## 4 Case Study--The Failure of the Gypsum Tailings Dam in East Texas in 1966 (FGT66)
### The Results from Three Different Rheological Models  
In this study, three different rheological models, Bingham Model (BM), Conventional Bi-viscosity Model (CBM), and Modified Bi-viscosity model (MBM) are employed to simulate the FTG66, as shown in Figures 6 and 7a. In the result from BM (Figure 6a), the mud thickness reduces gradually from the breach to the downstream toe. A sliding mud body is thicker in the breach center area. BM can simulate the stoppage of the material at about t = 90 s. The second result is obtained from CBM. The result in Figure 6b,c is produced by CBM with \(\dot{\gamma}_{y}=1\times 10^{-4}\) s\({}^{-1}\) and \(\dot{\gamma}_{y}=2\times 10^{-1}\) s\({}^{-1}\), respectively. In the CBM results, a high viscosity number is used to represent the un-yield phase, and a low viscosity number is used to represent the yield phase. The tailings shapes are similar between results of \(\dot{\gamma}_{y}=1\times 10^{-4}\) s\({}^{-1}\) (Figure 6b) and \(\dot{\gamma}_{y}=2\times 10^{-1}\) s\({}^{-1}\) (Figure 6c). They are also similar to those in the BM result (Figure 6a). However, the mud profiles at the center streamline are slightly different. The 'ridge' in the center of the breach (Figure 6b) is replaced by a relatively smooth hump (Figure 6c). In Figure 6, the results from CBM were nearly identical to those from BM. The flood distances predicted by BM and CBM were about 220 m. Compared to the field observation [60], the error of the predicted flood distance was about 27%. The field photo (Figure 7b) shows that the flood boundary was longer and narrower than the simulated results from BM and CBM. This might result from the sturdy behavior in the un-yield region. This sturdy behavior can be reached by increasing the un-yield viscosity \(\mu_{A}\) and yield strain \(\dot{\gamma}_{y}\). In this study, the un-yield viscosity \(\mu_{A}=10^{10}\) Pa s was chosen by the suggestion of [PERSON] [34], [PERSON] [34], and [PERSON] [28]. The yield strain rate was chosen to be \(\dot{\gamma}_{y}=2\times 10^{-1}\) s\({}^{-1}\) by matching the flood distance. Figure 7a shows the simulation of the deposited tailings from MBM. The flood distance at the freezing time t = 110 s was 310 m, which was 97% accurate to the filed data [60]. The result from MBM also showed a longer and narrower shape. However, it shall be noted that the white line segments in the aerial photo (Figure 7b) were not the elevation contour lines. The white line segments represent  
Figure 5: Numerical setup of the failure of the gypsum tailings dam in East Texas in 1966 (FGT66) based on the geometry reported in Jeyapalan [60]. the horizontal displacement of the gypsum tailings. They also indicate that the velocities along the central streamline were faster than those in the other regions. An indirect validation can be seen in the free-surface velocity profile, shown in Figure 9 at t = 30 s. However, the free-surface velocity will gradually reduce to zero as the freezing time is approaching. Figures 8 and 9 show the time evolution of the free-surface velocity of the mudflows from t = 0-110 s by using BM and MBM, respectively. The velocity at the early stage (about t = 0-10 s) of BM was higher than that of MBM. However, the simulated mudflow in BM stopped earlier (around 70-90 s). The surface velocity gradually approached zero from t = 70 s, and the flow came to a full stop at t = 90 s. The gypsum tailings distance was around 220 m, and the mean velocity was around 2.4-3.1 m s\({}^{-1}\) as shown in Figure 8. On the other hand, the flood distance from MBM was 310 m which was much closer to the field observation of 300 m [60]. The larger un-yield viscosity and yield strain rate limited the flood velocity at the early stage of the event (Figure 9).