Densification of urban areas is a global trend. Since many of the worlds cities are built on soils with poor engineering properties, e.g. soft natural clay, the urban developments increases the demand of efficient deep foundations that are capable of supporting increasingly larger loads. The installation of deep foundations using displacement piles into clay leads to disturbance which need to be quantified to prevent damage on adjacent structures. This work presents a coupled Eulerian numerical framework for the simulation of pile installation into natural soft clay. Furthermore, an advanced effective stress based constitutive model was implemented. The most important factor governing the magnitude of displaced soil volume is the volume of the installed pile. After installation, dissipation of excess porewater pressures leads to volumetric contraction in the soil. The displacements during this phase are in the reversed direction compared to the initial outward movement during installation. Incorporating the anisotropy and sensitivity of the clay in the analysis leads to increased displacements closer to the pile during penetration and larger reversed displacement trajectories in the subsequent porewater pressure equalisation stage. The overconsolidation ratio, elastic and plastic stiffness properties and the critical state friction angle are shown to be the most influential, both directly after installation and after equalisation of the excess porewater pressures. The differences between the mass displacements predicted from full vertical penetration and numerical horizontal cavity expansion, show that the far field (>10𝑅) displacement pattern are similar, while the displacement path of soil closer to the pile are not fully captured using horizontal cavity expansion. The Shallow Strain Path Method (SSPM) is shown to predict similar deformations as the Finite Element calculations using a failure criterion. For the investigated normalised penetration rates in natural soft clay the emerging response from the coupled analyses indicated near constant volume conditions. Hence, any simplified method acknowledging this condition will predict displacement in a similar order of magnitude as the advanced method. However, an effective stress based model that captures the response of the natural clay is required if the magnitude of mass displacements during and after the porewater equalisation phase is of interest.