Correlation between undrained shear strength and liquidity index of soils in Malaysia

Accuracy of soil undrained shear strength measurement is often governed by the quality of undisturbed soil sampling. Numerous previous attempts have been made to establish correlations between the undrained shear strength and various soil physical parameters. This paper aims to determine a correlation between the undrained shear strength (cu) and liquidity index (IL) based on 34 soil samples collected from selected sites in Peninsular Malaysia. Sieving, hydrometer analysis and Atterberg limit tests were performed to determine physical properties of the soils. The undrained shear strengths were determined using the Unconsolidated Undrained (UU) triaxial test. An attempt was made to correlate the undrained shear strength with liquidity index of all the soil specimens. However, the correlation was found to be considerably weak (r2 = 0.47). The correlation was improved significantly (r2 = 0.82) by limiting the data to soils with fines content of more than 65% only. The proposed equation was in the form cu = a exp(-b IL) where the values of constants a and b were determined empirically as 72.9 and 1.95, respectively.


Introduction
Undrained shear strength is an essential parameter for geotechnical designs. It is even more important for soft clay sites that are highly deformable and characterized by low shear strength [1]. A high-quality undisturbed sample is essential for obtaining an accurate measurement of soil shear strength. An undisturbed sample, however, can be found to be very difficult to obtain as the collection process causes it to be nearly impossible to have a perfectly undisturbed soil.
In order to overcome these issues, several studies have been conducted to establish correlations between the undrained shear strength and various parameters such as Atterberg limits, water content, plasticity index, and liquidity index to come up with ways of predicting the undrained shear strength. Numerous previous studies have made attempts in correlating the shear strength with the liquidity index of clays. The liquidity index is defined as the ratio of difference between natural water content and plastic limit to the difference between liquid limit and plastic limit. Schofield and Wroth [2] used the Vane Shear test data from Skempton and Northey [3] and came up with a conclusion that the liquid limit and plastic limit did correspond approximately to fixed strength which were in the proposed ratio of 1:100. Based on this conclusion, Wroth and Wood [4] proposed a relationship between shear strength and liquidity index: c u = 170.00 exp (-4.60 I L ) (1) where c u is the undrained shear strength and I L is the liquidity index [5]. Skempton [6] also made an attempt in finding the relationship between the undrained shear strength and the liquidity index. He found that the ratio of the undrained shear strength of a normally consolidated clay to the effective overburden pressure at the corresponding depth was a constant and a function of the plasticity index of the clay. Skempton and Northey [3] made a conclusion that there could be a possibility of a definite relationship between the liquidity index and the undrained shear strength of a fine-grained soil. However, no empirical equation was proposed by them. Yilmaz [7] conducted a study on silty clays collected from various locations in Turkey. He then investigated the relationship between the undrained shear strength and the liquidity index and came up with the equation: Yilmaz's equation can be observed to have a huge difference with the equation proposed by Wroth and Wood [4] as Yilmaz's equation suggested that the undrained shear strength at liquid limit was as high as 30.6 kPa [8]. There were also studies that correlated the undrained shear strength with the plastic limit and liquid limit. Several predictions have been made on the value of shear strength at liquid limit and plastic limit of soil. For an example, as early as 1939, Casagrande suggested that the average value of undrained shear strength at liquid limit is 2.65 kPa. Norman [9] reported that if using an apparatus conforming to the British standard to determine the liquid limit, the shear strength of soil will range from 0.8 to 1.6 kPa while if using an apparatus of ASTM standards, the value will range from 1.1 to 2.3 kPa. Youssef et al. [10] found that the values of shear strength of clay at the liquid limit of a large number of soils ranged from 2.4 to 1.3 kPa. Wroth and Wood [4] adopted 1.7 kPa as the average value of undrained shear strength of a remoulded soil at its liquid limit. From the results of Skempton and Northey [3], Wroth and Wood [4] concluded that the shear strength at the plastic limit is one hundred times the shear strength at liquid limit. Therefore, the shear strength at plastic limit will be 170 kPa. Sharma and Bora [11] plotted a log-to-log graph between the undrained shear strength and the water content. With a linear correlation and by applying the assumptions made by Wroth and Wood [4] in which the undrained shear strengths at liquid limit and plastic limit were taken as 1.7 kPa and 170 kPa, respectively, the following equation was obtained: (3) where C u (LL) is undrained shear strength at liquid limit, LL is liquid limit, PL is plastic limit, and w is water content. Equation (3) enables ones to predict the undrained shear strength at any water content if its liquid limit and plastic limit are known. The relationship between the undrained shear strength and the water content can be represented by a linear line when they are plotted in a log-to-log graph. The relationship can be expressed by a general equation [12].: log c u = log c + m log w (4) where c is a constant value and m is the gradient of the graph. There are numerous equations proposed by other researchers involving correlations of shear strength with different parameters, as summarized in Appendix 1. From the extensive list of correlations summarized in Appendix 1, none of the equation was established based on soil data in Malaysia. As a tropical country, Malaysia has abundant of residual soils that are characterized by soil grains of large variability depending on their degree of weathering. This paper aims to establish a relationship between undrained shear strength and physical properties of soils in Malaysia. Soil samples are collected from 34 random sites in Peninsular Malaysia. The samples are subjected to laboratory tests to obtain the required shear strength and physical properties for the correlations.

Review of previous established equations
It can be seen in Appendix 1 that there are common soil parameters that have been widely used to correlate with the undrained shear strength of soil. For instance, authors such as Wroth and Wood [4], Hong [13], Fedrico [14], Lee [14], Raheem [14], Sharma [11] and Vardanega and Haigh [15] have established a correlation between the undrained shear strength and the Atterberg limits and water content of soil. There are also correlations established by Sharma and Sridharan [12], Berilgen [14], Karakan and Demir [16] and O'Kelly [17] where the undrained shear strength can be predicted by just knowing the water content. Parameters such as plasticity index, water content ratio and void ratio has also been used by previous researchers to correlate with the undrained shear strength of soil. In this study, an attempt was made to establish a correlation between the undrained shear strength and the liquidity index as it has been proven to be successful based on previous studies [5,8,15,[18][19][20][21][22][23][24].

Data collection
A total of 34 soil samples were collected from random sites in Peninsular Malaysia. A series of soil tests were conducted in order to evaluate the soil parameters. Firstly, sieving and hydrometer analysis were performed to determine the particle size distribution of soil. The amount of fines content in each soil sample was obtained. The undrained shear strengths (c u ) of the soil samples were determined using the Unconsolidated Undrained (UU) triaxial test. Cone penetration test was carried out to determine the liquid limit, while the plastic limit was determined following the procedures recommended in BS 1377:2016. From the liquid limit (LL) and plastic limit (PL) obtained from these standard tests, the liquidity index (I L ) can be computed.

Regression analysis
In order to establish a correlation between the undrained shear strength and the liquidity index, the experimental data were first fitted to selected existing correlations [4, 7, 15, 22, 23, 25 -28]. The correlation that best-fitted to the present experimental data was identified and subsequently analyzed to determine the constants of the correlation.

Results and discussion
Based on the soil samples obtained, the undrained shear strength was plotted against liquidity index. Existing correlations were also plotted on the same graph to show comparisons, as presented in Fig. 1. Based on qualitative observation of the plotted experimental data and the existing correlations in Fig. 1, the experimental data was found to be able to fit reasonably well with the equation in the form of c u = a exp(-b I L ), as proposed by Wroth and Wood [4], Yilmaz [7], and Edil and Benson [27]. An attempt was subsequently made to determine the constants a and b to fit to the present experimental data. Fig. 2 shows the best-fitted equation proposed for the data.   (5) where the values of constants a and b are determined as 40.458 and 1.194, respectively. However, the R-squared value for this equation was found to be considerably low, i.e. 0.4711 indicating that the correlation was weak.
Another attempt was made in which only the data from soil samples with percentage of fines content more than 65% were considered in establishing the correlation. Fig. 3 shows the plot of undrained shear strength against the liquidity index with only considering the data with percentage of fines content more than 65%. Fig. 3. Correlations between the undrained shear strength and the liquidity index for lab data with fines content more than 65%. From Fig. 3, it can be observed that the R-squared value was improved significantly to 0.8187 indicating a strong correlation with the experimental data. The best-fit equation is given as: c u = 72.9 exp (-1.95 I L ) (6) where the values of constants a and b are determined as 72.9 and 1.95, respectively. Based on the results, it was found that an empirical equation can only be obtained for the soil samples that has fines content more than 65%. It can be interpreted that a proper correlation between the undrained shear strength and the liquidity index is only valid for finegrained soils. This finding showed good agreement with previous studies as most of the correlations summarized in Appendix 1 were developed based on fine-grained materials, mainly clayey soil. For instances, Yilmaz [7] proposed a correlation between the undrained shear strength and liquidity index based on silty clay soils collected from various locations in Turkey. Leroueil et al. [20] presented a relationship between the undrained shear strength and the liquidity index based on compacted clays. Sharma and Sridharan [12] proposed a linear log-to-log relationship between the undrained shear strength based on clay soils with different ranges of plasticity index. An attempt was made in this study to establish correlations regardless of the amount of fines content in soil. However, the poor correlation implied that the shear strengths of soils with a significant amount of coarse grains could be governed more dominantly by their grain angularity, amount and maximum size of coarse grains, and grain strength than their plasticity properties.  Table 1 tabulates the constants a and b, and undrained shear strength at plastic limit and liquid limit proposed by present and previous studies. The results indicated that soils in Malaysia have relatively lower undrained shear strength (72.9 kPa) when the water content is at plastic limit as compared with the shear strengths predicted from other proposed equations. The undrained shear strength at liquid limit (10.4 kPa) was deemed to be reasonable as the soil was expected to be very soft (< 20 kPa) at liquid limit.

Conclusion
In this study, attempts were made to correlate undrained shear strength with physical properties of soils collected from 34 selected sites in Malaysia. Following conclusions can be drawn from this study: 1) The undrained shear strengths of soil specimens collected from Malaysia can be correlated with liquidity index. The correlation, however, was found to be considerably weak (r 2 = 0.4711) 2) A strong correlation was obtained (r 2 = 0.8187) by limiting the correlation to soils with fines content of more than 65% only. The results showed that a reliable correlation can only be established based on fine-grained materials.
3) Based on the present proposed correlation between undrained shear strength and liquidity index, the undrained shear strength at plastic limit (72.9 kPa) was found to be lower than those of previous proposed correlations (102.6 -170 kPa). The undrained shear strength at liquid limit (10.4 kPa) was found to be reasonable.