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Reliability Analysis of Excavation Induced Basal Heave

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Abstract

The present study deals with the reliability analysis of basal heave caused by excavation considering uncertainty in the soil properties. The case study considered in the present work has been analyzed deterministically by Hsieh et al. (Can Geotech J 45:788–799, 2008). Taiwan building code is adopted in the method for analyzing the basal heave failure. The random variables (undrained shear strength and total unit weight of clay) are assumed to be normally distributed and uncorrelated. A series of parametric studies have been conducted to calculate the reliability index on the basis of the matrix formulation for the second moment method by Hasofer and Lind (J Eng Mech ASCE 100(1):111–121, 1974) considering different coefficient of variation of undrained shear strength and total unit weight of clay layers. It has been found that for a particular value of coefficient of variation of total unit weight, the reliability index with respect to occurrence of basal heave failure decreases with increase in the coefficient of variation of undrained shear strength. Moreover, the reliability index also decreases when the coefficient of variation of total unit weight increases. It has also been found that the probability of basal heave failure is lower with respect to factor of safety equals to 1.2, as compared to factor of safety equals to 1.0. Sensitivity analysis shows that the undrained shear strength of the bottommost layer and total unit weight of the second layer are the most significant random variables affecting the reliability index. Guidelines are provided for reliability based design where, for ‘target’ reliability index of 2.5 and 3.0, the factor of safety can be chosen such that all the related uncertainties are taken into account, especially with regard to undrained shear strength of the bottommost layer and total unit weight of the second layer. Design guidelines have been provided for this purpose.

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Abbreviations

B :

Width of excavation

D e :

Maximum excavation depth (final stage)

D b :

Embedment depth (final stage)

E :

Young’s modulus of soil

F :

Failure region

G :

Shear modulus of soil

K :

Bulk modulus of soil

K o :

Coefficient of lateral earth pressure at rest

K n :

Interface normal stiffness between wall and soil

K s :

Interface shear stiffness between wall and soil

M :

Vector of mean value of random variables

M r :

Resisting moment

M d :

Disturbing moment

N :

Average SPT value of soil

n :

Number of random variables

P f :

Probability of failure

S i :

Undrained shear strength of ith soil layer

t :

Thickness of the wall

X :

Vector of random variables

γ :

Total unit weight of soil

β :

Reliability index

λ i :

Sensitivity factor of the ith random variable

Φ(·):

Standard normal cumulative distribution function

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Authors and Affiliations

  1. Department of Civil Engineering, Heritage Institute of Technology, Kolkata, Kolkata, 700107, India

    Subha Sankar Chowdhury

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  1. Subha Sankar Chowdhury
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Chowdhury, S.S. Reliability Analysis of Excavation Induced Basal Heave. Geotech Geol Eng 35, 2705–2714 (2017). https://doi.org/10.1007/s10706-017-0272-2

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