Traffic and Highway Engineering - With Mindtap
Traffic and Highway Engineering - With Mindtap
5th Edition
ISBN: 9781305360990
Author: Garber
Publisher: CENGAGE L
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Chapter 18, Problem 16P
To determine

The initial trial asphalt content for different blends.

Expert Solution & Answer
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Answer to Problem 16P

  4.65%,

  4.69%

  and44.45%

Explanation of Solution

Given information:

Nominal maximum sieve of each aggregate blend = 19 mm.

  Traffic and Highway Engineering - With Mindtap, Chapter 18, Problem 16P

Calculation:

For trial blend 1, we have:

The amount of asphalt binder absorbed by the aggregates is estimated

from Eq. 18.18 as

  Vba=Ps(1Va)PbGb+PsG se[1Gsb1Gse]

Where, Vba is the volume of absorbed binder, cm3/cm3 of mix,

  Pb is the percent of binder (assumed  0.05 ),

  Ps is the percent of aggregate (assumed 0.95 ),

  Gb is the specific gravity of binder (assumed 1.02 ),

  Gse is the effective specific gravity of the aggregate blend

  Gsb is the bulk specific gravity of the aggregate blend

  Va is thevolume of air voids (assumed 0.04 cm3/cm3 of mix ).

Substitute the values in the required equation, we have

  Vba=Ps( 1 V a ) P b G b + P s G se [1 G sb1 G se]Vba=0.95( 10.04) 0.05 1.02+ 0.95 2.765[12.69812.765]Vba=0.95( 0.96)0.049+0.3436[0.3710.362]Vba=0.9120.3926[0.009]Vba=0.0209.

Estimate the percent of effective asphalt binder by volume using theempirical expression given as follows:

  Vbe=0.176(0.0675)logSn

Where, Vbe is the volume of effective binder content,

  Sn is the nominal maximum sieve size of the total aggregate in the trial aggregate

gradation (mm).

Substitute the values in the required equation, we have

  Vbe=0.176(0.0675)log(19)Vbe=0.176(0.0675)(1.2788)Vbe=0.1760.0863.Vbe=0.0896.

Now, calculate the mass of aggregate by using the following formula:

  WS=Ps(1Va)PbGb+PsG se

Where, WS is the mass of aggregate

Substitute the values, we have

  WS=0.95( 10.04) 0.05 1.02+ 0.95 2.765WS=0.95( 0.96)0.049+0.3436WS=0.9120.3926WS=2.323grams.

A trial percentage of asphalt binder then is determined for each trial

aggregate blend using the following equation.

  Pbi=Gb(V be+V ba)(Gb( V be + V ba ))+Ws×100 where

Where, Pbi is the percent of binder by mass of mix.

Substitute the values, we have

  Pbi=1.02( 0.090+0.021)( 1.02( 0.090+0.021 ))+2.323×100Pbi=1.02( 0.111)( 1.02( 0.111 ))+2.323×100Pbi=0.113220.11322+2.323×100Pbi=11.3222.43622Pbi=4.647Pbi=4.65%.

For trial blend 2, we have:

The amount of asphalt binder absorbed by the aggregates is estimated

from Eq. 18.18 as

  Vba=Ps(1Va)PbGb+PsG se[1Gsb1Gse]

Where, Vba is the volume of absorbed binder, cm3/cm3 of mix,

  Pb is the percent of binder (assumed  0.05 ),

  Ps is the percent of aggregate (assumed 0.95 ),

  Gb is the specific gravity of binder (assumed 1.02 ),

  Gse is the effective specific gravity of the aggregate blend

  Gsb is the bulk specific gravity of the aggregate blend

  Va is the volume of air voids (assumed 0.04 cm3/cm3 of mix ).

Substitute the values in the required equation, we have

  Vba=Ps( 1 V a ) P b G b + P s G se [1 G sb1 G se]Vba=0.95( 10.04) 0.05 1.02+ 0.95 2.766[12.69812.766]Vba=0.95( 0.96)0.049+0.3434[0.3710.361]Vba=0.9120.3924[0.01]Vba=0.023.

Estimate the percent of effective asphalt binder by volume using the empirical expression given as follows:

  Vbe=0.176(0.0675)logSn

Where, Vbe is the volume of effective binder content,

  Sn is the nominal maximum sieve size of the total aggregate in the trial aggregate

gradation (mm).

Substitute the values in the required equation, we have

  Vbe=0.176(0.0675)log(19)Vbe=0.176(0.0675)(1.2788)Vbe=0.1760.0863.Vbe=0.0896.

Now, calculate the mass of aggregate by using the following formula:

  WS=Ps(1Va)PbGb+PsG se

Where, WS is the mass of aggregate

Substitute the values, we have

  WS=0.95( 10.04) 0.05 1.02+ 0.95 2.766WS=0.95( 0.96)0.049+0.3434WS=0.9120.3924WS=2.324grams.

A trial percentage of asphalt binder then is determined for each trial

aggregate blend using the following equation.

  Pbi=Gb(V be+V ba)(Gb( V be + V ba ))+Ws×100 where

Where, Pbi is the percent of binder by mass of mix.

Substitute the values, we have

  Pbi=1.02( 0.090+0.022)( 1.02( 0.090+0.022 ))+2.324×100Pbi=1.02( 0.112)( 1.02( 0.112 ))+2.324×100Pbi=0.114240.11424+2.324×100Pbi=11.4242.43824Pbi=4.685Pbi=4.69%.

For trial blend 3, we have:

The amount of asphalt binder absorbed by the aggregates is estimated

from Eq. 18.18 as

  Vba=Ps(1Va)PbGb+PsG se[1Gsb1Gse]

Where, Vba is the volume of absorbed binder, cm3/cm3 of mix,

  Pb is the percent of binder (assumed  0.05 ),

  Ps is the percent of aggregate (assumed 0.95 ),

  Gb is the specific gravity of binder (assumed 1.02 ),

  Gse is the effective specific gravity of the aggregate blend

  Gsb is the bulk specific gravity of the aggregate blend

  Va is the volume of air voids (assumed 0.04 cm3/cm3 of mix ).

Substitute the values in the required equation, we have

  Vba=Ps( 1 V a ) P b G b + P s G se [1 G sb1 G se]Vba=0.95( 10.04) 0.05 1.02+ 0.95 2.764[12.71112.764]Vba=0.95( 0.96)0.0490+0.3437[0.36880.3618]Vba=0.9120.3927[0.0070]Vba=0.01626.Vba=0.0163.

Estimate the percent of effective asphalt binder by volume using the empirical expression given as follows:

  Vbe=0.176(0.0675)logSn

Where, Vbe is the volume of effective binder content,

  Sn is the nominal maximum sieve size of the total aggregate in the trial aggregate

gradation (mm).

Substitute the values in the required equation, we have

  Vbe=0.176(0.0675)log(19)Vbe=0.176(0.0675)(1.2788)Vbe=0.1760.0863.Vbe=0.0896.

Now, calculate the mass of aggregate by using the following formula:

  WS=Ps(1Va)PbGb+PsG se

Where, WS is the mass of aggregate

Substitute the values, we have

  WS=0.95( 10.04) 0.05 1.02+ 0.95 2.764WS=0.95( 0.96)0.049+0.3437WS=0.9120.3927WS=2.322grams.

A trial percentage of asphalt binder then is determined for each trial

aggregate blend using the following equation.

  Pbi=Gb(V be+V ba)(Gb( V be + V ba ))+Ws×100 where

Where, Pbi is the percent of binder by mass of mix.

Substitute the values, we have

  Pbi=1.02( 0.090+0.016)( 1.02( 0.090+0.016 ))+2.322×100Pbi=1.02( 0.106)( 1.02( 0.106 ))+2.322×100Pbi=0.108120.10812+2.324×100Pbi=108.122.43212Pbi=44.45%.

Conclusion:

Therefore, the initial trial asphalt content for1st, 2nd and 3rd blends is as follows 4.65%, 4.69% and 44.45% respectively.

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