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Modelling of engineered barrier systems (EBS) in deep geological disposals of spent nuclear fuel requires sophisticated approaches that include highly nonlinear constitutive models. The Barcelona Basic Model for Expansive soils (BBMEx) is an extension for highly expansive unsaturated soils of the Barcelona Basic Model (BBM) for slightly-to-moderately expansive unsaturated soils. In this extension, the parameter κ (logarithmic compliance with respect to changes in net pressure) of the BBM is extended to a function of suction and a set of parameters, and the parameter κs (logarithmic compliance with respect to changes in suction) of the BBM is extended to a function of net pressure, suction, and a set of parameters. On these functions, four conditions which are satisfied in the BBM are considered. For each condition, two results are obtained: (1) the ranges of the values of the parameters such that the condition is satisfied for all positive net pressures and all non-negative suctions and (2) for given values of the parameters, the maximum net pressure and the maximum suction such that the condition is satisfied for positive net pressures and non-negative suctions. The results should help prevent unrealistic predictions of the BBMEx. The extension was used for carrying out the simulation of an infiltration test in two different bentonites and the BBMEx model parameters analysed.