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Probabilistic Study of Liquefaction Response of Fine-Grained Soil Using Multi-Linear Regression Model

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Abstract

Liquefaction behavior of fine-grained soil is associated with numerous soil parameters; however, over the past few years, importance of plasticity in predicting liquefaction susceptibility of soil has been well established in the literature. Regardless of recent advancements, no evident correlation has been developed between plasticity of the soil and factors of safety against liquefaction. Henceforth, the present study evaluates the effect of plasticity on liquefaction behavior of fine-grained soil for seismically active regions of Bihar (India) by proposing an equation based on multi-linear regression (MLR) analysis for predicting factor of safety against liquefaction (FL). The results of the study are supported by reliability analysis (FOSM) which also establish a co-relation between FL, reliability index (β) and probability of liquefaction (PL). The validation of the results using real liquefaction data obtained from liquefied and non-liquefied sites of Chi-Chi earthquake in Taiwan as well as data from Indo-Gangetic plains has confirmed the consistency of the developed multi-linear regression equation. The study devices a substantial impact in the field of liquefaction prediction for fine-grained soil with moderate to high plasticity and aims to felicitate a significant contribution in the knowledge pool of liquefaction studies. The developed equation may also serve as a guideline for taking critical engineering decisions especially during preliminary design calculations of any civil engineering structures vulnerable to liquefaction.

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Abbreviations

CSR:

Cyclic stress ratio

CRR:

Cyclic resistance ratio

FOS:

Factor of safety

SPT:

Standard penetration test

PGA:

Peak ground acceleration

LL:

Liquid limit

PI:

Plasticity index

FC:

Fine content

(N1)60 :

SPT blow count value

Wc/LL:

Ratio of water content to liquid limit

σvo :

Total vertical overburden pressure

σ'vo :

Effective vertical overburden pressure

rd :

Stress reduction factor

amax :

Peak horizontal ground acceleration

MSF:

Magnitude scaling factor

Kσ:

Factor of effective overburden

M:

Earthquake magnitude

Z:

Depth

FOSM:

First-order second moment

R:

Resistance

S:

Static

Z:

Performance function

µ:

Mean value

σ:

Standard deviation

β:

Reliability index

Pf :

Probability of failure

COV:

Coefficient of variation

PDF:

Probability distribution function

MLR:

Multi-linear regression

FL :

Factor of safety against liquefaction

PL :

Probability of liquefaction

RMSE:

Root mean square error

R:

Co-relation coefficient

R2 :

Coefficient of determination

VAF:

Variance account factor

PI:

Performance index

FA :

Actual values of factor of safety

FP :

Predicted values of factor of safety

FMEAN :

Mean values of factor of safety

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Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Patna, Patna, Bihar, 800005, India

    Sufyan Ghani

  2. Department of Civil Engineering, National Institute of Technology Patna, Patna, Bihar, 800005, India

    Sunita Kumari

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Appendices

Appendix 1

See Table

Table 8 Calculation sheet for determining factor of safety of Darbhanga (BH-D1) as per [22] approach
Full size table

8,

Table 9 Selected input parameters for developing a regression model
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9,

Table 10 Normalized input variables for determining factor of safety of Darbhanga (BH-D1) as per regression model equation
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10,

Table 11 Calculation sheet for determining reliability indices (β) and probability of liquefaction failure (PF) of Darbhanga (BH-D1) as FOSM-based reliability analysis
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11

Appendix 2

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Table 12 Soil data selected for the liquefaction analysis (training and testing datasets)
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12

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Ghani, S., Kumari, S. Probabilistic Study of Liquefaction Response of Fine-Grained Soil Using Multi-Linear Regression Model. J. Inst. Eng. India Ser. A 102, 783–803 (2021). https://doi.org/10.1007/s40030-021-00555-8

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