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Based on the principle of virtual power, equilibrium conditions are established for the forces within a cross section of a tunnel top heading driven according the New Austrian Tunneling Method (NATM). External forces, namely impost actions and ground pressure distributions following a third-order polynomial, are analytically linked with internal forces, such as axial forces and bending moments, arising as integrals over the shell thickness, of circumferential normal stresses. The latter are related, via an aging viscoelastic shotcrete material model, to circumferential normal strains, as well as to radial and circumferential displacement components. This allows for analytical transformation of displacement measurement data collected at the crown and the footings of the shell segment, into ground pressure and impost action evolutions, together with all the associated force and stress quantities. For the Sieberg tunnel, driven in Miocene clay marl, our data-driven analytical mechanics model evidences virtually uniform ground pressure distributions, leading to a first rapidly increasing, and then mildly decreasing utilization degree of the shotcrete shell.