Figure 8 Probability of exceedance of r,* at Point A
Related Figures (16)
Figure 1: Integrated workflow for assessing the liquefaction triggering of dam foundations Table 2. Construction stages For the finite element analysis, a suitable material model is needed in order to model stress- strain behavior of the materials. Material model parameters are selected mainly referring to the previous studies on dams consisting of similar materials. Modeling parameter used in numerical analysis is presented in Table 3. * Representative values **Probability of occurrence of magnitudes and distance Table 1. Magnitude-distance bins Figure 2. Finite element mesh of the dam with foundation used in static and dynamic analyses Seismic response analysis of a 56 m high central clay core earthfill dam, founded on 24 m thick “loose” (Ni60 ~ 20 blows/30 cm) alluvial deposits, lying on the bedrock is performed by two- dimensional, explicit, finite difference software FLAC v4.0 (Fast Lagrangian Analysis of Continua) software and the adopted mesh is illustrated in Figures 2. For the purpose of realistically modeling construction stages, 12 stages are defined, as shown in Table 2. Table 3. Material Properties of the Dam Dynamic analyses of the dam were performed by using UBCSAND effective stress model (Byrne et al., 2004) on the dam foundation. No doubt that the finite element method has been one of the most powerful tools for evaluation the dynamic response of fill dams under earthquake loading. Figure 3. Cross section model of the earthfill dam Seismic response analyses are presented for five points located in the alluvium layer as shown in Figure 3. Point C is just beneath the center of the dam body. Points B and D are located 3 meter below the ground surface at the toes. Points A and E are located 3 meters below the ground surface at a distance of 40 m away from the toes. Table 4. Summary of seismic response analysis for points A, B, C, D and E For illustration purposes, excess pore pressure ratio, r, vs. time response is also shown for the earthquake scenario no 13 (i.e.: My = 6.4, and 1,,=53 km) in Figure 4. As this figure implies, r, reaches to a maximum value of 0.1 at point C (at a location right beneath the centerline of the dam body) which can be interpreted as “no-liquefaction”. However, for the same seismic scenario, liquefaction of the upstream region (Point A) and upstream toe region (Point B) is expected based on estimated large r, values (> 0.8). The distribution of the r, values throughout the foundation, as shown in Figure 5, also clarifies that upstream toe region of the alluvium is expected to liquefy. Figure 4. Excess pore pressure ratio, r, vs. time response for earthquake scenario bin 13, M, = 6.4, and rj,=53 km Figure 6. Annual probability of excess pore pressure ratio, r, After having explained the numerical assessment results for a specific earthquake case, (no 13) the probability-based liquefaction triggering assessment is now presented for all the earthquake scenario cases. The probability of occurrence of representative magnitude and distance bins are multiplied with the exceedence probabilities of excess pore pressure ratios for every bin. Figure 6 and Figure 7 show the annual probability of excess pore pressure ratio and annual probability of horizontal displacement respectively incorporating the activity rate of 0.299. Figure 7. Annual probability of horizontal displacements Figure 5. Excess pore pressure ratio, r, for earthquake scenario bin 13, M, = 6.4, and rj,=53 km Figure 9. Probability of exceedence of displacement at Point A Figure 10. o-c reduction based factor of safety
