Coordinated Use of Digital Construction Tools for Renewal Design of Low-Volume Roads: A Norwegian Case Study

Building information modeling (BIM) is a digital semantic representation of physical and functional features of real objects (Eastman et al. 2008) and has been applied to design, construct, monitor, and maintain built facilities (Cheng et al. 2016; He et al. 2017). As a computer-based workflow, BIM enriches three-dimensional (3D) computer-aided design (CAD) information with additional nD dimensions of an asset, such as time, cost, and sustainability (Ding et al. 2014; Lee et al. 2020). The implementation of BIM in the architecture, engineering, construction and operation (AECO) industry has been gaining traction during the last two decades, finally emerging into the mainstream and accruing significant technical and economic benefits (Azhar 2011; Bryde et al. 2013; Jung and Joo 2011; Succar 2009). Moreover, the application of BIM standards is becoming mandatory in many countries around the world, such as the Scandinavian region, the United Kingdom, and Singapore (Shou et al. 2015; Smith 2014; Wong et al. 2010).

As documented by several academic review studies, BIM has been initially implemented in buildings (Volk et al. 2014; Zhao 2017) and then in civil infrastructure belonging to the domains of transportation, energy, utility, and water management, only to name a few (Bradley et al. 2016; Salzano et al. 2023). In this regard, the application of BIM in academic research revolving around transportation infrastructure (e.g., highways, railways, airports, bridges, transit hubs, tunnels, and ports) has been slowly adopted (Moreno Bazán et al. 2020; Costin et al. 2018; Wu et al. 2022). This delay can be ascribed to the major differences existing between the more traditional vertical BIM (e.g., schools, high rises) and the horizontal BIM (e.g., roads, railways, tunnels): design requirements, spatial development, and construction and maintenance processes (Costin et al. 2018).

Low-volume roads (LVRs) are road pavements characterized by low annual average daily traffic (AADT), in general, AADT < 1,000 vehicles/day (Douglas 2016; Robinson and Thagesen 2004; Silyanov et al. 2020). Worldwide, their importance is obvious, considering that approximately 65% of the global road network, which is roughly 22 million km long, can be classified as LVR (Lay et al. 2021; Meijer et al. 2018; Silyanov and Sodikov 2017).

A traditional flexible road infrastructure includes several layers to transfer vehicle loads to a natural substrate. Starting from the top, the layers are generally classified as wearing, binder, base, and sub-base. Wearing and binder courses are usually bounded by bitumen or cement, while base and sub-base courses commonly comprise only unbound aggregates (unbound granular materials, UGMs) (Huang 2004; Islam and Tarefder 2020; Mallick and El-Korchi 2023; Thom 2014). When it comes to LVRs, the bound layers are often very thin (a few centimeters) or absent; in the latter case, the base layer is directly exposed to trafficking actions. Globally, LVRs often exhibit poor conditions and reduced accessibility mainly because of a lack of maintenance operations (Henning et al. 2014; Jalali et al. 2019; Keller and Sherar 2003; Labi et al. 2019). In Norway, it has been estimated that the backlog in required maintenance exceeds 100 million euros, thus possibly compromising the structural integrity of roads and leading to premature damage (Aursand and Horvli 2009; Barbieri et al. 2017).

As a possible solution to alleviate these problems, binder technologies can be employed to effectively improve the mechanical properties of UGM courses and contribute to environmental and economic savings (Gomes Correia et al. 2016). The stabilization process is an in situ operation consisting of mixing the existing aggregates or soil with the chosen binder technology (and water, if necessary) by means of a cold recycler machine. Currently, several stabilizers are available on the market (Jones 2017) and can be classified either as traditional binders (i.e., bitumen, cement) and as nontraditional binders (Tingle et al. 2007). A remarkable amount of academic field and laboratory research has been performed on traditional technologies (Douglas 2016; Huang 2004; Islam and Tarefder 2020; Mallick and El-Korchi 2023; Robinson and Thagesen 2004; Thom 2014). On the other hand, very few coordinated academic research efforts have focused on achieving a comprehensive understanding on nontraditional ones (Barbieri et al. 2022a, b; Santoni et al. 2002, 2005; Tingle and Santoni 2003), which can be categorized according to five types when it comes to the stabilization of coarse-graded aggregates: brine salt, clay, organic petroleum, organic nonpetroleum, and synthetic polymer.

Considering the current academic literature, the main research gap addressed by this research is to propose an integrated workflow produced by BIM and digital tools that can be used in the engineering design and renewal of LVRs. In this regard, this study refers to the rehabilitation of an LVR in Norway as an application case study. Here, it is important to mention that the identification of such an academic gap may not warrant sufficient knowledge gap definition, especially since BIM and related systems are industry tools and processes. In this research, considerations are made when stabilizing the UGM aggregates constituting the base layer by means of both traditional and nontraditional binders. Overall, the case study addresses the following main topics: road georeferencing and alignment tracing, estimation of material volumes and costs, achievement of road structural analysis, and, finally, evaluation of its service life. Based on these premises, this work offers new perspectives on BIM implementation and broadens its application for road transportation infrastructure, as illustrated in Table 1, for at least three reasons.

First, the existing academic studies have largely focused on the different life stages of high-trafficked roads [high-volume roads (HVRs)], such as highways and motorways. Kim et al. (2014, 2016) developed a system to automatically assess, cut, and fill quantities, costs, and schedules for different road alignments leveraging the computer-interpretable representation format in compliance with the international standard ISO 10303. Zhao et al. (2019) dealt with the identification of the best alignment by means of genetic algorithms integrating BIM tools, such as Autodesk Revit, Autodesk Civil 3D, and Autodesk Navisworks, with geographic information systems (GISs) such as Esri ArcGIS and Esri ArcMAP. When it comes to highway maintenance and management, Jing et al. (2019) used Autodesk Civil 3D, Autodesk Revit, and Autodesk InfraWorks to document the necessary operations for the rehabilitation of road, bridge, and ancillary facilities. Vignali et al. (2021) employed Autodesk Civil 3D and Autodesk Revit to facilitate the upgrade of a new highway segment. Jiang et al. (2022) detailed the operations of road demolition and related costs leveraging a combination of aerial photographs and government statistics to build cross sections based on horizontal and vertical road marking lines. Sankaran et al. (2016) and Zhang et al. (2020) synthetized the major lessons learned during collection, management, and utilization of digital information from an industrial standpoint and academic education perspective, respectively. When it comes to LVRs, Abbondati et al. (2020) showed the potential of Bentley OpenRoads and Bentley LumenRT software tools to achieve parametric modeling of a major rural road. Khalil et al. (2021) and Raya and Gupta (2022) leveraged Autodesk Civil 3D and Autodesk InfraWorks to perform a geometric design and hydraulic study of unpaved roads.

Second, only two academic studies in road engineering have shed light on the potential of visual programming (VP) algorithms and the importance of integrating BIM systems with structural analysis software (Tang et al. 2020a, b). Such research efforts centered on two main areas: (1) the development of an indirect data conversion interface between Autodesk Revit and the modelling software ABAQUS; and (2) the creation of a Python subroutine to enable the structural analysis of road structures parametrically defined in Autodesk Dynamo.

Third, a combination of BIM and innovative construction technologies can reduce the environmental impact of constructing, maintaining, rehabilitating, and demolishing civil infrastructures, which is a key area where the transition to carbon neutrality can benefit from BIM implementation (de Bortoli et al. 2023; Patel and Ruparathna 2023). Only a previous study integrated BIM models with laboratory results, which were derived from testing traditional asphalt concrete (Oreto et al. 2021), but no structural analysis was performed.

The position of existing transportation infrastructures and their spatial relationships can be defined by Autodesk InfraWorks. This software consents the integration of the GIS and BIM domain for model establishment and rendering (Biancardo et al. 2020a; Bosurgi et al. 2019; Oreto et al. 2021). The geopositioned objects corresponding to structures, water bodies, and terrains are built on a satellite map using OpenStreetMap (OSM), which employs the WGS-84 standard coordinate system. The Model Builder tool provided by Autodesk InfraWorks enables the creation of 3D models with a maximum area of 200 km², which are saved with .imx file extension. As the Model Builder leverages the open database source OSM to generate a terrain, the level of precision can vary depending on the area of the project. OSM elevations are fairly accurate on average, while the accuracy and completeness patterns for Norway are high (Haklay 2010; Schultz et al. 2017; Zhou et al. 2022). Field survey data could be used instead to achieve the best possible accuracy. The level of development (LOD) specification indicates the accuracy and completeness of the model geometry and related information. Currently, six different levels (LOD 100, LOD 200, LOD 300, LOD 350, LOD 400, and LOD 500) are defined and these levels display increased clarity and reliability (Bedrick et al. 2020; Latiffi et al. 2015). Autodesk Infraworks enables the creation of models embracing the entire spectra spanning from the conceptual design (LOD 100) to the as-built operational definition (LOD 500). For the considered case study, the related level can be estimated between LOD 300 and LOD 350 because the model includes the creation of details and elements precisely displaying size, shape, and location. However, this aspect does not hinder the general purpose of this work, namely, to employ the necessary digital tools that can define a repeatable workflow in LVR engineering.

After the definition of the road position, further construction details can be specified on the terrain model using Autodesk Civil 3D importing the .imx file generated by Autodesk InfraWorks. In this software, a road alignment is represented by a corridor consisting of horizontal and vertical alignments as well as cross sections at different stations. Autodesk Civil 3D can be employed to create draft, design, and construction documentation that streamline CAD and BIM workflows; for example, material quantities, work schedules, and operation costs (Kim et al. 2014; Lee et al. 2020; Oreto et al. 2021). From an economic point of view, an evaluation of the bill of quantities based on dimensions and volumes is a highly relevant exercise that exerts a major influence on project realization (Chong et al. 2016; Jiang et al. 2022; Vitásek and Matějka 2017; Zima 2017). Models created with Autodesk Civil 3D are saved with .dwg file extension.

The evaluation of the volume and cost of the materials needed for road construction is usually achieved in Autodesk Civil 3D. Nevertheless, Autodesk Dynamo represents an innovative plug-in software that can perform these calculations. Autodesk Dynamo is a VP algorithm; that is, it is a visual process chart composed of input and output blocks linked by connectors, which, to some extent, can replace traditional scripts containing code lines (Autodesk 2023). This versatile VP tool simplifies the creation of parametric processes and automatizes repetitive tasks without the need for having advanced programming knowledge (Saito et al. 2017). The visual scripts created using Autodesk Dynamo are saved using .dyn file extension and can be directly uploaded in the chosen host Autodesk suite.

Unlike architectural projects executed with Autodesk Dynamo having Autodesk Revit as the host software, VP tools have been scarcely applied in infrastructure engineering, as testified by academic literature, and they have been mainly used for bridges and tunnels (Collao et al. 2021). Because very few academic studies have shed light on the potential of Autodesk Dynamo in road engineering (Oreto et al. 2021; Tang et al. 2020a, b), this work performs the work of extraction of volume and cost by means of the VP tool instead of Autodesk Civil 3D. Here, it is important to mention that possible discrepancies between academic research and industry practice may exist, because large engineering firms employ VP tools quite extensively for automating various tasks. The main advantage offered by Autodesk Dynamo over Autodesk Civil 3D is that the user can easily leverage the visual script to appreciate the desired outputs (e.g., volume and cost) by modifying the value of the relevant inputs (e.g., road thickness and road width) contained in the corresponding input blocks. On the other hand, the same process performed in Autodesk Civil 3D would require the user to traverse through several lengthy dialog boxes, which can be customized to a much lesser extent.

The BIM design workflow and structural analysis are usually regarded as two separate parts. To integrate these, Autodesk developed Autodesk Robot Structural Analysis software, which, however, shows significant limitations (e.g., definition of structure geometry, selection of constitutive model), and its adoption is presented in very few academic studies (Biancardo et al. 2020b; Hasan et al. 2019). COMSOL Multiphysics is created by COMSOL Inc. and can be used to perform advanced numerical analysis also with regard to the mechanical response of road pavements (Barbieri et al. 2019, 2021b; Podolsky et al. 2017); the associated file extension is .mph. Because this software may become overly complicated for everyday engineering practice, this study models a road section with fully controllable parameters (i.e., geometry, mechanical properties) and boundary conditions using the Application Builder: geometrical parameters are specified by the user based on the Autodesk Civil 3D model, whereas the constitutive relationships derive from the results of the laboratory repeated load triaxial tests (RLTTs) performed on stabilized and unstabilized rock aggregates.

For each stress level (i.e., triaxial stress σ_t, deviatoric stress σ_d) obtained in the structural analysis performed with COMSOL Multiphysics, the corresponding experimental dataset of plastic strains measured with RLTTs is considered to estimate the road service life. In this regard, the RLTT data are analyzed according to regression models using MATLAB, which is a software developed by MathWorks. MATLAB is a programming language platform that is widely employed by users having varied numerical computing skills and professional backgrounds (Arif and Khan 2021; Assi 2011; Lu and Lee 2017); the file extension used to save a MATLAB script is .m.

The LVR considered in this study is the county road Fv 491 Gravberget located in Våler municipality, Innlandet county, Norway. The stretch between the localities (Holtsjøen and Gravberget) church is 6 m wide and has a length of approximately 25 km. Fig. 2 displays the geographical position of Gravberget. The portion of terrain lying in proximity is highlighted using the Model Builder of Autodesk Infraworks and covers 48.9 km².

The road structure is composed of a bituminous bound top surface stratum and an unbound base stratum lying on the natural subgrade. According to the limited historical information available, the road was built during the 1960s without following any precise design code indications, and the thin surface layer has been repaved several times since then. The aggregates used in the base layer were collected directly along the road alignment, and no standard tests were performed to ascertain their conformity with quality.

Recently, the Norwegian Public Roads Administration (NPRA) has started the upgrade of several county roads to accommodate higher trafficking loads, especially heavier timber trucks, in accordance with the project “Gross Weight 74 Tons” (NPRA 2020). As Gravberget is part of this program, some preliminary measurements, also comprising falling weight deflectometer (FWD), have been performed to characterize the geometry and bearing capacity of the existing road. The main information is reported in Tables 2 and 3. FWD measurements indicate an average resilient modulus of a subgrade equal to 300 MPa. The aim of this road renewal is to remove the aggregates currently forming the base layer and replace them with new and certified aggregates, and eventually apply a new asphalt layer on the top. This case study has been selected considering the central position of this road stretch in the project “Gross Weight 74 Tons.” However, the procedure discussed and findings obtained in this study can be extrapolated to similar projects; in this way, the proposed framework can also be further validated.

The amount of construction material necessary to renew the base layer of Gravberget can be reduced by employing binder technologies, which improve the mechanical properties of the aggregates (Celauro et al. 2015; Praticò et al. 2011). Bitumen (BIT) is considered as a typical traditional binder. With regard to nontraditional technologies, recent work has thoroughly compared the performance of all the existing types of additives to stabilize coarse-graded aggregates (Barbieri et al. 2022a, b 2023a). Based on the outcomes of these studies appraising the mechanical response of the stabilized material in terms of stiffness, permanent deformation, stripping potential, and resistance to 10 freeze–thaw (FT) cycles, this research considers the technologies that have offered the overall best performance, namely synthetic polymeric binders. These additives can be classified as polyurethane (POL), acrylate (ACR), styrene butadiene (STB), and acetate (ACE); their degree of toxicity varies from none to moderate (Kunz et al. 2022). Table 4 details their most relevant aspects: the amount of water dissolved in each binder, the price estimate excluding transport cost, and the considered application rate.

The main parameters that are necessary to numerically model the unstabilized and stabilized rock aggregates are the resilient modulus M_R and the permanent deformations, which can be evaluated in the laboratory by means of RLTTs (Barbieri et al. 2021a; CEN 2004; Wang et al. 2023). Unlike cyclic triaxial tests, which are cumbersome and time-demanding investigations, Los-Angeles (LA) and micro-Deval (MDE) are two test procedures that are routinely performed (CEN 2010, 2011), although they cannot provide information that is directly related to structural behavior, as in the case of RLTTs.

The construction materials to be used to renew the base layer are crushed rocks originating from the nearest quarry located in Ingeberg, which is a village in Hamar municipality approximately located 70 km away from Gravberget (Hamar Pukk og Grus AS 2023). The LA and MDE values of the aggregates from Ingeberg (LA = 17.3, MDE = 15.0) are very similar to the LA and MDE values of the aggregates from Vassfjell, which is a mountain area close to Trondheim municipality, and these values were investigated in two other previous studies (LA = 18.2, MDE = 14.2) (Barbieri et al. 2022a, b). Furthermore, the density of the crushed rocks from Ingeberg (2,800 kg/m³) and from Vassfjell (2,950 kg/m³) are similar. Compounding this with the fact that the LA and MDE values can be efficiently related to the results of RLTTs (Adomako et al. 2021), this study assumes that the RLTT data obtained for the crushed rocks from Vassfjell (Barbieri et al. 2022a, b) are also valid for the ones from Ingeberg. The price of the aggregates is 35 €/t and the gradation considered corresponds to a typical Norwegian base layer (NPRA 2014, 2018), as reported in Table 5. The appearance of the RLTT samples is depicted in Fig. 3.

A multi-stage low stress level (MSL SL) RLTT is composed of five load sequences. In turn, each of them is formed by six load steps, which correspond to a precise combination of deviatoric stress σ_d and triaxial stress σ_t. During each load step, σ_t is kept constant, while σ_d is applied 10,000 times following a sinusoidal pattern with the maximum values listed in Table 6 (Barbieri et al. 2021a; CEN 2004).

The resilient modulus M_R indicates the elastic stiffness of the material and is defined as the ratio between dynamic deviatoric stress σ_d,dyn and elastic axial strain ɛ_el,a (Lekarp et al. 2000a). Considering the RLTT experimental data, M_R can be calculated based on the well-known Hicks and Monismith (1971) formulationwhere σ_a is a reference pressure equal to 100 kPa, θ is the sum of the principal stresses σ₁, σ₂, and σ₃ (σ₂ = σ₃), and k₁ and k₂ are regression coefficients. As reported in Fig. 4, this study evaluates the resilient modulus as the average trend based on the results obtained by testing the samples both before and after the exposure to 10 FT cycles (Barbieri et al. 2022a, b 2023a).

Considering the models developed to fit the experimental data of permanent strain derived from RLTTs (Lekarp et al. 2000b), the well-known logarithmic formulation proposed by Sweere (1990) is employed to evaluate the accumulation of plastic axial deformation ɛ_pl,a as a function of the number of load repetition Nwhere a and b are regression coefficients. This formulation is used to analyze the permanent deformations measured during each load step independently from the previous ones (Gidel et al. 2001).

The Norwegian pavement design code “N200” implements a mechanistic-empirical methodology for road design and requires the definition of several input parameters (NPRA 2018). The stiffening effect engendered by the application of a binder, either traditional or nontraditional, allows for the reduction in thickness of the stabilized base layer, thereby also beneficially reducing the demand for new construction aggregates (de Bortoli 2023). This can be calculated starting from the RLTT results in terms of resilient modulus M_R, as indicated by the pavement design code “N200” (Barbieri et al. 2022b). The values of the base thickness for each stabilization scenario, conceptually depicted in Fig. 5, are reported in Table 7.

The elastic stiffness M_R deriving from RLTTs is a relevant mechanical property needed to perform the structural modeling appraising the stress level of the road pavement (Alnedawi et al. 2022; Ghadimi and Nikraz 2017; Titi and Matar 2018). The objective of the analysis is to characterize the typical stress state in the middle of the base layer, so that the corresponding plastic deformations and service life can be estimated using the Sweere model. The numerical modeling is performed with COMSOL Multiphysics considering a two-dimensional road section. The constitutive relationship implemented for the base layer is the Hicks and Monismith model (Barbieri et al. 2021b). As depicted in Fig. 6, the application builder enables an efficient parametric definition of the geometrical and mechanical inputs, which are specified by the user. Broadly speaking, the proposed framework can take into consideration and analyze different road sections independently. However, this investigation assumes that all possible sections of the selected 25- km road stretch have the same mechanical behavior and service life.

An evaluation of construction volumes is necessary to estimate the cost of the rock aggregates used in the renewal of the base layer. In this regard, the Autodesk Dynamo visual script depicted in Fig. 10 illustrates the code blocks and connections that are created to visualize the road alignment (depicted in blue) and calculate the volume for the specified thickness and width.

The construction volumes are assessed by inputting in the Autodesk Dynamo script the different thicknesses of both unstabilized and stabilized base layers, as displayed in Table 7. The material costs consider the prices of both aggregates (35 €/t) and binders applied according to the percentages reported in Table 4. The transport cost calculations are performed using a part of the “HERMES CO₂” spreadsheet tool, which was originally developed to quantify the amount of carbon dioxide emissions and related costs associated with the main stages of a road life span, such as production, construction, and use (Barbieri et al. 2021c). The content of the “HERMES CO₂” tool can be freely edited by the user, for instance by specifying the properties of the desired construction machines, the geometry of each layer course, and traffic volume. This study takes into consideration only the transport cost related to the construction phase assuming a typical medium on-road truck traveling at 50 km/h with average capacity equal to 13 m³, fuel consumption 0.25 L/km, and operating cost of 200 €/h. These average figures derive from the largest Norwegian companies providing rental equipment including operators (Barbieri et al. 2022b). As already stated, the considered average transport distance is 70 km and corresponds to the stretch between Gravberget and the nearest quarry. The results are reported in Table 8.

The use of binders contributes to a significant reduction in the quantity of needed rock aggregates and therefore envisages positive environmental effects such as reduction in the carbon footprint associated with the production and transport of natural resources (Balaguera et al. 2018; van der Merwe Steyn and Visser 2011). From a cost standpoint, all additives contribute to economic savings. In this regard, the only exception is represented by polyurethane POL, because its application is even more expensive than the creation of a base layer using unstabilized aggregates. Compared with the use of other nontraditional polymeric additives, the traditional binder bitumen BIT is the cheapest alternative. This finding is in good agreement with that of other studies, indicating that the higher costs of polymeric technologies are mainly due to the current small commercial scale (Bushman et al. 2005; Khoeini et al. 2019).

An estimation of the stress state in the base layer is important for the appraisal of the permanent deformation and associated service life. As illustrated in Fig. 11, the Application Builder in COMSOL Multiphysics allows for a parametric definition of the road geometry, which is composed of a top layer, base layer, and subgrade. The tire pressure is uniformly distributed and the standard axle load corresponds to 10 t (NPRA 2018). The constitutive behavior of the base layer is defined by the average nonlinear elastic relationships represented in Fig. 4. The elastic stiffness of the subgrade E_sub is 300 MPa, as already discussed. With regard to the elastic modulus of the top layer E_top, this case study considers the recent findings estimating the mechanical properties of the asphalt mixtures typically used throughout Norway (Chen et al. 2022, 2023a, b, c). Referring to this Norwegian dataset and the geographical location of Våler municipality, two extreme values are considered as representative of as many climatic and traffic conditions: E_top = 2,000 MPa (high temperature, slow loading) and E_top = 20,000 MPa (low temperature, quick loading).

Table 9 reports the triaxial stress σ_t and the deviatoric stress σ_d values assessed by COMSOL Multiphysics at the middle of the base layer as well as specifies the closest stress state achieved during RLTT among the ones listed in Table 6. For stabilized base layers, a slightly higher RLTT stress state (σ_t = 100 kPa, σ_d = 300 kPa) is associated with a stiffer top layer (E_top = 20,000 MPa), whereas a softer top layer (E_top = 2,000 MPa) is associated with a lower RLTT stress condition (σ_t = 70 kPa, σ_d = 280 kPa). Considering an unstabilized UGM base course, the deviatoric stress σ_d calculated with COMSOL Multiphysics is significantly higher than the associable σ_d values exerted during the LSL MS RLTT.

The accumulated plastic axial deformations ɛ_pl,a for the stress states listed in Table 9 are reported in Fig. 12 (for E_top = 2,000 MPa) and Fig. 13 (for E_top = 20,000 MPa). The trends obtained by testing the samples both before and after exposure to 10 FT cycles (Barbieri et al. 2022a, b 2023a), as well as the corresponding average trends, are calculated by using a MATLAB script that fits the experimental RLTT in accordance with the Sweere formulation based on the least-squares method.

The service life of the base layer is estimated by assessing the number of load repetition N leading to permanent deformation ɛ_pl,a = 1‰ (CEN 2004), as reported in Table 10. The unstabilized aggregates UGM exhibit the worst performance, because the corresponding N values are at least smaller by two orders of magnitude compared with stabilized materials. The beneficial effect provided by the application of additive binders in terms of prolonged service life and associated reduced frequency of maintenance operations is apparent for all stabilized materials. Acetate ACE is characterized by the best result because the corresponding N values have an order of magnitude of 22. Except for polyurethane POL, all polymeric binders, that is, acrylates ACR, styrene butadiene STB, and acetate ACE, offer responses that are better than that of the traditional binder bitumen BIT. Nevertheless, the bituminous binder BIT is the cheapest solution among the investigated ones: as already discussed, the costs of polymeric products are likely to diminish over time as the main barriers (e.g., low-scale production and current sales system) are removed (Huang et al. 2021).

Finally, it is worth noting that the experimental data of permanent deformation could have also been analyzed by implementing other regression approaches (Alnedawi et al. 2019; Chen et al. 2020; Pérez and Gallego 2010; Ullah et al. 2021). Based on the findings of these studies, it can be reasonable to assume that the ranking of the stabilization technologies derived adopting the Sweere formulation, as reported in Table 10, is not likely to change when considering other regression models. For instance, the resistance to permanent deformation assessed according to the Hyde model for all the RLTT stress levels reported in a previous study also indicates the better mechanical response of the nontraditional polymeric binders compared with bitumen and unstabilized aggregates (Barbieri et al. 2022b).

An important aspect of the research dealt with in this study is represented by the validation of the generalizable workflow. One approach to meet this aim entails the achievement of multiple experiments, which is an analysis of more case studies. On the other hand, another approach involves performing a sensitivity analysis to prove how the algorithms are not sensitive to changing project-based variables. Following the latter path, this section applies the same calculation framework already discussed for the case study to the combinations of the hypothetical values of the two main input parameters, as depicted in Fig. 5, namely, thickness and width of the stabilized base layers. Five values are assumed for the thickness: the actual one detailed in Table 7 as well as the other four corresponding to an increase or decrease by ±1 and ±2 cm. With regard to the road width, three values are considered: 5, 6 (actual case study), and 7 m.

In the first place, the visual script created using Autodesk Dynamo is run for all combinations of width and thickness values to assess the corresponding volume of aggregates needed to rehabilitate the base layer. The total costs including material supply and transport are then derived using the spreadsheet tool “HERMES CO₂.” The results displayed in Fig. 14 indicate a linear relationship between inputs (i.e., thickness, width) and estimated outputs (i.e., volume, cost). The red points correspond to the results already found in the case study. The stabilization by means of bitumen BIT is always the cheapest alternative, whereas the most expensive technology is represented by polyurethane POL; this finding agrees with the outcomes of the case study.

Following the proposed workflow, the structural analysis is successively conducted by leveraging the Application Builder and analyzing the parametric two-dimensional road section developed with COMSOL Multiphysics. The considered elastic modulus of the top layer E_top is 2,000 MPa. Based on the obtained values of triaxial stress σ_t and deviatoric stress σ_d displayed in Fig. 15, the closest stress states achieved during RLTT, which are listed in Table 6, are the same ones already identified for the case study reported in Table 9. Therefore, the service life values already computed in Table 10 are also valid for all the parameter combinations considered in the sensitivity analysis. This finding indicates the small influence exerted by changes in width or small variations (a few cm) in the thickness of the stabilized base layer on the estimated service life.