9.6.3 Undrained Behavior

If, in a geotechnical analysis, the permeability of a saturated soil is small in comparison with the loading rate, the behavior is incompressible in a short term. This undrained behavior can be modeled by defining an excess pore fluid pressure p_e in the material as

$$\varepsilon_{{\mathrm{v}}}^{}$$ (9.6)

with $\varepsilon_{{\mathrm{v}}}^{}$ the volumetric strain and K_f the undrained compression modulus which is equal to the drained compression modulus times a penalty factor: K_f = fac x K .

This method does not create separate degrees of freedom for the pore pressure, though it can be used in combination with mixture elements [Vol. Analysis Procedures]. Note that the drained compression modulus is derived from the specified constant Young's modulus and the Poisson's ratio. Therefore, in case of nonlinear elasticity, you should use this option with care. Also note that the theoretical formula

$${\frac{{ K_{\mathrm{f}} }}{{ n }}} \varepsilon_{{\mathrm{v}}}^{}$$ (9.7)

with n the porosity, is not applied because DIANA uses the fluid compression modulus only as a numerical artifice which value should be just sufficiently larger than the drained compression modulus.

    (syntax)

UNDRAI

If this term is specified, DIANA uses the undrained model. Value fac is the incompressibility penalty factor, i.e., the multiplication factor for the drained compression modulus: K_f = fac x K_D . [fac = 500]

To switch to drained behavior for subsequent load steps in a nonlinear analysis, you should issue the DRAINE command in the PHYSIC command block for step execution [Vol. Analysis Procedures]. For a new undrained phase in a phased analysis, you could also initialize the nonlinear analysis with the DRAINE command in the PHYSIC command block.

NUMBKF

bulkf is the fluid bulk modulus K_f . During the evaluation of the elements and their properties, DIANA determines the bulk modulus or, if you don't specify fac, takes it from the input bulkf. If you specify both fac and bulkf then DIANA will overrule the specified bulk modulus and give a warning message.