1 Introduction

There is overwhelming scientific consensus that human activities, particularly the emission of greenhouse gases (GHGs), are the main cause of climate change. This is supported by evidence such as the rise in global temperatures and sea levels, and the increased occurrence and severity of extreme weather events. Future climate change is commonly predicted using climate models, which are mathematical representations of the climate system on Earth. According to current climate models, the continuous increase in global mean yearly carbon dioxide levels is anticipated to impact infrastructure performance.

Future climate changes in Australia have been projected using climate models from the CMIP3 database (CSIRO and BOM 2007). These models predict that there will be a 1 and 3 °C rise in temperatures in Australia in 2030 and 2070, correspondingly, with little seasonal variation. However, the pattern of precipitation change is expected to be more complex, with both increase and decrease in different regions (CSIRO and BOM 2007).

Globally, forty per cent of energy consumption and thirty-three per cent of greenhouse gas emissions are attributed to buildings (Tricoire 2021). Although buildings generate GHG emissions throughout their entire lifecycle, including construction, maintenance, operation, and demolition, the operation stage of residential buildings typically contributes to 80–90% of the total emissions. Climate change can have significant and diverse impacts on residential buildings, such as increased energy consumption due to warmer climate, and damage caused by extreme weather events like heavy rain, flooding, and windstorms. According to the Climate Council of Australia, extreme weather events have cost Australia approximately $35 billion in the past decade and could cost as much as $100 billion annually in the next two decades (Climate Council 2022).

Additionally, climate change can significantly impact the foundation design of residential buildings, especially in areas with expansive soils. Expansive soils are types of clay soils that experience significant changes in volume when the water content changes, which can cause extensive damage to buildings. This problem is particularly challenging in Australia, where expansive soils cover around 20% of the land and affect six out of eight major cities. For example, in Melbourne alone, it has been estimated that over 4000 dwellings were damaged due to soil heave (The AGE 2014). This problem was compounded by a severe and prolonged drought that affected much of Australia, including the Melbourne region, between late 1997 and early 2010. Many of the affected houses were built during a drier period between 2003 and 2010 and experienced substantial slab heave caused by an excessive change of moisture in foundation soil following the installation of garden irrigation systems and the end of the prolonged drought in 2011 (Li and Sun 2015).

AS2870 (2011) is a national standard that has guided the design and construction of residential footings in Australia. Initially published in 1986, it was revised in 1988, 1990, 1996, and most recently in 2011. The Standard was developed to standardize construction practices throughout different states and reduce the financial strain on the community resulting from damage to residential buildings constructed on reactive soils. The Standard provides guidance for determining the depth of design soil suction change (Hs) that is needed to determine characteristic ground movement (ys) based on the Thornthwaite Moisture Index (TMI).

The TMI has been commonly employed in various scientific research fields and applications since its introduction by Thornthwaite in 1948. Engineers have utilized it to understand climate differences and estimate Hs. AS2870 (2011) incorporates a climate classification map for Victoria, Australia, that utilizes the TMI approach, which was originally developed by Aitchison and Richards (1965) and later expanded on by Smith (1993). However, this TMI map endorsed by the Standard is out of date as it employed the climate data from 1940 to 1960 (McManus et al. 2004) and may not reflect current conditions. Over the past two decades, several TMI maps for Victoria have been created. McManus et al. (2003) developed TMI maps for Victoria using weather data from 1961 to 1990, while Lopes and Osman (2010) and Leao and Osman (2013) utilized data from 1948 to 2007 and 1913–2012, respectively. Sun et al. (2017) developed three 20-year TMI maps for Victoria for the 1954–2013 period. In this work, we produced three TMI maps of Victoria for 1994–2013, and made predictions for 2030 and 2070. These maps provide valuable information for engineers to estimate Hs accurately and design residential footings more effectively in Victoria.

2 Materials and Methods

2.1 Residential Footing Design on Expansive Soils

Stiffened raft slabs and waffle raft slabs are the two common types of footing utilized in light industrial and residential construction across Australia (Li and Zhou 2013). Waffle raft footings consist of polystyrene pods or cardboard arranged in a grid pattern, 1.09 m by 1.09 m, and separated by narrow (110 mm wide) ribs which support an 85 mm steel reinforced concrete slab. The footing depth is limited to the chosen heights of pods, which range from 175 to 375 mm, providing an overall footing depth of 260 mm, 310 mm, 385 and 460 mm. The conventional stiffened raft concrete slabs consist of steel reinforced concrete beams (with a width of 300 mm) that are embedded into the ground and cast together with a steel reinforced slab with a minimum thickness of 100 mm.

To design a slab footing, AS2870 (2011) adopts an ‘equivalent beam assumption’ and divides the irregularly shaped footing layout into several overlapping rectangles (Fig. 1a). All external and internal beams and their contributory flanges are lumped into a single equivalent beam for each direction and each rectangle (Fig. 1b). The footing design is based on edge heave and center heave mound shapes, with the worst case governing the design. The design must satisfy three requirements, including adequate section ductility, the ability to withstand bending (flexural strength) and appropriate stiffness.

Fig. 1
figure 1

The equivalent beam assumption by AS2870 (2011) a Design rectangles for a footing plan b The lumped beam for section X–X of Rectangle 1

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2.2 Characteristic Surface Movement and Site Classification

The successful design of residential footings relies heavily on site classification. AS2870 (2011) classifies sites based on soil reactivity, which is determined by the expected free surface movement ys. This movement is calculated based on the design soil suction change profiles. As presented in Table 1, the Standard categorizes sites into five classes ranging between slightly reactive and extremely reactive.

Table 1 Site classification (AS2870 2011)
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The free ground movement caused by soil moisture changes for a site covered with expansive soil is referred to as the characteristic ground movement ys. It is unlikely to exceed 5% in the lifetime of a building. To determine ys, the displacement of each soil layer within the Hs is estimated and then summed up for all layers (Eq. 1).

$${y_s}=\frac{1}{{{\text{100}}}}\mathop \sum \limits_{{{\text{n =1}}}}^{N} {\left( {{I_{{\text{pt}}}}~\overline {{\Delta u}} h} \right)_{\text{n}}}$$
(1)

where, Ipt is the instability index, measuring the level of soil reactivity. It is calculated by multiplying a shrink-swell index Iss by a coefficient “α”, considering lateral restraint based on the expected seasonal cracking depth and the depth within the soil layer. Iss values typically range from 3 to 8% strain per log (kPa) for most expansive soils (Li et al. 2014). It is assumed that the average soil suction change \(\overline{\Delta{u}}\) over the layer thickness decreases linearly with depth, while the value of the maximum surface suction change, ∆us of 1.2 pF [log (kPa)] is provided by the Standard. The thickness of the soil layer is represented by h, and the number of layers within the Hs is expressed by N. To determine Hs for regions not specified in the Standard, the site classifier should consult a TMI map and utilize the correlation between TMI and Hs (Table 2) to acquire the required information.

Table 2 The relationship among TMI, Hs and climate zone (AS2870 2011)
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2.3 Thornthwaite Moisture Index

TMI is primarily determined by two factors: the amount of precipitation (P) and the potential evapotranspiration (\({e_i}^\prime\)). The calculation equation for TMI, as formulated by Thornthwaite (1948), can be expressed as follows:

$$TMI={I_h} - 0.6{I_a}$$
(2)

where Ih is the humidity index and Ia is the aridity index. Both indices can be calculated using the following equations:

$${I_h}=\frac{{100R}}{{{e_i}^\prime}}\begin{array}{*{20}{c}} {}&{}&{} \end{array}{I_a}=\frac{{100D}}{{{e_i}^\prime}}$$
(3)

where R refers to the excess amount of rainfall (mm) that remains on the surface or runoff when the soil is fully saturated; D is the moisture deficit (mm), which is the amount of water that is not available for evapotranspiration from a dry site and \({e_i}^\prime\) is the adjusted potential evapotranspiration (mm). The coefficient assigned to R and D assumes that a 6-inch water surplus during one season can compensate for a 10-inch water deficit during another season (Thornthwaite 1948).

As indicated in Eqs. 2 and 3, TMI is determined by three parameters, namely monthly values of R, D and \({e_i}^\prime\). The water balance method can be employed to derive the first two parameters, and McKeen and Johnson (1990) have provided a detailed calculation procedure. The water balance determination requires initial (S0) and maximum (Smax) water storage information. In general, such information is not readily available and therefore, it is necessary to rely on assumptions. \({e_i}^\prime\) reflects the atmosphere’s ability to convey water from the ground through the processes of evaporation and transpiration, which can be calculated using Eq. 4 (Thornthwaite 1948).

$${e_i}^\prime={e_i}\left( {\frac{{{D_i}{N_i}}}{{30}}} \right)$$
(4)

where Ni is the number of days; the factor corrected for the day length is expressed as Di; the non-adjusted potential evapotranspiration (cm) is denoted as \({e_i}\) and is given by Eq. 5:

$${e_i}=1.6{\left( {\frac{{10{t_i}}}{{{H_y}}}} \right)^a}$$
(5)

where ti is the mean monthly temperature (°C) calculated as the average of tmax and tmin; Hy is the annual heat index determined by summing the 12 monthly heat index values hi (Eq. 6); α is the power term (0 < α < 4.25) derived by Eq. 7.

$${h_i}={\left( {0.2{t_i}} \right)^{1.514}}$$
(6)
$$a=6.75 \times {10^{ - 7}}{H_y}^{3} - 7.71 \times {10^{ - 5}}{H_y}^{2}+0.017921{H_y}+0.49239$$
(7)

The TMI Eq. 2 has been extensively used by numerous researchers (McKeen and Johnson 1990; Fox 2002; Chan and Mostyn 2008; Jewell and Mitchell 2009; Lopes and Osman 2010; Mitchell 2012) for TMI calculation. Aitchison and Richards (1965) were the first to use it to create a TMI isopleth map for Australia, which was later used by Smith (1993) to produce TMI-based climate map for Victoria.

TMI calculation is on a yearly basis that is determined for a sufficient number of years to accurately represent the climate of a specific site. A drying climate is reflected by negative TMI indices where the precipitation is less than the potential evapotranspiration and the soil moisture is typically low. Conversely, a wet climate with soil water surplus is represented by positive TMI indices. Zero TMI indices indicate that the volume of precipitation that infiltrates into the soil matches the quantity of soil water lost due to evapotranspiration.

The calculation of TMI is usually performed using either the ‘year-by-year’ or the ‘average year’ method. The former has been the more widely used approach for TMI determination (Fox 2002; Chan and Mostyn 2008; Lopes and Osman 2010), while the latter is straightforward but highly dependent on the assumed value of S0.

2.4 Depth of Design Soil Suction Change

The soil suction profile demonstrates an equilibrium between processes that contribute to or remove water from any location within the profile. The design suction change profile (Fig. 2) is a simple approximation based on data collected from site investigations, and could be determined by analyzing soil suction measurements taken at varying depths during periods of wetness and dryness. The simplified suction profile has been incorporated into the Standard, assuming that the reduction in suction change is linear up to the Hs. It was found that the actual measurements of suction values during both wet and dry periods tend to decrease rapidly with depth, contradicting the assumption adopted by the Standard (Fityus et al. 1998; Sun et al. 2022; Sun and Li 2023a, b).

Fig. 2
figure 2

Typical soil suction profile

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To estimate ground movement for footing design, simplified design suction changes are combined with information about the soil profile. The depth at which there are no significant seasonal suction changes, Hs, is used to determine the soil suction change. However, obtaining Hs data through field measurement is rare and limited to specific regions. Ideally, determining Hs requires site monitoring of the changes in the soil profile under extremely dry and wet conditions over a long period. This process can take years or even decades, making it a challenging and time-consuming task. Fortunately, a correlation between TMI and the depth of Hs was proposed by Smith (1993), and this has been adopted in AS2870 (2011) to estimate Hs. However, The TMI-Hs relationship has a limited scientific basis, and the correlation presented in the Standard is largely based on anecdotal evidence and empirical experience, rather than scientific evidence. Thus, further investigation is needed to establish a more robust TMI-Hs correlation.

2.5 TMI Isopleth Map

TMI values for the 1994–2013 period were calculated for 70 weather observation stations distributed in the State of Victoria using fully recorded meteorological parameters purchased from the Bureau of Meteorology (BOM). Equation 2 and Eq. 4 were used for TMI and \({e_i}^\prime\) computation and in combination with the ‘year-by-year’ method. The 0 and 100 mm were adopted for S0 and Smax, respectively (Li and Sun 2015). The Surfer 11 (2012) was used to delineate TMI isopleth maps with climate zoning for Victoria based on the calculated TMI indices. To predict TMI for 2030 and 2070, temperature and precipitation data were estimated using the projected climate trends relative to 1990 (CSIRO, BOM and DCCEE 2014). TMI contour maps were also developed for 2030 and 2070 to compare with the climate condition for the 1994–2013 period. Given the significant discrepancies in the outcomes of climate models resulting from short-term changes in climate, the A1B emission scenario (a mid-range scenario) was utilized for 2030. On the other hand, the A1FI scenario (an extreme scenario) was used for climate changes centered on 2070 since they were more dependent on greenhouse gas emissions scenarios.

2.6 Case Study

An investigation was conducted as a case study to evaluate how climate change affects the required footing size and subsequent material costs for a one-story articulated masonry veneer building constructed in 1992, located in Melbourne, Australia (37°43′S, 144°56′E). It is worth noting that no noticeable geological anomalies exist at this site.

Meteorological data obtained from the Melbourne Regional Office weather observation station (086071) were utilized to determine the TMI value for 1992 (year of building construction). TMI indices were also determined for 2030 and 2070 relative to the climate conditions in 1990, using the climate trend presented in Table 3. Hs was determined using TMI- Hs correlation in Table 2  to allow the determination of ys using Eq. 1.

Table 3 Temperature and precipitation projections for Melbourne in 2030 and 2070 (CSIRO, BOM and DCCEE 2014)
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The size of the footing and the reinforcements required were determined using CORD©, a widely used finite element software in Australia for designing footings in residential buildings. This software is endorsed and recommended by the Standard. To verify whether the selected footing size satisfied the design requirement, the essential design variables for the footing at the study site were entered into CORD (2012). Figure 3 illustrates the beam layout and cross-section of the stiffened raft footing.

Fig. 3
figure 3

The stiffened raft footing at the experimental site a plan layout b section X–X (all dimensions are in millimetres)

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2.6.1 Soil Testing

Three boreholes (BHs) were drilled at different locations at the study site. Core samples obtained from these BHs were used to perform the Atterberg Limits test, shrink-swell test and establish soil profile.

2.6.1.1 Atterberg Limits

The Atterberg limits are essential in geotechnical engineering and soil science to assess the soil’s properties and its suitability for various construction purposes. The Atterberg limits tests comprised plastic limits (PL), liquid limits (LL) and linear shrinkage (LS), which were conducted following Australian Standards AS1289 (2008, 2009a, b). The soil samples taken from the selected depth of BHs were oven-dried at 105 °C for 24 h. Then, they were manually crushed with a hammer. The soil that passed through a sieve with a size of 425 μm was used for conducting Atterberg limits.

2.6.1.2 Shrink–Swell

The shrink-swell tests were conducted following Australian Standard AS1289 (2003). The tests include a core shrinkage test and a swelling test. The soil cores were cut to a 100 mm length, two times the size of the diameter. The top and bottom ends of the core were trimmed flat and inserted with a stainless drawing pin, allowing changes in sample length to be measured using a digital Vernier caliper. The sample was placed in a zip-lock plastic bag with a small opening to prevent surface cracking caused by moisture gradients during the air-drying process. Measurements of the sample’s mass and length were taken twice a day using a high-precision digital scale balance and a Vernier caliper until no further change was observed. Afterwards, the sample was oven-dried at 105 °C for 24 h to calculate its shrinkage strain \({\varepsilon}_{\text{sh}}\).

The soil sample extracted from a 20 mm high and 50 mm internal diameter steel ring was used to perform the swelling test. The steel ring was placed within a consolidation cell following the attachment of a porous stone to both ends of the ring. Initially, 5 kPa pressure was applied to the sample for 5 min, followed by an increase to 25 kPa for 30 min. Then, distilled water was added to the sample to induce swelling, and the displacements incurred were recorded by a data logger that was connected with a PC. These measurements were used to calculate the swelling strain \({\varepsilon}_{\text{sw}}\). Equation 8 was employed to calculate the shrink-swell index Iss once the \({\varepsilon}_{\text{sh}}\) and \({\varepsilon}_{\text{sw}}\) were determined.

$${I_{ss}}=\frac{{{\varepsilon _{sh}}+\frac{{{\varepsilon _{sw}}}}{{2.0}}}}{{1.8}}$$
(8)

3 Results and Discussions

3.1 TMI Isopleth Map for the State of Victoria

The TMI contour maps presented in Fig. 4 show that Victoria’s climate is projected to become hotter and drier, resulting in a significant increase in soil movement due to decreasing average TMI values. These maps demonstrate that the arid zone (Zone 6, TMI < − 40) and semi-arid zone (Zone 5, – 40 < TMI < − 25) are generally located in the north-western regions, while the wettest zone (Zone 1, TMI > 10) is distributed along the southern and eastern coastal regions. The highly negative TMI values observed in the north-west part of the State can be attributed to prolonged and frequent droughts, while the positive TMI indices observed in the southern regions reflect a humid coastal climate. A comparison of the TMI climate zones illustrated in Fig. 4 reveals that the boundaries of these zones have undergone significant transformations, with the most substantial changes projected for the year 2070.

A wet climate is predicted for south-eastern Victoria in 2030. For example, Omeo was located in the boundary of Zone 1 and Zone 2 for the 1994–2013 period, and the climate in this region is expected to be superseded by Zone 1 in 2030. Similarly, the growth of the moist climate in East Sale is predicted to change its climate from Zone 3 to Zone 2. The expansion of climatic aridity in East Sale, Omeo and Point Hicks areas is expected in 2070.

These maps reveal that the most densely populated Melbourne Metropolitan areas have experienced significant growth of drying since 1994, with its prevailing climate zone changed from Zone 3 (Fig. 4a) for 1994–2013 period to Zone 4 (Fig. 4b–c) in 2030 and 2070. Laverton and Avalon, which are located in the south-west region of Melbourne, are expected to suffer increased aridity, and consequently, the dry temperate Zone 4 (Fig. 4a) will be superseded by semi-arid Zone 5 (Fig. 4c). This means that these areas will have a significant depth of Hs and an increased frequency of excessive ground movement. It should be noted that due to limited data availability, only 70 weather stations were utilized to create the TMI contour maps. A more comprehensive TMI contour map could be generated by incorporating a larger number of weather stations.

Fig. 4
figure 4

TMI contour map for Victoria, Australia a 1994–2013 b 2030 c 2070

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3.2 Case Study

3.2.1 Soil test

The soil profile of the study site is presented in Fig. 5, which is fairly consistent among the three BHs. Figure 6 displays the results of the Atterberg limits test. The observed soil layers consist of a 0.1 m thick layer of sandy silt (ML), followed by a 2.9 m thick layer of high-plasticity silty clay (CH). As shown in Fig. 6b, the PL remained at around 16% within the top 1.5 m, increasing to 19% at 1.8 m and maintaining a consistent value of approximately 20% at 2.5 and 3.0 m. The LS of around 13% was observed at depths of 0.4 and 0.8 m, followed by a gradual increase to 19% at 3.0 m. The LL varied from 71% to 0.4 m to 60% at 1.5 m. The Iss was calculated at depths of 0.4 m, 0.8 m, 1.5 m, 1.8 m, 2.5 and 3.0 m using Eq. 8, and the results are shown in Fig. 5. The highest Iss of 4.98%/pF was found at a depth of 0.4 m, gradually decreasing to 3.85%/pF at 1.5 m, and slightly increasing to 3.92%/pF at 1.8 m. This was followed by a significant rise of 19% to 4.66%/pF at 3.0 m.

Fig. 5
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General soil profile for the experimental site

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Fig. 6
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Atterberg limits test results for the experimental site a LL versus PI b PL, LL and LS

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3.2.2 Assessment of the Impact of Climate Change on Footing Design

The TMI value of − 5 was calculated for 1992 for the experimental site, employing annual R, D and \({e_i}^\prime\)determined using Eqs. 2–4 and in combination with the ‘year-by-year’ approach. An illustration of TMI calculations for Melbourne in 1992 is given in Table 4.

Table 4 TMI calculation for Melbourne in 1992
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Relative to climate conditions in 1990, TMI of − 16 and − 24 is predicted for 2030 (A1B scenario) and 2070 (A1FI scenario), respectively, based on the projected temperature and precipitation trend (Table 3). Δus of 1.2 pF [log (kPa)] was used following AS2870 (2011). The Hs values for different study periods were determined by using TMI-Hs correlation provided in Table 2. The ys were calculated based on the soil suction change profile and shrink-swell indices Iss (Fig. 5), using Eq. 1. An example of ys determination for 2070 is presented in Table 5. The design values Hs of 2.93 m, Δus of 1.2 pF were used to calculate ys, and the value of 80 mm was determined, which corresponds to an extremely reactive site (Class E).

Table 5 The ys estimate for 2070
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The geometry of the footing layout presented in Fig. 7 was divided into two designed overlapping rectangles (ABCD defines Rectangle 1 and EFGD defines Rectangle 2). Each rectangle consists of three sub-beams in the long direction and four sub-beams in the short direction. Values of both internal and external beam depths associated with steel reinforcement details can be entered into CORD to obtain footing design properties. The required values were also generated for comparison. Table 6 gives an example of CORD programmed footing properties for 2070 based on the attempt values of internal and external beams (680 mm deep × 300 mm wide) reinforced with 2-N16 steel bar at the top and 3-N16 at the bottom and SL72 slab mesh (i.e., 6.75 mm longitudinal and cross wires at 200 mm intervals). Table 6 shows that the footing size and reinforcement details adopted have satisfied the design requirement

Table 6 Design information for a stiffened raft footing in 2070
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Fig. 7
figure 7

Design rectangles for the study site

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The changes in TMI, ys, site class and footing depth induced by climate change at the study site are compared for the years 1992, 2030 and 2070, as presented in Fig. 8. A highly reactive site (Class H1) with ys of 52 mm was determined for 1992, which required a footing beam of 400 mm deep and 300 mm wide, the same footing size as it was originally constructed. However, a 27% increase in ys is expected for 2030 due to a 220% decrease in TMI from − 5 to 1992 to − 16 for 2030. This led to a degradation in site class from H1 to H2, resulting in a deeper beam (i.e. 600 mm) and an additional top N12 steel bar for both edge and internal beams. By 2070, TMI is anticipated to decrease further to − 24, resulting in a 54% increase in ys, which subsequently supersedes the site class from H1 (in 1992) to Class E. Consequently, there will be a 280 mm increase in beam depth and an upgrade of top and bottom steel bars from N12 to N16 for both edge and internal beams, resulting in an approximately 111% increase in the cost of construction materials. The expense was estimated based on the unit cost information given by Scott Metals (2021) and Hanson Australia (2021).

Fig. 8
figure 8

Correlations between TMI, ys and beam depth

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4 Conclusions

The TMI as a climate indicator has been adopted by Australian Standard AS2870 to cope with the influences of climate change on footing design on expansive soils. In this work, three TMI contour maps of Victoria were developed using TMI values calculated from data collected from 70 weather observation stations from 1994 to 2013 and projecting climate trends derived from 23 climate models for 2030 and 2070. The maps reveal a significant increase in aridity for Victoria, with the most pronounced dryness predicted for 2070. The reduction in TMI indices across different regions of Victoria reveals a notable decline in soil water availability, which may result in greater ground movements for residential footings, leading to an increased incidence of slab edge heave and distortion in buildings constructed on expansive soils.

To assess the impact of climate change on footing size and construction cost, a case study was conducted on a single-story articulated masonry veneer building located in Melbourne, Australia. The study revealed that the footing constructed in 1992 would not be able to withstand the anticipated drying climate in 2070 without increasing the beam depth by 280 mm and an upgrade of top and bottom steel bars from N12 to N16 for both edge and internal beams, which would result in a construction material cost increase of approximately 111%.