Cost Effectiveness of Chip Seal and Hot Mix Asphalt Pavements

Abstract

Chip seal pavements, consisting of one or more layers of asphalt binder and fine aggregate, can be mechanically characterized as a surface treatment that enhances evenness and trafficability. This paper examines the geotechnical aspects of chip seal applicability compared to traditional hot mix asphalt pavements. An analytical model was employed to design unpaved roads and determine the required thickness of unbound layers. Eight optimization models were developed for hot mix asphalt pavements and four for chip seal pavements, aimed at achieving optimal designs for various input parameters. These outcomes were used to conduct a multi-parametric analysis, incorporating an optimization loop for each combination of design variables. The results indicate that, under low traffic conditions, a chip seal pavement structure can be up to 40% less expensive than an optimal hot mix asphalt pavement structure, particularly when the subgrade has low bearing capacity and is exposed to unfavorable climatic conditions. However, at medium traffic loads, with good subgrade bearing capacity and favorable climate, the chip seal pavement structure incurs costs that are 25% higher than those of the hot asphalt pavement structure. In addition, chip seal pavements should always be designed with integrated geosynthetic reinforcement to minimize construction costs, and chip seal is not as sensitive to frost as hot mix asphalt.

1. Introduction

Over the past century, there has been considerable population growth, which has been accompanied by the expansion of transport infrastructure. Today, virtually every urban area around the globe has an extensive road network with a significant amount of pavement [1]. To maintain the quality of the road network, at least 6% of the road network needs to be rebuilt or repaired every year, resulting in significant material and energy consumption and high costs. Pavements play a crucial role in road safety, sustainability and driving standards. They account for up to 40% of road construction costs and nearly 70% of maintenance and management costs.

A pavement structure is a relatively simple construction consisting of several layers. The uppermost layers consist of bound materials such as asphalt or concrete, while the base and subbase layers are composed of unbound aggregates. Below these layers is the subgrade, which can be either a natural surface or an embankment created by geological processes. The installation of geosynthetically reinforced soil (GRS) in pavement structures offers several advantages: it limits the lateral movement of unbound materials, increases their stiffness and shear strength, improves load distribution on the subgrade and reduces shear stress on the subgrade [2,3].

The key factors in the empirical method for determining pavement structure dimensions include the pavement’s service life, ground load-bearing capacity, the daily traffic load, the climatic and hydrological conditions, the material properties and the usability of the road surface at the end of its life cycle. A modern road network with high-quality pavements ensures efficient transportation. However, issues such as energy demand, environmental pollution and climate change are becoming increasingly important. It is generally recognized that human activities, in particular increasing greenhouse gas emissions, are the cause of current climate change [4]. Therefore, there is ongoing research into new energy solutions for transportation and the more efficient use of materials and energy in construction, particularly in road pavement design [5]. Developing alternative methods for pavement construction remains a continuous engineering challenge and has been the focus of many studies [6,7]. One possible solution to such problems is using chip seal instead of the standard pavement structure or upgrading the existing pavement structure with chip seal [8].

A chip seal is a surface treatment for pavements that involves applying one or more layers of asphalt binder followed by one or more layers of fine aggregate. The construction process is straightforward: first the asphalt binder is sprayed onto the prepared pavement surface, and then the aggregate (or chips) is immediately spread over it. Rollers are used to press the chips into the binder, and once hardened, the surface is swept to remove any loose aggregate. Chip seals are commonly used in various applications, primarily involving either single or double chip seal treatments. The use of chip seal dates back a century, when it was discovered in the USA that macadam roads can be improved with a simple mixture of bitumen and a certain stone aggregate. Since then, chip seal has been in constant use for the rehabilitation of existing paved roads or as a final coating for new road structures [9].

Chip seal is most commonly used to upgrade an existing damaged pavement by applying an asphalt binder and a stone aggregate to the surface of an existing pavement structure. By using chip seal processing, the construction also acquires better driving properties. Of course, the existing pavement construction must be mechanically in proper condition, otherwise the chip seal does not reach its potential. Therefore, any areas with major defects such as holes, rags and cracks must first be reconstructed, as the chip seal does not contribute to the bearing capacity of the roadway itself but is only a protective and driving layer.

The surface preparation for a chip seal is essential, even when constructing a new chip seal pavement. Various types of binders can be utilized for bituminous application, chosen based on the prevailing climatic and site-specific conditions. The primary function of the binder is to create a bond between the underlying structure and the stone aggregate layer. The most commonly used binders include low-viscosity modified bitumen emulsions and conventional bitumen emulsions [10]. The main benefits of chip seal are: (1) low construction costs; (2) adaptable design, which allows for various grades of material quality; (3) little need for periodic maintenance during service life; (4) a durable and flexible surface that can better handle the higher deflections typically seen on low-volume roads built with lower-quality materials; (5) less impact from construction errors, such as the over-application of binder, compared to conventional seals; and (6) increased durability, which makes it more resistant to damage from high solar radiation that can accelerate binder aging and surface degradation.

The first mix design procedure for asphalt surface treatments was developed by F. M. Hanson in New Zealand (1934/35), and its principles form the basis of all major methods used globally today [11]. The recent adaptation is the 2004 Chip Seal Design Guide from New Zealand. In North America, the modified Kearby and McLeod methods are most commonly used [12]. The Otta seal, developed by the Norwegian Road Research Laboratory, is applied as follows: (1) hot binder at 1.6–1.9 L/m², (2) aggregate at 1.3–2.0 m³/100 m², (3) compacting with a tired roller until binder rises between particles, and (4) low-speed traffic for two to three weeks to further embed the aggregate, with dislodged particles broomed back onto the surface.

The design of asphalt sealing requires laboratory and field tests to be carried out and the results used as input data for estimating the corresponding material quantities. As a result, those responsible for the design must: (1) have a thorough understanding of the properties of chip seal materials (both aggregate and binder), (2) assess the condition of the road before sealing and (3) incorporate this information into the design process [11]. This is very important for the quality and durability of chip seals. This paper deals only with the geotechnical aspects of chip seal pavement design, assuming that normative, environmental and economic conditions are satisfied. The chip seal is considered as a layer that serves the flatness and driving quality of the surface, but the load transfer to the pavement structure is the same as for unpaved roads.

This work contains a detailed description of the materials used in pavement construction, along with various pavement design methods. In particular, design methods for eight types of hot mix asphalt pavements and four types of chip seal pavements were presented and integrated into optimization models. The aim of these models was to minimize construction costs while considering various design constraints. A multi-parametric analysis was performed to determine the optimal pavement designs under different site conditions, climate factors and traffic loads (see, Figure 1). The aim of the article is to examine the applicability of the chip seal pavement compared to the standard asphalt pavement. For this purpose, the proposed chip seal pavement analysis procedure is shown below. Based on parametric analyses, the influence of the bearing capacity of subgrade, which is determined by the California Bearing Ratio (CBR) and the transitions of the Equivalent Single Axle Load (ESAL), on the thickness of the pavement layers is defined. A cost analysis was carried out for selected types of chip seal and hot mix asphalt pavement structures. For the design and cost analyses, EU standards and local technical specifications were used. While the model was developed in a general form, different standards and regulations can be applied.

2. Materials and Methods

Typical layers that follow the subgrade in standard asphalt pavement are: geosynthetic reinforcement (optional), one or more unbounded layers (subbase plus base) and asphalt layers. The chip seal pavement construction is similar, but without asphalt layers, it is finished only with chip seal instead of asphalt layers. Geomechanically chip seal pavement is thus considered similar to unpaved structures.

The asphalt layer can be treated in an analysis of the response to a single cycle load as an elastic material with a modulus of elasticity E_a and a Poisson ratio ν_a. Asphalt fatigue caused by repeated traffic loading is also considered. Fatigue is defined by the maximum number of load cycles, expressed as a function of the resulting deformation. The geomechanical analysis needs to consider that the tensile strain of the asphalt layer ε_t,a, increased by the safety factor SF, should be less than their permissible value. The standard procedure for determining the stiffness of asphalt layers, makes it possible to load the specimens of different types and with different bindings [13].

The lifespan of chip seal (also known as surface treatment) depends on several factors, including material quality, surface preparation and climatic conditions. The type and quality of bitumen and aggregates, such as gravel and sand, play a significant role in determining the durability of the surface. Proper surface preparation is also crucial; cleaning the roadway and repairing any damage before applying the chip seal ensures the better adhesion of materials, which in turn extends the surface’s lifespan. Additionally, climatic conditions like extreme temperatures, rain, snow and cycles of freezing and thawing can greatly accelerate surface deterioration [14]. In hot climates, bitumen can soften, while in colder regions, freeze–thaw cycles can lead to cracking. Additionally, heavy traffic loads, especially from a high volume of large trucks and other vehicles, can accelerate wear and reduce the lifespan of chip seal surfaces. The quality of installation also plays a crucial role; factors such as the even distribution of bitumen and aggregate, along with the correct application temperature, are essential for optimal performance. Poor installation can lead to rapid surface degradation and maintenance. All of these factors are critical in determining the precise lifespan under specific conditions. The lifespan of chip seal, based on the Equivalent Single Axle Load (ESAL), varies with traffic intensity and vehicle weight. For roads with low traffic (up to 100,000 ESAL over 20 years), such as rural roads, chip seal can last 7–10 years. On moderately trafficked roads (100,000–500,000 ESAL), its lifespan is 5–7 years. For high-traffic routes, such as highways frequented by heavy trucks (with 500,000 ESAL), the lifespan is reduced to 3–5 years due to the increased wear from these heavier loads. In cases with even heavier traffic, the lifespan may be even shorter.

2.1. Stone Aggregates

Experience with chip seal shows that uniformly classified aggregates will lead to the best results. If the aggregates are of uniform size and shape, they will ensure the even inclusion of all particles when the wheel presses on the road structure. The most commonly used aggregates have grain sizes ranging from 8 to 16 mm in diameter. When a double layer is applied, the aggregates in the second or top layer are typically about half the size, measuring approximately 4 to 8 mm. Just as the quality of the pavement structure depends on the quality of the aggregate, the quality of the aggregate depends on the strength, shape, strength, porosity and mineral composition. The cleanliness of the stone aggregate is important for the adhesion between the bitumen emulsion and the stone aggregate. Dirty or dusty aggregates are less susceptible to adhesion to emulsion, which can lead to excessive aggregate loss. The shape of the stone aggregate is also important. The best form of stone aggregate has proven to be in the form of cubes or rectangles. Due to their simple geometry, these particles are best interconnected, and traffic itself does not have a significant impact on their further orientation. What is important is not only the shape but also the quantity of these. As a rule, only one layer of aggregate is applied, as multiple layers can disrupt the even distribution of aggregate after the emulsion, potentially causing the material to come loose and leading to damage to vehicles. However, additional layers may be applied in areas of the road with sharp turning radii or intersections, where more aggregate improves the stability and durability of the surface [10].

The strength of stone aggregate is determined by its resistance to abrasion and degradation. The aggregate must be strong enough to endure when the final layer is exposed to the environment. Winter conditions often reveal issues, where proper shape, strength and emulsion compatibility help prevent material loss during plowing. Although aggregate typically has low porosity, care must be taken to prevent emulsion absorption, as this can weaken pavement cohesion due to an insufficient amount of binder [15]. The required properties of stone aggregate for subbase layer and for base layer of chip seal are the same as for standard pavements [16,17,18,19,20].

2.2. Bitumen

Prime coat application is one of the important asphalt pavement operations that provides the bond between the granular base surface and bituminous pavement and as a binder must be hard enough not to soften in the summer heat and elastic enough not to crack in the cold [12]. The advantage of chip seal is that the emulsion for optimal processing temperature is 52–85 °C, which uses less energy for heating and does not cause the evaporation of hazardous substances into the atmosphere. Another advantage is that the bitumen emulsion is less sensitive to climatic conditions such as rain and low temperatures [10]. The required properties of standard road bitumens are specified in standards [21,22].

2.3. Base and Subbase Layer

Most methods for dimensioning pavement structures assume that the base layer has isotropic properties. The modulus of elasticity for the base layer can either remain constant throughout or be defined as a function of stress. In this analysis, the modulus of elasticity is represented as a function of stress. Witczak and Uzan [23] adjusted the model by incorporating octahedral shear stress in place of deviator stress. The stress–strain relationships in the base, subbase layers (if present) and subgrade must stay within the failure limits in the p-q stress space [24]. The vertical strain of base layer ε_d,b, subbase ε_d,sb and subgrade ε_d,sg must be less than permissible value for each soil material.

The required properties of stone aggregate for subbase layer and for base layer are the same as for standard pavements. Quality criteria and procedures for the investigation of mixtures of stone grains, which are intended for unbound bearing layers are provided by European standards [16,17,18,19,20,25].

2.4. Geosynthetics

The use of a geosynthetic reinforcement layer between the subgrade and the (sub)base course offers several benefits: it reduces the required depth of the base course needed to achieve the specified compaction and bearing capacity, decreases rut depth depending on the traffic load and increases the service life of the pavement structure. The required properties of geosynthetics are the same as for standard pavements and are specified in relevant standards [26,27].

2.5. Subgrade

Typically, field investigations involve boreholes and excavation pits, along with sampling and stratification assessments, groundwater level measurement and various field tests. These tests may include the Standard Penetration Test (SPT), static and dynamic plate bearing tests (as per BS 1377, Part 9: 1990 [28]) and the indirect determination of the California Bearing Ratio (CBR). The resistance of the material to the effects of freezing and thawing (resistant/non-resistant) and hydrological conditions (favorable/unfavorable) are also determined.

The laboratory test [25,29] contains basic tests to determine the physical properties of the soil. The result of the CBR test is essential in the dimensioning of the pavement structure.

3. Design Methods for Hot Mix Asphalt and Chip Seal Pavement Structures

The pavement structure needs to be designed to support the pavement structure’s own weight, traffic loading on each single loading cycle and repeating loading. A simplified measure of traffic for pavement design, for an Equivalent Single Axle Load (ESAL) was used. For these analyses, ESAL is defined as a 100 kN dual tire axle with a tire pressure of 690 kPa.

The following design methods have been used to analyze asphalt pavements. For paved roads the Meyer and Elias method is used [30], with local technical specifications utilized in the design. For chip seal structures, the method of Giroud and Han is used in unpaved roads [2,3].

In the design method applied by Meyer and Elias [30], the maximum total bearing capacity of all layers must be calculated to check the bearing capacity and durability of the road structure. For this reason, safety factors for the unbound base course and the asphalt surface course as well as the bearing capacity of the subgrade are verified in this method.

The Finite Element Method (FEM) was used to calculate the stresses and deflections using computer programs such as Everstress [31] and Plaxis [32]. Comparison of both FEM results show good correlation between displacements and stresses. The basic inputs are thickness of layers and their modulus (for subgrade get from CBR). The next input is traffic load in one traffic pass. There are many options to input load, depending on type of the wheel, tire contact and tire pressure and width. Results of analyses for one pass of loading are stress and micro-strain in each point of FEM net of the structure.

Local technical specifications for roads, based on AASTHO and EU standards are used only for validation the results of mentioned calculation methods. Traffic load over a period of 20 years is calculated based on equivalent daily traffic load, number of traffic lanes, traffic load distribution factor in the pavement cross section, lane width, longitudinal inclination of the pavement level, annual traffic growth rate, duration and traffic increase and driving conditions.

Stress transfer in chip seal pavement structure is similar to unpaved road structure; therefore, roads paved with chip seal coating can be designed using the empirical and analytical model created by Giroud and Han [2,3].

The method used here is iterative and is based on laboratory and field tests. It also has several factors involved and takes into account several possible situations. The options are as follows: different layers and their load-carrying capacity, different number of passes of the equivalent vehicle, reinforcement using geotextiles or geogrids and their various mechanical characteristics and harmonized equations between laboratory and field tests.

The procedure for calculating the required thickness of the unbound layer is described as follows:

$$h={\displaystyle \frac{1.26+(0.96-1.46·J^2)·({\frac{r}{h})}^{1.5}·\log N}{f_e}}·\left(\sqrt{{\displaystyle \frac{P}{\pi ·r^2·m·N_c·C_u}}}-1\right)·r$$

(1)

where the parameters represent the following quantities: h—required base course thickness; P—wheel load; J—torsion of geogrid; r—radius of the equivalent tire contract area; N_c—a factor of the bearing capacity of the road structure; C_u—undrained shear strength of subsoil; log N—logarithmic value of the ESAL.

The equation is complex, so the solution need to be divided into steps. Step one—calculation of the equivalent radius of pressure on the bogie using input tire pressure force P and tire pressure p:

$$r=\sqrt{{\displaystyle \frac{P}{p·\pi }}}$$

(2)

Step two—calculation of undrained shear strength C_u. It is obtained from solid surface input, the California Bearing Ratio of subgrade (CBR_sg), and is calculated using the equation below:

$$C_u=f_c·{CBR}_{sg}$$

(3)

where f_c represents a constant that is 30 kPa.

Step three—determination of the mobilized soil load factor m:

$$m={\displaystyle \frac{s}{f_s}}·\{1-\epsilon ·e^{-\omega ·{\left({\displaystyle \frac{r}{h}}\right)}^n}\}$$

(4)

where s represents the rut depth. This should not exceed 75 mm. The value for the rut depth of 25 mm is used below. The factor f_s stands for the maximum permissible value of the rut depth, i.e., 75 mm. Other coefficients are determined with the help of field research and are constant. The values of the coefficients are as follows: ε = 0.9, ω = 1.0, n = 2.0.

Step four—since the fill layers have different moduli, there is a factor f_e which represents the impact of those different values:

$$f_e=1+0.204·(R_e-1)$$

(5)

The model is designed to be limited to CBR = 5%. This limit is described by the R_e factor. The problem of convergence arises for larger values of the CBR and indirectly also for larger values of the modulus of elasticity. Therefore, this method provides the best results for lower CBR values. The limitations result from the following equations:

$$R_e=\min ({\displaystyle \frac{E_{bc}}{E_{sg}}};5.0)=\min \left({\displaystyle \frac{3.48·{{CBR}_{bc}}^{0.3}}{{CBR}_{sg}}};5.0\right)$$

(6)

Step five—when all of the steps are calculated, all the values are included into the main equation and are as follows [2,3]:

$$h={\displaystyle \frac{0.868+\left(0.661-1.006J^2\right)·{\left(\frac{\sqrt{\frac{P}{\pi p}}}{h}\right)}^{1.5}·\log \left(N\right)}{1+0.204\left(\min \left(\frac{3.48·{{CBR}_{bc}}^{0.3}}{{CBR}_{sg}};5.0\right)-1\right)}}·\left(\sqrt{{\displaystyle \frac{P}{\left(\frac{s}{75}\right)·\left\{1-0.9·e^{-{\left(\frac{\sqrt{\frac{P}{p\pi }}}{h}\right)}^2}\right\}·N_c·30·{CBR}_{sg}}}}-1\right)·\sqrt{{\displaystyle \frac{P}{p\pi }}}$$

(7)

4. Parametric Analyses

A parametric study of chip seal and asphalt pavements was conducted to examine the effect of asphalt layers or chip seal, base and subbase layers, and reinforcement on pavement structure dimensions, taking into account ground conditions and ESAL. While engineering materials such as hot mix asphalt, chip seals and unbound granular fill have consistent properties in simulations due to manufacturing standards, subgrade properties such as CBR are site-specific and vary considerably. The simulations account for this variability by adjusting the input parameters for the subgrade based on site data, ensuring that the model reflects real-world conditions.

4.1. Thickness of Chip Seal Pavement

Numerical models of chip seal pavement structure consisting of the chip seal layer; the base layer, with different thickness d_b; the subbase layer, with different thickness d_sb; the reinforcement; and the subgrade with constant depth d_sg = 150 cm in FEM. The chip seal pavement is unreinforced or reinforced, and it is mechanically treated as similar to the unpaved road structure.

Two parameters were varied: ground condition was expressed with CBR value and number of passes life cycle 15 years N (1×10³–1×10⁶). Geotextile mechanical properties are N_C = 3.14 and J = 0.65.

The results of analyses are thickness of unbound layer d_unb (base plus subbase layer), according to the CBR value and number of passes N.

Table 1. Thickness of the unbound layer d_unb, according to the CBR value and number of passes N.

CBR	N
	1 × 103	5 × 103	1 × 104	5 × 104	1 × 105	5 × 105
	dunb (cm)/dunb,R (cm) 1
2	72/36	75/39	77/40	80/43	81/44	84/46
3	69/32	72/35	74/36	77/39	78/40	81/42
4	64/30	68/30	70/31	73/33	74/35	77/37
5	60/30	64/30	65/30	68/30	70/30	73/32
7	52/30	56/30	57/30	61/30	62/30	65/30
10	41/30	45/30	47/30	51/30	52/30	55/30

¹ without geosynthetic reinforcement/with geosynthetic reinforcement, lower limit is 30 cm.

presents results of unbound layer d_unb for unreinforced and reinforced chip seal pavement according to the CBR value and number of passes N.

Results indicated the expression of unbound layer d_unb by a simple Equation (8). The constants c₁ and c₂ that determine the thickness of chip seal pavement unbound layer d_unbCS are shown in

Table 2. Constants that determine the thickness of chip seal pavement unbound layer d_unbCS, according to the CBR value.

CBR (%)	c1·(-)	c2·(-)
3	55.734	1.940
4	50.327	2.064
5	45.994	2.064
7	37.839	2.098
10	25.668	2.279

. The limitation of the lower unbound layer thickness limit is given to the analysis as a special condition and is therefore not taken into account in the equation. The following equation is an approximated function of Equation (7) for the selected CBR value and other preselected parameters:

$$d_{unbCS}=c_1+c_2·\ln \left(N\right)$$

(8)

The ratio between the thickness of the unbound layer of reinforced and unreinforced chip seal pavement is calculated and referred to as the geosynthetic reinforcement coefficient (GRC). This ratio approaches to value 2.0 across different numbers of ESAL and CBR values between 2.0 and 7.0. Therefore, a constant GRC value of 2.0 is adopted for the analysis.

4.2. Thickness of Hot Mix Asphalt Pavement

Numerical models of (un)reinforced asphalt pavement structure consisting of the asphalt layer, with thickness d_a; the base layer, with thickness d_b; the subbase layer, with thickness d_sb; reinforcement; and the subgrade, with constant depth d_sg = 150 cm. The asphalt pavement is unreinforced or reinforced, and it is mechanically treated as similar as a multilayered road structure.

Two parameters were varied: ground condition, expressed with CBR (3–10%), and number of passes N (1 × 10³–1 × 10⁶), expressed for life cycle 20 years. Geotextile properties are N_C = 3.14, J = 0.65.

To check the load-bearing capacity and durability of the pavement structure, the maximum total load-bearing capacity of all layers must be calculated. For this reason, the method uses two factors, FS 1 and FS 2, which must be satisfied if the road structure can fulfill its task throughout its intended service life. The factors are calculated as follows:

$${\displaystyle \frac{P_y}{P_f}}>1,1 \left(\mathrm{F}\mathrm{S}1\right)$$

(9a)

$${\displaystyle \frac{P_u}{P_{e,s}}}>2,0 \left(\mathrm{F}\mathrm{S}2\right)$$

(9b)

where the parameters represent the following quantities: the bearing capacity of the fill P_y, pressure on the fill P_f, bearing capacity of the subsoil P_u and equivalent pressure on the subsoil P_e,s.

Results of parametric analyses are thickness of asphalt layers d_a (asphalt surface layer d_as plus asphalt bearing layer d_ab) and thickness of unbound layer d_unb (base layer, with thickness d_b, plus the subbase layer, with thickness d_sb) both according to the CBR value and number of passes N.

Results indicated expression of thickness of asphalt layers d_a by a simple Equation (10a):

$$d_a=c_3·N^{-c_4}$$

(10a)

Results of the unbound layer d_unb for unreinforced asphalt pavement can be expressed by a simple equation (Equation (10b)):

$$d_{unb}=c_5·\ln \left(N\right)+c_6$$

(10b)

The constants c₃, c₄, c₅ and c₆ that determine the thickness of hot mix asphalt pavements d_unbCS and d_unb are shown in

Table 3. Constants that determine the thickness of the hot mix asphalt layer d_a and d_unb as a function of the CBR value.

CBR (%)	c3·(-)	c4·(-)	c5·(-)	c6·(-)
3	0.657	0.217	23.152	5.541
4			20.543	4.896
5			17.278	4.322
7			14.498	3.339
10			3.870	2.362

.

The ratio (GRF) between the thickness of the reinforced unbound layer and the unreinforced unbound layer was determined as 1.5.

5. Cost Analyses

The cost analysis of the pavement structure was carried out on the basis of the methods described. The aim of the parametric study is to investigate the effects of hot mix asphalt pavement, chip seal, base course, subgrade and reinforcement on the dimensioning of the pavement structure, taking into account ground conditions, freezing zone, hydrological conditions and the number of traffic passes.

Several sub-models of the chip seal pavement structure were created, each consisting of a two-layer chip seal, one or two unbound layers and with or without reinforcement (see, Figure 2).

• Type CSUN1 chip seal, with one unbound layer (base layer) and unreinforced.
• Type CSUN2 chip seal, with one unbound layer (base layer plus subbase layer) and unreinforced.
• Type CSUN1R chip seal, with one unbound layer (base layer) and geosynthetically reinforced.
• Type CSUN2R chip seal, with two unbound layers (base layer plus subbase layer) and geosynthetically reinforced.

Several sub-models of hot-mix asphalt pavement structure were built [33]: one or two layers of asphalt and one or two unbound layers, with or without reinforcement (see, Figure 3).

• Type AS1UN1—one layer of asphalt (surface bearing layer), one unbound layer (base layer) and unreinforced.
• Type AS1UN2—one layer of asphalt (surface bearing layer), two unbound layer (base layer plus subbase layer) and unreinforced.
• Type AS2UN1—two layers of asphalt (surface layer plus bearing layer), one unbound layer (base layer) and unreinforced.
• Type AS2UN2—two layers of asphalt (surface layer plus bearing layer), two unbound layer (base layer plus subbase layer) and unreinforced.
• Type AS1UN1R—one layer of asphalt (surface bearing layer), one unbound layer (base layer) and geosynthetically reinforced.
• Type AS1UN2R—one layer of asphalt (surface bearing layer), two unbound layer (base layer plus subbase layer) and geosynthetically reinforced.
• Type AS2UN1R—two layers of asphalt (surface layer plus bearing layer), one unbound layer (base layer) and geosynthetically reinforced.
• Type AS2UN2R—two layers of asphalt (surface layer plus bearing layer), two unbound layer (base layer plus subbase layer) and geosynthetically reinforced.

5.1. Cost Objective Function of Different Types of Pavement Structure

The cost objective function includes the construction costs of different types of pavement structure (EUR/km), see Equation (11), can be written according to different types of pavement structures in 12 forms:

$$\mathrm{m}\mathrm{i}\mathrm{n}: COST=C_{exc,re}+C_{sta,base}+C_{geo}+C_{fill,sb}+C_{fill,b}+C_{as,sub}+C_{as,bl}+C_{as,cl}+C_{as,cbl}+C_{CS}$$

(11)

where COST designates the construction costs per unit of the pavement structure. The labels C_exc,re, C_sta,base, C_geo, C_fill,sb, C_fill,b, C_as,sub, C_as,bl, C_as,cl, C_as,cbl and C_CS designate the material and labor cost items (EUR/km) that are included in the cost objective function (see

Table 4. Material and labor costs included in the cost objective function.

Cost Item	Equation	Equation Number
Ground excavation	$C_{exc,re}=\left[L·H_{exc}·B\right]·c_{exc}$	(11a)
Stabilization of base	$C_{sta,base}=\left[L·B\right]·c_{sta}$	(11b)
Geotextile	$C_{geo}=\left[L·B\right]·c_{geo}$	(11c)
Subbase layer fill	$C_{fill,sb}=\left[L·B·d_{sb}\right]·c_{fill,sb}$	(11d)
Base layer fill	$C_{fill,b}=\left[L·B·d_b\right]·c_{fill,b}$	(11e)
Asphalt fine substrate	$C_{as,sub}=\left[L·B\right]·c_{fsub}$	(11f)
Asphalt bearing layer	$C_{as,bl}=\left[L·B\right]·c_{ab}$	(11g)
Asphalt surface layer	$C_{as,cl}=\left[L·B\right]·c_{as}$	(11h)
Asphalt surface-bearing layer	$C_{as,cbl}=\left[L·B\right]·c_{asb}$	(11i)
Chip seal layer	$C_{CS}=\left[L·B\right]·c_{CS}·{LS}_{CS}$	(11j)
Lifespan factor	${LS}_{CS}=N· 5· {10}^{-6}+1.82$	(11k)

and

Table 5. Unit prices for material and labor for the construction of a paving structure.

Item Label	Description	Unit Price
cexc	Unit price of ground excavation with transport to landfill	11.5 EUR/m3
csta	Unit price of the stabilization (leveling and compaction) of the excavated ground surface	3.2 EUR/m2
cgeo	Unit price of the geotextiles soil stabilization	4.2 EUR/m2
cfill,sb	Unit price of the subbase layer fill soil, including transport, leveling and compaction	31.0 EUR/m3
cfill,b	Unit price of the base layer fill soil, including transport, leveling and compaction	42.0 EUR/m3
cas,sub	Unit price of the asphalt fine substrate	2.0 EUR/m2
cab	Unit price of the asphalt bearing layer	260 EUR/m3
cas	Unit price of the asphalt cover layer	390 EUR/m3
casb	Unit price of the asphalt surface-bearing layer	330 EUR/m3
cCS	Unit price of the chip seal layer	7.3 EUR/m2

).

For asphalt pavement, the lifespan is 20 years. The chip seal pavement lifespan also depends on the ESAL. Based on an assumption (see Section 2), the lifespan of chip seal is given in

Table 6. Lifespan of the chip seal according to ESAL.

N	Lifespan (Years)	Lifespan Factor LSCS (-)
1 × 104	10	2.00
5 × 104	9.8	2.04
1 × 105	7.5	2.43
5 × 105	4	4.42
1 × 106	2.5	6.82

. Based on this assumption, the lifespan factor LS_CS is expressed (Equation (11k)). Geometrical and project-related data are summarized in

Table 7. Geometrical and project data.

L	Length of pavement structure	1 km
B	Width of pavement structure	8 m
Hex	Depth of ground excavation	Calculated (cm)
dsb	Thickness of subbase layer	Calculated (cm)
db	Thickness of base layer	Calculated, ≥20 cm
das	Thickness of the asphalt surface layer	4 cm
dab	Thickness of the asphalt bearing layer	Calculated, ≥6 cm
dasb	Thickness of the asphalt surface-bearing layer	Calculated, ≥7 cm
dCS	Thickness of the chip seal layer	3 cm
Hfr	Depth of freezing	40, 60, 80, 100 cm
ffr	Factor of freezing (depending on ground and hydraulic conditions)	0.8 (-)
N	Number of traffic load pass for the design life of the pavement	104, 105, 106 (-)
CBR	California Bearing Ratio	3, 5, 7%

.

5.2. Geotechnical Constraints

The geotechnical analysis and the design constraints impose restrictions on the cost objective function. This ensures that the design conditions comply with the required recommendations and standards.

Twenty-seven different equations for quantities (Equations (12)–(38)) and ten conditions (Equations (39)–(55)) have been defined in accordance with parametric analyses and the recommendations, which were added into the pavement optimization model as geotechnical constraints (see

Table 8. Quantities and conditions included in the optimization model.

Pavement stabilization, geotextile soil stabilization and fine substrate area		CSUN1, CSUN1R		CSUN2, CSUN2R
$A_{sta}=L·B$	(12)	$d_{unbCS}=d_b$	(13)	$d_{unbCS}=d_{sb}+d_b$	(14)
$A_{geo}=L·B$	(15)	$d_a=d_{CS}$	(16)	$d_a=d_{CS}$	(17)
$A_{fsub}=L·B$	(18)	$H_{exc}=d_b+d_{CS}$	(19)	$H_{exc}=d_{sb}+d_b+d_{CS}$	(20)
$A_{CS}=L·B$	(21)	AS1UN1, AS1UN1R		AS1UN2, AS1UN2R
Depth of ground excavation, depending on pavement type		$d_a=d_{asb}$	(22)	$d_a=d_{as}+d_{ab}$	(23)
$H_{exc}=d_{unb}+d_a$	(24)	$d_{unb}=d_b$	(25)	$d_{unb}=d_b+d_{sb}$	(26)
Where dunb is the thickness of base layer or sum of base layer plus subbase layer, and da is the thickness of one or more asphalt layers or chip seal layer		$H_{exc}=d_b+d_{asb}$	(27)	$H_{exc}=d_b+d_{as}+d_{ab}$	(28)
Depth of freezing, depending on climate zone		AS2UN1, AS2UN1R		AS2UN2, AS2UN2R
Hfr = 40 cm	(29)	$d_a=d_{as}+d_{ab}$	(30)	$d_a=d_{as}+d_{ab}$	(31)
Hfr = 60 cm	(32)	$d_{unb}=d_b$	(33)	$H_{exc}=d_{sb}+d_b+d_{as}+d_{ab}$	(34)
Hfr = 80 cm	(35)	$H_{exc}=d_{sb}+d_b+d_{asb}$	(36)	Asphalt surface layer thickness
Hfr = 100 cm	(37)			$d_{as}=4 \mathrm{c}\mathrm{m}$	(38)

,

Table 9. List of equations included in each chip seal pavement structure.

	Type of Chip Seal Pavement Structure
	CSUN1	CSUN2	CSUN1R	CSUN2R
Ground excavation Hexc	(13, 16, 19)	(14, 17, 20)	(13, 16, 19)	(14, 17, 20)
Stabilization of base Asta	(12)	(12)	(12)	(12)
Geotextile Ageo	-	-	(15)	(15)
Subbase layer fill dsb	-	(39)	-	(39)
Base layer fill db	(41, 42, 47)	(40, 41)	(41, 42, 48)	(40, 41)
Asphalt fine substrate Afsub	(18)	(18)	(18)	(18)
Asphalt bearing layer dab	-	-	-	-
Asphalt surface layer das	-	-	-	-
Asphalt surface-bearing layer dasb	-	-	-	-
Chip seal layer ACS	(21)	(21)	(21)	(21)

and

Table 10. List of equations included in hot mix asphalt pavement structure.

	AS1UN1	AS1UN2	AS2UN1	AS2UN2	AS1UN1R	AS1UN2R	AS2UN1R	AS2UN2R
Ground excavation Hexc	(22, 25, 27)	(23, 26, 28)	(30, 33, 36)	(32, 33, 34)	(31, 34, 38)	(23, 26, 28)	(30, 33, 36)	(31, 34, 38)
Stabilization of base Asta	(12)	(12)	(12)	(12)	(12)	(12)	(12)	(12)
Geotextile Ageo	(15)	(15)	(15)	(15)	(15)	(15)	(15)	(15)
Subbase layer fill dsb	-	(39)	-	(39)	-	(39)	-	(39)
Base layer fill db	(42)	(40)	(42)	(40)	(42)	(40)	(42)	(40)
Asphalt fine substrate Afsub	(18)	(18)	(18)	(18)	(18)	(18)	(18)	(18)
Asphalt bearing layer dab	-	(50)	-	(50)	-	(50)	-	(50)
Asphalt surface layer das	-	(38)	-	(38)	-	(38)	-	(38)
Asphalt surface-bearing layer dasb	(49)	-	(49)	-	(49)	-	(49)	-
Chip seal layer ACS	-	-	-	-	-	-	-	-

).

The overall thickness of frost-resistant layers exceeds the frost depth:

$$H_{exc}\ge f_{fr}·H_{fr}$$

(39)

The thickness of the subbase layer d_sb and the thickness of the base layer d_b are defined as:

$$d_{sb}=d_{unb}-d_b$$

(40)

$$d_b\ge 20 \mathrm{c}\mathrm{m}$$

(41)

Thickness of unbound layer:

$$d_{unb}={\displaystyle \frac{0.868+\left(0.661-1.006J^2\right)·{\left(\frac{\sqrt{\frac{P}{\pi p}}}{h}\right)}^{1.5}·\log \left(N\right)}{1+0.204\left(\min \left(\frac{3.48·{{CBR}_{bc}}^{0.3}}{{CBR}_{sg}};5.0\right)-1\right)}}·\left(\sqrt{{\displaystyle \frac{P}{\left(\frac{s}{75}\right)·\left\{1-0.9·e^{-{\left(\frac{\sqrt{\frac{P}{p\pi }}}{h}\right)}^2}\right\}·N_c·30·{CBR}_{sg}}}}-1\right)·\sqrt{{\displaystyle \frac{P}{p\pi }}}$$

(42)

$$d_{unb}=d_b\ge 30 \mathrm{c}\mathrm{m}$$

(43)

Thickness of unbound layer-one layer:

$$d_{unb}=d_b$$

(44)

Thickness of unbound layer-two layers:

$$d_{unb}=d_b+d_{sb}$$

(45)

$$d_b=20 \mathrm{c}\mathrm{m}$$

(46)

Thickness of unbound layer–chip seal pavement (GRC = 1 and GRC = 2 for geosynthetic chipseal pavement):

$$d_{unb}\ge (0.0366-0.655·CBR+0.0194·\ln \left(N\right))/GRC$$

(47)

Thickness of unbound layer–geosynthetic chip seal pavement (constants c₁ and c₂ are defined in Table 2):

$$d_{unbCS}=c_1+c_2·\ln \left(N\right)$$

(48)

Thickness of unbound layer–hot mix asphalt pavement (constants c₅ and c₆ are defined in Table 3):

$$d_{unb}=c_5·\ln \left(N\right)+c_6$$

(49)

Thickness of unbound layer–geosynthetic hot mix asphalt pavement:

$$d_{unb}\ge 1.5·c_5·\ln \left(N\right)+c_6$$

(50)

Conditions for asphalt layers for the ratio between the factor P_y (Equation (9a)) and P_f (Equation (9b)):

$$P_y/P_f=(0.6·R^{\prime }·{\gamma }_f·N_{\gamma })/({\displaystyle \frac{F_p}{\pi ·{\left(R^{\prime }\right)}^2}}+{\gamma }_a·d_a)\ge 1.1$$

(51)

where R’ is the radius of distributed load between tire asphalt and granular fill, R’’ is the radius of distributed load between granular fill, N_γ is the bearing capacity factor, F_p is the maximum wheel load for the paved situation, F_e is the equivalent wheel load, γ_a is the density of the asphalt layer, γ_f is the density of the fill layer and d_a is the thickness of asphalt layer.

Conditions for asphalt layers for the ratio between P_u and P_e:

$$P_u/P_{e,s}=(N_c·CBR·30·{\left({\displaystyle \frac{R^{″}}{R}}\right)}^2)/({\displaystyle \frac{F_e}{\pi ·{\left(R^{″}\right)}^2}}+{\gamma }_a·d_a+{\gamma }_f·d_{unb})\ge 2.0$$

(52)

The thickness of asphalt according to the number of traffic load:

$$d_a\ge 0.657·N^{-0.217}$$

(53)

The thickness of one-layer asphalt:

$$d_{asb}\ge 7 \mathrm{c}\mathrm{m}$$

(54)

The thickness of two-layer asphalt (where d_as = 4 cm):

$$d_{ab}\ge 6 \mathrm{c}\mathrm{m}$$

(55)

6. Sensitivity Analysis of the Mixed Integer Optimization Model

A sensitivity analysis of the mixed integer optimization was carried in order to obtain an optimal design and construction cost for the pavement structure. Different combinations were tested with the following different design parameters:

−

Eight different types of hot mix asphalt pavement structures: AS1UN1, AS1UN2, AS2UN1, AS2UN2, AS1UN1R, AS1UN2R, AS2UN1R and AS2UN2R.

−

Four different types of chip seal pavement structures CSUN1, CSUN2, CSUN1R and CSUN2R.

−

Four different climate zones, with frost depth H_fr: 40 cm, 60 cm, 80 cm and 100 cm.

−

Three different ground CBR: 3%, 5% and 7%.

−

Three different traffic loading passes: 1 × 10⁴, 1 × 10⁵ and 1 × 10⁶.

Following these design parameters, 432 individual mixed integer optimizations were performed. The analysis results are very extensive with 432 individual optimization solutions. Figure 4, Figure 5 and Figure 6 show the cost of the optimal pavement structure at different values of the variables defining ESAL, freezing depth and CBR. Different types of optimal asphalt pavements were identified, namely AS1UN1, AS1UN2, AS2UN1, AS2UN1R, AS2UN2R and CSUN1R.

At low freezing depths and high ESAL, the reinforced hot mix asphalt pavement structures were found to be the optimum pavement type. However, for the different values of the variables, only one pavement type with chip seal, CSUN1R, was found to be optimal. Therefore, the chip seal structure should always be designed with integrated geosynthetic reinforcement.

The frost depth has a significant influence on the thickness of the unbound layers and the cost of hot mix asphalt pavement, while the structure of the chip seal pavement is independent of the frost depth. It should be noted that the material fatigue of the bituminous seal due to freeze–thaw cycles and freezing temperatures was not considered as a constraint function.

Compared to hot mix asphalt, chip sealing is an optimal solution, especially with low traffic loads. Based on the calculated solutions, chip sealing is optimal up to N = 3 × 10⁵ ESAL, which is close to the limit between low and medium ESAL with respect to the local technical specifications.

The results indicate that, under low traffic conditions (ESAL = 1 × 10⁴), a chip seal pavement structure can be up to 40% less expensive than an optimal hot mix asphalt pavement structure, particularly when the subgrade has low bearing capacity and is subject to unfavorable climatic conditions. However, at medium traffic loads (ESAL = 1 × 10⁶), with good subgrade bearing capacity and favorable climate, the chip seal pavement structure incurs costs that are 25% higher than those of the hot asphalt pavement structure. The frost depth has a considerable influence on the construction costs of hot mix asphalt pavements, as the costs increase by 50% when the frost depth increases from 40 cm to 100 cm.

The Slovenian road network (see,

Table 11. Public roads in Slovenia.

Road Type (-)	Category (-)	Length (km)
AC, HC	Highways	779
G1, G2	Main roads	802
R1, R2, R3, RT	Regional and other roads	5947
LC, JP	Local and other roads	32,510

) comprises more than 6700 km of state roads, mostly with medium or higher ESAL (N > 1 × 10⁶) and 32,000 km of local and other roads, mostly with low levels of traffic (N < 1 × 10⁶). This is similar in other countries as well. Chip seal can therefore be an important alternative to hot mix asphalt pavements.

7. Conclusions

The geotechnical aspects of the applicability of chip seals compared to conventional hot mix asphalt pavements were investigated. An analytical model was used to design unpaved roads and determine the required thickness of the unbound layers. Eight optimization models for hot mix asphalt pavements and four for chip seal pavements were developed to obtain optimal designs for different input parameters. These results were used to perform a multi-parametric analysis that included an optimization loop for each combination of design variables. Optimizations were performed to obtain an optimal pavement design for different ESAL and site conditions (freezing depths). The results of this study provide engineers with important information on what type of pavement to select for different project data to minimize pavement construction costs.

−

For lower CBR values (up to 5%), hot mix asphalt pavement with geosynthetic reinforcement is the optimal solution among all hot mix asphalt pavement types.

−

Hot mix asphalt pavements with geosynthetic reinforcement are a more cost-effective solution, especially when the site conditions are favorable, with frost-resistant materials and good hydrological conditions, and when the thickness of the pavement structure is determined by the pavement thickness index and not by the required frost depth.

−

The sensitivity analysis has shown that the most important parameter for the optimal cost of a pavement design is ESAL.

−

At low freezing depth and high ESAL, reinforced hot mix asphalt pavement proved to be the optimum pavement type.

−

Only the reinforced chip seal pavement type was found to be optimal among all types of chip seal pavements. For this reason, chip sealing should always be designed with an integrated geosynthetic reinforcement.

−

Compared to hot mix asphalt, chip sealing is an optimal solution, especially with low traffic loads, up to the limit between low and medium ESAL.

−

The road network consists to a large extent of roads with low traffic volumes. In such cases, chip sealing can be an important alternative to hot mix asphalt pavements.

While it is acknowledged that the type and mineral composition of aggregates can significantly impact the quality, construction cost and lifespan of pavement structures, these parameters were not considered in the current models of chip seal pavements. Further research should be conducted to incorporate the influence of aggregate mineralogy in future studies to provide a more comprehensive understanding of its effect on pavement performance.