**4. Test Section**

### *4.1. Road Pavement Technology*

Because the embedded materials in the existing road pavement have lost their bearing capacity and fatigue durability, it was proposed to make this pavement in cold recycling technology with existing materials and to make a FAC mixture on their basis. The C3A3 mixture was built into the base layer of the road pavement. Before finishing the test section, the road had numerous damages, which are shown in Figure 8.

**Figure 8.** A section of the existing road—west lane.

A mobile deep recycler was used to produce the recycled FAC mixture—Figure 9.

**Figure 9.** Recycling on-site—crushing and mixing of ingredients.

To verify the compaction of the base layer, the compaction index was checked. This indicator was determined by comparing the bulk density of samples formed from the FAC mixture in the laboratory with the bulk density of samples out of the finished pavement layer. The compaction index was 0.98, which is a satisfactory value for the base layers [25].

After constructing the recycled layers, the surface of the experimental section was finished with asphalt layers: a base layer and a base course layer of asphalt concrete (with a high stiffness modulus (ACWMS) and a wearing course layer of the SMA mixture, see Figure 10.

**Figure 10.** Wearing course layer, SMA type.

The design of the innovative road pavement structure assumed the following layering:


According to [38], all implemented mineral-asphalt mixtures met the design requirements for the layers of flexible pavement road constructions in Poland. As a result of the applied technology of the road base made of FAC-type mixture, the road durability forecasting was carried out before the road traffic admission. For this purpose, measurements of deflections of the pavement were carried out, along with the identification of layer modules and the subgrade.

### *4.2. Identification of Layer Modules*

The measurements of pavement deflections were done on the street pavement using an FWD (Falling Weight Deflectometer). It is a device that induces a force impulse using a falling weight onto a measuring plate (through a specially designed spring system). The set of displacements determined on a given measuring stand creates the so-called "displacement bowl", which is then used to identify modules of layers and the subrade. Measurements of deflections made by FWD were carried out during the construction of the section on the layers: the FAC layer, the ACWMS layer, and the SMA wearing course layer.

During pavement tests, displacement was measured at the following distances from the load axis: d1 = 0.0; d2 = 0.2; d3 = 0.3; d4 = 0.45; d5 = 0.6; d6 = 0.9; d7 = 1.2; d8 = 1.5; d9 = 1.8 m. The tests were carried out at different temperatures. Figure 11 shows a diagram of deflection testing using an FWD deflectometer. Figure 12 shows a view of the FWD deflectometer during the testing of this pavement.

The results of deflection measurements were used to estimate the layer modules and the subgrade modules of the road pavement construction. The calculation model presented in Figure 13 was adopted for the identification calculations of the modules of the FAC layer. It is an elastic two-layer system, i.e., a layer arranged on the elastic half-space.

**Figure 11.** Measurement diagram done with an FWD deflectometer.

**Figure 12.** View of the FWD device during the test.

**Figure 13.** Calculation model of the tested pavement construction.

Particular layers model the layout of the pavement structure. The h2 layer models FAC, the h1 layer—an improved subgrade. The FAC layer is described by the E2 stiffness modulus and Poisson's ratio ν2. The subgrade is described by the modulus of elasticity E1 and Poisson's ratio ν1. The thicknesses were assumed by the in-depth identification h2 = 0.20 m. It was assumed that Poisson's ratio did not have a significant impact on the state of stress and strains and was assumed to be constant, i.e., ν2 = 0.3 and the factor ν1 = 0.35.

The essence of identification is to minimize the objective function described by Equation (2):

$$
\Delta = \frac{\sqrt{\frac{F}{k}}}{\frac{\sum\_{j=1}^{k} w\_j}{k}} \tag{2}
$$

where:

$$F = \sum\_{j=1}^{k} \left( w\_j - u\_j \right)^2 \tag{3}$$

*wj*—theoretical deflections calculated in the model,

*uj*—measured deflections,

*k*—the number of deflections measured at one point, forming the deflection bowl.

Of course, the number of layers n should be smaller than the number of k points forming the deflection bowl. Calculations were made on the basis of the CZUG program [41].

As a result of identification, the following values of modules (Ei) of the FAC layer and subgrade were obtained. Measurements of deflections on the FAC layer were made for different temperatures: −2 ◦C, +10 ◦C, +25 ◦C, +32 ◦C.

The obtained modulus values for the subgrade and the FAC layer are summarized in Table 6 for a 95% level of confidence.


**Table 6.** List of identified module values.

After the FAC layer was laid and FWD tests were done, mma layers were laid, after which the deflection bowl measurements were again carried out using an FWD deflectometer.

Figure 14 shows a model of the pavement structure after laying layers of mma. It is a three-layer system. Two layers are arranged on a half-space. The h3 layer is a layer with mma described by the E3 stiffness modulus and Poisson's ratio ν3. The h2 layer is the FAC layer described by the E2 stiffness modulus and Poisson's ratio ν2. The subgrade is described by the E1 modulus and Poisson's ratio ν1. It was assumed that h3 = 0.24 m, h2 = 0.20 m, ν3 = ν2 = 0.35, and ν1 = 0.3.

**Figure 14.** Calculation model of the tested pavement structure.

The module values were calculated on the basis of the deflection bowl measurements using the FWD deflectometer and optimization calculations. The results are summarized in Table 7. Measurements were taken at the approx. temperature +10 ◦C.

**Table 7.** List of identified modules for the temperature +10 ◦C.


Figure 15 summarizes the test results and compares the FAC mixture modules obtained in the laboratory and in situ layers.

**Figure 15.** Values of modules in the laboratory and in situ.

When analyzing the results from Tables 6 and 7 and Figure 15 the stiffness modulus value determined in the laboratory is comparable with the modules of the material used in situ. As a result of the analyzes, a good correlation between field and laboratory tests was obtained in the analyzed range of temperatures. The conversion factor of the modules "k" determines the relationship (4), which describes the ratio of the stiffness modules defined in the laboratory to the values of the field modules, as a function of temperature.

$$\mathbf{k} = 0.8417 \cdot e^{0.001 \cdot T} \,, \tag{4}$$

where:

> k—module conversion factor [-],

T—FAC layer temperature [◦C].

The "k" conversion factor takes values from 0.84–0.87 depending on the temperature—Table 8.


**Table 8.** List of conversion factor "k" values.

### *4.3. Fatigue Durability of Pavement Layers Structure*

Using the obtained module values and the model presented in Figure 14, the fatigue life of the structure was calculated for the designed thicknesses. Equation (5), developed by the authors, describes the criterion for the FAC mixture:

$$\varepsilon = \varepsilon\_{6^{\circ}}(\mathbf{k})^{0.78721} \cdot (\frac{\text{N}\_{\oplus}}{10^{6}})^{(-0.57403 \cdot \text{A} + 0.64234 \cdot \text{C})} \cdot f\_{1} \cdot f\_{2} \cdot f\_{3} \tag{5}$$

where:

ε—strain in the FAC layer,

<sup>ε</sup>6—strain at millionth load cycle, 0.000168 was adopted,

Nf/30—number of load cycles to achieve a decrease in the complex stiffness modulus to 30% of the initial value,

A—percentage of new asphalt in the FAC layer, 4.16% was adopted,

C—percentage of cement in the FAC layer, 3.38% was adopted,

k—a conversion factor of the modules defined in the laboratory to the modules in situ, for a temperature of 10 ◦C,

*f*1—a shift factor dependent on stiffness of FAC mixture, range between 0.8–1.0, was adopted 0.81,

*f* 2—a shift factor dependent on bearing capacity of subgrade, range between 0.8–1.0, was adopted 0.83,

*f* 3—a shift factor dependent on heterogeneity of FAC mixture, range between 0.8–0.95, was adopted 0.92.

For the identified modules and model from Figure 14, strains at the bottom of the FAC layer were calculated. ε = 0.0000412 was obtained. Using Equation (5), N = 29,500,000 axles of 115 kN were calculated (fatigue life). The required minimal number of load axles for the road pavement is equal 12,000,000 axles 115 kN.
