Boundary Conditions for Soil Consolidation in a Fully Saturated Model

[Kasra]

Dear All,

In a consolidation problem under the sae, for defining the boundary conditions for a model which is fully saturated - below 10 m of the sea level - I have considered the following boundary conditions. Please share with me your experience in this regard.

1. Initializing the pore pressure for all grid points with (Zone gridpoint ini PP)
2. Fixing the pore pressure on the top of the model for considering the permanent pore pressure due to the sea level (Zone gridpoint fix PP)
3. Applying the dead load of the water above the model (Zone face apply stress-normal )

My main Question is that if the side vertical boundaries and the bottom of the model need to have any pore pressure boundary condition.

Thanks

[Kh.Mohammadamini]

Yes, you must apply boundary conditions, fixed or apply at the model boundaries.
Zone gridpoint fix
zone face apply
Thanks,

[Kasra]

Thanks Dear Eng. Mohammadi. Already, you helped me too much. Because, when I applied or even fixed boundary conditions with a gradient to the side vertical boundaries within a range from top to the bottom, the pore pressures were gradually decreased via side boundaries like a drain condition. So, I was surprised because I expected that the pore pressures remain at the initial values.

[Kasra]

However during the analysis, the pore pressure went down like a drained system … on the top, the pore pressure is negative … So, I think something goes wrong! I have not fix the pore pressure in side boundaries… Because, according to the manual all boundaries are No Flow as a default. So, I am pondering how I can fix teh problem. I expected to have the pore pressure as same as the hydrostatic pressures in the far boundaries. But, It didn’t happen!

[dblanksma]

Hello @Kasra,
Would you be able to provide the commands you are using in your model?

[Kasra]

model new
model large-strain off
model title “Marine Consolidation - Coupled Analysis”
model config fluid

plot create
;============================================================================================================
; 1. Geometry
;============================================================================================================

zone create brick size 12 24 2 ratio 1 1 1 point 0 (0,-30,-1.75) point 1 (30,-30,-1.75) point 2 (0,30,-1.75) point 3 (0,-30,0) group ‘SR2’
zone create brick size 12 24 6 ratio 1 1 1 point 0 (0,-30,-12.45) point 1 (30,-30,-12.45) point 2 (0,30,-12.45) point 3 (0,-30,-1.75) group ‘SL1’
zone create brick size 12 24 2 ratio 1 1 1 point 0 (0,-30,-15.45) point 1 (30,-30,-15.45) point 2 (0,30,-15.45) point 3 (0,-30,-12.45) group ‘LA1’
zone create brick size 12 24 3 ratio 1 1 1 point 0 (0,-30,-19.25) point 1 (30,-30,-19.25) point 2 (0,30,-19.25) point 3 (0,-30,-15.45) group ‘LS’
zone create brick size 12 24 4 ratio 1 1 1 point 0 (0,-30,-26.45) point 1 (30,-30,-26.45) point 2 (0,30,-26.45) point 3 (0,-30,-19.25) group ‘LA1’
zone create brick size 12 24 5 ratio 1 1 1 point 0 (0,-30,-36.45) point 1 (30,-30,-36.45) point 2 (0,30,-36.45) point 3 (0,-30,-26.45) group ‘SL2’
zone create brick size 12 24 5 ratio 1 1 1 point 0 (0,-30,-45) point 1 (30,-30,-45) point 2 (0,30,-45) point 3 (0,-30,-36.45) group ‘ORV’

zone reflect dip 90 dip-dir 90 origin 0 0 0 merge on
zone face skin

;============================================================================================================
; 2. Material Properties - Mechanical
;============================================================================================================

zone cmodel assign mohr-coulomb range group ‘SR2’
zone property density 1700 bulk 7.5e6 shear 3.8e6 friction 26 cohesion 2e3 range group ‘SR2’ ;

zone cmodel assign mohr-coulomb range group ‘SL1’
zone property density 1750 bulk 7.5e6 shear 3.8e6 friction 34 cohesion 10e3 range group ‘SL1’

zone cmodel assign mohr-coulomb range group ‘LA1’
zone property density 1850 bulk 5.5e6 shear 2.0e6 friction 30 cohesion 30e3 range group ‘LA1’ position-z -15.45 -12.45

zone cmodel assign mohr-coulomb range group ‘LS’
zone property density 1900 bulk 11.1e6 shear 3.7e6 friction 32 cohesion 15e3 range group ‘LS’

zone property density 1900 bulk 4.0e6 shear 2.0e6 friction 30 cohesion 55e3 range group ‘LA1’ position-z -26.45 -19.25

zone cmodel assign mohr-coulomb range group ‘SL2’
zone property density 1900 bulk 24.0e6 shear 20.0e6 friction 36 cohesion 20e3 range group ‘SL2’

zone cmodel assign mohr-coulomb range group ‘ORV’
zone property density 1900 bulk 30.0e6 shear 20.0e6 friction 30 cohesion 300e3 range group ‘ORV’

zone face apply stress-normal=-35e3 servo ramp range position-x -5 5 position-y -5 5 position-z 0 ; Consolidation Load

;============================================================================================================
; 3. Fluid Model and Properties
;============================================================================================================

zone fluid cmodel assign isotropic

zone fluid property porosity 0.27 permeability 1e-9 range group ‘SR2’ ; 1e-9
zone fluid property porosity 0.35 permeability 5e-7 range group ‘SL1’; 5e-7
zone fluid property porosity 0.27 permeability 1e-8 range group ‘LA1’; 1e-8
zone fluid property porosity 0.30 permeability 1e-7 range group ‘LS’; 1e-7
zone fluid property porosity 0.32 permeability 1e-8 range group ‘LA1’; 1e-8
zone fluid property porosity 0.35 permeability 1e-5 range group ‘SL2’; 1e-5
zone fluid property porosity 0.27 permeability 1e-9 range group ‘ORV’; 1e-9

zone gridpoint initialize fluid-modulus 2e9
;zone fluid biot on
;zone gridpoint initialize biot 1
zone water density 1e3

;============================================================================================================
; 4. Initial Conditions
;============================================================================================================

model gravity (0,0,-10)

zone initialize-stresses ratio 0.5

zone gridpoint initialize saturation 1
zone gridpoint initialize pore-pressure 135.5e3 gradient (0,0,-1e4)

zone face apply pore-pressure 135.5e3 range position-z 0

;============================================================================================================
; 5. Boundary Conditions
;============================================================================================================

zone face apply velocity-x 0 range position-x -30.1 -29.9
zone face apply velocity-x 0 range position-x 29.9 30.1
zone face apply velocity-y 0 range position-y -30.1 -29.9
zone face apply velocity-y 0 range position-y 29.9 30.1
zone face apply velocity-z 0 range position-z -45
zone face apply velocity-y 0 range position-z -45
zone face apply velocity-x 0 range position-z -45

;============================================================================================================
; 6. Setting
;============================================================================================================

model mechanical active on
model fluid active on

;============================================================================================================
; 7. Histories
;============================================================================================================

history interval 10
model history mechanical unbalanced-maximum
model history name ‘time’ fluid time-total ;
zone history name ‘settlement_gp0’ displacement-z position (0,0,0)
zone history name ‘settlement_gp1’ displacement-z position (0,0,-3.89) ; Z=-17.9
zone history name ‘settlement_gp2’ displacement-z position (0,0,-8.17) ; Z=-21.90
zone history name ‘settlement_gp3’ displacement-z position (0,0,-21.65) ; Z=-34.90
zone history name ‘settlement_gp4’ displacement-z position (0,0,-26.45) ; Z=-39.90
zone history name ‘settlement_gp5’ displacement-z position (0,0,-36.45) ; Z=48.90
zone history name ‘pore_pressure_gp0’ pore-pressure position (0,0,-6.03) ; Z=20.26
zone history name ‘pore_pressure_gp1’ pore-pressure position (0,0,-10.31); Z=-25.26
zone history name ‘pore_pressure_gp2’ pore-pressure position (0,0,-24.05); Z=-36.70

;============================================================================================================
; 7. Undrained Response under Consolidation Load
;============================================================================================================

zone face apply stress-normal=-42.5e3 servo ramp range position-x -5 5 position-y -5 5 position-z 0 ; Consolidation Load

============================================================================================================
; 8. Coupled Response
;============================================================================================================

model solve mech time [1243600] fluid time [1243600] ; 1 day

ret

[dblanksma]

Hello @Kasra,
You need to:
(1) Solve to initial mechanical equilibrium just before the “6. Setting” title with fluid off and mechanical on.
(2) Run the undrained response with again mechanical on and fluid off and the consolidation loading you specify with zone face apply …
(3) Once that is complete you can run the coupled analysis with both mechanical on and fluid on. Keep in mind your current data file has a fully coupled (one fluid step of each mechanical step) setup. You may need to take mechanical substeps for your model to reach steady state quicker. Or look into uncoupling techniques - see Solving Flow-Only and Coupled-Flow Problems.

[Kasra]

Dear @dblanksma

After re-executing the code based on your advice and considering the following commands in my code, the pore pressures at the far-side boundaries dropped compared to the hydrostatic pressures caused by the constant head above the model. I have attached a figure showing the pore pressure distribution in the model. I expected the pore pressures to remain at the initial values, but they changed!

model fluid substep 100
model mechanical substep 10
model mechanical slave
model solve time-total [24*3600]

[dblanksma]

Hello @Kasra,
If you applied an undrained consolidation load (mechanical only) then ran a coupled fluid-flow calculation (mechanical on and fluid on) then yes, the pore pressure will (and should) certainly change. The system is calculating to a steady state as you can see in the degradation of the pore pressure from the initial increase in pore-pressure that was caused by the loading.

[Kasra]

Dear @dblanksma

Thank you for your response, it was very useful. By increasing the distance of the boundaries from the load location, the pore pressures at the boundaries matched the values consistent with hydrostatic conditions. However, my question still remains: I expected the pore pressures beneath the load location to increase immediately after applying the load (excess pore pressure), and then gradually decrease step by step to the hydrostatic values. This ambiguity has not yet been resolved.

[dblanksma]

Hello @Kasra,
Yes, there should be excess pore pressure after loading. Could you send your model files to flac3dsupport@oneitasca.com? I am not sure at this time what the issue could be.

[Kasra]

@dblanksma

flac3dsupport@oneitasca.com

Thank you for your attention. I have just sent it to the above-mentioned email address.