Gravity Dams

Amol Ashok Kamble

Unit 2: (06)

Gravity Dams –

Forces acting on dam, design criteria, theoretical and practical profile, high and low dam, stability calculations, materials and methods of Construction, Galleries, joints.

​

Arch Dams –

Types, Layout of Constant angle and Constant radius arch dam, Forces acting on arch dams.

Gravity Dams

• A gravity dam has been defined as a structure which is designed in such a way that its own weight resists the external forces.
• This type of a structure is most durable and solid, and requires very little maintenance.
• Dam are constructed by masonry or concrete.
• The ratio of base width to height of all these structures is less than 1:1.

Forces Acting On Gravity Dam

• Water Pressure
• Uplift Pressure
• Pressure due to earthquake forces
• Silt Pressure
• Wave Pressure
• Ice Pressure
• Weight of the dam

Typical Cross Section

Water Pressure

Water Pressure

Uplift Pressure

• Water seeping through the pores, cracks and fissures of the foundation material, and water seeping through dam body and then to the bottom through the joints between the body of the dam and its foundation at the base; exert an uplift pressure on the base of the dam.
• It is the second major external force and must be accounted for in all calculations.
• Uplift force virtually reduces the downward weight of the body of the dam and hence, acts against the dam stability.

Uplift Pressure

Uplift Pressure

Pressure due to earthquake forces

• Horizontal acceleration may cause the following two forces:
• Hydrodynamic pressure
• Horizontal inertia force

Hydrodynamic pressures

• Horizontal acceleration acting towards the reservoir causes a momentary increase in the water pressure,

Horizontal Inertia Force

Silt Pressure

Silt Pressure

Wave Pressure:

Wave Pressure:

Ice Pressure:

• The ice which may be formed on the water surface of the reservoir in cold countries, may sometimes melt and expand.
• The dam face has then to resist the thrust exerted by the expanding ice.
• This force acts linearly along the length of the dam at the reservoir level.
• The magnitude of this force varies from 250 to 1500 kN/m² depending upon temperature variations.
• On an average, a value of 500 kN/m² may be allowed under ordinary conditions.

​

Weight of the dam:

• The weight of the dam body and its foundation is the major resisting force.
• In two dimensional analysis of a gravity dam, a unit length of the dam is considered.
• The cross-section can then be divided into rectangles and triangles.
• The weight of each along with their c.g.s., can be determined.
• The resultant of all these downward forces will represent the total weight of the dam acting at the c.g. of the dam.

Combination of forces for Designs

• The design of a gravity dam should be checked for two cases,
• when Reservoir is full
• when Reservoir is empty.

Reservoir Full Case:

Major forces acting are:

• Weight of the dam
• External water pressure
• Uplift pressure
• Earthquake forces in serious seismic zones.

The minor forces are:

• Silt pressure
• Ice pressure
• Wave pressure.
• All the forces never act together hence, all the forces are not generally taken together.
• U.S.B.R. has classified the normal load combinations' and 'extreme load combination as given below :

Reservoir Full Case:

Normal Load Combinations

• Water pressure up to normal pool level + Normal uplift + Silt pressure + Ice pressure.

This class of loading is taken when ice force is serious.

• Water pressure up to normal pool level + normal uplift + earthquake forces + silt pressure.
• Water pressure up to maximum reservoir level (maximum pool level) + normal uplift + silt pressure.

Extreme Load Combinations

• Water pressure due to maximum pool level + extreme uplift pressure without any reduction due to drainage + silt pressure.

​

Reservoir Empty Case:

• Empty reservoir without earthquake forces to be computed for determining bending diagrams, etc. for reinforcement design, for grouting studies or other purposes.
• Empty reservoir with a horizontal earthquake force produced towards the upstream has to be checked for non- development of tension at toe.

​

Modes of Failure and Criteria For Structural Stability of Gravity Dams

A gravity dam may fail in the following ways:

• By over-turning (or rotation) about the toe.
• By crushing.
• By development of tension, causing ultimate failure by crushing
• By shear failure called sliding

Over Turning:

Compression or Crushing:

Compression or Crushing:

Compression or Crushing:

Tension

• Masonry and concrete gravity dams are usually designed in such a way that no tension is developed anywhere, because these materials cannot withstand sustained tensile stresses.
• These materials may finally crack.
• However, for achieving economy in designs of very high gravity dams, certain amount of tension may be permitted under severest loading condition.
• The maximum permissible tensile stress for high concrete gravity dams, under worst loadings, may be taken as 500 kN/m² (5 kg/cm²).

Effect Produced By Tension Cracks

Effect Produced By Tension Cracks

• The process continues; the effective base width goes on reducing and compressive stress at the toe goes on increasing; finally leading to the failure of the toe by direct compression.
• Hence a tension crack by itself does not fail the structure, but it leads to the failure of the structure by producing excessive compressive stresses.

​

No Tension Condition

Sliding

Sliding

Sliding

• Attempts are always made to increase this shear strength (q) at the base and at other joints.
• For this purpose, foundation is stepped at the base, as shown in Fig.
• Measures are taken to ensure a better bond between the dam base and the rock foundation

Principal and Shear Stresses.

Principal and Shear Stresses.

Principal and Shear Stresses.

Principal and Shear Stresses.

Stability Analysis

• The stability of a gravity dam can be
• Approximately and easily analysed by two dimensional gravity method.
• precisely analysed by three dimensional methods such as slab analogy method, trial load twist method, or by experimental studies on models.

Gravity Method�(Two Dimensional Stability Analysis)

Assumptions

• The dam is considered to be composed of a number of cantilevers, each of which is 1m thick and each of which acts independent of the other.
• No loads are transferred to the abutments by beam action.
• The foundation and the dam behave as a single unit; the joint being perfect.
• The materials in all parts are isotropic and homogeneous.
• The stresses developed in all parts are within elastic limits.
• No movements of the foundations are caused due to transference of loads.
• Small openings made in the body of the dam do not affect the general distribution of stresses and they only produce local effects as per St. Venant's principle.

​

Gravity Method

Gravity Method

Gravity Method

Gravity Method

Graphical method

• The entire dam section is divided into a number of horizontal sections where the slope changes,
• For each section the sum of the vertical forces (ΣV) and the sum of all horizontal forces (ΣH) acting above that particular section are worked out
• The resultant force (R) is drawn graphically.

​

• Resultant force should lie within the middle third, for no tension to develop.
• The procedure should be carried out for reservoir lull case as well as for reservoir empty

• Figure (1) shows the section of a gravity dam (non overflow portion) built of concrete. Calculate (neglecting earthquake effects). (13 mark) Dec 2016

i. The maximum vertical stresses at toe and heel of the dam

ii. The major principal stresses at the toe of the dam

iii. Intensity of shear stress on a horizontal plane near toe

Assume unit weight of concrete = 23.5 kN/m2.

Allowable compressive stress in concrete = 2500 kN/m².

Allowable shear stress in concrete = 420 kN/m².

Assume that reservoir is full of water upto M.W.L.

​

Elementary Profile of a Gravity Dam

• The elementary profile of a dam, subjected only to the external water pressure on the upstream side.
• Having zero width at the water level and a base width (B) at bottom
• The shape of such a profile is similar to the shape of the hydrostatic pressure distribution.

Stresses when the reservoir is empty

Stresses when the reservoir is full

• The resultant of all the forces, i.e. P, W and U (Fig. 19.14) passes through the outer most middle third point.
• The dam is safe in sliding.

Stresses when the reservoir is full

Stresses when the reservoir is full

High and Low Gravity Dam

Profile of A Dam From Practical Considerations

• Providing a straight top width, for a road construction over the top of the dam;
• Providing a free-board above the top water surface so that water may not spill over the top of the dam due to wave action, etc.

Design Considerations and Fixing The Section of A Dam

Design Considerations and Fixing The Section of A Dam

Design Considerations and Fixing The Section of A Dam

Construction of Gravity Dam

• Diversion Problem in Dams Construction
• Before the actual construction of a dam the water of the river channel must be temporarily diverted.
• It is advantageous to schedule the construction of the dam during low flow so as to minimise the diversion problem.
• Provision of a Diversion Tunnel.
• Diversion tunnel or a diversion open channel may be constructed to carry the entire flow around the dam site
• The diversion tunnel or channel will start from upstream of the upstream coffer-dam and will join the river again on the downstream of the downstream coffer-dam,

Diversion Problem in Dams Construction

• By constructing the dam in two stages.
• The flow is diverted and confined to one side of the channel by constructing a semi-circular type of a coffer dam.
• The construction work can be taken up in the water- free zone.
• When the work on the lower portion of the dam on half of its length in one side of the channel gets completed, the remaining half width of the channel is closed by a coffer dam,

Galleries In Gravity Dams

• Galleries are the horizontal or sloping openings or passages left in the body of the dam.
• They may run parallel to dam axis or normal to dam axis
• Galleries are provided at various elevations.
• All the galleries are interconnected by steeply sloping passages or by vertical shafts fitted with stairs or mechanical lifts.
• The size of a gallery will depend upon the size of the dam and the function of the gallery.

​

Types of Galleries in Dams

• Foundation Gallery / drainage gallery
• Foundations gallery provided near the rock foundations to drain off the water which percolate through the foundations.
• It runs longitudinally and is quite near to the upstream face of the dam,
• Its size usually varies from1.5 m x 2.2 m to 1.8 m x 2.4 m.
• Drain holes are drilled from the floor of this gallery to collect Seepage.
• The size of the gallery should be sufficient to accommodate at least a drilling machine.
• It may be helpful for drilling and grouting of the foundations, when this can not be done from the surface of the dam.

Types of Galleries in Dams

• Inspection Galleries
• The water which seeps through the body of the dam is collected by means of a system of galleries provided at various elevations.
• Al1 these galleries, besides draining off seepage water, serve inspection purposes.
• They provide access to the interior of the dam therefore, called as inspection galleries.

Functions Galleries In Dams

• They infect and drain off the water seeping through the dam body.
• They provide access to dam interior for observing and controlling the behaviour of the dam.
• They provide enough space for carrying pipes, etc. during artificial cooling of concrete.
• They provide access for grouting the contraction joints when this cannot be done from the face of the dam.
• They provide access to all the outlets and spillway gates, valves. All these gates, valves, etc. can be easily controlled by men, from inside the dam itself.

​

​

Cross-sections of Dam Galleries:

• Dam galleries are formed as the concrete is placed and its size depends upon the function of the gallery and also upon the site of the dam.
• In order to minimise stress concentrations at corner , the corners must be rounded smoothly.

Cracking of Concrete in Gravity Dams

• A tremendous amount of heat is generated, which will raise the temperature inside the body of the dam.
• But the temperature outside the dam remains equal to the atmospheric temperature.
• Due to these temperature differences, temperature stresses get developed in the dam body.
• Besides, due to shrinkage of concrete as it cools, shrinkage stresses get developed.
• These temperature stresses and shrinkage stresses will cause the concrete to crack unless remedial measures are undertaken.

Remedial Measures to Avoid Cracks

• Using minimum amount of cement in a given mix of specified strength. The quantity of cement can be decreased by better grading the aggregates.
• Low lifts should be used for concrete. Generally, 1.5 m lift is used in modern dams.
• By providing suitably spaced contraction joints, in addition to the normal construction joints.
• Special low heat cements may be used.
• The materials which go into the concrete may be cooled before mixing.
• Further cooling is accomplished by circulating cold water through pipes embedded in concrete.

​

Joints in Gravity Dam

• The concreting of the dam is usually placed in blocks.
• The size of blocks will depend upon the size of dam and necessity of contraction joints required from the considerations of cracking of concrete.

Joints in Gravity Dam

• Maximum height of a single pour of concrete (called lift,) usually is about 1.5 m
• The alternate blocks of the very first layer which is laid immediately over the rock foundation is taken as 0.75 m deep,

Joints in Gravity Dam

• The Vertical joints are called the transverse joints and they run through the entire height and extend through the full width of the dam section.
• The horizontal joints called longitudinal joints are developed at each lift height and will extend through the entire width of the dam section. They shall run through the entire length of the dam but shall be staggered between transverse joints,

Construction joints and Contraction joints.

• The joint left was needed from the considerations of practical difficulties in laying the concrete in a single stretch are known as construction joint
• While the joints which are mainly left for shrinkage of concrete are called the contraction joints.
• Truly speaking, every joint which so ever is left in the dam, shall be a construction joint and every construction joint will oppose contraction stresses, and hence will be a contraction joint.

Shear Keys or Key ways

• Where foundation conditions are such that undesirable differential settlements or displacements between adjacent concrete blocks may occur,
• Shear keys are formed in transverse vertical joints between sections to carry the shear from one section to the adjacent one and make the dam act as a monolithic structure.

Arch Dam

• An arch dam may be defined as a solid wall, curved in plan, standing across the entire width of the river valley, in a single span.
• This dam body is usually made of cement concrete, although rubble and stone masonry has also been used in the past.

Arch Dam

• This wall will structurally behave: partly as a cantilever retaining wall standing up from its base, and partly, the load will be transferred to the two ends of the arch span by horizontal arch action.
• The arch load will be transferred to the side walls of the canyon, which must be strong, stable and rocky.

Arch Dam

• The distribution of part of the load to the side walls of the canyon, reduces the load on the cantilever wall, thereby reducing its thickness, as compared to that in an ordinary gravity dam;
• This is the only benefit in arch dam with comparison to a gravity dam.
• The greater is the wall curvature (in plan), the greater will be the load that will be transferred to the sides of the canyon, and hence greater will be the economy in the dam thickness.

Arch Dam

• Economy in dam thickness can be further increased considerably by making the dam body not only curved in plan, but also curved in section.
• Such a non vertical dam is known as double curvature arch dam or a shell arch dam,
• Such dams are designed as shell-structures. Such three dimensional designs are quite complex.
• We find only one arch dam in our country.(Idukki Arch Dam, Kerala, 1976)
• This arch dam too, is not a simple arch dam, but a shell-arch dam.

Types of Simple Arch Dams

• Constant radius arch dams
• Variable radius arch dams
• Constant angle arch dams.
• A constant radius arch dam is the simplest in design as well as construction, but uses the maximum concrete.
• A constant angle arch dam uses about 43% of the concrete used by a constant radius arch dam.
• The variable radius arch dam is an intermediate choice, using around 58% of the concrete used by constant radius arch dam.
• The shell arch dams are much more economical than even the constant angle arch dams,

Types of Simple Arch Dams

• Constant radius arch dams
• Variable radius arch dams
• Constant angle arch dams.
• The famous Vajont dam of Italy is only 22 m thick at its base, inspite of being 261.6 m in height.
• The ldduki dam in India is only 45 m thick at its base, even with 170.7 m height.
• As compared to these thin sections, the famous Hoover dam of USA, which is a constant radius arch dam (with upstream face vertical) is 201 m thick at its base, with only 222 m height.

​

Constant radius arch dams

Constant radius arch dams

• The radii of the outside curved surface are equal at all elevations, from top to the bottom.
• The centres of all such circular arcs, called extrodos (External curve radius), will therefore, evidently lie on one vertical line.
• The introdos (Internal curve radious) has gradually decreasing radius from top to the bottom, so as provide increased concrete thickness towards the base for accounting the proportionally increasing hydrostatic water pressure of the reservoir.
• The dam body will be triangular in cross-section with upstream face vertical, and a minimum thickness at the top.
• Centres of extrodos lie on a straight vertical line that passes through the centre of the horizontal arch ring at the crest therefore, sometimes called a constant centre arch dam,
• The central angles of the arch rings of the the maximum being at the top of the dam, and the minimum at the bottom of the dam.

Variable Radius Arch Dams:

Variable Radius Arch Dams:

• A variable radius arch dam is the one in which the radii of the extrodos curves and of introdos curves vary at various elevations, being maximum at the top, and a certain minimum at its bottom.
• This makes the central angles as large as possible, so that the maximum arch efficiency may be obtained at all elevations.
• The downstream face of the dam at the central line (crown) is vertical ; while at all other locations, there is a batter on both the sides except it the Abutments, where again, the upstream side becomes vertical.
• The centres of the various arch rings at different elevations, do not lie on the same vertical line, it is also known as variable centre arch dam.

Constant Angle Arch Dams.

Constant Angle Arch Dams.

• The constant angle arch dam is a special type of variable radius arch dam, in which the central angles of the horizontal arch rings are of the same magnitude at all elevations.
• The design of such a dam can be made by adopting the best central angle of 133⁰-34';
• Such a dam are the most economical, out of the three types of ordinary arch dams,
• The design of such a dam usually involves providing overhangs at abutments, which require stronger foundations, and hence such a type cannot be used if the foundations are weak.

​

Forces Acting on Arch Dams

• The same forces act on an arch dam, which do act on a gravity dam.
• These forces are:
• Water pressure;
• Uplift pressure;
• Earthquake forces;
• Silt pressure;
• Wave pressure
• Ice pressure;
• The uplift pressure in an arch dam is small and is generally neglected.
• The stresses caused by ice, temperature changes, and yield of supports (i.e. abutments) are become quite important in arch dams.