PressureDependMultiYield

PressureDependMultiYield material is an elastic-plastic material for simulating the essential response characteristics of pressure sensitive soil materials under general loading conditions. Such characteristics include dilatancy (shear-induced volume contraction or dilation) and non-flow liquefaction (cyclic mobility), typically exhibited in sands or silts during monotonic or cyclic loading. Please visit http://cyclic.ucsd.edu/opensees for examples.

When this material is employed in regular solid elements (e.g., FourNodeQuad, Brick), it simulates drained soil response. To simulate soil response under fully undrained condition, this material may be either embedded in a FluidSolidPorousMaterial (see below), or used with one of the solid-fluid fully coupled elements (see below) with very low permeability. To simulate partially drained soil response, this material should be used with a solid-fluid fully coupled element with proper permeability values.

During the application of gravity load (and static loads if any), material behavior is linear elastic. In the subsequent dynamic (fast) loading phase(s), the stress-strain response is elastic-plastic (see MATERIAL STAGE UPDATE below). Plasticity is formulated based on the multi-surface (nested surfaces) concept, with a non-associative flow rule to reproduce dilatancy effect. The yield surfaces are of the Drucker-Prager type.

OUTPUT INTERFACE:

The following information may be extracted for this material at a given integration point, using the OpenSees Element Recorder facility (McKenna and Fenves 2001): "stress", "strain", "backbone", or "tangent".

For 2D problems, the stress output follows this order: s_xx, s_yy, s_zz, s_xy, h_r, where h_r is the ratio between the shear (deviatoric) stress and peak shear strength at the current confinement (0<= h_r<=1.0). The strain output follows this order: e_xx, e_yy, g_xy.

For 3D problems, the stress output follows this order: s_xx, s_yy, s_zz, s_xy, s_yz, s_zx, h_r, and the strain output follows this order: e_xx, e_yy, e_zz, g_xy, g_yz, g_zx.

The "backbone" option records (secant) shear modulus reduction curves at one or more given confinements. The specific recorder command is as follows:

recorder Element –ele $eleNum -file $fName -dT $deltaT material $GaussNum backbone $p1 <$p2 …>

where p1, p2, … are the confinements at which modulus reduction curves are recorded. In the output file, corresponding to each given confinement there are two columns: shear strain g and secant modulus G_s. The number of rows equals the number of yield surfaces.

nDMaterial PressureDependMultiYield $tag $nd $rho $refShearModul $refBulkModul $frictionAng $peakShearStra $refPress $pressDependCoe $PTAng $contrac $dilat1 $dilat2 $liquefac1 $liquefac2 $liquefac3 <$noYieldSurf=20 <$r1 $Gs1 …> $e=0.6 $cs1=0.9 $cs2=0.02 $cs3=0.7 $p_a=101>

1. NOTE:
2. The friction angle f defines the variation of peak (octahedral) shear strength t_f as a function of current effective confinement p':

Octahedral shear stress is defined as:

1. (Automatic surface generation) At a constant confinement p', the shear stress t (octahedral) - shear strain g (octahedral) nonlinearity is defined by a hyperbolic curve (backbone curve):

where g_r satisfies the following equation at p'_r:

(User defined surfaces) The user specified friction angle f is ignored. Instead, f is defined as follows:

where s_m is the product of the last modulus and strain pair in the modulus reduction curve. Therefore, it is important to adjust the backbone curve so as to render an appropriate f. If the resulting f is smaller than the phase transformation angle f_PT, f_PT is set equal to f.

Also remember that improper modulus reduction curves can result in strain softening response (negative tangent shear modulus), which is not allowed in the current model formulation. Finally, note that the backbone curve varies with confinement, although the variations are small within commonly interested confinement ranges. Backbone curves at different confinements can be obtained using the OpenSees element recorder facility (see OUTPUT INTERFACE above).

1. The last five optional parameters are needed when critical-state response (flow liquefaction) is anticipated. Upon reaching the critical-state line, material dilatancy is set to zero.

1. SUGGESTED PARAMETER VALUES

For user convenience, a table is provided below as a quick reference for selecting parameter values. However, use of this table should be of great caution, and other information should be incorporated wherever possible.