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Stiffness Degradation Method (SDM)




Implementation and validation of the Stiffness Degradation Method in ABAQUS and PLAXIS

Internal study

Project description:
Cyclic loading may lead to accumulation of plastic deformation. Horizontal deformations due to cyclic loading can for example be measured in the case of strip locks or offshore wind turbines. Likewise, permanent deformations can be measured in cyclic triaxial tests. In literature one can find simple analytical relationships describing the evolution of strains in such tests (e.g. Huurman 1996) for simple element tests. In a PhD thesis (Kuo 2008) at the University of Hannover this simple solution was transferred to complex problems like offshore wind energy plants. A method using three dimensional Finite Element analyses was proposed. The latter is based on a linear elastic, perfectly plastic model with stress dependent stiffness. On the basis of the initial stress state and the stress state after one cycle, the stiffness for the number of cycles N is reduced according to Huurman (1996). With this reduced secant stiffness the deformations after N cycles can be computed.
In an internal study this method was implemented in the FE codes ABAQUS and PLAXIS.

The subsoil in the considered lab tests and case studies consists of homogenous, medium dense to dense sand layers.

Scope of work:

  • Implementation of the SDM in the Finite Element Codes ABAQUS and PLAXIS.
  • Implementation of a linear elastic, perfectly plastic model with stress dependent stiffness.
  • Validation of the SDM by using element tests and a case study.
    • Back analysis of a cyclic triaxial test
    • Back analysis of a monopile foundation under cyclic loading

Used Finite Element Codes:
PLAXIS 3D Foundation V2.2

Used constitutive laws:
Linear elastic, perfectly plastic model with stress dependent stiffness

Typical domain size:
90 m  x  45 m  x  50 m
16,458 wedge elements with quadratic interpolation
45,892 nodes


Kuo, Y.S.: On the behavior of large-diameter piles under cyclic lateral load. Mitteilung des Instituts für Grundbau, Bodenmechanik und Energiewasserbau (IGBE) Leibniz Universität Hannover, Heft 65.
Huurman, M.: Development of traffic induced permanent strain in concrete block pavements. HERON, Vol. 41, No. 1, pp. 29-52.
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