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Probabilistic Uplift Resistance of Pipe Buried in Spatially Random Cohesionless Soil

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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

The lower bound finite element limit analysis technique in conjunction with the second-order conic optimization is used to determine the uplift resistance of pipeline buried in spatially random cohesionless soil. The Cholesky decomposition method is employed to produce the spatially random discretized soil domain. The Monte Carlo simulation technique is implemented to obtain the probabilistic responses. The mean uplift factor and the failure probability of the pipeline for a wide range of practical cases of soil spatial variability are provided as the design charts. It is found that for the smaller value of correlation distance, the deterministic uplift factor is always higher than the mean uplift factor; however, with the increase in the correlation distance, the difference between the deterministic uplift factor and the mean uplift factor reduces. The probability of failure of pipeline is found to be increasing with the reduction in the magnitude of correlation distance and factor of safety. The influence of the soil spatial variability on the failure mechanism is also studied in detail.

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Abbreviations

CDF:

Cumulative distribution function

COV:

Coefficient of variation

FS:

Factor of safety

LBFELA:

Lower bound finite element limit analysis

MCS:

Monte Carlo simulation

PDF:

Probability density function

\(\left[ {A^{{{\text{dc}}}} } \right]\) :

Matrix developed for the implementation of stress discontinuity conditions

\(\left[ {A^{{{\text{eq}}}} } \right]\) :

Matrix developed for the implementation of element equilibrium conditions

\(\left[ {A^{{{\text{sb}}}} } \right]\) :

Matrix developed for the implementation of stress boundary conditions

\(\left[ {A^{{{\text{socp}}}} } \right]\) :

Matrix developed for the implementation of yield criteria

\(\left[ {A_{{\text{P}}} } \right]\) :

Global equality matrix

\(\left\{ {B^{{{\text{dc}}}} } \right\}\) :

Vector developed for the implementation of stress discontinuity conditions

\(\left\{ {B^{{{\text{eq}}}} } \right\}\) :

Vector developed for the implementation of element equilibrium conditions

\(\left\{ {B^{{{\text{sb}}}} } \right\}\) :

Vector developed for the implementation of stress boundary conditions

\(\left\{ {B^{socp} } \right\}\) :

Vector developed for the implementation of yield criteria

\(\left\{ {B_{P} } \right\}\) :

Global equality vector

D :

Diameter of pipe

D c :

Total number of discontinuities

E :

Total number of elements

F γ :

Uplift factor

\(\left\{ g \right\}\) :

Global vector comprising of the coefficients of the objective function

H :

Embedment depth of pipe from the ground surface

\([I]\) :

Identity matrix

L h :

Horizontal extent of the domain

L v :

Vertical extent of the domain

N :

Total number of nodes

N i :

Total number of nodes along the circular periphery of the pipe

P f :

Probability of failure of Fγ

p u :

Average ultimate vertical uplift pressure

P u :

Ultimate vertical uplift resistance

\(\left\{ {Y_{{\text{P}}} } \right\}\) :

Global vector containing \(\left\{ \sigma \right\}\) and \(\left\{ \kappa \right\}\)

δ x :

Correlation distance in x direction

δ y :

Correlation distance in y direction

ϕ :

Angle of internal friction of soil

γ :

Unit weight of soil

{κ}:

Vector of the conic constraints

μ Fγ :

Mean uplift factor

μ ln tan ϕ :

Mean of log-normally distributed tanϕ

ρ :

Autocorrelation function

\(\left\{ \sigma \right\}\) :

Nodal stress vector

σ ln tanϕ :

Standard deviation of log-normally distributed tanϕ

σ x :

Normal stress in x direction

σ y :

Normal stress in y direction

τ xy :

Shear stress

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Acknowledgements

This work used the Supercomputing facility of IIT Kharagpur established under National Supercomputing Mission (NSM), Government of India, and supported by Centre for Development of Advanced Computing (CDAC), Pune.

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  1. Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Debarghya Chakraborty

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Chakraborty, D. Probabilistic Uplift Resistance of Pipe Buried in Spatially Random Cohesionless Soil. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 93, 355–368 (2023). https://doi.org/10.1007/s40010-022-00808-6

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