9.3.4 Friction

Coulomb friction for interface elements may be specified according to the following syntax. See also §21.4 for background theory.

    (syntax)

FRICTI

indicates use of the Coulomb friction criterion [Fig.9.12].

Figure 9.12: Coulomb friction criterion

FRCVAL

describes the friction criterion: ch is the cohesion c , tph is tan$\phi$ of friction angle $\phi$ ( tan$\phi$ > 0 ) and tps is tan$\psi$ of dilatancy angle $\psi$ . Associated plasticity if $\psi$ = $\phi$ , nonassociated plasticity if $\psi$ < $\phi$ . ( 0 < tan$\psi$ $\leq$ tan$\phi$ )Nonassociated plasticity gives an asymmetrical tangential stiffness matrix. Low to moderate degrees of asymmetry |$\phi$ - $\psi$| < $\approx$ 20° , are best solved with DIANA's nonsymmetric solver. For high degrees of asymmetry the Constant or Linear Stiffness iteration methods should be applied [Vol. Analysis Procedures].

HARDIA

specifies a cohesion hardening diagram with values ch1 to chn (n $\leq$ 25 )the cohesions c and up1 to upn the corresponding equivalent plastic relative displacements $\Delta$u_p .

FRCDIA

specifies a fraction hardening diagram: tph1 ...tphn (n $\leq$ 25 )are the tan$\phi$ of friction angles $\phi$ and up1 ...upn the corresponding equivalent plastic relative displacements $\Delta$u_p .

GAP

extends the friction criterion with a gap criterion. DIANA assumes that a gap arises if the tensile traction t_n normal to the interface exceeds a certain value. After gap formation, t_n is reduced to zero immediately (brittle cracking).

GAPVAL

ft is the tensile strength f_t . ( 0 $\leq$ f_t $\leq$ c/tan$\phi$ )The default value corresponds to the apex of the Coulomb friction criterion. [ f_t = c/tan$\phi$ ]

MODE2

mo2 is the number of the Mode-II model after gap appearance.
MODE2 0 for `brittle' (default). [MODE2 0]
MODE2 1 for `constant shear retention'.
MODE2 2 for shear retention according to the `aggregate interlock' relation of Walraven and Reinhardt.

MO2VAL

mv2 is the value of a parameter for the Mode-II model: the reduced stiffness for `constant shear retention', the compressive strength (in MPa) of the concrete for `aggregate interlock'. No parameter is necessary for the `brittle' model.

Sand structure    (file.dat)

'MATERI'
 1   DSTIF  1.E+5 1.E+3
     FRICTI
     FRCVAL 0. 0.36 0.
     GAP

This example specifies a sand structure interface with zero cohesion, a friction angle of 20° and a zero dilatancy angle. It includes gap formation with a default tensile strength.

Hardening    (file.dat)

'MATERI'
 2   DSTIF  1.E+5 1.E+5
     FRICTI
     FRCVAL 1.  0.5  0.
     HARDIA 1.  0.   2.  0.05    2.  10.
     FRCDIA 0.5 0.   1.  0.05    1.  10.

Position dependency.

For some materials the cohesion may depend on the position of the material in space. A typical example is soil where c may vary with the depth in the soil layer. To model such a dependency, DIANA can apply gradient characteristics to the Coulomb friction model for interface elements.

    (syntax)

REFPOS

specifies the reference position where xref, yref, and zref respectively are the coordinates ( X_ref, Y_ref, Z_ref ) of the reference point R for which c_{$\mathsf {R}$} = c_ref .

COHGRD

specifies the gradient of the cohesion in the global XYZ directions: $\partial$c/$\partial$X = grx , $\partial$c/$\partial$Y = gry , $\partial$c/$\partial$Z = grz .

DIANA will calculate the cohesion for each element integration point via linear interpolation:

$${\frac{{ \partial c }}{{ \partial X }}} {\frac{{ \partial c }}{{ \partial Y }}} {\frac{{ \partial c }}{{ \partial Z }}}$$ (9.4)

where c_ref is the reference cohesion whose value is supposed to be specified in the hardening diagram via input items FRCVAL and HARDIA [§9.3.4].