Validation of Semi-empirical Models for the Prediction of Swelling Stress for Compacted Unsaturated Expansive Soils

Unsaturated swelling soil behaviour is governed by the matric suction, thus the predetermination of swelling stress for expansive unsaturated soil requires rigorous procedures. However, some swelling stress equations assume full saturation of the soil, which leads to the over-design of infrastructure. This study focused on the validation of predictive swelling stress models that correlate suction with other soil properties. Three models were developed, and independent data were used for the validation of the developed models. The predicted swelling stress values were compared to the values predicted by the randomly selected predictive models from the literature. initial studies include the determination of basic soil characterization and swelling stress along with soil mineralogical compositions were conducted to determine their geotechnical properties with their corresponding degree of expansiveness. The replicated expansive soils were also studied for suction, using filter paper techniques to obtain the soil’s unsaturated parameters. Based on the obtained experimental results, three models were developed using a mathematical software package (NCSS11). Independent data obtained from a group of final year students working on the swelling stress response of expansive unsaturated soils at the geotechnical engineering Laboratory from the University of Johannesburg were used for the validation. The developed models showed good agreement with the independent data, having a coefficient of determination (R 2 ) of 0.858, 0.931, and 0.890 for Eq. 4, 5, and 6, respectively. Compared to models selected from literature, which recorded R 2 values of 0.796 and 0.636 with an average variance of 0.097 and 0.257 respectively. The correlation variables showed that the degree of expansion represented by swelling stress demonstrated a proportionality with the moisture capacity along the drying and wetting path of the suction curves. Results suggest that the developed models can reasonably predict the swelling stress of compacted expansive soils at high suction values.


Introduction
Swelling soil is one of the problematic soils that cause damage to various civil engineering structures due to its swelling and shrinking potential upon contact with water. Swelling soils behave differently from other soils due to their tendency to swell and shrink at a very great degree. Because of this swelling and shrinking behavior, expansive soils may cause the following problems in structures or construction projects: Structural damage to lightweight structures such as sidewalks and driveways, Lifting of buildings, damage to basements, and building settlement, Cracks in walls and ceilings Damage to pipelines and other public utilities, Lateral movement of foundations and retaining walls due to pressure exerted on vertical walls, Loss of residual shear strength causing instability of slopes, etc. Therefore it is essential to check for the presence of expansive soil and a suitable treatment method should be adopted before commencing any construction projects. In some cases, postconstruction treatment of expansive soil may be required if the situation has not been dealt with before construction. Swelling stress is widely found in semi-arid and arid regions of the world, and South Africa is situated within these areas due to high suction values associated with the soils located within this region [1]. Geotechnical structures such as pavement, foundations, earth dams, and bridges are most vulnerable to volumetric deformation due to swelling activities [2,3]. In geotechnical practice, soils are situated in unsaturated conditions, as such structures are located above the groundwater table. Structures constructed on expansive soils are often subjected to large uplift forces caused by swelling, and it induces heaving, cracking, triggering a collapse of foundations and pavements.
Swelling stress is considered imperative for the design and performance analysis of structures. However, oedometer and zero swelling tests are commonly used to evaluate the swelling stress values in engineering practice. Moreover, one of the limitations of the tests includes sample disturbance and time required for full completion of swelling shrinkage cycles. Expansive soils are randomly distributed across the Free State, Northern Cape, KwaZulu-Natal, Mpumalanga, and some parts of the Northwest area of South Africa, with predominant clay minerals known as montmorillonite clay [4]. The swelling potential is influenced by the composition of clay minerals, dry density, void ratio, cementation, and soil macrostructure, though, the most significant factor is clay mineral [5]. Numerous laboratory tests such as free swell, zero swells, loaded swell, restricted swell, constant volume, swell-consolidation, and double oedometer tests, have been proposed in various testing standards to evaluate the swelling stress of compacted soil. Reference [6] determined and compared the swelling characteristics of compacted sand-bentonite and pumice-bentonite mixtures using standard Proctor tests and constant volume swell tests. The results indicated that pumice-bentonite mixtures recorded low dry unit weights, higher optimum moisture contents, and greater swelling potentials than equivalent sand-bentonite mixtures. Reference [7] proposed an empirical equation for swelling pressure using plasticity index, initial water content, and clay content of expansive soils. The proposed equation estimated the swelling pressure with minimum errors within the range of 0.3 to 0.8%. Besides, several empirical relationships have been developed between swelling stress and basic soil index [8][9][10]. These investigations predicted swell stress value as a function of Atterberg limits, dry density, water content, clay fraction, and cation with a determination coefficient of greater than 0.7. Researchers like (Çimen et al. [11], Vanapalli and Lu [12], Israr et al. [13]) suggested that swelling stress predictive models could be developed based on investigations performed on a limited number of soils. The challenges of the results are the huge discrepancies between measured and predicted values with R 2 of less than 0.6. These models are proclaimed not to be universally valid for all types of expansive soils due to a limited number of samples.
Recent research is geared towards developing empirical methods using the soil-water retention curves (SWRC). The relationship between the volumetric water content and matric suction is used as a tool to predict the swelling stress [14,15]. In connection with the studies, expansive unsaturated soils were investigated. The mathematical swelling stress predictive model is developed based on thermodynamic relationships between swelling pressures and suction [16]. According to the results, swelling stress increases with an increase in bentonites quantities, dry density, and total suction. The results are found to be in good concurrence with the experimental data and the data obtained from the literature for the same bentonite. However, several reports in the literature have shown reliable prediction of swelling stress using empirical and semiempirical models for compacted expansive soils [17][18][19]. In furtherance, some available predictive models are developed for different types of expansive soils, ranging from undisturbed, compacted, and laboratory-built expansive soils. As such, the difference in soil type could significantly influence predictive models. Most times, the percentage of errors between the measured and predicted values varies from 10% to 67% for swelling pressure. Despite the existing models, geotechnical engineers still require a deep understanding of the hydromechanical properties of expansive unsaturated soils concerning swelling stress prediction. To extend the hydromechanical response of expansive soils, this study developed three predictive models for three South African expansive soils. The models were developed as a function of gravimetric water content, matric suction, dry unit weight, free swell index, and Atterberg limits. The developed models are suggested to be useful in the prediction of swelling stress for compacted unsaturated expansive soils. Thus, the models are limited as modifications could be required before utilized for another type of soil. Generally, the developed models rationally predicted reliable results for expansive soils when validated with independent data set without going through tedious processes, i.e., the standard oedometer test especially when many tests are required for a particular project. The developed models are also trusted to save high costs accompanied by running oedometer tests and time-consuming.

Soils
The soil samples used in this study were collected from 4 different locations across Free State. With different values of plasticity, the soils in this Province are categorized as highly expansive as highlighted in green according to Fig 1. The soil from each site is labelled in alphabetical order as presented in Table 1.
The collected soil samples classification ranges from CH to CL, showing predominantly clay with high plasticity according to the unified soil classification system (USCS). Different cores were drilled at each site, and representative soil samples were collected at a depth of 1.2m, sealed in airtight plastic bags to minimize moisture loss. The soils were batched by blending different particle sizes obtained from dry sieve analysis of each soil. The particle size blending was employed to avoid particle size discrepancies that could affect the test results. The granular and fine batches were thoroughly mixed and air-dried for seven days. Dry sieving was conducted by firstly passing the particles through a 9.5mm sieve and subsequently sieved using 4.75mm and 75μm sieves to separate fines, sand, and gravel. The soils that passed through a 75μm sieve were further subject to a hydrometer test to differentiate percentages of silt and clay for the representative soils following ASTM D1140 [20]. The cumulative percentages of the soils passing through the American Society for Testing and Materials (ASTM) sieve size of #200 vary between 75% and 100%, as presented in Table 1.  The geotechnical index properties of the investigated soils as presented in Table 1 show that the liquid limit and shrinkage results confirm that soils are of a high degree of expansiveness. The plasticity values of the soils are within the range of 35 to 50%, whereas the obtained linear shrinkage is within the values range of 15% to 23%. In the winter season, when the samples were sampled, the soil generally experiences a net water deficit given the semi-arid climate prevalent in the province. The degree of saturation ranges from 82 to 92 and the value reflects the unsaturated state of the samples in the field, as the high liquid limit and plastic limit indicate the high-water adsorption capability of the soils. Thus, it could be attributed to the presence of expansive clay minerals such as smectite, montmorillonite, Kaolinite-and vermiculite. The percent of the fine-grained and clay minerals of the soils suggests that the soils have a high-water retention capacity. Overall, the soil was classified as CH (clay with high plasticity) with few classified as CL (clay with low plasticity) according to the Unified Soil Classification System (USCS).
The index properties of clayey material depend on the type and content of clay minerals, which considerably influence the swelling stress of expansive soils [21]. Therefore, to evaluate the mineralogical compositions responsible for swelling activities, the investigated soils were subject to X-Ray Diffraction (XRD) testing using the Rigaku TTRA III diffractometer, and tests were performed at Cu Kα radiation (1.5418 Å) level as presented in Table 2. The presented XRD results analysis also confirms that the investigated soils are expansive consisting of dominant phases of, smectite, illite, silica, calcite, and other clay minerals evaluated at trace level.

Sample Preparations
Prior to sample preparation, a Proctor compaction test was carried out on the soils following ASTM D-698, [22]. Specifically, this test is designed to determine the optimum moisture content (OMC) of soil with its corresponding maximum dry density (MDD). Generally, the investigated soils respond in a similar trend as the optimum moisture content ranges between 18.24%, to 33.31%, whereas the dry densities at the optimum moisture content range from 17.74 kN/m 3 to 21.85 kN/m 3 for the investigated soils. This implies that the soils are composed of high plasticity with significant swelling potentials. The soil samples were prepared at various MDDs with their corresponding moisture content, as initially obtained from the compaction test. Given quantities of soils were weighted and thoroughly mixed after representative amounts of water were added. The mixing continued until homogeneous soil mixtures were obtained. The soil mixtures were covered in airtight plastic bags for 8 h before specimen fabrication to ensure uniform distribution of moisture. The specimens were deemed suitable for testing when the density after preparation was at least 97% of the targeted MDD obtained from the preliminary compaction test for each soil.

Experimental Testing Procedures
Series of laboratory Civil Engineering testing programs routinely used to measure Geotechnical properties were conducted on the soil materials. The free swell index was conducted on the studied soils according to the Indian standard Is-2720; (Part 40) [23] test method to evaluate the swelling potential of the soils. The soils were passed through 425 μm sieve size (#40) and the soils were oven-dried at a temperature of 115°C. The expression in Equation 1 is used to evaluate the FSI values.
Where FSI is the free Swell Index, is the volume of soil in kerosene and is the volume of soil in water. The samples contained in the kerosene jar are used as the control, due to the non-expansiveness of the soils in kerosene.
In this study, matric suction was determined by the filter paper method in conformance with ASTM 5298 [24]. After 14 days, the contact and no-contact filter papers were retrieved, weighed and their water contents were determined following the procedures suggested by [25]. The filter paper moisture contents were converted to matric suction using Eq 2.
where ω is filter paper water content.

Zero Swelling Test
The ZST was carried out following IS 2720 (Part 41) [26]. The soil samples passing through ASTM sieve size of 4.75 mm (#4) were used. The specimens were prepared according to the initial compaction test, at various moisture contents and corresponding dry unit weights. The specimens were demolding and cut into slices of 25-mm height and 75 mm in diameter bearing the shape of a consolidation ring, and the oedometer ring was fitted into the sliced specimens. It was then wetted on a high-pressure oedometer frame under vertical stress of 0.1 MPa using distilled water as the specimens are loaded. Once the swelling starts, the vertical load was increased to prevent any vertical swelling. During this process, maximum swell and the vertical strain was allowed. When the swelling was complete, the total applied load was recorded. This is defined as swelling stress and this method has been widely employed internationally in determining the soil swelling stress [27]. The zero swelling experimental setups are shown in Fig 2. The same procedure continued until no additional swelling was recorded on the dial gauge. The swelling stress of the specimens was computed according to Equation 3.
where P s is the swelling stress in kPa, ∑ = 1 is the total sum of surcharge, g is the acceleration due to gravity 9.81 m/s 2 , is the beam ratio of the oedometer arm, ⁄ is the internal area of the ring.

Results and Discussions
The experimental test results covered the following test results: Atterberg limit, free swell index, swelling stress, and filter paper test. The laboratory results illustrate the geotechnical properties, and the results were carefully interpreted using an average of three specimens of each tested soil to eliminate discrepancies that might affect the test results. The study first evaluates the relationship between swelling stress and plasticity index. Subsequently, the correlations were used to develop predictive mathematical models for swelling stress.

Swelling Stress -PI Correlation
The interaction between swelling stress and the plasticity index of compacted expansive soil is illustrated in Fig 3. The soils demonstrate that swelling stress increases as the plasticity index increased. This increase was within the range of 35.71% to 43.93% with the corresponding swelling stress of 210 kPa to 880kPa, respectively. There is a great proportionality between the swelling stress and soil plasticity as the correlation for coefficients of determination are in the range of R 2 = 0.982 to 0.960. The test results could be associated with the fact that expansive soil undergone hydromechanics transformation from liquid limit to plastic limit and finally to plasticity. At these transformational phases, the soil swelling potential increases. The result agrees with the study published elsewhere by [28,29].  The swelling stress and free swell index values obtained at the dry side of moisture content were plotted as shown in Fig 4. It is observed that there is a great proportionality of the linear relationship between swelling stress and FSI with coefficient variability R 2 = 0.9055. Generally, it is noted that all the tested soils indicate a band of scattered points that rendered increasing trends of swelling stress with an increase in the free swell index. This implies that the soils are of high plasticity and could be attributed to their mineralogical composition. The tremendous amount of pressure exerted by expansive soil with high plasticity during swelling is a source of damages to lightweight structures such as shallow foundations and pavements. Thus, the relationship between the swelling stress and FSI is dominated by a combination of factors including the water content and percentage of available clay minerals. Several studies have been done on correlated clay content to swelling potentials. The soil with a higher percentage of smectite clay minerals renders higher swelling stress values and absorbed the highest amount of water during FSI testing. The FSI of the investigated soils ranges from 80% to 150% swelling of the measured initial percentage volumes due to sufficient specific surface with intermolecular forces of attractions. Based on the test results the mechanism of swelling for the expansive soil can be explained as follows. During the process of saturation water, the divalent cations (Ca 2+ , Mg 2+ ) in the surface soil layer migrate downward along with water molecules and aggregate around clay particles, eventually form the electrical environment. In this process, the cation exchange with expansive soil occurs where the bivalent cations (Ca 2+ , Mg 2+ ) enter into the diffuse double-layer (DDL) of clay particles and interlayer of montmorillonite crystals, resulting in the modification effect to restrain the swelling potential of the lower expansive soil layer. On the other hand, the hydrated exchangeable cations adhere to the soil particles and formed the adsorbed water film surrounding the aggregates, which produces crystalline swelling and diffuse double-layer swelling. Therefore, the FSI has a significant impact on swelling stress values. Reference [30,31] pointed out that the behaviour of the expansive soils depends on the fraction of macropores among soil particles, which is likely to account for an increase in swelling stress under moisture conditions.

Swelling Stress -Gravimetric Moisture Content Relationship
The swelling stress is classified in terms of its threat to structures, swelling stress values that are less than <150 kPa is classified as non-critical. Whereas the swelling stress values within the ranges of 150-170 kPa and 180-250 kPa are considered marginal and critical, respectively. Furthermore, swelling stress values greater than 250 kPa are classified as very critical according to [26]. The obtained swelling stress values of the investigated soils range from 250 kPa to 1000 kPa. This implies that the investigated soils are classified as critical to very critical classification. These values can generate problems and trigger serious consequences for existing structures. The scattered plot in Fig. 5 illustrates the correlation between swelling stress and moisture content of the investigated soils. It is noted that water content increases with a decrease in swelling stress. This implies that the soils recorded higher swelling stress values at low densities. The lower swelling stress values were noted at the wet side of the optimum as the dry density increases. The results concord with the outcome of the investigation conducted by [32] on the swelling pressure and meso-mechanism of Gaussian distribution under constant volume conditions, which revealed that the relation of expansive stress and initial moisture content depends on the change in the microstructure with diverse moisture contents. In addition, dry density and vertical stress influence expansive properties were also correlated with swelling stress.
The received correlation between water content and swelling stress is best reflected by a linear function and the regression coefficient R 2 of >0.911. However, the relation between expansive stress and moisture content in this study is in line with a report published by Çimen et al. [33] which demonstrated that expansive stress decreased while moisture content was increased. This difference could be associated with samples prepared at the dry side of the optimum which rendered smaller initial water content with more macropores. Therefore, the internal space was enough to allow for higher swelling stress. With an increase in the initial water content, the proportion of macropores decreased, causing the swelling stress to become large due to the restricted space to swell during the wetting process. A drop in swelling stress was observed as the initial moisture content shifted from the dry to wet side of the optimum.

Swelling Stress -Matric Suction Relationship
The suction and swelling stress relationships are presented in Fig 6. It is noted that swelling stress increases with increasing soil matric suction. The swelling stress and suction correlation are bi-linear and are typically described with linear curve fitting. Thus, the relationship portrayed an increase in swelling stress at a rapid rate with soil suction [34,35]. Moreover, at the initial water content blow the plasticity index, the swelling stress and matric suction recorded the highest values, respectively. At a phase beyond the plasticity index and optimum moisture content both swelling stress and matric suction, continue to increase. This implies that water content filled up the voids within the soil pores, therefore allowing no space for expansion. However, the type of clay minerals could also impact the response of the investigated soils. The obtained result agrees with the study initially published by [36], which states that the high content of smectite clay minerals influences the suction and swelling stress value of expansive soil up to 68%. The soil with low content of smectite clay minerals records low swelling stress and suction values. Thus, matric suction correlation with swelling stress is stress state variables of unsaturated soils that account for volume changes.
Based on the extrapolation of gravimetric moisture content versus, and dry densities used in this study with the corresponding matric suction values, ( ), all test data points were interpolated using model 4, and the suction matric curve against swelling stress was obtained as shown in Fig 6. = + 0.0585 , 2 = 0.9043 ( ℎ ) (4) where is the swelling stress, 0.0585 is the fitting parameter and 0.9043 is the coefficient of determination calculated from the slope of swelling stress against matric suction curve, which is relatively influenced by dry unit weight and moisture content of the soils as prescribed on the curve.

Figure 6. Swelling stress and suction correlation
Generally, the correlation between the swelling stress, plasticity index, FSI, GMC, dry density and matric suctions has been evaluated. A great proportionality between the swelling stress and matric suction rendered a variability coefficient of R 2 = 0.9043. However, this bi-linear relationship is influenced by soil mineralogy. Therefore, the investigated unsaturated expansive soil collected across Bloemfontein could trigger significant upward swelling stress beyond 250 kPa. Beyond this value, swelling stress is considered critical for lightweight structures. The presence of clay minerals responsible for swelling activities recorded a considerable influence on the swelling stress of the investigated soils.
Suction demonstrates the water retention capacity of the expansive soil, which is the driving force of water flow in unsaturated soil. Table 3 presents the variation of the matric suction with gravimetric moisture content. It is noted that the total and matric suction curves for the investigated soils response with gravimetric moisture content in a similar trend. Therefore, the gravimetric moisture content and matric suction values are summarized in Table 3. At the dry side of the optimum, the values of matric suction were high within a greater moisture range. A change in total suction is fundamentally equivalent to a variation in matric suction. Thus, soils with a high content of smectite clay minerals recorded the highest suction value because of their high potentials to retain water. The results demonstrate that matric suction dominated 85% of the total suction component as reported by Leong et. al, [37], which could be attributed to the soil's capillarity, pore size distribution, and hydromechanical interactions which are highly dependent on the soil mineralogy.

Development of Multi-regression Predictive Models for Swelling Stress
The variables presented in Table 3 are utilized as correlation matrices to perform multi-regression analysis using the NCSS11 program. The developed model in this investigation is based on the plasticity index, FSI, gravimetric moisture contents, and matric suction of highly expansive soils across Bloemfontein. These properties were selected due to their high coefficient of determination (R 2 ) values as presented earlier in this study. The soil properties are designated as independent variables, whereas swelling stress is set as a dependent variable. it was considered desirable to perform multilinear regression analysis based on each of the measured soil properties to predict the dependent variable and validate models with an independent dataset. Regression analysis is applied to assess the relationship between soil properties and swelling stress particularly for expansive soils [38,39]. The experimental data in Table 3 were used to develop the models, due to the influence of FSI, GMC, P.I., and matric suction on swelling stress.
The correlation matrix related to model 5 and 6 are presented in Table 4, as two constitutive models were developed to predict the swelling stress of compacted unsaturated expansive soils: Model 5 is built up with the following independent variables: plasticity index (P.I.), dry unit weight (γ d ), free swell index (FSI), and matric suction (ψ m ) with coefficients of correlation presented as: Model 6 is developed with the following independent variables: dry unit weight (γ d ), free swell index (FSI), and matric suction (ψ m ) with coefficients of correlation been summarized as: 1 , 2 , 3 and the intercept 0 .

Models Validation and Comparison
The data used for the model validation are presented in Table 5 and the geotechnical properties of the soils for the validation data indicated that the soil sample is of high expansiveness. Two equations reported by [40,41] were used for the validation of swelling stress, and equations are expressed in Eqs. 7, and 8a and b.
However, Plastic index (P.I.), GMC, FSI, dry density, and suction are factors that govern the swelling behaviour of expansive soils, because they are determined from the physicochemical mechanism of the soil. These properties are largely a phenomenological and user-defined concept. Thus, the determination of these properties for identical expansive soil samples has been reported to produce reliable results with a mean square error of close to zero, though it is sensitive to the specimen preparation method.  The validation of the developed swelling stress models using independent data set is presented in Figs. 7 through 9. The equations were compared with a randomly selected swelling stress equation as presented in equations from Table 4. The graphical illustration of the scatter plot followed the trend of a 1:1 line for the models. 4, 5, and 6 were developed by the Authors. This implies that the predicted values portrayed a good correlation concerning the independent values, with negligible disparities as presented in the curve. The Author's model 4 rendered the highest R 2 magnitudes corresponding to R 2 values of 0.858, the predictive equation is based on suction. Models 5 and 6 recorded the second-highest R 2 values of 0.931 and 0.890, respectively. It is noted that the model with only dry unit weight, FSI, and suction closely predicted the swelling stress values of unsaturated expansive soils due to the strong affinity of these soils with moisture and suction. It is also noted that for highly clayey unsaturated expansive soils, swelling is dependent on electrical, chemical, and physical forces that act on the surface of clay platelets. This surface force attraction is related to the interaction between the suction and moistures with capillary force. Furthermore, the hydromechanical properties of suction which reflect how the soil particles are bonded together by tension surface force as well as the structure of the clay minerals rendered a good fit of proportionalities between the suction and other soil properties.   Based on the independent data presented in this research, a comparison was conducted between the Authors and other models. It was observed that model 5 developed by the Authors rendered a very close approximation compared to the models by [40,41] which overestimated swelling stress. Generally, the summary performance of all the validated models is presented in Table 6. it is observed that the equations used for the prediction in this study provided a reliable degree of accuracy in the prediction of swelling stress based on the R 2 values. Contrary to other predictive models, Tu et al [41] equation rendered R 2 values of 0.796, this implies that the equation has low correlation capability compared to the models developed in this study.

SEM
SEM test was used to examine the morphological features of the investigated soils. EDS was also employed to aid the identification of chemicals and dominant phases through the elemental micrograph. Figs 10 through 14 illustrate the SEM micrographs of average soils from the five visited sites. The soil is comprised mainly of quartz grains interspersed with sparsely present smectite, silica, K-feldspar, plagioclase, illite, and calcite as the dominant clay minerals. Also, the structure of soils has dispersed fabric in a natural state as presented and consists mainly of flaky-like texture particles. This confirmed the high values of swelling stress as reported earlier in this study. The surface morphology of soils seems plain with content precursors of quartz, kaolinite, and hematite precipitates within micropore spaces at trace level. The formation of a flocculated soil structure is highlighted on the micrographs; the presence of a tetrahedral layer could be seen on the surface of each micrograph. The micrograph of the soils has a smooth surface in which the hydroxyls rendered a tetrahedron-enclosed silicon atom. The tetrahedron layer is combined in a sheet-like structure with a common plane.

Conclusions
In this study, assessment of swelling stress predictive models for compacted unsaturated expansive soils was investigated using models developed by the authors and models randomly selected from the literature. The models were validated using independent data set, based on the obtained validation curves, it was concluded that.
The performance level attained by the author's developed models implies that the three models could be used as a tool to minimize the uncertainties encountered in soil engineering projects with a high degree of accuracy.
Overall, the validity of the developed equations was checked using independent data, the check revealed a high level of coefficient of correlation compared to the selected models from the literature. The study clearly shows that the independent swelling stress data showed good agreement with the estimated values from the developed equations.
SEM analysis revealed that the soils are expansive, as confirmed by their corresponding values of micrographs analysis revealing, smectite, silica, K-feldspar, plagioclase, illite, and calcite as the dominant clay minerals.
The correlation of swelling stress with suction and gravimetric moisture content greatly influences the swelling stress values as it allowed for the development of a predictive equation with corresponding R 2 value of 0.9045 and 0.9235 respectively. The independent data proved that the developed models are reliable for predicting the swelling stress of compacted unsaturated expansive soils at high suction.
The plotted data points are close to the 1:1-line, standard deviator < 3%, mean squared errors for the developed models are approximately zero, the determination coefficient R 2 is greater than > 0.8. Graphical comparisons demonstrate a better correlation between the proposed models. These models could be reliably used as a tool to predict the swelling stress with allowable accuracy.