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ESTIMATING MAXIMUM DRY DENSITY AND OPTIMUM MOISTURE CONTENT OF COMPACTED SOILS Conference Paper · July 2015
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International Conference on Advances in Civil and Environmental Engineering 2015 © Faculty of Civil Engineering, Universiti Teknologi MARA Pulau Pinang
ESTIMATING MAXIMUM DRY DENSITY AND OPTIMUM MOISTURE CONTENT OF COMPACTED SOILS
NG K.S.*, CHEW Y.M., OSMAN M.H., MOHAMAD GHAZALI S.K. Faculty of Civil Engineering, UiTM Pulau Pinang, 13500, Permatang Pauh, Penang, Malaysia *Corresponding Author:
[email protected]
Abstract Laboratory determination of compaction properties namely the maximum dry density and optimum moisture content is both time consuming and costly. Therefore, it is useful if simple correlation equations can be developed to estimate the compaction properties using relatively easier index properties test. This study aims to investigate the relationship between maximum dry density and optimum moisture content and their correlation function with index properties. Based on the results of nine soil samples using standard proctor compaction test, the maximum dry density and the optimum moisture content was well correlated. These two compaction properties have much better correlation with the plasticity index than they have with other index properties. Three best predictive models were proposed to estimate the compaction properties based on multilinear regression (MLR) analyses. Additiona l variables are included in the MLR analyses such as grain size distribution and specific gravity other than the index properties. The recommended model requires only the plasticity index and specific gravity. Keywords: Maximum dry density, Optimum moisture content, Index properties, Regression analyses
1. Introduction Compaction of soil by mechanical mean is a common soil modification method to improve the engineering properties of soils. The effectiveness of the compaction maximum dry density (MDD) and optimum moisture content (OMC). Understanding of the soil compaction properties (MDD and OMC) is important in construction project such as earth dams, road and railway embankments, landfill liners and backfills of retaining structure. However, considerable of time and effort are required in the laboratory tests in order to obtain the compaction B-1
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K.S. Ng et al.
Nomenclatures Compaction energy Fines Gravel Coefficient of correlation Sand Specific gravity
E F G R S Gs
Abbreviations
LL MDD MLR OMC PI PL SE
Liquid limit Maximum dry density Multilinear regression Optimum moisture content Plasticity index Plastic limit Standard error
properties. It would be useful if predictive models can be developed to relate the compaction properties with the physical properties of soils which can be obtained easily. Few prediction models can be found in the literature to predict the compaction properties of soil based on several geotechnical properties such as grain size, plastic limit (PL), liquid limit (LL), plasticity index (PI) specific gravity (Gs) and compaction energy ( E ). Based on the compaction results of 22 clayey soils, Blotz et al. [1] discovered that the compaction properties were best correlated with liquid limit and thus proposing the following relationships: MDD B
(2.27 log LL 0.94) log E 0.16 LL 17.02
(1)
OMC B
(12.39 12.21log LL) log E 0.67 LL 9.21
(2)
On the other hand, Sridharan& Nagaraj [2] developed the prediction model for standard proctor test using only plastic limit: MDD R
0.23(93.3 PL)
(3)
OMC R
0.92 PL
(4)
Meanwhile, Noor et al. [3] incorporated plastic limit, plasticity index and specific gravity to predict the compaction properties of the standard proctor test. The relationships are presented as: MDD N
27 PL0.6 PI 0.33
OMC N
0.55 PL 0.36 PI
Gs
(5)
(6)
2.7 Gs
2.7
The aim of the current study is to develop empirical predictive models based on regression equations to estimate the maximum dry density and the optimum moisture content using standard proctor (SP) test data. The statistical data consist
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of consistency indexes (LL, PL & PI), grain size distribution (gravel, sand and fines content percentages) and specific gravity (G s).
2. Materials and methods Nine soil samples were collected from various sites in Penang and fall in the ML and MH regions of the plasticity chart. T he fines content ranges from 34% to 91% while the LL ranges from 43% to 52% and plastic limit ranges from 26% to 34%. Basic tests such as particle size distribution, specific gravity and Atterberg limits were performed according to British Standard practice (BS 1377) [4]. All soils were compacted using standard proctor test procedure with compaction energy of 3 592.5 kJ/m . The results of these geotechnical properties tests are summarized in Table 1 and are used in the multilinear regression (MLR) analyses. The accuracy of the results by MLR is verified with statistical tool such as the coefficient of correlation ( R) and the standard error (SE). Table 1. Experimental results used in the current study. No.
Gravel (%)
Sand (%)
Silt (%)
Clay (%)
Fines (%)
LL
PL
PI
Gs
OMC (%)
MDD (Mg/m3)
Soil 1
7
39
41
13
54
43
27
16
2.55
18
1.66
Soil 2
9
46
36
9
45
53
34
19
2.45
24
1.47
Soil 3
3
28
50
19
69
51
33
18
2.56
24
1.48
Soil 4
1
8
64
27
91
47
30
17
2.57
19.5
1.60
Soil 5
20
46
31
3
34
44
28
16
2.56
14
1.72
Soil 6
0
25
40
35
75
46
29
17
2.54
17
1.57
Soil 7
10
46
32
12
44
42
26
16
2.55
17
1.65
Soil 8
26
30
26
18
44
43
28
15
2.58
14.5
1.72
Soil 9
20
46
23
11
34
41
26
15
2.60
13.5
1.74
3. Maximum dry density versus optimum moisture content The plot of maximum dry density versus optimum moisture content for nine samples is presented in Fig. 1. The maximum dry density reduces as the optimum moisture content increases. The correlation of the maximum dry density and the optimum moisture content is strong (Coefficient of correlation, R = 0.91) and the relationship can be well represented as a linear equation: MDD
2.065 0.024OMC
Fig. 1. Maximum dry density versus optimum moisture content.
(7)
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The above equation gives the maximum SE of 5.5 % for soil no.7. The compaction properties in the current study are further compared with the power function equations developed by Sivrikaya et al. [5] and Matteo et al. [6] (shown as Eq. 8 and Eq. 9 respectively) and the results are presented in Fig. 2 and Fig. 3. Both prediction models over predict the maximum dry density with the maximum discrepancies of 11% in the former model and 8% in the latter model. 0.0184OMC (8) MDDS 23.72 e
MDD M
36.635OMC 0.2564
(9)
Fig. 2. Comparison with model proposed by Sivrikaya et al. [5].
Fig. 3. Comparison with model proposed by Matteo et al. [6].
4. Compaction properties and index properties In this study, the correlations of MDD and OMC with Atterberg limit are given in Fig. 4 and Fig. 5. It is clear that as the index properties (i.e. LL, PL, & PI) increases, the maximum dry density reduces and the optimum moisture content increases. The maximum dry density and the optimum moisture content have a considerably good correlation with plasticity index in comparison to liquid limit and plastic limit. This study also shows that liquid limit has a better correlation than plastic limit. It is found that the linear correlation of MDD with PI has an R of 0.96 while it is R = 0.92 for correlation between OMC and PI. The relation equations for MDD and OMC with PI are established as the following: MDD
2.845 0.073 PI
OMC 2.726 PI 27.19
(10) (11)
The compaction properties from this study are compared with different prediction models (Eq. 1 6) as shown in Fig. 6-8. Generally, Noor et al. [3] gives the best prediction for MDD with the average error (i.e. bias) of 0.008 3 Mg/m compared to Blotz et al. [1] and Sridharan & Nagaraj [2] with the average 3 3 error of 0.166 Mg/m and 0.115 Mg/m predicts higher MDD with the maximum error of 16.8% while Sridharan & Nagaraj [2] under predict MDD as much as 11.1%. On the other hand, OMC is best predicted by Blotz et al.[1] with the average error of 0.04% while the average error for Noor et al. [3] is 3%. Sridharan & Nagaraj [2] significantly over predicts the OMC with average error of 8.7%. The large discrepancies of this prediction is because the correlation (i.e. Eq. 4) is solely based on plastic limit which the current results viz. Fig. 5 has shown that plastic limit is not well correlated to OMC compared to plasticity index and liquid limit.
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(a)
(b)
(c) Fig. 4. (a) MDD versus LL, (b) MDD vs PL, and (c) MDD vs PI.
(a)
(b)
(c) Fig. 5. (a) OMD versus LL, (b) OMD vs PL, and (c) OMD vs PI.
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(a)
(b)
Fig. 6. Comparison of current study with Blotz et al. [1].
(a)
(b)
Fig. 7. Comparison of current study with Sridharan & Nagaraj [2].
(a)
(b)
Fig. 8. Comparison of current study w ith Noor et al. [3].
5. Multilinear regression analyses Besides correlation with index properties, the relationship of compaction properties (MDD and OMC) with other properties such as grain size distribution and specific gravity were investigated in this study. Multilinear regression (MLR) analyses are performed by the method of least squares where OMC and MDD are the dependent variables while gravel ( G), sand (S ), fines (F ), liquid limit (LL), plastic limit (PL), plasticity index (PI) and specific gravity ( Gs) are the
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independent variables. The unit for all variables are in the percentage except the 3 unit for MDD is Mg/m and specific gravity is non unit variable. In this study, several models are constructed and three best fit models are shown in Table 2 for estimating MDD and Table 3 for estimating OMC. In these relationships, the correlation of coefficient ( R) and standard error (SE) are determined to verify the accuracy from a statistical point of view. Among these models, model no.3 is relatively easy since it requires only plasticity index and specific gravity which the tests only require small amount of soil sample and easy to carry out. Hence, model no. 3 is recommended. Table 2. Correlation Equation for MDD. Model no. 1 2 3
Correlation equations
R
MDD = 0.0285G + 0.0273S + 0.0270F 0.0666PI MDD = 0.0219G + 0.02347S + 0.02457F 0.01854LL MDD = -0.0475PI + 0.9443 G
1.0 1.0
SE 3 (Mg/m ) 0.03 0.03
1.0
0.05
Table 3. Correlation Equation for OMC. Model no. 1 2 3
Correlation equations
OMC = -0.2929G 0.1174S 0.1551F + 0.7378LL OMC = -0.2646G 0.2612S 0.2452F + 2.6111PI OMC = 2.4480PI - 8.8502 G
R
0.998
SE (%) 1.70
0.997
1.91
0.996
1.74
6. Conclusion Maximum dry density (MDD) and optimum moisture content (OMC) are important compaction properties used for field compaction control. This study investigated the relationship between the compaction properties and the index properties of fine grained soils for standard proctor test. Multilinear regression (MLR) analyses were conducted to develop predictive model from a statistical point of view to estimate MDD and OMC. Several conclusions can be made from this study: i) ii)
Maximum dry density was well correlated with optimum moisture content. MDD and OMC were best correlated with plasticity index (PI) compared to liquid limit (LL) and plastic limit (PL). iii) Correlation equations by Sivrikaya et al. [5] and Matteo et al. [2] over predicted MDD when the values for OMC are known. iv) Predictive model by Noor et al. [3] gave the best estimation for MDD while OMC was best predicted by Blotz et al. [1] work. v) MLR analyses provide reliable predictive models and Model no.3 which only involve index properties and specific gravity (G s) is recommended. However, these models should be limited to soils with similar characteristics as the soil in this study and more samples are needed to improve the prediction with broader scope in terms of OMC, MDD, LL, PI, and G s.
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References 1.
Blotz, L. R.; Benson, C. H.; and Boutwell, G. P. (1998). Estimating optimum water content and maximum dry unit. Journal of Geotechnical and Geoenvironmental Engineering, 907 912.
2.
Sridharan, A.; and Nagaraj, H. B. (2005). Plastic limit and compaction characteristics of finegrained soils. Proceedings of the ICE-Ground Improvement , 9(1), 17-22.
3.
Noor, S. C. (2011). Estimation of proctor of compacted fine grained soils fron index and physical properties. International Journal of Earth Sciences and Engineering, 4, 147 - 150.
4.
Standard, B. 1377 (1990). Methods of Test for soils for civil Engineering Purposes. British Standards Institution, London.
5.
Sivrikaya, O.; Togrol, E.; and Kayadelen, C. (2008). Estimating compaction behavior of fine-grained soils based on compaction energy. Canadian Geotechnical Journal, 45(6), 877-887.
6.
Matteo, L. Di; Ph, D.; Bigotti, F.; and Ricco, R. (2009). Best-Fit Models to Estimate Standard Proctor Properties of Compacted Soil. Journal of Geotechnical and Geoenvironmental Engineering, 992 996.
