By Thomas R. Barnard, Daniel R. Parker and Kathy Zancanella
This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.
When Lost Creek Dam was built as a constant-angle radial arch dam in 1923 and 1924, it reflected the state-of-the-art in design for its time. Its rehabilitation has required leading edge analysis to ensure the dam will withstand potential floods and earthquakes for another century.
California’s Lost Creek Dam, on a tributary of the south fork of the Feather River, was completed in 1924. The Jorgensen-type constant angle, variable radius unreinforced concrete arch dam is part of the 120-MW South Feather Power Project, owned by South Feather Water and Power Agency (SFWPA). Lost Creek Reservoir is just downstream of 13.5-MW Sly Creek and is operated as a reregulating reservoir for 60-MW Woodleaf downstream. The reservoir has a maximum width of about 1,118 ft and maximum depth of about 100 ft near the dam, with gross storage of 5,361 acre-ft. A geo-composite membrane liner on the upstream face was installed to reduce seepage.
SFWPA needs to modify Lost Creek Dam to meet probable maximum flood (PMF) design and evolving safety requirements established by the Federal Energy Regulatory Commission (FERC) and California Department of Water Resources, Division of Safety of Dams (DSOD). The dam crest height, spillway configuration, reservoir volume, annual storage curve and flood operation rules were developed when the reservoir was created, prior to the project being licensed as part of a hydroelectric system in the 1950s. Hydrometeorological data used to determine PMF flows have since changed.
In 2004, SFWPA conducted a hydraulic study that included an estimate of PMF flows for Lost Creek Dam that is consistent with current FERC guidelines and dam safety regulations. The PMF study was updated in response to FERC comments in 2006, and results indicated the dam crest would be overtopped unless the deck is raised and spillway modified to maintain adequate freeboard and spillway capacity. In addition, inspections mandated by FERC under Part 12 revealed substantial deterioration of the dam’s downstream face, which could affect the capacity to resist loads during a PMF event.
The proposed work included increasing the dam spillway openings, raising the crest outside of the spill section to elevation 3,291.5 feet, reinforcing the downstream face, and protecting the plunge pool area to prevent scouring of the foundation material.
The spill crest will be about the same length as the existing spillway, but the number of piers will be reduced and the span between piers increased to about 40 ft. The deteriorated concrete on the dam’s downstream face (about 6 in to 2 ft deep) will be removed. Loose, fractured or damaged foundation material and debris will be removed from the margin between the foundation and the existing dam to expose sound foundation material within the limits of the contact for the new facing concrete.
That sound material will be dowelled into and covered with concrete 4.5 ft thick designed to provide resistance to the anticipated loads. The low level outlet works will be extended about 150 to 200 ft downstream from the dam face so the area at the base can be dried out for work.
The work also includes placing a layer of reinforced concrete where a plunge pool would form during a PMF event to protect against scouring of the foundation material. Loose material and debris will be removed to create a “clean” foundation or incorporated into the work for scour protection. Corrosion-resistant glass-fiber-reinforced polymer (GFRP) bars will be used to reinforce the scour protection concrete and to anchor it to the rock foundation.
Maximum design earthquake
FERC and DSOD wanted the SFWPA design team to develop Acceleration Response Spectra (RSA) and time-history curves to compare to the DSOD curves. Three sets of ground motion records were generated for Lost Creek Dam to satisfy the latest FERC guidelines. All three sets of records reflect parameters that are consistent with the DSOD criteria: Scaled PGA = 0.25 g; Magnitude = 6.25; Distance to fault rupture = 9.45 km; and Site Category = B (Vs â‰¥ 760 m/s).
The cross-canyon, upstream-downstream and vertical acceleration time history records, derived from the 1989 Loma Prieta earthquake, were used primarily for the analyses because the most significant damage to the existing structure occurred when subjected to this record. Two additional sets of motions were derived based on measurements at Morgan Hill in Gilroy and the Chi-Chi earthquake in Taiwan and were used for analyses after the final round of design revisions to satisfy FERC.
This investigation was designed to nondestructively evaluate concrete condition on the downstream face and through the cross-section in the dam’s center. spectral analysis of surface waves (SASW) and acoustic tomography (AT) methods were used.
Concrete coring and testing program
The high-density laser scan survey and non-destructive testing revealed the amount of section loss and the apparent distribution of the concrete strength across the surface and through the thickness of the dam inferred from the velocity profiles in the tomograms. The results of a 2007 coring and testing program were analyzed to establish representative distributions of the concrete properties within the arch structure.
The strength results of the test concrete were represented as contour plots across the dam surface. Because it was equally important to understand the distribution through the thickness of the dam, plots were created to show the strength variation on cross-section views of the arch. The concrete strengths measured in 2007 were generally lower than those documented in a 1988 study. Samples taken for the 1988 report were limited to the areas near the left and right abutments (when looking downstream), with testing performed on the 6-in-diameter core samples from the upper 20 ft of the core holes. The 1988 report also incorporated data from a 1986 investigation, which took six samples from the upstream face near the crest, six from the downstream face closer to the ground surface, and one within the right center portion of the arch.
To establish correlation between the velocity profiles from the AT and the concrete strengths, core sampling was performed along or directly adjacent to where the AT and SASW testing were performed. Holes were cored from the downstream face, penetrating 41 in to 109 in, depending on arch thickness. The concrete strength of samples from the upstream face is generally higher than those from the downstream face. The lower downstream strength likely relates to through-dam seepage and exposure to annual freeze/thaw cycles. This difference in concrete properties was recognized in the 1986 evaluation, where average downstream and upstream compressive strengths were 1,580 and 2,340 psi, respectively. The corresponding static tensile strengths were 230 psi and 300 psi, respectively, and the corresponding dynamic values were 353 psi and 458 psi.
Nonlinear finite element analysis
The scope of the investigation was to perform a three-dimensional finite element nonlinear time history (NLTH) analysis of Lost Creek Dam as an independent check on the linear elastic response spectra and time history analyses using the SAP2000 finite element program, conducted by engineers at AECOM. A second NLTH analysis was performed on a model reflecting the modifications to the crest and downstream face to assess adequacy to resist potential seismically induced loads.
ANATECH generated a 3D finite element model (FEM) from the geometry and concrete material property distribution extracted from the SAP2000 models while refining the mesh by approximately a factor of 3 in all directions and incorporating the nonlinear ANACAP-U concrete constitutive material model. The model developed used the 20-node quadratic integration continuum elements within the library of the Abaqus general purpose finite element program, to further increase fidelity of the analysis. Element size was chosen based on the judgement and experience of the analyst using the ANACAP model. From experience at ANATECH, these elements are the most robust when coupled with the ANACAP concrete constitutive model to prevent spurious hourglass, shear locking and other behaviors that lead to inconsistent calculations.
|The maximum principal strain contours on the upstream face, downstream face and a vertical cut through the mid-section of the dam show [what, exactly?]. * T = 5.62 seconds, Mag. x 25|
The proposed modifications were built into the model mesh and include rebuilding the spillway and dam crest with steel-reinforced concrete and the originally proposed 3 ft layer of new concrete on the downstream face. Dowels will be grouted into the concrete and covered by the facing concrete as well as layers of vertical and horizontal reinforcement at the inner and outer faces of the new concrete. All the downstream facing reinforcement is specified to be GFRP. All the steel and GFRP bars were modeled with two-node truss elements. The mesh for the reinforcement was developed discontinuous from the continuum dam elements and used the Abaqus embedded element technique to superimpose the reinforcement bar/truss element kinematic response onto the concrete/continuum elements mesh to simulate a typical reinforced concrete section. The vertical control joints were simulated by activating the pre-crack option in ANACAP-U along a vertical plane in the elements at the joint locations. This option sets an initial crack along a defined plane. No tension stress can be carried across this plane, although compression and shear will be transmitted. The shear modulus is reduced to 40% of the uncracked shear modulus and reduces further as a function of the tensile strain (crack opening) across the defined plane.
Loading conditions, analysis procedure
Analyses were performed with the winter extreme loading condition (maximum credible earthquake, MCE) section based on FERC engineering and design guidelines. Conditions are minimum mean concrete temperatures; normal high water level, assumed at top of spillway crest; dead load; and MCE.
The first step was to perform a steady state heat transfer analysis to establish temperature distribution for the thermal condition. Two thermal analyses were performed, minimum winter and maximum summer temperature, based on historical ambient air and water temperatures as a function of depth. The second step was to perform a static stress analysis in which the dead load and hydrostatic water pressure were applied to the structure. The nodal temperature results from the thermal analysis are read in by the analysis code and the appropriate thermal stresses are calculated in addition to the dead load stresses. The water loading is resisted by the existing arch section without any contribution from the facing. Incremental water head above the drawdown level is resisted by the combined section consisting of the existing arch and new facing concrete.
The final step was to perform the dynamic time history analysis on the thermal and dead load initialized model.
Static dead load
For the static dead load analysis, performed to initialize in-situ stresses in the structure, a uniform gravity load was applied to the dam elements and the hydrostatic water pressure was applied to the upstream face assuming the reservoir height at the top of the spillway crest. Nodal temperature results from the steady state thermal analysis are read in by the analysis code and the thermal stresses are computed concurrently with the mechanical stresses. A grout closure temperature of 40 degrees Fahrenheit was assumed to calculate the temperature differential at the individual integration points throughout the FEM.
It was judged that the bridge along the dam crest is significantly more flexible than the dam itself and was not explicitly included in the model. However, the mass of the bridge and piers were included as nodal lumped masses distributed at the pier locations along the top of the spillway and crest.
Dynamic time history analysis
After the model had been initialized with the expected in-situ mechanical and thermal stresses, a dynamic time history analysis was performed as a “restart” from the static load step. A base acceleration was applied as nodal boundary conditions at the rock faces of the model, including two horizontal and one vertical components.
Following Corps guidance, the foundation was modeled as massless. The added-mass representation of dam-water interaction was represented with lumped nodal masses on the upstream face of the dam based on the generalized Westergaard equation.
At each node point, the added mass was represented by individual diagonal mass matrices with horizontal components proportional to the normal direction cosine at each location on the upstream face.
Concrete performance and material properties
Modeling of the concrete is a key ingredient for the nonlinear seismic assessment analyses and is provided through the ANACAP-U model. The behavior of concrete is highly nonlinear with a small tensile strength, shear stiffness and strength that depend on crack widths, and compressive plasticity. The main components of the concrete model are tensile cracking, post-cracking shear performance, and compressive yielding when the compressive strength is reached.
The concrete properties varied widely throughout the dam. The distribution of concrete strength and associated modulus and cracking strain criteria used within the Abaqus models followed the distribution from the SAP2000 linear elastic response spectra and time history models across the breadth, height and thickness of the structure. Concrete strength was 1,020 psi to 2,753 psi. Young’s modulus is calculated as 57,000fc’1/2, the dynamic tensile strength is 2.3fc’2/3, and the tensile fracture strain is the tensile strength divide by the modulus. The new concrete was specified as 4,000 psi for the crest and new downstream facing layer.
The foundation rock was modeled as solid elements, linear-elastic with a modulus of 4.0E+06 psi and a Poisson’s ratio of 0.27.
Based on interactions with the governing regulatory agencies and SFWPA, a conservative solution was preferred because the dam is close to 100 years old, the site-mined aggregate-based concrete is highly variable in quality and strength, and SFWPA desired to extend useful life of the structure as much as possible.
Thus, a combination of grade 60 rebar, GFRP rebar, and high-strength all-thread anchor bars were specified for use in the dam crest and downstream facing modifications. In the crest and new piers, grade 60 rebar was modeled as an elastic-plastic material with a modulus of 2.9E+07 psi and a piecewise stress-strain relationship adjusted to reflect true stress and strain values. Tie-down anchors at the new bridge piers were represented with a high-strength steel material with 150 ksi yield strength. GFRP rebar material properties were assigned to all dowels between the existing concrete and new downstream facing as well as the inner and outer layers of horizontal and vertical bars in the new facing. Based on manufacturer specifications, #8 sized GFRP bars have an ultimate tensile strength of 90 ksi, modulus of 6.7E+06 psi and ultimate strain of 1.34%.
In evaluating seismic vulnerability of the dam, failure criteria must be defined to establish limit states on the structural response where the structure can no longer withstand the upstream hydrostatic pressure. For the reinforced concrete components, failure occurs when tensile loads cause rebar to yield and rupture or when shear forces across a section exceed the shear capacity. Under bending loads, concrete crushing may develop on the compressive side, but failure of the section can still be attributed to rebar rupture on the tension side of the section. Section shear failure develops when sufficient cracking extends across a section such that the shear capacity of the concrete due to aggregate interlock is reduced below that needed to support the shear demands. Section shear failure can also occur when compressive struts develop due to arch action within a member and initiate concrete failure in compression, which then rapidly degrades the shear capacity of the section.
Thus, the criteria used to establish structural failure of the dam in the global modeling are: strain level in rebar causing rupture of the bar (modified condition), level of shear strain across a structural section that indicates shear capacity is exceeded, and stress level causing compressive crushing failure. Shear stress at the dam base and rock interface will be examined but failure within the rock foundation is not expected as the rock strength is much greater than that of the concrete. These established failure criteria are based on previous work and benchmarking on structural specimens in support of Sandia National Labs, structural research labs at the University of California San Diego and Berkeley, University of Nevada at Reno, and U.S. Army Corps of Engineers Waterway Experiment Station.
As an initial check on the FEM, the natural frequencies and mode shapes were calculated for the Abaqus model representing the in-situ stress case for the summer and winter thermal static stress cases. Table 1 on page 45 lists the first 10 modes extracted from the Abaqus models, along with those from the in-field 2011 dynamic investigation performed by STRAAM Corporation.
The frequencies from the Abaqus FEM summer thermal condition compare well with the results from the dynamic investigation by STRAAM, indicating that the baseline stiffness of the theoretical model accurately represents the stiffness of the existing structure. The slightly reduced frequencies from the winter thermal analysis correspond with the thermal contraction of the structure resulting in lowered compression across the control joints and a “reduced” global stiffness of the structure.
As-built NLTH analysis
Analysis of the existing condition shows significant cracking develops in a horizontal plane across the two interior monoliths at an elevation about 2/3 to 3/4 the height from the base. This crack plane originates at the downstream face and propagates through the dam thickness. Additional diagonal cracking spreads up towards the crest from this horizontal position near the vertical control joint closest to the right abutment, appearing as a crescent shape in the upper portion. A second horizontal crack plane develops entirely across the two interior monoliths, originating at the upstream face and penetrating almost entirely through the dam thickness, with tensile strains exceeding eight times the defined fracture strain for the concrete. Figure 1 on page 40 presents maximum principal strain contours of the upstream face, downstream face and a vertical cut through the mid-section at 5.62 sec into the acceleration record. Large values of maximum principal strain indicate the location of crack planes developing. Shear strains exceed +/-0.5% through the entire dam section at various locations along the upper horizontal and diagonal crack planes that form. Time history displacement records show a pronounced drift toward the downstream direction at piers 12 and 15. In the cross-canyon and upstream-downstream displacement time histories, there was a nodal displacement record at about ¼, ½, ¾ height and crest elevation at pier 15.
|The maximum principal strain contours at 12.48 seconds reveal significantly less cracking or damage that develops in the main body of the dam as compared with Figure 1. * T = 12.48 seconds, Mag. x 25|
The combination of extensive horizontal and diagonal crack planes with sustained periods of high tensile strain and excessive shear strains indicates a significant potential of a sliding shear failure of the upper region of the dam across the two interior monoliths. In concert, the actual drift shown in the displacement history indicates a global shear sliding in the downstream direction.
With the baseline crest and downstream face modifications added to the model, the structure showed significantly reduced damage during seismic loading. There are no regions of significant shear strain that would indicate a potential shear failure. Horizontal and diagonal cracks form within the new facing on the downstream surface, but these do not develop into full crack planes through the entire dam section. The GFRP reinforcement helps limit the spread and penetration of significant cracking throughout the structure. The maximum stress in the reinforcement is about 38% of the ultimate capacity at a localized region in the outer layer of reinforcement. With the vertical bars doubled, the global response of the dam was essentially unchanged but peak stresses in the GFRP reinforcement were reduced by about 28%.
The proposed modifications were revised to lessen the cracking that develops on the upstream and downstream surfaces. Thermal analysis was not included as part of the static stress initialization step prior to the NLTH analysis, as this was determined to not have a significant effect in previous dynamic analyses.
The thickness of the new concrete facing on the downstream surface was increased 18 in so the total nominal new facing will be 54 thick. Spacing of the GFRP dowels remained unchanged although the length was increased to maintain about 6 in cover from the outside face. The density of the vertical GRFP bars was increased within the new facing.
Analysis of the dam with these additional modifications showed significantly improved performance when subjected to the Loma Prieta ground motions. Figure 2 on page 44 shows upstream-downstream displacements at an elevation of about ¾ the dam height at piers 12 and 15, respectively. These time history plots are for the as-built structure, baseline modification and Revision 2 modifications. It is evident that the retrofit modifications significantly enhance performance. No significant cracking or damage develops in the main body of the dam. Figure 3 on page 48 presents maximum principal strain contours at 12.48 seconds. In comparison to Figure 1, significantly less cracking or damage develops in the main body of the dam. There will be moderate cracking at the base of the bridge piers, but the main reinforcement is stressed to less than 50% of yield and the concrete compressive stress is less than 50% of the concrete compressive capacity. The cracking at the upstream face under the new bridge piers will primarily be surface split cracking and spalling due to compression in the crest from upstream movement of the bridge piers and the discontinuity of concrete strength between the existing and new concrete. Peak stresses in the pier anchor bars is less than 40 ksi or 27% of the yield capacity of the high strength bars. Axial stress along the length of the anchor bars at pier 2 peaks two different times of peak demand. These peak stresses develop at the pier/crest interface for the “downstream” bars that are fully embedded in the new concrete of the crest and facing. On the “upstream” side, the peak stresses in the anchor bars develop near the interface of the existing and new crest concrete. The analyses would indicate that the development length for the anchor bars is about 6 ft and 8 ft for the downstream and upstream bars respectively. Below this depth, the axial stress developed is relatively small.
Analysis of Lost Creek Dam with the proposed modifications indicates the structure can withstand the seismic demands imposed by the Loma Prieta earthquake. While the baseline modifications prevented catastrophic failure of the rehabilitated structure, the formation of horizontal and diagonal cracks on the downstream face that penetrate through the new facing could potentially have done sufficient damage to the upstream face that the geo-composite membrane liner would have to be removed to allow inspection and repair. The described modifications to Lost Creek Dam are under way, with construction to be completed by the end of 2017.
Barnard, T.R., D.R. Parker, and K. Zancanella, “Nonlinear Finite Element Seismic Analysis of Proposed Modifications to an Existing Unreinforced Concrete Arch Dam,” Proceedings of HydroVision International 2015, PennWell Corp., Tulsa, Okla., 2015.
Thomas Barnard is vice president and principal engineer with AECOM. Daniel Parker is a consultant with ANATECH. Kathy Zancanella, now retired, was power division manager of South Feather Water and Power Agency at the time this work was performed.
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