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Finite Element Limit Analysis with Application to Geotechnical Stability Analysis Prof KK Phoon (Department of Civil and Environmental Engineering)
In any geotechnical project stability during construction is clearly prime importance, particularly for the case in urban environments where the consequence of a structure collapse will be significant. Historically, geotechnical stability analysis is performed by various techniques based on the notion of limit equilibrium. The major disadvantage is the need to presuppose an appropriate failure mechanism in advance, which is feasible for simple cases such as homogeneous soil. For some problems involving heterogeneous soil profiles (e.g., layered profiles), complex loadings, or structural geometries, however, it is very difficult to make a reasonable assumption for the mode of failure a priori. In this situation, inappropriate failure mechanism may yield inaccurate predictions of the true failure load.
An alternative method for predicting the collapse load of geotechnical structures is the displacement-based finite element method. Theoretically, this method can deal with the above complex problems. In practice, however, this method must be applied in the fully plastic range with caution, as the results can be very inaccurate due to the occurrence of ‘locking’. This phenomenon, which is characterized by a constantly rising load-deformation response, occurs when the displacement field becomes over-constrained by the requirement of an incompressible plastic flow rule. Moreover, the conventional finite element method is a complete analysis which produces solutions not necessary for collapse evaluation and hence could be too computationally tedious for large-scale problems.
Failure by plastic collapse is the basic design check in all geotechnical problems. It may be more efficient to combine limit theorems with the finite element formulation to compute the collapse load. This method is called the finite element limit analysis. This method does not require assumptions for the mode of failure, and use only simple strength parameters that are familiar with geotechnical engineers. In addition, this method is completely general and can deal with layered or more complex spatially variable soil profiles. Figure 1(b) shows the plastic zone produced by a load acting the surface of a sand layer overlying a clay layer. Stability solutions for a number of practical problems such as tunnels under surcharging loads as shown in Figure 2 can be determined by this method as well. In summary, finite element limit analysis can provide a reasonable estimate of the stability number as well as the failure mechanism represented approximately by the black dashed line in Figure 1(b) and 2(b). No assumption on the geometric of the failure mechanism is needed. The computation is also more efficient than classical finite element analysis, which makes this method more suitable for stability analysis of large-scale 3D soil-structure interaction problems.
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