**3. Fatigue cracks classification**

In Kazakhstan, the fatigue and other types of cracks on an asphalt concrete pavement for diagnostics and evaluation of road condition are considered in the standard [12], in which all defects on the pavements are divided into two groups: the defects, certifying inadequate strength and the defects, which do not certify inadequate strength in explicit form. Analysis of these defects shows that:


**Figures 4** and **5** show the photos from the Guide [13], which demonstrate visually the levels of

**Figure 5.** Fatigue failure of asphalt concrete pavement for the highway according to the Guide [13]: (a) low level; (b)

As it is seen, contrary to the Kazakhstan Guide, the American Guide identifies the fatigue cracks separately from other types of cracks and three levels have been established for their development. Another American standard document [14] subdivides the fatigue cracks into two types: surface-down fatigue cracking and bottom-up fatigue cracking; admissible limit values have been shown for these types of cracks for surface-down—1000 ft./mile = 190 m/km

The works [15–17] based on provisions of thermodynamics of irreversible processes and nonlinear dynamics (synergetics) show that the asphalt concrete pavement with low-temperature cracks is a specific dissipative structure, which is the form of adaptation for a thermodynamic system to the external conditions and each time, when air temperature reaches the critical temperature of pavement, the crack occurs. This is regularity, determined by collective behavior (self-organization) of structural elements of the asphalt concrete pavement in critical

the fatigue failure for the asphalt concrete pavement under the adopted classification.

**Figure 4.** All levels of fatigue failure of asphalt concrete pavement for the highway according to the Guide [13].

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and for bottom-up—25–50% of the lane area.

**4. Self-organization**

middle level and (c) high level.

conditions.

The largest and wide scale program on investigation of performance for road structures (highway pavements) was started within the so-called Strategic Highway Research Program (SHRP) in the USA in 1987. The road agencies of the American States and 15 other countries have been collecting the data for 20 years for state of repair of pavements, climate, volume and density of traffic on more than 1000 experimental sections of the highways.

A special guide has been developed to perform data collection under the unique method, which was published three more times in the following years [13]. This Guide gives the following definition for the fatigue cracks in asphalt concrete pavement: "They occur in the areas subjected to repeated traffic loadings (wheel paths). They can be a series of interconnected cracks in early stages of development. They develop into many-sided, sharp-angled pieces, usually less than 0.3 m on the longest side, characteristically with a chicken wire/alligator pattern, in later stages. The fatigue cracks are divided into three levels. Low level: an area of cracks with no or only a few connecting cracks; cracks are not spalled or sealed; pumping is not evident. Moderate level: an area of interconnected cracks forming a complete pattern; cracks may be slightly spalled; cracks may be sealed; pumping is not evident. High level: an area of moderately or severely spalled interconnected cracks forming a complete pattern; pieces may move when subjected to traffic; cracks may be sealed; pumping may be evident."

Fatigue Destruction of Asphalt Concrete Pavement: Self-Organization and Mechanical… http://dx.doi.org/10.5772/intechopen.75536 65

**Figure 4.** All levels of fatigue failure of asphalt concrete pavement for the highway according to the Guide [13].

**Figure 5.** Fatigue failure of asphalt concrete pavement for the highway according to the Guide [13]: (a) low level; (b) middle level and (c) high level.

**Figures 4** and **5** show the photos from the Guide [13], which demonstrate visually the levels of the fatigue failure for the asphalt concrete pavement under the adopted classification.

As it is seen, contrary to the Kazakhstan Guide, the American Guide identifies the fatigue cracks separately from other types of cracks and three levels have been established for their development. Another American standard document [14] subdivides the fatigue cracks into two types: surface-down fatigue cracking and bottom-up fatigue cracking; admissible limit values have been shown for these types of cracks for surface-down—1000 ft./mile = 190 m/km and for bottom-up—25–50% of the lane area.

#### **4. Self-organization**

**3. Fatigue cracks classification**

of these defects shows that:

64 Modified Asphalt

In Kazakhstan, the fatigue and other types of cracks on an asphalt concrete pavement for diagnostics and evaluation of road condition are considered in the standard [12], in which all defects on the pavements are divided into two groups: the defects, certifying inadequate strength and the defects, which do not certify inadequate strength in explicit form. Analysis

**Figure 3.** Fatigue failure of asphalt concrete pavement: alligator cracks (Sharjah city, United Arab Emirates, August, 2010).

• in spite of the fact that they have different causes for their occurrence and progress character, cracks of various types (fatigue, thermal, reflected, sagging) are not identified separately;

• the maximum allowable measures are not contained for the cracks, including the fatigue ones.

The largest and wide scale program on investigation of performance for road structures (highway pavements) was started within the so-called Strategic Highway Research Program (SHRP) in the USA in 1987. The road agencies of the American States and 15 other countries have been collecting the data for 20 years for state of repair of pavements, climate, volume and

A special guide has been developed to perform data collection under the unique method, which was published three more times in the following years [13]. This Guide gives the following definition for the fatigue cracks in asphalt concrete pavement: "They occur in the areas subjected to repeated traffic loadings (wheel paths). They can be a series of interconnected cracks in early stages of development. They develop into many-sided, sharp-angled pieces, usually less than 0.3 m on the longest side, characteristically with a chicken wire/alligator pattern, in later stages. The fatigue cracks are divided into three levels. Low level: an area of cracks with no or only a few connecting cracks; cracks are not spalled or sealed; pumping is not evident. Moderate level: an area of interconnected cracks forming a complete pattern; cracks may be slightly spalled; cracks may be sealed; pumping is not evident. High level: an area of moderately or severely spalled interconnected cracks forming a complete pattern; pieces may move when subjected to traffic; cracks may be sealed; pumping may be evident."

• the staged development nature is not reflected for fatigue cracks;

density of traffic on more than 1000 experimental sections of the highways.

The works [15–17] based on provisions of thermodynamics of irreversible processes and nonlinear dynamics (synergetics) show that the asphalt concrete pavement with low-temperature cracks is a specific dissipative structure, which is the form of adaptation for a thermodynamic system to the external conditions and each time, when air temperature reaches the critical temperature of pavement, the crack occurs. This is regularity, determined by collective behavior (self-organization) of structural elements of the asphalt concrete pavement in critical conditions.

In thermodynamics [18, 19], the systems, which exchange their energy and mass with the environment, are considered as open ones, and they are structurally complex. Due to the complexity of open systems, the various forms of structure occur in them in critical conditions. Energy dissipation plays the constructive role in the formation of these structures. To emphasize that I. Prigozhin introduced the term "dissipative structures" [20–23], and H. Haken introduced the term "synergetics" to stress the role of collective behavior for substructural elements in formation of dissipative structures [24, 25].

Prigozhin I. showed that the entropy variation *ds* for open thermodynamics system can be considered as the sum of two summands [19–21]:

$$ds = \, ds\_e + ds\_\rho \tag{1}$$

where *dse* is entropy variation, connected with its inflow or outflow; *dsi* is an amount of entropy, produced inside a system.

For short, *dsi* is simply called "entropy production."

Component *dse* can have as positive sign, as well as negative one depending on the fact if the system receives or give energy as the result of interaction with environment. According to the second law of thermodynamics, entropy production *dsi* is positive or equal to zero:

$$ds\_l \ge 0,\tag{2}$$

For the simplicity, the cell is considered as a sphere with radius R. Entropy production inside

<sup>3</sup> *π R*<sup>3</sup>

where *А* and *В* are the parameters of proportionality, which have appropriate dimensions.

The cell grows with the growth of the organism, and radius of the sphere *R* increases. The cell under the mechanism of self-organization tries to remove the excess of the accumulated

<sup>3</sup> *πR*<sup>3</sup> − *B* ⋅ 4*πR*<sup>2</sup>

, and the entropy outflow increases proportionally to the square of the radius *R*,

, then the gradual accumulation of entropy occurs under the expression (Eq. (3)).

, and entropy outflow from the cell *dse*

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. Then, according to the expression (Eq. (1)), we have:

increases proportionally to the cube of the radius *R*,

, (3)

is pro-

is proportional to its volume *V* = \_\_4

**Figure 7.** Dependence of heat transport rate on temperature difference.

portional to the area of its surface *Sпов*. <sup>=</sup> <sup>4</sup>*πR*<sup>2</sup>

*ds* <sup>=</sup> *<sup>A</sup>* <sup>⋅</sup> \_\_4

entropy. As the entropy production *dsi*

the cell *dsi*

**Figure 6.** Benar's effect.

that is, *R3*

that is, *R2*

Equal-zero entropy production, that is, *dsi = 0* will occur only under condition of balance.

#### **4.1. Benar's effect**

It is known that Benar's effect [26–28] is one of the famous examples for formation of dissipative structures in an open thermodynamic system. It occurs at critical difference of temperatures ∆*Tcr* of bottom and upper surfaces of the thin layer of the viscous liquid (for example, in silicon oil) in a dish, heated from below. When reaching *Tcr*, the behavior of the liquid varies dramatically—convection occurs, and the liquid is divided into hexagonal cells (**Figure 6**). The new structure is created by joint cooperative molecular motion of the liquid. As it is seen from **Figure 7**, the sharp break occurs for a dependence of heat transport rate *dQ/dt* on temperature difference ∆*T* at ∆*Tcr* and formation of a new structure occurs. The outflow (export) of entropy is precisely compensated by entropy production inside the liquid up to ∆*Тcr*, and when reaching ∆*Тcr*, the heat transport rate increases due to the convective mechanism of the heat exchange.

#### **4.2. Cell separation**

The work of M.V. Volkenstein [26] showed one more example of the formation for the dissipative structure in the open thermodynamics system. This is a cell separation of the living organism.

Fatigue Destruction of Asphalt Concrete Pavement: Self-Organization and Mechanical… http://dx.doi.org/10.5772/intechopen.75536 67

**Figure 6.** Benar's effect.

In thermodynamics [18, 19], the systems, which exchange their energy and mass with the environment, are considered as open ones, and they are structurally complex. Due to the complexity of open systems, the various forms of structure occur in them in critical conditions. Energy dissipation plays the constructive role in the formation of these structures. To emphasize that I. Prigozhin introduced the term "dissipative structures" [20–23], and H. Haken introduced the term "synergetics" to stress the role of collective behavior for substructural

Prigozhin I. showed that the entropy variation *ds* for open thermodynamics system can be

system receives or give energy as the result of interaction with environment. According to the

*dsi* ≥ 0, (2)

It is known that Benar's effect [26–28] is one of the famous examples for formation of dissipative structures in an open thermodynamic system. It occurs at critical difference of temperatures ∆*Tcr* of bottom and upper surfaces of the thin layer of the viscous liquid (for example, in silicon oil) in a dish, heated from below. When reaching *Tcr*, the behavior of the liquid varies dramatically—convection occurs, and the liquid is divided into hexagonal cells (**Figure 6**). The new structure is created by joint cooperative molecular motion of the liquid. As it is seen from **Figure 7**, the sharp break occurs for a dependence of heat transport rate *dQ/dt* on temperature difference ∆*T* at ∆*Tcr* and formation of a new structure occurs. The outflow (export) of entropy is precisely compensated by entropy production inside the liquid up to ∆*Тcr*, and when reaching ∆*Тcr*, the heat transport rate increases due to the convective mechanism of the

The work of M.V. Volkenstein [26] showed one more example of the formation for the dissipative structure in the open thermodynamics system. This is a cell separation of the living

Equal-zero entropy production, that is, *dsi = 0* will occur only under condition of balance.

can have as positive sign, as well as negative one depending on the fact if the

is entropy variation, connected with its inflow or outflow; *dsi*

, (1)

is positive or equal to zero:

is an amount of

elements in formation of dissipative structures [24, 25].

considered as the sum of two summands [19–21]:

entropy, produced inside a system.

where *dse*

66 Modified Asphalt

For short, *dsi*

Component *dse*

**4.1. Benar's effect**

heat exchange.

organism.

**4.2. Cell separation**

*ds* = *dse* + *dsi*

second law of thermodynamics, entropy production *dsi*

is simply called "entropy production."

**Figure 7.** Dependence of heat transport rate on temperature difference.

For the simplicity, the cell is considered as a sphere with radius R. Entropy production inside the cell *dsi* is proportional to its volume *V* = \_\_4 <sup>3</sup> *π R*<sup>3</sup> , and entropy outflow from the cell *dse* is proportional to the area of its surface *Sпов*. <sup>=</sup> <sup>4</sup>*πR*<sup>2</sup> . Then, according to the expression (Eq. (1)), we have:

$$ds = A \cdot \frac{4}{3}\pi R^3 - B \cdot 4\pi R^2 \,\text{\AA} \tag{3}$$

where *А* and *В* are the parameters of proportionality, which have appropriate dimensions.

The cell grows with the growth of the organism, and radius of the sphere *R* increases. The cell under the mechanism of self-organization tries to remove the excess of the accumulated entropy. As the entropy production *dsi* increases proportionally to the cube of the radius *R*, that is, *R3* , and the entropy outflow increases proportionally to the square of the radius *R*, that is, *R2* , then the gradual accumulation of entropy occurs under the expression (Eq. (3)). Stationary state is achieved at *<sup>R</sup>* <sup>=</sup> \_\_\_ <sup>3</sup>*<sup>B</sup> <sup>A</sup>* , that is, *ds* <sup>=</sup> 0. And at *<sup>R</sup>* <sup>&</sup>gt; \_\_\_ <sup>3</sup>*<sup>B</sup> <sup>A</sup>* , that is, *ds* > 0, therefore, at *Rcr* <sup>&</sup>gt; \_\_\_ <sup>3</sup>*<sup>B</sup> A* (*Rcr*: critical size of the cell) the cell should be separated, otherwise, it will die. The volumes of the mother cell and two daughter cells are similar, and the total area of the surfaces of new cells is bigger.

**3.** Asphalt concrete samples in the form of beam with dimensions 4 × 4 × 16 cm have been tested at various temperatures on mechanical press with the use of special device under transverse bending scheme according to standard ST RK 1218-2003 [33]. The deformation

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**4.** Asphalt concrete sample strength of various shapes (cylindrical and rectangular), various dimensions and at various temperatures at direct compression has been determined by their testing on the mechanical press under standard ST RK 1218-2003 [33]. The deforma-

**Indicators Unit Requirement of ST RK 1373-2013 Value of indicators**

**Indicators Unit Requirements of ST RK 1225-2013 Value of indicators**

Average density g/cm<sup>3</sup> — 2.38 Water saturation % 1.5–4.0 3.4 Air voids of mineral filler % ≤19 15.1 Air voids of asphalt concrete % 2.5–5.0 3.8

0°С MPa ≤13 7.4 20°С ≥2.5 3.5 50°С ≥1.3 1.38 Water resistance — ≥0.83 0.80 Shear resistance MPa ≥0.38 0.39 Crack resistance MPa 4.0–6.5 4.5

/s ≥180 329.0

25°С 0.1 mm 101–130 110 0°С 30 37 Penetration index — −1.0… + 1.0 −0.82

25°С cm ≥90 135 0°С ≥4.0 6.6 Softening point °С ≥43 44.0 Fraas point °С ≤−22 −30.2 Dynamic viscosity, 60°С Pa·s ≥120 121.0

rate was 3 mm/min.

tion rate was 3 mm/min.

Kinematic viscosity, 135°C mm2

**Table 1.** Main standard indicators for bitumen.

**Table 2.** Main standard indicators for asphalt concrete.

Compression strength

Depth of needle penetration

Ductility

The abovementioned examples for self-organization in thermodynamics systems—Benar's cells and cell separation can be used further for the explanation of the fatigue failure phenomenon for the asphalt concrete pavement.

Fatigue failure of the asphalt concrete pavement, of course, has been directly connected with the asphalt concrete strength.
