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FEM
The frame "Analysis methods" in conjunction with the "Analyses" tab sheet allows for selecting the option "Advanced input". The advanced input offers in addition:
| - | defining additional material parameters of soils (e.g. the Biot parameter, bulk modulus of water, coefficient of thermal expansion) |
| - | three node elements become available |
| - | additional output parameters become available |
By default this option is turned off. On the other hand, it may become particularly useful when doing research or during teaching. This input mode can be turned on/off at any time, but this action will always result into deleting all previous results.
Adopting Enhanced input option in the frame "Analysis methods" allows the user to further specify the selected material model by choosing the type of soil and setting the Biot parameter α and the coefficient of thermal expansion αt.
Default setting assumes drained (long term) boundary conditions (steady state conditions). In such a case the deformation of soil does not change the values of the prescribed pore pressure. Pore pressures then appear as an additional source of external load and stay constant during the analysis (state at the end of consolidation after full dissipation of the excess pore pressure ue). This particular component of total active pore pressure u is denoted as us. On the contrary, undrained boundary conditions assume that entire boundary surrounding the particular soil is impermeable. This results in the solution of a fully coupled problem of evolution of pore pressures in dependence on the deformation of soil assuming that all changes are instantaneous (short term conditions) with no influence of time (state at the beginning of consolidation). These excess pore pressures are denoted in the program as ue. The overall active pore pressure then follows from:
The analysis requires specification of the effective bulk modulus of water Ke:
| where: | Ke | - | effective bulk modulus |
| Ks | - | bulk modulus of grains | |
| Kw | - | bulk modulus of water | |
| n | - | porosity (volume of pores / volume of skeleton) | |
| α | - | Biot’s parameter |
The actual value of this parameter does not have a major influence on the resulting pore pressures providing it is sufficiently high. Typically it is chosen from the interval 1000-10000.
The Biot parameter α depends on the bulk modulus of skeleton Ksk and grains Ks of the basic material in the form:
| where: | α | - | Biot’s parameter |
| Ksk | - | bulk modulus of skeleton | |
| Ks | - | bulk modulus of grains |
Default setting assumes incompressibility of grains (Ks>>Ksk) and therefore α=1. The total stress then provided by:
| where: |
|
- | total stress tensor |
|
|
- | effective stress tensor | |
|
|
- | overall strain tensor | |
|
Dijkl |
- |
elastic stiffness tensor | |
|
|
- | Kronecker’s delta | |
|
u |
- |
active pore pressure |
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