The dynamic finite element strength discount method is an effective method for solving the seismic safety factor of slopes. The key of this method is to select a reasonable destabilization criterion for soil slopes. Due to the complexity of the damage mechanism of soil slopes, the destabilization criterion of soil slopes in the ultimate damage state has not been unified. At present, three types of criteria are commonly used, namely, plastic zone penetration （equivalent plastic strain）, numerical simulation computation does not converge, and the displacement of the characteristic points of the sudden change, through the above criteria to obtain the location of the sliding surface of the slope and the slope strength reserve safety factor. Nowadays, most scholars believe that the equivalent plastic strain penetration is a sufficient but not necessary condition for slope damage, and the selection criterion of the plastic strain amplitude has a certain degree of non-determinism and other human factors. The problem of non-convergence of finite element calculation as a criterion is that the convergence criterion is limited by the selected software, and the convergence error can be adjusted, and the physical significance as a criterion of slope instability is unclear and affected by human factors. The displacement of the characteristic point is not converged or the displacement is not converged, usually the selection of the characteristic point is at the foot of the slope, the mid-point of the slope and the shoulder, this situation can only reflect the local state of the slope, the slope may be in the local instability, but not the overall instability. Therefore, these three types of criteria have some differences and subjectivity in practical application.
In this study, the concept of rainbow-shaped displacement map is proposed based on the theoretical reasoning and simulation results of the dynamic numerical simulation calculation of the slope, and the rainbow-shaped displacement map is established as the basis for judging the seismic stability of the slope. That is to say, when the slope is destabilized and damaged as a whole, the displacement map should satisfy the following three conditions:
1） The soil unit inside the landslide body slides along the circular sliding surface relative to the internal stabilization zone of the slope. The internal stable zone of the slope and the landslide body should show a clear circular arc boundary in the permanent displacement map of numerical simulation.
2） The displacement of the landslide body shows a circular arc-shaped band distribution along the downslope direction. The layering is obvious and similar to rainbow-like, so it is defined as rainbow-like displacement cloud map.
3） The displacement of each layer of the landslide body from the slope surface to the interior of the slope body has the phenomenon of increasing and then decreasing abruptly, and the maximum value of the layer band is the sliding surface of the slope.
In order to verify the reliability of the rainbow-shaped displacement map as the basis for judging the seismic stability of slopes, this study compares and analyzes the safety coefficients of slopes under the three commonly used criteria and the rainbow-shaped criterion of the displacement map. The results show that there is not much difference between the safety coefficients obtained by using the sudden change of displacement at characteristic points, the displacement time curve, and the rainbow-shaped criterion of displacement maps, which indicates the consistency between the criterion proposed in this study and the previous three types of criterion. Zheng Yingren et al. mentioned that the plastic zone penetration is a necessary but not sufficient condition for the slope soil damage, and the results obtained in this paper can also prove this point, the safety coefficient derived from the criterion of plastic zone penetration is relatively small, and the error is 1.6% compared with the other criteria, and the reason for this discrepancy may be related to the precision of the mesh delineation and the accuracy of the calculation. The slope instability under dynamic action is more complicated, if we use the final displacement mutation of the characteristic point or the displacement time course mutation as the criterion, then we need to calculate the reduction factor several times, and whether the displacement monitoring point is steeply increasing or not depends on the researcher's subjective judgment, so it is not convincing to use it as the criterion.
The main conclusions of this study are as follows:
1） There is not much difference between the safety coefficients obtained from the four criteria of plastic zone penetration, sudden change of final displacement at characteristic points, displacement time curve and rainbow displacement map, among which the safety coefficients obtained from the criterion of sudden change of displacement have a subjective variability, and can be taken as a range scale value.
2） The appearance of rainbow displacement map can be used as a criterion for the overall instability damage of soil slope under seismic action, with clear physical significance and easy operation. At the same time, it can also be combined with other criteria such as plastic zone penetration to confirm the accuracy of the safety factor.
3） When using the characteristic point displacement mutation criterion, when selecting the characteristic point, several places should be selected on the slope surface, and the monitoring point at the foot of the slope may cause inaccurate results because it is above the shear outlet.
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