We develop a new particle finite element method (PFEM) model for dynamic analysis of saturated porous media based on the so-called u-p formulation. The model developed combines the advantages of a nodal integration technique and a generalised Hellinger-Reissner variational principle such that (i) linear triangular elements of high computational efficiency can be used without encountering volumetric locking issues; (ii) tedious post-remeshing mapping of field variables is avoided; (iii) no regularisation is required to stabilise the numerical solution to stress or pore water pressure fields; (iv) an implicit time integration scheme can be used for dynamic analysis of saturated porous media. In this work, we present the details of the model formulation, including the spatial domain discretisation, the nodal integration over cells, and the time-marching method as well as the solution scheme that reformulates the calculation into a standard second order cone programming problem that can be efficiently resolved using the advanced interior point method. We conduct a thorough validation of our model for simulating geotechnics-related dynamic behaviour of saturated porous media and compare our results with available laboratory experiments or other independent numerical simulations. Our work provides a useful tool for studying large deformation problems in many geotechnical engineering applications.