Pore-Water Pressure Definition for a Levee Stability Analysis

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1 Pore-Water Pressure Definition for a Levee Stability Analysis GEO-SLOPE International Ltd , 700-6th Ave SW, Calgary, AB, Canada T2P 0T8 Main: Fax: Introduction This example explores the effect of a flood event on the stability of a levee underlain by a confined aquifer. The stability is analyzed using: 1) the simulated transient pore-water pressure response from a finite element SEEP/W analysis; and, 2) piezometric lines. A comparison of the results highlights the limitations of using piezometric lines to define pore-water pressure conditions, particularly for complex hydrogeological systems. The comparison also reveals that a reasonable approximation of the flow system by means of piezometric lines requires knowledge of the transient pore pressure response, which paradoxically requires a water transfer analysis unless detailed field measurements are available. Numerical Simulation The levee cross-section has a crown width of 10 ft and a side slope of 1:2 (Figure 1). The levee is constructed of compacted clay and overlies a confined flow system. The confined flow system comprises a 5 foot thick, surficial, silty clay layer overlying a sandy aquifer. The lateral extent of the domain is relatively large so that the left and right boundaries do not influence the pore-water pressure response under the levee. The project analysis tree is presented in Figure 2. Figure 1. Model domain illustrating the levee placement above a silty clay layer and confined sandy aquifer. 1

2 Figure 2. Analysis tree for the project. This project considers two alternatives for representing the pore-water pressures within and beneath the levee during a flood event. The first case uses the transient pore-water pressures simulated by SEEP/W. A steady-state SEEP/W analysis established the initial pore-water pressure conditions before flooding. A total head of 50 ft was applied to the ground surface to the left of the levee (i.e. on the riverside) and a potential seepage face was applied to the landside. A transient SEEP/W analysis was used to simulate the pore-water pressure response during a 40-day flood event. The flood event was defined by a standard dimensionless unit hydrograph: h h 0 = e M h p h 0 ( t t 0 t p M( ) t t 0 M e t p ) Equation 1 where h is the river level, h 0 is the initial river level, h p is the peak river level, M is a shape factor, t is the t 0 time, is the time at the onset of the flooding event (0 days), and is the time to the peak river level. Equation 1 can be rearranged to obtain the river level at any point in time in terms of total head, h(t), given assumed or measured attributes of a flood event. In this case, the initial river level was set at the elevation of the floodplain (50 ft), the river level was assumed to peak at 68 ft (2 ft below the levee crest) and at a time of 10 days, and a shape factor of 3.94 was used. Figure 3 shows the resulting head function that was used as the boundary on the floodplain and riverside slope of the levee. A seepage face boundary condition was applied to the landside ground surface of the domain. t p 2

3 Water Total Head (ft) Time (d) Figure 3. River hydrograph applied as the transient SEEP/W boundary condition on the floodplain and left levee slope. The saturated-unsaturated material model was used to characterize all three materials within the domain for the SEEP/W analyses. The volumetric water content and hydraulic conductivity functions were defined by the values listed in Table 1. Table 1. Soil properties associated with each material. Property Levee Blanket Aquifer Material Type Clay Silty-clay Sand Saturated Water Content Soil Compressibility (1/kPa) 1 x x x 10-6 Saturated Hydraulic Conductivity (ft/d) Unit Weight (pcf) Cohesion (psf) Phi (degrees) The slope stability analyses (Case 1, Case 2a, and Case 2b) check the stability of the landside of the levee using the Morgenstern-Price limit equilibrium method. The entry and exit slip surface search definition is shown in Figure 4. The Mohr-Coulomb material model characterized the strength of all three materials using the properties presented in Table 1. 3

4 Figure 4: Slip surface definition for all three stability analyses. In Case 1, the factor of safety was calculated at every saved time step of the transient SEEP/W analysis, making it possible to investigate the time associated with the minimum factor of safety during the flood event. The simulated pore-water pressures corresponding to the minimum factor of safety were used as the basis for defining the piezometric lines in Cases 2a and 2b (Figure 5). In Case 2a, a single piezometric line was used to characterize the pore-water pressures in the aquifer and confining unit. In Case 2b, a unique, and gently sloping, piezometric line was added to characterize the pore-water pressures in the aquifer. The piezometric line for the aquifer is above the ground surface over a portion of the landside, indicating an artesian condition. Case 2a. Case 2b. Figure 5: Piezometric line definition for Case 2a and 2b slope stability analyses. Results and Discussion The pressure head contours, phreatic surface, and flow vectors generated by the transient seepage analysis at the peak river level are shown in Figure 6. Even though the river level is near the levee crown, the pore water pressures within the levee have not changed substantially due to the relatively quick rise in the water level. The wetting front is very close to the sloped surface, forming a phreatic surface that wraps back on itself. This complexity could not be captured by a piezometric line because each point defining the line must have an equal or greater x-coordinate than the previous point. 4

5 Figure 6: Finite element pore water pressures computed for day 10 of the transient seepage analysis. The pressure head contours indicate elevated pressures within the confined aquifer. Water generally moves downward from the floodplain through the blanket material until it reaches the confined aquifer where it travels more easily towards the drainage ditch and right side of the domain. Water also moves through the levee over the clay blanket, causing the pore-water pressure response shown in Figure 7. The pore-water pressure reaches the maximum at day 15, which is 5 days after the flood level peaked (Figure 3). A similar peak in pore-water pressure was also present in the confined aquifer below the levee toe; however, the peak occurred a day earlier, at day 14, despite being further downstream and overlain by the clay blanket (Figure 8). The quicker response in the aquifer is primarily the result of the significant recharge area on the riverside of the levee Water Pressure (psf) Time (d) Figure 7: Case 1 pore-water pressure response where the levee contacts the clay blanket at coordinate (13,50). 5

6 Water Pressure (psf) Time (d) Figure 8: Case 1 pore-water pressure response in the confined aquifer below the toe at coordinate (45,42). Figure 9 shows the factor of safety versus time for stability Case 1. The minimum critical factor of safety (1.31) was reached at a duration of 14 days, which corresponds to the peak in pore-water pressure in the aquifer (Figure 8). The factor of safety and corresponding pore-water pressures for day 14 are illustrated in Figure Factor of Safety Time (d) Figure 9: Case 1 minimum factor of safety over time. 6

7 Figure 10: Case 1 levee stability at a duration of 14 days. The critical factor of safety was 1.63 when a piezometric line defines the pore-water pressures (Case 2a; Figure 11). However, even a simple visual comparison of the pressure contours illustrates the difficulty of using a piezometric line to define pore-water pressures in SLOPE/W, as the wetting front within the levee and elevated pore-water pressures within the underlying confined aquifer are not captured. This is also evident when comparing the pore-water pressure at the base of each slice over the same slip surface for each stability case (Figure 12). Figure 11: Case 2a levee stability given one piezometric line applied to all materials. 7

8 Pore-water Pressure (psf) , Case 1 Case 2a Case 2b -1, Slice Number Figure 12: Pore-water pressure at the base of each slice for all three stability cases (slip surface 134). The total head along the top of the unconfined aquifer for day 14 of the transient seepage analysis is shown in Figure 13. These values were used to define the second piezometric line applied to the domain in Case 2b. Given the application of two piezometric lines, the original one to the levee and blanket material, and the second one to the unconfined aquifer, a different factor of safety was obtained compared to Case 2a. The critical factor of safety was 1.44 (Figure 14). In this case, the pore-water pressures within the confined aquifer better represented the elevated conditions, as evident in Figure 12; however, the difference in the factor of safety as compared to Case 1 reveal that the piezometric lines still do not fully capture the flow system. This is due in part to the fact that pore-water pressures at the base of slices 7 through 15 (Figure 12) do not reflect the pore-water pressure increase observed at the contact between the levee and clay blanket by day 14 (Figure 7) Water Total Head (ft) X (ft) Figure 13: Total head computed by the transient seepage analysis at top of the unconfined aquifer on day 14. 8

9 Figure 14: Case 2b levee stability given two piezometric lines. A reasonable estimate for the piezometric line corresponding to the confined aquifer was only possible in Case 2b because a water transfer analysis was completed. In the absence of such a simulation, a reasonable estimation of the pore-water pressure regime would require intensive field measurements during a flood event. Even then, proper representation of the pore-water pressure regime could not be accomplished easily via piezometric lines. The use of a spatial function provides a reasonable alternative for defining the pore-water pressures; however, data would then have to be collected in the confining unit and levee (also during a flood event). The better alternative is to numerically simulate the physical system using a water transfer analysis. Summary This example demonstrates the benefits of using a SEEP/W analysis to establish the pore-water pressure conditions for a stability analyses. The piezometric line functionality in SLOPE/W was not able to capture the conditions within the levee system and confined aquifer. Additionally, some knowledge of the flow system is required in order to use piezometric lines for defining pore-water pressure conditions. This typically requires detailed field measurements. 9