Dam owners and engineers have access to a variety of advanced analytical tools for assessing the safety of a dam. When using these tools, it’s important to remember that a mathematical tool is only as good as the data that supports it. Each dam site and its environment is unique, with different characteristics governing performance. This requires sensibly interpreting specific site conditions and their effect on dam safety.
By Robert B. Jansen
The survival of most dams suggests that their engineering has been amply conservative – or that their worst trials are yet to come. However, the level of conservatism in the design of an individual dam cannot be determined without a verified comparator. The ultimate measure is actual behavior under extreme forces.
Now armed with capable software and hardware, analysts are encouraged to use these tools to refine dam designs. In pursuing this opportunity, they must give attention to the remaining sources of error, largely in the dam site and its environs. Improved skills enable analysis of features that could not be quantified previously, making possible more realistic representation of structural and foundation elements. This requires enough investigation to determine the characteristics that will govern dam performance, as well as the degree and extent of deterioration to be anticipated. Engineers attracted by the intricacies of some numerical procedures must be continuously aware of the need to relate them to real conditions sensibly interpreted.
Most dam disasters can be attributed to overlooked or misunderstood project flaws and/or underestimated floods. Notable dam failures include:
– Taum Sauk in Missouri in 2005: Overtopping, misoperation, and weak rockfill and foundation contact.
– Nahal Oz in Israel in 2001: Fill breached by erosion of soils with unrecognized deficiencies.
– Teton in Idaho in 1976: Internal erosion of fill without filter; unsealed foundation rock joints.
– Frias in Argentina in 1970: Overtopping of rockfill, which was sealed on both faces without internal drains.
– Baldwin Hills in California in 1963: Leakage through fill and foundation cracks from land subsidence.
– Malpasset in France in 1959: Arch collapse through foundation rock displacement.
– Vega de Tera in Spain in 1959: Breakaway of buttresses of flat-slab dam due to poorly bonded joints.
– St. Francis in California in 1928: Gravity dam ruptured upon washout of very weak foundation rock.
Extracting value when limited data are available
For some dams where field and laboratory investigations have been limited, engineers have conducted sensitivity studies to draw the boundaries of possible dam behavior and to assess the relative influence of key parameters. For these analyses, various combinations of assumed data are used to weigh potential dam and foundation reactions to loadings, and thus to estimate the level at which structural capacity might be exceeded. For sites that do not appear to present interpretive challenges or aspects that might suggest the possibility of hidden problems, this type of analysis has been considered helpful in spanning information gaps.
Sensitivity analysis may be especially useful in analyzing older concrete dams with incomplete records and/or for which only rudimentary exploration and testing were done. Concrete structures have an important advantage, as composites of integral blocks able to bridge defects and thereby continue as intact units. In contrast, earth embankments cannot tolerate weakening of individual constituents without risking loss of the whole. Therefore, sensitivity analysis is more suitable for concrete sections that may have substantial ranges of unit strength but averages above an acceptable threshold.
Unknown conditions are not always detrimental. Curtailing exploration and testing might offer false economy if better knowledge of site assets could permit refinement of designs that otherwise would need to be excessive to compensate for lack of data. The difficulty of the search is not a valid excuse for lesser effort that leaves critical conditions in doubt.
Deficiencies that escaped attention during investigation and construction may be revealed once a dam is placed in service. To ensure detection early enough for remedial action, continuous monitoring must be conducted by seasoned observers who know the signs of abnormal behavior. Dams that have benefited from timely response to sinkholes, cracking, leakage surges, or other disorders include WAC Bennett in British Columbia, Fontenelle in Wyoming, Jatiluhur in Indonesia, Logan Martin and Walter Bouldin in Alabama, Matahina in New Zealand, Navajo in New Mexico, New Exchequer in California, and Willow Creek in Montana.
Factors that affect dam behavior
Several factors affect the behavior of a dam, among them loads, slope conditions, and structural capability of concrete dams.
When a dam has been in service long enough to adjust to normal loading under a fully established seepage regime, it has demonstrated its capability under those conditions. As time passes, changes occur that affect dam performance favorably or unfavorably. Benefits may accrue from seasoning of an embankment or the continuing increase in strength of concrete. Detriment may be caused by erosion of soils and soft rock in embankments and foundations or by cement leaching or alkali-aggregate reactivity. Normal operation may not test a dam unless its structural capacity is reduced by degradation or loss of materials.
Transient effects of natural events are less predictable. Nonovertopping surcharges from floods generally put only moderate incremental load on a structure. The most severe condition may be caused by seismic loading, with its significantly different multidirectional pounding at varying amplitude and frequency. Fractures could be actuated by amplification of acceleration at higher levels in the dam. Seismic vibration is likely to be most dangerous at interfaces that may separate, as at structural or foundation contacts and at joints. Shaking at contact surfaces may initiate or extend cracks, as well as open and close gaps and result in variations in internal water pressures. These conditions can be modeled mathematically by increasingly sophisticated methods that take into account the dam and foundation units that might participate in destabilization.
Mathematical models have been used to visualize the possible behavior of a dam under various loadings. Three-dimensional nonlinear finite-element analysis allows more detailed consideration of features that were too complicated for calculation by the oversimplified practices common in earlier times. The interaction of a dam and its foundation and structural interfaces can be approximated if actual site characteristics are known sufficiently. However, complicated models that combine detailed structural components with poorly defined boundary elements may be of questionable value. Nonessential factors must be de-emphasized while clarifying those that have greatest influence on performance. For unassailable validation, particularly of structures on complex foundations, extensive tests in the laboratory and in situ may be needed to supplement thorough exploratory effort.
Advocates of state-of-the-art analysis say old methods may find a dam to be substandard when it is not. The same might be said for new methods. Also, either the old or the new might indicate a dam is safe when it is not. Such appraisals must be scrutinized to be sure they properly reflect the character of the dam and its environs and the potential damaging forces. In the case of extreme earthquake, the release and attenuation of energy from ground movement might be beyond confident prediction even if the location of the source is known. Analysis is complicated further by the scanty records from observation and measurement of dam reaction to severe seismic effects.
Reality checks that have been made by comparison of computed and actual dam performance have raised doubts about some numerical models. Criticism has been related less to theory and process than to lack of demonstrably representative data. In one illustrative case, retrospective finite-element analysis was made of a well-instrumented and extensively tested earth dam that withstood a strong earthquake with known acceleration at the site.
The dam’s calculated settlement and pore-water pressure rise during the event were several hundred percent higher than measured values. In examining these grossly misleading results, consideration was given to recalculation by adjusting the assumed embankment stiffness and degree of saturation. The effect of this recalculation would be to calibrate the mathematical model to the observed dam response. The hope was that the revised model then might be of some value in predicting performance in a greater earthquake. Simulation would be influenced by the alteration of dam and foundation conditions in the past seismic shaking, as well as by other changes with the passage of time.
In hindsight, any combination of input data might be adjusted until the computed and true behaviors are similar. Usefulness of the derived model would have to be proven.
Nonuniform and varying conditions may weigh heavily in analysis of earth and rock slopes. Material properties may change because of deterioration, cracking, clogging, solution, or cementation. Throughout the years of operation, cyclic variations in reservoir loading can cause softening of embankment zones. Conditions such as soil fabric, interbedding, and segregation are not readily quantified. Numbers may not be assignable to some foundation irregularities.
The shape and character of the site can have major influence on the load-carrying capability of the dam. This applies to the geologic features and the inevitable changes in foundation rock and soils that affect resistance to movement or deterioration. Restraint may be conducive to arching of the fill in a narrow canyon or a deep foundation trench. Consideration also must be given to problems where the embankment abuts structures or conduits, including leakage through structural joints and cracks. Stirring all these ingredients into a mathematical mix should not be expected to produce more than a rough estimate of real performance.
Structural capability of concrete dams
Determining the structural capability of concrete dams has been facilitated by improved finite-element procedures that enable replication of structural faces and foundation anomalies. The quality of the simulation will depend on the extent to which local conditions are known. Foundation rock may include bedding planes, joints, shear zones, faults, clay seams, and solution channels. The orientations, gaps, and interface materials of these features could be vital determinants of resistance to shearing and compressive forces, as well as their function as hydraulic conduits or aquicludes (water barriers). Shear strength of potential sliding surfaces may be reduced by stress relief and weathering. The most vulnerable zones may be along such altered features that extend continuously through the dam site.
Cracks in concrete dams are likely to originate at points of concentrated stress, as at changes in abutment slope. If the rock at the site is compressible, differential foundation deformations and consequent cracking may occur at concrete monoliths of different height. Arch dams are sensitive to abutment displacement on adversely oriented or weak rock planes. They may accommodate uniform site settlement but have little tolerance for shifts in the supporting rock. Configuration and properties of their foundation contacts are very important.
Slender members of some flat-slab (Ambursen) and multiple-arch dams built in the first half of the twentieth century may need careful analysis because of their susceptibility to deterioration in severe climates and their sometimes marginal resistance to lateral seismic loading. Advanced analytical practices are useful in evaluating measures taken to strengthen these dams, including rock bolting; post-tensioning; supplemental layers of concrete, shotcrete, or gunite; injection of synthetic adhesive; and shear walls or struts or concrete filling between buttresses.
Estimating probabilities by means of statistical analysis
The nature and scope of risk related to dams may defy prediction, mainly because of the unknowns of the site, structure, and seismic and hydrologic environments. This uncertainty has been viewed as a justification for estimating probabilities by statistical analysis. This requires rational examination of information and weighing the possible effect of its deficiencies.
Reckoning of the extremes imposed by flood or earthquake may not be refined much by probabilistic study unless the database is strong. Statistical extrapolation is most appropriate if performed on an ample, unbiased, continuous, minimally scattered record of the same kind of events during which there were no significant changes in governing factors. The reliability of the projection into the future diminishes rapidly for extrapolations that are many times the period of recorded data.
Statistical analysis will not provide reliable estimates of floods with return periods as long as hundreds of millennia, which has been assumed for the probable maximum flood. Historical records alone may not be adequate for extrapolating more than 1,000 years. Estimating of very rare events may be hampered by lack or poor quality of gaging. In some cases, the data can be supplemented by study of observed effects of ungaged floods, such as movements of boulders whose shapes and sizes can be correlated with calculated hydraulic velocity and depth thresholds at which dislodgement and transport will occur. Projections also can be enhanced by paleohydrological study in regions where evidence of prehistoric floods may be found.
The practical and broadly accepted alternative for estimating extreme flows is the hydrometeorological method. This method is based on maximization and transposition of large recorded storms from other watersheds to determine the probable maximum precipitation that might be possible in the drainage area being studied. Adjustments are made for differences in air moisture and other rain-producing parameters. New software provides improved definition of watershed characteristics and spatial and temporal rainfall patterns. Various techniques have been used for positioning the transposed storm on the subject basin. Regions must have similarities in environment and storm types that make this transposition appropriate.
Records of rare storms in other basins can increase the hydrologic database substantially. Historic dam losses due to undersized spillways (Canyon Lake in South Dakota, Johnstown in Pennsylvania, Machhu II in India, and many others) might have been prevented by using today’s transposition techniques.
Estimates of potential ground motion are especially difficult for dams near seismic sources. The nature of shaking varies with the size of the earthquake. Extrapolation from a limited record of lower-magnitude events might not tell much about a future great earthquake. Yet, predictions often have been made in this way. Probability of exceedance of a given intensity or acceleration has been shown by isoseismal contours for various periods of return, usually thousands of years. Whether this practice is realistic at all will depend on the length, volume, and content of the historical record and on supportive evidence such as from tectonic strain measurement and paleoseismic interpretation.
Statistical analysis has been used in risk assessment of variable dam or foundation materials. A weakness of such study in some cases may be in the transfer of data from one site to another. Each dam has a combination of setting and structural characteristics not exactly like any other. The unique nature of each project demands strong focus on local conditions.
Sheffield Dam failed by liquefaction of loose silty sands of the embankment and its foundation in the 1925 Santa Barbara earthquake.
Proponents of probabilistic analysis of soil deposits are handicapped by the difficulty of quantifying actual spatial stochastic variation. In the usual investigation, sampling is not spaced closely enough to provide more than a crude approximation of variations in the entire soil body. A statistical model could be questioned if only limited averaging is possible. The applicability of an average used in analysis will depend on the parameter and its range and pattern of variation throughout the earth mass being studied.
For example, an average of shear strengths that vary moderately might be used appropriately in a slope stability analysis, but an average permeability might be misleading in a seepage analysis. Individual values that differ sharply may determine points of concentrated leakage. At one dam in the southern U.S. where a grouted cutoff was established in floodplain alluvium, unit grout takes in holes on a spacing of 3 feet varied radically across the treated section, differing as much as 30 times between adjacent holes.
Attempts have been made to probe the uncertainties of earth slopes by probabilistic study. This study considered variation of density and shear strength, as well as hydraulic conductivity, which governs seepage and pore-water pressures and therefore effective stress. A complete analysis would have to include anomalies and directional variations in properties (anisotropy) as well as stationary variability. These features pertinent to slope behavior may be so singular that they are not amenable to statistical processing. Probabilistic studies of this kind do not tell what the safety margin is, any more than can be learned by conventional deterministic analysis. They indicate only the possible range of behavior corresponding to an array of soil models with different assumed distributions of properties. Safety factors indicated by such hypothetical study could vary widely, with the true value in an indefinite place between the extremes.
Statistical analysis of the influence of material and permeability variations has been used to estimate the exit gradient of seepage emerging from an embankment face or a natural slope. This is a critical determination in evaluating the potential for backward piping, which is a major cause of dam failure. In an approach that combines statistical and finite-element techniques, each mesh element has its own randomly distributed permeability, so that the flow net is irregular. Analysis with a range of permeability patterns enables estimation of maximum possible exit gradients. The presence of highly pervious but ill-defined strata would complicate any seepage study.
Some probabilistic ideas born and nurtured in academia have earned a measure of acceptance by engineers responsible for dams, particularly where they are joined with well-tested deterministic methods. For instance, statistical procedures for estimating the probability of liquefaction have been drawn from simplified approaches for defining liquefaction thresholds based on correlations of observed behavior and corresponding measurements of shear wave velocities, standard penetration, or cone penetration. Many engineers still prefer the deterministic methods, without coupling with statistical analysis. However, assessment of probabilities can enhance understanding of comparative safety margins.
Rating and fixing deficiencies
Relative risk of the dams in a system in terms of economics and loss of life can be evaluated on a common system-wide statistical basis to set priorities for preventive or remedial action. Probabilistic calculation is helpful in weighing the merits of alternatives for corrective work.
Dam analysis requires recognition of environmental characteristics that preclude accurate numerical conclusions. The reliability of calculations will depend on the quality of the database, most importantly the extent of knowledge of site conditions and of the extreme forces that might be imposed. Evaluation of a dam’s capability must be focused on reducing the unknowns so that the analytical model is as representative of the actual project as possible. The limitations of methods, including mathematical modeling and probabilistic analysis, must be acknowledged. They are worth only as much as their factual input.
Mr. Jansen may be reached at 509 Briar Road, Bellingham, WA 98225; (1) 360-647-0983.
Bob Jansen, consulting civil engineer, was chairman of USCOLD (now the U.S. Society on Dams) and director of design and construction for the U.S. Department of the Interior’s Bureau of Reclamation and the California Department of Water Resources. He was chief of the California Division of Dam Safety and directed investigations of the Baldwin Hills and Teton dam failures.