Limit Analysis of Modified Pseudodynamic Lateral Earth Pressure in Anisotropic Frictional Medium Using Finite-Element and Second-Order Cone Programming
Publication: International Journal of Geomechanics
Volume 21, Issue 2
Abstract
This paper aims at analyzing the active and passive lateral earth pressures exerted on retaining walls due to the anisotropic medium of dry and noncohesive backfill subjected to the modified pseudodynamic earthquake loading. To this end, the well-established lower bound limit analysis in conjunction with the finite-element discretization method using second-order cone programming is exploited to evaluate the corresponding states of seismic earth pressures on the retaining structure. The earthquake loading is simulated by the propagation of the shear and primary waves through nonconstant inertia forces in the horizontal and vertical directions, respectively. The inherently anisotropic behavior of the soil medium is also accounted for by differentiating between the internal friction angles in different directions. Results generally show that, unlike the active state, inherent anisotropy bears a notable influence on the passive earth pressure; however, the effect of seismic loading on the lateral earth pressure is more pronounced in the active state. The dominant influence of anisotropy occurs at the critical state of seismic loading, i.e., the resonance condition. Using the results of numerical simulations, the influence of internal friction angle, soil–wall roughness, imposed wavelength, material damping, and inherent anisotropy on the lateral earth pressures is thoroughly evaluated and discussed.
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Notation
The following symbols are used in this paper:
- [A]
- matrix of linear constraints;
- {b}
- vector of linear constraints;
- Cs, Csy
- modified pseudodynamic inertia force coefficients;
- D
- material damping ratio;
- H
- wall height;
- Ka, Kp
- active and passive lateral earth pressure coefficients;
- kh, kv
- horizontal and vertical acceleration coefficients;
- Nα
- rate of anisotropy;
- Pa, Pp
- total active and passive lateral earth pressures;
- Pr, Pr−1
- total lateral earth pressures at rth and (r− 1)th iterations;
- Qh, Qv
- horizontal and vertical inertia forces;
- R
- yield function ratio;
- Ss, Ssy
- modified pseudodynamic inertia force coefficients;
- T
- dominant period of earthquake excitation;
- t
- time of shaking;
- Vp
- compression (primary) wave velocity;
- Vs
- shear wave velocity;
- x
- horizontal coordinate;
- y
- vertical coordinate;
- z
- nodal auxiliary variable;
- zs1, zs2
- modified pseudodynamic inertia force coefficients;
- β
- anisotropy ratio;
- γ
- soil unit weight;
- δ
- soil–wall interface roughness angle;
- ɛ
- maximum allowable convergence tolerance;
- θ
- angle of major principal stress direction with horizontal axis;
- μ
- shear-strength parameter;
- μh, μv
- shear-strength parameter in the horizontal and vertical directions;
- μr, μr−1
- vectors of shear-strength parameter for all nodal points at rth and (r − 1)th iterations;
- σ
- total normal stress;
- τ
- shear stress;
- φ
- internal friction angle;
- φh, φv
- internal friction angle in the horizontal and vertical directions;
- ψ
- dilation angle; and
- ω
- angular frequency of earthquake excitation.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 9, 2020
Accepted: Sep 23, 2020
Published online: Dec 10, 2020
Published in print: Feb 1, 2021
Discussion open until: May 10, 2021
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