Advanced Analysis

Evaluation of Dam Stability using Finite Element Analysis

Group 6:

Trent Ellis

Mahdi Habibi

Nicholas Johnny

1

Executive Summary The Salah-Mars Gulch Dam was over half- way through its second and final phase of construction when signs of localized distress were observed. The wet season is approaching quickly, and the city of Nowater, AZ wants to know whether the dam can be safely completed, or if it needs to be breached prior to any potential flooding. Group 6 has analyzed the situation to determine the nature of the problem that is causing the localized distresses. In the opinion of group 6, the dam is unstable and should be breached before flooding is likely to occur. Background / Methodology The dam was scheduled to be constructed during the dry season in two different phases, the total duration of which panned two years. The edge sections were successfully completed during the first phase of construction. During the next dry season (current dry season -- 2009), the interior of the dam was constructed to an elevation of +676 ft. Under normal circumstances, the dam could be raised to its final elevation of +685 ft in approximately one month. However, large tension cracks “as deep as a shovel” have been observed in the crest and downstream toe of the embankment. Bulging of the soil just downstream of the toe has been noticed, and inclinometers have indicated significant lateral movements in the downstream half of the dam. Test data from drained and undrained triaxial tests have been provided for the subsequent analysis. The data were used to develop modeling parameters for advanced finite element analysis. The soil hardening model in Plaxis was used to analyze the dam based on known conditions and material properties. This model’s parameters are closely related to the Duncan hyperbolic parameters, which were developed straight from the triaxial test data. Due to the time sensitivity of this situation, the material parameters and finite element program were set up rather quickly. Given the importance of this dam to the citizens of Nowater, AZ, it was important to calibrate the model against known measurements. For this reason, the soil hardening model parameters were calibrated by trial-and-error until the Plaxis model predicted horizontal displacements within a reasonable tolerance of those displacements measured by the inclinometers. After calibrating the FEA model, the construction of the dam was modeled as a staged construction. The gravel and foundation soils were defined and stressed to match initial field stress and moisture conditions before the embankment was added. The embankment was added in a series of eleven lifts of varying thicknesses. The thicknesses were set to match the fill heights at the times when the inclinometers were read so that the results would be directly comparable. The first nine fill stages represent stages that have already been physically completed. The last two stages (from elev. +676 to + 685 ft), as well as the hydrostatic load from floodwater, represent future loads that would be applied if the construction of the dam were to move forward. Field observations indicate that a slope failure is at least likely – at worst, imminent – across the downstream side of the dam. Plaxis was used to analyze the reaction of the soil due to the loads that have been applied and the loads that could be applied. If the stresses and strains throughout the soil mass support the idea of a slope failure, the must be considered unstable. In this case, group 6 is not prepared to offer recommendations for any type of bracing or remediation to increase stability. A specialist may be able to recommend adequate measure that could save the dam at a price more economical than a complete replacement. The dam could only be confidently approved for further construction if (1) Plaxis indicated that another mechanism was responsible for the distress observations, and (2) if that mechanism was in fact something that could be reversed quickly and economically.

2

Comments on Model Parameters As mentioned, the model parameters for this analysis were first developed from triaxial test results as Duncan hyperbolic parameters. These values were then used to determine appropriate parameters for the Plaxis Soil Hardening model. This was done by trial-and-error until Plaxis performed reasonably in modeling the laboratory tests from which its model parameters were developed. The difficulty of that task alerted group 6 to the difficulties that would be faced in attempting to model the Salah-Mars Gulch dam with the soil hardening model. The model parameters would need a considerable amount of tweaking against field measurements. The two on-site inclinometers (A and B) recorded the data that is presented in Figure 1. Inclinometer B was in place for a good while longer than inclinometer A, and it offered a lot more valuable information for the calibration. The field measurements show that maximum horizontal displacements occur near an elevation of +630 ft, and the general trend of the displacements is continuous through the increase in fill height.

Figure 1. Inclinometer Data

600  

610  

620  

630  

640  

650  

660  

670  

680  

0   1   2   3   4   5   6  

Inclinometer  A  

Fill  Elev  =  676  

600  

610  

620  

630  

640  

650  

660  

670  

0   1   2   3   4   5   6  

Inclinometer  B  

Fill  Elev  =  676  

Fill  Elev  =  673  

Fill  Elev  =  668  

Fill  Elev  =  664  

Fill  Elev  =  661  

Fill  Elev  =  656  

Fill  Elev  =  650  

Fill  Elev  =  643  

Fill  Elev  =  636  

3

Inclinometer B provided data through a larger range of fill heights, which was very good for developing models that were useful through a range of stresses. Considering the simultaneous variation in fill height, lateral displacement and elevation, several ideas can be taken away from Figure 1. Most importantly, the lateral displacements are consistently increasing with fill height. The last addition of fill height (only 3 feet) caused a deflection approximately equal to all of the lateral displacements caused by the previous 9 feet of fill. This type of behavior generally indicates a plastic state in which more horizontal movement can be expected with very little applied load. On the other hand, the same type of phenomenon occurred when filling from elevation 661’ to 664’, and the soil began reacting as a stiffer material for the 9’ of fill that was placed after elevation 664’. Extrapolating the same pattern for fill heights beyond the current elevation would predict steady increases in lateral displacement followed by another sharp increase once the dam was brought to its final elevation. This would not be a reasonable engineering calculation, but the general trends do show that (1) lateral displacements will continue to increase with the remaining 9 ft of fill height, and (2) peak displacements should continue to occur between elevations of 630’ and 640’, which puts the displacements adjacent to the toe drain material. Table 1 shows the model parameters that were chosen after modeling an exhaustive set of Plaxis trials. The trial-and-error process was expedited by performing a casual sensitivity analysis as the trials went on. For instance, discrepancies in lateral displacements were found to be more sensitive to the modulus values than the exponent values. The trial-and-error component of the analysis indicated that “m” was not responsible for the lateral displacements, and the subsequent sensitivity analysis provided insight on how to best tweak the modulus parameters and match field data. Though we intended to keep all parameters within a range of theoretically reasonable values, the main priority was to develop a set of parameters that cause the soil hardening model to make realistic predictions. Table 1. Plaxis Soil Hardening Model Parameters for the Salah-Mars Gulch Dam

Parameter Embankment Toe Foundation (unsat / sat) Gravel

γunsat 110 120 110 / 117 122

γsat 115 125 115 / 120 125

E50ref 100,000 785,000 350,000 / 350,000 1,000,000

Eoedref 120,000 323,900 450,000 / 380,000 734,100

Eurref 900,000 2,830,000 900,000 / 1,000,000 3,000,000

m 0.3 0.68 0.3 / 0.3 0.4

C 1300 486 700 / 700 10

φ 8.2 34.6 13 / 13 55

ψ 0 8 0 / 0 0

Pref 2116 2116 2116 / 2116 2116

Rf 0.8 0.69 0.8 / 0.8 0.9

4

Figure 2 shows the geometry that was used to model the dam. Group 6 considered modeling a portion of the weathered conglomerate as a stiff rock material, but it seemed likely that any failure path would pass through the soil layers and not the weathered rock. For that reason, the conglomerate was modeled as a rigid boundary. The parameters for all remaining materials were obtained as previously described.

Figure 2. Salah-Mars Gulch Dam Geometry and Staged Construction Each geometric layer in Figure 2 contains a number to identify its stage in the construction process. The gravel, foundation and key material were all modeled as an existing foundation. These materials were used to generate the initial stresses for the problem, and they were not added as a separate stage during construction. This is not technically what occurred in the field, but it was the most realistic way that Plaxis could model reality. Symmetry was not used in the modeling of this situation because of slight dimensional inconsistencies, a sloped bedrock layer and the likelihood of a sloped groundwater table. The embankment is discretized into a number of horizontal layers that correspond to the fill elevations at which the lateral displacements from Figure 1 were observed. While these lift thicknesses may not represent the actual construction sequence, there is no appreciable loss in accuracy. Note that the downstream toe was constructed with the embankment lifts; it was not considered part of the initial foundation. Construction was modeled up through the elevation that was actually achieved in the field by stages 1 through 9. Stages 10 and 11 modeled the fictitious construction of the dam to its final elevation, and stage 12 models the completed dam under a hydrostatic load from retained water on the upstream side.

5

Analyzing the Salah-Mars Gulch Dam in Plaxis Current Condition The parameters from Table 1 were used to model each major stage of the dam’s construction up to present situation and through the potential completion of the dam. After modeling the current status of the dam, several plots were generated to show the current state of stress. Figure 3 shows the distribution of total stresses throughout the structure. Clusters of very high stresses can be seen in the gravel, which is indicative of the relatively large stiffness that defines the gravel. Otherwise, the distribution of stress is fairly symmetric about the centerline of the dam. The only inconsistency is a slight eccentricity of higher stresses toward the downstream side of the dam. This is probably because of the slightly downward slope of the underlying layer of weathered conglomerate.

Figure 3. Current Distribution of Total Stresses in Salah-Mars Gulch Dam Figure 4 shows the distribution of displacements throughout the dam. Knowing that there has been cracking and bulging near the top and side of the dam, respectively, it is reasonable to search for displacement vectors that indicate the surface of a slope failure. Indeed, a gradient of approximately 0.3 ft of total displacement is seen to extend from an elevation of approximately +660 ft (downstream surface of dam) underneath the toe drain material

6

and up to the ground surface on the downstream side of the toe drain material. This zone will be monitored throughout the analysis in case it does represent the surface of a slope failure.

Figure 4. Current Distribution of Displacements in Salah-Mars Gulch Dam Model to Completion After examining the current condition, the completion of the dam was also modeled in Plaxis using the same parameters and techniques. The remaining 9 feet of the dam was modeled in two stages of construction, or two lifts. Figures showing the distribution of stress and displacement throughout the dam after construction are shown in Figure 5 and 6, respectively. The distress trends that were observed from modeling the current state of the dam are seen to be exacerbated by an increased loading. An important feature of Figure 5 is the eccentricity of total stresses. The stress distribution is more or less symmetric, but the slight slope of the rigid underlayer seems to be shifting the peak total stresses to the right (toward the downstream toe drain) of the system. This is an important consideration since it verifies that the highest stresses are acting in the region where workers have reported local fatigue. Figure 6 shows that the largest total displacements occur (and will occur throughout any subsequent construction) near the top of the dam. This is due to the accumulation of strains through the depth of the embankment and foundation. This also goes along with the on-site reports of cracking and lateral deformation near the top of the dam. In addition, the potential

7

failure surface from Figure 4 is observed to exist in approximately the same magnitude and direction even after the completion of the dam. This indicates that the soils through which the failure surface passes still possess enough strength to prevent a slope failure as the remainder of the dam is constructed. The completed model does not suggest imminent failure, but it does show that the idealized completed dam should show its most critical distresses in the locations where they are being seen in the field. This indicates that the observed fatigue is representative of the most critical potential failure in the dam, and that this zone needs to be analyzed under the design flood load.

Figure 5. Distribution of Total Stresses in Salah-Mars Gulch Dam After Completion

8

Figure 6. Distribution of Displacements in Salah-Mars gulch Dam After Completion Model Under Design Flood Load The dam must be able to withstand the loads from its design flood load. Otherwise, it could fail during flooding in the upcoming wet season. To check this important parameter, the previous methods were employed one last time to check the performance of the dam under the design flood load. The flood load was modeled in the FEA by creating a line load that covered the entire upstream side of the dam, up to the design spillway elevation. The pressure exerted by the design flood is assumed to act hydrostatic and isotropic. Plaxis could not apply the prescribed loading for the design flood load stage. This doesn’t necessarily mean that the dam failed in the traditional sense, but it does mean that excessive deformations or stresses have caused Plaxis to predict failure somewhere in the dam. For comparison with the earlier results, the flood load response of the dam is presented in Figures 7 and 8. Figure 7 shows the distribution of stresses once the flood load is added, and Figure 8 shows the distribution of displacements. The maximum stresses are still located toward the downstream toe drain section, and the increased load has caused larger total stresses to spread out both vertically and laterally. However, the addition of the flood load causes the gradients to become noticeably more eccentric. The previously observed potential slope

9

failure surface is now much more pronounced in Figure 8, and Figure 7 illustrates a gradient for total stresses of approximately 2,000 psf that could be causing the failure surface to form. It is clear that the flood load is causing increased distress in the dam. Even if complete failure doesn’t occur, more localized distresses should be expected. This could reduce the functionality of the dam and facilitate the development of other problems as well. This information is certainly ominous for the future of the dam, but some quantification of the situation is warranted before making an ultimate decision.

Figure 7. Distribution of Total Stresses in Salah-Mars Gulch Dam Under Design Flood Load

10

Figure 8. Distribution of Displacements in Salah-Mars Gulch Dam Under Design Flood Load Slope Stability Analysis Using Plaxis Plaxis allows users to analyze the predicted model response to each stage of construction with a “phi/c reduction” model to determine a factor of safety. Plaxis defines the factor of safety as the ratio of the maximum available shear strength to the magnitude of shear strength that is needed to maintain equilibrium. Plaxis determines this quantity by decreasing ΣMsf in increments until failure is predicted by the model. Equations 1 and 2 describe how ΣMsf affects the factor of safety.

………………………………………… Eq. 1

………………………………………… Eq. 2

11

The factor of safety was thus calculated separately for each of the 11 stages of construction. A phi/c reduction analysis could not be run for the flood loading since Plaxis sensed a failure in that stage. The factor of safety was determined to stay very close to 1.534 from the construction of the foundation material all the way through the final elevation of +685 ft. Typical slope failure problems use a factor of safety of 1.5, and even though the case could be made to require a factor of safety greater than 1.5 for such an important situation, it will suffice for the remaining analysis of this problem. The transition from Figures 5 and 6 (dam constructed to final height) to Figure 7 and 8 (dam under flood load) indicates that the mechanisms for slope failure will become much more pronounced as the dam begins to hold water. This will reduce the factor of safety by some amount. Even without calculating this quantity, it is clear that any significant drop from the dam’s factor of safety for prior loadings (1.534) will lead to a dangerous situation. Considering further that this situation probably deserves a factor of safety of at least 2.0, group 6 must conclude that the dam will not be safe under the design flood load. Figure 9 shows a representation by Plaxis of the shape of the failure mechanism from the results of the phi/c reduction analysis. Clearly, the major concern is a slope failure through the downstream side of the embankment and toe drain material.

Figure 9. Plaxis Representation of Failure Mechanism