Effective stress models for soft Scandinavian clays
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The modelling of soft Scandinavian clays requires an effective stress based approach, if a complete stress response is to be provided for different loading conditions. Although, the observed behavior is complex, it is seen to follow certain principles, which can be used in constitutive modelling, such as the critical state concept and asymptotic behavior, rotational hardening, destructuration, time-dependence and yielding. A key characteristic of geotechnical design is the use of undrained shear strength parameters, the peak shear stress obtained by modes of deformation without changes in volume. An effective stress based model for soft clays will predict the peak as a consequence of the formulation, rather than as direct input as is the case for total stress based models. This thesis explores different ways in providing the undrained shear strength to an effective stress based model as input using two approaches: By using an optimization procedure or solving a system of equations at the initial stage. Two models have been developed and implemented in the finite element program Plaxis, using the above mentioned approaches. Their advantages and disadvantages are elaborated on in this thesis. First, a framework is developed that makes it easier to implement models into a finite element code (e.g. Plaxis) by using symbolic mathematics in the computing environment program Matlab, and subsequently converting the code into the programming language Fortran by built-in methods. It is then used in an implicit integration scheme as part of the compiled DLLs. The first model is based on existing formulations using plasticity theory. The model includes non-associated flow, time dependence, rotational hardening and destructuration. A new failure criterion, Generalized Mohr-Coulomb, is implemented together with a fix for concavity of surfaces. A new simplified target formulation for rotational hardening is proposed. The input of the undrained shear strength is achieved by replacing certain parameters of the Generalized Mohr-Coulomb criterion using an optimization procedure, not visible to the user, but done internally. The second model provides the constitutive behavior using linear differential equations by separating the processes occurring during loading into relatively simple parts. Whereas the theory of plasticity assumes a separation of strain, this model proposes the separation of stress. In addition a key component of the framework of Barodesy is used. An advantage to this approach is that the constitutive behavior can be integrated analytically, making the undrained shear strength as input possible by solving a system of non-linear equations. Two boundary value problems, a deep excavation and an embankment are used to test the models in a coupled analysis with consolidation, where the first boundary value problem loses capacity over time while the second gain strength.