Simulations
The finite element program numgeo is used for the back-calculation of the laboratory tests with the different constitutive models needed for the automatic calibration. How the individual tests are exactly simulated is described in detail in the following sections.
Table of contents
Finite Element representation
For the simulation of laboratory tests we perform so-called ‘‘single-element-simulations’’ with the FE program numgeo and by doing so enforce element test assumptions, i.e. a homogeneous distribution of stress/strain within the test sample. Details on the simulation strategies for the different laboratory tests are given in the following sections:
Oedometer tests
Triaxial tests
- Drained monotonic triaxial test (CD)
- Undrained monotonic triaxial test (CU)
- Undrained cyclic triaxial test (CUcyc)
Maximum runtime
Given the nature of heuristic optimization algorithms, occasionally parameter combinations are tested that unstable but do not necessarily lead to an abortion of the simulations but rather reveal themselves by exceptionally high runtimes of the simulations. This was particularly observed for the SANISAND constitutive model. To filter out such parameters, we limit the runtimes of the simulations as per default follows:
- Oedometric compression tests: 10 seconds (usual simulation time with good parameters is $\leq$ 1 s)
- Drained monotonic triaxial compression tests: 10 seconds (usual simulation time with good parameters is $\leq$ 1 s)
- Undrained monotonic triaxial compression tests: 15 seconds (usual simulation time with good parameters is $\leq$ 1 s)
- Undrained cyclic triaxial compression tests: 300 seconds (usual simulation time with good parameters is $\leq$ 20 s)
If pnly one of above conditions is violated, the parameter set is disregarded.
Maximum deviatoric stress
In cyclic undrained triaxial tests parameter combinations might be found by the optimization algorithm that lead noticeable overshooting of the deviatoric stress $q$ for stress states close to liquefaction ($p=\sigma_{ii}/3 \rightarrow 0$ kPa). This is especially true for elasto-plastic constitutive models. To discard such parameter sets, we require that the maximum/minimum deviatorc stresses in the simulation do not deviate from the overall maximum/minimum deviatoric stress from the experiment within a tolerance of 1 kPa:
\[\left| \dfrac{q_{max}^{sim}}{q_{max}^{sim}} \right| \leq 1 ~~~\text{and}~~~\left| \dfrac{q_{min}^{sim}}{q_{min}^{sim}} \right| \leq 1\]If above condition is violated, the parameter set is disregarded.