Elasto-Plastic Analysis of Machine Foundations Under Harmonic and Pulse Loading with Negative Phase

This study uses a semi-analytical approach to analyse a machine foundation under in influence of combined harmonic and pulse loading. The system is modelled as elastic-perfectly plastic, elastic–plastic hardening, and elastic–plastic softening single degree-of-freedom (SDOF) system using bilinear resistance function. Pulse loading induced due to a distant blast is described by the modified Friedlander’s equation that accounts for both positive and negative phases. Three computational cases of analysis are considered, and analytical expressions are formulated. Response of the SDOF system in term of displacement–time history is obtained employing appropriate initial conditions. The response time histories obtained for various input parameters are utilized to investigate the impact of negative phase of blast loading on the machine soil-foundation system. This is found to be quite significant especially for more flexible systems and systems with lower damping ratio values. Two peak values of displacement are observed and for a specific value of wave decay parameter, b, the absolute value of second peak displacement can be twice as high as that of first peak displacement. Influence of parameters such as damping ratio, mass of soil-foundation system, magnitude of applied loads, hardening/softening index affect the response significantly which is quantified for various cases of the analysis.