Liquefaction potential mapping of Newtown, Kolkata, India using Deterministic and Reliability analysis


 Liquefaction is a phenomenon where the effective stress of the soil gets reduced to zero and the soil losses its shear strength completely. Such occurrence is common during an earthquake and hence the need for evaluating the liquefaction potential of soil arises. The region of Newtown-Rajarhat is undergoing a massive industrial and residential growth and as the area has layers of sand and silt mixed with clay and organic matter, it is essential to determine its liquefaction potential. In this study, the deterministic methods proposed by Youd et al. (2001) and Boulanger and Idriss (2014) were utilized to evaluate the liquefaction potential of the region using 102 borehole data for earthquake magnitudes of 6 and 7. However it was observed that both methods gave different results for the same input parameters. The parameter uncertainties were identified and a reliability analysis was performed to represent the liquefaction potential in terms of reliability index and probability of liquefaction. The First-Order-Second-Moment (FOSM) method was utilized here and contour maps were prepared for depths of 7m and 13m for both the earthquake magnitudes. It was concluded that the study area is vulnerable to liquefaction at a depth of 13m in the regions of Newtown, Rajarhat and Sector V.


Introduction
1 During earthquakes, one of the major causes for massive building damage and destruction is the occurrence of 2 liquefaction. Vigorous shaking, which occurs during an earthquake, can lead to build up of pore water pressure in 3 undrained fine sands and silty soils. This can reduce the effective stress of the soil to zero, thereby resulting in 4 complete loss of shear strength in soil. This phenomenon is known as liquefaction and it can result in sand boils, 5 lateral spreading of soil, etc. An effective way to prevent this is by determining the liquefaction potential of soil.

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There are several ways to calculate the liquefaction potential eg. deterministic methods, probabilistic methods, etc.

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The deterministic method expresses the liquefaction potential of soil by a factor of safety which is calculated using 8 SPT value, CPT value, shear wave velocity of a soil. Initially this method was only applicable for sands but recent 9 advances have made it possible to apply it on all types of soil.

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However, this method has its disadvantages, the most common being that it lacks precision and is conservative in 11 nature. It has been found that certain assumptions made in the method have proven to give uneconomical results 12 thereby making it uncertain in nature. To address the uncertainties, reliability analysis along with deterministic 13 methods can be used to determine the liquefaction potential of soils. Reliability methods express the liquefaction 14 potential of a soil by a reliability index and probability of liquefaction. Not only does it determine the safety of a soil 15 against liquefaction, but it also helps us understand how much safe or unsafe a soil is by using probability 16 percentages.

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The deterministic approach was first developed by Seed and Idriss (1970) and has been since known as 'The

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Newtown and Rajarhat were found to be at high soil liquefaction risk.

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Previous literature review shows that different deterministic methods were developed to evaluate the liquefaction 64 potential of soil among which some methods continue to be used in construction projects. The uncertainties related 65 to parameters and analytical models remain unaddressed in deterministic approaches which can make them 66 conservative in nature. Reliability analysis methods have been studied and implemented on field cases where the liquefaction potential of soil is measured by a probability of liquefaction. Results of reliability analysis are not only 68 economical but they represent the soil susceptibility to liquefaction in a way which is better suited to the engineer.

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The objective of this paper is to evaluate the liquefaction susceptibility of Newtown-Rajarhat study area for two 70 earthquake magnitudes of 6 and 7. Comparative study is conducted by two deterministic methods of Youd et al.

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where amax = maximum horizontal acceleration at ground surface, g = acceleration due to gravity, σv = total vertical 124 stress at depth z, σ'v = effective vertical stress at depth z, rd = shear stress reduction factor.

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As the soil is not a rigid column, a factor to consider the flexibility of soil is used which is known as shear stress 126 reduction factor. Its maximum value is 1 which is at the ground surface and its value decreases with increase in 127 depth (z). It is evaluated using the following equations:

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The term Δ(N1)60 is a function of fines content (FC) and is expressed as Rajarhat region, is presented in Table 2 and Table 3 showing the soil properties along depth and calculated values of 178

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The factor of safety (FS) determined by the deterministic models is being used as the performance function. The

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The mean and coefficient of variation of CSR is determined by where ′ = correlation co-efficient between σv and σ'v. The coefficient of variation of CRR is determined as: Therefore Reliability Index (β) is a ratio of mean to standard deviation and is represented by After obtaining the value of β, the probability of liquefaction can be expressed as where φ(β) = normal cumulative probability distribution of random variables.

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The soil shows susceptibility to liquefaction up to 30m of depth for factor of safety and reliability index graphs. To  Table 4 and Table 5 respectively.

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(2014) for earthquake magnitudes of 6 and 7 at depth 7m and 13m which are presented in Fig. 6 to Fig. 9.

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Comparing the contour maps it can be seen that Boulanger and Idriss (2014)

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The Rajarhat-Newtown area is evaluated for liquefaction potential for two earthquake magnitudes of 6 and 7.

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Deterministic methods of Youd et al. (2001) and Boulanger and Idriss (2014) were used to calculate the factor of 280 safety of the study area and their contour maps were constructed at 7m and 13m depths. Reliability analysis was 281 conducted on both the deterministic procedures using FOSM method for the two earthquake magnitudes of 6 and 7.

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Contour map study was done for the method of Boulanger and Idriss (2014) at 7m and 13m depth as this method 283 was observed to give lesser conservative values. The contour maps were studied to assess the depth and the regions 284 in the study area which are most susceptible to liquefaction.

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Measuring the liquefaction susceptibility of a region in terms of factor of safety gives much lower results than their 286 corresponding reliability index values. This is clearly seen in Fig. 4 where the moderately critical and safe zone 287 contains considerably more factor of safety points than the reliability index points in the same zones in Fig. 5.

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Deterministic methods do not account for the various uncertainties in the parameters and factors used in calculation 289 of factor of safety. Using reliability analysis along with deterministic methods account for these uncertainties, the study area to be susceptible most at 13m depth in the regions of Newtown, Rajarhat and Sector V. The soil in 295 these regions, in the first 15m, greatly comprises of alternating layers of soft, clayey silt and fine silty sand along 296 with decomposed wood and organic matter with the ground water table at an average depth of 3m to 5m from the 297 surface. Therefore it can be concluded that the Newtown-Rajarhat area is highly susceptible to liquefaction at most 298 of the regions and proper mitigation measures should be adopted during any constructions.