A Survey on the Relationships between Compression Index, Coefficient of Consolidation, and Atterberg Limits

2.1. Compression Index and Liquid Limit Relations

Compression index (Cc) and coefficient of consolidation (Cv) are two soil characteristics that can determine a soil's compressibility: capacity to reduce volume under pressure (Cv). The coefficient of consolidation is used to forecast how long it will take for a given amount of compression to occur, whereas the compression index is used to estimate settlement. Since Atterberg's limits of the soil's liquid limit (LL) and plastic limit (PL) can be determined quickly, cheaply, and quickly using representative soil samples collected during field exploration [1, 2] efforts have been made to predict the value of compression index of fine-grained soils from these limits ever since. Several scientists have studied the Compression Index and Liquid Limit Relations. Hamza Güllü et al. [3] conducted a study in Baghdad and aimed to establish empirical correlations between soil index properties, water content, liquid limit, initial void ratio (e) and the compression index for 69 fine-grained soil samples. The liquid limit values of the samples ranged from 32% to 62%. The relationship between the Cc and the LL was the most reliable among these correlations. The developed correlation in this study is suitable for the Baghdad region. (CC=0.00454LL – 0.01246, R2=0.87)(1) Kok Shien Ng et al. [4] showed a correlation between the Cc with the LL. The study was conducted on five remolded cohesive soil samples with different plasticity properties. The liquid limit values of the samples ranged from 29% to 46%. The correlation of the LL with the Cc presented a very high correlation coefficient. (CC=0.0062LL + 0.0165, R2=0.9241)(2) The soil samples used in the study by Kumar K [5] were collected from 6 different regions of India. Fine-grained soils (CH) are classified according to the Indian Standard (IS). The liquid limit values of the samples ranged from 63% to 70%. The R2 value shows a strong linear relationship between the Cc and the LL. (CC=0.001(LL) – 0.013, R2=0.865)(3) In the study of Puri et al. [6], soil samples were collected from North India. Geotechnical data were obtained from 1053 different locations in the state of Haryana. They created different relationships between the Cc and the LL using Linear Regression (LR) Analysis, Artificial Neural Network (ANN), Support Vector Machine (SVM), Random Forest (RF), and M5 Tree (M5P) models. According to R2 values, the accuracy of the M5P model was found to be the highest. Puri proposed three different empirical correlations according to varying liquid limit ranges. These correlations were suitable for use in Haryana and surrounding areas.

(CC=(0.0092LL) – 0.1091, R2 =0.92) LL≤29.25(4) (CC=(0.0017LL) + 0.1235, R2=0.92) 29.25< LL <37.35

Solanki [7] aimed to create empirical correlations between Cc and soil index properties with 135 literature data from 10 regions in Gujarat, India. The mineralogy of soil samples was fine-grained montmorillonite and kaolinite. The liquid limit values of the samples ranged from 30% to 60%. The correlation created in the model produced for shallow foundations provides a strong relationship between the LL and the Cc. (CC=0.0061LL – 0.0024, R2=0.8435)(7) Other researchers created empirical correlations through the compression index parameter and soil index properties; Sridharan and Nagaraj [8] performed conventional consolidation tests on ten soil samples. The initial water contents of these samples were kept almost equal to the liquid limits. While applying traditional consolidation tests, the British Standard is taken as a basis. In the study conducted on remolded clay samples, the liquid limit values of the soil samples ranged from 30% to 60%. The study showed a pretty strong relationship between the Cc and the LL as follows: (CC=0.008 (LL – 12), R2=0.8285)(8) Vinod P. and Bindu J. [9] performed studies on remolded marine soil. Eighteen highly plastic soil samples were collected from Kerala in India with gray and black marine clay characteristics. The liquid limit values of the soil samples ranged from 70.8% to 276.3%. The correlation between the Cc and the LL as a result of this study was developed, which had a perfect correlation coefficient. (CC=0.0055 (LL – 1.8364), R2=0.9407)(9) Slamet W. and Abdelazim I. [10] studied 20 samples collected from 10 boreholes in Pontianak, Indonesia. Independent variables associated with the compression index were; void ratio, water content, and liquid limit. The liquid limit values of the soil samples ranged from 17.1% to 62.46%. In the correlation between the Cc and the LL, the R2 value showed that the relationship between the two parameters is weak. (CC=0.01706 LL – 0.02209, R2=0.349)(10)

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Zaman et al. [11] used 14 undisturbed clay samples their study collected from Bangladesh. The liquid limit values of the soil samples ranged from 33.73% to 67.097%. The correlation between the Cc and the liquid limit was quite strong. This equation was suitable for use in Bangladesh soils. (CC=0.01 (LL – 13.61), R2=0.9805)(11) Binod Tiwari and Beena Ajmera [12] obtained 82 different natural samples by mixing montmorillonite, illite, kaolinite, and quartz in the laboratory. The soil samples in the study were collected from natural disaster areas in Japan. As a consequence of this study, the correlations between Cc and LL were determined as two types. The first of these (12) was for soils having activity less than 1. (CC=0.0075(LL), R2=0.920)(12) The equation proposed for soils with activity greater than 1 is very efficient with R2 value. (CC=0.012(LL), R2=0.943)(13) It was observed that most montmorillonite soil samples have an activity greater than 1. The researchers stated that the empirical equations created with the LL showed the highest performance among the correlations they created between the Cc and other soil index properties. In the study executed by Amit N. and S.S. DeDalal [13], they used 50 samples mixed with river sand and clay in different proportions. They mainly used bentonite and kaolinite, collected from West Bengal, India. Fourteen of the samples were classified as CH (High-plastic clay), 14 of the samples as CI (Intermediate-plastic clay), 20 samples as CL (Low-plastic clay), Low plastic silty- clayey soil (CL-ML), and a plastic limit of 1 sample could not be determined. In the study, Cc and LL together showed high compliance. (CC=0.0124LL – 0.1761, R2=0.993)(14) Ayşen Lav and Atilla Ansal [14] suggested correlations between the compression and soil index parameters. For this study, they used 300 soil specimens collected from laboratory data in Türkiye. The liquid limit values of the soil samples ranged from 23% to 166%. They presented an insufficient relationship between Cc and LL for all soils (Eq. 15). They suggested another correlation for Normally-Consolidated clays (NC) with sufficient R2 value (Eq. 16).

Gil Lim Yoon et al. [15] used 1200 marine clay samples collected from 3 different regions of Korea to establish correlations between Cc and soil index properties. Undisturbed soil samples were classified as CL, CH, Low-Plastic Silt (ML), and High-Plastic Silt (MH). Three hundred fifty-six soil samples were used for the west coast, and their liquid limits ranged from 24.5% to 77.9%. 603 samples were used for the east coast, and liquid limits ranged from 23% to 107%. 278 soil samples were used for the south coast, with liquid limit values ranging from 28.4% to 120.2%. Relatively strong correlations were observed between the Cc and the LL. (CC=0.012(LL + 16.4), R2=0.64) South coast

Akayuli and Ofosu [16] aimed to produce correlations between Cc and Atterberg limit properties by performing tests on 90 soil samples collected from Kumasi in Ghana. 60 of these samples were used directly in the model, and the other 30 were used to confirm the model in the estimation of the Cc. The samples used in the study were taken from the laboratory and collected under the same conditions. Samples were classified as weathered Brimian phyllites; their liquid limits ranged from 14.6% to 67.6%. As a result of the research, a reasonable correlation has been developed between the Cc and the LL for use in this region. (CC=0.004LL – 0.03, R2=0.784)(20) Kumar, Jain, et al. [17] created empirical equations in their study using soil samples collected from 16 different regions of Bhopal, India. Soil samples were classified as nine black-cotton soils, four red soils, three yellow soils, two bentonite soils, and five black-cotton soils with different proportions of bentonite. Their liquid limit values ranged from 41.28% to 140.56%. They used ten soil samples under the same conditions to verify their proposed equation. As a result of the study, Cc has a strong relationship with LL. (CC=0.0067 (LL) – 0.0364, R2=0.94)(21)

Salih [18] worked on soil samples from various Iraq regions. While obtaining this correlation, 76 undisturbed soil samples were used, and their liquid limit values ranged from 30% to 70%. As a result of this study, it was observed that there was a weak correlation between Cc and LL.

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Al-Khafaji et al. [19] aimed to generate new empirical equations using 1906 samples from previous studies. They used Robust Bi-Square software in MATLAB to avoid data outliers and obtain more realistic results. First, they produced a correlation (23) for LL >16 using conventional regression analysis. The authors stated that a low Root Mean Square Error (RMSE) value means that the model is 95% reliable. Then an equation (24) was created using Robust Bi-Square. This equation (24) provided higher accuracy with a lower RMSE and was deemed suitable for liquid limit values LL >17. Since most of the mineral soils are evaluated in the 16< LL <100, a reanalysis was performed on the data in this range using Robust Bi-Square. The equation (25) was created as a result of this analysis. The equations (24) and (25) obtained using Robust Bi-Square were almost similar and suitable for use in samples within the specified liquid limit ranges. (CC=–0.1096 + 0.01049LL‚ R2=0.7688)(23) (CC=–0.012 (LL – 17)‚ R =0.8617)(24) 2

(CC=0.0116 (LL – 16.6)‚ R2=0.7066)(25) Dway and Thant [20] studied six disturbed samples collected at 3 and 6 feet from 3 locations in Mandalay. Four of the soil samples were classified as CH (High- Plastic Clay) and 2 as CL (Low- Plastic Clay), and their liquid limit values ranged from 41% to 70.1%. Correlations between Cc and soil index properties were established using linear regression. The proposed equation between the LL and the Cc has been found to have a low correlation coefficient and cannot be used to predict the compression index. (CC=0.0027LL + 0.1994, R2=0.250)(26) In the study presented by Laskar and Pal [21], they studied three different soil samples collected from different regions of India. The study observed that the correlation between the Cc and the LL was quite reliable. (CC=0.0046(LL –1.39), R2=0.994)(27) Abbasi et al. [22] estimated the Cc using 26 soil samples from 5 provinces of Iran. The soil samples used in this study were fine-grained and disturbed. The researchers took care that the liquid limit values of the soil samples were below

2.2. Compression Index and Plasticity Index Relations

Bello et al. [31] studied eight migmatite-gneiss-derived laterite samples collected from Southwest Nigeria. Soils were classified as 37% low-plastic clay (CL), 37% medium-plastic clay (CI), 13% high-plastic clay (CH), and 13% medium-plasticity clay (MI). The plasticity index (PI) values ranged between 8% to 33.65%. Bello established correlations between the Cc and SI (Shrinkage Index), which is the range between liquid limit and shrinkage limit, LS (Linear Shrinkage), which shows a decrease in one dimension of soil expressed as a percentage of its original dimension, when the water content is reduced from its given value up to shrinkage limit, and PI. The most effective of these correlations was found to be the relation between the Cc and the PI. (CC=0.0028PI – 0.0052, R2=0.90)(37) Kok Shien Ng et al. [4] also found a correlation between the Cc and the PI. The PI values of soil samples ranged from 8% to 18%. Although this correlation is not very strong, it is usable without other index properties. (CC=0.0032PI + 0.1817, R2=0.7186)(38) Solanki [7] also presented a correlation between Cc and PI. PI values of soil samples ranged from 15% to 30%. The R2 value was satisfactory, although not as good as the liquid limit correlation. (CC=0.0082PI + 0.0915, R2=0.7862)(39) The equation proposed by Vinod P. and Bindu J. [9] was created for use in remolded marine soils. PI values ranged from 34.8% to 235.5%. The coefficient of this correlation was found to be relatively high. (CC=0.0086 (PI + 24.2674), R2=0.970)(40)

The correlation suggested by Zaman et al. [11] also showed a strong relationship between the Cc and the PI. In this study, PI values of soil samples ranged between 12.083% to 44.287%. (CC=0.0091PI + 0.128, R2=0.8864)(41) Like other researchers, Sridharan and Nagaraj [8] suggested a strong correlation between Cc and PI. The plasticity indexes of the soil samples ranged from 9.5% to 37.9%. (CC=0.014 (PI + 3.6), R2=0.91)(42) In Akayuli and Ofosu [16] study, when they examined the relationship between the Cc and PI, the R2 value showed a good relationship. (CC=0.007PI + 0.01, R2=0.580)(43) Gil Lim Yoon et al. [15] studied marine clay in Korea. Soil samples are divided into three subgroups according to their plasticity characteristics as the east, west, and south coasts. The relationship between Cc and PI was created only for the east coast compared to other soil index properties. This correlation demonstrated a good relationship between the Cc and PI. (CC=0.014PI + 0.165, R2=0.61)(44) Salih [18] worked with soil samples he collected from Sulaymaniyah city in Iraq. The correlation he created as a result of this study showed that the PI is unsuitable for finding the Cc. (CC=–0.0049PI + 0.2882, R2=0.44)(45) The correlation established by Dway and Thant [20] presented an inadequate relationship. In this study, the PI values of soil samples ranged between 25% and 48.8%. (CC=0.0038 PI + 0.22, R2=0.303)(46) In the article they published, Laskar and Pal [21] worked on only three soil samples. Plasticity index values ranged from 5% to 35%, and the correlation presented a relatively high R2 value. (CC=0.0058 (PI+13.776), R2= 0.991)

Barlett and Lee [32] presented a relatively low correlation for Cc estimation. (CC=0.0099PI + 0.2039, R2=0.1789)(48) Nesamatha and Arumairaj [25] used 5 different remolded stiff clays collected from India in this study. They established a correlation with Regression Analysis in Eq. (49). The R2 value was relatively high.

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(CC=0.003PI – 0.081, R2=0.91)(49) The study of Rashed et al. [26] was conducted using 46 undisturbed fine-grained soil samples collected from Iraq. The plasticity indexes of these soil samples ranged from 15.26% to 28.2%. According to the empirical equation, a strong correlation was found between the Cc and the PI.

cent. The empirical correlation they created presented an excellent relationship. (CC=0.007PL – 0.005, R2=0.75)(56) Ara S et al. [30] proposed a weak correlation between Cc and PL.

Shaikh et al. [28] derived a robust correlation between the Cc and the PI using organic clays with poor bearing strength from Khulna city, Bangladesh.

2.4. Compression Index and Water Content Relations

Vinod P. and Bindu J. [9] developed a reasonably strong correlation between Cc and natural water content (wn). The wn values of these samples varied between 64.7 and 184.3 percent. This correlation is suitable for use for marine clays in India.

(CC=0.017PI + 0.180, R2=0.904)(51) Jain et al. [33] conducted research using 44 soil samples from geotechnical studies in various regions of India. The samples were laboratory data obtained under the same conditions. The empirical equation they produced was found to be reasonably sufficient for the estimation of the Cc. It was stated that the equation in this study is valid for soil samples with PI values between 5 and 35 percent. (CC=0.0082PI + 0.0475, R2=0.8984)(52) Kootahi and Moradi's [29] study used data from approximately 500 marine clay samples from different researchers' studies. The soil samples used in this study had different plasticity and consolidation properties. As a result, the relationship between the Cc and the PI was found to be entirely satisfactory. (CC=0.013 + 0.020PI, R2=0.85)(53)

2.3. Compression Index and Plastic Limit Relations

Few studies in the literature examined the relationship between Cc and PL. One of these studies is by Kok Shien Ng et al. [4]. As a result of the study, a sufficiently good relationship was observed between these two parameters. (CC=0.0133PL – 0.0833, R2=0.6809)(54) Akayuli and Ofosu [16] also correlated the Cc and PL. They created an invalid relationship between these two parameters in their study on Brimian phyllites in the Kumasi area. (CC=0.003PL + 0.055, R2=0.43)(55) Another study that presented a strong correlation between the PL and the Cc was by Rashed et al. [26]. In this study, 45 undisturbed soil samples were used, and these samples were selected from among 60 samples collected from various parts of the Iraqi city of Sulaymaniyah. The PL values of these samples varied between 20 and 37 per-

(CC=0.0072 (wn – 12.625), R2=0.878)(58) Solanki [7] also created a correlation between the Cc and water content on soil samples collected from India. The soil samples' water content values ranged from 15% to 30%. The R2 produced an excellent relationship. (CC=0.0091wn + 0.0522, R2=0.77)(59) Slamet W. and Abdelazim I. [10] produced an imperfect correlation between Cc and natural water content. (CC= 0.01wn + 0.12, R2=0.24)(60) The correlation suggested by Zaman et al. [11] was strong and suitable for use in Bangladesh soils and similar types of soils. (CC=0.0158wn – 0.179, R2=0.8997)(61) Alptekin and Taga [33] performed Atterberg tests on 58 soil samples collected from Türkiye's Mersin city; samples were selected as 18 marine and 40 terrestrials. 4 were not plastic, so Atterberg tests were not performed on these four samples. The soil samples used in this study were undisturbed. For this reason, it is thought that more realistic results are obtained. (CC=0.0064wn – 0.0607, R2=0.598)(62) Soil samples used in the study of Lav and Ansal [14] were collected from Türkiye's different regions. Additionally, the authors divided the 300 soil samples into subgroups according to their consolidation properties. Relatively strong correlations were found between the water content and the Cc. The correlation produced for all soil is as seen in Eq. (63). Eq. (64) was produced for normally consolidated clays. (CC=0.012wn – 0.1, R2=0.758)(63)

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Soil samples used in the research by Yoon et al. [15] were collected from various regions of Korea. The 1200 data used in this study were characterized as undisturbed marine clay. Correlations were created for soils specific to 3 different regions of Korea. While estimating the Cc, it was understood that the water content would be sufficient for each coast.

In the study presented by Barlet and Lee [23], it was observed that there is a sufficiently strong correlation between the natural water content and the Cc.

Güllü et al. [3] conducted a study suggesting a correlation between Cc and natural water content. The correlation established on 69 fine-grained soil samples obtained from Baghdad city is suitable for use in the Baghdad region. (CC=0.00553wn + 0.05321, R2=0.53)(68) In the study of Akayuli and Ofosu [16], the correlation they formed between the Cc and the moisture content was considered to be weak for the Ghana region. (CC=0.002wn + 0.14, R =0.382)(69) 2

In the research of Sari and Firmansyah [34] 425 of 466 soil samples obtained from 25 different regions in Indonesia were used. This research was carried out to compare the correlations in the literature and check their suitability for use. Samples were divided into subgroups. Correlations were not suitable for use. (CC=0.0143wn – 0.0165, R2=0.5102) LL=0 – 100%; PI=0 – 70%

The empirical equation proposed by Dway and Thant [20] between wn and Cc was found to be moderately usable. (CC=0.01wn + 0.027, R2=0.491)(71) In their study, Laskar and Pal [21] used 3 different soil samples, and the water contents varied between 15 and 32 percent. (CC=0.0134 (wn – 7.034), R2=0.985)(72) Abbasi et al. [22] correlated the water content and the compression index using 26 fine-grained soil samples collected from different regions of Iran. Most of the soil samples were classified as low-plasticity clay. The correlation coefficient given by this correlation showed a strong relationship between these two parameters.

(CC=0.0163wn – 0.247, R2=0.6572)(74) McCabe et al. [24] examined 61 soil samples in their study on Irish soil. The water contents of these samples ranged from 34.7% to 244.1%. A robust correlation was observed between the Cc and the natural water content. Although this equation is unsuitable for use instead of oedometer tests in Irish soil, it was found to be reasonably sufficient in terms of preliminary prediction. (CC=0.014wn – 0.3175, R2=0.858)(75) Al-Ameri and Al-Kahdaar [27] produced an empirical equation using 40 different soil sample data from geotechnical reports in Ammarah, Iraq. The R2 value of this equation showed that a powerful equation was presented. (CC=0.0092wn, R2=0.946)(76) The equation by Kootahi and Moradi [29] is proposed for marine clays. These marine clays were collected from studies in the literature from different parts of the world. The R2 value of the equation showed that the water content parameter could be used to estimate the Cc. (CC=–0.093 + 0.012wn, R2=0.91)(77)

2.5. Coefficient of Consolidation Relations

Kassou et al. [35] studied settling and consolidation rates in the High-Speed Rail Project in Morocco. They showed that the elastic method using the pressure-gauge modulus gives more accurate results than the iodometric method. This correlation they produced agrees with the US Navy correlation and the Cv estimate. (CV=26.917LL – 2.57)

Asma Y. and Abbas F. [36] tried to estimate and define the relationship between the CV and LL in their studies in Central and Southern Iraq. The soil samples consisted of 280 undisturbed silty clay. The Casagrande method was used in liquid limit calculations, and Taylor's Square Root of Time Method was used in calculating the consolidation coefficient. Comparing data from Iraqi soil with data from other studies (US Navy study), it was seen that the curves overlap when LL equals 60, and there are deviations when it is less than or greater than 60. The presented curve was compared with the curve formed by the US Navy, and it was observed that the curves agree at one point (LL=60). As a result of the study, a good relationship was established between CV and LL.

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Figure 2. Relationships between Cc and PI. (CV=4258LL–1.758, R2=0.721)(79) Devi et al. [37] produced correlations between the consolidation coefficient and the Atterberg limit properties. Soil samples were collected from different regions in the

Manipur Valley (India). The five undisturbed samples included clay, silt, sand, and organic content. CV values were calculated by the Casagrande method. Among the liquid limit, plasticity index, and shrinkage indices, it was seen that the CV was better associated with the LL.

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(CV=–4x10–9 LL + 4x10–7, R2=0.8298)(80) (CV=–1x10–7 ln(PI) + 6x10–7, R2=0.5954)(81) (CV=1x10 e –6

Solanki's [7] study aimed to predict the consolidation parameters in alluvial deposits as much as possible. This study was conducted with data collected from 10 different regions of Surat (India). Soil samples contained montmorillonite and kaolinite clay. It was studied with 135 test data obtained from the literature. Correlations of CV with LL and PI were found to be entirely satisfactory. (CV=7.7525PI

(CV= 108 LL–6.7591, R2=0.7867)(84) Kok Shien Ng et al. [4] examined the relationships between CV and Atterberg limits conducted on five cohesive soil samples in Malaysia. Samples were designated as CI, CL, MI, and CI. CV values were determined by the Taylor method. It was concluded that CV was best associated with PI. The relationship with LL also gave good results. (CV=0.6155 –0.0183PI, R2=0.9599)(85) (CV=0.7519 – 0.0102LL, R2=0.8608)(86) (CV=0.859 – 0.0202PL, R2=0.6505)(87) In this experimental study, Sridharan and Nagaraj [38] investigated the relationships between CV and LL, PI, and Shrinkage Index (SI) on ten disturbed soil samples. Soil samples contained varying proportions of silt, sand, and mainly kaolinite clay. As a result of the study, it was found that CV had a good relationship with the plasticity index, and the best relationship was with the shrinkage index. (CV=4,3x107 (PI)–4.7, R2=0.6087)(88) (CV=3x10–2 (SI)–3,54, R2=0.8836)(89) Bello et al. [31] studied eight disturbed samples in southwestern Nigeria. The liquid limit values of the samples were almost the same. As a result of the studies, it was observed that the correlation between CV and PI was more substantial than other parameters. (CV=1x10–9 PI–0,35, R2=0.62)(90) Jadhav's experimental work [39] was carried out on 20 different soil samples from different parts of Begaldot district, Karnataka state, India. At the end of the study, it was

found that the relationship between the coefficient of consolidation and shrinkage index (SI) was. (CV=128.7/ (SI) 3.54 + 0.0002, R2=0.715)(91) Shaikh e al. [28] correlated the consolidation coefficient with LL and PI in 2 relationships. The R2 values of these relations were found to be entirely satisfactory. (CV=0.241e–0.08LL, R2=0.818)(92) (CV=0.022e–0.12PI, R2=0.790)(93) In the study of Vinod P. and Bindu J. [9], the slope value of the correlation they created between the compression index and the plasticity index was given as 0.0086 in Eq. (40). However, the slope value was found to be 0.0056 in the equation reconstructed with the help of linear regression as seen in Figure 1. In addition, the R-square value was calculated and found to be 0.9407 in Eq. (94). (CC=0.0056PI + 0.2086, R2=0.9407)(94) Figure 2 depicts the relationship between CC and PI. Data obtained from several research have been compared with each other. As it can be seen, the correlation factors show a good consistency between the mentioned parameters.