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Investigation of Surface Settlement and Wall Deflection Caused by Braced Excavation in Spatially Variable Clays Based on Anisotropic Random Fields

  • Research Article-Civil Engineering
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Abstract

This research aims to assess the influences of the spatial variability of soil parameters on the ground surface and retaining wall deformation induced by braced excavation. A series of anisotropic random fields are generated and used for the finite difference analysis in this paper. A procedure for automating the Monte Carlo simulation is employed to ascertain the influences of coefficient of variation and scale of fluctuation (SOF) of soil stiffness parameters on the excavation-induced responses. In addition, the effects of horizontal SOF and vertical SOF are distinguished in the anisotropic framework. The stochastic results indicate that the presented computational framework is effective in the investigation of excavation-induced deformations. Further probabilistic analyses are performed to evaluate the failure probabilities of surface settlement (SS) and retaining wall deflection (RWD). This study shows the importance of addressing the spatial variability of stiffness parameters for soil and structure problems. A series of modes for SS and RWD are presented with consideration of the effects of weak stiffness regions. The effects of vertical SOF on excavation-induced deformations are larger than those of horizontal SOF. The concept of vertical SOF correlation is proposed to explain that the most scattered result occurs when the vertical SOF is close to the size of the excavation. The research can provide a beneficial reference for advance warning of failure or hazard when performing probabilistic assessment of excavation-induced deformations.

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Abbreviations

SS:

Surface settlement

RWD:

Retaining wall deflection

SLS:

Serviceability limit state

SOF, SOFs:

Scale of fluctuation

COV, COVs:

Coefficients of variability

PH-SS model:

The plastic hardening-small-strain model

CMDM:

The covariance matrix decomposition method

ACF:

Auto-correlation function

MCS:

Monte Carlo simulation

LSF:

The limit state function

RFDM:

Random finite difference method

F s :

The factor of safety against basal heave

q a :

The asymptotic value of the deviatoric stress

q :

The deviatoric stress

E i :

The initial soil Young’s modulus at a very low-strain (< 10−6)

G 0 :

The initial or very small-strain shear modulus

G :

The shear modulus

γ 0 .7 :

The shear strain at which G = 0.7G0

γ :

The shear strain

ε 1 :

The axial (vertical compressional) strain

\(E_{{{\text{oed}}}}^{{{\text{ref}}}}\) :

Tangent stiffness for primary oedometer loading (kN/m2)

\(E_{{50}}^{{{\text{ref}}}}\) :

Secant stiffness in standard drained triaxial test (kN/m2)

\(E_{{{\text{ur}}}}^{{{\text{ref}}}}\) :

Unloading/reloading stiffness at engineering strains (kN/m2)

\(G_{0}^{{{\text{ref}}}}\) :

Reference shear modulus at very small strains (< 10−6) (kN/m2)

φ′:

Effective angle of internal friction (°)

c′:

Effective cohesion (kN/m2)

υ :

Poisson’s ratio

m :

Exponent of the stress-dependency of stiffness

p ref :

Reference stress for stiffnesses (kN/m2)

τ x :

The absolute distance between any two spatial points in the horizontal direction (m)

τ z :

The absolute distance between any two spatial points in the vertical direction (m)

θ x :

The horizontal SOFs (m)

θ z :

The vertical SOFs (m)

\(\rho \left( {\tau _{x} ,\tau _{z} } \right)\) :

The auto-correlation coefficient between any two spatial points

C n × n :

The auto-correlation matrix

L :

A lower triangular matrix

L T :

The transpose of the matrix L

Y :

A randomly generated vector

P f :

The probability of failure

Z :

The limit state function (LSF)

S sto :

The response of stochastic calculation

S lim :

The limiting value of the corresponding response

N :

The number of MCSs

I[–]:

The indicator function. When Z < 0, I[–] is 1, otherwise zero

K n :

The normal stiffness (kN/m2)

K s :

The shear stiffness (kN/m2)

K :

The average value of the soil bulk stiffness (kN/m2)

G :

The average value of the soil shear stiffness (kN/m2)

Δz :

The element size on the low-stiffness side in the adjacent soil element

H :

The final depth of excavation (m)

B :

The half-width of excavation (m)

μ ln :

Mean of the lognormal distribution

σ ln :

Standard deviation of the lognormal distribution

μ :

Mean of the normal distribution

σ :

Standard deviation of the normal distribution

δ vm/H :

The dimensionless parameter for maximum SS

δ hm/H :

The dimensionless parameter for maximum RWD

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos 51909259, 52079135, and 52008122), the International Partnership Program of Chinese Academy of Sciences (Grant No. 131551KYSB20180042), the Science and Technology R & D Project of China State Construction International Holdings Limited (No. CSCI-2020-Z-21), and Ningbo Public Welfare Science and Technology Planning Project (No. 2019C50012). The authors are also grateful to the reviewers and editors for their valuable comments and suggestions.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, People’s Republic of China

    Shun Yi, Jian Chen, Juehao Huang & Yuefeng Qiu

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Shun Yi, Jian Chen, Juehao Huang & Yuefeng Qiu

  3. Hubei Key Laboratory of Geo-Environmental Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, People’s Republic of China

    Shun Yi, Jian Chen & Juehao Huang

  4. State Key Laboratory of Geomechanics and Geotechnical Engineering, Soft Soil Research Center, Ningbo University of Technology, Ningbo, 315211, People’s Republic of China

    Shun Yi, Jian Chen & Juehao Huang

  5. China-Pakistan Joint Research Center on Earth Sciences, Islamabad, Pakistan

    Jian Chen

  6. National-Local Joint Engineering Research Center of Underwater Tunnelling Technology, Wuhan, 430063, People’s Republic of China

    Jian Chen

  7. School of Civil Engineering, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Jianbin Li

  8. China Construction Third Bureau First Engineering Co., LTD, Wuhan, 430000, People’s Republic of China

    Weijun You

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  1. Shun Yi
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Correspondence to Jian Chen.

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Yi, S., Chen, J., Huang, J. et al. Investigation of Surface Settlement and Wall Deflection Caused by Braced Excavation in Spatially Variable Clays Based on Anisotropic Random Fields. Arab J Sci Eng 47, 4059–4077 (2022). https://doi.org/10.1007/s13369-021-05853-8

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