9.7.3 Bowl

For a summary of the background theory of the Bowl model see §24.3. The input data of the Bowl model starts with the BOWL model specifier. See also DIANA's Test Suite on Test/nl/liqu/bo* with some validation tests.

    (syntax)

PREF

sigref is the reference effective isotropic pressure $\sigma{^\prime}_{{\mathrm{m.ref}}}$ in Equation (24.36).( $\sigma{^\prime}_{{\mathrm{m.ref}}}$ > 0 )

SHRREF

is the reference shear modulus G_ref at the reference effective mean stress $\sigma{^\prime}_{{\mathrm{m}}}$ . This parameter is used to determine the pressure dependent actual shear modulus in Equation (24.36).

GAMMAR

gamref is the reference shear strain $\gamma_{{0.5}}^{}$ at the value G/G_ref = 0.5 in Equation (24.37).

HMAX

hmax is the maximum damping ratio h_max in Equation (24.37).

KAPPA

kappa is the swelling parameter $\kappa$ = C_s/ln10 ( $\kappa$ > 0 ) for the exponential elasticity model in Equation (24.40). This parameter relates the drained tangent bulk modulus K_t to the effective mean stress $\sigma{^\prime}_{{\mathrm{m}}}$ .

POROSI

[n₀ = 0 ] n0 is the initial porosity n₀ = e₀/(1+e₀) ( 0 $\leq$ n₀ $\leq$ 1 )where e₀ is the initial void ratio in Equation (24.40).

A

a is the parameter A in Equation (24.42).

B

b is the parameter B in Equation (24.42).

C

c is the parameter C in Equation (24.43).

D

d is the parameter D in Equation (24.43).

XL

xl is the lower limit of the liquefaction resistance X_lim = $\sigma_{{xy}}^{}$/$\sigma{^\prime}_{{\mathrm{m}.0}}$ . This parameter is used according to Equation (24.46) to determine the threshold value R_e of the shear increment at which no increase in negative dilatancy can occur.

Example    (file.dat)

'MATERI'
  1  YOUNG    146512.8
     POISON   0.333333333333333
:
     LIQUEF   BOWL
     PREF     100.0
     SHRREF   55080.0
     GAMMAR   0.0008
     HMAX      0.22
     KAPPA    0.0026
     A        -3.0
     B         1.6
     C        10.0
     D        30.0
     XL        0.1

Customization.

You may customize the Bowl liquefaction model via the user-supplied subroutine option. Therefore you must specify some additional data items [§11.6.1] and the source code of subroutine BOWLIQ [§11.6.5].