Dam Safety: Stability and Rehabilitation of "Smaller" Gravity Dams
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
Material properties
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.
