Evaluation of the pseudo-dynamic bearing capacity of surface footings on cohesionless soils using finite element lower bound limit analysis

ABSTRACT

Design of shallow foundations subjected to dynamic loading is an important topic in the geotechnical engineering practice. In this study, an attempt has been made to evaluate the seismic bearing capacity of a strip footing founded on a soil deposit using the lower bound limit analysis method merged with the finite element formulation adopting the second-order conic programming (SOCP) approach. To this end, a well-established pseudo-dynamic loading scheme has been employed to apply the seismic loading on the surface footing. Accounting for the various conditions of the underlying soil layer, the results of the so-called ‘conventional pseudo-dynamic (CPD)’, ‘spectral pseudo-dynamic (SPD)’ and ‘modified pseudo-dynamic (MPD)’ bearing capacity analyses are compared with one another and their pseudo-static counterparts in terms of the value of $N_{\gamma }$ parameter. The results show the notable influence of the amplification factor, the impedance factor and the site characteristics on the seismic bearing capacity of shallow foundations. In addition, the results obtained from the MPD, CPD and SPD methods are observed to bear a good agreement with each other. Moreover, the MPD approach was observed to render the most conservative seismic bearing capacity values.

KEYWORDS:

• Seismic bearing capacity
• lower bound limit analysis
• finite element
• pseudo-dynamic
• spectral bearing capacity
• SOCP

Nomenclature

[A]	=	Matrix of constraints
[B]	=	Vector containing the static and pseudo-static loading coefficients
c	=	Soil cohesion
Cp	=	Coefficient of MPD approach
Cpz	=	Coefficient of MPD approach
Cs	=	Coefficient of MPD approach
Csz	=	Coefficient of MPD approach
fa	=	Amplification factor
$g$	=	Gravitational acceleration
$\left[g\right]$	=	Objective function coefficient
$H$	=	Soil deposit thickness
kh	=	Horizontal coefficient of acceleration
kv	=	Vertical coefficient of acceleration
Nγ	=	Bearing capacity coefficient due to soil unit weight
qu	=	Ultimate bearing capacity
$Q_c^3$	=	Conic quadratic constraint for Mohr-Coulomb yield criterion
Sp	=	Coefficient of MPD approach
Spz	=	Coefficient of MPD approach
Ss	=	Coefficient of MPD approach
Ssz	=	Coefficient of MPD approach
T	=	Period of harmonic seismic acceleration
t	=	Time of earthquake
Vp	=	Compressive (primary) wave velocity
Vs	=	Shear (secondary) wave velocity
{X}	=	Global variable consisting of nodal stresses
yp1	=	Coefficient of MPD approach
yp2	=	Coefficient of MPD approach
ys1	=	Coefficient of MPD approach
ys2	=	Coefficient of MPD approach
z	=	Depth from the ground surface
${\alpha }_z$	=	Impedance factor
γ	=	Unit weight of the soil
δ	=	Roughness
ξ	=	Material damping
$\theta$	=	Seismic angle
$\lambda$	=	Shear wavelength
$\sigma$	=	Normal stress
τ	=	Shear stress
ϕ	=	Internal friction angle
ω	=	Angular frequency of the motion

Disclosure statement

No potential conflict of interest was reported by the author(s).