1 Introduction

Excessive moisture within pavement layers is a predominant cause of road failures. Within Australia's road network, unbound pavements with sprayed seals constitute most surfaced roads [2]. These pavements' base and subbase layers are typically constructed using unbound granular materials (UGMs) [5, 22, 23, 27]. These layers are compacted on top of a compacted subgrade and are the primary structural layers sustaining traffic loads. The shear strength of UGM layers is significantly influenced by their moisture content [1, 2, 6, 11, 12, 19, 22, 23, 32, 37, 42], thereby significantly affecting the structural capacity of the entire pavement structure. After compaction, the sprayed seals are applied to the UGM layers to prevent moisture ingress into the underlying structural layers [4, 15, 16]. These seals consist of an aggregate layer over a bitumen layer, and the number of layers depends on the construction technique. Single-single seals, comprising one layer of bitumen and one layer of aggregates, are the most common sprayed seals used in Australia [2, 4].

While a seal intends to stop moisture ingress, achieving complete impermeability in the construction and maintenance of sprayed seals is unfeasible [16, 25, 30]. Prior studies have shown that the saturated permeability of sprayed seals can range from 10–5 to 10–10 m/s and depends on factors such as age, the severity of cracking, and resealing conditions, among others [8, 9, 21, 25, 30, 40]. As a result, moisture can migrate between the ambient environment and pavement layers through these somewhat permeable seals.

After pavement construction, the moisture content in each layer changes over time due to prevailing climatic conditions, as moisture can move between the pavement layers and the ambient environment [1, 17, 18, 31, 33]. The moisture state of each layer reaches an equilibrium state after several months of construction, achieved through initial drying or wetting [1, 18, 24, 25]. However, even after getting this equilibrium condition, the moisture state can fluctuate around the equilibrium moisture content due to seasonal wetting and drying cycles determined by the ambient climate. Given that the ambient climate affects both the equilibrium moisture state and temporal moisture fluctuations of pavement layers, the structural performance of pavements is directly impacted by climate conditions [7, 10, 26, 43]. Therefore, incorporating climate considerations into pavement design is essential for resilient pavement performance.

The current Australian pavement design [2] discusses environmental factors in Chapter 4, which has recommended considering the moisture state of pavement layers during their service life. Specifically, it recognises the importance of climatic factors in determining the service moisture condition. The "service moisture condition" in the guide is called the equilibrium moisture condition, and it recommends that pavement layers' structural strength and stiffness properties be experimentally determined at this moisture condition. Recommendations are provided for determining the service moisture condition at which the subgrade's California Bearing Ratio (CBR) should be evaluated based on annual rainfall and drainage parameters [2]. Despite recognising the potential impact of climatic factors on moisture variations in unbound granular material (UGM) layers, the existing design provides limited guidance on UGMs. For instance, while blanketly acknowledging that UGM can experience significant performance losses when its degree of saturation \(({S}_{r})\) exceeds 70%, the design fails to offer detailed guidance for determining the service moisture conditions and temporal moisture fluctuations of UGM layers. Incorporating daily, seasonal, or annual variations of climate that result in temporal moisture fluctuations in pavement layers has not yet been addressed in the current design process.

The main objective of this study is to evaluate the impact of climate on the moisture variations in pavement layers of unbound pavements with sprayed seals in different Australian climatic conditions. The study simulates moisture variations of six different pavement configurations under seven typical Australian climates using a computer model previously developed and validated by the authors of the current study [24, 25]. The model developed incorporates the daily variations of rainfall, evaporation, relative humidity, and atmospheric temperature in the prediction of moisture variations of pavement layers in terms of \({S}_{{\text{r}}}\) and suction (\(s)\) by capturing the essential physics of the moisture flow through the pavement layer. The equilibrium moisture condition and the temporal fluctuations in pavement layers, such as UGM and subgrade layers, were analysed under different climates. A simplified model was developed to predict the service moisture condition, also known as the equilibrium moisture condition, based on the results of 126 simulations. Moreover, the effects of climate on subsequent pavement performance resulting from temporal moisture variations are analysed, and simplified approaches that can be useful for improved design are highlighted.

2 Methodology

Maha Madakalapuge et al. [24] developed a computer model to predict moisture variations in unbound pavements with thin seals. The intention was to advance the current Australian pavement design process. The model was validated using field data [24] and targeted laboratory experiments [25]. This developed model is capable of predicting the variations of moisture conditions at different depths of pavement layers in terms of the degree of saturation \({(S}_{{\text{r}}})\) and suction (\(s)\), occurring throughout the service life of the pavement, accounting for daily variations of precipitation, pan evaporation, relative humidity, atmospheric temperature, and water table depth. In this study, the model is used to simulate the moisture variations in unbound pavements with sprayed seals under seven different Australian climates to evaluate the effect of the ambient climate on moisture variation in pavements.

Figure 1 illustrates six distinct pavement configurations defined, using typical pavement materials reported in earlier studies [9, 24, 25] to evaluate their hydraulic characteristics, such as permeability and water retention properties. Two common crushed rock unbound materials and three single-single sprayed seals, commonly used in pavement construction in Australia, were considered [2, 4, 5].

Fig. 1
figure 1

Pavement configurations considered in the study (UGM = Unbound Granular Material, CS = Compacted Subgrade and US = Uncompacted Subgrade)

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The authors experimentally assessed the saturation permeability and water retention curve of two single-sprayed seal samples from an actual pavement in New South Wales, Australia (Seals 1 and Seal 2) in their earlier research [25]. The saturated permeabilities of these seals were found to be in the range of 10–6 to 10–7 m/s. The hydraulic properties of another single-single sprayed seal sample (Seal 3) retrieved from an actual pavement in New South Wales, Australia, were reported by Lee [21]. These three samples' saturated permeability ranged from 10–6 to 10–9 m/s, representing typical sprayed seal conditions in operation. Therefore, these seals represented three different sprayed seal conditions in this study.

This study employed two distinct crushed rock materials, UGM A and UGM B, of which hydraulic properties were previously characterised. UGM A, a 20 mm crushed basalt road base material, was obtained from a commercial quarry (Holcim’s Sheraton Road pit near Dubbo) in New South Wales. As reported in the author’s PhD study, Carteret [9] experimentally determined its hydraulic properties and constructed a test pavement from this material. UGM B is a 20 mm Class 2 crushed rock obtained from the Boral Wollert Quarry in Victoria, Australia, and was used in soil columns replicating the pavement cross section in earlier studies by the authors of the current study [25]. The present study considered these two materials as unbound granular materials commonly employed in real pavement construction projects. UGM A was compacted at the maximum dry density obtained from a standard Proctor compaction test. In contrast, UGM B was compacted at the modified Proctor compacted maximum dry density, resulting in respective dry densities of 2100 kg/m3 [9] and 2350 kg/m3 [25]. The consideration of these two compaction conditions arises from differing recommendations by road agencies. Some recommend the use of modified conditions, while others advocate for standard Proctor compaction conditions. The UGM layers had a thickness of 300 mm, which is also considered typical in unbound pavements.

The subgrade of all the pavements simulated in this study consisted of a typical sandy clay material that was characterised by Carteret [9]. The in situ material was compacted at the top layer before placing the structural layer to increase density and provide sufficient support for the layers above. Therefore, the top 200 mm of the subgrade was designated as compacted subgrade (CS) due to its relatively high dry density and lower saturated permeability than the in situ material. The remaining portion of the subgrade was referred to as uncompacted subgrade (US), which represents the in situ material.

It is required to define the Soil Water Retention Curve (i.e. the relationship between \(\theta\) and\(h\)) and the unsaturated permeability function (i.e. the relationship between \(K\) and \(h\)) of all the pavement materials in the numerical modelling. The van Genuchten–Mualem model [13] was employed to define those two functions for all the pavement layers. The van Genuchten model is illustrated below (Eq. 1).

$$\theta \left( h \right) = \left\{ {\begin{array}{*{20}c} {\theta_{r} + \frac{{\theta_{s} - \theta_{r} }}{{\left( {1 + \left| {\alpha h} \right|^{n} } \right)^{m} }} ; h < 0 } \\ {\theta_{s} ; h \ge 0} \\ \end{array} } \right.$$
(1a)

where

$$m = 1 - \frac{1}{n} ;\quad n > 1$$
(1b)

The other fundamental property required is the isothermal permeability function of the liquid phase (\(K(h)\)). \(K(h)\) is also defined by van Genuchten [13], utilising the same set of parameters, as shown in Eq. 2:

$$K\left( h \right) = K_{s} S_{e}^{l} \left[ {1 - \left( {1 - S_{e}^{\frac{1}{m}} } \right)^{m} } \right]^{2}$$
(2a)
$$S_{e} = \frac{{ \theta - \theta_{r} }}{{ \theta_{s} - \theta_{r} }}$$
(2b)

In the above equations, \({\theta }_{r}\) and \({\theta }_{s}\) denote the residual water content and the saturated water content, respectively; \({K}_{s}\) is the saturated hydraulic conductivity; \(\alpha\) is the inverse of the air-entry value (or bubbling pressure);  \(n\) is a pore-size distribution index; and \(l\) is a pore-connectivity parameter, which was assigned a value of 0.5 as an average of many soil types [28]. Table 1 summarises the van Genuchten–Mualem model [17] parameters to define the permeability function and Soil Water Retention Curve (SWRC) for all pavement materials.

Table 1 van Genuchten's [13] model parameters of SWRC and permeability function
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2.1 Numerical modelling

The total water flux through unsaturated media is formulated as the summation of isothermal liquid flow, isothermal vapour flow, thermal liquid flow, and thermal vapour flow, as depicted in Eq. 3 [14].

$$\frac{\partial \theta \left( h \right)}{{\partial t}} = \frac{\partial }{\partial x}\left( {\left( {K\left( h \right) + K_{vh} } \right)\left( {\frac{\partial h}{{\partial x}}} \right) + \left( {K_{LT} + K_{vT} } \right)\frac{\partial T}{{\partial x}}} \right)$$
(3)

where \(\theta\) is the total volumetric water content, which is the sum of the volumetric liquid water content and the volumetric water vapour content, which is also expressed in terms of equivalent water content [L3L−3]; \(h\) is the water pressure head [L]; \(t\) is the time [T] ([T] signifies the dimension of time); \(x\) is the spatial coordinate (positive upward and dimension [L]); \(T\) is the temperature [K]. \(K(h)\) [LT−1] and \({K}_{LT}\) [L2K−1 T−1] are the isothermal hydraulic conductivity and thermal–hydraulic conductivity functions, respectively, for the liquid phase fluxes due to gradient in \(h\) and \(T\); \({K}_{vh}\) [LT−1] and \({K}_{vT}\) [L2K−1 T−1] are isothermal and thermal conductivities of the vapour flow hydraulic conductivity, respectively, for the vapour phase [34]. \({K}_{vh}\) and \({K}_{vT}\) are functions of temperature and relative humidity, and detailed equations are provided by Simunek et al. [34].

Maha Madakalapuge et al. [24] demonstrated that the influence of non-isothermal liquid and vapour flow is minimal under typical Australian climatic conditions, which do not involve extreme hot or freezing temperatures. Consequently, they proposed a simplified isothermal model as given by Eq. 4.

$$\frac{{\partial \theta_{T} \left( h \right)}}{\partial t} = \frac{\partial }{\partial x}\left( {\left( {K\left( h \right) + K_{vh} } \right)\left( {\frac{\partial h}{{\partial x}}} \right)} \right)$$
(4)

The simplified model proposed by Maha Madakalapuge et al. [24] effectively reduces computational costs in terms of both time and complexity without compromising accuracy appreciably. The data analysis shows that the average annual temperature of all the selected climates is around 20 °C, and there is no evidence of any extremely hot or freezing weather. Therefore, the present study utilises this simplified model to simulate temporal moisture variations within the pavement layers of unbound granular materials (UGM), the compacted subgrade (CS), and the uncompacted subgrade (US) of selected pavements (as depicted in Fig. 1) under seven distinct climatic conditions.

2.2 Selection of climates

Australia is well known for its diverse range of climatic conditions, which vary significantly across the country. Depending on the intended application, numerous classification systems have been introduced to classify the Australian climate. One such classification system that has gained widespread acceptance in engineering is the climate zones established in the National Construction Code (NCC). Thornthwaite Moisture Index (\({\text{TMI}}\)) can also be identified as a widely used parameter used to classify soil climate in agriculture concerning pavements and other infrastructure applications [3, 20, 41]. In 1948, Thornthwaite [39] proposed TMI to classify the climate reflecting the aridity or humidity of the soil and climate. \({\text{TMI}}\) is calculated, accounting for the collective effect of precipitation, evapotranspiration, soil water storage, moisture deficit and runoff [3, 36, 38, 39].

For this study, seven distinct climates were selected based on the NCC classification system, as they represent a broad range of climatic zones ranging from dry to wet. The selection of these seven climates ensured that the study was representative of the diverse climatic conditions observed across Australia, thus enhancing the generalizability and applicability of the study findings. Figure 2 shows the selected climates marked on Google Maps.

Fig. 2
figure 2

Selected climates for the study as marked on Google Maps

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A summary of annual climatic factors and the NCC classification of all selected climates are shown in Table 2.

Table 2 A summary of the climates selected
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Moisture exchange between the pavement surface and the ambient atmosphere primarily occurs in the central region of the pavement, where lateral flow is restricted. The actual surface flux during the service life is dependent on the ambient environmental conditions and the seal conditions. This was modelled numerically by taking the absolute value of the surface flux (\(E\)) defined as a function of the seal permeability (\(K^{\prime}\)), as indicated in Eq. 5 [24].

$$E = \left| { - K^{\prime}\frac{\partial h}{{\partial x}} - K^{\prime}} \right|$$
(5)

The ambient climatic conditions determine the minimum and maximum inflow and outflow allowed in a given climate. The following boundary conditions are introduced to the hydraulic head \(h\) and \(E\) as described in Eq. 6 [29].

$$E = \left| { - K\frac{\partial h}{{\partial x}} - K} \right| \le E_{0} \, {\text{at}} \, x = L$$
(6a)

and

\(h_{A} \le h \le h_{s}\) (6b)

where \({E}_{0}\) is the potential surface flux across the surface that is solely governed by the ambient environment. The potential upward surface flux (i.e. maximum outflow) is similar to the potential (pan) evaporation under a given climatic condition. The maximum downward surface flux is equal to the precipitation.

The pressure head at the surface, \(h\), is also constrained by the prescribed maximum and minimum pressure heads (\({h}_{s}\) and \({h}_{A}\) respectively) allowed under the prevailing surface conditions. The minimum pressure head (\({h}_{A}\)) value is determined by the equilibrium condition between the atmospheric water vapour and the surface water, which can be calculated from the relative humidity \({(H}_{r})\) as shown in Eq. 7 [34].

$$h_{A} = \frac{{{\text{RT}}}}{{{\text{Mg}}}}{\text{ln}}\left( {H_{r} } \right)$$
(7)

where \(M\) is the molecular weight of water (= 0.018045 kg/mol); \(g\) is gravitational acceleration (= 9.81 m/s2); \(R\) is the gas constant (= 8.314 J/mol/ K); and \(T\) is the temperature in Kelvin. However, the absolute value of \({h}_{A}\) should not be less than the suction corresponding to the surface material's residual soil water content (\({\theta }_{r}\)). The maximum pressure head (\({h}_{s}\)) allowed at the surface is defined by the pressure head generated by any water ponding on the surface. Zero water ponding was assumed on top of the surface, considering that cross fall of pavements allows excess water to remove from the surface immediately.

Hence, the precipitation, pan evaporation, relative humidity and atmospheric temperature are required to define the top boundary condition in simulations of daily moisture variations of pavement layers. The daily climatic data for all the selected locations collected from the Bureau of Meteorology (BOM) weather stations for 10 years from 2000 to 2010 are shown in Figs. 3, 4, 5, 6, 7, 8 and 9.

Fig. 3
figure 3

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Melbourne climate (C1)

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Fig. 4
figure 4

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Adelaide climate (C2)

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Fig. 5
figure 5

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Perth climate (C3)

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Fig. 6
figure 6

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Sydney climate (C4)

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Fig. 7
figure 7

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Hobart climate (C5)

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Fig. 8
figure 8

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Brisbane climate (C6)

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Fig. 9
figure 9

Daily variations of a precipitation and pan evaporation, b average atmospheric temperature and relative humidity in Cairns climate (C7)

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The bottom boundary of the pavement model, which is the bottom of the uncompacted subgrade, is defined by the water table depth in the simulations. Three different depths were selected, 1500, 3000, and 6000 mm from the pavement surface, to capture the impact of varying water table depths. It is necessary to consider the density of each pavement layer in calculating \({S}_{r}\). Thus, in this study, the initial densities of each layer were assumed to be constant. For further details on the numerical modelling methodology, theoretical background, and definition of boundary conditions, readers can refer to the study by Maha Madakalapuge et al. [24].

3 Results and discussion

This section presents the findings derived from 126 simulations performed in the study. The section comprises three parts, the first of which delves into the analysis of moisture variations in both the UGM and subgrade layers under different climatic conditions, with an emphasis on the degree of saturation \(({S}_{r})\) as a metric for assessing the moisture fluctuations in pavement layers. Particular emphasis was placed on selecting the \({S}_{r}\) as the key indicator of moisture condition, as it is widely recognised as the primary factor contributing to rutting in pavements [11, 35]. The second subsection is dedicated to developing an empirical model for predicting the service moisture condition of the UGM layer. The model takes into consideration both the degree of saturation \({S}_{r}\) and \(s\) of the UGM layer and utilises annual climatic data such as annual rainfall and annual pan evaporation as key predictors. The third subsection comprehensively analyses the pavement performances under varying moisture conditions induced by ambient climatic changes. A novel approach is proposed to integrate climatic factors into the current Australian pavement design of unbound pavements with thin seals.

3.1 Effect of climate on moisture condition of pavement layers

The evaluation of the climatic effect on \({S}_{r}\) variations of pavement layers focuses on both the equilibrium condition and the temporal moisture variations that occur after reaching the equilibrium state. In line with the approach taken by Maha Madakalapuge et al. [24], the equilibrium \({S}_{r}\) \(\left({S}_{r eq}\right)\) is calculated by averaging the \({S}_{r}\) values that occur during the service life, excluding the initial time required to reach the equilibrium (\({t}_{ {\text{eq}}})\). The determination of \({S}_{r {\text{eq}}}\) is carried out similarly in the present study. For instance, Fig. 10 presents the values of \({S}_{r {\text{eq}}}\) and \({t}_{ {\text{eq}}}\) of the UGM layer of a typical pavement.

Fig. 10
figure 10

Graphical representation of the equilibrium \({S}_{r}\) \(\left({S}_{\mathrm{r eq}}\right)\) and the time to reach an equilibrium \({{\text{S}}}_{{\text{r}}}\) \(\left({t}_{\mathrm{ eq}}\right)\) of the UGM layer

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The temporal \({S}_{r}\) variations that occur after reaching the equilibrium conditions, such as seasonal drying and wetting, are referred to as temporal \({S}_{r}\) variations in this study. The \({S}_{r}\) variations in pavement layers, including the UGM layer, the compacted subgrade (CS), and the uncompacted subgrade (US) of six selected pavement configurations, are presented in Figs. 11, 12, 13, 14, 15 and 16 under seven climates when the water table depth is at 3000 mm. This section discusses the behaviours of \({S}_{r}\) variations in UGM layers and subgrades.

Fig. 11
figure 11

\({S}_{r}\) variations of pavement layers of P1 (S1_UGM A) a Melbourne (C1), b Adelaide (C2), c Perth (C3), d Sydney (C4), e Hobart (C5), f Brisbane (C6), g Cairns (C7) (WT depth 3000 mm)

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Fig. 12
figure 12

\({S}_{r}\) variations of pavement layers of P2 (S1_UGM B) a Melbourne (C1), b Adelaide (C2), c Perth (C3), d Sydney (C4), e Hobart (C5), f Brisbane (C6), g Cairns (C7) (WT depth 3000 mm)

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Fig. 13
figure 13

\({S}_{r}\) variation of pavement layers of P3 (S2_UGM A) a Melbourne (C1), b Adelaide (C2), c Perth (C3), d Sydney (C4), e Hobart (C5), f Brisbane (C6), g Cairns (C7) (WT depth 3000 mm)

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Fig. 14
figure 14

\({S}_{r}\) variations of pavement layers of P4 (S2_UGM B) a Melbourne (C1), b Adelaide (C2), c Perth (C3), d Sydney (C4), e Hobart (C5), f Brisbane (C6), g Cairns (C7) (WT depth 3000 mm)

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Fig. 15
figure 15

\({{\text{S}}}_{{\text{r}}}\) variation of pavement layers of P5 (S3_UGM A) a Melbourne (C1), b Adelaide (C2), c Perth (C3), d Sydney (C4), e Hobart (C5), f Brisbane (C6), g Cairns (C7) (WT depth 3000 mm)

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Fig. 16
figure 16

\({{\text{S}}}_{{\text{r}}}\) variations of pavement layers of P6 (S3_UGM B) a Melbourne (C1), b Adelaide (C2), c Perth (C3), d Sydney (C4), e Hobart (C5), f Brisbane (C6), g Cairns (C7) (WT depth 3000 mm)

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The authors noted that the degree of saturation variations (\({S}_{r}\)) of the unbound granular material (UGM) layer in all pavement configurations remained unchanged with variations in the water table depth for a given climate for simulated subgrade conditions. This observation supports the conclusion drawn by Maha Madakalapuge et al. [24], which states that the water table depth does not influence moisture variations in UGM layers for the pavements considered. Consequently, the current study did not consider the water table effect when assessing the UGM layers' moisture conditions. However, prior studies [24, 31, 33] have indicated that the water table influences the moisture condition of subgrades when it is located within the first 6 m from the surface. Hence, the water table effect was considered in the evaluation of \({S}_{r}\) of subgrade layers.

As depicted in Figs. 11, 12, 13, 14, 15 and 16, the \({S}_{r}\) variations of the UGM layer of a given pavement depict seven distinct patterns across the seven different climates considered, indicating a significant influence of ambient climate on the moisture condition of UGM layers over their service life. This climatic effect is more pronounced in pavements featuring relatively high permeable seals, namely P1 (S1_UGMA), P2 (S1_UGMB), P3 (S2_UGMA), and P4 (S2_UGMB), compared to those with relatively low permeable seals of P5 (S3_UGMA) and P6 (S3_UGMB). Additionally, the \({S}_{r}\) variations of the compacted subgrade (CS) in pavements with high permeable seals are also influenced by the ambient climates.

Figures 11, 12, 13, 14, 15 and 16 provide evidence of the impact of ambient climatic conditions on both \({S}_{r eq}\) and the temporal fluctuations of \({S}_{r}\). For instance, let us compare the \({S}_{r}\) variations of UGM layer in the same pavement, namely P1 (S1_UGMA), under different climates, such as those encountered in Adelaide and Cairns, as illustrated in Fig. 17.

Fig. 17
figure 17

Comparison of \({S}_{r}\) variations of the middle UGM layer of P1 (S1_UGMA) under Cairns and Adelaide climate

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In Table 2 and Fig. 4, the climatic data collected reveal that Adelaide experiences the lowest annual precipitation rate, averaging 402 mm/year, while Cairns has the highest annual average rainfall of 1955 mm/year. The rainfall intensity during events is considerably higher in Cairns' climate, with a maximum intensity of approximately 270 mm/day, as depicted in Fig. 8. In contrast, Adelaide's daily average precipitation intensities are significantly lower, with a maximum intensity of only 40 mm/day (refer to Fig. 4). During the summer period, Adelaide experiences relatively high temperatures, with the daily average soaring close to 35 °C. In contrast, in Cairns, it remains close to 30 °C. However, Adelaide experiences significantly lower temperatures during winter, dropping close to 5 °C, while Cairns' temperature only reduces to 15 °C. Adelaide receives rainfall for 109 days on average, whereas Cairns experiences it for 156 days. Accounting for these climatic factors, Adelaide can be characterised as having a relatively arid climate compared to Cairns.

As depicted in Fig. 17, the \({S}_{r {\text{eq}}}\) of the UGM layer under the Cairns climate (i.e. 0.69) is relatively higher than that of the Adelaide climate (i.e. 0.6). Moreover, the number of wetting events in Cairns is substantially greater than that in Adelaide. The wetting fluctuations also exhibit higher intensities in the Cairns climate compared to the Adelaide climate. For instance, the \({S}_{r}\) reaches the fully saturated condition (i.e. \({S}_{r}\) = 1) in 349 days in Cairns, whereas it only attains full saturation condition in 44 days in Adelaide climate.

Furthermore, the UGM layer in Adelaide tends to dry out more compared to that of Cairns, as evidenced by the lower average value of the minimum \({S}_{r}\) occurrences. As a result of having a higher number of intense wetting fluctuations, the \({S}_{r {\text{eq}}}\) in Cairns becomes higher. Conversely, the significant drying events that occur in Adelaide's climate result in less \({S}_{r {\text{eq}}}\) of the UGM layer. The current observation indicates that UGM layers dry out more readily in arid climates.

However, it is not as simple as stating that pavement moisture remains drier in arid climates and wetter in humid climates while experiencing intense wetting cycles in humid climates and drying cycles in arid climates. For example, let us compare the \({S}_{r}\) variations of the UGM layer of the same pavement P1 (S1_UGMA) in Adelaide and Perth as shown in Fig. 18.

Fig. 18
figure 18

Comparison of \({S}_{r}\) variations of the middle UGM layer of P1 (S1_UGMA) in Adelaide and Perth climates

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Perth and Adelaide are classified as warm climates according to the NCC classification. The average number of days of precipitation in both climates is almost similar and less compared to other climates considered. However, the average rainfall intensities are slightly higher in Perth. The annual potential pan evaporation, relative humidity and temperature in both climates are similar. As previously observed, arid climates tend to cause UGM to dry out quickly, resulting in a minimum \({S}_{r}\) (\({S}_{r {\text{min}}}\)) that is almost identical in both climates. However, despite these similarities, it is important to note that pavements in Perth experience a greater number of wetting events compared to Adelaide’s pavements and the maximum \({S}_{r}\) occurred following a wetting event is higher under Perth climatic conditions. Moreover, the number of days that exceed optimum degree of saturation (\({S}_{r {\text{opt}}}\)) is prominently higher in Perth. Hence, it would be inaccurate to conclude that dry climates experience less frequent or less intense wetting fluctuations than other climates. This finding emphasises that even in a climate classified as warm, there is the possibility of experiencing intense wetting fluctuations in the pavement's UGM layer.

Furthermore, it is observed that annual rainfall alone does not accurately indicate the moisture condition or wetting fluctuations of the UGM layer. To illustrate this point, let us compare the \({S}_{r}\) variations of UGM layers in Melbourne and Brisbane. In Table 2, despite the annual average rainfall of Brisbane (1081 mm/year) being almost twice Melbourne’s (525 mm/year), variations of the UGM layer are similar in both climates across all pavements. Figure 19 presents a comparison of \({S}_{r}\) variations of UGM layer of P1 (S1_UGMA) in Melbourne and Brisbane climates. Although the daily precipitation values in Brisbane exhibit significantly higher intensities than those in Melbourne, the number of wetting and drying events and the maximum and minimum intensities of temporal fluctuations are relatively similar in both climates.

Fig. 19
figure 19

Comparison of \({S}_{r}\) variations of the middle UGM layer of P1 (S1_UGMA) in Melbourne and Brisbane climates

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These observations suggest that other factors, such as the intensity and frequency of precipitation events and evaporation rates, must be considered in addition to annual rainfall to accurately characterise moisture conditions and predict potential wetting fluctuations in UGM layers. Hence, to make more accurate predictions, it is necessary to consider daily climatic factors such as rainfall, evaporation, temperature, and relative humidity. Incorporating these factors into predictive models will provide a complete understanding of moisture conditions in UGM layers during service life.

3.2 Development of an empirical model to predict service moisture condition of UGM

This study proposes a practical and simplified model for determining the service moisture condition of UGM layers, which represents the equilibrium condition. The model is developed based on the simulations performed under all seven climates, considering daily climatic factors as mentioned before. The Australian design guide, Austroads [2], does not provide any guidance on how to obtain the service moisture condition of the UGM layer by incorporating climatic factors. Therefore, the primary aim is to address this knowledge gap by developing a simplified model for practical use.

A regression analysis was conducted to establish a correlation between annual climatic data and the equilibrium moisture condition of UGM layers. The analysis found no correlation between equilibrium suction or \({S}_{r}\) and individual values of annual precipitation (\(P\)) or pan evaporation (\(PE\)). However, an improved correlation was observed between the equilibrium moisture condition in terms of both \({S}_{r}\) and \(s\), and the \(\frac{P}{PE}\) ratio. Figures 20 and 21 show the relationships between equilibrium \({S}_{r}\) and \(s\) with \(\frac{P}{PE}$$\) ratio of the UGM layers in all six pavements.

Fig. 20
figure 20

Equilibrium \({S}_{r}\) of UGM layer vs \(\frac{P}{PE}\)

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Fig. 21
figure 21

Equilibrium suction (kPa) of UGM layer vs \(\frac{P}{{\text{PE}}}\)

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Figures 20 and 21 demonstrate that in regions with relatively higher \(\frac{P}{PE}\) ratios, the average service moisture condition (i.e. equilibrium condition) tends to remain relatively wet, whereas in areas with lower \(\frac{P}{PE}\) ratios, the average service moisture condition tends to be relatively dry. This observation indicates that the ratio of annual precipitation (\(P\)) to potential evaporation (\({\text{PE}}\)) has a significant impact on the moisture condition of the service environment.

Even though the annual precipitation in Brisbane is twice that of Melbourne, the \(\frac{P}{PE}\) ratio in both climates is similar since the potential annual evaporation in Brisbane is also twice that of Melbourne. Consequently, the service moisture condition in both climates remains almost similar, despite the difference in annual precipitation. Thus, the ratio of \(\frac{P}{PE}\) can be considered a more accurate indicator of the service moisture condition of UGM layers than the individual value of \(P\).

Referring to Fig. 21, an empirical model is proposed to capture the relationship between the equilibrium suction (\({s}_{eq \space in \space UGM}\)) and the \(\frac{P}{PE}\) ratio for all pavement configurations considered, shown in Eq. 8. The R2 value, which measures the model's goodness of fit, was greater than 0.65 for all pavement configurations.

$$s_{{\text{eq in UGM}}} = a \times (\frac{P}{{PE}})^{b}$$
(8)

where \(a\) and \(b\) are regression coefficients, as shown in Table 3.

Table 3 Values of \(a\) and \(b\) in Eq. 8
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Equation 8 was generalised by introducing the saturated permeability of the seal (\({K}_{s}\)) as an additional factor, leading to an improved correlation with an R2 value of 0.92 between factor \(a\) and \({K}_{s}\). This enhanced correlation underscores the importance of \({K}_{s}\) in determining the equilibrium suction of UGM layers and highlights the need to consider this factor in the design and management of pavement systems. The updated equation is presented in Eq. 9.

$$S_{{\text{eq in UGM}}} \left( {{\text{kPa}}} \right) = a_{1} \times \left( {\frac{{K_{s} }}{{K_{s0} }}} \right)^{{a_{2} }} \times \left( {\frac{P}{{PE}}} \right)^{{b_{1} }}$$
(9)

where \({a}_{1}=2848.02\) kPa, \({a}_{2}=0.31\) and \({K}_{s0}\) = 1 m/s. The values for \({b}_{1}\) are shown in Table 4 based on the saturated seal permeability and the UGM compacted density.

Table 4 Values for \({b}_{1}\) in Eq. 9
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The generalised model (i.e. Eq. 9) exhibits an R2 value of 0.89, indicating a strong correlation between the predicted and numerically determined values. The accuracy of the model is further validated in Fig. 22, which presents a comparison between the predicted and actual values.

Fig. 22
figure 22

Predicted (using Eq. 9) vs equilibrium suction from the numerical model (kPa) of UGM layer

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The equilibrium \({S}_{r}\) of the UGM can be written as follows (Eq. 10), considering the relationship between the suction and \({S}_{r}\), derived from the van Genuchten equation [13].

$$S_{{\text{r eq in UGM}}} = S_{{r {\text{res}}}} + \frac{{1 - S_{{r {\text{res}}}} }}{{\left( {1 + \left| {\alpha ( a_{1} \left( {\frac{{K_{s} }}{{K_{s0} }}} \right)^{{a_{2} }} \times \left( {\frac{P}{{PE}})^{{b_{1} }} } \right)} \right|^{n} } \right)^{m} }}$$
(10a)
$$S_{{r {\text{res}}}} = \frac{{\theta_{r} }}{{\theta_{s} }}$$
(10b)

where \(\alpha \space in \space \frac{1}{kPa}\), \(n\), \(m\) are van Genuchten [13] parameters of the UGM material.

When only annual climatic data are available, and daily climatic data are not readily obtainable, the proposed regression model can be a valuable alternative for estimating service moisture conditions.

The \({\text{TMI}}\) is a widely used parameter to classify the climate. Mather [38] presented a simplified equation for the calculation of \({\text{TMI}}\) as shown in Eq. 11.

$${\text{TMI}} = 100 \times \left( {\frac{P}{{PE}} - 1} \right)$$
(11)

Hence, Eqs. 9 and 10 can be simplified by considering the relationship between \(\frac{P}{PE}\) ratio and the \({\text{TMI}}\) to determine the service moisture conditions as a function of \(TMI\) as shown below in Eq. 12.

$$S_{{\rm{eq\; in\; UGM}}} = a_{1} \times K_{s}^{{a_{2} }} \times \left( {\frac{{{\text{TMI}}}}{100} + 1} \right)^{{b_{1} }}$$
(12a)
$$S_{{\rm{r\; eq\; in \;UGM}}} = S_{{r {\text{res}}}} + \frac{{1 - S_{{r {\text{res}}}} }}{{\left( {1 + \left| {\alpha \left( {a_{1} \left( {\frac{{K_{s} }}{{K_{s0} }}} \right)^{{a_{2} }} \times \left( {\frac{{{\text{TMI}}}}{100} + 1} \right)^{b_1} } \right)} \right|^{n} } \right)^{m} }}$$
(12b)

The proposed empirical models serve as a valuable tool for determining service moisture conditions where advanced modelling of temporal variations is impractical. This regression model is based on simulation results incorporating daily variations in climatic factors, such as rainfall, pan evaporation, relative humidity, and atmospheric temperature. By considering these factors, the model can estimate the average service moisture condition throughout the service life while also accounting for temporal moisture variation to some extent.

However, the authors recommend utilising the complete simulation of temporal moisture variations, incorporating daily climatic factor variations, in pavement performance evaluations. This approach captures all fluctuations in moisture conditions that significantly impact long-term pavement performance. In this way, the complete simulation provides a more comprehensive and accurate representation of pavement behaviour over time. The following section discusses the long-term pavement performance analysis performed utilising the simulations of moisture variations under different climates.

3.3 Pavement performance analysis

As previously discussed, the results indicate that the moisture condition of the UGM layers features distinct behaviour in varying climates, even when all other pavement properties, including water table depth, are the same. This finding underscores the importance of tailoring pavement design and construction to the specific climatic conditions of a given location to achieve optimal pavement performance. Despite this, Australia's current pavement design practices have not yet developed to account for such climate-specific factors. This study proposes a practical approach to account for the ambient climatic factors, as discussed below.

When the UGM layer reaches a state of full saturation, the pavement becomes vulnerable to performance losses, as the shear strength of the UGM layer, which serves as the primary structural layer, is significantly reduced. Frequent occurrences of this condition increase the likelihood of pavement failures due to excessive moisture. To assess the potential for such failures, the number of days during which the degree of saturation (\({S}_{r}\)) reaches a full saturation condition (i.e. \({S}_{r}\)= 1), expressed as a percentage of the total number of days, which has been considered and is summarised in Table 5 for all six pavements under the various climatic conditions studied.

Table 5 The number of days that UGM reaches full saturation condition as a percentage of total days of service life
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Table 5 shows that pavements with less permeable seals, namely P5 (S3_UGMA) and P6 (S3_UGMB), have not reached full saturation condition during their 10-year service life in any of the climates considered. However, the UGM layers of the other four pavements, namely P1, P2, P3, and P4, have experienced full saturation conditions in various climates to different degrees. Specifically, the UGM layer has attained full saturation conditions for the Adelaide climate less than 2% of the time for any of the four pavements. This indicates a lower likelihood of moisture-related road failures in this region. However, in Cairns, the values are relatively high compared to all other climates, suggesting that pavements in this region may be more susceptible to performance losses due to moisture-related issues.

Although it is widely acknowledged that UGM loses its structural strength completely at full saturation conditions due to zero suction, it is worth noting that the material begins to experience a significant reduction in strength and excessive accumulation of plastic strain (or rutting) when the \({S}_{r}\) exceeds its optimum value \(({S}_{r {\text{opt}}})\) [5]. Therefore, in the analysis of pavement performance, the number of days that \({S}_{r}\) exceeds the \({S}_{r {\text{opt}}}\) of UGM as a percentage of the total service life is also considered and presented for comprehensive analysis, as shown in Table 6. The experimental results indicate that the \({S}_{r {\text{opt}}}\) of UGM A and UGM B is 0.84 and 0.9, respectively [12, 37].

Table 6 Number of days that \({S}_{r }\mathrm \,{exceeds }\,{S}_{\mathrm{r opt}}\) as a percentage of total days of service life
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The analysis of Table 6 indicates that Cairns and Perth exhibit the highest percentage of days where \({S}_{r}\) exceeds \({S}_{r {\text{opt}}}\) for all six pavement configurations. As mentioned before although Perth is characterised as a warm climate, it still exhibits the highest or second-highest percentage of days where \({S}_{r}\) exceeds \({S}_{r {\text{opt}}}\). This suggests that numerous wetting fluctuations exceeding the optimum condition can lead to performance losses even if the UGM layer stays relatively dry during service life (refer to Figs. 20 and 21). Therefore, it is crucial to account for temporal moisture fluctuation during pavement performance evaluation, during the design stage, rather than solely relying on the service moisture condition. Adelaide, which is also categorised as a warm climate, exhibits the lowest values in Table 6 for all pavement configurations. This observation reinforces the previous finding that Adelaide has a favourable climate regarding moisture-related performance losses. Upon analysing the various observations, it can be reinforced that the impact of ambient climate variations must be considered throughout the entire lifespan of pavement when evaluating its performance.

As mentioned before, even though the pavements with lower permeable seals (i.e. P5 (S3_UGMA) and P6 (S3_UGMB)) have not reached full saturation condition at all during the service life under any climate (Table 5). Table 6 presents considerably larger values, indicating frequent occurrences of exceeding optimum conditions for those two pavements. Moreover, referring to Figs. 11, 12, 13, 14, 15, and 16, it can be observed that \({S}_{r {\text{eq}}}\) is close to optimum condition. However, the intensity of \({S}_{r}\) fluctuations of wetting and drying are more minor than pavements with high permeability seals. For further clarification, the distributions of \({S}_{r}\) values of P1 (S1_UGM2) and P5 (S3_UGM2) under Melbourne climate are shown in Fig. 23.

Fig. 23
figure 23

Distributions of \({{\text{S}}}_{{\text{r}}}\) values (obtained after reaching equilibrium) of; a P1 (S1_UGM2) and; b P5 (S3_UGM2) under Melbourne climate

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The \({S}_{r}\) distributions of pavement with less permeable seals, P5 (S3_UGM2), features approximately a normal distribution, whereas P1 (S1_UGM2) represents a skewed distribution (i.e. lognormal). Although the equilibrium value of \({S}_{r}\) is lower for the high permeable seal (Fig. 23a), there are more values close to or at 1 than for the less permeable seal P5, meaning that P1 (S1_UGM2) can have more instances of vulnerable conditions for excessive damage. Hence, rutting evaluations should be conducted based on the temporal moisture variations under given conditions to perform a comprehensive quantitative evaluation.

In unbound pavements with thin seals, the primary distress mode of UGM can be identified as rutting [2]. A recent development of Dutta and Kodikara [11] related rutting to the initial state of the material, namely, initial dry density \(({\rho }_{d,0}\)) and initial degree of saturation \(({S}_{r,0}\)). However, as demonstrated in the present study, \({S}_{r}\) changes over the service life in response to the prevailing climate conditions. Hence, rutting should be calculated in an incremental form by accounting for daily \({S}_{r}\) fluctuations, as simulated in the current study. Then, they can be added to calculate the final rutting during the service life. Further research on this topic is ongoing at SPARC hub Monash University.

4 Conclusions

The present study endeavours to comprehensively analyse the influence of the ambient climate on moisture variations and subsequent pavement performance. The investigation entails an assessment of the degree of saturation (\({S}_{r}\)) variations of pavement layers, simulated under different climates using a model developed and validated by the authors in prior studies. The authors evaluated the moisture variations of the unbound granular material (UGM) layer, the primary structural layer of unbound pavements with thin seals. To comprehensively examine the behaviours of moisture conditions of pavement layers throughout the ten-year service life, the temporal moisture variations of six different typical sprayed sealed pavements were modelled under seven different Australian climates, viz. Melbourne, Adelaide, Perth, Brisbane, Sydney, Hobart, and Cairns, by incorporating daily climatic factors.

This study reveals that the ambient climate significantly impacts the moisture variations of unbound granular layers, especially when the seal is relatively permeable. The service moisture condition, referred to as the equilibrium moisture condition, remains relatively low in dry climates such as Adelaide and Perth. At the same time, it tends to equilibrate at rather wet conditions in wet climates such as Cairns and Brisbane. However, this study showed that the individual values of annual rainfall and evaporation are not suitable parameters to determine the service moisture condition of the UGM layer, as no correlation was found with the service moisture condition and these parameters. Instead, the ratio between annual rainfall (\(P\)) and annual pan evaporation (\({\text{PE}}\)), i.e. (\(\frac{P}{{\text{PE}}}\)) combined with the saturated permeability of the seal (\({K}_{s })\), demonstrated a strong relationship between the service moisture condition of the UGM layer. This finding led to the development of a novel model that can estimate the service moisture condition of the UGM layers. The proposed approach provides a practical solution to the challenging task of predicting the service moisture condition of pavements, which is not currently available in the Australian pavement design guide.

Moreover, this study highlights the importance of considering the temporal moisture variations induced by the daily climatic fluctuations in pavement design. The long-term pavement performance analysis was conducted by considering the days the moisture condition of UGM layers reached full saturation and exceeded optimum conditions. It showed that the likelihood of road failure due to moisture variations in Cairns could be higher, as those values are relatively high for that climate. Compared to other climates, Adelaide can be identified as a favourable climate concerning moisture-related deteriorations as there is a relatively low chance for the UGM layer to exceed the optimum condition and reach full saturation throughout the service life. It showed that even though the service moisture condition stays relatively dry in some climates like Perth, the possibility of moisture-related failures may be high as UGM experiences frequent wetting fluctuations. Therefore, it is necessary to take a more comprehensive approach to incorporate the daily climatic factors in pavement design beyond considering the service moisture condition in a conservative approach. Hence, the numerical model developed by the authors that simulates temporal moisture variations in terms of the degree of saturation can be used in the incremental rutting calculation of pavement layers to advance the current Australian pavement design incorporating climatic effects for practical use.