Design and Analysis of Asphalt Pavements

Chapter 13 highlights the design and analysis of asphalt pavements which is an important part of pavement engineering that deals with structural-empirical as well as empirical-mechanistic designs of asphalt pavements and the analysis of these pavements for stresses, strains, and deflections. The main inputs for empirical design of asphalt pavements include traffic loading, material properties, reliability, performance indicators, and pavement drainage quality. The mechanistic-empirical (M-E) design, on the other hand, takes into consideration the mechanistic analysis of the pavement structure and its performance over time regarding fatigue, rutting, and thermal cracking based on the available traffic, material, and environmental inputs. Consequently, the availability of this data to input in the M-E design defines three levels of M-E design. Level 3 provides the least level of accuracy in M-E design. This level may be used for less important roads or highways such as low-volume roads where the consequences of early failure are minimum. In this level, normally typical default values (such as average values) for the design inputs in the area are used and selected by the user. Level 2 offers an intermediate level of accuracy and uses values for the design inputs from available data sources of the agency, from limited testing, or based on correlations. The user selects these values to be used in the design. On the other hand, Level 1 provides the highest level of accuracy, and, therefore, has the least uncertainty (or error) level. This level, due to its high reliability and accuracy, is used for major highways and important roads with heavy traffic where the safety and economic consequences of early failure are high. In this level, the values of the design inputs are based on laboratory or field testing that requires more resources and time than other levels. The mechanistic analysis of asphalt pavements focuses on the determination of stresses, strains, and deflection on critical locations in the pavement structure under traffic loading. The analysis of asphalt pavements is composed of three different types: (1) the first one deals with one-layered pavement systems where the pavement structure is considered as one layer with infinite thickness, (2) the second type deals with two-layered pavement systems where the asphalt pavement structure is considered as two layers; one with finite thickness over another layer with infinite thickness, and (3) the third type considers asphalt pavements as three-layered systems; the first two layers with finite thickness over the last underneath layer with an infinite thickness. The second and third types are very close to reality and the real-life situation. The two-layered pavement systems represent full-depth asphalt pavements where there is an asphalt pavement layer over a subgrade layer. The three-layered pavement systems represent the conventional (traditional) asphalt pavements where there is an asphalt layer over base layers over a subgrade layer. The analysis of pavements goes in parallel with design due to its high correlation with design, particularly M-E design. The mechanistic analysis of an asphalt pavement provides an idea of how the different pavement layers would dissipate the high stresses and strains on the surface of the pavement as it gets deeper and deeper in the pavement structure. Pavement structures with high-quality materials or high-thickness layers would dissipate more stresses and strains than layers with low-quality materials or low-thickness layers. Therefore, reliability and cost play a big role in the entire design process. This section will provide questions and practical problems that deal with design as well as analysis of asphalt pavements. The analysis part will focus on multilayered pavement systems because they represent the real-world situation. 13.1 Select a typical or reasonable value from the set in the second column for each item (or property) of the group in the first column in Table 13.1 . 376 Solution: See Table 13.2 . 377 13.2 Indicate the effect of the increase in the value of each of the following design inputs on the design thickness of the hot-mix asphalt (HMA) layer of a flexible pavement (see Table 13.3 ). Solution: See Table 13.4 . 13.3 Order or rank the asphalt pavement structures subjected to different traffic loadings as shown in Figure 13.1 according to fatigue performance from best to worst assuming that the environmental conditions are the same. 378 379 Solution: All the pavement structures have the same subgrade layer with the same modulus (E 3 ). Therefore, the ranking will be based on the thickness of the HMA layer, the traffic loading, and the thickness of the base layer taking into consideration the following points: Higher traffic loading results in lower pavement performance. Higher number of load repetitions leads to lower performance. Dual loads lead to higher pavement performance. Higher HMA layer thickness leads to higher pavement performance. Higher base-layer thickness also leads to higher pavement performance. Higher modulus results in higher pavement performance. The replacement of a base layer with an asphalt layer with a higher modulus leads to higher pavement performance. Based on the above points, the following ranking is obtained (see Table 13.5 ). Pavement Structure #6: load (13 ton), load repetitions (1000000), modulus of HMA layer (2E 1 ), HMA layer thickness (D 1 +D 2 ), dual wheels. Pavement Structure #5: same as #6 except for modulus: load (13 ton), load repetitions (1000000), modulus of HMA layer (E 1 ), HMA layer thickness (D 1 +D 2 ), dual wheels. Pavement Structure #2: load (13 ton), load repetitions (1000000), modulus of HMA and base layers (E 1 and E 2 , respectively), two layers (HMA and base) with total thickness (D 1 +D 2 ), dual wheels. Pavement Structure #1: same as pavement structure #2 except for dual wheels: load (13 ton), load repetitions (1000000), modulus of HMA and base layers (E 1 and E 2 , respectively), two layers (HMA and base) with total thickness (D 1 +D 2 ), single wheels. Pavement Structure #3: same as pavement structure #1 except for the load: load (20 ton), load repetitions (1000000), modulus of HMA and base layers (E 1 and E 2 , respectively), two layers (HMA and base) with total thickness (D 1 +D 2 ), single wheels. Pavement Structure #4: same as pavement structure #3 except for the load repetitions: load (20 ton), load repetitions (2000000), modulus of HMA and base layers (E 1 and E 2 , respectively), two layers (HMA and base) with total thickness (D 1 +D 2 ), single wheels. 380 13.4 State the mistake in each of the following flexible pavement structure designs and correct it (see Figure 13.2 ). Solution: Pavement Structure Design #1: the modulus of the HMA layer is smaller than the modulus of the base layer. A correction can be: E 1 = 300 ksi and E 2 = 100 ksi. Pavement Structure Design #2: the thickness of the HMA layer is higher than the thickness of the base layer. A correction can be: D 1 = 4 in and D 2 = 5 in. Pavement Structure Design #3: the modulus of the subgrade layer is very high (not typical). A correction can be: E 3 = 10 ksi (see Table 13.6 ). 381 13.5 Compute the predicted total number of equivalent single-axle loads (ESALs) for a highway flexible pavement for a new six-lane rural highway with a first-year annual average daily traffic (AADT) of 3000 veh/day for both directions. The design lane factor (f d ) is 0.4, the traffic growth rate is 4%, the design period is 10 years, and the traffic mix is as shown in Figure 13.3 . Ignore the ESALs of passenger cars. What is the truck factor of the truck in the third category? Which load is considered the critical load? 382 Solution: The total ESALs is calculated as shown in the following procedure: 13.1 ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429054297/5885f92e-b0a3-419d-837a-bad4e02024b0/content/TNF-CH013_eqn_0001.tif"/> Where: ESAL i = equivalent single-axle loads for traffic/axle category i AADT i = annual average daily traffic for category i 365 = number of days per year f d = lane distribution factor for the highway G = growth factor N i = number of axles with the same type and load f LE-i = load equivalency factor for axle category i The growth factor is calculated using the formula below: 13.2 G = ( 1 ) − 1 Where: G = growth factor for the design = traffic growth rate = design period the single axle in f d = in the N = 2 there are two axles with the same type and two single f = = = 10 G = ( 1 ) − 1 G = ( 1 ) 10 − 1 = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL = ( ) ( 365 ) ( ) ( ) ( 2 ) ( ) = The load equivalency factor is using the in this for single-axle loads based on in the of the load equivalency from the Design , as shown in the following (see Figure 13.4 ). The that the the load and the load equivalency factor for single-axle loads is a with high of determination 2 ) as shown below: 13.3 f LE = 10 − ( ) Where: f LE = load equivalency factor for single-axle loads = single-axle load in f LE = 10 − ( ) = loads and the following are The load equivalency factor is using the in this for loads based on in the of the load equivalency from the Design , as shown in the following (see Figure 13.5 ). The that the the load and the load equivalency factor for loads is a with high of determination 2 ) as shown below: 13.4 f LE = 10 − ( ) Where: f LE = load equivalency factor for loads = load in the load equivalency factor is using the in this based on in the of the load equivalency from the Design , as shown in the following (see Figure 13.6 ). The that the the load and the load equivalency factor for loads is a with high of determination 2 ) as shown below: 13.5 f LE = 10 − ( ) Where: f LE = load equivalency factor for loads = load in The ESAL results of the other axle types are in Table based on the same The truck factor is calculated using the following f = ( N i ) ( f LE − i ) Where: i = number of axles for axle category i f LE-i = the load equivalency factor for axle category i f = 1 1 1 = The critical load is the load with the highest load equivalency Therefore, in this the critical load is the The used to the ESALs in this is shown in Figure . 13.6 A highway flexible pavement is for a design period of The traffic that is to the highway pavement is of the type shown in Figure . the first-year annual average daily traffic (AADT) of this type of is in both the annual traffic growth rate is and the design lane factor is the total equivalent single-axle loads Solution: The total ESALs is calculated as shown in the following procedure: ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) The growth factor is calculated using the formula below: G = ( 1 ) − 1 the AADT = f d = in the N = 4 there are two axles with the same type and two f = = = G = ( 1 ) − 1 G = ( 1 ) − 1 = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL = ( ) ( 365 ) ( ) ( ) ( 4 ) ( ) = The for the load equivalency factor of loads will be used to f LE for the load as shown below: f LE = 10 − ( ) f LE = 10 − ( ) = The ESAL results of the other axle types are in Table based on the same The used to the ESALs in this is shown in Figure . Design a flexible pavement for a new six-lane rural highway that two using the design to the traffic mix shown in Table . The base and layers will be using the same material and one thickness be used for both layers. The material are also in Table The annual average daily traffic (AADT) that is to the highway in both is veh/day in the first the traffic growth rate is and the design of the pavement is 10 that the traffic growth rate will the same the design of the = i = = it is that it will one for to be from the and the pavement structure will be to levels of the time (see Figure ). Solution: The following formula is used for the design of asphalt pavements following the design 10 = 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 − Where: = predicted number of single-axle load = for a reliability = = number of the pavement = i i = = = modulus this pavement there are three 1 , 2 , and 3 ) as shown below: 1 = a 1 D 1 Where: 1 = 1 above the base layer a 1 = of 1 asphalt (HMA) D 1 = thickness of 1 (HMA 2 = a 1 D 1 a 2 2 D 1 Where: 2 = 2 above the layer a 1 = of 1 asphalt (HMA) a 2 = of 2 D 1 = thickness of 1 (HMA D 2 = thickness of 2 3 = a 1 D 1 a 2 2 D 1 a 3 3 D 3 Where: 3 = 3 above the subgrade layer a 1 = of 1 asphalt (HMA) a 2 = of 2 a 3 = of 3 D 1 = thickness of 1 (HMA D 2 = thickness of 2 D 3 = thickness of 3 A of the third is used to the data of the modulus of the HMA layer the layer 1 ). The data used to this is from the for of Based on the in the for Design of Pavement This can be used to the layer 1 ) modulus value (see Figure ). Therefore, a 1 = 3 − 2 Where: a 1 = of 1 (HMA = or modulus of 1 or HMA layer 5 a 1 = ( ) 3 − ( ) 2 ( ) = The of 2 base is by the following formula for Design of Pavement , a 2 = ( E 2 ) − Where: a 2 = of 2 E 2 = modulus of 2 or base layer a 2 = ( ) − = The of 3 is also by the following formula for Design of Pavement , a 3 = ( E 3 ) − Where: a 3 = of 3 E 3 = modulus of 3 or layer a 3 = ( ) − = Based on the highway in the the highway is a major rural highway that two main Therefore, the value for the reliability level would be to according to Table . The highest value is selected in this to be in the a reliability level of the is to according to Table . = = i − Where: i = = = − = the total ESALs be as shown in the following procedure: ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) The growth factor is calculated using the formula below: G = ( 1 ) − 1 for the the axle in AADT = = the highway is a six-lane the lane distribution factor is according to the values in Table . based on the values in Table , for three in each f d = in one The traffic in this is for both therefore, a value of will be used for f d . f d = N = 2 there are two axles with the same type and two f = The for the load equivalency factor of loads above in 13.5 will be f LE = 10 − ( ) f LE = 10 − ( ) = = 5 = 10 G = ( 1 ) − 1 G = ( 1 ) 10 − 1 = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL = ( ) ( 365 ) ( ) ( ) ( 2 ) ( ) = The results of the other axle types are in Table based on the same using the modulus of the subgrade layer and based on the design ESALs that the pavement structure be of the number 3 ) is using the formula below: 10 = 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 − 10 ( ) = − ( ) 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 ( ) − = − ( ) 10 ( 1 ) − 10 ( − ) ( 1 ) 10 ( ) − The is used as shown in the below: The of the is set = Design ESALs In this = Design ESALs = the of the is set = 10 − ( ) 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 ( ) − is as the the and the and in this the is as = ( ) − ( ) 2 the is or that is is to the correct Therefore, the will by value the to a value of or value will be the of The is used three each the modulus is to the 3 , the modulus of the subgrade is 2 , the modulus of the is for 1 , the modulus of the base is The total ESALs is the same for the three (see Figure ). Based on the following results are obtained (see Table ). the thickness of each layer is as in the following procedure: N 1 = a 1 D 1 = D 1 D 1 = in in The drainage for the base and layers 2 and 3 ) are from Table based on the drainage data the one the of drainage is and for the of the time the pavement structure is to levels the drainage value is Therefore, 2 = 3 = average value in the has (see Table ). N 2 = a 1 D 1 a 2 2 D 1 = ( ) ( ) D 2 D 2 = N 3 = a 1 D 1 a 2 2 D 1 a 3 3 D 3 = ( ) ( ) ( ) ( ) D 3 D 3 = in in the same material the same is used for the base and the the thickness of the layer to be In other one layer will be used for the pavement structure a total thickness of The design will be as (see Table and Figure ). In the the pavement design would to the thickness of the HMA layer and the cost of the highway Therefore, another for a base material has A new base material with an modulus of will be The material will be used for the layer. the same design inputs to the new HMA layer thickness and the thickness of the other pavement layers (see Table and Figure ). = = i = = 2 = 3 = f d = = = 10 predicted ESALs = Solution: the same and using the to the three of the pavement 1 , 2 , and 3 ), the following results are obtained (see Table ). The with the used to for the results of this are shown in Figure . a 1 is the same the HMA material is the therefore, a 1 = a 2 = ( E 2 ) − a 2 = ( ) − = a 3 is the same the material is the therefore, a 3 = The thickness of each layer is as in the following procedure: N 1 = a 1 D 1 = D 1 D 1 = in 5 in N 2 = a 1 D 1 a 2 2 D 1 = ( 5 ) ( ) D 2 D 2 = in in N 3 = a 1 D 1 a 2 2 D 1 a 3 3 D 3 = ( 5 ) ( ) ( ) ( ) D 3 D 3 = in in The design will be as shown in Table . the number of equivalent single-axle loads (ESALs) that the asphalt pavement structure shown in Figure is of a reliability level of ) of of and 2 = Solution: The following formula is used for the design of asphalt 10 = 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 − this pavement there are two 1 and 2 ) as shown in Figure . a 1 = 3 − 2 a 1 = ( ) 3 − ( ) 2 ( ) = N 1 = a 1 D 1 N 1 = ( ) = The of 2 base is by the following a 2 = ( E 2 ) − a 2 = ( ) − = N 2 = a 1 D 1 a 2 2 D 1 N 2 = ( ) ( ) ( ) = a reliability level of the is to based on the pavement number 2 ), the pavement structure will be to ESALs calculated based on the design formula below: 10 = 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 − 10 = − ( ) 10 ( 1 ) − 10 ( − ) ( 1 ) 10 ( ) − = = ESALs The used to the ESALs in this is shown in Figure . A highway would to set a on the number of that a rural highway pavement that is to an equivalent single-axle loads (ESALs) of for a design period of 10 The truck traffic that is to the highway pavement is of the type shown in Figure the first-year annual average daily traffic (AADT) of this type of that the traffic growth factor is and the design lane factor is Solution: The total number of ESALs is calculated using the formula and based on the AADT ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) the single f d = in the N = 1 there is one axle with the same type and one single f = The for the load equivalency factor of single-axle loads will be used to f LE for the single-axle load as shown below: f LE = 10 − ( ) f LE = 10 − ( ) = = 10 G = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL = ( AADT ) ( 365 ) ( ) ( ) ( 1 ) ( ) = AADT the single f d = in the N = 1 there is one axle with the same type and one single f = 1 = 10 G = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL = ( AADT ) ( 365 ) ( ) ( ) ( 1 ) ( 1 ) = AADT the highway pavement is to design ESALs of therefore, AADT AADT = AADT = The used to the of this is shown in Figure . A highway flexible pavement is to an equivalent single-axle loads (ESALs) of for a design period The traffic that is to the highway pavement is of the type shown in Figure the first-year annual average daily traffic (AADT) of this type of is the annual traffic growth rate is and the design lane factor is the design for this pavement in Solution: The total number of ESALs is calculated using the formula and based on the AADT ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) the single f d = in the N = 1 there is one axle with the same type and one single f = The for the load equivalency factor of single-axle loads will be used to f LE for the single-axle load as f LE = 10 − ( ) f LE = 10 − ( ) = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL = ( ) ( 365 ) ( ) ( G ) ( 1 ) ( ) = G the f d = in the N = 4 there are axles with the same type and f = The for the load equivalency factor of loads will be used to f LE for the load as f LE = 10 − ( ) f LE = 10 − ( ) = ESAL i = ( AADT i ) ( 365 ) ( f d ) ( G ) ( N i ) ( f LE − i ) ESAL − = ( ) ( 365 ) ( ) ( G ) ( 4 ) ( ) = G Therefore, the number of ESALs based on the AADT data is ESALs = G G the highway pavement is to design ESALs of the ESALs to the design Consequently, G G = G = G = ( 1 ) − 1 G = ( 1 ) − 1 = = The used to the of this is shown in Figure . The full-depth asphalt pavement shown in Figure is to an equivalent single-axle loads (ESALs) of for a design period of a reliability level of the modulus of the subgrade that be used under the HMA layer the ) is and is (see Figure ). Solution: The layer is for layer 1 (HMA as below: a 1 = 3 − 2 a 1 = ( ) 3 − ( ) 2 ( ) = N 1 = a 1 D 1 N 1 = ( ) = a reliability level of the is to 10 = 10 ( N 1 ) − 10 ( − ) ( N 1 ) 10 − 10 ( 10 ) = − ( ) 10 ( 1 ) − 10 ( − ) ( 1 ) 10 ( 2 ) − = − ( ) 10 ( 1 ) − 10 ( − ) ( 1 ) 10 ( 2 ) − the above for provides the following 2 = Therefore, a subgrade with a modulus of be used under the full-depth asphalt layer that the pavement will be of a traffic level of The used to the ESALs in this is shown i