This research develops a two-dimensional logarithmic spiral dynamic failure model to solve the problem of heading face instability of shield tunneling. By discretizing the dynamic failure model

the dissipation power of the system in the failure zone can be calculated accurately

and the upper bound solution of support pressure can be derived by using the upper bound method. Based on the current solution

the failure mode of instability and the corresponding limit support pressure at collapse were obtained by optimization. Through parameter analysis

the influence of soil strength on the failure mode and limit support pressure was analyzed. The results showed that with the increase of soil strength

the failure zone becomes smaller and the failure height and support pressure decrease correspondingly. The analytical solutions

including the failure mode and limit support pressure

obtained by the two-dimensional logarithmic spiral model were compared with those obtained by the numerical simulation and the existing analytical solutions. The comparative analysis showed that the analytical solutions by the proposed model are in good agreement with those from numerical simulation and other existing theoretical models. Finally

the model test was selected as an example to verify the model and the results showed that the solutions from the proposed model are close to the previous test results. The analytical solutions from the two-dimensional logarithmic dynamic failure model can provide a theoretical basis for engineering design in predicting the failure mode and limit support pressure.