In this study, the life safety and immediate occupancy of asymmetric-plan reinforced concrete dual structures under the simultaneous effect of torsion and soil-structure interaction in the near-fault pulse-like earthquakes were evaluated using a probabilistic framework. An 8-story R/C dual lateral load resistant building consisting of shear walls and moment-resisting frames was used. The sub-structure method was used to simulate the SSI effect. The impedance functions were calculated with the Novak semi-analytical method (DYNA5 software). The structure was modeled in the CANNY software considering the nonlinear behavior to perform the nonlinear time history analysis. All of the ground motion records were selected from the near-fault pulse-like records. Incremental dynamic analysis was employed to extract and fragility curves. To determine the life safety and immediate occupancy limit states, the strain of steel and concrete (as a micro index) were used rather than the usual macro indexes such as story drifts that lead to increase the accuracy of results. One of the most important of the conclusion is that neglecting the SSI effect in the life safety and immediate occupancy limit states for the plan-asymmetric structure is not in the safe side and lead to overestimation in the structural capacity. Also, an increase in the mass eccentricity leads to a decrease in the base conditions' importance and SSI effect. Another considerable observation is that an increase in the shear wave velocity of soil can lead to a decrease in the torsional response and the seismic response of asymmetric structure approaches to the symmetric one.