**1. Introduction**

Currently, the most commonly used materials in the base and subbase layers of a pavement designed to support asphalt mix layers are known as the unbound granular materials (UGMs). The unbound granular layers and the subgrade of a pavement structure provide a significant support for the structure as a whole. Hence, the mechanical properties of these materials are important for the overall performance of the structure [1].

A proper characterization of UGMs and subgrade soils is essential in the design and rehabilitation of pavement structures. The characteristics of the individual materials are of extreme importance during the design of pavement structures, and this includes the determination of optimum moisture content, grain size distribution, resilient modulus, and permanent deformation of all the materials that are to be used during the construction. Pavement layers formed by granular materials demonstrate a non-linear, time-dependent, and elastoplastic response under traffic loading. On the other hand, traditional elasticity theories consider the response of granular materials as linear-elastic, which requires a resilient modulus and Poisson's ratio. The parameters that influence the behavior of UGMs and fine-grained soils under repeated loads are stress level, density, gradation, fines content,

**Citation:** Stehlik, D.; Hyzl, P.; Dasek, O.; Malis, L.; Kaderka, R.; Komenda, R.; Sachr, J.; Vesely, P.; Spies, K.; Varaus, M. Comparison of Unbound Granular Materials' Resilient Moduli Determined by Cyclic Triaxial Test and Innovative FWD Device. *Appl. Sci.* **2022**, *12*, 5673. https://doi.org/ 10.3390/app12115673

Academic Editors: Amir Tabakovic, Jan Valentin and Liang He

Received: 19 April 2022 Accepted: 1 June 2022 Published: 2 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

grain size, aggregate type, particle shape, and moisture content or matric suction. The resilient modulus is mostly influenced by the level of applied stresses and the amount of moisture content in the material [2–4].

The resilient modulus is an important mechanical characteristic widely used for the analysis and design of pavements. Therefore, the determination of the resilient modulus of pavement materials is of vital importance for any mechanistically based design/analysis procedure for pavements. A laboratory resilient modulus test and a falling weight deflectometer (FWD) test are usually used to obtain the resilient modulus of a subgrade. However, the difference between the resilient moduli obtained from these two methods is considerably large due to the fact that these tests are conducted under quite different conditions [5–8].

Comprehensive research in this field is provided in [9]. A comparison was made between resilient moduli obtained from (i) a conventional small-scale resilient modulus test, (ii) a large-scale model experiment (LSME), and (iii) a falling weight deflectometer (FWD) in the field. The elastic moduli were back-calculated from the FWD data using the program MODULUS. The reasonable correspondence between the elastic moduli measured at different scales was obtained when empirical corrections were made for strain amplitude using a backbone curve for granular materials and by matching stress levels.

The differences between the back-calculated MR values of various types of roadbed soils and those obtained in the laboratory were presented and discussed in [10]. It was shown that the laboratory test results corresponded very well to the back-calculated ones. It was also shown that the MR of the roadbed soils was more or less constant, whether the soils were supporting flexible or rigid pavements.

Planning a pavement rehabilitation is based on pavement structure diagnostics, by which it is possible to determine the extent of pavement disruption as well as the cause of the disruption and thus subsequently remove this cause [11,12].

Possible causes of disruption include:


The above-mentioned disruptions of existing pavements can be prevented in the case of unbound mixtures in base layers by the functional testing of the resilient moduli using a cyclical triaxial device (Mr,CTT). The most frequently used test to determine the bearing capacity of the entire pavement structure is the impact load test with determination of the resilient moduli (Mr,FWD) [14–16].

The optimal solution is to design unbound mixtures for base pavement layers by functional testing so that it subsequently fulfills the requirements for the entire structure during control tests performed later [17].

The objective of the research described in this study was to find utilization for the adjustment of the frame (holder of geophones) of FWD and to describe the optimal way of designing UGMs by performance testing, which more accurately simulates the load on the tested base layers. Another objective was to find correlations between bearing-capacity characteristics derived using:


### **2. Monitored Sections and Methods**

Data regarding the determination of bearing capacity at the monitored sections were analyzed in order to compare Mr,CTT and Mr,FWD and the development of the measuring frame of FWD. The following monitored sections were selected for research purposes (see Figure 1 and Table 1):


**Figure 1.** Pavement structure schemes.

**Table 1.** Pavement structures of the monitored roads.


1GMA,B: granular mixtures according to EN 13285; 2 asphalt macadam course: granular course 32/63 grouted with bitumen approximately 5 kg/m<sup>2</sup> and filled by finer fraction of aggregate.

The standard design and assessment of unbound mixtures do not commonly include functional (performance) testing of the pavement base and subbase layers. In addition to the common laboratory tests of gradation, compactability, and water and frost resistance, the individually designed mixtures were also subjected to experimental functional tests to determine the modulus in accordance with the EN 13286-7 standard. This European standard is intended specifically for testing UGMs. The resilient modulus Mr,CTT was determined after a constant curing period of the testing specimens. Before the actual determination of Mr,CTT, the properties of the used building materials were determined.

The properties of UGMs were verified in a CTT. The Mr,CTT of the compacted cylindrical testing specimens was determined, taking into account the assumed number of standard axles based on the conditions for designing flexible pavements [20].

The measurement of the pavement's bearing capacity was performed using the FWD deflectometer Sweco. The bearing capacity measurement was performed during different seasons and various weather conditions. Material samples taken from the probes focused especially on unbound base layers.

The Mr,CTT determination was performed using CTT (see Figure 2). The course of the Mr,CTT of the compacted UGMs was monitored and determined using FWD.

The bearing capacity was determined using FWDs. The dynamic tests (drop of weight through bumpers to loading plate) simulated the passing of a heavy vehicle at a speed of 60 km/h. At the same time, the values of deflection from sensors (geophones) deployed on the longitudinal frame to a distance of up to 2500 mm from the center of the loading plate were recorded.

**Figure 2.** CTT device.

In order to be able to gather information about the transversal course of deformation as well, the standard FWD frame was equipped with a transversal frame with four additional sensors. These sensors recorded the values of deflection in the transversal direction and allowed us to make a comparison of the shape of deflection bowl in 3D and calculate the modulus of the structural layers or half-space in both directions to describe the pavement stiffness also close to the edge of the structure (see Figure 3).

**Figure 3.** Layout of an auxiliary cross frame.

The PRIMAX FWD trailer by Sweco was mounted on a double-axle trailer. It was independent of the towing vehicle. The operator controlled all FWD functions from the PC, which was placed in the towing vehicle.

The standard trailer-mounted FWD was supplied with a personal computer, Windows FWD software, time-history module, transport lock, DMI (Distance Meter Indicator) integrated in the software, three temperature sensors, four-split loading plate, nine geophones in the longitudinal direction, and four geophones in the transversal direction. The impact loading applied to the pavement was 50 kN. The scheme of the load frame, including the position of the geophones, is provided in Figure 4.

**Figure 4.** Scheme of the frame.

A back-calculation software for road data analysis was used for data treatment. However, the files generated from the equipment can be applied in any other back-calculation program.

We used the Primax design system from SWECO based on the following theory: When a force is transmitted to a load plate, this results in a deflection of the road surface—a "deflection bowl". The deflection is the largest at the center of the plate and decreases as the distance from the center becomes greater. The layer stiffness in a road structure is also called the E-modulus of a layer.

Based on this theory, the shape of a deflection bowl is symmetrical, and deflections measured using a standard beam normally positioned parallel with the horizontal axis of the communication should be equivalent also in the transversal direction in the case of ideal structures. If the measured deflections at geophones are larger than those in the transversal beam, it means that the structure is less durable in this direction, either due to a smaller thickness of the structure layers or their lower quality, or due to greater disruption of these layers. By comparing the deflections at the same distance from the loading plate in horizontal and transversal direction, one can determine the differences in pavement durability in that particular direction. We are currently in the process of verifying the adjusted setup of the evaluation software so that we can directly compare the elasticity moduli (E-moduli) of the structure layers of an n-layered system in transversal and horizontal direction.

The calculation of a road surface deflection is based on the theory of elasticity and the method of equivalent thickness, as framed by engineers Messrs. J. M. Kirk and N. Odemark on the basis of Boussinesq's equations. The deflection is the sum of the deformation in

the layers and the subgrade. The deformation of one layer is linearly elastic, i.e., the deformation is directly proportional to the force and the thickness of the layer, but inversely proportional to the stiffness of the layer. The deformation of the subgrade is calculated from the stress and stiffness.

In accordance with the Czech national standards, sampling at national and regional communications is required every 25 m. During special measurements or in the case of severely damaged communications, the distance between two subsequent measuring points can be up to 5 m in a traffic lane.
