Gravity dams about 100 feet high and smaller often require special considerations when evaluating stability and rehabilitation of these structures. Three case histories are presented that illustrate some of the unique challenges in the stability evaluation and upgrading of these dams.
By Gregory S. Paxson, David B. Campbell, Michael C. Canino, and Mark E. Landis
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.
For many, the terms “gravity dam” and “concrete dam” conjure images of large structures, such as the Hoover and Grand Coulee dams. However, most masonry and concrete gravity dams in the U.S. are much smaller structures. According to the National Inventory of Dams, 90 percent of gravity dams categorized as high or significant hazard structures are less than 100 feet tall.1
Design features common to large gravity dams often are not incorporated into these smaller structures. For example, many smaller dams do not include foundation drainage systems. In addition, large dams in steep canyons typically are keyed into bedrock at the abutments, while for smaller structures the non-overflow sections may only extend a limited distance beyond the original ground surface and many times are not abutted into sound rock.
Geologic investigations and methods for stability evaluation often are less rigorous and complex for smaller structures. The behavior of larger dams necessitates a better understanding of the foundation conditions and a more in-depth analysis of the performance of the structure under various loading conditions, including finite element and deformation analyses. This article discusses the stability analysis and rehabilitation of smaller (less than 100 feet tall) gravity dams.
Gravity dam stability analysis
The most common failure mode for gravity dams is sliding or overturning along or beneath the dam/foundation interface.2 Stability analysis for gravity dams often is simplified into a two-dimensional rigid body analysis of a cross section of the structure (see Figure 1) and is focused on stability against sliding. In this analysis, overturning of the dam is considered within the context of its potential influence on sliding. Overturning tendencies express themselves through development of tensile stresses at the heel of the dam. In these cases, sliding stability is analyzed considering a cracked base, which reduces sliding resistance. While the gravity dam stability analysis often is simplified to evaluate failure along the base, it is important to consider kinematically feasible failure mechanisms along joints, foliations and bedding planes or within the rock mass.3
In addition to failures through the foundation and along the dam/foundation interface, the stability analysis should consider failure through the dam, commonly along horizontal construction joints. This “partial section” analysis usually is performed using the same methods applied to the stability evaluation of the entire structure.
Guidance documents for the evaluation and design of gravity dams have been developed by U.S. agencies that own or regulate dams, including the Federal Energy Regulatory Commission, Bureau of Reclamation, and U.S. Army Corps of Engineers. In Canada, the Canadian Dam Association and BC Hydro provide similar guidance for the evaluation of gravity dams.3,4
The selection of physical and mechanical properties of the dam and foundation are critical to the stability evaluation of a gravity dam. Unit weight of the concrete or masonry is a key component of the analysis. Estimates of the shear and tensile strength of concrete in the dam can be estimated from laboratory testing of representative samples and/or using available guidance documents.4,5,6
The shear strength along the dam-foundation interface or through the foundation is probably the most important parameter to define. Shear strength is comprised of the friction angle and cohesion of the material(s) or interface. Typical shear strength values are available.6,7,8 Friction angle often is estimated using material testing and/or correlation with empirical data for similar materials. Estimating cohesion (or adhesion along the base of the dam) is more difficult, and the selected value has a significant effect on the stability analysis results. FERC recognizes the difficulty in accurately defining cohesion along the base of the dam and provides alternate requirements for stability if cohesion is not relied upon in the analysis.9
Loading conditions and safety factors
Most regulatory agencies, including FERC, categorize loading conditions as “usual,” “unusual” and “extreme,” and the required safety factor increases with the probability of a given loading condition. Typical loading combinations to be considered include normal operating conditions (usual), flood discharge loading (unusual or extreme), loading from ice (unusual) and earthquake forces (unusual or extreme).
The stability analysis for flood conditions should consider a range of floods to identify the combined reservoir (headwater) and tailwater loading that results in the lowest safety factor. The largest hypothetical flood, or probable maximum flood, is not always the most critical flood loading scenario.
As noted earlier, FERC guidelines allow a reduction in the required safety factor if cohesion is not considered in the analysis. For example, the minimum required safety factor for normal operating conditions is 3.0 if cohesion is included but otherwise only 1.5.
Uplift forces within the dam, on the base of the structure, and within the foundation rock mass are important in stability evaluations. For structures without an internal drainage system or other special features, and with fairly uniform foundation conditions, it is typical to assume that uplift varies linearly from full headwater at the heel to full tailwater at the toe of the dam. For dams with a drain system, reduction in these pressures should only be allowed when it can be verified that the drain system is effective.
Cracked section analysis
The gravity method of analysis requires that the resultant of all forces acting on the dam lie within the middle one-third of the base to avoid tensile stresses at the heel. When the resultant lies outside the middle one-third, tensile stresses are assumed to develop along the base of the dam. Most regulatory agencies (including FERC) require a cracked section (or cracked base) analysis when tension develops at the heel of the dam. Full uplift is then assumed to act on the cracked section of the base (except under seismic loading, where full uplift is assumed not to develop due to the rapid cycling from seismic loads), and the analysis is revised to reflect this modified uplift distribution, with cohesion, if considered, acting only along the uncracked portion of the base.
Most agency guidance suggests an iterative approach to the cracked section analysis for static loadings. However, the crack length and reaction pressure at the toe of the dam can be solved explicitly.10,11 For earthquake forces, the crack length can more easily be computed.
Rehabilitation of gravity dams
The most common methods for rehabilitation of gravity dams that do not meet stability criteria include buttressing or anchoring. Buttressing consists of adding mass to the downstream portion of the structure to resist sliding. This can be accomplished using conventional mass or roller-compacted concrete. High-capacity post-tensioned rock anchors have been used to stabilize gravity dams since the 1960s, with more than 300 dams in North America being anchored.12 Vertically installed post-tensioned anchors add normal force, increasing the sliding frictional resistance and preventing the development of tension at the heel of the dam. Anchors installed at an angle will provide additional sliding resistance by directly offsetting applied horizontal forces, but installation can be more costly than vertical anchors.
Gravity dams with inadequate spillway capacity can be allowed to overtop during extreme floods, provided the dam meets stability criteria under the flood loading conditions and overtopping flows can be shown not to erode foundation support from the toe of the dam or abutments.
For many smaller gravity dams, the non-overflow sections do not extend to bedrock at the abutments but are simply buried in the earth abutment (see Figure 2). This typically is acceptable, provided the fill materials are satisfactory and the spillway can pass the design flood without overtopping the non-overflow sections or abutments. If these sections do overflow, there is potential for erosion and failure of the earth abutment, resulting in a potential dam failure or loss of reservoir. In some cases, these dams have cutoff walls that extend further into the abutments than the gravity section. However, these walls typically are intended to reduce abutment seepage rather than prevent erosive failure from overtopping. Dams lacking non-overflow sections that tie into bedrock abutments may require modifications to prevent overtopping or erosion of the earthen abutment.
The following case histories include discussion of the gravity dam stability analysis, the importance of parameter selection, rehabilitation to address stability issues and the potential for abutment erosion and failure.
Sugar Hollow Dam
Rivanna Water and Sewer Authority owns Sugar Hollow Dam near Charlottesville, Va. This 80-foot-high concrete gravity dam was completed in 1947 and consists of spillway and non-overflow gravity sections, with cutoff walls extending into earth abutments. In the mid-1990s, the Virginia Dam Safety program identified the dam as having inadequate spillway capacity, and analyses indicated that the dam did not meet stability criteria for extreme flood loadings.
The authority planned to install 30 vertical multi-strand, post-tensioned rock anchors through the gravity sections to increase the frictional resistance and prevent overturning under extreme flood conditions. Anchor sizes ranged from five to 36 strands, with a maximum design load of about 1300 kips. Anchors were designed, installed and tested in accordance with Post-Tensioning Institute standards.13
Because the non-overflow sections would overtop during the PMF, there was potential for erosion and failure of the earth abutments and cutoff walls. Alternatives to address this concern included armoring the abutments, stabilizing the cutoff walls assuming downstream soils eroded, and raising the abutments to prevent overtopping flows of these areas. Raising the earthen abutments by 10 feet with earthfill was found to be the most cost-effective approach. The ends of the non-overflow sections were also raised with concrete to confine overflow to the central valley.
The project received the Association of State Dam Safety Officials award for National Rehabilitation Project of the Year in 2000.
Stony Creek Dam
Stony Creek Dam is a 35-foot-high concrete gravity dam constructed in the late 1920s for water supply. The dam, owned and operated by the City of Burlington, N.C., has a 200-foot-long spillway section with concrete non-overflow sections that tie out to earth abutments. State dam safety regulations require safe passage of half of the PMF. Although the concrete of the dam is in good condition, the non-overflow sections and abutments overtop at about the 100-year storm event, and stability analyses demonstrate the dam does not meet the required safety factor for events greater than an estimated 300-year storm. For the modeled half PMF, the abutments overtop by 12 feet, which would result in a breach of the reservoir.
|A concrete gravity section was built at Stony Creek Dam to tie the dam into the bedrock at the left abutment (foreground). The right abutment will be reinforced using a secant shaft wall, and the spillway will be stabilized with post-tensioned rock anchors.|
The rehabilitation design for Stony Creek Dam includes post-tensioned anchors installed in the spillway and non-overflow sections, spaced 10 feet apart with design loads up to nearly 800 kips. The left abutment will be protected by constructing a concrete gravity section extension, and the right abutment will be reinforced by the installation of a 48-inch-diameter secant shaft wall with steel H sections placed in alternate shafts and socketed 15 feet into rock and secondary shafts terminated at the top of rock. The secant wall is designed to provide cantilever resistance at half PMF water levels, with erosion to rock on its downstream side.
Construction of the upgrades to Stony Creek Dam began in spring 2011, and this work is expected to be completed by the end of the year.
Green Lane Dam
Green Lane Dam is a 103-foot-high, 800-foot-long concrete gravity dam northwest of Philadelphia. The dam, owned by Aqua Pennsylvania, was constructed in the mid-1950s for water supply. The design flood for this high hazard dam is the PMF, which was re-evaluated in the late 1990s and found to overtop the non-overflow sections of the dam by about 2 feet. A preliminary stability evaluation indicated that the dam did not meet generally accepted criteria, and the owner’s previous consultant recommended performing more in-depth field explorations and analyses to support a rehabilitation design. Initial estimates for stabilizing the dam with post-tensioned rock anchors were $1 to $3 million.
As-built drawings and original construction photos indicated that significant rock excavation (15 to 30 feet) was performed. Concrete at the base of the dam was cast against the bedrock, indicating that sliding could not occur without mobilizing a significant rock wedge (shear through bedrock). In addition, the roller bucket energy dissipater in the spillway section has a minimum 5-foot concrete thickness and is anchored into the foundation bedrock, thereby providing supplemental sliding resistance.
|At Green Lane Dam, subsurface information obtained and detailed analysis indicated the dam met stability criteria of the Pennsylvania Department of Environmental Protection.|
A subsurface exploration indicated that the dam’s concrete was of good quality. Most of the horizontal construction joints were unidentifiable by visual inspection, indicating bond at these joints. However, the rock at the concrete/bedrock interface was highly fractured, suggesting that cohesion at the interface could not be relied upon in a stability analysis.
Laboratory testing included unit weight and compressive strength tests of the concrete and rock samples. Concrete samples had an average dry unit weight of 157 pounds per cubic foot (pcf), compared to the typical unit weight of good quality mass concrete of 145 pcf to 155 pcf.
More detailed analyses were performed to estimate downstream flood levels because tailwater can have a significant effect on stability. The HEC-RAS river modeling package, developed by the Corps, was used to model flow in the creek and floodplain downstream of the dam. For the spillway section, the tailwater computed using HEC-RAS was adjusted to reflect effective tailwater against the dam, as influenced by high-velocity flow through the spillway and roller bucket.
Corps guidance suggests that the effective tailwater force downstream of a spillway can be reduced to as little as 60 percent of the depth in the downstream channel, a default value used when supporting documentation is not provided. Using model studies performed as part of the original design and guidance provided by the Corps,14 the effective tailwater for the Green Lane Dam roller bucket was estimated to be about 85 to 90 percent of the downstream tailwater depth.
The findings of the documentation review, subsurface exploration, laboratory testing and hydraulic analysis provided information that contributed to a refined evaluation of the stability of the structure, including:
- Unit weight of the concrete was higher than expected;
- Tailwater levels during the PMF were higher than assumed in previous analyses; and
- The dam is “keyed” into the rock foundation.
An updated analysis was performed in 2004 incorporating these findings, and the results demonstrated that Green Lane Dam meets the Corps criteria for gravity dam stability, eliminating the need for an upgrade.
Summary and conclusions
Smaller gravity dams commonly are evaluated using simplified two-dimensional analyses with conservative assumptions for strength along the dam/foundation interface and within the foundation rock. For dams not meeting stability criteria, stabilization is often performed using post-tensioned rock anchors or buttressing. In addition to stability concerns, many smaller gravity dams are not “keyed in” to bedrock at the abutments, creating the potential for abutment erosion and failure.
These case histories demonstrate approaches for the rehabilitation of gravity dams with stability issues or potential for abutment erosion. The case history for Green Lane Dam illustrates the importance of detailed review of dam construction records, advanced hydraulic analysis for estimating effective tailwater, and laboratory testing (especially related to unit weight and bond) when it comes to stability analysis results.
1National Inventory of Dams website, https://nid.usace.army.mil.
2Douglas, K.D., M. Spannagle, and R. Fell, “Analysis of Concrete and Masonry Dam Incidents,” International Journal of Hydropower and Dams, Volume 6, No. 4, 1999, pages 108-115.
3Guidelines for the Assessment of Rock Foundations of Existing Concrete Gravity Dams, BC Hydro Report No. MEP67, Vancouver, British Columbia, Canada, 1995.
4Dam Safety Guidelines, Canadian Dam Association, Moose Jaw, Saskatchewan, Canada, 2007.
5Draft Engineering Guidelines for the Evaluation of Hydroelectric Projects, Federal Energy Regulatory Commission, Division of Dam Safety and Inspection, Washington, D.C., 2000.
6Uplift Pressures, Shear Strengths and Tensile Strengths for Stability Analysis of Concrete Gravity Dams, EPRI Report TR-100345, Electric Power Research Institute, Palo Alto, Calif., 1992.
7Engineering and Design Rock Foundations, EM 1110-102908, U.S. Army Corps of Engineers, Washington, D.C., 1994.
8Khabbaz, H., and R. Fell, Concrete Strength for Stability Analysis of Concrete Dams, unpublished report, School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia, 1999.
9Engineering Guidelines for the Evaluation of Hydropower Projects, Federal Energy Regulatory Commission, Washington, D.C., 2002.
10Campbell, D., “Gravity Dam Stability Analyses,” Proceedings of the ASDSO 6th Annual Conference, Association of State Dam Safety Officials, Lexington, Ky., 1989.
11Paxson, G., T. Fernandes, and D. Campbell, “Green Lane Gets Green Light: Parameter Sensitivity in Gravity Dam Stability Analysis,” Dam Safety 2005 Proceedings, Association of State Dam Safety Officials, Lexington, Ky., 2005.
12Bruce, D.A., and J. Wolfhope, “Rock Anchors for North American Dams: The National Research Program Bibliography and Database,” Institution of Civil Engineers, London, England, 2007.
13Recommendations for Prestressed Rock and Soil Anchors, Fourth Edition, Post-Tensioning Institute, Phoenix, Ariz., 2004.
14Hydraulic Design of Spillways, U.S. Army Corps of Engineers, Washington, D.C., 1990.
The authors thank the Rivanna Water and Sewer Authority, City of Burlington, and Aqua Pennsylvania, owners of the dams referenced in the case histories of this article.
Greg Paxson, PE, a principal with Schnabel Engineering, was a designer for the Sugar Hollow Dam project, performed stability analysis for Green Lane Dam and served as a reviewer for the Stony Creek Dam project. Dave Campbell, PE, director of dam engineering for Schnabel, was the principal-in-charge for the Sugar Hollow and Green Lane Dam projects. Mike Canino, PE, the West Chester, Pa., branch leader for Schnabel, has been involved with the evaluation of numerous gravity dams. Mark Landis, PE, a principal with Schnabel, is the project manager for the Stony Creek Dam project.