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A Numerical Study on the Estimation of Liquefaction-Induced Free-Field Settlements by Using PM4Sand Model

  • Geotechnical Engineering
  • Published:
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Abstract

The present paper treats the estimation of liquefaction-induced, free-field settlements using two-dimensional, fully coupled, finite element (FE) analyses. The PM4Sand model is used to simulate the liquefaction behavior of a homogeneous sand layer with three different relative densities of 35%, 55%, 75% under eleven different strong ground motions. The results of FE analyses are compared with those obtained from the well-known, semi-empirical methods in the literature. The numerical analyses show that, in case of a relative density of 35%, in general, the majority of earthquake-induced settlements occur in the period, in which the excess pore water pressure resulting from the strong ground motion begins to dissipate. The liquefaction-induced settlements are influenced by not only the moment magnitude and peak ground acceleration, but also other parameters of the ground motion. Furthermore, it has been shown that the evaluation of the liquefaction potential using finite element and semi-empirical methods gives similar results. However, the semi-empirical methods yield mostly larger settlements than those obtained from the FE analyses.

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Abbreviations

acc.:

Acceleration

a max :

Peak horizontal ground acceleration on the sand surface

C :

Damping matrix

c′:

Effective cohesion

CSR :

Cyclic stress ratio

CSR SS,20,1D,1atm :

Cyclic stress ratio at the one-dimensional, 20 uniform loading cycles, under a confining pressure of 100 kPa

D R/D R0 :

Relative density

e :

Void Ratio

e max :

Maximum void ratio

e min :

Minimum void ratio

E oedref :

Tangent stiffness for primary oedometer loading

E urref :

Unloading-reloading stiffness

E 50ref :

Secant stiffness in standard triaxial test

EQ :

Earthquake

f 1 :

First frequency parameter for Rayleigh damping

f 2 :

Second frequency parameter for Rayleigh damping

f eq :

fundamental frequency of the input earthquake motion

f max :

Highest frequency of the input earthquake motion

FE :

Finite element

G 0 :

Shear modulus

G 0ref :

Reference shear modulus at very small strains

H :

Layer thickness

h po :

Contraction rate parameter

HSS :

Hardening Soil Model with small strain stiffness

I a :

Arias intensity

I min :

Minimum length between two nodes of an finite element

K :

Stiffness matrix

M :

Mass matrix

m :

Rate of stress dependency

M w :

Moment magnitude

N1,60/SPT N1,60,cs/SPT-N1,60,cs :

Corrected SPT-N value

n b :

Bounding surface parameter

n d :

Dilatancy surface parameter

P a :

Atmospheric pressure

PEER:

The Pacific Earthquake Engineering Research Center

PGA:

Peak ground acceleration

P ref :

Reference stress level

Q, R :

Critical state line parameters

q c,1 :

Overburden corrected cone tip resistance

R f :

Failure ratio

R u :

Pore water pressure ratio

SPT-N:

Standard penetration resistance test blow count

S3:

Earthquake-induced settlement at the end of Stage 3

S4:

Earthquake-induced total settlement at the end of Stage 4

T :

Duration of the earthquake

V s,min :

Lowest shear wave velocity in the layer

V s,mean :

Average shear wave velocity of layer

V s,layer :

Shear wave velocity of layer

α, β :

Rayleigh coefficients

γ dry :

Dry unit weight

γ max :

Maximum shear strain

γ sat :

Saturated unit weight

γ 0.7 :

Shear strain ration where G/G0 = 0.7

Δt :

The critical time step

ε v :

Volumetric strains

ν :

Poisson’s ratio

ξ 1,2 :

Target damping ratios

σ′ v :

Vertical effective stress at the end of the dynamic analysis and

σ′ v0 :

The initial effective vertical stress prior to the strong ground motion

ϕ′ :

Angle of internal effective friction

ϕ cv :

Critical state friction angle

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Acknowledgments

Ozan Subasi, who took part in this study, is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) within the scope of the 2211-A National Ph.D. Scholarship Program.

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Authors and Affiliations

  1. Dept. of Civil Engineering, Istanbul Technical University, Istanbul, 34469, Turkey

    Ozan Subasi & Recep Iyisan

  2. Dept. of Civil Engineering, Turkish-German University, Istanbul, 34820, Turkey

    Ozan Subasi

  3. HPC AG, Stuttgart, 70563, Germany

    Serdar Koltuk

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  1. Ozan Subasi
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  2. Serdar Koltuk
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Correspondence to Ozan Subasi.

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Subasi, O., Koltuk, S. & Iyisan, R. A Numerical Study on the Estimation of Liquefaction-Induced Free-Field Settlements by Using PM4Sand Model. KSCE J Civ Eng 26, 673–684 (2022). https://doi.org/10.1007/s12205-021-0719-0

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