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Article

Network-Scale Analysis of Sea-Level Rise Impact on Flexible Pavements

1
Department of Civil and Environmental Engineering, Florida International University, Miami, FL 33174, USA
2
Program Studi Teknik Sipil, Universitas Ibn Khaldun, Bogor 16162, Indonesia
3
Sustainable Road Engineering Inc., Sunrise, FL 33326, USA
*
Author to whom correspondence should be addressed.
Water 2023, 15(23), 4163; https://doi.org/10.3390/w15234163
Submission received: 28 September 2023 / Revised: 2 November 2023 / Accepted: 27 November 2023 / Published: 1 December 2023

Abstract

:
This study investigates the potential damage to flexible pavements caused by rising groundwater tables resulting from sea-level rise. A case study was conducted in Miami-Dade County, Southeast Florida, a low-lying area at high risk of inundation and rising groundwater table due to sea-level rise. Flexible pavement specifications are differentiated using functional classification, and the reduced service life for various roadway types due to rising groundwater tables is predicted. The study utilized regional groundwater table maps for future sea-level rise scenarios to identify the saturated unbound layers for each roadway. An improved multilayer linear elastic model incorporating an unsaturated modulus resilient module, capable to handle saturated subgrade to base layer, is employed to quantify pavement response for each classified road at a network scale. The results indicate that the groundwater table response due to sea-level rise will extend further inland, impacting coastal infrastructure and inland areas. This study contributes to a network-scale deterministic pavement model tailored specifically for assessing the impact of sea-level rise on pavement performance. Given the increasing threats posed by sea-level rise, flooding, and infrastructure vulnerability, a comprehensive tool is provided for planners, pavement engineers, and policymakers.

1. Introduction

Southeast Florida is considered among the most at-risk areas in the United States regarding extreme weather events and rising sea levels. Due to its low-lying terrain, the region is vulnerable to permanent flooding caused by rising sea levels. The rate of sea-level rise (SLR) in Southeast Florida has been accelerating over the past decades and is forecasted to continue. The SLR in the region has been measured at a rate of 6–9 mm per year since 2003, which is higher compared to 3.2–3.7 mm per year of the global mean SLR rate [1,2]. According to the Southeast Florida Regional Climate Change Compact, Miami-Dade County is one of the most vulnerable areas in the world to SLR, with a projected SLR of 15.24–25.4 cm by 2030 and 35.6–66 cm by 2060 [3]. SLR is also expected to increase the frequency and intensity of tidal flooding, storm surge, and saltwater intrusion, which could cause significant damage to the region’s infrastructure, economy, and environment [3]. As the region’s infrastructure and economic activity are closely linked, such flooding can potentially disrupt the strong Gross Regional Product (GRP) that has consistently outperformed that of the rest of the country over the past four decades [4].
The unconfined, shallow Biscayne aquifer underlies the study area. The Biscayne aquifer is highly permeable due to porous limestone [5]. Difference in density results in the saltwater interface pushing further inland beneath the freshwater as sea-level rise is projected to progress, potentially leading to an increase in groundwater table. The sea-level condition was shown to influence groundwater table further inland. Both rainfall recharge and saltwater intrusion will affect the water table condition. However, the study area already experiences sunny day flooding (i.e., nuisance flooding) which is caused by high groundwater table especially during the high tide periods, a situation that worsens during King Tide occurrences with any extent of sea-level rise [5,6,7]. Miami-Dade County stands out among Southeast Florida counties for its significant economic activity [4]. The county’s road infrastructure experiences the highest traffic volume per lane mile, making it crucial for the roads to withstand climate-related stressors to protect economic well-being.
The overall pavement structure can be weakened due to high moisture condition. For the asphalt layer, the adhesive bond between aggregate particles is weakened, leading to the loss of aggregate and a rough surface texture [8,9]. The unbound layers of pavement are vulnerable to high moisture conditions and potentially weaken the overall pavement structure [10,11,12,13,14,15,16,17,18]. The main reasons behind unbound layers vulnerability to high moisture condition are as follows: (1) high moisture reduces the bearing capacity of the subgrade soil, leading to the settlement and deformation of the pavement, (2) high moisture reduces the resilient behavior of the foundation soil. The projected rise in groundwater table associated with sea-level rise (SLR) is expected to cause damage to the base and subbase layers of the roadways, thereby reducing the road’s service life. Additionally, a forecasted increase in the frequency and intensity of high rainfall events will further burden the pavement drainage system and result in higher ground saturation levels, posing a challenge for the region [6,19]. It has also been found that the loss of pavement life is significant for long-duration and higher-cycle extreme events [20]. Along with high traffic loading, the combination of stressors will accelerate pavement failure.
The most effective and efficient approach for spatial identification in vulnerable transportation assets is through Geographic Information System (GIS)-based asset management. Currently, it has been widely adopted by most states (Department of Transportations (DOT) and Metropolitan Planning Organization (MPO) or Transportation Planning Organization (TPO) in the US) [21,22,23]. Several well-documented mapping efforts have been identified related to the SLR impact on transportation involving Southeast Florida [24,25,26]. The existing mapping products in Southeast Florida consider only storm surge, flooding, and SLR inundation as surface flooding. The exclusion of groundwater information can significantly underestimate the impact of SLR because it does not account for rising groundwater levels. The variation of groundwater level is contextual to a specific location and is not the same throughout a region. The degree of rising groundwater level depends on factors like the hydrogeological features of the area, the distance to the coast, and groundwater-flow-influencing factors like groundwater pumping and discharge. The effect of this rising groundwater on the lifespan of pavements is also influenced by the depth to groundwater table and the pavement structure in the specific area [13,27].
A significant body of literature has focused on pavement deterioration in the absence of flood-related conditions, with most models being executed at the project level [12]. This trend can be attributed to the limited data available at the network level and its high computational costs. Nevertheless, despite these challenges, network-scale models are invaluable as they facilitate the identification of vulnerable pavement sections. Therefore, developing a tool that serves this purpose would aid in making informed decisions for mitigation at the network level [12].
Asphalt is the most used material for roadways in the United States, and concrete is used for the remaining paved roads. Of the roadways in the US, 94% were surfaced with either asphalt (79%) or concrete (15%), while the remaining 6% were gravel or earth roads. In terms of lane miles, asphalt accounted for approximately 93%, and concrete accounted for approximately 7% of the total lane miles in the US [28,29,30]. Furthermore, asphalt pavements were more vulnerable than their concrete counterpart, as found in post-flood surveys [10,31]. Water can weaken the asphalt binder due to its ability to penetrate the binder over time, reducing adhesion to the aggregate and increasing asphalt layer susceptibility to further damage [9,32]. However, the unbound layers were found to be the most vulnerable part of the pavement when pavement layers were exposed to high moisture conditions [13,16,33,34]. Therefore, studying asphalt pavement service life, defined as allowable traffic load application and its reduction due to SLR, is essential for mitigating the impact of these stressors on the road infrastructure.
Given the importance of pavement quantification for mitigation, the objectives of this paper are as follows: (1) to identify the potential location of the most affected roadway by rising groundwater; (2) to develop a network-level approach, which involves integration between GIS and pavement response model to predict the asphalt pavement performance based upon multiple SLR scenarios; and (3) to quantify the reduced service life of asphalt pavement SLR-induced rising groundwater table with a case study in Miami-Dade County, Southeast Florida.
This paper is structured as follows: First, the analysis methodology is described, which includes vulnerable road segment identification, pavement response model, service life calculation, and data collection and components for the analytical framework. Second, the vulnerable road mapping is presented, and pavement response model calibration is discussed. Third, the network scale result is presented by discussing the overall road network map and selected road segments based on road class and TPO area. Fourth, the groundwater flow effect on pavement performance due to local pumping is analyzed.

2. Materials and Methods

The SLR impact assessment in this study comprised two primary stages: (1) identification of vulnerable road segments and (2) modeling of pavement response, fatigue cracking, and rutting performance. In the first stage, the Florida Department of Transportation (FDOT) recommendation based on the clearance between the base and groundwater level was utilized to identify vulnerable road segments. The depth to water table (DTW) information was applied to the road network to determine which road segments have the potential for reduced resilient modulus value and, consequently, reduced overall performance. The selected segments with the lowest depth to water table for each transportation planning region are highlighted. In the second stage, the service life was calculated based on a simplified mechanistic-empirical framework that included multilayer elastic analysis to calculate the pavement response and an empirical transfer function to convert the pavement response to the service life cycle. The pavement response model was calibrated against field data. The analytical framework was then implemented into the roadway network.
The overall methodology to determine the pavement service life is shown in Figure 1. Roadway shapefile data with functional classification were obtained and were subsequently overlaid with topography, resulting in the acquisition of surface elevation levels for each road segment. The functional classification was utilized to determine layer specifications such as thickness and material type. The bedrock level was derived from the regional bedrock map, which was overlaid with the pavement layer thickness. The unbound pavement layer was then sublayered for the layers situated between the bedrock and asphalt. As in the first stage, the results from the regional groundwater model were employed. The regional groundwater table was combined with topography, producing the depth to groundwater from the pavement surface. This depth to groundwater table was subsequently employed to determine the depth-varying matric suction. The soil–water characteristic curve (SWCC) was then utilized to determine soil moisture, which was subsequently converted to the degree of saturation (DOS). Following this, the DOS-dependent resilient modulus was calculated. The multilayer elastic method was employed to derive deflection, stress, and strain values. These values were then transformed into a service life as an allowable traffic number utilizing empirical transfer equations.

2.1. Pavement Network and Roadway Characteristics

The pavement characteristics were determined based on their functional classification. The roadway dataset and its characteristics are obtained from the FDOT Open Data Hub [35]. The obtained roadway dataset includes surface types distinguishing between asphalt and concrete pavement. The concrete segments were removed because this analysis is focused on asphalt pavements. The features such as advance intersections and bridges were also removed to ensure that the flexible pavements being quantified were placed on the ground.
The roadway layer was organized into seven classes following a standard FHWA recommendation for the HPMS (Highway Pavement Management System): Principal Arterial (Interstate, Freeways, Expressways), Minor Arterial, Major Collector, Minor Collector, and Local. The classes express the character of the service they provide and thus reflect expected different traffic loading and service life [36]. The arterial system delivers the highest level of traffic movement while most local facilities directly connect to property owners. The collector system was designated to connect the arterial and local systems. The roadway network was then placed into the Miami-Dade TPO region context. Miami-Dade County is split into seven distinct geographical areas known as Transportation Planning Areas, which have been designated by the Miami-Dade TPO. The transportation planning regions are (1) North, (2) Northwest, (3) Miami Beach, (4) Central, (5) Central Business District (CBD), (6) West, and (7) South. Each Transportation Planning Area possesses unique features like development rates, necessities, and challenges in transportation [37]. The roadway network was segmented into 1 mile (1.6 km) segments, and then a pavement layer structure was assigned based on Table 1 according to their functional classification. The segmentation yielded 3341 segments for the entire Miami-Dade TPO region (Figure 2).

2.2. Groundwater Table, Topography, and Bedrock Level

The DEM (Digital Elevation Model) shown in Figure 3a was obtained from the Miami-Dade County Open Data Hub [38]. The DEM is bare-earth 1.524 m horizontal high resolution, created from the LiDAR (Light Detection and Ranging) survey. The projected groundwater table of Miami-Dade County was used to identify vulnerable road infrastructure that will be affected by the rising groundwater table. Groundwater table raster data were obtained from a supplemental dataset in the Florida Building Commission Project report shown in Figure 3b [39]. The raster datasets were the output of the UMD (Urban Miami-Dade) model.
The UMD model is developed based on MODFLOW-NWT, specifically calibrated within the scope of Miami-Dade County and serves in the area for planning purposes. The model includes flood control structures and wells that are spread over the entire domain. The groundwater head data for the 2060–2069 projection during the Wet Season (May–Oct) were obtained. Future rainfall patterns were considered in the UMD model using the Localized Constructed Analogs (LOCA) dataset, where MRI-cGCM3 was chosen and bias-corrected against local stations [26,27]. SLR is represented as ocean boundary conditions. The study used the Intergovernmental Panel on Climate Change (IPCC) AR5 RCP 8.5 median curve and the US Army Corps of Engineers (USACE) high curve from the Unified Sea Level Rise Projections developed by the Southeast Florida Regional Climate Change Compact [4,28]. The study implemented tide prediction and added the projected SLR curve to the predicted tides, and the effect of storm surge was not considered. Both climate scenarios are used throughout this study and referred to as low (AR5 RCP 8.5) and high (USACE) SLR scenarios, respectively.
The DEM was then subtracted by the groundwater table to obtain DTW as both data were expressed with respect to the NAVD88 (North American Vertical Datum of 1988) (Figure 3c). The DEM was also used to determine a representative elevation of each 1 mile (1.6 km) road segment. As shown in Figure 3d, the county scale bedrock level was generated from Topo to Raster interpolation, which was implemented in ArcGIS 10.8 [40,41]. The bedrock information was based on test drilling for lithologic samples [42]. Furthermore, the combination of topography and bedrock constitutes the uppermost layer and the bedrock elevation for each roadway segment. The bedrock elevation varies on location; therefore, an adjustment was required when combining topography, pavement layer structure, and bedrock. The pavement layers were prioritized wherever possible when overlying the DEM as pavement surface elevation and the bedrock raster; therefore, the pavement network was preserved even though a higher bedrock level than pavement surface elevation could possibly be found due to interpolation. The bedrock depth guided the cutoff depth or extension for the subgrade layer. For example, in the area of the Atlantic Coastal ridge, the pavement layer that is shallower than the bedrock will have an extended subgrade, ensuring continuity between the pavement layer and the bedrock. Meanwhile, if the interpolated bedrock was shallower than the pavement layer, the pavement layer was cut off to the minimum possible subgrade layer of 12 in (30.48 cm). This method of combining bedrock depth and DEM assumes that the DEM is more accurate than the interpolated bedrock raster.

2.3. Pavement Layer Samples

The range of pavement specifications was obtained from the FDOT public soil boring database for each roadway functional class (Table 1) [43]. The pavement cores were taken as a representation and are interpreted as typical pavement layers. Thus, they will constitute the performance in the other location with the same functional classification. The cores were also chosen based on their strength and thickness. For example, road class 11 was represented by two different pavements: 11A was taken from I-95 North Miami with an asphalt thickness of 229 mm, and 11B was taken from I-95 to the Turnpike connector that has 102 mm asphalt thickness. The lithographic layers contained in the FDOT public soil boring database use AASHTO or USCIS soil classification. Therefore, the resilient modulus parameter can be obtained from the Mechanistic-Empirical Pavement Design Guide (MEPDG) level 3 input for optimum moisture content condition as an initial parameter where each resilient modulus value is associated with AASHTO/USCIS soil classification. Poisson’s ratio was obtained from past reports conducted in Florida [44]. The other soil parameters were taken from the LTPP (Long-Term Pavement Performance) database located in the Miami-Dade region (LTPP 12-4103).
Table 1. Representative core pavement parameters for each road class as interpreted from the FDOT soil boring database [43].
Table 1. Representative core pavement parameters for each road class as interpreted from the FDOT soil boring database [43].
Core SourceFunctional ClassificationLayer TypeGeneralized MaterialSoil ClassMR (MPa)µThickness (mm)
ID.Description
I-95 North Miami11APrincipal Arterial—InterstateAsphaltHMAn/a24130.35229
BaseSand, silt with limerockGM2650.351006
SubgradeSandy limestoneSP1930.32134
SandSP1930.32438
Bedrockn/a51710.2Infinite
I-95 NB to Turnpike Connector11BPrincipal Arterial—InterstateAsphaltHMAn/a24130.35102
BaseSand, silt with limerockGM2650.351128
SubgradeSand, silt with limerockSM2210.251524
SandSP1930.31829
SandSP1930.32438
Bedrockn/a51710.2Infinite
SR-826/SR-836 Palmetto Expressway12APrincipal Arterial—ExpresswayAsphaltHMAn/a24130.35366
BaseSand, silt with limerockA-1-b2620.35183
SubgradeSand, silt with traces of limerockA-2-42210.251128
SandA-32000.30610
Sandy SiltA-41650.33610
SandA-32000.302438
Bedrockn/a51710.2Infinite
SR-826/1-7512BPrincipal Arterial—InterstateAsphaltHMAn/a24130.35152
Base Sand, silt with limerockA-1-b2620.35762
SubgradeSandA-32000.30914
Sand, silt with limerockA-1-b2620.35610
SandA-32000.302438
Bedrockn/a51710.2Infinite
US 1/SR 5 SB SW 214 Street14APrincipal Arterial—OtherAsphaltHMAn/a24130.35305
BaseSand, silt with limerockA-1-b2620.35305
SubgradeSand, silt with limerockA-1-b2620.35305
Bedrockn/a51710.2Infinite
SR A1A/Indian Creek Drive14BPrincipal Arterial—OtherAsphaltHMAn/a24130.3558
BaseSand, silt with limerockA-1-b2620.35213
SubgradeSand, silt with traces of limerockA-2-42210.25945
SandA-32000.301829
Bedrockn/a51710.2Infinite
SR 2516AMinor ArterialAsphaltHMAn/a24130.35122
BaseSand, silt with limerockSM/SP-SM2210.35244
SubgradeSand, silt with limerockSP/SP-SM1930.25732
Bedrockn/a51710.2Infinite
SR-826/SR836 Interchange16BMinor ArterialAsphaltHMAn/a24130.3538
BaseSand, silt with limerockA-1-b2620.35204
SubgradeSand, silt with traces of limerockA-2-42210.25305
SandA-32000.31524
Bedrockn/a51710.2Infinite
SR 925/NW 3 RD Court17AMajor CollectorAsphaltHMAn/a24130.35221
BaseSand, silt with limerockA-1-b2620.35305
SubgradeSandA-32000.30518
SandA-32000.31524
Bedrockn/a51710.2Infinite
NW 103 ST and W16 Ave17BMajor CollectorAsphaltHMAn/a24130.3533
BaseSand, silt with limerockA-1-b2620.35204
SubgradeSand, silt with traces of limerockA-2-42210.25305
SandA-32000.31524
Bedrockn/a51710.2Infinite
SR-826/SR836 Interchange18AMinor CollectorAsphaltHMAn/a24130.3561
BaseSand, silt with limerockA-1-b2620.352377
SubgradeSandA-32000.301067
Sand, silt with traces of limerockA-2-42210.25610
Bedrockn/a51710.2Infinite
NE 124TH Street18BMinor CollectorAsphaltHMAn/a24130.3551
BaseSand, silt with limerockA-1-b2620.35204
SubgradeSandA-32000.30305
SandA-32000.31524
Bedrockn/a51710.2Infinite
NE 205TH Street19ALocalAsphaltHMAn/a24130.35102
BaseSand, silt with limerockGM2650.35204
SubgradeSandy LimestoneSP1930.251219
Bedrockn/a51710.2Infinite
NE 128TH Street19BLocalAsphaltHMAn/a24130.3525
BaseSand, silt with limerockA-1-b2620.35204
SubgradeSandA-32000.30305
SandA-32000.30244
Bedrockn/a51710.2Infinite

2.4. Vulnerable Road Identification Due to Rising Groundwater

A vulnerable roadway was identified through level classification. This classification level improves the identification described in previous work [27]. The level classification is based on the depth to the water table, which will affect the saturation condition in unbound base to subbase or subgrade layer through the aggregation of the DTW raster into a 1 mile (1.6 km) road segment. The depth splitting aligns with the recommendation of FDOT practice. FDOT recommends a 25% reduction in subgrade layer resilient modulus where the base clearance to the water table is between less than 91.44 cm (3 ft) and greater than or equal to 60.96 cm (2 ft), and a 50% reduction in resilient modulus when the base clearance is less than 60.96 cm (2 ft) and greater or equal than 30.48 cm (1 ft) [45,46]. The main improvement from the previous work is that instead of using uniform DTW classification for all road classes, in this study, level classification is based on base clearance applied to each specific road class with different asphalt and base thickness, as found in Table 1. The base clearance value was calculated from DTW subtracted by the asphalt and base thickness average. Then, the level classification was applied, as shown in Table 2. Therefore, a more specific condition was applied to each road segment.

2.5. Pavement Response Model

Adaptive Layered Viscoelastic Analysis (ALVA), an open-source MATLAB-based program for calculating pavement response, was used in this study. ALVA was used to evaluate pavement response at different DTW conditions. ALVA is based on a multilayer elastic model and has been validated against similar software [47,48]. Open-source code is an attractive option due to transparency, the flexibility to modify the program, integration into a larger calculation framework, and the ability to transfer the results despite the absence of a commercial software license. The parallel computing feature in MATLAB 2021a also makes the process more efficient in calculating 6682 segments from two types of pavements implemented in 3341 road segments.
A constant loading of 9000 lbs. (4086 kg) was adopted for this study. A radius of 4.89 inch (12.4 cm), contacting between load and pavement, was used. The loading represents a single-axle single-tire and is commonly used to simulate the pressure exerted on pavements. The loading can be applied in all functional classifications and thus represents typical axle loads. The loading is also available in FWD (Falling Weight Deflectometer) testing, making it convenient for analysis and comparison. A resilient modulus formula given in Equation (1) was combined with an elastic linear model to add the capability of simulating saturated and unsaturated unbound layers. The moisture or saturation dependence of the resilient modulus formula was adopted by the mechanistic-empirical pavement design guide (MEPDG) [49,50]. Elshaer et al. (2018) [51] suggested dividing the subgrade layer into several sublayers to improve deflection accuracy. A sublayering increment of 150 mm was adopted for this analysis. The sublayered subgrade resilient modulus (MR) value was then implemented into the elastic layer model. The bedrock layer’s MR was fixed to 750,000 psi (5171.07 MPa). The combination between the sublayered unbound layer and the nonlinear elastic layer model did not produce a better result than KENLAYER in linear mode [15]. Therefore, this study used the sublayered subgrade approach combined with the elastic linear mode in ALVA, as illustrated in Figure 4. The pavement profiles shown in Table 1 were evaluated to cover the uncertainty in field conditions. In reality, the layer thickness condition might lie between the two different pavement specifications defined as pavement A and B in this study.
The formula for calculating the resilient modulus MR with moisture effect is as follows [52].
Log M R M R O P T = a + b a 1 + exp ln b a + k m S S O P T
where MROPT is the resilient modulus at optimum moisture content (OMC) condition; S is the DOS; SOPT is the DOS at optimum moisture content condition; a is the minimum of log (MR/MROPT); b is the maximum of log (MR/MROPT); and km is the regression coefficient. Parameter values a = −0.5934, b = 0.4, and km = 6.1324 were selected for fine-grained soils, and parameter values a = −0.3123, b = 0.3, and km = 6.8157 were selected for coarse-grained soils.
The DOS is determined through soil–water characteristic curve (SWCC) relationships. The relationship proposed by Fredlund and Xing (1994) [53] that has been widely adopted in the pavement research community was used in this study.
S = C ψ x   1 ln exp 1 + ψ a b     c
C ψ = 1 ln 1 + ψ ψ r ln 1 + 10 6 ψ r
where S is the DOS; ψ is the matric suction; and ψ r is typically set to 1500 kPa or 3000 kPa. Fredlund and Xing’s SWCC parameters can be estimated by the formula proposed by Perera et al. [54]:
Plasticity index = 0
a = 0.8627 ( D 60 ) 0.751
b ¯ = 7.5
c = 0.1772 ln D 60 + 0.7734
ψ r a = 1 D 60 + 9.7 e 4
Plasticity index > 0
a = 0.00364 ( w P I ) 3.35 + 4 w P I + 11
b c = 2.313 w P I 0.14 + 5
c = 0.514 w P I 0.465 + 0.5
ψ r a = 32.44 e 0.0186 ( w P I )
where a = the soil parameter, which is a function of the air entry value of the soil; b = the soil parameter, which is primarily a function of the rate of water extraction from the soil once the air entry value has been exceeded; c = a fitting parameter which is a function of the residual water content; ψ r = a fitting parameter which is mainly a function of the suction at which the residual water content occurs; C(h) = a correction factor, which is a function of the matric suction; D60 = the grain diameter corresponding to 60% passing in sieve analysis; and b ¯ = an average value of fitting parameter b. Finally, the matric suction was defined from hydrostatic capillary pressure as follows.
u a u w = γ w h
where ua is the pore air pressure, uw is the pore water pressure, γw is the unit weight of water, and h is the distance from the point above the water table, assuming that the water table is constant for a period of time.
An asphalt modulus correction was needed to accommodate temperature variation. A formula to adjust asphalt moduli is given by [55]:
E T = e b   ×   T T R E F   × E R E F
where ET = the back-calculated AC modulus at the tested temperature, b = a material constant estimated in Indirect Tensile Test (IDT) stiffness tests carried out at different temperatures, T = the AC temperature at the time of testing, TREF = the reference temperature, and EREF = the reference AC modulus at the reference temperature.
To measure the pavement performance, two equations to predict fatigue cracking and rutting were adopted. The equations are simple and straightforward, and were used in previous research [13]. The number of cycle formulas uses horizontal tensile strain, calculated at the bottom of the asphalt concrete layer, and vertical compressive strain, calculated at the top of the subgrade layer [56]. The allowable cycle number for fatigue cracking and rutting is given by Equations (14) and (15)
N f C = 2.83 × 10 6 10 6 ε t 3.148
N f R = 1.00 × 10 16 1 ε v 3.87
where NFC is the number of load applications to fatigue cracking in 10% of the wheel path area, εt is the horizontal tensile strain at the bottom of the asphalt layer in microstrain, NFR is the number of load applications to limit rutting, and εv is the vertical compressive strain at the top of subgrade in microstrain. Finally, the changes in NFC and NFR values for fatigue cracking and rutting resulting from rising groundwater were evaluated by using the ratio of the NFC and NFR values at the predicted groundwater level to the NFC and NFR values at the baseline sea-level scenario.

3. Results and Discussion

3.1. Zone Classification Based on Base Clearance to Groundwater Table

The impact of rising groundwater on a regional scale was measured using the length of roadway lanes, as this approach is more convenient when calculating the cost of production and maintenance. This cost is typically determined by the dollar amount per lane per mile or kilometer. The roadway length impacted by the rising groundwater table in Miami-Dade County is summarized in Table 3. The high SLR scenario increases the percentage of roadway in level 3 from 275.31 km (10%) to 492.73 km (17%) and level 4 from 114.49 km (4%) to 242.16 km (9%).
Mapping the roadway by superimposing it into the DTW shows that rising groundwater impact varies throughout the study area as shown in Figure 5. Miami Beach region is subjected to more roadways with level 4, as indicated with red lines; meanwhile, most of the roadway in the CBD region will perform optimally despite the high SLR scenario due to the roadway elevation. The other region that will be affected is the region closer to the coast and regions in the western part of Miami-Dade County, such as the Northwest, West, and part of the South region. The effect of roadway elevation plays an important role in the protection against potential premature failure, especially regarding moisture damage caused by rising groundwater levels.
The impact of rising groundwater was then divided specifically according to the functional classification and transportation planning areas for low SLR and high SLR scenarios (Table S1 in Supplementary Materials). Almost all Interstate and Expressway/Freeway road segments are in levels 1 and 2 in all regions and in both SLR scenarios. Miami Beach and Northwest are the two regions that will be most affected by the rising groundwater. The Other Arterial, Major Collector, Minor Collector, and Local road classes will be more affected than Interstate and Freeways/Expressways.
In the Northwest area, for the low SLR scenario, there are 19.6%, 3.4%, 13.9%, 19%, and 5.4% length km affected for the Other Arterial, Minor Arterial, Major Collector, Minor Collector, and Local road class, respectively. In the high SLR scenario, 11.9% of Interstate, 1.95% of Freeways, 22.5% of Other Arterial, 6.7% of Minor Arterial, 32.1% of Major Collector, 40.2% of Minor Collector, and 17.8% of Local roads in the Northwest region are predicted to be in level 4.
The low SLR scenario in the Miami Beach region generates 13.5% of Other Arterial, 31.8% of Minor Arterial, 43.4% of Major Collector, 75.9% of Minor Arterial, and 37.6% of Local road class in level 4. Meanwhile, 5% of the Interstate road class will be in level 4 in the high SLR scenario. As many as 34.7%, 46.4%, 67.4%, 75.9%, and 75.1% will be in level 4 for Other Arterial, Minor Arterial, Major Collector, Minor Collector, and Local road class, respectively.
An ongoing multiyear project showcased a significant effort in the Miami Beach region. The project has been executed to mitigate SLR in the Miami Beach region, including a new pump station building [57]. The Northwest region will also experience premature pavement failure due to rising groundwater levels. Despite not being as severe as in the Miami Beach region, the Northwest region also plays a vital role in the economy of Southeast Florida due to its strategic location by providing transportation links with Port Miami, Miami International Airport, and surrounding areas [37].

3.2. Pavement Response Model Calibration

Prior to the implementation of the pavement response model to the entire pavement network, a thorough evaluation was conducted by comparing our results with past research results found in the literature. The case study conducted in the previous study was utilized to verify the ALVA code performance against field measurements [15,51], which was based on the Long-Term Pavement Performance Seasonal Monitoring Program (LTPP-SMP) dataset [58]. The LTPP-SMP dataset relates pavement performance to environmental monitoring. The case study from Minnesota was selected because it was the best-performing model compared to FWD deflection. Additionally, the pavement layers in Minnesota 27-1018 location were found to be similar to those typically found in Southeast Florida.
Furthermore, the absence of data available in the LTPP-SMP program installed in the Miami-Dade area required the use of the Minnesota case study. The parameters used for the calibration run are presented in Table 4. Figure 6 displays a comparison between the average and standard deviation from FWD data, ALVA, and model results found in previous research. Overall, the ALVA result agrees with the FWD deflection. The difference in deflection performance between models could be attributed to differences in asphalt modulus and interlayer bonding parameters, as the ALVA uses a similar resilient modulus formulation and parameter from LTPP 27-1018. The asphalt modulus value from the LTPP database was utilized for the ALVA, while Elshaer et al. (2017) [51] used the recommended value from MEPDG input level 3. Furthermore, the interlayer bonding parameter was tuned through trial and error to improve the ALVA. Further, we employed the ALVA to calculate the pavement response under the baseline and SLR conditions in the Miami-Dade area.

3.3. Network Scale Pavement Performance under SLR

The pavement response and service life ratio were calculated for the entire network within the scope of Miami-Dade County. However, only the most severe condition was highlighted for this analysis based on DTW for each planning region and road functional classification, as shown in Figure 7. Figure 7 shows a variety of bedrock depths for each pavement profile representative. Two similar pavement profiles were assumed to represent each class, but they have different bedrock depths depending on location. In cases with no specific road class in a planning region, the not applicable symbol (n/a) was shown. For instance, no roadway was identified in the South region as Principal Arterial (11). Figure 7 also shows that not all segments of roadways will be equally affected by rising groundwater.
There is no Principal Arterial Interstate road across all the planning regions that experiences a high groundwater table lower than 1.5 m from the surface. Elevated construction practices are employed on the Interstate road system to mitigate flood risks. This structure confirms that the vulnerability of the road to the rise of groundwater associated with SLR is greatly influenced by the pavement’s vertical structure [13].
In the high SLR scenario, three segments belonging to the Expressways class, located in the Miami Beach region (William Lehman Cswy.), the Central region (NW 25 ST Viaduct), and the Northwest region (Turnpike Extension), exhibit a DTW of less than 100 cm. For the Other Arterial road class, only two segments in the CBD region (Biscayne Blvd Way) and South region (Krome Ave./SW 177 Ave.) show a DTW lower than 50 cm in the high SLR scenario. In contrast, other selected segments are at risk of having their base layer inundated. Only two segments exhibit base clearance in the Minor Arterial road class: Card Sound Road in the South region and West Flagler St. in the West region. In the Major Collector road class, a road segment in the Central (NW 14 ST) and another in the Miami Beach region (Indian Creek Drive) will potentially have their base layer inundated in the high SLR scenario. Furthermore, there are only road segments from the North area (NE 10 Ave) in Minor Collector and NW 109 Ave from the Northwest area in the Local road class that will have base clearance in the high SLR scenario.
The results of the pavement response modeling are displayed as the ratio between the number of load cycles to failure at the predicted SLR and the baseline scenario, representing the reduction in service life in a worst-case condition following the groundwater table that was simulated only for the future wet season (Figure 8). The bar height in each plot represents the average between pavement types A and B for each road class, while the error bars show the load cycle to failure for pavement types A and B, based on the assumption that the performance in the field will lie between the two extreme values. The saturated base layer condition was also considered in this study, which differs from the framework presented in Knott et al. (2018) [13], where the saturated base was excluded from the analysis due to modeling limitations.
The load cycle value for fatigue cracking (NFC) is less than that for rutting (NFR) in all pavement samples, which implies that fatigue cracking controls the service life prediction, similar to findings by Knott et al. (2018) [13]. The most significant service life reduction will be experienced by roads in the Miami Beach region, for example, SR-112 for the Interstate class, with a 35% reduction in cracking and a 75% reduction for rutting. The other Interstate road that will be affected is I-75, located in the Northwest region. On average, there will be a 20% reduction in cracking performance and a 64% reduction in rutting performance, relative to the baseline condition, for a high SLR scenario. However, pavement type B would only have 23% remaining in rutting performance compared with pavement type A, which still has a 72% service life.
In the Freeways class category, a segment in the Miami Beach region would have its service life reduced by 37% in cracking performance and 74% in rutting performance, relative to the baseline condition, with 50 cm DTW. The effect of bedrock depth can be seen from the NW 25 ST Viaduct from the Central region compared with the Turnpike Extension from the South region. A 95 cm DTW would only cause approximately 4% and 6% reduction in cracking and rutting performance for the NW 25 ST Viaduct with 120 cm depth to bedrock. At the same time, the Turnpike Extension located in the South region will experience a 30% and 50% reduction in cracking and rutting performance due to the 120 cm DTW. The analysis revealed that the depth of bedrock influences pavement performance, where bedrock provides better support than sand subgrade.
In the Other Arterial class, the segment from Miami Beach (44 ST) would experience the most severe SLR impact with a 60% reduction in cracking and 84% reduction in rutting performance, followed by a segment located in the North region (NW 82 ST) with 58% cracking and 94% reduction in rutting performance. Both segments would experience an inundated base layer in the wet season of 2060–2069.
In the Minor Arterial class, NW 107 Ave in the Northwest region would experience the highest reduction of service life where the segment exhibits as much as 68% reduction in cracking performance and 78% reduction in rutting performance, relative to the baseline condition with DTW of 40 cm in the high SLR scenario.
In the Major Collector class, NE 135 ST in the North region would experience the most severe reduction in service life. On average, there would be a 44% reduction in cracking performance and a 51% reduction in rutting performance. The service life reduction would be more severe at the weaker pavement type, which can cause an 88% reduction in cracking and a 92% reduction in rutting performance, relative to the baseline condition.
The thinnest by-design pavement is generally categorized as Minor Collector and Local road class. The Miami Beach region experiences the highest reduction in service life. For example, as much as a 40% reduction in cracking and 65% reduction in rutting performance would occur in the 2060–2069 high SLR scenario in W Mastha Drive, and a 45% reduction in cracking and 62% in rutting performance for NW 32 PL, relative to the baseline condition.
Considering DTW = 175 cm as the reference point for 100% fatigue cracking performance, the data indicate a general trend of decreased performance as the groundwater table gets shallower across various road classes. For Principal Arterial—Interstate (11), the performance data are not applicable or not found due to their elevated structures. In the case of Expressways, a DTW of 150 cm shows no differences to 175 cm, with no available data for shallower DTW. Road class 14 maintains a high cracking performance at deeper groundwater levels but demonstrates a noticeable decrease in performance at shallower depths, dropping to as low as 26.5% for 14B at DTW 25 cm. In Minor Arterials, class 16A performance drops from 92.8% at 75 cm to 46.8% at 25 cm, and 16B shows a significant decrease from 99.3% at 75 cm to 15.2% at 25 cm, highlighting a pronounced sensitivity to water table depth. Major Collectors 17A and 17B also display performance reductions, with 17A going from 98% at 150 cm to 55.1% at 25 cm and 17B decreasing from 99.8% at 75 cm to 11.8% at 25 cm. Minor Collectors 18A and 18B, as well as Local roads 19A and 19B, similarly show decreased performance at shallower DTWs, with 18A dropping from 100% at 150 cm to 38.3% at 25 cm, 18B from 98% at 125 cm to 20.4% at 25 cm, 19A from 97% at 125 cm to 25.3% at 25 cm, and 19B from 99% at 125 cm to 13.7% at 25 cm. In the case of rutting performance, Table 5 shows a similar trend to fatigue cracking performance where an increased DTW produces a better rutting performance across various road classes.
The analytical framework proposed in this study takes advantage of using open-source code to simulate all road segments simultaneously. Pavement mapping through GIS gives a comprehensive view of service life prediction on the road segments being analyzed, as shown in Figure 9. The road network GIS shapefile as the output of the analytical framework contains the information related to the pavement response modeling input and output such as DTW, depth to bedrock, base layer clearance-based vulnerability level, and the number of load cycles of cracking and rutting for each sea-level rise scenario. The information in the shapefile improves the SLR vulnerability mapping, which previously focused on the impact of surface flooding.
The framework is designed to anticipate future changes in projected rising groundwater. The changes in operation rules and retrofitting of hydraulic structures spread in the county may happen in the future to adapt to higher sea levels. The changes are also subject to the updating process of the unified SLR projection Southeast Florida Regional Climate Compact.

3.4. Analysis of Groundwater Flow Effect

As groundwater wells were found throughout the Miami-Dade area, the groundwater flow effect needs to be considered in this study. Two road segments located at relatively the same elevation, pavement specification by road class, and distance to the coastline are used to investigate the effect of the groundwater flow regime. The two road segments have different proximity to pumping wells (Figure 10). The Westward Drive road segment is located between individual wells just north of Miami International Airport, while W 32 ST is located 2 km to the north of the individual wells. Each individual well has an average rate of 20,011 m3/day [5]. In the Westward Drive road segment, the DTW in the high SLR scenario would only reach approximately 85 cm, resulting, on average between the two types of pavements, in a reduction of 53% in cracking and a 77% reduction in rutting performance, relative to the baseline condition. A slightly different relative cracking and rutting performance are shown in the W 32 ST segment, where the segment exhibits a 56% reduction and an 84% reduction in cracking and rutting performance, respectively. The effect of the groundwater flow regime on pavement performance is confirmed in this case study, which is also shown by Knott et al. (2017) [13]. From this analysis, groundwater pumping helps lower the DTW and is thus beneficial for pavement performance. It is worth noting that the South Florida Water Management District’s (SFWMD) strategies to maintain the groundwater table at a certain level to hold the saltwater intrusion may affect pavement performance. The study of flood and salinity control structure effect in the groundwater modeling aspect is beyond the scope of this study. However, the integrated analytical framework presented in this study would accommodate the changes in existing groundwater maps or more modeling results from additional groundwater model runs that may be available in the future.

4. Uncertainty and Future Research

Determining pavement layer specification was found challenging regarding the variability in constructed asphalt pavements. The uncertainty arises from field conditions in layer compaction and specific material used to place pavement layers. It was assumed that there was no distress on the flexible pavement under prevailing conditions. The pavement will likely experience increased strains induced by loading under higher groundwater table conditions, leading to a more significant reduction in service life than the baseline conditions. Therefore, future research can consider the current pavement condition and its potential for further deterioration when considering the impact of groundwater table on pavement service life. The enhancement can be done by integrating the information generated in this study with information in the Pavement Management System (PMS) since the transportation data used in this study will likely have a similar data structure in the PMS used by road stakeholders. A comprehensive statistical analysis based on multi-scenario simulation can be conducted in the future. The analysis can cover more uncertainty factors affecting sea-level rise such as future management rules for flood and salinity control structures, and other factors like future temperature, future traffic loading, and more pavement types and specifications.
Although there are limitations in this study, the framework can be implemented in other regions that are facing similar challenges due to SLR. These regions include but are not limited to neighboring counties in Southeast Florida, like Broward and West Palm Beach County. Furthermore, with data input customization like typical pavement parameters, the framework can be implemented anywhere for coastal cities likely to experience similar problems of rising groundwater table.

5. Conclusions

The three objectives of this study have been achieved. The SLR impact was quantified based on two SLR scenarios, low (IPCC AR5 RCP 8.5 median curve) and high (USACE high curve). The potential locations of the most affected road segments were identified. An integrated network-scale analytical framework was developed which was then used to predict pavement service life ratio under SLR conditions.
The Miami Beach region is the most affected region by rising groundwater measured in lane km for each road class. As much as 5% of Interstate, 34.7% Other Arterial, 46.4% Minor Arterial, 67.4% Major Collector, 75.9% Minor Collector, and 75.1% Local road base layers will be inundated in the 2060–2069 high SLR scenario. The second most affected region is the Northwest region, where in the high SLR scenario, 11.9% of Interstate, 1.95% of Freeways, 22.5% of Other Arterial, 6.7% of Minor Arterial, 32.1% of Major Collector, 40.2% of Minor Collector, and 17.8% of Local roads are predicted to be inundated.
The pavement response model used in the analytical framework was validated using field measurements from the LTPP-SMP dataset. ALVA performs better than the model in previous research. The differences found in deflection results between models were potentially attributed to variations in asphalt modulus and interlayer bonding parameters, with ALVA being calibrated through adjustment in these parameters.
The most severe reduction in performance was found located in the Miami Beach region, with a 60% reduction in cracking and 84% reduction in rutting performance, followed by a segment located in the North region (NW 82 ST) with a 58% reduction in cracking and 94% reduction in rutting, and one in the Northwest region (NW 107 ST) with 68% cracking and 78% in rutting performance, relative to the baseline condition.
The performance of asphalt pavement depends on the pavement’s vertical structure, thickness, elevation, depth to bedrock, and the vicinity of the groundwater pump facility. The topographical elevation is a more influential factor in predicting pavement performance than the distance to the coastline. From the analysis, it was found that there are no Principal Arterial Interstate road across all the planning regions that experience a high groundwater table. Elevated construction practices on the Interstate road system can mitigate flood risks. This confirms that the vulnerability of the road to the rise of groundwater associated with SLR is greatly influenced by the pavement’s vertical structure. Therefore, road classes with thin structure by design, like Collector and Local roads, are the most vulnerable class to SLR impact.
The analysis results from this study serve as a foundation for adaptation planning, offering comprehensive insights from the thinnest to the thickest pavement core samples across each road class. Moreover, integrating groundwater information significantly enhances the quality and completeness of the existing transportation vulnerability maps. The analytical framework developed in this study provides flexibility to the automation process as anticipation for changing the SLR prediction where more groundwater simulation results with different scenarios than in this study can be incorporated as input. Other environmental factors, such as projected temperature rise, and future traffic loading factors should be considered in the analytical framework. Other distress models also can be included to calculate for more pavement distresses like IRI (International Roughness Index), using AASHTO-MEPDG equations. Finally, the road segments identified should be closely monitored for transportation performance measures and future research, as the model requires field calibration.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/w15234163/s1. Table S1: Road length impacted by rising groundwater table classified by roadway functional classification and TPO region.

Author Contributions

Conceptualization, A.R., H.R.F., and H.A.; methodology, A.R. and C.M.C.; software, A.R.; validation, A.R.; formal analysis, A.R.; investigation, A.R.; resources, C.M.C.; data curation, A.R.; writing—original draft preparation, A.R.; writing—review and editing, A.R., H.R.F., and C.M.C.; visualization, A.R.; supervision, H.R.F., C.M.C., and H.A.; funding acquisition, A.R., H.R.F., C.M.C., and H.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Florida International University through the University Graduate School Dissertation Evidence Acquisition and Dissertation Year Fellowship Awards.

Data Availability Statement

The data presented in this study are available on reasonable request from the corresponding author.

Acknowledgments

The authors would like to express their gratitude for the support received while conducting this research. This study was made possible through funding from the Dissertation Evidence Acquisition fellowship and the Dissertation Fellowship Year granted by the University Graduate School at Florida International University. Furthermore, we would like to sincerely thank the Florida Department of Transportation, Miami-Dade County, Miami-Dade TPO, and FIU-Sea Level Solution Center for providing essential data and valuable literature.

Conflicts of Interest

Author H.A. was employed by the company Sustainable Road Engineering. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Schematic illustration of the methodology used to analyze the impact of SLR on flexible pavement.
Figure 1. Schematic illustration of the methodology used to analyze the impact of SLR on flexible pavement.
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Figure 2. Roadway assets in Miami-Dade County categorized with the FHWA-approved functional classification for the Highway Pavement Management System.
Figure 2. Roadway assets in Miami-Dade County categorized with the FHWA-approved functional classification for the Highway Pavement Management System.
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Figure 3. (a) DEM for Miami-Dade County area [38]. Topographical features in Miami consist of plain and higher elevations known as part of the Atlantic Coastal Ridge. (b) Groundwater head at high SLR scenario. (c) Projected DTW at high SLR scenario. (d) Interpolated bedrock limestone level.
Figure 3. (a) DEM for Miami-Dade County area [38]. Topographical features in Miami consist of plain and higher elevations known as part of the Atlantic Coastal Ridge. (b) Groundwater head at high SLR scenario. (c) Projected DTW at high SLR scenario. (d) Interpolated bedrock limestone level.
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Figure 4. Elastic layer pavement analysis with sublayering and variation in degree of saturation (DOS).
Figure 4. Elastic layer pavement analysis with sublayering and variation in degree of saturation (DOS).
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Figure 5. Roadway impacted by rising groundwater table: (a) low sea-level rise scenario; (b) high sea-level rise scenario with selected road segments for further analysis.
Figure 5. Roadway impacted by rising groundwater table: (a) low sea-level rise scenario; (b) high sea-level rise scenario with selected road segments for further analysis.
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Figure 6. Deflection comparison between FWD, ALVA, and past research [15].
Figure 6. Deflection comparison between FWD, ALVA, and past research [15].
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Figure 7. The pavement profile for each road class and planning region shows the groundwater level at baseline and the SLR scenario.
Figure 7. The pavement profile for each road class and planning region shows the groundwater level at baseline and the SLR scenario.
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Figure 8. Service life reduction in selected asphalt pavements for the selected segments.
Figure 8. Service life reduction in selected asphalt pavements for the selected segments.
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Figure 9. Service life reduction relative to the baseline condition in the selected asphalt pavements for the entire Miami-Dade area: (a) fatigue cracking; (b) rutting. Green line means TPO region boundary.
Figure 9. Service life reduction relative to the baseline condition in the selected asphalt pavements for the entire Miami-Dade area: (a) fatigue cracking; (b) rutting. Green line means TPO region boundary.
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Figure 10. Condition and performance comparison between road segments located at individual wells (WESTWARD DR) and 2 km away from the individual wells (W 32 ST.).
Figure 10. Condition and performance comparison between road segments located at individual wells (WESTWARD DR) and 2 km away from the individual wells (W 32 ST.).
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Table 2. Zone classification using base clearance to water table depth.
Table 2. Zone classification using base clearance to water table depth.
LevelRequirement
1Base Clearance > 91.44 cm
291.44 cm ≤ Base Clearance > 60.96 cm
360.96 cm ≤ Base Clearance > 30.48 cm
430.48 cm > Base Clearance
Table 3. Roadway length km per lane impacted in Miami-Dade County according to zone classification.
Table 3. Roadway length km per lane impacted in Miami-Dade County according to zone classification.
SLR ScenarioLevel 1Level 2Level 3Level 4
Low1877.3 (66%)580.55 (20%)275.31 (10%)114.49 (4%)
High1529.05 (54%)583.74 (20%)492.73 (17%)242.16 (9%)
Table 4. Soil parameters for the Minnesota case study at LTPP site 27-1018.
Table 4. Soil parameters for the Minnesota case study at LTPP site 27-1018.
SurfaceBaseSubgrade
TypeAsphalt ConcreteTypeUncrushed GravelTypeCoarse-Grained Soils: Poorly Graded Sand with Silt
Thickness (mm)112Thickness (mm)132AASHTOA-3
AASHTOA-1-bPercent passing #2006.2
Percent passing #2006.9D60 (mm)0.38
Plasticity Index PINPPlasticity Index PINP
D60 (mm)2.6Percent of coarse sand42
OMC (%)7Percent of fine sand34
In situ dry density (kg/m3)2030Percent of silt4.5
Specific gravity (Gs)2.713Percent of clay1.5
Void ratio (e)0.34Optimum moisture %8
Max lab dry density (kg/m3)2195In situ dry density (kg/m3)1828
Specific Gravity (Gs)2.65
Void ratio0.45
Max lab dry density (kg/m3)1970.3
Porosity0.31
Depth to bedrock2.5 m from the top of the subgrade layer
Table 5. Fatigue cracking and rutting performance relative to a DTW of 175 cm. n/a means not applicable or the data were not found from the modeling results. Color in the table shows different performance. Excellent, satisfactory, marginal, poor performance were represented by green, yellow, orange, and red, respectively.
Table 5. Fatigue cracking and rutting performance relative to a DTW of 175 cm. n/a means not applicable or the data were not found from the modeling results. Color in the table shows different performance. Excellent, satisfactory, marginal, poor performance were represented by green, yellow, orange, and red, respectively.
Road ClassFatigue CrackingRutting
DTW (cm)DTW (cm)
255075100125150175255075100125150175
11An/an/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a
11Bn/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a
12An/a n/a n/a n/a n/a 100%100%n/a n/a n/a n/a n/a 100%100%
12Bn/a n/a n/a n/a n/a 100%100%n/a n/a n/a n/a n/a 100%100%
14A50%51%87%100%100%100%100%18%18%62%100%100%100%100%
14B26%34%99%100%100%100%100%10%16%98%100%100%100%100%
16A47%47%93%100%100%100%100%16%17%87%100%100%100%100%
16B15%83%99%100%100%100%100%8%62%99%100%100%100%100%
17A55%56%57%63%83%98%100%15%16%16%23%56%92%100%
17B12%45%100%100%100%100%100%8%35%99%100%100%100%100%
18A38%39%42%69%92%100%100%11%11%13%42%82%99%100%
18B20%21%32%69%98%100%100%7%7%15%53%94%100%100%
19A25%25%37%71%97%100%100%8%8%16%53%93%100%100%
19B14%14%28%67%99%100%100%6%6%15%55%96%100%100%
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Rojali, A.; Fuentes, H.R.; Chang, C.M.; Ali, H. Network-Scale Analysis of Sea-Level Rise Impact on Flexible Pavements. Water 2023, 15, 4163. https://doi.org/10.3390/w15234163

AMA Style

Rojali A, Fuentes HR, Chang CM, Ali H. Network-Scale Analysis of Sea-Level Rise Impact on Flexible Pavements. Water. 2023; 15(23):4163. https://doi.org/10.3390/w15234163

Chicago/Turabian Style

Rojali, Aditia, Hector R. Fuentes, Carlos M. Chang, and Hesham Ali. 2023. "Network-Scale Analysis of Sea-Level Rise Impact on Flexible Pavements" Water 15, no. 23: 4163. https://doi.org/10.3390/w15234163

APA Style

Rojali, A., Fuentes, H. R., Chang, C. M., & Ali, H. (2023). Network-Scale Analysis of Sea-Level Rise Impact on Flexible Pavements. Water, 15(23), 4163. https://doi.org/10.3390/w15234163

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