The Empirical Correlation Using Linear Regression of Compression Index for Surabaya Soft Soil

*Putu Tantri Kumala Sari, Yerry Kahaditu Firmansyah

Faculty of Civil Engineering and Planning, Sepuluh Nopember Institute of Technology

(ITS), Surabaya, 60111, Indonesia. Email: tantrigeoteknik@gmail.com;dedariku@cs.its.ac.id

Faculty of Civil Engineering and Planning, Pembangunan Nasional “ Veteran “ East Java (UPN), Surabaya, 60294, Indonesia.

Email: yerry_kaha@yahoo.com

ABSTRACT

Laboratory consolidation testing to obtain the value of compression index (Cc) is time consuming and costly compared with another laboratories soil testing, so the empirical formulation is preferred in the application for designing. Empirical formula to obtain the value of compression index has been developed since the 1940s in many countries, but there is still a view empirical formula derived from soft clay in Indonesia whereas the characteristics of the soil in Indonesia with other countries is not necessarily the same. This study was conducted to compare dozens of existing empirical formula with 466 soil samples from 77 points of data bore holes at 25 locations spread in Surabaya area, Indonesia. Based on a comparative analysis of existing empirical formula with the soil sample data indicates that, there is a difference between the values of Cc empirical formula with the results of laboratory testing soil data. Then the comparison results are used to find the empirical formula of index compression by linear regression method for Surabaya soft soil. 1. INTRODUCTION Compression index value is required by the geotechnical to determine the soft clay soil settlement. The value of soil settlement needed to do for a lot of designing of building simple houses and build roads embankment. Calculation of soil settlement is considered very important to avoid differential settlement which led to cracks in the building structure thereon shallow foundation. If the compression calculations are eliminated, then of course the danger of damage structures can occur that result in increasingly high price of repair of the building structure. In the calculation of soil settlement, Compression index value is very decisive than the other soil characteristics value such as void ratio and soil unit weight. However, the value of Compression index testing in the laboratory requires much more time and the cost of laboratory testing is relatively expensive compared to other soil characteristics testing. For comparison, the calculation of unit weight and void ratio can be completed within 1-2 day, while the calculation of the Compression index with one-dimensional

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consolidation test in laboratory is completed in more than 1 week. Whereas planners and engineers usually needed that data quickly, so the use of the empirical formula is preferred. Lots of empirical formula approach has been tested on soft clay soils in some developing countries. The empirical formulations derived from correlate the soil consistency values and soil characteristics which are more easily tested in the laboratory. Some predictions formulation of empirically based from Liquid limit value has been tested by Skempton (1944); Terzaghi & Peck (1967) and Bowles (1979), based from Plasticity Index has been tested by Jian-Hua Yin (1999); AmithNath and DeDalal (2004) based from Shrinkage Index has been tested by Sridharan and Nagrai (2001). Other formulas also been extensively tested in several countries, among others: Azzouz et al (1976) who tested Chicago clay, Brazilian clay, Clay Motley from the city of San Paulo and USA clay as well as in Greece based on the value of water content, void ratio and Liquid Limit; Nacci et al (1975) conducted tests on clay in the North Atlantic based on the value of plasticity index. Not only those, dozens of other formulations have also been developed to correlate the characteristic value of void ratio, specific Gravity and water content. Some of these formulations are developed by Azzouz, Krizek and Corotis (1976); Wroth and Wood (1978); Nagaraj and Murthy (1986; 1986); Ostenberg (1972); Cozzolina (1961); Sower (1970); Moran, Proctor, Mueser and Rutlrdge (1958). The formula offered to the entire soft clay. Empirical formulas that have been developed in an 80 years period are slightly helps the engineer to performing design calculations. However, the developed formula is only the correlation result of the clay types that exist in other countries not in Indonesia, especially in the city of Surabaya. Whereas, this type of soft clay in Surabaya, Indonesia is not necessarily the same as the type of soil in other countries. Moreover, Indonesia is a tropical country with has 2 seasons through where have a lot of the river flow on each island by the type of soil will differ from one island to the other islands and regions with other regions. The characteristics of the soil types in each of the island in Indonesia are different, and also the Indonesian soil conditions when compared to soil in another country, it will be much different. Unfortunately, in order to shorten the testing time and reduce the cost of consolidation test, the use of empirical formulas soil test results in other countries more often used by planners in Indonesia. To avoid planning errors due to empirical formula of selection fault for obtaining the value of compression index, it is necessary to test the soil sample especially in the city of Surabaya to obtain empirical formula index values for Surabaya soil. Previously, testing the empirical formula for soft clay in Indonesia have been done, but still in small scale laboratory tests. Tests conducted by Kosasih and Mochtar (1997) who obtained an empirical formula to obtain the value of compression index of the relationship of the value of void ratio, water content and plasticity index. The formulation of multiple samples obtained from laboratory testing on soft clay soils; the Liquid limit on the value is the variable. Results of this empirical formula are used for comparison in this study. The data used in this study were all consolidated soil test data with the one-dimensional Oedometer test on clay soil in Surabaya. The data obtained from the soil mechanics laboratory, Sepuluh Nopember Institute of Technology Surabaya. Samples were taken in the vulnerable period of the last 20 years, from the 1980’s until the 2000’s

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because it was considered more accurate and valid results. Number of samples is considered worthy (clay soil consistency) for testing is taken from 25 locations in Surabaya with 77 numbers of borehole and 466 test sample. The purpose of this study is to compare the results of the compression index data from laboratory test results with empirical formulations that already exist. Then, if the value of compression index results with empirical formulation is very much different from the value of the data consolidation testing laboratory, a linear regression test is needed to obtain values for the empirical formulation of soil data in Surabaya. Expected, the resulting empirical formula can be used to calculate the value of index compression in order to reduce the time and cost of testing. 2. TEST RESULTS AND COMPARATIVE SAMPLE Soil sample test results can be seen from Fig.1 which is based on the value of void ratio, water content, soil consistency based on the value of LL, PL and IP, unit weight, specific Gravity the value of compression index. The soil is saturated clay which has a unit weight value between 1.5 to 2 t/m3, void ratio between 0.4 to 3.7. The Limitation value of the soil and the consistency of the soil types tested can be seen in Fig.2.

0

0.5

1

1.5

2

2.5

3

0 50 100 150

Compretion Index Cc

Water content Wc (%)

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5

(t/m3)

0

0.5

1

1.5

2

2.5

3

0 50 100 150

Compretion Index (Cc)

Sr (%)

0

0.5

1

1.5

2

2.5

3

0 50 100 150

Plastic  Limit PL (%)

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Fig.1. Soil data (water content (%), Weight Volume (t/m3), Degree of saturation (%), consistency of soil (LL, PL, IP (%)), void ratio, Specific Gravity (%)) from results of

laboratory testing

The implementations of the other soil sample test are conducted by looking at the value of the soil consistency by Atterberg Limit testing. Liquid limit and plastic limit has been used extensively by the civil engineering expert for determine the correlation from several soil parameters and also for identify soil. Casagrande (1932) have studied the plasticity index and liquid limit of a variety of original soil incorporated in a chart. Terms that important in the chart is an empirical A-line that separates soil clays inorganic and silt inorganic. Soil clays inorganic are located above the A-line and soil silt inorganic located below the A-line. Inorganic silt soil with moderate compression is below A-line with LL that range between 30-50%. Organic clays being in the same area as inorganic silt soil with high compressible ability (below the A-line with LL greater than 50%). Based on the consistency of the soil in Fig.2, the type of soil is dominated by inorganic clay which is the plasticity values tend to be moderate to high and to very high. Some of the data in above the U-line and below the A-line (silty likely) is deleted and not used in this study.

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4

Compretion Index Cc

Void Ratio  eo

0

0.5

1

1.5

2

2.5

3

0 50 100 150Index Plasticity  IP (%)

0

0.5

1

1.5

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2.5

3

0 50 100 150

Compretion Index Cc

Liquid Limit LL (%)

0

0.5

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1.5

2

2.5

3

1.5 2 2.5 3 3.5Specific Grafity (Gs)

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Fig.2. Plasticity chart for soil data in Surabaya.

Based on the results of data sorting from the Atterberg limit consistency and classification soil value, from the 466 existing data only decent 425 soil samples used in the testing data. After testing the soil data, then compared the index compression value with the existing laboratory data. The data compared with 28 existing empirical formula. Results of the comparison formula can be seen in Table 1 below.

Table 1. The percentage value of goodness of fit in a comparison of the empirical formula result with the existing soil data.

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

0 20 40 60 80 100 120 140

Plasticity Index (Ip) (%

)

Liquid Limit (%)

A‐Line

Laboratorium result

U‐Linenon‐cohesivesoil

anorganic clay with low plasticity

anorganic clay with medium plasticity

anorganic clay with high plasticity

anorganic siltwith low comprecibil ity

anorganic si ltwith medium comprecibilityand organic silt

anorganic siltwith high comprecibi lityand organic clay

% satisfy

67.69

42.69

52.36

29.48

38.21

26.89

38.44

34.91

20.05

10.14

31.84

46.23

41.51

49.76

46.46

48.82

50.71

47.88

33.02

22.64

53.77

45.75

52.12

53.30

35.85

45.99

44.34

55.42

T. S. Nagaraj and B. R. Murthy (1985)

T. S. Nagaraj and B. R. Murthy (1986)

Cc= ‐0.156+0.41eo+0.00058Wc

Cc= 0.5.Gs.PI

Cc= 0.2343Wc.Gs

Cc= 0.009Wc+0.002.LL‐0.10

Empirical corelation description of the research

A. S. Azzouz, R. J. Krizek, and R. B. Corotis (1976)

A. S. Azzouz, R. J. Krizek, and R. B. Corotis (1976)

C. P. Wroth and D. M. Wood (1978)

Cc= 0.37 (eo+0.003LL‐0.34)

Cc= 0.007 (LL‐10)

Cc=0.01.Wc

Cc=0.0046(LL‐9)

Cc=1.21+1.005(eo‐1.87)

Cc= 0.009 (LL‐10)

Cc=0.208eo+0.0083

Cc=0.02+0.014(PI)

Cc=0.141.Gs^1.2 

Cc=0.156eo+0.0107

Cc=1.15(eo‐0.27)

Rendo‐Herrero (1980)

Nishida (1956) All clay

Hough (1957) Inorganic cohesive soil: silt, silty clay, 

Hough (1957) Inorganic cohesive soil: silt, silty clay, 

Azzouz (1976)Clay USA and Greece

Kosasih dan Mochtar (1997), Surabaya clay based from 

lab.testing

Cc=0.30(eo‐0.27)

Cc=0.0102(Wc‐9.15)

Cc=0.4049(eo‐0.3216)

Cc=0.4(eo‐0.25)

Cc= 0.007LL +0.0001 Wc^2 ‐ 0.18

Terzhagi Peck (1967) undisturbed

Terzhagi Peck (1967) remolded

Azzouz dkk (1976) Chicago clay

Azzouz dkk (1976) Brazilian clay

Azzouz dkk (1976) Motley Clays from Sao Paulo City

Azzouz dkk (1976)Chicago clay

Nacci dkk (1975) North Atlantic clay

Rendo‐Herrero (1983)

Hough (1957) all clays

Kosasih dan Mochtar (1997), Surabaya clay based from 

lab.testingCc= 0.006LL + 0.13eo^2‐0.13

Cozzolina (1961)

Sower (1970) for low platicity

Azzouz (1976)

Moran,Proctor,Mueser and Rutlrdge (1958)

Cc=0.01 (Wc‐5)

Cc=0.01 Wc

Cc = 0.256 +0.43 (eo‐0.84)

Cc=1.21+1.055(eo‐1.87)

Cc=0.75(eo‐0.5)

Cc=(Wc/100)‐0.05

Cc=1.15.10^‐2.Wc

Azzouz (1976) USA and Greece Clay

Ostenberg (1972) All Natural soil

Cozzolina (1961)

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Based on the test results, it appeared that some existing formula only has the percentage of similarity less than 30% of the existing soil data, whereas some other formulation has a percentage of similarity between 30-60%, only one empirical formula that has the data above 67%. From those result, it can be seen that the existing empirical formulas are still not able to represent the data land in Surabaya. It is necessary to test the laboratory data to obtain empirical formula corresponding to the conditions of soil data in Surabaya. Linear regression was use in obtaining empirical formula on the ground data.

ANALYSIS RESULTS USING LINEAR REGRESSION

Empirical formulation performed using linear regression to find the value of R2 which is close to 1. R2 is often called the coefficient of determination; its function is to measure custom goodness (goodness of fit) of the regression equation, i.e. giving the proportion or percentage of the total variation in the dependent variable explained by the independent variables. R2 values lie between 0-1, and the model fit R2 is said to be better if closer to 1. The calculations performed on 425 soil data that has been collected compared with 28 empirical formulas preexisting. Results of the formulation on all existing data shows the R2 values smaller than 0.5, that subsequently performed variety of data sorting and grouping data based on the value of Liquid limit and plasticity limit is restricted to obtain a higher R2 value. Some results of the formulation shown in Fig.3a and 3b. Formulation of the comparison results indicate that there are significant enough differences from empirical formulations of existing soil data and test results in the laboratory.

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Fig.3a (top). The relationship between Cc and void ratio; The empirical formula of laboratories data.Fig.3b (bottom). The relationship between Cc and Water content; The

empirical formula of laboratories data

The empirical formula calculations performed using grouping value Liquid limit and plasticity index values. This is due to the large distribution data resulting the R-square value is smaller than 0.5 so that the model fit not be designated. To approximate the value of R square to 1, the grouping based on the value of soil plasticity needs to conduct. Results of linear regression for empirical formula of Liquid limit grouping by values can be seen in Fig.4a and 4b.

Fig.4a. Graph showing the relationship of compression index (Cc) with moisture content (Wc (%)) and void ratio (eo) with a value of 0-100% LL

y = 0.0143x ‐ 0.0165R² = 0.5102

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100 120 140

Compretion Index Cc

Water Content Wc (%)

LL = 0‐100%

y = 0.5574x ‐ 0.0938R² = 0.4934

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5

Compretion Index Cc

void ratio

LL 0‐100%

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Fig.4b. Graph showing the relationship compression index (Cc) with moisture content (Wc (%)) and void ratio (eo) with LL grouped by value.

y = 0.8901x ‐ 0.2913R² = 0.3454

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

Cc

eo

LL 0‐30 %

y = 0.6787x ‐ 0.1933R² = 0.5643

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3

Cc

eo

LL 30‐50 %

y = 0.0327x ‐ 0.3819R² = 0.5265

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40Wc

LL 0‐30 %

y = 0.0179x ‐ 0.1005R² = 0.5341

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100

Wc

LL 30‐50 %

y = 0.58x ‐ 0.1428R² = 0.4996

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3

Cc

eo

LL 50‐70%

y = 0.5485x ‐ 0.0846R² = 0.3687

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4

Cc

eo

LL 70‐100 %

y = 0.0137x + 0.0034R² = 0.498

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120Wc

LL 50‐70 %

y = 0.0151x ‐ 0.0833R² = 0.4106

0

0.5

1

1.5

2

2.5

3

0 50 100 150Wc

LL 70‐100 %

y = 0.0121x + 0.189R² = 0.3155

0

0.5

1

1.5

2

2.5

0 50 100 150Wc

LL 100‐150 %

y = 0.4172x + 0.2243R² = 0.2772

0

0.5

1

1.5

2

2.5

0 1 2 3 4

Cc

eo

LL 100‐150 %

3015

In addition of grouping based on Liquid limit value, it also grouped based on the value of the plasticity index. Plasticity index values are grouped into 0-70% according to the constraints on the plasticity chart and 0-120% according to the value of IP in all soil samples. According to Skempton (1953), the values of the soil plasticity are increased by a straight line with increasing percentage of clay-sized fractions contained by soil. The Increased the value of IP the greater the percentage of fine clay. Thus limiting the value of IP is conducted to limiting the value of soft and high plasticity clay. Fig.5 shows the relationship curve of compression index value to the value of water content and void ratio with a limit value of IP.

Fig.5. Graph showing the relationship compression index (Cc) with moisture content (Wc (%)) and void ratio (eo) with IP values are grouped.

The linear regression result of the data suggests that there are various values of empirical formula with the R2 values are also different in each grouping of data has been done. Recapitulation of the formulation and the value of R2 can be seen in Table 2.

Table 2. Empirical correlation result.

Explanation Empirical correlation R2 LL = 0-150% ; IP = 0-70% Cc=0.0136 Wc + 0.0156 0.4871 LL = 0-150% ; IP = 0-120% Cc=0.0141 Wc + 0.0078 0.4913 LL = 0-100% ; IP = 0-70% Cc=0.0143 Wc – 0.0165 0.5102 LL = 0-100% ; IP = 0-70% Cc=6.23Wc + 0.115 LL 0.5099 LL = 0-100% ; IP = 0-70% Cc=0.4044 (eo+0.01Wc)-0.0795 0.5024

y = 0.0136x + 0.0156R² = 0.4871

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100 120 140

Compretion Index Cc

Water Content Wc (%)

IP = 0‐70% 

y = 0.0141x + 0.0078R² = 0.4913

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100 120 140

Compretion Index Cc

Water Content Wc (%)

IP 0‐120%

y = 0.5316x ‐ 0.0569R² = 0.4713

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4

Compretion Index Cc

Void Ratio

IP = 0‐70% 

y = 0.5359x ‐ 0.0463R² = 0.4673

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4

Compretion Index Cc

Void ratio

IP 0‐120%

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LL = 0-100% ; IP = 0-70% Cc=1.0941(0.123eo+0.01Wc)-0.0415 0.5101 LL = 0-100% ; IP = 0-70% Cc=0.2867 (1.567eo+0.01Wc)-0.0843 0.5001

LL = 0%-30% Cc= 0.0327Wc-0.3819 0.5265 LL = 30%-50% Cc=0.6787eo-0.1933 0.5643 LL = 30%-50% Cc=0.0179Wc-0.1005 0.5341 LL = 50%-70% Cc=0.58eo-0.1428 0.4996 LL = 50%-70% Cc=0.0137Wc+0.0034 0.4980

CONCLUTION AND DISCUSSION Based on a comparative analysis of existing empirical formula with the soil sample data indicates that, there is a difference between the values of Cc empirical formula with the results of laboratory testing soil data. Percentage of the index compression value in accordance with results of laboratory testing is less than 60% so that the existing empirical formula cannot represent the value of the compression index clay in Surabaya. By approaching the characteristic value of soil data to get a formula which produces some empirical formula with R2 value approximately 0.5 is needed. Grouping of data IP and LL values conducted to obtain the value of R2 close to 1. However it cannot obtain the value of R2 close to 1. Maximum value obtained is 0.5643 for the empirical formula Cc = 0.6787eo- 0.1933, which means that the model resulting from the empirical formula only fit with part of the data sample tested. So that to obtain an empirical formula with R2 values by approaching more data is needed. Furthermore re-testing laboratory data in some soil samples in Surabaya also needs to be done as a comparison of the results of the testing data is land that has been done before. However, further research is still needed to obtain the empirical formula is closer to the value of the existing and also necessary to test the feasibility of existing laboratory data. REFERENCES Ardana.,M.,S.,Mochtar I.B.,(1999), “Pengaruh Tegangan Overburden Effective dan

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