Keywords: multi-criteria parameter identification, evolutionary algorithms, unsaturated soils modelling, inverse problems.

The main objective of this paper is to present a multi-criteria direct automatic identification and uncertainty estimation methodology that can be applied satisfactorily to obtain the best matching parameters of constitutive models for unsaturated clay soils. Basically, in geotechnical engineering, the denomination of the inverse problem or parametric calibration refers to an iterative process of comparison between the measured data and the numerical predicted data, both data sets defining the objective function- obtained from the numerical model that allows determining the best fitting parameters of the model. This methodology is useful to define soil engineering standards for geotechnical applications.

In this work we describe the behaviour of a clay soil by means of a three-dimensional elasto-plastic model for unsaturated soils [1]. This constitutive model is within the framework of the global mechanical problem of the unsaturated soils, regarding the volume deformations, preconsolidation stress and shear states. The influence of suction on the mechanical behaviour of unsaturated soil is taken into account by using a principle of stress, which is obtained adding a function of the suction to the net mean stress.

A series of experimental analyses [2] accounting for different features in the behaviour of the soil were carried out to validate this constitutive law.

Different optimisation methods could be used to get the best fit. Basically, there are two types of methods: indirect and direct methods. In the second group of methods only values of the objective function at different points, set of parameters, are used. In order to accomplish the parameter identification problem of the model [1] with the soil selected, we propose in this paper the use of Pareto optimisation for multi-criteria parameter identification and calibration. Multi-objective optimisation gives us a more general procedure for balancing different types of information in the model parameter identification and calibration, as it is more flexible with respect to the definition of objective functions, and eliminates problems with improper balances between different data types.

We have developed a multi-objective evolutionary algorithm to approximate the Pareto set, because generating the Pareto set can be computationally expensive and often infeasible for exact methods. Evolutionary algorithms, in general, are more effective for the optimisation of non-linear models than gradient-based search. Efficient for estimation of the entire Pareto and ideally suited for parallel computing. At the same time, the use of population based search algorithms for the parameter identification and calibration allows to have a compressive evaluation of trade-offs between calibration objectives, highlighting possible model structural errors and offers an elaborate framework for comparison of different models or model conceptualisation.

The fitting methodology proposed has been applied with satisfactory results to a group of geotechnical tests carried out with a low-plasticity silty sand soil [2]. The results obtained have been also compared with those obtained from a mono-objective calibration methodology. Finally, the benefits of the multi-objective optimization are indicated.

1

J. Robles, "A computational constitutive driver for an elasto-plastic model of unsaturated soil behaviour", VII International conference on computational plasticity: COMPLAS. 2003.

2

L.R. Hoyos, "Experimental and computational modelling of unsaturated soil behaviour under true triaxial stress states", PhD. Dissertation. Georgia Institute of Technology. 1998.

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