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In this work, we consider the Biot problem with uncertain poroelasticcoefficients. The uncertainty is modelled using a finite set of parameters withprescribed probability distribution. We present the variational formulation ofthe stochastic partial differential system and establish its well-posedness. Wethen discuss the approximation of the parameter-dependent problem bynon-intrusive techniques based on Polynomial Chaos decompositions. Wespecifically focus on sparse spectral projection methods, which essentiallyamount to performing an ensemble of deterministic model simulations to estimatethe expansion coefficients. The deterministic solver is based on a HybridHigh-Order discretization supporting general polyhedral meshes and arbitraryapproximation orders. We numerically investigate the convergence of theprobability error of the Polynomial Chaos approximation with respect to thelevel of the sparse grid. Finally, we assess the propagation of the inputuncertainty onto the solution considering an injection-extraction problem.

Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods