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.
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:
- While placing RCC during a hot time period, the surface of the concrete absorbs heat from the sun. This increases the temperature of the mixture at a rate that may be greater than the rate at which heat from internal hydration is generated. The longer the surface is exposed, the more solar energy is absorbed, which can produce a higher peak internal temperature. Faster placement in this situation will help reduce internal temperatures.
- With RCC placement during cooler times of the year, the large exposed RCC lift surface loses heat to the atmosphere. Also, materials going into the mix, as well as the mix itself on the way to the placement, are naturally pre-cooled. This results in lower placing temperatures and, consequently, lower peak temperatures. If the time interval until placement of the next lift is long, some of the early heat from hydration can be dissipated to the atmosphere. But if the peak temperature does not occur before placement of the next lift, faster placing can reduce the beneficial effect of losing heat to the atmosphere.
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.
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:
- c is unit cohesion;
- A is the area of cross section;
- N is the component of confining force normal to the sliding surface;
- U is the uplift force acting on the cross section;
- w is the angle of sliding friction; and
- T is the driving force parallel to the sliding surface.
- It is not reasonable that an isolated section of an RCC dam would slide away, leaving behind another portion of the dam that remains bonded at a lift joint. Consequently, over-reaction should be avoided if a FEM analysis indicates that shear stress exceeds shear strength (with the appropriate factor of safety) for a small portion of a large lift surface;
- Estimated shear strengths should include appropriate consideration for the reasonable amount of debonded area to be expected on lift joints;
- When a “back-analysis” is done using results of cores or shear blocks extracted from a dam, the percent of debonded lift joints should be considered. A debonded lift joint typically will have the same friction as bonded joints, but it has no cohesion or tensile capacity. After excluding cores that were broken by mechanical forces of coring or handling, the remainder of debonded cores should be assigned a cohesion value of “zero” when the average cohesion is calculated; and
- One unacceptable lift joint is all that is required for failure. It is inappropriate to average good values from adjacent lifts with bad values from a clearly identifiable bad lift joint.
SFF = (cA + (N — U) tan w)/T
Most design criteria require a minimum SFF of safety against sliding of 2 to 4, based on normal high headwater and low tailwater conditions. This can drop to 1.5 to 2 under flood conditions, and typically is defined as greater than 1 for seismic loads. Although it is not considered by most codes and authorities, a true “fail safe” criterion for stability of an RCC dam is that the SFF of safety against sliding is greater than 1 for all load conditions, using a cohesion value of zero and a realistic residual friction angle after sliding, with realistic uplift for debonded lift joints. Precedents exist for this very conservative design approach. The most notable is the design of the new Saluda Dam on the Saluda River in South Carolina, United States.6
Shear properties at lift surfaces depend on a number of factors, including mixture properties, joint preparation, elapsed time from mixing to compaction, and lift exposure conditions (lift joint maturity). Actual values used in final designs should be based on tests of the materials to be used or estimated from tests on RCC mixtures from other projects with similar aggregates, cementitious material content, aggregate gradations, and joint preparation. As with any dam design, the designer of RCC structures should be confident that design assumptions are realistically achievable with the anticipated construction conditions and available materials.
For initial planning purposes, a conservative value of lift joint cohesion of 5 percent of the design compressive strength with a coefficient of friction of 1 (corresponding to a w friction angle of 45 degrees) is generally used. This should be adjusted as site-specific mixes and material properties are better evaluated. Cohesion tends to be slightly lower for dry consistency RCC mixes and slightly higher for wetter consistency mixes. Where bedding mix is used, the cohesion value will be essentially the same as that value of the unjointed RCC mass, which typically is weaker than the bedding. This normally approximates at least 10 percent of the compressive strength of the unjointed RCC.
Determining design values for shear
Design values for shear strength at lift joints can be determined in several ways. Drilled cores can be removed from RCC test placements and tested in shear and direct tension, but this is difficult, costly, and time-consuming. Drilling at an angle minimizes lift joint de-bonding and damage, but makes direct shear testing of the sample more complicated. If cores are drilled at two different angles steeper than the friction angle, the cores can be tested in a compression machine to determine the actual friction angle and cohesion.
Individual specimens can be fabricated in the laboratory with simulated lift joints if the mixture is of a consistency and the aggregate is of a size that permits fabrication of representative individual samples. It is imperative that these specimens represent the true full-scale conditions. Care is needed to realistically correlate laboratory-prepared samples to what will be achieved in the field.
At many RCC dams, realistic lift joint shear tests have been performed by using a series of large blocks of the total RCC mixture cut from test placements compacted with full-scale equipment or walk-behind rollers that simulate the energy of a large roller.6,7 Various lift joint maturities and surface conditions of the actual mixture for the project are evaluated and used to confirm or modify the design and construction controls. For example, a comprehensive series of tests was performed for Saluda Dam, where the design was based on residual shear strength after sliding.6
In-situ direct shear tests also have been performed at various confining loads on blocks cut into field placements made with full production equipment and procedures. They also can be done by shearing blocks at saw cuts made into an RCC gallery floor.
In all cases, shear testing of RCC is delicate and unique. Testing requires experienced personnel, special equipment, and special procedures. In-situ tests are probably the most difficult, requiring extra care and attention to details.
Shear property estimates and shear analyses should take into account several key factors, including:
Non-linear stress-strain behavior
RCC mixtures, especially those with low cementitious contents, tend to havenon-linear stress-strain behavior with strain softening (see Figure 1). That is, at increasing stress levels the material deforms or strains more than it does for the same unit increase in stress at a lower stress level. Strain softening occurs similarly in both tension and compression. This can have the beneficial effect of decreasing peak stresses that otherwise would occur in isolated areas such as the toe or heel of a high dam, and at other stress concentrations that usually are related to earthquakes. As deformation in the area of high stress increases with increasing load, very little added stress occurs. Instead, most of the stress that would have been added to this area if the concrete had linear elastic properties is re-distributed to adjacent areas of lower stress.
Examples of this situation include reductions in peak stress for the non-linear properties of RCC at Mujib Dam on the Mujib River in Jordan.8 This dam was completed in 2003, primarily to impound water for irrigation.
Uplift and upstream watertightness
Proper estimates of uplift within the dam are essential, regardless of whether it is constructed with conventional concrete or RCC. Recent practice and industry guidelines have established that the designer should evaluate imperviousness at the upstream face based on precedent, trial sections, and experience for the method being used to establish the expected degree of watertightness and uplift control on each project.9 This is a change from the past practice of assuming 100 percent uplift at the upstream face and 67 percent reduction of uplift at the drilled drains. If the procedure to be used to estimate uplift (with the anticipated degree of quality control) demonstrates that uplift will be less than 100 percent near the upstream face, it may be appropriate to use this reduced uplift in the stress and stability analysis.
As an example, consider a dam design with a proper impervious upstream watertight barrier with face drains. When this type of system is properly designed and installed, it allows total control of uplift pressures at the upstream face. A conservative approach initially was taken in the design of earlier RCC dams using this system, by applying 50 percent uplift reduction at the upstream face, with 67 percent additional reduction at drilled internal drains within the mass of the RCC. This results in significant improvements in stability and reduction of heel stresses.8
However, experience and performance of this type of system (an impervious upstream membrane or facing used in conjunction with a drain between the facing and RCC to relieve any pressure that may migrate past the facing) has shown reliable 100 percent reduction of uplift at the upstream membrane when properly designed and constructed. Thus, the 50 percent reduction of uplift at the face is overly conservative.
Many RCC dams are constructed with stair-stepped spillways, using formed RCC, grout-enriched RCC, or conventional IVC for the steps. The horizontal lift joint surface between steps is typically not watertight. Any lift joint seepage that migrates to the downstream face normally can escape along the lift joint. In some cases, drains have been installed through the steps to assure that uplift pressure can escape. If the pressure cannot escape — for example, if a continuous slab of concrete is used to create a smooth conventional spillway over the RCC — uplift is trapped on the RCC lift joint behind the slab. The design should address the implications of this potential increased uplift both within the mass and against the spillway slab, or drainage should be provided under the slab.
Low-cementitious-content RCC with drier consistency typically has low, but adequate, lift joint tensile strength in most of the dam with no special joint treatment. Although it varies from dam to dam, with lift joint maturity, and with the degree of inspection, the overall long-term average lift joint strength for these types of mixes tends to be about 30 to 80 percent of the unjointed RCC tensile strength. Lower percentages are applicable to leaner mixes, older lift joint maturities, shorter set times, and more damage or contamination at the lift surface. Higher percentages are applicable to higher cementitious content mixes, younger lift joint maturities, longer set times, and better-quality lift surfaces. When bedding mix (mortar or concrete) is used between lift joints, the lift joint typically will achieve 100 percent of the tensile strength of the unjointed RCC.
Drains (see arrow) installed through the steps of stair-stepped spillways provide an outlet for escape of uplift pressure in roller-compacted-concrete dams.
Lift joint bonding is of interest from the perspectives of tensile strength (usually under earthquake load), cohesion for sliding resistance, and watertightness. Static strengths are discussed below. Tests of various concrete mixes have shown that the dynamic or fast-loading strength applicable to earthquakes is higher, with the dynamic increase factor (DIF) being greater for faster loads and for lower strength concrete and lower for slower loads and higher strength concrete. Without site-specific test data, RCC typically is assumed to have a DIF of 150 percent of the static tensile strength. Interestingly, tests of lower-strength concretes show the DIF to be higher than for higher-strength concretes. Tests also have shown that the DIF increases dramatically at very rapid rates of loading.
Additional considerations for lift joints
RCC mixtures that exhibit bleeding of mix water contain more water than is necessary for optimum performance. Water contents should not extend into this range. Eliminating the occurrence of bleed water in the mix is one of the purposes of trial mixing during the design phase (recommended) or just prior to construction. The water content of the mixture depends on the characteristics of the materials being used, primarily the quality of the aggregate fines and pozzolanic materials. Bleed water can deposit laitance on the surface of the RCC lift. In sufficient quantity, laitance can seriously degrade the shear performance of the lift. Where bleeding occurs in mixtures with high cementitious contents, an increase in laitance deposition is possible. This should be avoided.
One example of such a phenomenon is during recent evaluations of density, compaction, and lift joint quality at Saluda Dam. The test section lift joints showed the appearance of good bond with wetter consistency RCC containing 125 to 175 pounds of cement per cubic yard, plus a similar amount of fly ash, no retarder, and no forced cooling (but placed in generally mild conditions). Visual examination of saw cuts through the cross section of mass placements indicated excellent bond with good contact between lifts. However, when one set of saw cut blocks was removed for testing, the blocks debonded where there was just slight evidence of laitance. This occurred at the surface of mixtures with lower VeBe times and mixes that tended to bleed. No other test blocks separated at the lift.
To achieve shear properties approaching that of parent concrete, it is critical that lifts be placed before the “initial set” of the underlying lift. Highly workable RCC containing high proportions of cementitious materials can achieve high shear performance without supplemental bedding mortar only if placement is done on surfaces that have not yet set. Many factors contribute to the setting characteristics of RCC surfaces. Examples include the chemical composition of the cement, fineness of the cement, amount of pozzolan that is used, temperature of the mix when it is placed, ambient temperature, effectiveness of moist cure prior to placing the next layer of RCC, and effectiveness and quantity of any admixtures.
Dr. Schrader may be reached at Schrader Consulting, 1474 Blue Creek Road, Walla Walla, WA 99362 USA; (1) 509-529-1210; E-mail: [email protected]
Ernie Schrader, PhD, P.E., is a consultant with more than 30 years of experience in roller-compacted concrete (RCC). He has been involved in more than 30 RCC dams that are complete and operational, several under construction, and many undergoing design and feasibility studies. The projects range from the world’s highest and largest to the smallest RCC dams.
- Tatro, S., and Ernest K. Schrader, “Thermal Analysis for RCC—A Practical Approach,” Roller-Compacted Concrete III, American Society of Civil Engineers, New York, 1992.
- “Thermal Studies of Mass Concrete Structures,” Engineering Manual 1110-2-542, U.S. Army Corps of Engineers, 1997.
- “Report on Thermal and Volume Change Effects on Cracking of Mass Concrete,” 207.2R-07, American Concrete Institute, Farmington Hills, Mich., 2007.
- Schrader, Ernest K., “Building Roller-Compacted-Concrete Dams on Unique Foundations,” HRW, Volume 14, No. 1, March 2006, pages 28-33.
- Schrader, Ernest K., “Roller-Compacted-Concrete Dams on Difficult Foundations: Practical Examples,” HRW, Volume 14, No. 2, May 2006, pages 20-31.
- Schrader, Ernest K., and Paul C. Rizzo, “Extensive Shear Testing for Saluda Dam Roller Compacted Concrete,” Roller Compacted Concrete Dams, 4th International Symposium on Roller Roller Compacted Concrete (RCC) Dams, Spanish National Committee on Large Dams, Madrid, Spain, November 2003.
- Nawy, E.G., Concrete Construction Engineering Handbook, Chapter 20, CRC Press, Boca Raton, Fla., 2007.
- Schrader, Ernest K. and A. Rashed, “Benefits of Non-Linear Stress-Strain Properties & Membranes for RCC Dam Stresses,” Roller Compacted Concrete (RCC) Dam Construction in the Middle East 2002, Jordan University of Science and Technology (JUST) & Technische Universitaet Muenchen (TUM), 2002.
- “Design of Gravity Dams,” Engineering Manual 110-2-2200, U.S. Army Corps of Engineers, 1995.