Multiphysics phenomena and coupled-field problems usually lead to analyses which are computationally intensive. Strategies to keep the cost of these problems affordable are of special interest. For coupled fluid-structure problems, for instance, partitioned procedures and staggered algorithms are often preferred to direct analysis. In this paper, we describe a new strategy for solving coupled multiphysics problems which is built upon the LArge Time INcrement (LATIN) method. The proposed application concerns the consolidation of saturated porous soil, which is a strongly coupled fluid-solid problem. The goal of this paper is to discuss the effciency of the proposed approach, especially when using an appropriate time-space approximation of the unknowns for the iterative resolution of theuncoupled global problem. The use of a set of radial loads as an adaptive approximation of the solution during iterations will be validated and a strategy for limiting the number of global resolutions will be tested on multiphysics problems.