Theoretical and practical methodology for recognizing the road surface structure

A recognition indicator of the possibility of further use of the road during transferring transport loads are changes in the condition of the road surface. If the surface condition indicates incorrect parameters of its equality, rutting, or cracks, the road durability is qualitatively assessed. In this case, the actual load capacity rating and possible reconstruction of the structure begins. Values of dynamic defl ections can be used to recognize the modulus of elasticity and thus the possibility of assessing the durability of a structure. The mechanistic method is used to dimensioning the structure due to the movement planned. It allows a fl exible approach to further construction, giving the opportunity to assess whether part or all of it should be left or apply an additional layer to meet future requirements. The elastic modulus needed for this pavement structure design method for existing layers has been recognized by identifi cation as backcalculation methodology that have been used for many years.


Introduction
In recent years, the road network in Poland has been signifi cantly expanded. Many kilometers of roads have been created. The development of the car transport and the increase in the number of vehicles on Polish roads will result in the need for maintenance and repair. Appropriate recognition of the surface condition enables an adequate assessment of the structure and a decision as to the type of a repair method. In order to compare the practical and theoretical methods of a structure recognition, research and analysis were performed using two methods. The practical method chosen for the study is the Falling Weight Defl ectometer (FWD) dynamic defl ectometer test and the theoretical method -by means of backcalculation methodology [1][2].

Backcalculation method
The analysis of the implementation of the backcalculation methodology as the surface identifi cation was carried out for 2-, 3-and 4-layer systems. Calculations of the elastic defl ections were made with the strictly theoretical method according to the theory of the cylindrical layout of the structure. The center of the wheel load of the computational car was adopted as its center. The model with 5 or more layers was omitted due to the solution being too long even in a computerized approach. These models were loaded with a car wheel with a diameter of 30 cm and a road pressure of 0.707 MPa. The lowest layer in this case is of infi nite thickness. The numbering of the layers has been taken from the bottom to the top, in which the lowest is 1, and the highest number is related to the number of layers.

Two-layer model
The construction of the model is shown in the fi gure below.  The backcalculation methodology is the determination of the modulus of elasticity of the model layers based on defl ections and other parameters such as the layer thickness, load, and Poisson's coeffi cients. The method of determination in the normal case would be a longer, 2-layer, equal to 2 unknowns. To shorten the calculations, the methodology was changed from the 2 to 1 of the unknown. Instead of the modules, their quotient E1/E2 was assumed in relation to the wi/wo defl ection quotient. The successive changes of the E1/E2 value and the calculation of the quotient of appropriate defl ections for the changing model lead to the determination of the correct quotient of the modules. Using the back-calculating method, models for the basis point and subsequent points were calculated. The assumed defl ection value with an accuracy of 1 μm and 0.001 μm indicates how different the elasticity modules are. Leaving them gives the answer how exactly defl ections should be measured using the FWD and Heavy Weight Defl ectometer HWD [3][4].

Three-layer model
The model data as in Fig. 2 was used for the analysis.  (1) and (2) is dependent respectively on (3) and (4). After determining the values of the e 13 and e 23 quotients, the values of the E 1 , E 2 , and E 3 modules are determined.

Four-layer model
The analysis of the model was carried out for the data shown in Fig. 3.  Identifi cation of the 4-layer model on the basis of defl ections calculated was carried out similarly to the previous one. The (5),(6),(7) modulus quotients were successively changed for the remaining data to obtain for these theoretical models the defl ections quotients. If the defl ections quotients matched with the quotients of the corresponding known values from Table 7 the (8),(9),(10) function and the modules quotients were obtained. The modules of the searched model were obtained on the basis of the quotients of the modules and the E z replacement module. The list of identifi cation (back-calculating) for defl ections from below to 1μm is given in Tab  Similarly, the backcalculation methodology was performed for some combinations of defl ections, but with their accuracy up to 0.001 μm. The identifi cation results obtained are presented in Table 9. The values of the modules were given with an accuracy of 0.01 MPa, and defl ections with an accuracy of 0.001 μm.

Examples of identifi cation on rebuilt roads
When assessing the bearing capacity of a road undergoing reconstruction, measurements with the use of the FWD are often carried out to determine the suitability of existing layers for the new structure. In this case, the identifi cation analysis was carried out based on the recognition of the existing surface -what are the materials in the layers, and what are the thicknesses of the layers. Materials can be determined from archival data or from the smallsized boreholes. The layer thickness can also be determined by a georadar or other possible method. In the measurement itself, the unit pressure value under the plate, the diameter of the plate, and the temperature of the test are known [5][6][7][8].

Kraśnik -Janów Lubelski road DK-19 km 376+000,00 -377+200,00
The following defl ections were converted to a pressure of 0.707 MPa, so that the average values for individual geophones can be determined from the measurement set in the section. After converting the measurement temperature of 20 °C to 10 °C, the modules shown in Tab. 12 were received.    Note: the ground substrate is the clay sand or clay; geophones were spaced from the center of the load plate -26.5, 45, 60, 82.5, 120, and 144 cm.

Conclusion
Analysis of the results obtained from the theoretical method and practical tests was performed. When comparing both methods and the results, the following conclusions were noted: 1. The most accurate results are always for the lowest layer for the 2, 3 and 4-layer models. 2. The closest to the correct set of modules is in the case of known defl ections with an accuracy of 10 -3 μm and those with the smallest roundness.
3. The largest deviations in relation to the correct module are when a set of defl ections with the extreme points from the set is used. 4. It is possible to recognize the structure model by omitting the zero point and taking further into account. 5. A set of more results for a homogeneous section gives better possibilities of identifying modules due to the equalization of discrepancies and possible incorrect readings. 6. To determine the modules with the method, it is best to take the average reliable values after rejecting the extreme values based on the Chauvenet criterion. 7. The modulus of elasticity will be most likely for readings from geophones the closest to the FWD loading board.