RCC Dam Design: Analyzing Stress and Stability

By Ernest K. Schrader

The author — who has been involved in the design and construction of more than 100 RCC dams in 35 countries — shares recommendations on how best to conduct stress and stability analyses when designing an RCC dam.

One important area of consideration in designing an RCC dam is stress and stability analysis. This involves including provisions for proper control for thermal stresses. Without proper thermal control, cracking can occur that leads to unacceptable leakage and potential for failure by sliding or overturning. Properly performing stress and stability analyses for a variety of situations and dam sections is critical to the design of any dam, including RCC. By using the proper methods and evaluating the relevant parameters, designers can ensure an RCC dam will provide adequate safety and stability under all foreseeable conditions.

Temperature studies and thermal control

Because thermal volume changes in concrete can lead to increased stresses or cracking, the design of any concrete dam (whether conventional concrete or RCC) should include provisions for dealing with the inherent temperature changes and resulting volume changes of any concrete mass. The principal concerns related to cracking in RCC and other concrete gravity dams are stability of the structure, appearance, durability, and leakage control. Although it is not usually a critical factor in structural stability, uncontrolled leakage through transverse cracks in a concrete dam can result in an undesirable loss of water from the reservoir, create operational and/or maintenance problems, and be visually undesirable. Leakage can be extremely difficult to control.

Typically, thermal stresses and associated volume changes result in transverse cracking of the concrete structure. However, RCC dams experiencing high thermal stresses also may exhibit unseen cracking parallel to the axis of the dam. This type of cracking has occurred in both conventional concrete and RCC dams and can have serious implications with regard to structure and stability. A dam with this type of cracking probably will be safe and stable for normal load conditions if the crack is closed and does not contain water, although with reduced factors of safety. However, experience has shown that this type of cracking can jeopardize sliding and overturning stability if the crack opens and fills with water. The source of water can be the foundation, seepage through lift joints, monolith joints with failed waterstops, or transverse cracks.

When attempting to predict the degree of cracking a structure may experience, a number of factors should be evaluated. Simple analyses that combine very generalized conditions yield very general results. Complex analyses combine very specific determination of conditions to yield more exacting results. At a minimum, dam designers should consider daily and monthly ambient temperature fluctuations, the conditions during construction for aggregate production and RCC mixing that lead to the temperature range at which RCC will be placed, a realistic placing schedule, and realistic material properties. In many cases, the results of a thermal study are key to determining mixture proportions, construction schedule, and cooling and jointing requirements.

More so than for conventional concrete dams, comprehensive, state-of-the-art analyses that account for the time-dependent effects of temperature — including adiabatic heat rise, ambient climatic conditions, simulated construction operations, and time variant material properties — are necessary to properly analyze thermal issues in RCC dams. This is partly because each RCC lift is relatively thin (usually 1 foot), with a small mass compared to the exposed surface area. By contrast, conventional mass concrete typically is placed in thick lifts (usually 5 feet), with a large mass compared to the exposed surface area. Also, RCC material properties typically are much more dependant on maturity and load than conventional concrete. As a result, RCC thermal analyses typically require more detail. Various analytical methods, ranging from hand computations to more sophisticated finite element methods (FEM), are available to provide an estimate of the temperature and thermal stress or strain distributions throughout a structure. The U.S. Army Corps of Engineers and others have published information on temperature evaluations unique to RCC.1,2

Placing concrete at night is one effective way to minimize thermal stresses during construction of a roller-compacted-concrete dam.
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Specific actions can be effective in minimizing thermal stresses in RCC dams. These include substituting pozzolan for some of the cement, limiting RCC placement to cool weather, placing RCC at night, lowering the placing temperature, and providing appropriate formed jointing. When the option is available, selecting an aggregate of low elastic modulus and low coefficient of thermal expansion also is helpful. The American Concrete Institute, in a 2007 report, discusses cooling options that have been effective for RCC.3

The exposure of relatively thin lifts of RCC during initial hydration may contribute to an increase or decrease in peak temperatures, depending on ambient conditions and the length of exposure. Each situation must be separately and carefully evaluated. For example:

Methods for stress and stability analysis

Approaches to stress and stability analysis for RCC dams are similar to those used for conventional concrete structures. However, for RCC, there is added emphasis on tensile strength and shear properties of the horizontal lift joints, and on non-linear stress-strain behavior.

With regard to horizontal lift joints, some RCC dams have lift joints with cross slope or “dip” of 5 degrees or more, to facilitate surface drainage during construction. The effect of this dip on stability does exist but is minimal. It effectively adds or subtracts about 1 or 2 degrees from the coefficient of friction for the lift surface, depending on whether the lift surface slopes upward (positive benefit) or downward (negative effect) when going from the upstream to downstream face. Technically, it is better to have a slight upward slope from upstream to downstream. However, some practitioners find that a horizontal cross slope is much easier to construct, so they prefer no slope, while other practitioners have found the cross slope to be beneficial for clean-up and surface drainage, without any real effect on constructability.

During initial design of an RCC dam, designers perform static stress analysis. For dams in wide canyons, or with contraction joints that will be open, a two-dimensional gravity or FEM analysis is adequate to calculate stresses.

More complex methods of analysis — such as the trial-load twist method or three-dimensional FEM — have been used. These are mostly applied for large dams, dams with high earthquake loadings, and dams located in narrow “V” canyons where even a straight axis orientation can have three-dimensional benefits with reduced stresses and improved stability.

For dams in seismically active areas, a dynamic stability analysis is necessary using a two- or three-dimensional FEM, whichever is appropriate for the site conditions and canyon shape. Special attention must be given to considering whether the monolith joints will be open or closed. The monolith joints will tend to open due to thermal contraction, with more opening for wider joint spacings and greater thermal gradients. However, the joints will tend to typically be tighter at the foundation and wider higher up in the dam. They also can close due to three-dimensional effects from a curved axis or a straight axis dam in a narrow “V” canyon. Closed joints will impart more three-dimensional benefits, whereas open joints cannot easily transfer these three-dimensional effects from one monolith to the other.

Unless there is site-specific justification, recommended safety factors to be applied for the complete range of loading conditions for RCC dams should be the same as for conventional concrete dams.

Shear-friction factor

For the purposes of this discussion, the focus will be on shear within an RCC dam. Foundation shear and stability should be evaluated as a related but separate issue.4,5

As with a conventional concrete gravity section, resistance to sliding within an RCC section depends on cohesion, the confining stress on the potential failure plane, and the coefficient of sliding friction along the failure plane. In addition to sliding or shear along lift joints, shear through the mass (crossing lift joints) also should be considered, especially if there are thinned sections in the mass, such as at an extended toe. However, the typical controlling shear plane will be along the weakest lift joint relative to applied sliding force, as it is for conventional concrete dams. However, RCC has many more lift surfaces than traditionally placed mass concrete, and RCC is more likely to have lower cohesion at the lift surface than traditionally placed internally vibrated concrete (IVC) (especially with leaner mixes and with excessive lift joint maturity). Thus, the probability of at least some weak lift surfaces can be greater with RCC than with IVC. This is minimized through proper mix designs, construction equipment and procedures, concrete set retarding admixture, and diligent inspection.

Fortunately, the friction component of shear resistance along lift surfaces is essentially unaffected by the type of mix, maturity, and marginal construction. However, the cohesion component of sliding shear resistance along lift joints is very sensitive to: content and quality of cementitious materials; construction means, methods, and quality; and lift joint maturity, including initial set time of the mix.

The classic structural design parameter of the shear-friction factor (SFF) is a measure of a dam’s stability against sliding. The SFF on any horizontal plane in the dam is the same for RCC as it is for conventionally placed IVC. That is:

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