Reliability of long heterogeneous slopes in 3d: Model performance and conditional simulation

Yajun Li

Research output: ThesisDissertation (TU Delft)

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Highway embankments, river dykes and sea dykes usually have a uniform cross-section and extend for a long distance in the third dimension. These long soil structures are generally characterised by spatially varying soil properties, i.e. soil heterogeneity. Slope stability failures of these structures may have significant economic and societal consequences. Thus, it is of particular interest for engineers to investigate the influence of soil spatial variability on the stability and failure mechanisms of long ‘linear’ structures. For example, earthen levee flood protection systems can be viewed as series systems, where failure at one location, or failure of one component, can result in catastrophic failure of the entire flood protection system and result in tragic loss of life, damage to fundamental infrastructure, and substantial economic impact to the immediate and surrounding regions. In order to ensure the desired level of flood protection system performance, standards in the Netherlands explicitly require probabilistic designs. For example, this may include the use of semi-analytical tools, such as Calle’s 2.5D method and the 3D method of Vanmarcke. However, these (semi-) analytical models make certain simplifying assumptions; in particular, that of a finite length cylindrical failure mechanism. The random finite element method (RFEM) has found increasing use for long engineered slopes in recent years, due to its conceptual simplicity to implement and its capability to comprehensively analyse the effects of soil spatial variability. As a simulation method, RFEM can be applied to large and complex systems, without the need to include some of the rigid idealisations and/or simplifications necessary for analytical solutions, resulting in more realistic models. Therefore, RFEMcan be used as a comparative tool in investigating the performance of simpler methods. Its biggest disadvantage is that it tends to be computationally expensive. The main body of this thesis is devoted to comparative studies (in terms of statistics of the realised factor of safety, the reliability and the failure consequences with respect to potential failure length and volume) of the three above models, for a range of spatial statistics of the soil shear strength. In particular, the relative performance of RFEM and Vanmarcke’s model is investigated for a relatively short slope (of length 10 times the height) for which the length effect may be ignored. For horizontal scales of fluctuation that are large compared to the slope length, the two approaches give similar results, because most of the failure surfaces computed in the RFEM analyses are then approximately cylindrical and propagate along the entire length of the slope, thereby matching Vanmarcke’s assumption and resulting failure length for this limiting condition. In contrast, for smaller values (i.e. less than the slope length), the two approaches can give significantly different results, with the RFEM response of the slope generally being much weaker than the Vanmarcke solution, apparently due to different predicted failure lengths and the influence of the cylinder ends in the simpler model. A second comparative study using all three models involves the so-called length effect (i.e. the increase of the probability of failure as the total slope length increases) for very long slopes (of length up to 100 times the height), using HPC strategies developed in this thesis. In contrast to the level crossing approach adopted in the two (semi-) analytical models, a simple power law equation was utilised with RFEM, which was validated based on the principles of probability of multiple independent (failure) events within the length of the slope. It is shown that RFEM predicts the smallest reliability indices for the range of cases considered. However, the solutions predicted by Vanmarcke’s and Calle’s models move closer to the RFEMresults at larger horizontal scales of fluctuation. Discrete failure lengths have been quantified in RFEMand comparedwith predicted failure lengths using the simpler models, in order to provide a rational explanation for the differences observed. Moreover, the ® factor used with Calle’s model in Dutch practice was investigated thoroughly via random fields for various degrees of spatial variability, enabling a comprehensive evaluation of its influence. While the unconditional RFEM is used as a baseline stochastic method to make the comparative studies, the conditional RFEM was implemented and applied in the last part of the thesis to two example geotechnical applications. The first example focuses on the efficient design of site investigation plans (i.e. optimum locations and sampling intensity) in a 3D soil deposit. A sampling efficiency index was defined and used as an indicator of the efficiency of a site’s plan. A ‘posterior’ distribution of the structure performance, after taking account of the spatial distribution of all the measured CPT data, was derived and showed a significant reduction in the uncertainty compared to the ‘prior’ distribution of the structure response by using the unconditional simulation based on random field theory. An optimal sampling position for the excavation of a slope was identified, both for a single stage of site investigation and a two stage site investigation. Moreover, an optimal sampling distance of half the horizontal scale of fluctuation was identified when an exponential correlation function is used. The second example is devoted to cost-effective designs of an excavated 3D slope. For the problem analysed, a steeper slope was found to be sufficiently reliable (i.e. in line with Eurocode 7) when conditional random fields were used. This was in contrast to the finding of unconditional simulations, due to the greater uncertainty due to only making partial use of available measurement data. The potential benefit of a 3D conditional simulation in geotechnical cost-effective designs has therefore been highlighted.
Original languageEnglish
QualificationDoctor of Philosophy
  • Hicks, M.A., Supervisor
Thesis sponsors
Award date24 Feb 2017
Print ISBNs 978-94-92516-44-2
Publication statusPublished - 2017


  • conditional simulation
  • heterogeneity
  • length effect
  • reliability
  • risk
  • slope stability

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