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Wanapum Dam Spillway Monoliths 711

LINEAR AND NONLINEAR SEISMIC ANALYSIS FOR THE POST TENSIONING SYSTEM DESIGN OF THE WANAPUM DAM SPILLWAY

MONOLITHS

Juan E. Quiroz, Ph.D., P.E. 1 Bashar S. Sudah, P.E. 2 Bryan J. Brumley, P.E. 3 Richard E. Barrie, P.E. 4

David P. Thompson, P.E. 5

ABSTRACT This paper presents analyses and evaluation methodologies used to assess the seismic stability of the Wanapum Dam spillway structure, located on the Columbia River south of Vantage, Washington. Early in 2014, a horizontal crack was discovered in one of the 120 foot tall spillway structure monoliths that extended the entire 65-foot monolith width. Investigations determined that the crack propagated below the pier reinforcement to the downstream side of the monolith. Repairs using post-tensioned anchors were completed recently. This paper presents the evaluation of the seismic performance of the repaired monolith under the Maximum Design Earthquake (MDE). To assess the state of the structure prior to the application of earthquake loads static stress analyses and transient thermal analyses were performed to identify potential failure mechanisms due to the cyclical thermal loading and the development of hydrostatic pressure within the crack. The seismic analysis was then performed for the MDE with a magnitude of 7.1 and a peak ground acceleration (PGA) of 0.42g. Seismic analysis of the Wanapum cracked spillway monolith, indicates the importance of performing non-linear analyses capable of capturing dominant mechanisms that can be used effectively to assess the stability of the structure and to evaluate potential failure modes.

INTRODUCTION Wanapum Dam is owned and operated by Public Utility District No. 2 of Grant County, Washington (the District). Wanapum Dam is located in south-central Washington State on the main stem of the Columbia River that separates Grant County from Kittitas County. The dam is situated at river mile 415, about midway between Seattle and Spokane. Wanapum Dam is part of the overall Priest Rapids Hydroelectric Project that includes Priest Rapids Dam, located about 15 miles downstream of Wanapum Dam.

1 MWH Global, 350 N. Orleans St., Suite 1301, Chicago, IL 60654, [email protected] 2 Brookfield Renewable Energy Group, Los Angeles, CA 90017, [email protected] 3 MWH Global, 2353 130th Ave NE, Suite 200, Bellevue, WA 98005, [email protected] 4 MWH Global, 350 N. Orleans St., Suite 1301, Chicago, IL 60654, [email protected] 5 MWH Global, 2353 130th Ave NE, Suite 200, Bellevue, WA 98005, [email protected]

712 USSD 2016 Annual Conference

During a routine survey of the spillway structure monoliths, large displacement was observed in Monolith No.4 that significantly exceeded historic values. Follow up evaluations conducted by a dive team revealed that a crack had formed on the upstream face of Monolith No.4 at approximate El. 485 feet. As a result, the reservoir was lowered to reduce the load acting on the monolith and the uplift pressure within the crack. Available construction records indicated the location of the observed crack coincides with the construction joint elevation corresponding to the termination point of the vertical pier reinforcement. Concrete core explorations were carried out to evaluate the condition of the monolith and evaluate the presence of the observed opening at El. 485 and the extent of the crack into the ogee. Remedial designs for the monolith were performed in accordance with the requirements of the Federal Energy Regulatory Commission (FERC) Engineering Guidelines for Evaluation of Hydropower Projects, including evaluations of normal, unusual and extreme loading conditions, for which all acceptance criteria have been met. The repairs using post-tensioned anchors were completed in 2015. The analyses and evaluation methodologies used to assess seismic stability of the Wanapum Dam spillway structure are presented in this paper. These included static analyses, transient thermal analyses, and the evaluation of the seismic performance of the repaired monolith under the Maximum Design Earthquake (MDE). The results of the thermal model indicate that the monolith experiences annual cyclic thermal stresses that vary from upstream face compressive stresses during the warm weather season to tensile stresses during the cold weather season. The stresses estimated from this analysis were combined with the other loads to determine design stresses to remediate the structure. Based on structural analyses considering static plus thermal loads, an anchoring scheme using post- tension rock and concrete anchors was developed to satisfy stability criteria. The seismic performance was then evaluated using dynamic, finite element, computer modeling techniques. The seismic analysis was then performed for the MDE with a magnitude of 7.1 and a peak ground acceleration (PGA) of 0.42g. The seismic evaluation considered three spectrally matched, deterministic seismic events; two crustal events and one interface (subduction zone) event. In addition, the design considered a fourth time history that was developed by scaling to the crustal response spectrum. Based on the total structure downstream movement as a result of initial seismic modeling, additional anchors were required to limit stream direction deformations and the analysis was repeated. Post-earthquake stability requirements in accordance with FERC guidelines were also satisfied with the anchors installed.

WANAPUM SPILLWAY The project is owned and operated by the District, who is the original developer of the Project. The dam was completed in 1963 and consists of left and right earth embankments, left and right bank fish ladders (concrete gravity sections), concrete gravity spillway with 12 radial gates, future units intake section (concrete gravity section)


and a 10-unit reinforced concrete powerhouse with a reinforced concrete erection bay. Overall, the dam is 8,637 feet long and has a maximum height of 186.5 feet. The Wanapum spillway is a reinforced concrete structure with 13 monoliths. A concrete stilling basin slab extends beyond the spillway to provide energy dissipation and hydraulic control. Each radial gate is 50 feet wide by 67 feet high. Each of the monoliths (2 to 12) are 65 ft. wide, with a center pier with one-half of a gate bay on each side, and is separated from their adjacent monoliths by unkeyed and ungrouted contraction joints. Monoliths Nos. 1 and 13 comprise the right and left ends of the spillway, respectively, and contain only one-half of a gate bay. A typical monolith section is presented on Figure 1.

Figure 1. Typical Monolith – Cross-sectional View


Material Properties The material properties used for rigid body and finite element analyses are listed on Table 1. No field investigations or verifications were performed as part of these analyses, except for rock parameters.

Table 1. Material Properties

Spillway Concrete

Unit weight 150 pcf

Poisson’s Ratio, n 0.2 (3)

Static Young’s Modulus, Ec 57,000 (f’c)½

Dynamic Young’s Modulus, Ed 1.0 Ec

Rock Foundation

Poisson’s ratio of rock mass (massive basalt), 0.22

Static Young’s Modulus of rock mass, Ec 3,000,000 psi

Dynamic Young’s Modulus of rock mass, Ed 1.0 Ec

Rock/Concrete Interfaces Friction Angle 56.4 deg

Cohesion (when considered) 25.6 psi

Reinforcement Existing rebar yield stress, fy 40,000 psi

APPROACH FOR ANALYSIS The spillway remediation and post-tensioned anchor design was evaluated using three-dimensional finite element analysis (FEA). Load cases included dead load, silt load, thermal load, uplift pressure within existing crack and foundation interface and external water load acting on the structure. Seismic analyses incorporated sliding planes along cracks, lift joints and along foundation plane. Figure 2 shows the crack profile within Monolith No. 4. Post-earthquake case was performed considering damage that may have occurred during the earthquake. The key requirements for stability are that force (sliding) and moment (overturning) equilibrium shall be maintained with adequate factors of safety along the crack surface and at the foundation contact. The limits of concrete strength, bearing capacity of foundation and concrete/foundation interface strength are evaluated with appropriate factors of safety. Other considerations such as the effects of thermal stress, loss of tensile strength at lift joints and changes in uplift pressure were considered in evaluating potential failure mechanisms.


Figure 2. Monolith No. 4 Crack Location

The FEA model was used to evaluate seasonal thermal behavior and its effects on lift joints and internal water loads. The results of the thermal model indicate that the monolith experiences annual cyclic thermal stresses, which vary from upstream face compressive stresses during the warm weather season to tensile stresses during the cold weather. It has been concluded from thermal FEA that during the winter, the concrete between the crack and the ogee surface, at the contraction joint, tends to separate locally as a result of the temperature differential between the ogee surface and interior crack. Therefore, winter temperature effects were considered for the remedial design. For Normal Operating Conditions:

First, material properties were calibrated with respect to seasonal deflection measurements. Then, a static analysis was performed for each load case including winter temperatures. The anchors were adjusted to develop a zone of compression from contraction joint to contraction joint at El. 485, upstream of existing inclined crack. With the anchor layout, the sliding stability requirements along existing crack were confirmed. These sliding safety factors were calculated by using finite element analysis and reducing friction angle incrementally until sliding was initiated. Concrete stresses and cross-stream deformations were verified to be within acceptable limits for all load cases.

For MDE and Post-Earthquake Conditions:

Dynamic analysis were performed considering full headwater pressure in the open crack upstream of the compression zone as determined from the normal headwater operating condition in winter. The post-earthquake analysis considered damage to the structure and was performed with winter temperature loads.

LOAD CASES Water and Uplift Pressures Hydrostatic and silt pressures were included along with the resulting gate loads. For seismic load case, the uplift condition along the foundation is to remain unchanged during the earthquake. For the post-earthquake load case, loss of foundation drain efficiency was considered.


Thermal Loads The transient thermal analysis was performed for a period of five years to investigate the temperature distribution within the structure due to the seasonal temperature and water temperature variations. The starting temperature for the transient analysis in both the concrete and rock was set to the average annual temperature at the site. Minimum winter temperature was determined to be the critical thermal case for Monolith 4. The temperature distributions within the structure resulting from the seasonal variation at the site were applied to a structural model as body loads to be combined with dead, hydrostatic, uplift and post-tension anchor loads. As a result of winter thermal analysis, the upstream end of the horizontal El. 485 joint that was not in compression was pressurized with headwater pressure. A trapezoidal uplift distribution was assumed from headwater at the tip of the thermal opening to tailwater at the downstream side of the ogee. Seismic Motions The design considered three spectrally matched, deterministic seismic events; two crustal events and one interface (subduction zone) event. In addition, the design considered a fourth time history that was developed by scaling to the crustal response spectrum. The earthquakes chosen for the analysis are the Chi-Chi, Cape Mendocino, the Cascadia interface, and the Iwate motions. Each earthquake consists of three components of motion (stream, cross-stream and vertical). All three components are applied to the structure concurrently for analysis. The seismic analysis was then performed for the MDE with a magnitude of 7.1 and a peak ground acceleration (PGA) of 0.42g. Based on the total structure downstream movement as a result of initial seismic modeling, additional anchors were required to be added to limit stream direction deformations of the structure and the model was re-run.

ACCEPTANCE CRITERIA Since Wanapum Dam is classified as a high hazard potential dam, the acceptance criteria was based on FERC guidelines (FERC, 2002). The spillway's behavior during the earthquake motion and stability under post-earthquake static loading considering damage from the earthquake was evaluated. The seismic behavior of the monolith with installed post-tension anchors was evaluated to verify that no additional failure modes were present. The response of the repaired monolith during the earthquake motion should approach monolithic behavior with the installed anchors. During the earthquake, seismic induced stresses could exceed the strength of materials. If the dynamic analysis indicates that tensile cracking, shear displacements, or rocking are likely to occur, post-earthquake static allowable capacities, such as friction angle are downgraded accordingly. If dynamic analysis indicates that shear failure will occur, then


residual shear strengths are used. No cohesion was assumed at the concrete/rock interface and along any cracked concrete lift joint.

FEA MODEL Mesh The model incorporates 68,800 nodal points and 64,300 elements. Figure 3 presents an overall view of the mesh. The concrete portion (17,700 elements) includes the pier, ogee and stilling basin slab. There are 4,700 elements that make up the contact surfaces and anchors. The monolith is supported on a foundation block (rock) consisting of 41,800 rock elements. The foundation extends away from the spillway about one and a half times the height of the structure. The foundation rock is included to provide appropriate support stiffness to the structure. A detailed evaluation of the foundation itself is not included in this study.

Figure 3. Finite Element Model - Concrete

The spillway and foundation is modeled with eight node brick elements. The material modeling is linear elastic. Nonlinearity in the model is provided by discrete joint or interfaces. Main gate features are modeled as presented in Figure 4.


Figure 4. Finite Element Model – Gate Features

Interfaces Interfaces were included between the ogee and foundation, and the crack within the model. The properties of these interfaces are presented in Table 1. The crack orientation in the model incorporates the latest field data and it is modeled to converge with the horizontal interface at the foundation. A concrete/foundation interface is modeled at El. 450 starting at the upstream face of the ogee and extending through the toe of spillway and continuing under the stilling basin slab as shown in Figure 5. The interfaces are modeled such that the ogee above the crack has the capability to slide with respect to the concrete below the crack and that the concrete structure has the capability to slide along the foundation.

Figure 5. Finite Element Model – Interfaces


Boundary conditions The base of the foundation block is restrained against any movement and the sides of the foundation block are placed on “rollers” which prevent movement perpendicular to the planes. The ogee sides in the model are located at the contraction joints and are not restrained by adjacent monoliths. Post-tensioned Anchors The post-tensioned anchors were modeled using tension-only truss elements. The cross sectional area and elastic material properties for each of the anchors and tendons were included in the model. The coefficient of thermal expansion was also included with a temperature load to initiate the tension in the truss elements that corresponds to 60% of the ultimate tensile strength. Thermal Analysis & Calibration The seasonal temperature distributions from the transient thermal analysis for the average annual ambient and water temperatures were used to verify that the model behavior is within an acceptable range, as compared to the deflection measurements from the available survey data for monuments located on top of the piers, and to validate whether the material properties used in the structural design analyses were adequate. FEA vs Rigid Body Analyses To validate the FEA model, safety factors against sliding for static loads obtained from the RBA were compared to those from the FEA model. Sliding safety factors for FEA approach were computed by reducing the joint friction incrementally until sliding was initiated. The comparison of sliding safety factor obtained from RBA and FEA revealed that the results were rather close to each other and, therefore, validated the finite element approach for sliding stability. Additional base pressure comparisons were performed and stability analysis for final design were performed using FEA because of the ability to include thermal effects as it provides a better representation of the pressure distribution at the base and lift joints.

ANCHORS/REPAIR WORK Post-tension anchors for Monolith No. 4 were defined through an iterative design process. The model with the anchors are presented in Figure 6. Anchors were used to provide adequate safety factors per FERC guidelines (FERC, 2002) for concrete stresses including sliding evaluation. Three 61-strand tendon anchors at the upstream end of Pier No. 4, eight 3-inch diameter rock bar anchors at the upstream side of the ogee, four 2 ¼-inch diameter concrete anchors above the gallery, eight 3-inch diameter concrete anchors upstream of the gate near the contraction joints and fourteen 3-inch diameter concrete anchors installed perpendicular to the face of the downstream ogee were required to satisfy overturning and sliding stability requirements for operating load conditions. To


satisfy sliding stability requirements and to limit downstream movement during the design seismic events, twenty (20) 3-inch diameter downstream ogee anchors were provided. The addition of these anchors limit total downstream movement to less than 1.5 inches at the base of the structure and to approximately 0.5 inch of differential movement from above and below the crack. Post-earthquake stability requirements in accordance with FERC guidelines have been satisfied with the anchors installed.

Figure 6. Finite Element Model – Post-Tension Anchors

SEISMIC ANALYSIS RESULTS

Seismic Displacements The seismic displacements from the four earthquakes are summarized in Table 2 below. Cross-stream values are instantaneous pier displacements. Stream direction values are residual displacements due to sliding. The maximum displacement in the cross stream direction occurs for Earthquake 4 (0.95 inches), and the maximum sliding distance occurs for Earthquake 1 (1.91 inches). The structure’s response to Earthquake 3 is very minimal and considered insignificant.


Table 2. Earthquake Displacements

Direction

Earthquake 1 (Chi Chi)

Earthquake 2 (Cape Mendocino)

Earthquake 3 (Interface)

Earthquake 4 (Scaled Iwate)

Maximum Displacement

(in)


(in)


(in)


(in)

Cross-Stream 0.93 0.94 0.124 0.95

Stream 1.91 1.37 0.03 1.63

Nonlinear seismic analyses indicate sliding along the crack, and along the base of the structure in the downstream direction. The stream direction deformations represent sliding deformation. Figure 7 depicts the deformed shape at the end of the earthquake.

Figure 7. Deformed Shape – End of Earthquakes

Sliding in the seismic analysis occurs at the crack interface in addition to the structure base (concrete-rock interface). Figure 8 shows the relative downstream displacement at the upstream end of the crack at El. 485, and the upstream end of the concrete-rock interface at El. 450 for the Chi Chi Earthquake.


Figure 8. Relative Displacements at Crack and Concrete-Rock Interface

Anchor Forces Maximum anchors forces for the two crustal earthquakes are presented in Table 3. The anchor forces for the interface event are much smaller. Anchors on the pier and on the ogee generally remain below their initial jacking force (0.8 x fpu) during the earthquake. The upstream anchors have seismic loads which occur for a short duration during the earthquakes. Therefore, the anchors on pier are considered to be sufficient to maintain the integrity of the ogee for the earthquakes evaluated. Similarly, the downstream ogee anchors also remain below the initial jacking force and are also considered to be sufficient to resist the sliding forces

Table 3. Maximum Anchor Loads during Earthquake

Anchor Group 0.8 fpu (kips)

EQ-1 (Chi Chi)

EQ-2 (Cape Mendocino)

EQ-4 (Scaled Iwate)

Pier Tendons 2,853 2,175 2,174 2,162

US Ogee Anchors (3”) 776 630 616 595

US Ogee Anchors (2 ¼ “) 491 418 408 387

DS Ogee Anchors (3”) 776 736 776 812


Post-Earthquake Stability During the earthquake sliding occurs at the foundation due to the dynamic motion. As a result, the friction angle at the rock-concrete interface was reduced to 45 degrees for post-earthquake analysis. Downstream sliding of the monolith above the crack increased the tension in the downstream ogee anchors during the seismic event. The downstream displacement has also relaxed the upstream ogee anchors. The forces in the anchors were adjusted accordingly for the post-earthquake analysis. Downstream earthquake displacement of about 0.5 inches presented in Figure 8 resulted separation along the inclined portion of the crack. Friction is only resisted on the upstream and downstream horizontal crack planes. A shear plot at the crack interface is presented in Figure 9.

Figure 9. Post-Earthquake Friction Stress at Crack (psf)

Sliding stability requirements along existing crack were evaluated using FEA by reducing the friction angle incrementally until sliding was initiated. Safety factors are computed by comparing the design friction angle with the friction angle prior to sliding. The post-earthquake sliding evaluation is presented on Figure 10.


Figure 10. Post-EQ Sliding Evaluation

CONCLUSION

Several analyses were conducted to assess stability of the spillway monolith. The results indicated the importance of performing non-linear analysis to understand the global structural behavior including the interfaces at the base and within the ogee, and allowed the evaluation of dominant mechanisms. The downstream sliding at both interfaces was instrumental for the determination of the post-tensioning system not only for the static cases, but also for control of seismic deformations and for the post-earthquake stability. The stability of the structure can be assessed more rigorously as well as the potential failure modes.


REFERENCES

ACI 207.2R-07, Report on Thermal and Volume Change Effects on Cracking of Mass Concrete, September 2007. ACI 318-11, Building Code Requirements for Structural Concrete, 2011. ANSYS Mechanical, A General Purpose Finite Element Program, Version 15.0, 2012. Bruce, The Stabilization of Concrete Dams by Post-Tensioned Rock Anchors: The State of American Practice, Ground Anchorages and Anchored Structures, Proceedings of the International Conference, Institution of Civil Engineers, 1997. Douglas and Arthur, A Guide to the Use of Rock Reinforcement in Underground Excavations. Report 101, 1983. FERC, Engineering Guidelines for Evaluation of Hydropower Projects, Chapter 3, Gravity Dams, October 2002. Mills-Bria, B., Nuss, L., O'Connell, D., & Harris, D., State-of-Practice for the Nonlinear Analysis of Concrete Dams at the Bureau of Reclamation. Denver, CO. Bureau of Reclamation, 2006. PTI, Acceptance Standards for Post-Tensioning Systems, 1998. PTI, Recommendations for Prestressed Rock and Soil Anchors, Fourth Edition, 2004. USACE, Rock Foundations, Engineering Manual 1110-1-2908, 1994. USACE, Time History Dynamic Analysis of Concrete Hydraulic Structures, Engineering Manual 1110-2-6051, 2003. USACE, Earthquake Design and Evaluation of Concrete Hydraulic Structures, Engineering Manual 1110-2-6053, 2007. Zicko, Bruce and Kline, The Stabilization of Gilboa Dam, New York, Using High Capacity Rock Anchors: Addressing Service Performance Issues, International Conference on Ground Anchorages and Anchored Structures in Service, Institution of Civil Engineers, 2007.

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LINEAR AND NONLINEAR SEISMIC ANALYSIS FOR … AND NONLINEAR SEISMIC ANALYSIS FOR THE POST ... [email protected] 3 MWH Global, 2353 130th Ave NE, Suite 200, Bellevue,