# 4.15.6.2. PressureDependMultiYield¶

nDMaterial('PressureDependMultiYield', matTag, nd, rho, refShearModul, refBulkModul, frictionAng, peakShearStra, refPress, pressDependCoe, PTAng, contrac, *dilat, *liquefac, noYieldSurf=20.0, *yieldSurf=[], e=0.6, *params=[0.9, 0.02, 0.7, 101.0], c=0.3)

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.

 matTag (int) integer tag identifying material nd (float) Number of dimensions, 2 for plane-strain, and 3 for 3D analysis. rho (float) Saturated soil mass density. refShearModul (float) ($$G_r$$) Reference low-strain shear modulus, specified at a reference mean effective confining pressure refPress of p’r (see below). refBulkModul (float) ($$B_r$$) Reference bulk modulus, specified at a reference mean effective confining pressure refPress of p’r (see below). frictionAng (float) ($$phi$$) Friction angle at peak shear strength in degrees, optional (default is 0.0). peakShearStra (float) ($$\gamma_{max}$$) An octahedral shear strain at which the maximum shear strength is reached, specified at a reference mean effective confining pressure refPress of p’r (see below). refPress (float) ($$p'_r$$) Reference mean effective confining pressure at which $$G_r$$, $$B_r$$, and $$\gamma_{max}$$ are defined, optional (default is 100. kPa). pressDependCoe (float) ($$d$$) A positive constant defining variations of $$G$$ and $$B$$ as a function of instantaneous effective confinement $$p'$$ (default is 0.0) $$G=G_r(\frac{p'}{p'_r})^d$$ $$B=B_r(\frac{p'}{p'_r})^d$$ If $$\phi=0$$, $$d$$ is reset to 0.0. PTAng (float) ($$\phi_{PT}$$) Phase transformation angle, in degrees. contrac (float) A non-negative constant defining the rate of shear-induced volume decrease (contraction) or pore pressure buildup. A larger value corresponds to faster contraction rate. dilat (list (float)) Non-negative constants defining the rate of shear-induced volume increase (dilation). Larger values correspond to stronger dilation rate. dilat = [dilat1, dilat2]. liquefac (list (float)) Parameters controlling the mechanism of liquefaction-induced perfectly plastic shear strain accumulation, i.e., cyclic mobility. Set liquefac[0] = 0 to deactivate this mechanism altogether. liquefac[0] defines the effective confining pressure (e.g., 10 kPa in SI units or 1.45 psi in English units) below which the mechanism is in effect. Smaller values should be assigned to denser sands. Liquefac[1] defines the maximum amount of perfectly plastic shear strain developed at zero effective confinement during each loading phase. Smaller values should be assigned to denser sands. Liquefac[2] defines the maximum amount of biased perfectly plastic shear strain $$\gamma_b$$ accumulated at each loading phase under biased shear loading conditions, as $$\gamma_b=liquefac[1]\times liquefac[2]$$. Typically, $$liquefac[2]$$ takes a value between 0.0 and 3.0. Smaller values should be assigned to denser sands. See the references listed at the end of this chapter for more information. noYieldSurf (float) Number of yield surfaces, optional (must be less than 40, default is 20). The surfaces are generated based on the hyperbolic relation defined in Note 2 below. yieldSurf (list (float)) If noYieldSurf<0 && >-100, the user defined yield surface is used. You have to provide a list of 2*(-noYieldSurf), otherwise, the arguments will be messed up. Also don’t provide user defined yield surface if noYieldSurf>0, it will mess up the argument list too. Instead of automatic surfaces generation (Note 2), you can define yield surfaces directly based on desired shear modulus reduction curve. To do so, add a minus sign in front of noYieldSurf, then provide noYieldSurf pairs of shear strain (r) and modulus ratio (Gs) values. For example, to define 10 surfaces: yieldSurf = [r1, Gs1, …, r10, Gs10] e (float) Initial void ratio, optional (default is 0.6). params (list (float)) params=[cs1, cs2, cs3, pa] defining a straight critical-state line ec in e-p’ space. If cs3=0, ec = cs1-cs2 log(p’/pa) else (Li and Wang, JGGE, 124(12)), ec = cs1-cs2(p’/pa)cs3 where pa is atmospheric pressure for normalization (typically 101 kPa in SI units, or 14.65 psi in English units). All four constants are optional c (float) Numerical constant (default value = 0.3 kPa)