A mixed 3D-1D finite element formulation for analysis of geomaterial structures with embedded curvilinear inclusions: application to load transfer in mooring anchor systems

A finite element model for structural analysis of media with embedded inclusions is presented. The “embedded element concept” is adopted to model the contact interaction of two medium components along the contact interface considering a mixed 3D-1D formulation. The Mohr-Coulomb interface model is employed to define the bond-stress and bond-slip relation and strains associated with bond-slip are assumed to remain infinitesimal along the interface. Nonlinear analysis is performed with a corotational kinematics description introduced in the context of embedded approach. The problem of load transfer in mooring anchor systems was investigated and reasonable results were obtained using the present model.

Keywords
embedded inclusion; bond-slip model interface; finite element modeling; embedded model; corotational kinematics

Authorship

Alexandre Luis Braun ^**Corresponding author

Centro de Mecânica Aplicada e Computacional - CEMACOM, Programa de Pós-Graduação em Engenharia Civil - PPGEC, Universidade Federal do Rio Grande do Sul - UFRGS, Porto Alegre, Rio Grande do Sul, Brasil. E-mail: alexandre.braun@ufrgs.br, andrebruch@hotmail.com, samir.maghous@ufrgs.brUniversidade Federal do Rio Grande do SulBrazilPorto Alegre, Rio Grande do Sul, Brazil Centro de Mecânica Aplicada e Computacional - CEMACOM, Programa de Pós-Graduação em Engenharia Civil - PPGEC, Universidade Federal do Rio Grande do Sul - UFRGS, Porto Alegre, Rio Grande do Sul, Brasil. E-mail: alexandre.braun@ufrgs.br, andrebruch@hotmail.com, samir.maghous@ufrgs.br

André Brüch

Samir Maghous

*Corresponding author

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (21)
Tables (6)

Properties		Values
Matrix	Elastic modulus $E$	$25000 MPa$
	Poisson ratio $ν$	$0.2$
	Yield strength $σ_{y}$	$2 .2 MPa$
Inclusion	Cross-section area $A_{c}$	$1 .0 \times 1 0^{- 4} m^{2}$
Inclusion	Elastic modulus $E_{c}$	$210000 MPa$
Soil-cable interface	Tangential stiffness modulus $k_{s}$	$2 .0 \times 1 0^{1} - 2 .0 \times 1 0^{11} Pa / m$
	Normal stiffness modulus $k_{n}$	$1 0^{6} \times k_{s}$
	Cohesion $c$	$0.25 - 1.0 kPa$
	Internal friction angle $ϕ$	$30^{\circ}$
	Dilatancy angle $ψ$	$0^{\circ}$

c (MPa)	K_s (Pa/m)	$u_{s}^{\max}$ (m)	$u_{s}^{\max}$ - ANSYS (m)	$u_{c}^{\max}$ (m)	$u_{c}^{\max}$ - ANSYS (m)	R (KN)	R - ANSYS (KN)
0.25	2.0x10¹	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10³	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁵	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁶	3.99x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	83.9	83.9
	2.0x10⁷	3.95x10^-3	3.96x10^-3	3.95x10^-3	3.96x10^-3	82.5	82.7
	2.0x10⁸	3.78x10^-3	3.80x10^-3	3.80x10^-3	3.82x10^-3	76.6	77.1
	2.0x10⁹	3.77x10^-3	3.79x10^-3	3.78x10^-3	3.81x10^-3	75.1	76.1
	2.0x10¹⁰	3.71x10^-3	3.79x10^-3	3.73x10^-3	3.81x10^-3	73.4	76
	2.0x10¹¹	3.71x10^-3	3.79x10^-3	3.73x10^-3	3.81x10^-3	73.4	76
0.5	2.0x10¹	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10³	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁵	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁶	3.99x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	83.9	83.9
	2.0x10⁷	3.95x10^-3	3.96x10^-3	3.95x10^-3	3.96x10^-3	82.5	82.7
	2.0x10⁸	3.62x10^-3	3.66x10^-3	3.65x10^-3	3.68x10^-3	72.4	73.3
	2.0x10⁹	3.54x10^-3	3.59x10^-3	3.57x10^-3	3.62x10^-3	66.8	68.3
	2.0x10¹⁰	3.48x10^-3	3.59x10^-3	3.52x10^-3	3.62x10^-3	64.6	68
	2.0x10¹¹	3.45x10^-3	3.59x10^-3	3.49x10^-3	3.62x10^-3	63.6	68
0.75	2.0x10¹	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10³	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁵	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁶	3.99x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	83.9	83.9
	2.0x10⁷	3.95x10^-3	3.96x10^-3	3.95x10^-3	3.96x10^-3	82.5	82.7
	2.0x10⁸	3.56x10^-3	3.61x10^-3	3.59x10^-3	3.64x10^-3	71.2	72.3
	2.0x10⁹	3.03x10^-3	3.24x10^-3	3.39x10^-3	3.44x10^-3	61.4	61.3
	2.0x10¹⁰	2.73x10^-3	2.99x10^-3	3.37x10^-3	3.44x10^-3	60.7	60
	2.0x10¹¹	2.64x10^-3	2.99x10^-3	3.35x10^-3	3.44x10^-3	59.6	59.7
1.0	2.0x10¹	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10³	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁵	4.00x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	84	84
	2.0x10⁶	3.99x10^-3	4.00x10^-3	4.00x10^-3	4.00x10^-3	83.9	83.9
	2.0x10⁷	3.95x10^-3	3.96x10^-3	3.95x10^-3	3.96x10^-3	82.5	82.7
	2.0x10⁸	3.56x10^-3	3.61x10^-3	3.59x10^-3	3.64x10^-3	71.2	72.3
	2.0x10⁹	2.39x10^-3	2.55x10^-3	3.28x10^-3	3.33x10^-3	61.4	61.4
	2.0x10¹⁰	2.09x10^-3	2.34x10^-3	3.27x10^-3	3.33x10^-3	60.5	59.9
	2.0x10¹¹	2.04x10^-3	2.31x10^-3	3.27x10^-3	3.33x10^-3	60.3	59.2

Properties		Values
Soil	Undrained shear strength $S_{u} (y) = α \| y \|$	$α = 1.4 kPa/m$
	Elastic modulus $E (y) = β S_{u} (y)$	$β = 300$
	Poisson ratio	$ν = 0.495$
	Saturated specific weight	$γ = 15.1 {kN/m}^{3}$
Mooring cable	Equivalent bar diameter	$d_{c} = 0.24 m$
Mooring cable	Axial rigidity	$E_{c} A_{c} = 1.1 \times 1 0^{6} kN$
Soil-cable interface	Tangential stiffness modulus	$k_{s} = 2.43 \times 1 0^{3} kPa / m$
	Normal stiffness modulus	$k_{n} = 1 0^{6} \times k_{s}$
	Cohesion	$c = 0 kPa$
	Internal friction angle	$ϕ = 30^{\circ}$
	Dilatancy angle	$ψ = 0^{\circ}$

Displacements	Average value	Value at the load peak
Axial displacement	0.119 m	0.157 m
Relative displacement	0.0159 m	0.0414 m

Anchoring depth	Average attenuation	Attenuation at the load peak
15 m	20.7%	23.5%
20 m	24.6%	26.4%
25 m	26.8%	27.9%

Soil stiffness	Average attenuation	Attenuation at the load peak
E(z) = 300 S_u(z)	20.7%	23.5%
E(z) = 500 S_u(z)	23.2%	26.9%