The paper summarizes the state-of-the-art in Robust Design Optimization in geomechanics with special emphasis on sensitivity and robustness analysis as well as optimization. An academic example related to roof anchorage of an underground opening is used to illustrate the general procedure. A thermo-mechanical analysis of a dam is used to illustrate the application of sensitivity analysis in the engineering practice followed by exemplary robustness analysis for a dynamic loaded foundation plate.

1 Introduction

Today the rock mechanical engineer is forced to develop safe and economic designs for systems, which are characterized by many influencing factors (technical parameters, rock mass parameter, economical parameters, environmental parameters etc.). In such systems it is more and more difficult to find optimal solutions and to define those parameters, which are really decisive. Therefore, classical procedures like parameter studies, ‘trial-and-error’-procedures and simple parameter fitting is replaced more and more by so-called mathematical optimization techniques. These techniques involve the following analysis methods:

  • Sensitivity analysis

    Within a sensitivity analysis the influence of individual input parameters on the model output is investigated. Based on the sensitivity analysis insignificant parameters can be excluded from further design and interaction of different parameters can be revealed.

  • Uncertainty analysis

    Uncertainty analysis investigates the uncertainty of input variables and their impact on the model response. Uncertainty estimates are used to assess the confidence of model results.

  • Robustness analysis

    Within the robustness analysis it is estimated how robust the model response is in relation to uncertainty in the input parameters or in other words: how stable is our model response if the input variables scatter in a certain manner.

  • Reliability analysis

    Reliability analysis investigates the boundary violation of output due to the variability of input parameters. Reliability analysis can either predict the failure probability or proof, that all constraints scatter within defined boundaries.

  • Optimization

    Optimization means the mathematical based selection of best fitting object in respect to defined criteria.

This leads to the maximizing or minimizing of functions by choosing input values/functions from a certain parameter set or range. Different deterministic and stochastic optimization schemes are available. Popular deterministic approaches are: response surface methods, hill climbing methods or gradient based strategies. Typical stochastic approaches are: evolutionary algorithms, neural network approaches, particle swarm algorithms or the Fuzzy logic theory based methods. Of great importance is multi-objective optimization, where an optimum is searched not only for one parameter or function, but for several and sometimes also contradictionary objective functions (Pareto- Optimization).

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