Question

Two routes connect an origin and destination with performance functions t1 = 5 + 3x1 and t2 = 7 + X2, with t's in minutes and x's in thousands of vehicles per hour. Total origin-destination demand is 7000 vehicles in the peak hour. Traffic is consisted of 6100 passenger cars (each with two 2-kip single axles), 800 buses (each with two 2-kip single axles) and 100 heavy trucks (each with one 12-kip single axle and two 34-kip tandem axles.) How many ESALs will travel of the pavement of route 1 and route 2 during the peak hour? Assume user equilibrium exists between origin and destination. Both routes are constructed with flexible pavement. The pavement is design with 10-inch sand-mix asphaltic surface, 10- inch crushed stone base, and a 10-inch crushed stone subbase. All drainage coefficients are 1.0, and the final PSI is 2.5.

Answer 1

We have two routes from A to B

Route 1 - has x1 (thousands of vehicles) and at ravel time of 5 +3x1

Route 2 - has x2 (thousands of vehicles) and at ravel time of 7 +x2

For user equilibrium we know that the Z function is

where t(x1) = 5 +3x1 and t(x2) = 7 +x2

Also we know that x1 + x2 = 7

only two paths so the travel time should also be equal

therefore

5 +3x1 = 7 +x2

So solving for x1 and x2 we get x1= 2.25 and x2 = 4.75

Therefore 2250 vehicles travel on Route 1 and 4750 vehicles travel on Route 2

Now that we know flows, we can calculate the ESALS.

WE know the vehicle composition by vehicle type. This is shown below.

Vehicle Composition cars 6100 0.871429 buses 800 0.114286 trucks 1001 0.014286 7000

So for each route, we can calculate the number of cars, buses and trucks as follows

Total vehicles 2250 Cars 1960.71 4139.29 Buses 257.14 542.86 Trucks 32.14 67.86 4750

We know that for each vehicle type the # of kips is as follows

Cars 2 Buses 2 Trucks 80 kips

So calculate the kips on each route as follows and hence the ESALS

1 ESAL = 18 kips

so for route 1 we have

1960.71*2 + 257.14 * 2 + 32.14 * 80 = 7007.143 kips = 7007.143/18 = 389.286 ESAL

so for route 2 we have

4139.29*2 + 542.86*2 + 67.86*80 = 14792.86 kips = 921.825 ESAL