Computational Mechanics:
|
Project leader: Günter Hofstetter
Institute for Basic Sciences in Civil Engineering - Unit for Strength of Materials and Structural Analysis
Partially saturated soils consist of a deformable soil skeleton and the two fluid phases water and air, which are filling the entire void space (Figure 1). The surface tension at the water-air interfaces causes a difference between the air pressure and the water pressure, which is denoted as matric suction or capillary pressure. Depending on the type of soil, the latter may have a strong influence on soil behavior, e.g., an increase of the capillary pressure due to a decreasing degree of water saturation results in increasing soil stiffness and shear strength, whereas a decrease of the capillary pressure due to an increasing degree of water saturation may produce irreversible volumetric compaction.
|
|
| Figure 1: Partially saturated soil |
Within the field of Computational Mechanics multi-phase models for partially saturated soils are an ongoing research topic. In recent years a three-phase model for partially saturated soils, based on the finite element method (FEM), was developed by the group of G. Hofstetter. The model takes into account the interactions of the flow of water and air in the soil with the deformations of the soil. Furthermore, a constitutive model for partially saturated sands and silts was developed and validated by extensive test data.
The DK-plus programme offers the opportunity to strengthen and to extend these activities of the group by G. Hofstetter with respect to (i) constitutive modelling, (ii) the algorithmic treatment of constitutive models and (iii) large-scale three-dimensional (3D) numerical simulations in collaboration with colleagues in civil engineering (C. Adam), computer science (T. Fahringer) and mathematics (M. Oberguggenberger, A. Ostermann).
Ph.D. project 1: Evaluation of partially saturated soil models and extension to swelling soil behaviour
Ph.D. project 2: Large-scale 3D numerical simulations of tunnelling involving multi-phase soil models
Computational Mechanics:
|
In recent years great efforts have been made in developing constitutive models for partially saturated soils. Hence, a relatively large number of models for partially saturated soils have been published in the literature. E.g., Figure 2 shows the yield surfaces of the Barcelona Basic Model (BBM), which is probably the most well known material model for partially saturated soils, for two different values of the capillary pressure. Despite of the relatively large number of existing unsaturated soil models, the development of partially saturated soil models and their implementation into FE-programs are still ongoing research topics.
A research topic to be tackled in this PhD project refers to the stress update algorithm for partially saturated soil models within the framework of nonlinear FE analyses. It consists of computing the internal variables and the stresses for given initial conditions and for a given strain increment. Partially saturated soil models are commonly formulated within the framework of plasticity theory and, in general, the stresses must be integrated numerically. Popular stress integration methods are explicit Runge-Kutta schemes with adaptive sub-stepping and error control and implicit return mapping algorithms. Both are characterized by specific advantages and drawbacks, but only few comparisons of stress integration algorithms of both categories with respect to accuracy, stability and computing time are available for partially saturated soil models. Since the stability and efficiency of the stress integration scheme are of particular importance for the large-scale numerical simulations to be conducted in the second PhD project and for the PhD projects proposed by C. Adam, a comprehensive study of both explicit and implicit integration schemes will be conducted for selected partially saturated soil models in collaboration with A. Ostermann.
 |
| Figure 2: Yield surfaces of the BBM for different values of the capillary pressure |
Since constitutive models for partially saturated soils are characterized by a relatively large number of material parameters reliable methods for parameter identification are required. To this end, both local gradient based optimization methods and global optimization techniques for the identification of the material parameters will be evaluated in this PhD project and related sensitivity analyses conducted in collaboration with M. Oberguggenberger and A. Ostermann.
The third research topic of this PhD project refers to the extension of a partially saturated soil model to swelling soil behaviour. The latter may be encountered, e.g., during the advance of a tunnel in argillaceous rock. It is characterized by a time-dependent volume increase of the soil, caused by the presence of water in combination with the stress relief due to the excavation. When the deformations of swelling soil are restrained, e.g., by a lining, then large swelling pressures may develop, which may result in damage or even destruction of the lining. Since in engineering practice up to now only simplified approaches for considering swelling pressures or swelling strains are employed, the extension of the three-phase model will provide a consistent continuum mechanical model for swelling soil behaviour.
Some references for further reading:
- R. Kohler, G. Hofstetter: A cap model for partially saturated soils, International Journal for Numerical and Analytical Methods in Geomechanics, 32 (2008), 981-1004.
- M. Hofmann, T. Most, G. Hofstetter: Parameter identification for a partially saturated soil model, Proceedings of the 2. International Conference on Computational Methods in Tunneling, Eds.: G. Meschke, G. Beer, J. Eberhardsteiner, M.Thewes, Aedificatio Publishers, Germany, 2009, 701-708.
- M. Hofmann, M. Pertl, G. Hofstetter: Coupled solid-fluid FE-analysis of geotechnical problems involving partially saturated soils, eingereicht zur Veröffentlichung in den GAMM-Mitteilungen.
Computational Mechanics:
|
The currently available version of the three-phase model for soils will be used as the basis for large-scale numerical simulations taking into account both partially and fully saturated soil behaviour (in contrast to the commonly employed single phase soil models or water saturated soil models). Since the air phase is explicitly included in the three-phase formulation (in contrast to the often made “passive air assumption”, which restricts the air pressure to atmospheric conditions) also special construction methods like tunnelling below the groundwater table with displacing the groundwater in the vicinity of the tunnel face by means of compressed air can be simulated (Figure 3).
 |
| Figure 3: Numerical simulation of displacing the groundwater with compressed air |
In particular, large-scale 3D numerical simulations of tunnelling involving multi-phase soil models are time-consuming because of the required large 3D domain to be meshed, the large number of excavation steps and securing steps to be simulated and the larger number of degrees of freedom (compared to single phase formulations). Hence, even on the basis of an efficient numerical formulation such simulations require a powerful basis. Thus, it is the aim of the PhD project to implement the developed three-phase formulation into an OpenSource FE-program (OpenSees) and to optimize the code with respect to its performance. Time stepping algorithms characterized by adaptive time integration schemes with error control will increase the efficiency of the code. In addition, it is planned to adapt the code to the special needs of tunnelling. The optimization of the developed routines will be supported by collaborating with T. Fahringer. The OpenSource code will also be used within the DK-plus programme as basis for PhD projects, supervised by C. Adam, M. Oberguggenberger and A. Ostermann.
The 3D multi-phase FE-model for tunnelling will allow the realistic simulation of excavation steps and securing measures of a tunnel. This is quite standard in numerical simulations considering the soil as a single phase material, however, it is more involved in the present case, in which in every step changes of the boundary conditions for the fluid phases, associated with the advance of the tunnel face, have to be taken into account. Moreover, combining the 3D model with the developments of the first PhD project will allow simulating the tunnel advance in swelling soil taking into account the interactions of seepage flow with the deformations and stresses of the matrix of swelling soils.
Some references for further reading:
- R. Kohler, G. Hofstetter: A cap model for partially saturated soils, International Journal for Numerical and Analytical Methods in Geomechanics, 32 (2008), 981-1004.
- M. Hofmann, T. Most, G. Hofstetter: Parameter identification for a partially saturated soil model, Proceedings of the 2. International Conference on Computational Methods in Tunneling, Eds.: G. Meschke, G. Beer, J. Eberhardsteiner, M.Thewes, Aedificatio Publishers, Germany, 2009, 701-708.
- M. Hofmann, M. Pertl, G. Hofstetter: Coupled solid-fluid FE-analysis of geotechnical problems involving partially saturated soils, eingereicht zur Veröffentlichung in den GAMM-Mitteilungen.