We present an extension of the Local Effect Model (LEM) to include time-dose relationships for predicting effects of protracted and split-dose ion irradiation at arbitrary LET. With this kinetic extension, the spatial and temporal induction and processing of DNA double strand breaks (DSB) in cellular nuclei can be simulated for a wide range of ion radiation qualities, doses and dose rates. The key concept of the extension is based on the joint spatial and temporal coexistence of initial DSB, leading to the formation of clustered DNA damage on the µm scale (as defined e.g., by the size scale of Mbp chromatin loops), which is considered to have an increased cellular lethality as compared to isolated, single DSB. By simulating the time dependent induction and repair of DSB and scoring of isolated and clustered DSB upon irradiation, the impact of dose rate and split dose on the cell survival probability can be computed. In a first part of this work, we systematically analyze the predicted impact of protraction in dependence of factors like dose, LET, ion species and radiosensitivity as characterized by the photon LQ-parameters. We establish links to common concepts that describe dose rate effects for low LET radiation. We also compare the model predictions to experimental data and find agreement with the general trends observed in the experiments. The relevant concepts of our approach are compared to other models suitable for predicting time effects. We investigate an apparent analogy between spatial and temporal concentration of radiation delivery, both leading to increased effectiveness, and discuss similarities and differences between the general dependencies of these clustering effects on their impacting factors. Finally, we conclude that the findings give additional support for the general concept of the LEM, i.e. the characterization of high LET radiation effects based on the distinction of just two classes of DSB (isolated DSB and clustered DSB).