
Design ESAL using Truck Factors:
ESALi = fd ∗ Grn ∗ AADTi ∗ 365 ∗ fi , ESAL = ∑ ESALi
fi= Truck Factor for vehicles in truck category i – From Table 4 using the
type of rural/urban system and vehicle type to get the truck factor.
∑ESALi
π‘₯ 365
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘‡π‘Ÿπ‘’π‘π‘˜π‘ 
∑(# π‘œπ‘“ π‘Žπ‘₯𝑙𝑒𝑠(π‘‘π‘Ÿπ‘’π‘π‘˜π‘ ) π‘₯ πΏπ‘œπ‘Žπ‘‘ πΈπ‘žπ‘’π‘–π‘£π‘’π‘™π‘’π‘›π‘π‘¦ π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ (𝐿𝐸𝐹))π‘₯ 365
=
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘‡π‘Ÿπ‘’π‘π‘˜π‘ 
Overall Truck Factor =
→Traffic Factor is the same as truck factor but considering all vehicles and
not just trucks
→ 365 is to convert to ESAL/year
→ ESAL refers to the damage on the road and it is not linear because
different loads have different load distributions.
→The effect of the passenger cars and the motorists is negligible for the
damage of the road compared to trucks, which means they can be ignored.
→ π‘€π‘Ÿ = 1500 𝐢𝐡𝑅 (𝑓𝑖𝑛𝑒 π‘”π‘Ÿπ‘Žπ‘–π‘›π‘’π‘‘ π‘ π‘œπ‘–π‘™π‘ , 𝐢𝐡𝑅 ≤ 10)
→ π‘€π‘Ÿ = 220 𝐢𝐡𝑅 (𝑓𝑖𝑛𝑒 π‘”π‘Ÿπ‘Žπ‘–π‘›π‘’π‘‘ π‘ π‘œπ‘–π‘™π‘ , 𝐢𝐡𝑅 ≤ 10)
𝑙𝑏
π‘€π‘Ÿ ( 2 ) = 1000 + 555 ∗ (𝑅 − π‘£π‘Žπ‘™π‘’π‘’)π‘“π‘œπ‘Ÿ 𝑅 ≤ 20
𝑖𝑛
𝐾𝑁
π‘€π‘Ÿ ( 2 ) = 145 + 80.4 ∗ (𝑅 − π‘£π‘Žπ‘™π‘’π‘’)π‘“π‘œπ‘Ÿ 𝑅 ≤ 20
π‘š
4) Materials of Construction → π‘Ž3 , π‘Ž2 , π‘Ž1
Quality of materials of pavement layers is determined using:
π‘Ž3 (π‘ π‘’π‘π‘π‘Žπ‘ π‘’), π‘Ž2 (π‘π‘Žπ‘ π‘’), π‘Ž3 (π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’)
𝑆𝑁 = π‘Ž1 𝐷1 + π‘Ž2 𝐷2 π‘š2 + π‘Ž3 𝐷3 π‘š3
- get π‘Ž3 – subbase - from chart using CBR or Mr or R or Triaxial
- get π‘Ž2 – base course - from chart using CBR or Mr or R or Triaxial
- get π‘Ž1 – surface course – from Graph using elastic or resilient modulus
πΉπ‘œπ‘Ÿ
∑ESALi =∑(# π‘œπ‘“ π‘Žπ‘₯𝑙𝑒𝑠(π‘‘π‘Ÿπ‘’π‘π‘˜π‘ ) π‘₯ πΏπ‘œπ‘Žπ‘‘ πΈπ‘žπ‘’π‘–π‘£π‘’π‘™π‘’π‘›π‘π‘¦ π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ (𝐿𝐸𝐹))
→Find LEF’s from Table with single, Tandem, and tridem axles.
π‘š2
∑𝑒𝑓
5) Environment → 𝑒𝑓 =
𝑛
Temperature and rainfall are the two main environmental factors used to
evaluate pavement performance in AASHTO. Mr is determined using the above
formula and Table 19.6, n is the number of Mr’s used. The formula represents
average.
6) Drainage → π‘š2 π‘Žπ‘›π‘‘ π‘š3
Effect of drainage calculated for base (π‘š2 ) and subbase (π‘š3 )
– π‘š2 = π‘š3 𝑒𝑛𝑙𝑒𝑠𝑠 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑
→Use drainage quality and % time of saturation to get m2 and m3
The mi factors are based on both the percentage of time during which the
pavement structure will be nearly saturated and on the quality of drainage,
which is dependent on the time it takes to drain the base layer to 50 percent
of saturation.
7) Reliability (R)
Reliability design level (R) is introduced to account for uncertainties in the
traffic and performance predictions. Determine Reliability from table.
Overall standard deviation (So) is 0.4-0.5 (flexible pavement) and 0.3-0.4 (Rigid
pavement).
Next, SN could be determined by using the monograph.
1. Draw a line joining the reliability level and the overall standard
deviation So, and extend this line to intersect the first TL line at
point A.
2. Draw a line joining point A to the desired ESAL of , and extend
this line to intersect the second TL line at point B.
3. Draw a line joining point B and resilient modulus (Mr) of the
roadbed soil, and extend this line to intersect the design
serviceability loss chart at point C.
4. Draw a horizontal line from point C to intersect the design
serviceability loss (PSI) curve at point D.
5. Draw a vertical line to intersect the design SN, and read this
value
Pavement is made of of 4 layers:
From top to bottom: subsurface course(a1), base(a2),
sub-base(a3), subgrade
To get SN at first – use 𝑴𝒓 of subgrade layer, then,
→ π‘ˆπ‘ π‘’ π‘€π‘Ÿ π‘œπ‘“ π‘‘β„Žπ‘’ π‘π‘Žπ‘ π‘’, π·π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘’ 𝑆𝑁1 (π‘π‘œπ‘šπ‘œπ‘”π‘Ÿπ‘Žπ‘β„Ž)
𝑆𝑁1 = π‘Ž1 𝐷1 𝑔𝑒𝑑 𝐷1 , Round D → D∗ → 𝑆𝑁1∗ = π‘Ž1 𝐷1∗
π‘β„Žπ‘’π‘π‘˜ π‘šπ‘–π‘›π‘–π‘šπ‘’π‘š π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ 𝐷1 𝑒𝑠𝑖𝑛𝑔 π‘‡π‘Žπ‘π‘™π‘’ , 𝑓𝑖𝑛𝑑 𝐷1∗
→ 𝑒𝑠𝑒 π‘€π‘Ÿ π‘œπ‘“ π‘‘β„Žπ‘’ π‘ π‘’π‘π‘π‘Žπ‘ π‘’. π·π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘’ 𝑆𝑁2 (π‘π‘œπ‘šπ‘œπ‘”π‘Ÿπ‘Žπ‘β„Ž)
𝑆𝑁2 = π‘Ž1 𝐷1∗ + π‘Ž2 𝐷2 π‘š2 , 𝑔𝑒𝑑 𝐷2
π‘β„Žπ‘’π‘π‘˜ π‘šπ‘–π‘›π‘–π‘šπ‘’π‘š π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ 𝐷2 𝑒𝑠𝑖𝑛𝑔 π‘‡π‘Žπ‘π‘™π‘’, 𝑓𝑖𝑛𝑑 𝐷2∗
→ 𝑒𝑠𝑒 π‘€π‘Ÿ π‘œπ‘“ π‘‘β„Žπ‘’ π‘ π‘’π‘π‘”π‘Ÿπ‘Žπ‘‘π‘’. π·π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘’ 𝑆𝑁3 (π‘π‘œπ‘šπ‘œπ‘”π‘Ÿπ‘Žπ‘β„Ž)
𝑆𝑁3 = π‘Ž1 𝐷1∗ + π‘Ž2 𝐷2∗ π‘š2 + π‘Ž3 𝐷3∗ π‘š3 , 𝑔𝑒𝑑 𝐷3
π‘β„Žπ‘’π‘π‘˜ π‘šπ‘–π‘›π‘–π‘šπ‘’π‘š π‘£π‘Žπ‘™π‘’π‘’ π‘œπ‘“ 𝐷3 𝑒𝑠𝑖𝑛𝑔 π‘‡π‘Žπ‘π‘™π‘’, 𝑓𝑖𝑛𝑑 𝐷3∗
OR since 𝑆𝑁3 = SN from step 6, then just find D3 simply.
Note: Always round up 1 or 2 inches for the diameter
Equations of Motion
𝑣 = π‘Žπ‘‘ + 𝑣0 ,
𝐷𝑏 =
Dilemma Zone
(𝑣 2 − 𝑣02 )
= π‘Ž(π‘₯ − π‘₯0 ),
2
𝑣02 − 𝑣 2
, 𝐷 = π‘π‘Ÿπ‘’π‘Žπ‘˜π‘–π‘›π‘” π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’.
2𝑔(𝑓 ± 𝐺) 𝑏
1
π‘₯ = π‘Žπ‘‘ 2 + 𝑣0 𝑑 + π‘₯0
2
π‘Ž2 =
𝑣02
𝑣02
𝑣0
𝑀+𝑙
, π‘₯𝑐 = 𝑣0 𝛿2 + ∗ , πœπ‘šπ‘–π‘› = 𝛿2 + ∗ +
2(π‘₯ − 𝑣0 𝛿2 )
2π‘Ž2
2π‘Ž2
𝑣0
2π‘₯
π‘Ž1 = (𝜏−𝛿
2
1)
+
2(𝑀+𝐿−𝑣0 𝜏)
(𝜏−𝛿)2
, τπ‘šπ‘–π‘› = δ2 +
v0
2a∗2
+
w+L
v0
Vertical Curve Crest
πΏπ‘šπ‘–π‘› = 2𝑆 −
200(√β„Ž1 +√β„Ž2 )
|𝐴|
2
(𝑆 ≥ 𝐿), πΏπ‘šπ‘–π‘› =
|𝐴|𝑆 2
200(√β„Ž1 +√β„Ž2 )
2
(𝑆 ≤ 𝐿), 𝐴 = |𝐺2 − 𝐺1 | [π‘Žπ‘›π‘ π‘€π‘’π‘Ÿ 𝑖𝑛 %]. π‘‡π‘œ 𝑓𝑖𝑛𝑑 πΏπ‘šπ‘–π‘› → 𝑠𝑝𝑒𝑒𝑑, 𝑆𝑆𝐷, 𝑆 < 𝐿 π‘œπ‘Ÿ 𝑆 𝐿, πΏπ‘šπ‘–π‘› (𝑓𝑑)
𝐿
𝐿
𝐿
π‘‡π‘œ π‘ π‘œπ‘™π‘£π‘’ π‘£π‘’π‘Ÿπ‘‘π‘–π‘π‘Žπ‘™ π‘π‘’π‘Ÿπ‘£π‘’ → 𝐴, 𝐾 π‘“π‘Ÿπ‘œπ‘š π‘‘π‘Žπ‘π‘™π‘’, 𝐿 = 𝐾𝐴, π‘†π‘‘π‘Ž. 𝐡𝑉𝐢 = π‘†π‘‘π‘Ž. 𝑃𝑉𝐼 − , π‘†π‘‘π‘Ž. 𝐸𝑉𝐢 = π‘†π‘‘π‘Ž. 𝑃𝑉𝐼 + , 𝐸𝑙𝑒𝑣. 𝐡𝑉𝐢 = 𝐸𝑙𝑒𝑣. 𝑃𝑉𝐼 + 𝑔1 ,
2
2
2
𝐿
𝐿𝐺1
2
𝐺1 −𝐺2
𝐸𝑙𝑒𝑣. 𝐸𝑉𝐢 = 𝐸𝑙𝑒𝑣. 𝑃𝑉𝐼 + 𝑔2 , [ π‘‹β„Žπ‘–π‘”β„Ž =
, π‘Œβ„Žπ‘–π‘”β„Ž =
𝐿𝐺12
200(𝐺1 −𝐺2 )
] π‘“π‘œπ‘Ÿ π‘†π‘Ž π‘Žπ‘›π‘‘ πΆπ‘Ÿ,
𝑃𝑒𝑙𝑒 = [𝑉𝑃𝐢𝑒𝑙𝑒 + (
𝐺1
100
π‘₯ 2
) π‘₯] + 𝑦, 𝑦 = 4𝐸 ( ) , 𝐸 =
𝐿
𝐴𝐿
800
Vertical Curve Sag
Same steps as Vertical Curve Crest except πΏπ‘šπ‘–π‘› is found differently. πΏπ‘šπ‘–π‘› = 2𝑆 −
CHAPTER 3 – Traffic Stream Flow Models
π‘ž = π‘“π‘™π‘œπ‘€, π‘˜ = 𝑑𝑒𝑛𝑠𝑖𝑑𝑦, 𝑣, 𝑒 = 𝑠𝑝𝑒𝑒𝑑, β„Ž = π‘‘π‘–π‘šπ‘’ β„Žπ‘’π‘Žπ‘‘π‘€π‘Žπ‘¦, 𝑆 = π‘ π‘π‘Žπ‘π‘–π‘›π‘”
1⁄2 (𝑣 2 − 𝑣02 ) = π‘Ž(π‘₯ − π‘₯0 ) (π‘Ž = π‘Žπ‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›,
𝑣 = 𝑠𝑝𝑒𝑒𝑑,
π‘₯ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘œπ‘›)
2
π‘₯𝑙 = 𝑣 ⁄2𝑑 (𝑑𝑙 = π‘‘π‘’π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘™π‘’π‘Žπ‘‘π‘’π‘Ÿ)
𝑙
2
π‘₯𝑓 = 𝑣 ∗ 𝛿 + 𝑣 ⁄2𝑑 (𝑑𝑓 = π‘‘π‘’π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘“π‘œπ‘™π‘™π‘œπ‘€)
𝑓
π‘₯𝑓 = 𝑆 + π‘₯1 − 𝑁𝐿 − π‘₯0 ,
2
(𝑁 = π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘Ÿπ‘ , 𝐿 = π‘™π‘’π‘›π‘”π‘‘β„Ž π‘œπ‘“ π‘π‘Žπ‘Ÿ)
2
200(β„Ž+π‘†π‘‘π‘Žπ‘›π›½)
𝐴
(𝑆 > 𝐿), πΏπ‘šπ‘–π‘› =
𝐴𝑆 2
200(β„Ž+π‘†π‘‘π‘Žπ‘›π›½)
(𝑆 < 𝐿),
Horizontal Curve
5729.6
1719
βˆ†
𝑅(𝑓𝑑) =
, 𝑅(π‘š) =
, , 𝑇 = π‘…π‘‘π‘Žπ‘› ( ),
π·π‘Ž
π·π‘Ž
2
𝐿=
π‘…βˆ†πœ‹
180
=
100βˆ†
D
,,
βˆ†
βˆ†
βˆ†
𝐿𝐢 = 2𝑅𝑠𝑖𝑛 ( ) , 𝑀 = 𝑅 (1 − π‘π‘œπ‘  ( )) , 𝐸 = 𝑅 (sec ( ) − 1) ,
2
2
2
𝑆 = 𝑣 ∗ 𝛿 + 𝑣 ⁄2𝑑 − 𝑣 ⁄2𝑑 + 𝑁𝐿 + π‘₯0
𝑓
𝑙
Stopping Sight Distance
𝑆 = 1⁄π‘˜ = β„Ž ∗ 𝑒 ,
𝑣02 − 𝑣 2
𝑣02 − 𝑣 2
(β„Ž 𝑖𝑠 β„Žπ‘’π‘Žπ‘‘π‘€π‘Žπ‘¦(𝑠), β„Ž 𝑖𝑠 π‘π‘œπ‘›π‘ π‘‘. π‘ π‘π‘Žπ‘π‘–π‘›π‘”, 𝑆 𝑖𝑠 β„Žπ‘’π‘Žπ‘‘π‘€π‘Žπ‘¦(π‘š), 𝑒 𝑖𝑠 π‘šπ‘’π‘Žπ‘› 𝑠𝑝𝑒𝑒𝑑)
(π‘’π‘β„Žπ‘–π‘™π‘™),
(π‘‘π‘œπ‘€π‘›β„Žπ‘–π‘™π‘™)
𝐷
=
𝐷
=
1
𝑏
𝑏
β„Ž = ⁄π‘ž
2𝑔(𝑓 + 𝐺)
2𝑔(𝑓 − 𝐺)
1
π‘‡π‘–π‘šπ‘’ π‘€π‘’π‘Žπ‘› 𝑆𝑝𝑒𝑒𝑑: 𝑒𝑖 = ⁄𝑁 ∗ ∑𝑣𝑖
𝑓 = 0.6 π‘‘π‘Ÿπ‘¦, 0.3 𝑀𝑒𝑑 𝐷𝑏 = π‘π‘œπ‘ π›Ό, 𝐺 = π‘‘π‘Žπ‘›π›Ό
1
𝐷
𝑆𝑆𝐷 = 𝑣 ∗ 𝛿 + 𝐷𝑏 ,
𝛿 = π‘…π‘’π‘Žπ‘π‘‘π‘–π‘œπ‘› π‘‘π‘–π‘šπ‘’
π‘†π‘π‘Žπ‘π‘’ π‘€π‘’π‘Žπ‘› 𝑆𝑝𝑒𝑒𝑑; 𝑒𝑠 = 1⁄1 1 π‘‘π‘Žπ‘£π‘” = ∗ ∑
𝑁
𝑣𝑖
∑
Curvilinear Motion
𝑁 𝑣𝑖
π‘ž = 𝑒 ∗ π‘˜ (π‘ž = π‘“π‘™π‘œπ‘€,
𝑒 = π‘šπ‘’π‘Žπ‘› 𝑠𝑝𝑒𝑒𝑑, π‘˜ = π‘π‘œπ‘›π‘π‘’π‘›π‘‘π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›)
𝑣2
𝑒 + 𝑓𝑆 = (1 − 𝑓𝑠 𝑒), 𝑒 = π‘‘π‘Žπ‘›π›½, 𝑒𝑓𝑆 = 0 π‘“π‘œπ‘Ÿ π‘‘π‘¦π‘π‘–π‘π‘Žπ‘™ β„Žπ‘–π‘”β„Žπ‘€π‘Žπ‘¦
1
𝑒2
𝑒2
𝑔𝑅
π‘ˆπ‘›π‘–π‘“π‘Ÿπ‘œπ‘š πΉπ‘™π‘œπ‘€: π‘˜ = = 1⁄(𝑒𝛿 +
−
+ 𝑁𝐿 + π‘₯0 )
𝑆
2𝑑𝑓 2𝑠𝑑𝑙
𝑒
π‘ž =𝑒∗π‘˜ =
= π‘˜ ∗ 𝑒(π‘˜)
Regime
Decelerating of leading
Decelerating of following
⁄(𝑒𝛿 + 𝑒2 − 𝑒2 + 𝑁𝐿 + π‘₯ )
0
A
∞
dn
2𝑑𝑓 2𝑠𝑑𝑙
B
de
dn
π‘†π‘‘π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘Ÿπ‘¦ π‘‚π‘π‘ π‘’π‘Ÿπ‘£π‘’π‘Ÿ π‘Žπ‘›π‘‘ π‘€π‘œπ‘£π‘–π‘›π‘” π‘‰π‘’β„Žπ‘–π‘π‘™π‘’; π‘ž
𝑁0⁄
C
∞
de
=
𝑇 (𝑁0 𝑖𝑠 # π‘£π‘’β„Žπ‘–π‘π‘™π‘’π‘ , π‘ž 𝑖𝑠 π‘“π‘™π‘œπ‘€, 𝑇 𝑖𝑠 π‘‘π‘–π‘šπ‘’ )
D
Dec of leading = Dec of following
𝑁𝑝
π‘‚π‘π‘ π‘’π‘Ÿπ‘£π‘’π‘Ÿ π‘šπ‘œπ‘£π‘’π‘ , π‘‘π‘Ÿπ‘Žπ‘“π‘“π‘–π‘ π‘ π‘‘π‘œπ‘π‘π‘’π‘‘; π‘˜ = ⁄𝐿 , 𝑁𝑝 = π‘˜π‘‰π‘‡
E
No Braking
( π‘˜ 𝑖𝑠 π‘π‘œπ‘›π‘π‘’π‘›π‘‘π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› 𝑁𝑝 = #π‘π‘Žπ‘ π‘ π‘’π‘‘, 𝐿 = π‘™π‘’π‘›π‘”π‘‘β„Ž, 𝑉 = 𝑠𝑝𝑒𝑒𝑑, 𝑇 = π‘‘π‘–π‘šπ‘’)
π‘‚π‘π‘ π‘’π‘Ÿπ‘£π‘’π‘Ÿ π‘šπ‘œπ‘£π‘’ π‘€π‘–π‘‘β„Ž π‘ π‘‘π‘Ÿπ‘’π‘Žπ‘š; 𝑁𝑒𝑒𝑑 π‘‘π‘€π‘œ π‘Ÿπ‘’π‘›π‘  π‘“π‘œπ‘Ÿ π‘π‘œπ‘‘β„Ž π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’π‘  π‘£π‘Žπ‘Ÿπ‘¦π‘–π‘›π‘” 𝑠𝑝𝑒𝑒𝑑𝑠. 2π‘’π‘žπ‘›′ 𝑠
Passing Sight Distance
𝑀 = 𝑀0 − 𝑀𝑝 = π‘žπ‘‡ − π‘˜π‘‰π‘‡ (π‘€π‘œ 𝑖𝑠 # π‘œπ‘£π‘’π‘Ÿπ‘‘π‘Žπ‘˜π‘–π‘›π‘”, 𝑀𝑝 𝑖𝑠 #π‘π‘Žπ‘ π‘ π‘’π‘‘)
π‘Žπ‘‘
2𝑑
𝑀⁄ = π‘ž − π‘˜π‘‰, 𝑀𝑀⁄ = π‘ž − π‘˜π‘‰ , π‘€π‘Ž⁄ = π‘ž − π‘˜π‘‰ , π‘ž = (𝑀𝑀 + π‘€π‘Ž )⁄
𝑑1 = 1.47𝑑 [𝑣 − π‘š + ( 1 )] , 𝑑2 = 1.47𝑉𝑑2 , 𝑑4 = 2 , 𝑑3 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛.
𝑀
π‘Ž
2
3
𝑇
𝑇𝑀
π‘‡π‘Ž
(𝑇𝑀 + π‘‡π‘Ž )
𝑀𝑀
π‘ž 𝐿
Lateral
Displacement
π‘†π‘π‘Žπ‘π‘’ π‘€π‘’π‘Žπ‘› 𝑆𝑝𝑒𝑒𝑑;
=π‘ž− ( )
𝑇𝑀
𝑒 𝑇𝑀
πœƒπ‘–π‘  π‘Žπ‘›π‘”π‘™π‘’ π‘œπ‘“ π‘‘π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘, π‘Ž 𝑖𝑠 π‘Žπ‘π‘π‘’π‘™. ,
π‘‘πœƒ
π‘£π‘Ž
𝐿
𝑀𝑀
𝑀𝑀
𝑙 𝑖𝑠 π‘™π‘’π‘›π‘”π‘‘β„Ž π‘‘π‘œ π‘‘π‘–π‘ π‘π‘™π‘Žπ‘π‘’. ,
= 2 2 (
)
π‘„π‘’π‘Žπ‘›π‘‘π‘–π‘‘π‘¦; = π‘‘π‘Žπ‘£π‘” = π‘‡π‘Žπ‘£π‘’ = 𝑇𝑀 −
,
𝑇𝑀 − π‘‡π‘Žπ‘£π‘’ =
𝑑𝑑
π‘Ž +𝑙
𝑒
π‘ž
π‘ž
𝑣 𝑖𝑠 𝑠𝑝𝑒𝑒𝑑
(𝑇𝑀 𝑖𝑠 π‘‘π‘–π‘šπ‘’ π‘‘π‘Ÿπ‘Žπ‘£π‘’π‘™ π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘›, 𝑀𝑀 𝑖𝑠 π‘π‘œπ‘’π‘›π‘‘ π‘‘π‘’π‘Ÿπ‘–π‘›π‘” π‘Ÿπ‘’π‘›, π‘ž 𝑖𝑠 π‘“π‘™π‘œπ‘€)
Super-elevation Design
(−𝑀𝑀 ); π‘‡π‘Žπ‘£π‘’ > 𝑇𝑀 (𝑇𝑒𝑠𝑑 π‘“π‘Žπ‘ π‘‘π‘’π‘Ÿ π‘‘β„Žπ‘Žπ‘› π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’)
(+𝑀𝑀 ); π‘‡π‘Žπ‘£π‘’ < 𝑇𝑀 (𝑇𝑒𝑠𝑑 π‘ π‘™π‘œπ‘€π‘’π‘Ÿ π‘‘β„Žπ‘Žπ‘› π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’)
𝑣2
𝑒
+
𝑓
=
𝑀𝑀 = 0 (𝑇𝑒𝑠𝑑 𝑖𝑠 π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’)
𝑆
𝑔𝑅
𝐿
𝑒=
(π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘ π‘‘π‘Ÿπ‘’π‘Žπ‘š 𝑠𝑝𝑒𝑒𝑑)
π‘‡π‘Žπ‘£π‘’
π‘†β„Žπ‘œπ‘π‘˜π‘€π‘Žπ‘£π‘’π‘ :
π‘žπ‘ − π‘žπ‘Ž
𝑒𝑠𝑀 = (
)
π‘˜π‘ − π‘˜π‘Ž
(π‘žπ‘ 𝑖𝑠 π‘“π‘™π‘œπ‘€ 𝑒𝑛𝑑, π‘žπ‘Ž 𝑖𝑠 π‘“π‘™π‘œπ‘€ π‘ π‘‘π‘Žπ‘Ÿπ‘‘, π‘˜π‘ 𝑖𝑠 π‘π‘œπ‘›π‘. 𝑒𝑛𝑑, π‘˜π‘Ž 𝑖𝑠 π‘π‘œπ‘›π‘. π‘ π‘‘π‘Žπ‘Ÿπ‘‘)
(+)𝑒𝑠𝑀 𝑖𝑠 𝑖𝑛 π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘ π‘‘π‘Ÿπ‘’π‘Žπ‘š π‘“π‘™π‘œπ‘€, (−)𝑒𝑠𝑀 𝑖𝑠 π‘’π‘π‘ π‘‘π‘Ÿπ‘’π‘Žπ‘š π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘›, 𝑒𝑠𝑀
= 0 𝑖𝑠 π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘Ÿπ‘¦
Level of Service (Freeway)
Step 1: Compute FFS → 𝐹𝐹𝑆 = 𝐡𝐹𝐹𝑆 − π‘“πΏπ‘Š − 𝑓𝐿𝐢 − 𝑓𝑁 − 𝑓𝐼𝐷 ,
FFS = Free Flow Speed,
BFFS = base free-flow speed, 110 km/h (urban), 120 km/h (rural)
Adjustments: fLW=Lane Width , fLC=right shoulder Lateral Clearance,
fN=Number of Lanes ( rural freeway - fN = 0) , fID=Interchange density
Step 2: Compute vp→ 𝑣𝑝 =
𝑉
𝑃𝐻𝐹∗𝑁∗𝑓𝑝 ∗𝑓𝐻𝑉
, 𝑓𝐻𝑉 =
1
1+𝑃𝑇 (𝐸𝑇 −1)+𝑃𝑅 (𝐸𝑅 −1)
vp=15 min passenger car equivalent flow rate (pc/h/ln),
PHF=Peak hour factor, 𝑃𝐻𝐹 =
π»π‘œπ‘’π‘Ÿπ‘™π‘¦ π‘£π‘œπ‘™π‘’π‘šπ‘’
4∗π‘π‘’π‘Žπ‘˜ 15 min π‘£π‘œπ‘™π‘’π‘šπ‘’
(Typically b/w 0.8 & 0.95)
V
= π‘€π‘Žπ‘₯ 15 min π‘“π‘™π‘œπ‘€ π‘Ÿπ‘Žπ‘‘π‘’
PHF
V=hourly peak vehicle volume in one direction (veh/h),
N=Number of travel lanes in one direction,
fp=Driver population factor (0.85-1.0, use 1 for commuter traffic)
fHV=Heavy vehicle adjustment factor
PT=% of trucks (in decimal), PR=% of recreation vehicles (in decimal),
ET=Truck adjustment Factor, ER=Recreation vehicle adjustment Factor
ET and ER depend on type of terrain (Level, Rolling, Mountainous)
For upgrades, ET and ER also depend on upgrade (%)and length(km),
For Downgrades, ET depends on downgrade%) and length, but ER is treated as
a level terrain
Step 3: Average passing car speed (S)
Use 𝒗𝒑 and FFS Curve in Curve to find average passenger car speed (S) OR
Use:
For 90 < FFS ≤ 120 km/h and (3100 – 15FFS) < vp ≤ (1800 + 5FFS)
𝑣𝑝 +15𝐹𝐹𝑆−3100 2.6
1
𝑆 = 𝐹𝐹𝑆 − [28 (23𝐹𝐹𝑆 − 1800) (
20𝐹𝐹𝑆−1300
)
𝑣𝑝
𝑆
]
Vp = flow rate (pc/km/ln), S = average passenger-car speed (km/h)
Step 5: Compute LOS using Table or Graph for Freeway
* compare the calculated D with the density range in Table 1 – Freeway – LOS
+ When comparing – Choose lower LOS at all times !
** the only difference between upgrade and downgrade is the 𝑓𝐻𝑉 factor –
The effect of heavy trucks is more severe in the upgrade section which means
that LOS of Upgrade will be less than LOS of Downgrade.
Find Capacity - Use LOS E and find Vp in PC/hr/lane using FFS limits in table
V
PHF∗N∗fp ∗fHV
→ vp ∗ 𝑁 ∗ 𝑓𝑝 ∗ 𝑓𝐻𝑉 =
V
PHF
V
Then, Hourly Volume =
∗ 𝑃𝐻𝐹
PHF
Find Number of Lanes – Using the LOS and the FFS – determine the vp and
then use
𝑁=
V
vp ∗PHF ∗𝑓𝑝 ∗𝑓𝐻𝑉
,
V
PHF
& No passing Zone
𝑉
1
,𝑓 =
,
𝑃𝐻𝐹 ∗ 𝑓𝐺 ∗ 𝑓𝐻𝑉 𝐻𝑉 1 + 𝑃𝑇 (𝐸𝑇 − 1) + 𝑃𝑅 (𝐸𝑅 − 1)
π»π‘œπ‘’π‘Ÿπ‘™π‘¦ π‘£π‘œπ‘™π‘’π‘šπ‘’
𝑃𝐻𝐹 =
4 ∗ π‘π‘’π‘Žπ‘˜ 15 min π‘£π‘œπ‘™π‘’π‘šπ‘’
vp=Passenger car equivalent flow rate for peak 15min period,
V=hourly volume (vph), fHV=adjustment factor for heavy vehicles,
fG=grade adjustment for level or rolling terrain
PT and PR = Decimal partition of trucks (buses) and RV’s in traffic,
ET and ER = Passenger car equivalent
𝑣𝑝 =
To calculate 𝒗𝒑 → Estimate vp using PHF, use 𝑣𝑝 =
𝑉
𝑃𝐻𝐹
calculated value of
Then, calculate BPTSF & fd/np AND find PTSF and get LOS from table
, D=Density (pc/Km/ln)
Find max 15 min flow rate - vp =
𝑃𝑇𝑆𝐹 = 𝐡𝑃𝑇𝑆𝐹 + 𝑓𝑑/𝑛𝑝 ,
𝐡𝑃𝑇𝑆𝐹 = 100(1 − 𝑒 −0.000879𝑉𝑝 ),
PTSF=Percent spent following for both directions (%),
BPTSF=Base percent time spent following for both directions (%),
fd/np=adjustment in PTSF (%), - found from table using vp & Directional Split
vp to estimate fG, ET and ER which will provide value of vp close to vp initially
calculated. and check that new vp and old vp are in the same range. If yes,
Continue, If not, use new vp and find new fG & fHV, and so on.
For 90 < FFS ≤ 120 km/h and vp ≤ (3100 - 15FFS) → 𝑆 = 𝐹𝐹𝑆
Step 4: Compute the density (D)
𝐷=
Level of Service (Two Lane)
Capacity of two-lane highways is 1,700 pc/hr for each direction and will
normally not exceed 3,200 pc/hr for both directions for long section of the
highway
Class I two-lane highways – LOS depends on % time spent following(PTSF)
in platoons & Average travel speed (ATS). Then Compare, take lower LOS
Class II two-lane highways - LOS depends only on the % time spent
following (PTSF)
Step 1: Compute PTSF→
= π‘€π‘Žπ‘₯ 15 min π‘“π‘™π‘œπ‘€ π‘Ÿπ‘Žπ‘‘π‘’ – and
use vp & FFS in Graph to see whether Number of Lanes meets the
required LOS
→A freeway is a divided highway with full access control and two or more lanes in
each direction. → An LOS is a performance measure of a highway at traffic volume less
than capacity
→LOS A - Free-flow operation β–ͺ Vehicles are completely free to manoeuvre β–ͺ Effects of
incidents or point breaks are easily absorbed - Density (D) ≤ 7 pc/km/ln
→LOS B - Free-flow operation β–ͺ Ability to maneuver is only slightly restricted β–ͺ Effects
of minor incidents still easily absorbed - Density (D) ≤ 11 pc/km/ln
→LOS C - Speeds at or near FFS β–ͺ Freedom to maneuver is noticeably restricted β–ͺ
Queues may form behind any significant blockage. - Density (D) ≤ 16 pc/km/ln
→LOS D - Speeds decline slightly with increasing flows β–ͺ Density increases more quickly
β–ͺ Freedom to maneuver is more noticeably limited β–ͺ Minor incidents create queuing Density (D) ≤ 22 pc/km/ln
→LOS E - Operation near or at capacity β–ͺ No useable gaps, and little room to
manoeuvre β–ͺ Any disruption causes queuing Density (D) ≤ 28 pc/km/ln
→LOS F - Breakdown in flow β–ͺ Queues form behind breakdown points β–ͺ Demand >
capacity - Number of cars arriving at a point > the number discharged
Step 2: Compute ATS
𝐴𝑇𝑆 = 𝐹𝐹𝑆 − 0.0125𝑣𝑝 − 𝑓𝑛𝑝 ,
ATS=Average travel speed for both directions of travel combined (mi/h),
fnp=adjustment for the percentage of no passing zones
𝐹𝐹𝑆 = 𝐡𝐹𝐹𝑆 − 𝑓𝐿𝑆 − 𝑓𝐴 (π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’)
FFS=Free flow speed (Km/h).
fLS=Adjustment for lane and shoulder width
fA=Adjustment for number of access points per mile
𝑉𝑓
𝑝𝑐
𝐹𝐹𝑆 = 𝑆𝐹𝑀 + 0.0125 ∗
(𝑓𝑖𝑒𝑙𝑑 π‘šπ‘’π‘Žπ‘ π‘’π‘Ÿπ‘’π‘šπ‘’π‘›π‘‘ π‘Žπ‘‘ > 200 ),
𝑓𝐻𝑉
β„Ž
SFM=Mean Speed of traffic measured in the field (mi/h),
Vf = observed flow rate for period when field data was obtained (veh/h)
fHV = heavy-vehicle adjustment factor
𝑉
1
𝑣𝑝 =
, 𝑓 =
,
𝑃𝐻𝐹 ∗ 𝑓𝐺 ∗ 𝑓𝐻𝑉 𝐻𝑉 1 + 𝑃𝑇 (𝐸𝑇 − 1) + 𝑃𝑅 (𝐸𝑅 − 1)
fG=grade adjustment for level or rolling terrain
fG & fHV are dependant on vp, therefore, 𝑣𝑝 =
𝑉
𝑃𝐻𝐹
, then determine fG & fHV,
and check that new vp and old vp are in the same range. If yes, Continue, If
not, use new vp and find new fG & fHV, and so on.
Then, find fnp and calculate ATS and get LOS from table.
Step 3: Compute LOS for Class I and Class II
1) First comparing vp with the two-way capacity of 3,200 pc/h
2) If vp is greater than capacity, the LOS is F
3) Also, if the demand flow rate in either direction (vp times directional
split) is > 1700 pc/h, the LOS is F
Class I uses both ATS and PTSF , Class II uses only PTSF
Chapter 1 – Introduction
→A transportation system may be defined as consisting of the fixed facilities, the flow
entities, and the control system that permit people and goods to overcome the friction
of geographical space efficiently in order to participate in a timely manner in some
desired activity.
→Transportation system classification: Land, Air, Water, Pipelines.
Chapter 2 – Roadway Design
→Braking Distance is affected by the original speed of the vehicle, the type of brake
system in use, and the coefficient of friction between its tires and the road surface.
→ Banking or super-elevation – components of vehicle’s weight increase the resistance
to the sliding tendency
→ Stopping distance = Braking distance + Time for perception-reaction x speed
→ Freeways β–ͺ Uninterrupted traffic flow β–ͺ Full control of access (access to and exit from
these facilities are permitted only at controlled locations such as entrance and exit
ramps) → Highways β–ͺ Uninterrupted traffic flow β–ͺ Partial control of access (access or
exit may have permitted directly from or to abutting property or via a limited number
of at-grade intersection) → Arterial roads: high-capacity urban roads. The primary
function of an arterial road is to deliver traffic from collector roads to freeways.
→ Super-elevation design
β–ͺ Normal crown: typical cross section on a tangent section (no super-elevation)
β–ͺ Remove crown (Reverse crown): a super-elevated cross section which is sloped
across the entire traveled way in the same direction and at a rate equal to the typical
cross slope on tangent section (e.g. 2%)
β–ͺTangent runout: change from a normal crown section to a point where the adverse
cross slope of the outside lane is removed (i.e. the outside lane is level)
β–ͺSuper-elevation runoff: change in cross slope from the end of tangent runout to a
section that is fully super-elevated.
Chapter 3 – Traffic Stream Flow Models
→Traffic Flow Elements →• Flow (q) • Density/Concentration (k) • Speed (v, u) • Time
Headway (h) • Space Headway or Spacing (S)
→ Free-flow condition: very low concentration and very high speed (speed ↑,
spacing ↑, concentration ↓)
→ Free-flow speed, uf: maximum speed at zero concentration (when concentration
approaches zero)
→Concentration (k): ratio of the number of vehicles appearing on the photograph to
the length of the roadway segment.
→Time headway (h): difference between the time when the front of a vehicle arrives
at a point on the highway and the time the front of the next vehicle arrives at the
same point
→h = (constant spacing) / (constant speed of operation) → h = 1/ q **
→Space headway (S): difference in position between the front of a vehicle and the
front of the next vehicle
Chapter 5 – Pavement Design - Part 1:
Pavement materials & Types:
Asphalt
ο‚· Strong cement, readily adhesive, highly waterproof, and durable (Asphalt Institute)
ο‚· Asphalt concrete
ο‚· Flexible pavement: maintains intimate contact with and distributes loads to the
subgrade and depends on aggregate interlock, particle friction, and cohesion for
stability
Portland cement
ο‚· Rigid pavement
ο‚· More advantages compared to asphalt pavement in terms of strength requirement
ο‚· Distribution of loads to the subgrade, Portland-cement concrete slab of relatively
high bending resistance
Pavement Design
Traffic load (Most important – thickness of pavement), Soils, Environment, Reliability
Subgrade Soil Classification
Resilient Modulus – Mechanical Behavior - measure of material stiffness
Granular base/subbase layers: elastoplastic behavior. Designed to simulate the
behavior of soils and granular materials when subjected to traffic loading within a
pavement system. Similar to modulus of elasticity.
Depends on Density, Gradation, fine contents, and moisture content, At low levels of
moisture content: increase in the resilient modulus due to suction. At high levels of
moisture content: reduction in the resilient modulus due to pore pressure.
California Bearing Ratio - Relative strength of a soil with respect to crushed rock.
Penetration test for evaluation of the mechanical strength of natural ground,
subgrades and basecourses. Determination of the load deformation curve of the soil
in the laboratory using the standard CBR testing equipment.
Chapter 5 – Pavement Design - Part 2:
Flexible Pavement Design
Layers(bottom to top): 1. Subgrade, 2. Subbase Course, 3. Base Course, 4. Surface
Course.
Subgrade: natural materials, foundation of the pavement structure, certain strength
properties
Subbase:
• A layer of granular materials that is located between the subgrade and base course
• Quality of materials is superior to that of the subgrade but inferior to that of the
base course
• Can be omitted if the quality of the subgrade material meets the requirements of
the subbase
• Specifications are in terms of plasticity, gradation, and strength
• Main functions: • Reduces the stresses applied on the subgrade
• Serves in water drainage
• Protects the base course against volume changes of the subgrade
Granular base:
• Usually granular materials such as crushed stone, crushed or uncrushed gravel or
slag, and sand
• Strict specifications for plasticity, gradation, and strength
• Can be stabilized using Portland cement, asphalt, or lime when a higher strength is
required or when the available materials do not meet the specifications
• Main functions: • Acts as a foundation to the surface course
• Distributes the stresses on the subbase into a large area
• Protects the surface course against volume changes that may take place in the
subgrade
Surface:
The surface course is the upper course of the road pavement consists of: a mixture of
mineral aggregates and asphalt.
Main functions: • Transmits the wheel loads to the underlying layers within
acceptable limits. • Resists abrasive forces due to traffic.
• Provides skid-resistant driving surface.
• Preventing the penetration of surface water into the underlying layers and
withstands high tire pressures.
• The thickness of the surface layer can vary from 3 in. to more than 6 in., depending
on the expected traffic on the pavement.
Asphalt:
Natural substance that has some amazing physical properties
β–ͺ Adhesive, elastic, able to stretch, bend and flex without breaking (cohesive)
β–ͺ Waterproofing β–ͺ At air temperatures, very thick liquid (highly viscous)
β–ͺ When heated, it becomes thinner and easier to use
Properties of Asphalt Materials:
Consistency β–ͺ Vary from solid to liquid β–ͺ Consistency of asphalt + associated
temperature
βœ“ Aging and temperature sustainability
β–ͺ When exposed to environmental elements: deterioration, loose plasticity and
become brittle
β–ͺ This natural deterioration of the asphalt material is known as weathering.
β–ͺ Durability: resistance of the asphalt material to weathering.
Asphalt Mixtures:
Asphalt cement + coarse aggregate + fine aggregate + other materials
β–ͺ Hot-mix, hot-laid/hot-mix, cold-laid/cold-mix, cold-laid
β–ͺ Resist deformation from imposed traffic loads, be skid resistant even when wet,
and not be affected easily by weathering forces
β–ͺ Hot-mix, hot-laid asphalt mixture is produced by properly blending asphalt cement,
coarse aggregate, fine aggregate, and filler (dust) at temperatures ranging from about
80 C to 160 C.
β–ͺ Hot-mix, hot-laid asphalt mixture normally is used for high type pavement
construction
Asphalt Mixtures: hot-mix, cold-laid
β–ͺ Manufactured hot and then shipped and laid immediately or stockpiled for used at a
future date β–ͺ Small jobs β–ͺ Patching high-type pavement (asphalt concrete surfaced)
Asphalt Mixtures: cold-mix, cold laid
β–ͺ Emulsified asphalts and low-viscosity cutback asphalts are used to produce cold-mix
asphalt mixtures. β–ͺ Immediately after production or stockpiled for use later
General Principles of Flexible Pavement Design β–ͺ Multilayered elastic system
• Objective: is to determine the minimum thickness of pavement layers that is enough
• To Avoid overloading or overstressing the subgrade
• Avoid overloading or overstressing any one or more of the pavement layers
• Maintain good serviceability performance along the pavement design life
Pavement structure required on top of a specific layer is expressed in terms of a
Structural number (SN) which is an index number which may be converted to
thickness of various flexible pavement layers through the use of layer coefficients
Related documents
APA Perpetual Pavement Award - Pennsylvania Asphalt Pavement
APA Perpetual Pavement Award - Pennsylvania Asphalt Pavement
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Personal Narrative
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Assignment2
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Course Introduction
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