Introduction

The geotechnical properties of soils are important parameters to sketch better engineering designs. These geotechnical properties can be grouped into the physical and engineering properties of the soil. Physical properties are which represent the behavior of the soils at the in situ level; generally, these properties are influenced by the geology of the area, while the engineering properties are mostly used in engineering design calculations. The testing procedures were selected based on the accuracy of the results, the cost for the testing, method and accepted a degree of disturbance during the sampling, soil type, project requirements, and time limitation (O’Neill et al. 1995; Vipulanandan et al. 2006, 2007a, b; Siraruban 2008; Mohammed 2018a, b, c, d). The availability of better correlations between geotechnical properties minimizes the cost of experiments as well as speeds up the design steps. Hence, many researches are being conducted to investigate the relationship between important geotechnical properties (strength, modulus, density) and easily measurable soil properties (liquid limit, plastic limit and moisture content) (Ganstine 1971; Bilgin et al. 2013; Arulrajah et al. 2008). Dennehy (1978), investigated relationship between Su with LL for remolded marine clay soil samples which were prepared at different moisture content. There are many relations reported in the literature between undrained shear strength (Su) and index properties for field deposits of clay soils (Duncan 2005; Ganji 2006). Ganji (2006) investigated the linear relationship between the physical and engineering properties of Houston clay soils. Vipulanandan et al. (2007a, b) have developed linear relationships between the geotechnical properties of clay soils. It is considered that Atterberg limit tests are not only convenient but may also provide a cheaper method of assessing the quick undrained shear strength of clays (Yilmaz 2000). Since undrained shear strength (Su) is considered as the main strength parameter, in this study, nonlinear relations between Su and the index properties of Sulaimani soils are investigated with better correlations of coefficients (R). Both the deltaic and marine clay deposits are bounded by the U-line and A-line in the plasticity chart. In the past, many researchers have developed correlations between the soil index properties, strength parameters and consolidation parameters for various clayey soils (Arulrajah et al. 2008).

This study focused on characteristics of the consolidation and strength properties of soils using the results of 85 boreholes with depth of 6 m underground and presents the experimental results using ArcGIS map. Horpibulsuk et al. (2007) investigated the relationship between the PI and LL of Bangkok marine clay, as mentioned in Eq. (1), with R2 of 0.94.

$${\text{PI}} = 0.79 \times {\text{LL}} - 10.27.$$
(1)

The behavior of fine soils is defined based on their index properties such as liquid limit (LL), and plasticity index (PI). A major stage in geotechnical engineering is to establish geotechnical properties of soil models based on the empirical equations using the experimental test data. Undrained shear strength (Su) and compression index (Cc) are the main parameters in the state design of the footings, pavements, or stability assessment of existing structures or slopes. However, Su is not a fundamental soil property but depends on factors such as the moisture content, index properties and density (Westerberg et al. 2015). The undrained shear strength (Su) and compression index (Cc) were used to predict the amount of bearing capacity and consolidation settlement of the footings, respectively (Sridharan et al. 2000). The engineering behavior of soils mostly depends on the constitution of the controlling parameters of clay soils, such as moisture content and index properties, strength, and density. There are several soil property relationships that have been quantified in the literature, which are summarized in Table 1. Vipulanandan et al. (2007a, b) investigated relations between undrained shear strength (Su) of the soft deltaic clay to the moisture content of the soil. It is considered that Atterberg limit tests are not only convenient but may also provide an easy procedure method for assessing the quick undrained shear strength of soils (Su) (Yilmaz 2000; Tiwari et al. 2011). Geotechnical investigation contributes predominantly to the total cost of the project. Therefore, this aspect is overlooked due to the absence of an abundance of sufficient funds available for this important task. Geotechnical data gathered from various governments and private organizations in the midst of project planning are accepted to be a fundamental part in the framework of building and foundation works.

Table 1 Literature review on geotechnical properties correlations of the clay soil
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Geographical information system (GIS) is an extremely powerful tool for catching, showing and examining topographically referenced information (Sivaruban 2008; Mahar et al. 1983; Keller et al. 1985). This work has been performed in the field of Sulaimani City soil mapping zones, utilizing GIS tools. Also, in this study, interest was in the correlations and statistical variation of Sulaimani City soil properties, such as liquid limit, plasticity index, density, and undrained shear strength (Su), since the method of statistics is a tool used to analyze the special variation of data. Statistical tools including mean, standard deviation, variance, range, and COV were used in the analyses. Since undrained shear strength (Su) was considered as an important strength parameter, nonlinear relations between (Su) and the index properties (LL and PI), moisture content (MC) and dry density (γd) of Sulaimani City soils were investigated and it correlated well based on the coefficient of determination (R2) and the root mean square error (RMSE).

Vipulanandan correlation model

For shear thinning fluids, the shear stress–shear strain rate relationship is nonlinear with a limit on the maximum shear stress tolerance. Similar trends have been observed in many other engineering and environmental applications and have been modeled using the Vipulanandan correlation model (Qadir et al. 2019a, b; Abdulla et al. 2019; Mohammed and Vipulanandan 2014; Mohammed and Mahmood 2018a, b, 2019a, b). Qadir et al. (2019a, b) and Mahmood et al. (2019) used Vipulanandan correlation model to represent the change in grouted sand properties and cement mortar with curing time. Mohammed and Vipulanandan (2014) used the hyperbolic relationship to predict the relation between compressive and tensile strength of sulfate-contaminated CL soils with and without polymer treatment. In addition, Vipulanandan and Mohammed (2014, 2015, 2018a, b) used the Vipulanandan correlation model to predict shear stress versus shear strain rate and the maximum shear stress of drilling mud and oil well smart cement.

Methods and materials

The boreholes were drilled, and the disturbed and undisturbed soil samples were collected from the northwest of the Sulaimani City area as shown in Fig. 1, and then all the data were digitized for analysis. Around 630 soil properties data were collected from 85 boreholes (BH) (Fig. 1b). This data set was extruded, tested and reported by the Ministry of Construction and Housing/Construction Laboratories/Sulaimani City in between 2017 and 2019. Most of the data were taken from the clay type of soil. SC type of soil has the lowest percentage distribution. Every 1.5 m depth up to 6 m were taken into account in this analysis. The mean, maximum, and minimum soil properties were reported for each BH and the standard deviation and coefficient of variance were also reported.

Fig. 1
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ArcGIS map of Sulaimani City: a study area and b main streets and boundary line with BH locations

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The study area

The area of study is located between two latitudes 29.840 N and 30.54 N and between two longitudes 74.70 E and 75.32 E. The area of study is 1 of the 22 districts of Sulaimani City, Kurdistan Region, Iraq. The total area of study district is 131.227 km2.

Georeferencing of boreholes

The georeference tab is a tool in ArcGIS. It is used to georeference a normal borehole map with a known coordinate map. Using this tool, the boreholes were located on the parcel map. This map was georeferenced using the street names with the Sulaimani City parcel maps. The locations of all the boreholes were more concentrated on the northwest part of Sulaimani City as shown in Fig. 1. Atterberg limits and shear strength were taken as the major variables. The spatial variations of Atterberg limits studies were also performed up to a depth of 6 m underground.

Test methods

The soil samples were extruded, tested, and reported by the Ministry of Construction and Housing/Construction Laboratories/Sulaimani, and all the tests were performed according to ASTM standards.

Particle size distribution (ASTM D 6913)

Both sieve analysis and hydrometer analysis for the field soils were used to determine the particle size distribution of the soils.

Atterberg limits

Liquid limit and plastic limit tests were conducted on the soil samples based on ASTM D 4318.

Unconfined compression tests (UCS)

The test for the undisturbed soil samples was conducted according to ASTM D-5102. The unconfined compressive strengths (qu) were determined from the stress–strain relationships. The undisturbed soil samples were extruded from the Shelby tubes using a hydraulic jack. Soil samples were weighed to crosscheck the wet unit weight.

Vipulanandan correlation model

Nonlinear relationships between the physical properties, compression properties, and free swelling of the Sulaimani soils were investigated. Based on the inspection of the test data and the data collected from the literature, the following relationship is proposed (Vipulanandan and Mohammed 2014):

$$\Delta y = Y - Y_{\text{o}} = \frac{X}{(A + B \times X)},$$
(2)

where Y is the soil property (dependent variable); Yo, A and B are the model parameters (Table 3) and X is the soil property (independent variables).

Results and analyses

The liquid limit, plasticity index, density, moisture content and undrained shear strength values were imported into ArcGIS up to a depth of 6 m. The values were interpolated over the selected area to identify the spatial distribution of soil properties. The statistical details and the histograms were developed for each depth data set to identify the distribution. The statistical results are summarized in Table 2. The histograms of liquid limit, plasticity index, density, moisture content and shear strength are as shown in Fig. 2. The liquid limit values are imported into ArcGIS up to a depth of 6 m. The values were interpolated over the selected area to identify the spatial distribution of liquid limit. The statistical details and the histograms were developed for each depth data set to identify the distribution.

Table 2 Statistical parameters of geotechnical properties for Sulaimani City soils
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Fig. 2
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Histogram of the Sulaimani City soil properties: a dry density, b moisture content, c liquid limit, d plasticity index, e undrained shear strength

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Soil type

Soil type is the most critical issue in geotechnical engineering that is identified with a number of cases. In the study area, the real collection of soil for the most part found was silt, clay, and sand. The conduct of each type of soil is different, in view of its geotechnical engineering characteristics. Consequently, the motive of soil investigation is truly important to understand the soil types prior to the start of a project. The suitability of the test additionally relies upon the kind of soil. There are two types of results used to present the data, i.e., statistical results and results in the form of zonation maps using ArcGIS tools.

Silt and clay contents

Silt and clay content if present in a large percentage is problematic for the foundation of buildings. Therefore, it is necessary to evaluate its presence. The range of percentage of silt and clay at 1.5 m depth is 27–97%, and the minimum silt and clay content go on decreasing as we go deeper into the soil reaching 5% at 6 m depth. The average silt and clay content varies from 97% at 1.5 m to 27% at 6 m depth. The standard deviation of the silt and clay content at 1.5 m depth is 18.6 but at 6.0 m depth, its value is 22. The coefficient of variation ranges between 0.28 and 0.82, which signifies that variation goes on increasing with depth.

Data presentation using ArcGIS

Liquid limit

Thematic maps showing the variation of soil type along the 6.0 m depth of soil strata at different locations of Sulaimani City, Kurdistan Region, Iraq are presented. Four zonation maps have been presented in this paper at depths 1.5 m and 6 m, respectively, as shown in Fig. 3. In all the cases, depth has been taken from natural ground level (NGL). All the maps are divided into six major zones. Each zone is represented by a unique color. The type of soil at 1.5 m depth is shown in Fig. 3a. At this depth, the major portion of map is covered with yellow and green signifying the presence of silt and clay content (fine content) of more than 50%. The portion under silty sand increases as compared to area at 1.5 m depth, as represented by brown and pink colors in the map as shown in Fig. 3. At a depth of 6 m, it can be viewed that about 50% of the area is brown and pink, which represents silty sand. Liquid limit with a range of 45–50% is presented only at very few locations as represented in green color. Here the area under poorly graded sand increases as clear from ceramic brown color, as shown in Fig. 3d. Similarly, it can be seen from the Fig. 4 that as we move deeper, the area under silty sand in blue color and poorly graded sand in dark color is more and goes on increasing with depth. This depicts that the sand content goes on increasing, and silt content goes on decreasing with depth.

Fig. 3
figure 3figure 3

Spatial variation of liquid limit with depth: a 1.5 m, b 3 m, c 4.5 m, d 6 m

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Fig. 4
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Spatial variation of plasticity index with depth: a 1.5 m, b 3 m, c 4.5 m, d 6 m

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Statistical variation of Sulaimani City soils

The histograms were analyzed and it was found that every depth has a good distribution of data. The maximum and minimum values were in the allowable ranges. The spatial variations of moisture content, Atterberg limits, density and undrained shear strength are shown in Fig. 2.

Dry density (γd) (ASTM D 7263)

Based on the total of 630 γd data for Sulaimani City soils, the data varied from 1.15 to 1.92 g/cm3 with a mean of 1.65 g/cm3, the standard deviation of 0.1 g/cm3, and the coefficient of variation (COV) of 0.06% as shown in Fig. 3a. The dry density of the Sulaimani City soils was calculated from moisture content and wet density.

Moisture content (MC %) (ASTM D 2216)

Based on the 630 MC data for Sulaimani City soils, the data varied from 8 to 32% with a mean of 18%, standard deviation of 6%, and coefficient of variation (COV) of 0.30% as shown in Fig. 2b.

Liquid limit (LL)

Based on a total of 630 liquid limit (LL) data of Sulaimani soil values, the average LL was 39%. The LL varied from 28 to 50%, with a standard deviation of 5.3% and the coefficient of variation (COV) of 0.13% (Table 2). Based on the tested data for Sulaimani City soils and 3702 data records from the literature, the LL with the plasticity index (PI) was represented using Eq. (3) and the coefficient of determination (R2) for the relationship was 0.96.

As shown in Fig. 5, Sulaimani City soils are compared with 3702 data records collected from the literature and bounded by U-line and A-line in the plasticity chart. There was a good relationship between PI and LL which was identified as follows with a higher R2 of 0.96.

Fig. 5
figure 5

Linear variation of liquid limit (LL) and plasticity index (PI) for Sulaimani City soils

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$${\text{PI}} = 0.72 {\text{LL}} - 8.3\quad {\text{No}}.{\text{ of data}} = 3 70 2,{\text{ RMSE}} = 3. 5\% , \, R^{ 2} = 0. 9 6.$$
(3)

Plasticity index (PI)

Depending on the 630 PI data records for the Sulaimani soils, the data varied from 11 to 25% with a mean of 18%, standard deviation of 3.53%, and coefficient of variation (COV) of 0.19% as shown in Fig. 2d and summarized in Table 2.

Undrained shear strength (Su)

Based on the tested data and a total of 630 undrained shear strength (\(S_{\text{u}} = \frac{{q_{\text{u}} }}{2}\)) data for the CH soil collected from literature, the data varied from 10 to 119 kPa with a mean of 76 kPa, standard deviation of 19 kPa, and coefficient of variation (COV) of 0.24% as summarized in Table 2.

Nonlinear regression model

Based on experimental and collected data from literature, it was assumed that the undrained shear strength (Su) (kPa) of soils will be influenced by the liquid limit (LL %), plasticity index (PI %), dry density (γd) (g/cm3) and moisture content (MC %). The models were analyzed using multiple regressions; because of nonlinear predictions, logarithmic values were selected for this analysis. The logarithmic multiple regression is:

$$S_{\text{u}} = k \times \frac{{({\text{LL}})^{a} \times ({\text{PI}})^{b} \times (\gamma_{\text{d}} )^{c} }}{{({\text{MC)}}^{d} }},$$
(4)

where k, a, b, c and d are nonlinear model parameters.

Sulaimani City soil properties correlation

The relationship between moisture content (MC) and dry unit weight (\((\gamma_{\text{d}}\))

A total of 800 soil data records were collected from various research studies. The tested data and the data collected from the literature were quantified using the Vipulanandan correlation model (Eq. 2), as shown in Fig. 6. The model parameters Yo, A and B are summarized in Table 3, while the coefficient of determination (R2) and root mean square error (RMSE) for the Vipulanandan correlation model relationship were 0.98 and 0.021, respectively, as summarized in Table 3.

Fig. 6
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Non-linear variation of moisture content (MC) and dry density (γd) of Sulaimani City soils compared with data collected from the literature

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Table 3 Vipulanandan correlation model parameters for Sulaimani City soils
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The relationship between liquid limit (LL) and free swelling (FS)

A total of 93 clay soils data were collected from various research studies. The data collected from the literature were quantified using the Vipulanandan correlation model (Eq. 2) as shown in Fig. 7. The change in the LL with \({\text{FS }}\) of clay soils was represented using Eq. (2) and the model parameters Yo, A and B are summarized in Table 3. The coefficient of determination (R2) and root mean square error (RMSE) for the relationship were 0.81 and 0.02, respectively, as summarized in Table 3.

Fig. 7
figure 7

Non-linear variation of liquid limit (LL %) and free swelling for clay soils

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The relationship between liquid limit (LL) and void ratio (eo)

A total of 62 clay soils data were collected from the various research studies. Based on a total of 62 eo data records for the soils collected from literature, the data varied from 0.5 to 1.04 with a mean of 0.91, standard deviation of 0.19, and coefficient of variation (COV) of 0.25% (Table 2).

The initial void ratio eo with LL of the clay soil was represented using inverse Vipulanandan correlation model (Eq. 2) as shown in Fig. 8 and the model parameters Yo, A and B are summarized in Table 3, while the coefficient of determination (R2) and root mean square error (RMSE) for the relationship were 0.80 and 0.001, respectively, as summarized in Table 3.

Fig. 8
figure 8

Non-linear variation of liquid limit (LL) and initial void ratio (eo) for clay soils

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The relationship between undrained shear strength (Su), index properties, moisture content and dry density

The correlation between Su with MC, Su with LL and Su with PI has been studied. Based on the R2 and RMSE, there were no correlations were observed between shear strength of the soils and LL, PI, MC and density, as shown in Fig. 9. It was assumed that the undrained shear strength (Su) (kPa) will be influenced by the liquid limit (LL %), plastic index (PI %), dry density (γd) (g/cm3), and moisture content (MC %). The models were analyzed using multiple regression. The nonlinear multiple regression is:

Fig. 9
figure 9

Variation of undrained shear strength (Su) for the clay soils with a moisture content, MC (%), b liquid limit, LL (%), c plasticity index, PI (%), d dry density

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$$S_{\text{u}} = 26.3 \times (\gamma_{\text{d}} )^{1.9} \frac{{({\text{LL}})^{0.5} }}{{({\text{PI}})^{0.3} \times ({\text{MC}})^{0.2} }}.$$
(5)

The coefficient of determination (R2) and RMSE of 376 numbers of data were 0.87 and 1.05, respectively, as shown in Fig. 10. Figure 11 presents undrained shear strength of the Sulaimani City soils at 6 m depth.

Fig. 10
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Comparison between measured and predicted undrained shear strength for soils

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Fig. 11
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Typical spatial variation of undrained shear strength of the Sulaimani soils at the depth of 6 m

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Conclusions

The focus of this study was to characterize the Sulaimani soils based on its geotechnical and strength properties. Geostatistical properties of Sulaimani soils and GIS mapping were also investigated. Correlation between geotechnical properties was examined based on experimental data and collected data from literature and analytical model. Based on this, the following conclusions were advanced:

  1. 1.

    GIS is an effective tool for collecting, displaying and reading geographically documented information. GIS showed numerous uses in geotechnical engineering projects, and interpolation for exploit statistics at inaccessible places through processed graphs, maps, and charts.

  2. 2.

    The majority of soil profile consists of silt of low compressibility to silty sand with few traces of clay, especially for shallow depths to 6.0 m depth. Poorly graded sand was encountered at noticeable locations at a depth of 4.5 m or more.

  3. 3.

    The variation of geotechnical properties of the clay soils showed a good correlation between the compression properties such as undrained shear strength (Su) and compression index (Cc) with easy geotechnical properties measurement of clay soils.

  4. 4.

    Based on the R2 and RMSE, there were no direct correlations between the undrained shear strength (Cu) and index properties (LL and PL), moisture content (MC) and density (γ) of the clay soils.

  5. 5.

    The undrained shear strength (Su) of clay soils was in the range of 10–119 kPa. The compression index (Cc) of clay soils was in the range of 0.05–0.55. Undrained shear strength (Su) of soils quantified very well as a function of index properties, moisture content and dry density of the soils.

  6. 6.

    These results can help structural and foundation engineers during the process of foundation analysis, estimation of geotechnical investigation cost and planning and execution of different projects associated with civil engineering.