This guide explains figure 26 from the gravity dam design engineer manual, focusing on how engineers apply the diagram to check stability under different load conditions. Figure 26 presents a combined failure envelope that links sliding, overturning, and foundation compression behavior into one decision tool.
Readers can use the table and layout details below to interpret the axes, limit states, and design factors shown in figure 26, ensuring that safety and serviceability requirements are met for both gravity and roller-compacted concrete dams.
| Parameter | Definition | Check Based on Figure 26 | Typical Acceptance Criterion |
|---|---|---|---|
| Resultant Force Envelope | Combination of horizontal and vertical forces under all load cases | Location relative to failure envelope | Envelope margin ≥ 1.5 under ULS |
| Sliding Safety Factor | Resisting friction and keying divided by horizontal water and seismic forces | Shift of resultant away from toe | FS_slide ≥ 1.3 |
| Overturning Safety Factor | Resisting moment about toe divided by overturning moment | Position of resultant within middle third | FS_overturn ≥ 1.5 |
| Foundation Contact Pressure | Net pressure profile including uplift | Check for tension and excessive eccentricity | Max e/L ≤ 0.35, no tension at ULS |
| Load Cases | Combination of dam weight, water head, silt, seismic, and temperature | Plot each case in figure 26 to verify envelope | All cases lie within acceptable margin |
Gravity Dam Stability Criteria Overview
Stability Under Service Loads
Figure 26 helps engineers assess dam stability under normal service conditions where water levels are moderate and seismic activity is low. The resultant force must remain within the middle third to avoid tension at the base, while safety factors for sliding and overturning exceed code-prescribed limits. Uplift reduction measures and drainage improvements can shift the pressure envelope toward a safer distribution, making figure 26 a quick reference for service-level verification.
Stability Under Extreme Events
During extreme floods or strong earthquakes, the dam may experience higher horizontal loads and fluctuating reservoir levels. Figure 26 plots the expanded envelope of resultant forces, allowing engineers to verify that the dam remains stable even when safety factors temporarily reduce. Load combinations used in this check include rapid drawdown, sudden uplift pressure rise, and simultaneous high water plus seismic ground motion.
Structural Interaction and Foundation Response
Mechanism of Sliding and Overturning
Sliding occurs when horizontal water and seismic forces overcome frictional resistance at the base, while overturning involves rotation around the toe due to moment imbalance. Figure 26 combines these two checks into a single set of axes, making it easier to see how uplift and keying influence the location of the resultant. Proper foundation treatment and drainage design move the pressure centroid away from the toe region, improving both factors simultaneously.
Seismic Considerations
In seismic regions, figure 26 extends the failure envelope to include pseudo-static accelerations that add to horizontal forces. Engineers adjust the friction coefficient and introduce effective weight to model potential sliding surfaces during strong shaking. Codes often demand increased margin under seismic load cases, and figure 26 visually highlights any cases where the dam approaches the allowable region.
Foundation Preparation and Drainage Implementation
Preparing the Bedrock Surface
Before placing the dam body, contractors profile the foundation to remove weak zones and ensure intimate contact. Grouting fractures and installing drainage curtains beneath the dam reduce uplift pressures, which in turn moves the resultant inward and improves factors in figure 26. These steps are reflected in design calculations, and the final check aligns the post-grouting envelope safely inside the acceptance boundary.
Operational Drainage Systems
Operational drains control seepage paths and limit prolonged high uplift during extended reservoir levels. By tuning toe drains and hillside galleries, engineers control the pressure distribution plotted in figure 26, pushing the resultant toward the center of the base. Continuous monitoring during filling and operation validates that the assumed uplift reductions match field performance.
Key Takeaways for Practicing Engineers
- Use figure 26 to verify sliding, overturning, and pressure eccentricity in a single coordinated check.
- Include uplift reduction measures early in design to keep the resultant inside the acceptable region.
- Validate assumptions against monitored pressures and settlement data during construction.
- Apply code-specific factors and load combinations to each load case before plotting in figure 26.
- Iterate the geometry and drainage layout if any envelope crosses the limit lines.
FAQ
Reader questions
How should I interpret the position of the resultant relative to the failure envelope in figure 26?
Position the resultant inside the envelope with a clear margin; if it crosses the envelope under any load case, redesign the dam base or improve drainage to increase resisting forces.
Does figure 26 account for time-dependent effects like foundation creep or material aging?
Figure 26 focuses on immediate load conditions; time-dependent effects are treated separately in long-term serviceability checks and may require additional safety factors or monitoring provisions.
Can I use the same figure for roller-compacted concrete gravity dams as for conventional concrete gravity dams?
Yes, the same failure envelope applies, but the friction coefficient and construction joint behavior may differ, so engineers adjust the sliding and overturning checks to reflect material and joint characteristics specific to roller-compacted concrete.
What should I do if the resultant lies exactly on the allowable line in figure 26 during an intermediate load case?
Treat this as a warning; add margin by improving drainage, increasing base width, or including partial safety factors for uncertainty so that the service envelope remains comfortably inside the limits.