Dams and Reservoirs

Learning Objectives

  • Classify dams by structural behavior and construction material.
  • Assemble concurrent dam and foundation actions into project-defined load cases and evaluate stability checks.
  • Explain seepage, uplift, drainage, filters, and internal erosion.
  • Describe how sediment deposition affects reservoir storage.
  • Explain how spillway operation and reservoir storage affect flood routing.

An engineering overview of dam systems, foundation response, reservoir storage, and the analyses used to assess safety and hydraulic performance.

Overview

Dams retain water for purposes such as supply, irrigation, hydropower, and flood management. Their analysis joins structural behavior, foundation and seepage conditions, hydrology, hydraulics, operation, and the governing project basis. No single load combination or acceptance threshold applies to every dam.

  1. Types of Dams

Dam Classification

Dams are classified by their structural behavior and construction materials. Gravity dams resist water thrust mainly through their mass and foundation interaction. Arch dams transfer much of the load to competent abutments through arch action. Embankment dams use compacted earth or rock zones, filters, and drainage to control seepage while maintaining stability. Roller-compacted concrete is a construction method used for concrete dams; the design and material properties remain project-specific.

Gravity Dam

A concrete or masonry dam whose stability against the applicable loads depends primarily on its mass, geometry, structural capacity, and interaction with the foundation.

Arch Dam

A curved concrete dam that transfers a substantial portion of its water load to its abutments through arch action; suitability depends on the geometry and strength of the abutments and foundation.

Embankment Dam

A dam formed from compacted earth, rock, or both, typically arranged in zones with seepage-control and filter/drainage features selected for the foundation and material properties.

  1. Loads and Stability of a Concrete Gravity Dam

Stability Analysis

A gravity-dam review evaluates the structure and its foundation for each governing design situation. The concurrent loads, water levels, pore-pressure assumptions, resistance model, and acceptance criteria must all use the same project-defined basis.

Actions to consider by load case

  • Hydrostatic pressure (PwP_w): For a vertical face under a hydrostatic depth HH, the pressure resultant per unit face width is horizontal and acts at the centroid of the triangular pressure distribution.
  • Dam self-weight (WW): The weight and center of gravity depend on the actual section and material unit weights.
  • Uplift pressure (UU): Foundation and joint pressures act upward. Their distribution depends on geology, discontinuities, seepage, and the assumed effectiveness of drains or grout curtains.
  • Other applicable actions: Tailwater, silt, ice, earthquake effects, thermal effects, construction stages, and operating conditions are included when required by the governing project basis.

Hydrostatic Resultant on a Vertical Face

For a hydrostatic pressure distribution extending from the free surface to depth H, this gives the horizontal force per unit face width.

Pw=12γwH2P_w = \frac{1}{2}\gamma_w H^2

Variables

SymbolDescriptionUnit
PwP_wHorizontal hydrostatic resultant per unit face widthkN/m
γw\gamma_wUnit weight of waterkN/m3kN/m^3
HHVertical water depth on the facem
Gravity-Dam Load Actions

Forces and their locations determine the resultant and moments for each concurrent load case.

The water resultant shown assumes a vertical face and hydrostatic pressure. The uplift arrows indicate direction only; use the pressure distribution supported by the project foundation and seepage model. Add tailwater, silt, seismic, and other actions only in the cases where the governing basis requires them.
Idealized gravity-dam section with upstream water thrust toward downstream, self-weight downward, uplift upward under the base, and labelled heel and toe.

Load Cases and Project Criteria

Project-Defined Load Case

A documented combination of actions, water levels, operating or construction conditions, and response assumptions that occur concurrently for one design situation under the governing project basis.

Keep Load Cases Consistent

Develop the case set from the applicable law, design standard, owner criteria, and project basis. Candidate situations may include construction, normal operation, flood or surcharge operation, drawdown, seismic loading, and unusual combinations; include only those required for the specific dam.

For each case, use compatible upstream and downstream levels, gate or outlet states, silt and ice actions where applicable, uplift assumptions, and seismic effects. Do not combine unrelated maximum actions or transfer a load combination from an unrelated project. Record the source and version of every acceptance criterion.

Distinct Stability Checks

Resultant and Base Contact Pressure

A resultant offset from the base center can produce a nonuniform contact-pressure distribution.

The pressure block illustrates a linear full-contact model only. Whether the foundation may carry tension, open at a joint, or respond nonlinearly must be determined from the adopted structural and geotechnical analysis basis. The diagram does not state a universal middle-third or allowable-bearing criterion.
Dam base with an eccentric resultant and an illustrative linear compressive contact-pressure distribution that increases from heel to toe.
Uplift Distribution and Drainage Sensitivity

Uplift is a pressure field under the dam and foundation, not a universally triangular force.

Derive the adopted pressure profile from foundation conditions, discontinuities, seepage analysis, drain/grout configuration, and available monitoring or investigation. The two curves are illustrative sensitivity cases, not prescribed boundaries or acceptance criteria.
Dam foundation section and two schematic uplift-pressure profiles showing higher pressure when drainage is less effective.
Gravity-Dam Stability Review and Redesign

Establish the project load cases, verify the uplift model, evaluate four separate stability responses, and route unresolved results through reconciliation or a criteria-based hold.

Use the governing project, regulatory, and adopted code basis to define the complete set of concurrent load cases and the acceptance criteria for each check. No universal factor of safety, eccentricity limit, bearing-pressure cutoff, uplift shape, or load combination is supplied here. Do not combine mutually exclusive actions unless the governing basis requires that combination. For every adopted case, verify signs and locations; substantiate uplift and drain assumptions from the foundation model and available evidence; then carry uplift consistently into the vertical resultant, moment balance, sliding resistance, and contact-pressure response. Evaluate sliding, overturning/equilibrium, bearing/contact, and uplift/pressure-relief response separately against their adopted criteria. The final decision passes only when every separate check passes for every adopted case. If criteria, inputs, or uplift modeling remain unsupported, hold the review and seek resolution under the governing basis. If results disagree or a check fails, reconcile the case and resistance models. Revise geometry or foundation measures only when justified under the resolved basis, then reanalyze the full case set and report the governing results and assumptions.

Gravity-Dam Stability Review and RedesignEstablish the project load cases, verify the uplift model, evaluate four separate stability responses, and route unresolved results through reconciliation or a criteria-based hold.. Use the governing project, regulatory, and adopted code basis to define the complete set of concurrent load cases and the acceptance criteria for each check. No universal factor of safety, eccentricity limit, bearing-pressure cutoff, uplift shape, or load combination is supplied here. Do not combine mutually exclusive actions unless the governing basis requires that combination. For every adopted case, verify signs and locations; substantiate uplift and drain assumptions from the foundation model and available evidence; then carry uplift consistently into the vertical resultant, moment balance, sliding resistance, and contact-pressure response. Evaluate sliding, overturning/equilibrium, bearing/contact, and uplift/pressure-relief response separately against their adopted criteria. The final decision passes only when every separate check passes for every adopted case. If criteria, inputs, or uplift modeling remain unsupported, hold the review and seek resolution under the governing basis. If results disagree or a check fails, reconcile the case and resistance models. Revise geometry or foundation measures only when justified under the resolved basis, then reanalyze the full case set and report the governing results and assumptions.. Start stability review → Project criteria, verified section, foundation and hydraulic data; Project criteria, verified section, foundation and hydraulic data → Are criteria and required input data resolved?; Are criteria and required input data resolved? — Yes → Define distinct concurrent load cases from the adopted project basis; Are criteria and required input data resolved? — No → Hold: confirm governing criteria and required data; Define distinct concurrent load cases from the adopted project basis → For every case, assemble only concurrent loads, signs and locations; For every case, assemble only concurrent loads, signs and locations → Is this case's uplift model supported by the foundation basis?; Is this case's uplift model supported by the foundation basis? — Yes → Carry concurrent actions and uplift into force, moment and base response; Is this case's uplift model supported by the foundation basis? — No → Hold: substantiate this case uplift model; Carry concurrent actions and uplift into force, moment and base response → Evaluate sliding resistance against its adopted case criterion; Evaluate sliding resistance against its adopted case criterion → Evaluate overturning and equilibrium against their adopted criteria; Evaluate overturning and equilibrium against their adopted criteria → Evaluate contact stress and foundation bearing against adopted criteria; Evaluate contact stress and foundation bearing against adopted criteria → Evaluate uplift and pressure-relief response against the project basis; Evaluate uplift and pressure-relief response against the project basis → Do all four checks pass for every adopted case?; Do all four checks pass for every adopted case? — Yes → Record each case, separate check, criterion, result and assumptions; Do all four checks pass for every adopted case? — No → Reconcile discrepant loads, signs, resistance models or results; Reconcile discrepant loads, signs, resistance models or results → Is the basis resolved and a design revision justified?; Is the basis resolved and a design revision justified? — Yes → Revise geometry or foundation measures under the same criteria; Is the basis resolved and a design revision justified? — No → Hold: resolve the material discrepancy under the governing basis; Revise geometry or foundation measures under the same criteria → Reanalyze the complete adopted case set after revision; Reanalyze the complete adopted case set after revision → Define distinct concurrent load cases from the adopted project basis

Start stability review → Project criteria, verified section, foundation and hydraulic data; Project criteria, verified section, foundation and hydraulic data → Are criteria and required input data resolved?; Are criteria and required input data resolved? — Yes → Define distinct concurrent load cases from the adopted project basis; Are criteria and required input data resolved? — No → Hold: confirm governing criteria and required data; Define distinct concurrent load cases from the adopted project basis → For every case, assemble only concurrent loads, signs and locations; For every case, assemble only concurrent loads, signs and locations → Is this case's uplift model supported by the foundation basis?; Is this case's uplift model supported by the foundation basis? — Yes → Carry concurrent actions and uplift into force, moment and base response; Is this case's uplift model supported by the foundation basis? — No → Hold: substantiate this case uplift model; Carry concurrent actions and uplift into force, moment and base response → Evaluate sliding resistance against its adopted case criterion; Evaluate sliding resistance against its adopted case criterion → Evaluate overturning and equilibrium against their adopted criteria; Evaluate overturning and equilibrium against their adopted criteria → Evaluate contact stress and foundation bearing against adopted criteria; Evaluate contact stress and foundation bearing against adopted criteria → Evaluate uplift and pressure-relief response against the project basis; Evaluate uplift and pressure-relief response against the project basis → Do all four checks pass for every adopted case?; Do all four checks pass for every adopted case? — Yes → Record each case, separate check, criterion, result and assumptions; Do all four checks pass for every adopted case? — No → Reconcile discrepant loads, signs, resistance models or results; Reconcile discrepant loads, signs, resistance models or results → Is the basis resolved and a design revision justified?; Is the basis resolved and a design revision justified? — Yes → Revise geometry or foundation measures under the same criteria; Is the basis resolved and a design revision justified? — No → Hold: resolve the material discrepancy under the governing basis; Revise geometry or foundation measures under the same criteria → Reanalyze the complete adopted case set after revision; Reanalyze the complete adopted case set after revision → Define distinct concurrent load cases from the adopted project basis

  • Start stability review: terminator
  • Project criteria, verified section, foundation and hydraulic data: data
  • Are criteria and required input data resolved?: decision
  • Define distinct concurrent load cases from the adopted project basis: process
  • For every case, assemble only concurrent loads, signs and locations: process
  • Is this case's uplift model supported by the foundation basis?: decision
  • Carry concurrent actions and uplift into force, moment and base response: process
  • Evaluate sliding resistance against its adopted case criterion: process
  • Evaluate overturning and equilibrium against their adopted criteria: process
  • Evaluate contact stress and foundation bearing against adopted criteria: process
  • Evaluate uplift and pressure-relief response against the project basis: process
  • Do all four checks pass for every adopted case?: decision
  • Record each case, separate check, criterion, result and assumptions: document
  • Reconcile discrepant loads, signs, resistance models or results: process
  • Is the basis resolved and a design revision justified?: decision
  • Revise geometry or foundation measures under the same criteria: process
  • Reanalyze the complete adopted case set after revision: process
  • Hold: resolve the material discrepancy under the governing basis: terminator
  • Hold: confirm governing criteria and required data: terminator
  • Hold: substantiate this case uplift model: terminator

  1. Seepage and Internal Erosion in Embankment Dams

Flow Paths, Phreatic Surface, and Filters

Water moves through an embankment and its foundation according to material properties and hydraulic boundary conditions. A flow net represents this field using flow paths and equal-head contours; in an ideal isotropic region these families intersect approximately at right angles. The phreatic surface is the zero-pressure line in the seepage field, not a universal straight line.

Uncontrolled concentrated seepage or an unfiltered exit can transport soil and progress to internal erosion or piping. Properly designed filters retain protected soil while allowing seepage to drain; gradation compatibility, continuity, and discharge capacity must be verified for the actual materials and foundation.

Seepage, Filter, and Drainage Path

The filter and drain intercept seepage so it can exit through a designed route instead of an unprotected downstream slope.

This is a conceptual section, not a design flow net. Actual seepage analysis must represent boundaries, foundation flow, layering, anisotropy, and material properties. Filter compatibility and internal-erosion criteria require project-specific verification.
Zoned embankment cross-section with reservoir, central low-permeability core, phreatic surface, conceptual seepage paths and head contours, chimney filter, and toe drain.

  1. Reservoir Sedimentation

Sediment Transport and Storage

A reservoir can trap part of the incoming sediment load as flow slows and particles settle. Deposits change the bed geometry and the storage-elevation relation, affecting available storage and potentially intakes or outlets. Sediment yield, deposition pattern, and capacity loss must be assessed from appropriate basin and reservoir data.

Empirical trap-efficiency relations, including Brune-type curves, are estimates whose applicability depends on the reservoir and sediment context. They do not replace site-specific sediment investigations, repeated capacity surveys, or an adopted sediment-management analysis.

Sediment Deposition and Remaining Storage

Deposited material occupies reservoir volume and changes the storage available at a given pool.

The cross-section is schematic and not to scale. Determine capacity change from reservoir surveys and project data; do not infer sediment yield, trap efficiency, storage zones, or a service life from this illustration.
Reservoir section showing an incoming sediment deposit over the prior bed, the dam, and remaining water storage at the shown pool.

  1. Spillways and Reservoir Routing

Reservoir Routing

A calculation that tracks reservoir storage and outflow as an inflow hydrograph passes through the reservoir, using continuity together with the applicable storage-elevation, outlet/spillway, and operating relationships.

Reservoir Continuity

The net inflow over a time interval changes reservoir storage; a routing method applies this balance through the event.

I−O=ΔSΔtI - O = \frac{\Delta S}{\Delta t}

Variables

SymbolDescriptionUnit
IIInflow rate to the reservoirm3/sm^3/s
OOOutflow rate from the reservoirm3/sm^3/s
ΔS\Delta SChange in reservoir storage over the intervalm3m^3
Δt\Delta tRouting time intervals
Inflow and Routed Outflow

Routing resolves how reservoir storage and operating rules change the timing and magnitude of outflow.

These curves are illustrative, not measured or a design event. Actual attenuation and timing depend on the inflow, initial pool, stage-storage and stage-outflow relations, spillway/outlet configuration, and operation. A routed peak is not guaranteed to be lower by any fixed amount.
Illustrative inflow and routed-outflow hydrographs with the inflow peak earlier and higher and a shaded period of storage accumulation.

Spillway Function

Spillway capacity and operating rules are selected and verified against the hydrologic criteria and hazard basis governing the specific dam. The required design flood may be a probable maximum flood or another project-defined event; it is not a universal assumption for every facility. Freeboard, gate reliability, outlet capacity, and energy dissipation must be coordinated with the same project basis.

Ogee and chute spillways are among the available configurations. Stilling basins and other energy dissipators may be used where their hydraulic design and downstream conditions support them. Uncontrolled overtopping can severely damage an embankment dam, so it must be addressed under the applicable safety and hydraulic criteria.

Key Takeaways
  • Gravity, arch, and embankment dams rely on different structural systems and site conditions.
  • Evaluate each concurrent action set as a distinct, project-defined load case.
  • Check uplift, sliding, overturning/equilibrium, and bearing/contact separately and consistently.
  • Seepage controls depend on verified foundation and material conditions; filters require compatibility checks.
  • Sedimentation and flood routing change storage and outflow according to site data and operating relationships.
  • Use governing local and project criteria; an illustrative model or generic threshold does not establish acceptance.

References