Parameters are specified in the PLAXIS input in the following order:
Parameter 1 - critical state friction angle
Parameter 2 - - shift of the mean stress due to cohesion. The effective stress
used in the model formulation is replaced by
.
Non-zero value of is needed to overcome problems with stress-free state.
If , it will be replaced by a default value of 1 kPa. Any other value can be input by user (for basic hypoplasticity, set to very low number, e.g. ).
Parameters 3-9 - parameters of the basic hypoplastic model for granular materials , , , , , , .
Parameters 10-14 - the intergranular strain concept parameters (, , , , ). If the intergranular
strain concept is switched off and the problem is simulated using the basic hypoplastic model.
Parameter 15 - not used.
Parameter 16 - initial void ratio corresponding to the zero mean stress or initial void ratio . If
, then
is calculated from the mean stress and from
using Bauer [1] formula. If
, then
.
Parameters 17-22 - initial values of the intergranular strain tensor
in Voigt notation (
,
,
,
,
,
).
State variables:
The routine uses 14 state variables:
State v. 1-6 - intergranular strain tensor
in Voigt notation (
,
,
,
,
,
).
State v. 7 - void ratio .
State v. 8 - not used.
State v. 9 - Effective mean stress.
State v. 10 - Number of evaluation of the constitutive model in one global time step (for postprocessing only).
State v. 11 - Mobilised friction angle
in degrees (for postprocessing only).
State v. 12 - Normalised length of the intergranular strain tensor
(for postprocessing only).
State v. 13 - Suggested size of the first time substep (for calculation controll).
State v. 14 - free.
The hypoplastic model for granular materials is implemented via user defined subroutine usermod. To use the model in PLAXIS, copy the files UDSM_HPS.dll and UDSM_HPS64.dll into the PLAXIS installation directory. Then, select "user-defined model" from the Material model combo box in the General tab sheet (Fig. 4.1).
Figure:
Selecting user defined model in the Material model combo box.
(Fig. 4.1). After selecting the user-defined model, correct user-defined dynamic library (typically UDSM_HPS.dll) needs to be selected in the "Available DLL's" combo box under "Parameters" tab sheet. In the "Models in DLL" combo box, model with ID 1 (Hypoplas. - sand) must be selected. The parameters can then be input into the parameter table (Fig. 4.2).
Figure:
Selecting sand hypoplasticity model in the "Parameters" tab sheet.
Parameters of the sand hypoplastic model for different soils have been evaluated by Herle and Gudehus [2]. They are given in Table 4.1. Parameters of the intergranular strain concept for granular materials are in Tab. 4.2.
Table 4.1:Typical parameters of the hypoplastic model for granular materials (Herle and Gudehus [2])
Hochstetten gravel
36
32
kPa
0.18
0.26
0.45
0.5
0.1
1.9
Hochstetten sand
33
1.5
kPa
0.28
0.55
0.95
1.05
0.25
1.5
Hostun sand
31
1.0
kPa
0.29
0.61
0.96
1.09
0.13
2
Karlsruhe sand
30
5.8
kPa
0.28
0.53
0.84
1
0.13
1
Lausitz sand
33
1.6
kPa
0.19
0.44
0.85
1
0.25
1
Toyoura sand
30
2.6
kPa
0.27
0.61
0.98
1.1
0.18
1.1
Table 4.2:Parameters of the intergranular strain concept for sandy soils (Niemunis and Herle [8])