arXiv:2507.22334v2 Announce Type: replace Abstract: An inherent regularization strategy combined with block Schur complement preconditioning is investigated for linear poroelasticity problems discretized using the lowest-order weak Galerkin method in space and the implicit Euler scheme in time. At each time step, the resulting saddle point system becomes nearly singular in the locking regime due to the near incompressibility of the solid. The regularization arises from an inherent identity in the original system, preserves the exact solution, and ensures nonsingularity. For the regularized systems, standard inexact block Schur complement preconditioning is shown to be effective, and preconditioned MINRES and GMRES methods exhibit convergence essentially independent of the mesh size and locking parameter -- in terms of both convergence factors and asymptotic error constants. Numerical experiments in two and three dimensions confirm the robustness of the regularization strategy and the effectiveness of the block preconditioners with respect to mesh size and locking for the regularized systems.