Internal forces of underground structures from observed displacements

This paper presents a method that provides a solution to the long standing problem of calculating internal force distributions based on displacement measurements of piles, retaining walls and tunnels. It is based on the principle of virtual work and therefore, analytically correct in the linear elastic range, and works without the need of any boundary conditions. The validation against multiple case studies, showcasing loading conditions including seismic, earth pressures, external loads, or sliding slopes in multiple ground conditions and construction processes, confirms its flexibility and applicability to any structure where displacements are observed. Although the validation presented here applies to bending moments and axial forces, the method is theoretically correct and applicable to other internal force distributions.