1 Introduction

Expansive soils affect engineering works across the globe, causing damage to structures and reducing their bearing capacity (Pooni et al. 2019). These soils undergo volumetric variation, swelling as they absorb moisture, usually due to rainfall, and subsequently contracting during evapotranspiration. The swelling is governed by the size and shape of particles, which depend on their mineralogy, degree of aggregation, and chemical interaction with adsorbed water (Terzaghi et al. 1996). Nelson and Miller (1992) proposed that expansion is a more complex phenomenon that essentially depends on three factors: soil properties, environmental conditions, and stress state.

In the Southwest of the Brazilian Amazon, studies on expansive soils for geotechnical purposes are still incipient, despite the recorded damages caused by these soils (Barbosa, 2018; Seixas 1997; Córdova 2011; Oliveira and Ferreira 2006). The problem is further compounded when it is necessary to conduct exploratory surveys for long stretches of roads or rail works. In such cases, direct approaches for identifying expansive soils, such as undisturbed samples and edometric tests, become impracticable and too expensive. Consequently, methodologies that disregard intrinsic aspects of local soils, such as the CBR method for expansion, are often used, which is unsuitable for identifying expansive soils.

Laboratory infrastructure in the region is still very limited and distant from the country's major centers, thus knowledge of subgrade soils is limited, which contributes to numerous problems associated with shrink-swell susceptible soils, as shown in Fig. 1. Another limitation is the high cost of crushed stone due to the absence of rock formations in the state (Barbosa, 2018). Crushed stone is essential for infrastructure works over expansive soil deposits, as it is used to reinforce the subgrade and in road drainage systems. This scenario highlights the need to make better use of scarce local resources, in addition to conducting more detailed studies of the expansive characteristics of soils.

Fig. 1
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The effects of soil expansion in Rio Branco city, showcasing a cracks in the flexible pavement, b uplift and cracks at the edges of a road, and c cracks in the building's counter floor

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To mitigate geotechnical risks in the Amazon region, it is crucial to establish a method for estimating the shrink-swell susceptibility of the local soils. This method should utilize simple tests commonly employed in geotechnical practice, allowing for easy and low-cost performance in soil laboratories, requiring minimal sample volumes, and enabling broad coverage at various depths. Moreover, the method should deliver reasonably precise outcomes across an extensive geographical range.

The use of Atterberg limits to classify soil shrink-swell susceptibility is a common approach. Researchers such as Seed et al. (1962) and Van der Merwe (1964) have proposed procedures to estimate soil expansion based on Atterberg Limits. They developed charts to classify soils into four expansiveness ranges using equations based on Atterberg limits and soil size.

Mckeen and Hamberg (1981) also presented a method to empirically obtain the suction compression index, γh, without conducting tests that involve the use of filter paper or psychrometers. In this method, γh can be obtained through a graphical procedure that relates different mineralogical groups to Skempton's activity, cation exchange capacity (CEC), and COLE expansion tests. Covar et al. (2001) improved this method using 6,500 soil samples from the United States Department of Agriculture (USDA).

The methods presented in Seed et al. (1962), Van der Merwe (1964), and McKeen and Hamberg (1981) should be used with caution. The direct application of soil classifications developed for different geological formations can lead to significant discrepancies in results. Therefore, it is necessary to develop a classification method based on the tests conducted in the specific region and that is also practical and easy to use due to logistical reasons.

The main objective of this research is to propose a method that mitigates geotechnical risks associated with expansive soils in pavements, by increasing their design life and reducing costs. The proposed method relies solely on conventional engineering tests related to particle size and Atterberg Limits.

2 Geotechnical Characterization

2.1 Localization

The studied region is in the state of Acre (152,581 km2), which is the westernmost region of the Brazilian Amazon and shares borders with Bolivia and Peru (Fig. 2). According to the Köppen Classification, the climate in Acre is of the AW type, which is a humid tropical climate. The average annual temperature is around 25 ºC, and the average annual precipitation varies from 1700 mm to 2000 mm (IBGE, 2005; Embrapa, 2017).

Fig. 2
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Adapted from SEMA (Acre, 2010)

Area of study illustrating the Acre soil classes.

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The subsoil in Acre is part of a sedimentary basin with a wide variety of soils (Fig. 2 and Table 1), whose genesis is directly related to the uplift of the Andes. About 80% of the state is located within the Solimões Formation, which has a high occurrence of silt–clay sediments composed of 2:1 clay minerals, resulting in poor drainage and a low leaching rate.

Table 1 Soil class distribution and potential for swelling in the Acre region.
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"Less weathered soils and a drier pedoclimate are predominant, which is an unexpected characteristic considering the local hot and humid climate, and differs from other soils in the Amazon basin (Amaral, 2007; SEMA, Acre, 2010). Since Brazilian deposits are mainly composed of typical tropical soils with low silt content, it might not be possible to simply extrapolate these parameters to the high silt content Acre soils (Kotlar et al. 2020).

From the Pedological Map of Acre, a predominance of argisols and cambisols can be observed. Despite the map's small scale, it is estimated that at least 70% of the area has a high potential for expansion, with a greater concentration in the central region, as evidenced by the frequent reconstruction of the BR-364 Highway.

2.2 Geotechnical Database

EMBRAPA is a federal government corporation that conducts agricultural research and maintains a database of thousands of soil profile samples from across Brazil. These samples were obtained through technical-scientific projects conducted by the institution's researchers and provide a detailed description of the morphological, physical, chemical, and mineralogical characteristics of the soil profiles. The resulting data are compiled in the Brazilian Soil Information System (SISolos), which is maintained by EMBRAPA (Embrapa, 2020).

For this study, we compiled all data related to the Solimões Formation in the state of Acre from 1975 to 2010. The samples were taken from soils of different pedological classifications, with a predominance of investigations conducted along the BR-364 road, the only east–west road segment in the state of Acre, as shown in Fig. 2.

Among the parameters conventionally employed by EMBRAPA researchers in the SISolos database, physical and chemical tests were used to identify the mineralogical composition of the clay fraction. Chemical data was utilized to analyze the weathering indice Ki and the CEC. Initially, 635 samples were selected for the study, but some of them lacked chemical attributes for correlation analysis. After conducting the data analysis, only 321 samples from Solimões Formation were retained, and approximately 99% of these samples had particles with an equivalent diameter < 2.0 mm, as demonstrated in Table 2.

Table 2 Main parameters analyzed from the EMBRAPA database for the Solimões Formation in the state of Acre
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2.3 Physical Properties

Physical indexes commonly used in geotechnical characterization are not typically utilized by agricultural researchers, resulting in the absence of Atterberg Limits in EMBRAPA's soil investigation routine. These indexes are fundamental to understanding expansive soil behavior; therefore, the physical indexes corresponding to the 321 samples compiled in Table 2 were inferred through correlation.

The physical indexes were obtained through linear regressions applied to a dataset of 100 soil tests conducted in Rio Branco by Borges (2019). Consequently, linear equations with high determination coefficients were obtained for the liquidity limit (LL), plasticity limit (PL), and plasticity index (PI), based on the clay fraction (%), as illustrated in Fig. 3. As expected, the linear regression analysis revealed a strong correlation between the < 2 µm fraction of soil particles and their plasticity, with a determination coefficient R2 = 0.94. Figure 3 displays the data of the linear regressions.

Fig. 3
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Relationship between the Atterberg Limits and clay fraction from 100 samples collected in Rio Branco. The plots include a % clay x plasticity index (PI), b % clay x plastic limit (PL), and c % clay x liquid limit (LL)

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2.4 Weathering Index Ki

Concentration of oxides, or their interrelation, provides important indications for soil characteristics such as weathering and probable mineralogical composition. Smectites are formed in conditions where silica (SiO2) is abundant due to the 2:1 structure (silica:alumina), like the flocculated structures formed between silica and alumina. These structures are formed in soils with high pH, high electrolyte concentration, and higher concentrations of Mg2+ and Ca2+ than Na+ and K+. Additionally, climatic conditions with higher evapotranspiration than precipitation, and poorly drained sites with low leaching also contribute to smectite formation, which is the source of swelling in expansive soils (Mitchell, 2005).

To evaluate the soil's expansive behavior, it is necessary to distinguish highly weathered clayey soils from soils with more expansive clay minerals. Therefore, soils with a predominance of smectites in the clay fraction usually have a higher molecular ratio of SiO2 to Al2O3 greater than 2. On the other hand, values below 2 indicate that highly weathered soils, formed by kaolinite and iron and aluminum sesquioxides, are not related to expansive behavior (Mitchell, 2005; IBGE, 2005).

In this study, the weathering index Ki utilized was determined using Eq. 01 (IBGE, 2005), with the oxide content determined through the solubilization of soil samples with a 1:1 H2SO4 (sulfuric acid attack), as described by Embrapa (2017). Soils with a high degree of weathering have Ki values ≤ 2.0, while soils with a low degree of weathering have Ki values > 2.0 (Mitchell, 2005).

$$Ki = 1.7 \times \left( {\frac{{S_{i} O_{2} }}{{Al_{2} O_{3} }}} \right)$$
(1)

2.4.1 Cation Exchange Capacity (CEC) of the Clay Fraction

In general, the expansion potential increases with the total number of exchangeable cations required to balance negative charges on the surface of clay minerals, also known as cation exchange capacity (CEC). Higher CEC values indicate the presence of more reactive clay minerals, such as smectites, which are associated with higher soil activity. Conversely, lower CEC values indicate the presence of more stable clay minerals, such as kaolinite, which are associated with lower soil activity (Nelson et al. 2015).

The clay fraction cation exchange capacity (CEC) is defined as the CEC of soil particles divided by the clay fraction of the soil. CEC values ≥ 27 cmolc / kg of clay indicate high activity, while < 27 indicate low activity, according to the classification adopted by the USDA (1999) and EMBRAPA (2018). The CEC values used in this study correspond to the T-value, which is determined by the sum of exchangeable cations and the potential acidity (H+  + Al3+) (Embrapa, 2017).

3 Method for Assessing the Shrink-Swell Susceptibility of Studied Soils

3.1 Physical and Chemical Attributes

The main physical and chemical attributes of the Solimões Formation soils in the state of Acre state were selected and analyzed on box plots, using the procedures presented in item 2. Figure 4a shows a predominance of the silt and clay fractions, with fractions varying between 20 and 50%, respectively, from the first to the third quartile. Granulometry is one of the factors that most influence the physical–chemical factors related to volumetric variations in soils (Mitchell, 2005), thus it is the first to be analyzed. From these results, it can be deduced that the occurrence of expansive soils in the region is possible since expansive behavior is associated with decreasing particle sizes.

Fig. 4
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Box plots of the physical characteristics of Solimões Formation soils in the state of Acre, illustrating granulometry a and Atterberg Limits b

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The Atterberg Limits were analyzed in Fig. 4b, where LL varied between 28 and 48%, from the 1st to the 3rd quartile; PL had a smaller range, with a median value of 19%; and high plasticity, with PI varying between 11 and 27%, and a median of 19%. Soils with higher plasticity tend to have more expansive clay minerals (Nelson et al. 2015).

The parameters related to soil mineralogy are presented in Fig. 5. The median Ki value is 2.7 and the median CEC value is 47 cmolc / kg, both of which are associated with soils containing expansive clay minerals.

Fig. 5
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Box plots of the chemical characteristics of Solimões Formation soils in the state of Acre, illustrating Ki a and CEC b

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The results presented in Figs. 4 and 5 indicate a high shrink-swell susceptibility of the Solimões Formation soils samples from Acre, which is consistent with field observations. Correlating these parameters is necessary to determine the range that indicates expansive soils.

3.2 Correlations Analysis of Data

After identifying the predominance of silt and clay fractions in the soils, the granulometry was correlated with Ki and CEC parameters. Subsequently, the mineralogical relationships were expressed in terms of parameters routinely used in transportation engineering works, such as the Plasticity Index. Figure 6 illustrates the relationship between silt/clay ratio and plasticity index, with data sorted according to the mineralogical divisions presented in Sects. 2.4 and 2.5.

Fig. 6
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Results of geotechnical tests carried out on 321 soil samples collected from the state of Acre. The following correlations were investigated: a Silt/Clay x PI x Ki; b Silt/Clay x PI x CEC

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The presented data in Fig. 6 demonstrates a noticeable trend, particularly in the range indicating the prevalence of expansive clay minerals. According to Table 3, the exponential regression model exhibits the best fit for the given data.

Table 3 Silt/Clay x PI models
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3.3 Chart for the Assessment of the Shrink-Swell Susceptibility of Soils in the Solimões Formation in the State of Acre

Using the models presented in Table 3, a 95% confidence interval was applied to determine the lower and upper limits of the range for shrink-swell susceptibility of soils in the Solimões Formation, considering the clay fraction Ki and CEC attributes (Fig. 7). The two limits were then combined to obtain a region with a higher probability of occurrence of expansive soils, and the resulting chart is presented in Fig. 8. All analyses were performed using MATLAB and its Curve Fitting Toolbox.

Fig. 7
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Confidence intervals for Ki > 2 and CEC ≥ 27 cmolc / kg of silty clay soils in the state of Acre

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Fig. 8
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Chart for assessment of the shrink-swell susceptibility of silty-clay soils in the state of Acre

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3.4 Evaluation of the Shrink-Swell Susceptibility of Samples From Brazil.

After developing the graph depicted in Fig. 8, the subsequent step involved comparing the proposed method with established procedures documented in the literature, utilizing additional tropical Brazilian soils associated with expansive behavior.

Figures 9, 10, and 11 illustrate the soil swelling susceptibility of 37 Brazilian samples using different methods. Table 4 summarizes the data of the 37 samples utilized, comparing the swelling susceptibility obtained in this study with that of the Van der Merwe (1964) and Seed et al. (1962) methods. The first 27 samples investigated in Seixas (1997) and Barbosa (2022) relate to the subgrade of the Rio Branco International Airport and its surroundings, which exhibit an expansive nature that causes the frequent occurrence of ripples and cracks in nearby pavements.

Fig. 9
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Van der Merwe (1964) classification chart for the swelling susceptibility of 37 Brazilian soil samples with a history of failures related to expansive soils

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Fig. 10
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Seed et al. (1962) classification chart for the swelling susceptibility of 37 Brazilian soil samples with a history of failures related to expansive soils

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Fig. 11
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Proposed classification chart for the swelling susceptibility of 37 Brazilian soil samples with a history of failures related to expansive soils

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Table 4 Comparison of the swelling susceptibility of 37 Brazilian soil samples associated with expansive behavior
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There is a correspondence between the proposed method and the charts widely used in the literature to assess the susceptibility of soil samples to expansion, particularly for samples from the Solimões Formation, ranging from 01 to 22. Additionally, it is worth noting that the graph proposed in this research better identifies the expansive behavior in soils with high silt/clay ratios, as evidenced by samples 28, 35, 36, and 37. This finding suggests the high cation exchange capacity in these soils, despite their lower clay fraction when compared to other deposits.

3.5 Flowchart of the Shrink-Swell Susceptibility Identification Method

The flowchart of the procedures required to determine the degree of soil sample's swelling susceptibility is illustrated in Fig. 12, which employs the graph depicted in Fig. 8.

Fig. 12
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Flowchart representing the method for identifying the swelling susceptibility

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4 Conclusions

A broad database was utilized in this study to devise a graphical method for the initial assessment of soil shrink-swell susceptibility in the Solimões formation in Acre. The implementation of agricultural tests has been demonstrated to be technically suitable, which is critical for transportation engineering in the region, where limited geotechnical data is accessible.

The chart provides the benefit of using low-cost and simple geotechnical tests commonly employed in transportation geotechnics, such as the Atterberg Limits and complete granulometric analysis, including sedimentation. Moreover, it is applicable to a broad spectrum of soils found in Brazil.

Due to the high silt content in soils of Acre, correlations based on granulometric attributes have demonstrated greater statistical significance with the silt/clay ratio content compared to the percentage of clay. This methodology could potentially be extended to forecast expansive behavior in other regions of Brazil, particularly those possessing similar physical–chemical characteristics.

It is important to note that although the chart provides an indication of the swelling susceptibility of soils in the state of Acre, its use does not provide a definitive identification of expansive soils. Therefore, it is recommended for preliminary studies and to plan more detailed tests for infrastructure projects. It could be a useful tool for construction managers to identify and investigate the occurrence of expansive soils at specific locations.