Planning and design of concrete gravity dam. Further simulating a model of the dam using Finite Element Software STAAD PRO and then using the model to analyze the seismic response of dam and suggest improvements.
Seismic Analysis of Concrete Gravity Dam using FEM
SEISMIC ANALYSIS OF CONCRETE GRAVITY DAM
USING FINITE ELEMENT METHOD
DAMIT SURANA 10102024
YOGESH KR. SINGH 10102090
DEPARTMENT OF CIVIL ENGINEERING
DR. B.R. AMBEDKAR NATIONAL INSTITUTE OF TECHNOLOGY, JALANDHAR
Gravity dams are solid concrete structures that maintain their stability against design loads from the geometric
shape and the mass and strength of the concrete. Generally, they are constructed on a straight axis, but may be
slightly curved or angled to accommodate the specific site conditions. Gravity dams typically consist of a non
overflow section(s) and an overflow section or spill- way.
Earthquakes have affected several large concrete dams in the past. Although no catastrophic failure has yet
been reported unless a dam crossed a fault, historical events have shown that severe seismic damage could be
imparted to concrete dams. For example. Koyna Dam Earthquake. Koyna Dam is a 103 meter high gravity
structure, which was visited by a strong earthquake of magnitude 6.5 on December 11, 1967. During the
Earthquake, the dam suffered severe distress. Thus, the study of seismic analysis of dams become
The design of concrete dams involves consideration of various construction materials during the investigation
phase. An assessment is required on the availability and suitability of the materials needed to manufacture
concrete qualities meeting the structural and durability requirements, and of adequate quantities for the volume
of concrete in the dam and appurtenant structures. Construction materials include fine and coarse aggregates,
cementitious materials, water for washing aggregates, mixing, curing of concrete, and chemical admixtures. One
of the most important factors in determining the quality and economy of the concrete is the selection of suitable
sources of aggregate. In the construction of concrete dams, it is important that the source have the capability of
producing adequate quantities for the economical production of mass concrete. The use of large aggregates in
concrete reduces the cement content.
The feasibility study will establish the most suitable and economical location and type of structure.
Investigations will be performed on hydrology and meteorology, relocations, foundation and site geology,
construction materials, appurtenant features, environmental considerations, and diversion methods.
A concrete dam requires a sound bedrock foundation. It is important that the bedrock have adequate shear
strength and bearing capacity to meet the necessary stability requirements.
The topography is an important factor in the selection and location of a concrete dam and its appurtenant
The criteria set forth for the spillway, power- house, and the other project appurtenances will play an
important role in site selection.
FINITE ELEMENT METHOD
The Finite Element Method (FEM) permits the engineer to closely model the actual geometry of the structure
and account for its interaction with the foundation. Finite element analysis allows not only modeling of the
dam, but also the foundation rock below the dam. One of the most important parameters in dam/foundation
interaction is the ratio of the modulus of deformation of the rock to the modulus of elasticity of the dam
FINITE ELEMENT ANALYSIS SOFTWARE
STAAD.PROV8i is based on FEM and shall be used to simulate the response of the masonry and RCC structures
under impact and blast loadings.
We can import geometry from many different CAD software packages.
Using STAAD.PRO, we could be able to use various different material models to simulate the behavior of most
typical engineering materials including metals, rubber, polymers, composites, reinforced concrete, crushable and
resilient foams, and geotechnical materials such as soils and rock.
STAAD.PRO offers a wide range of capabilities for simulation of linear and nonlinear applications. Problems
with multiple components are modeled by associating the geometry defining each component with the appropriate
material models and specifying component interactions. In a nonlinear analysis Abaqus automatically chooses
appropriate load increments and convergence tolerances and continually adjusts them during the analysis to
ensure that an accurate solution is obtained efficiently.
PROCESSES OF FINITE ELEMENT
Every complete finite-element analysis consists of 3 separate stages:
Preprocessing: The user constructs a model of the part to be analyzed in which the geometry is divided into a
number of discrete sub-regions, or elements, connected at discrete points called nodes. Certain of these nodes
will have fixed displacements, and others will have prescribed loads. These models can be extremely time
consuming to prepare, and commercial codes with one another to have the most user-friendly graphical
preprocessor to assist in this rather tedious chore. Some of these preprocessors can overlay a mesh on a
preexisting CAD file, so that finite element analysis can be done conveniently as part of the computerized
Analysis: The dataset prepared by the preprocessor is used as input to the finite element code itself, which
constructs and solves a system of linear or nonlinear algebraic equations
PROCESSES OF FINITE ELEMENT
Kij × uj= fi (1.1)
Where u and f are the displacements and externally applied forces at nodal points
Post-processing: In the earlier days of finite element analysis, the user would pore through realms of
numbers generated by the code, listing displacements and stresses at discrete positions within the model. It is
easy to miss important trends and hot spots this way, and modern codes use graphical displays to assist in
visualizing the results. A typical post-processor display overlay colored contours representing stress levels on
the model showing a full-field picture similar to that of photo elastic experimental results.
Bhattacharjee and Leger (1994) carried out a study on Application of NLFM models to predict cracking in
concrete gravity dams. The tensile strain softening behavior of finite elements was modeled using a secant
modulus stiffness formulation. The softening of shear resistances in the cracked elements were considered in
two constitutive frameworks: (1) A coaxial rotating crack model (CRCM); and (2) a fixed crack model with a
variable shear resistance factor (FCM- VSRF). An indirect displacement control analysis technique had been
adopted to predict the ultimate resistance and the post failure behavior of concrete structures. The model was
verified and used to analyze three different models: Shear beam with single notch, model concrete dam and full
size concrete gravity dam. In the shear beam analysis, the FCM-VSRF provided a substantially high post peak
structural resistance. The CRCM model performed better than FCM- VSRF model in all three cases and was
found more reliable.
Leger et.al. (1995) carried out a study on Evaluation of earthquake ground motions to predict cracking response
of gravity dams. Smooth design spectra were used to describe the seismic excitation imparted by the maximum
design earthquake. Cracking response subjected to historical records and spectrum compatible accelerograms
were studied. Seismic hazard maps were used to scale spectral shapes. A concrete model based on nonlinear
fracture mechanics (NLFM) principle was used to represent crack formation and propagation in the dams. It was
found that the seismic fracture response of gravity dams depend on the dynamic amplification of record and
variation of its time history.
Guan et.al (1996) carried out a study on New techniques for modelling reservoir-dam and foundation-dam
interaction. A hybrid numerical procedure was proposed for the dynamic frequency domain response of earth
dams resting on a multi-layered foundation. It was found that vertical response was significantly influenced by
the foundation condition.
Hatami (1997) carried out a study on Effect of reservoir bottom on earthquake response of concrete dams. A
model was proposed for the absorption effects of the reservoir bottom in the earthquake analysis of the dam. The
model utilized the wave reflection coefficient approach and was based on the solution of the wave equation in a
sediment layer of viscoelastic material. Different model for the interaction of reservoir water with its foundation
were considered i.e. Rigid Reservoir Foundation, Partially absorptive with and without sediment layer. It was
found that reflectivity of the reservoir bottom is reduced with increase in thickness of sediment layer.
Guanglun et. al. (1999) carried out a study on Seismic fracture analysis of concrete gravity dams based on non-
linear fracture mechanics. A numerical scheme based on nonlinear crack band theory was presented to study the
2D seismic fracture behaviour of concrete gravity dams. This procedure was verified using test results for a
notched beam and then applied to the seismic fracture analysis of the Koyna dam in India as a demonstration of
prototype application. It was found that the element boundaries to be parallel with the orientation of the principal
tensile stresses was more effective to depict the curved crack extension path. It was also found that the length of
crack decreases as the fracture energy of the material increases.
Uddin (1999) carried out a study on A dynamic analysis procedure for concrete-faced rockfill dams subjected to
strong seismic excitation. A dynamic analysis procedure for CFR (concrete faced rockfill) dams was followed.
The dam was subjected to strong seismic shaking and analysis was done using a realistic modeling for the
embankment material, the slab and the slab-rockfill interface. The rockfill was modeled as an equivalent-linear
material, whose strain dependent shear modulus was proportional to the square root of the confining pressure. It
was found that dams built in narrow canyons were likely to develop much higher mid-crest accelerations for the
same base excitation.
Oskoueia and Dumanoglu (2000) carried out a study on Nonlinear dynamic response of concrete gravity dams:
cavitation effect. A finite element method for the dynamic analysis of concrete gravity dams with displacement
based formulation for both fluid and structural domains was presented. Cavitation effect and local impact
phenomena (as a result of change of direction of ground motion) was studied for Pine Flat Dam, located in Kern
Country. It was noticed that the cavitation slightly reduces the maximum horizontal displacement of the dam
crest in downstream direction but the maximum horizontal displacement toward upstream was slightly increased.
It was found that the change of response in the upstream direction was more than the downstream direction. Most
cavitation and impact phenomenon took place in the upper part of the dam surface causing high local stress and
resulting erosion of the surface.
Chen et. al. (2001) carried out a study on Simulation analysis of thermal stress of RCC dams using 3-D finite
element relocating mesh method. A 3-D finite element relocating mesh method was developed depending on the
relation between specific properties and age of concrete such that as the elastic modulus, creep or hydration heat
changed the relocation of meshes started. This 3-D simulation analysis could be realized by microcomputer at the
site and temperature control measures could be applied. Reducing the RCC placement temperature was found
very useful in controlling the highest temperature in the dam. It was found that when the air temperature will
increase, the compressive stress will occur and when the air temperature will decrease, the tensile stress will
Malkawi et. al. (2003) carried out a study on Thermal-structural modeling and temperature control of roller
compacted concrete gravity dam. A coupled thermal-structural analysis was carried out using both a two- and a
three-dimensional finite-element method using ANSYS. Thermally induced stresses were computed for the 60 m
high RCC Tannur Dam in Jordan. The actual temperature distribution in the body of the dam measured by
thermocouples was compared with that obtained by ANSYS. The method was found efficient and reliable. The
temperatures and the stress distribution in the dam as predicted by the finite-element method were reasonable and
predict the evolution of temperature and thermal stress with time.
Javanmardi et. al. (2004) has carried out a study on Seismic structural stability of concrete gravity dams
considering transient uplift pressures in cracks. A theoretical model was developed to compute uplift pressure
variations along a tensile seismic concrete crack with known crack wall motion history. The proposed model was
and implemented in a finite element computer program for dynamic analysis of gravity dams considering hydro-
mechanical water–crack coupling. It was found that water can penetrate into part of a seismically initiated crack
and saturate it partially. During the crack opening mode the saturated length was small, while during the crack
closing mode the saturated length was large. The seismic uplift pressure generated during crack opening mode
was found very small relative to the dam weight and hence the critical sliding safety factor (SSF) can be
computed by considering zero uplift pressure in the crack region subjected to seismic tensile opening.
Li et.al. (2004) carried out a study on Experimental and numerical seismic investigations of the Three Gorges
Dam. A seismic analysis of the powerhouse monolith of the Three Gorges Dam was done through model testing
at a geometric scale of 1:100 on a shaking table and numerical simulation using a three dimensional finite
element model of the structure in MODAL. It was found that the data measured from the model test were in
satisfactory agreement with the calculated results for the case of an empty reservoir and rigid foundation.
Pekau et.al (2004) carried out a study on Failure analysis of fractured dams during earthquakes by DEM. The
whole process of the two possible failure modes of the cracked dam, i.e. overturning or sliding of the top separated
block during earthquakes were simulated. Three crack shapes were studied to analyze the stability of top profile
i.e. horizontal, upstream sloped and downstream sloped. Different values of damping had been assigned for
different parts of the fractured dam. It was found that the dam would be safe if the crack shape is horizontal or
upstream sloped but if the friction coefficient of the crack is abnormally low then there would be large sliding
displacement of the top block.
Calayir and Karaton (2005) carried out a study on Seismic fracture analysis of concrete gravity dams including
dam–reservoir interaction. The seismic fracture response of concrete gravity dams was investigated considering
the effects of dam–reservoir interaction. A co-axial rotating crack model (CRCM), which includes the strain
softening behavior, was selected for concrete material. Two-dimensional seismic analysis of Koyna gravity dam
was performed by using the 1967 Koyna earthquake records for numerical application. It was found that cracks
initiated near stress concentrations in the dam monolith, mainly at the base and near the changes in the slope of the
faces. It was also found that cracking changed the vibration period of the dam–reservoir system.
Leger et.al. (2006) carried out a study on Seismic stability of concrete gravity dams strengthened by rockfill
buttressing. Simplified methods for seismic stability analysis of composite concrete-rockfill dams were discussed.
A typical 35m concrete gravity dam, strengthened by rockfill buttressing was considered. The results of analyses
confirmed that backfill can improve the seismic stability of gravity dams by exerting pressure on the dam in
opposition to hydrostatic loads.
Leger et.al. (2006) conducted a study on Seismic Stability of cracked concrete dams using rigid block models. A
methodology was developed to perform a direct transfer in the frequency domain from the specified base input
spectra to the in-structure response spectra (ISRS) adapting computational algorithms and verified. It was found
that the use of accelerograms compatible with the linear dam to perform transient rigid body sliding response
analysis was un-conservative. An envelope of nonlinear ISRS computed from cracked beam models of the dam
was recommended to obtain compatible accelerograms.
Zhu and Pekau (2006) carried out a study on Seismic behavior of concrete gravity dams with penetrated cracks
and equivalent impact damping. The damping effect was introduced in the incremental displacement constraint
equations (IDCE) model to simulate the energy dissipation during impact based on the concept of the restitution
coefficient for collision between two point masses. The effectiveness of this IDCE damping contact model was
verified for rigid and flexible blocks. Then a typical concrete gravity dam with different crack cases was
investigated to evaluate the seismic behavior of concrete gravity dams with penetrated cracks. The impact
damping was found very important in the estimation of the seismic response. It was found that the sliding,
rocking and jumping of the cracked dam with multi-cracks are much reduced when compared with the single
Noorzaei et. al. (2006) carried out a study on Thermal and stress analysis of Kinta RCC dam. The variables used
for the analysis was heat of hydration; foundation temperature; RCC placing temperature; temperature of mixing
ingredient; solar radiation and wind speed. The predicted temperatures obtained from the finite element code that
was developed are found to be in good agreement with actual temperatures measured in the field using
thermocouples installed within the dam body. The crack index variation was found helpful in prediction of crack
occurrence. The downstream region was found more prone to cracks.
Komodromos (2007) carried out a study on Simulation of the earthquake – induced pounding of seismically
isolated buildings. The superstructure was modeled as a shear-beam building with lumped mass at the floor
levels. A 4-story building was considered under three different circumstances i.e. fixed supported, seismically
isolated without the possibility of impacts and seismically isolated with 0.15m seismic gap on either side. It was
found that pounding may lead to substantial increase in floor acceleration and interstory deflections and
excitation of higher modes of deformation. Collision bumpers were suggested as potential practical mitigation
measures against pounding.
Wei et.al. (2007) conducted a study on Failure analysis of high-concrete gravity dam based on strength reserve
factor method. Nonlinear finite element method (FEM) analysis was used to calculate the resistance to sliding of
a high concrete gravity dam Xiangjiaba Hydropower Station on Jinshajiang River in Yunnan Province, China,
while it was under construction . The strength reserve factor (SRF) method was adopted to simulate progressive
failure and possible unstable modes of the dam’s foundation system, and the method for determining the ultimate
bearing resistance of this system. The calculation shows that the failure of the dam is related to the strength (or
weakness) of the silt-laden layer at the dam’s foundation, and the strength reserve factor of final failure was 2.6.
Remmers et.al. (2007) conducted a study on The simulation of dynamic crack propagation using the cohesive
segments method. The cohesive segment method was used to simulate fast crack propagation in brittle solids.
Cracks were introduced as jumps in the displacement field by employing the partition of unity property of finite
element shape functions. It was found that adding degrees of freedom during a simulation did not affect the
energy conservation. The performance of the cohesive segments method illustrated by dynamic shear test was
found to be in agreement with analytical studies.
Bayraktar et.al. (2008) carried out a study on Stochastic dynamic response of dam– reservoir– foundation
systems to spatially varying earthquake ground motions. Stochastic dynamic responses of dam–reservoir–
foundation systems subjected to spatially varying earthquake ground motions were investigated using the
displacement-based fluid finite elements by computer program SVEM. The effect of the wave passage was
investigated by using various wave velocities. Homogeneous medium and firm soil types were selected for
considering the site-response effect where the foundation supports are constructed. It was concluded that
spatially varying earthquake ground motions have important effects on the stochastic dynamic response of dam–
Cascone et.al. (2008) carried out a study on Evaluation of the seismic response of a homogeneous earth dam. The
response of an earth dam to seismic loading was studied through displacement-based analyses and finite element,
effective stress dynamic analyses. The FE analyses were carried out using a constitutive model capable to
reproduce soil non- linearity, calibrated against laboratory measurements of the stiffness at small strains. FE
dynamic analyses were compared with displacement-based analyses and a fair agreement was obtained provided
that ground response analysis was accounted for when using the displacement-based approach.
Arabshahi et.al. (2008) carried out a study on Earthquake response of concrete gravity dams including dam-
foundation interface non-linearities. A plasticity based formulation was used in the local stress space of interface
elements to model sliding and partial opening along the dam base. Dam-Reservoir interaction was considered to
estimate the effect of water compressibility on the response of the dam. A linear model of the dam was analyzed
and it was found that large tensile stresses were developed near the base as a result of rigid foundation
assumption and near the discontinuity in the slope of the downstream face of the dam due to stress concentration.
Results showed that uplifting could both reduce and amplify the response values.
Yuchuan et. al. (2009) carried out a study on Nonlinear seismic analyses of a high gravity dam with and without the
presence of reinforcement. Three different models of the Jin’anqiao gravity dam (160 m high with a 150 m deep
reservoir) were simulated and analyzed under seismic load. The horizontal steel was ignored in the simulation. It
was found that the cracks near the upstream face close when the earthquake impulses result in the dam deformation
toward upstream. There was little difference in the dam response calculated from the reinforcement analyses with
and without bond slip which shows that the modified embedded-steel model used was applicable to evaluating the
effectiveness of the reinforcement strengthening. The reinforcement was found effective in reducing the maximum
opening and extension of the major crack.
Zheng et.al.(2010) carried out a study on A three-dimensional procedure for evaluating the stability of gravity dams
against deep slide in the foundation. A rigorous three-dimensional procedure was developed, which can
accommodate failure surfaces of any shape and satisfy all equilibrium conditions. The reinforced concrete plugs
were laid between the sliding body and the rock foundation. Nearly equal factor of safety against deep slide was
kept in the design of all dam monoliths. It was found that the method satisfied all equilibrium conditions. The idea
of “the design of equal safety” had the probability of reducing the price of dam construction.
Moftakhar and Ghafouri (2011) carried out a study on Comparison of stability criteria for concrete dams in
different approximate methods based on finite element analysis. The accuracy of the approximate methods of U.S.
regulations (Army Corps of Engineers, U.S. Bureau of Reclamation, and U.S. Federal Energy Regulatory
Commission regulations for gravity dams) and Finite element method were determined and compared with each
other. The finite element method was found more accurate than the three U.S. regulatory methods and
recommended specifically at the level of the dam near the base, where the elasticity properties of the foundation
were very effective.
Lotfi et.al. (2011) carried out a study on Application of H-W boundary condition in dam-reservoir interaction
problem. Dynamic analysis of unbounded reservoir was studied. Hagstrom and Warburton ‘s non-reflecting
boundary conditions (NRBC) were used and harmonic response was calculated. The performance and accuracy of
NRBC was examined by comparing the results with exact solution. The numerical results confirmed very good
behavior of the NRBC in the frequencies above the fundamental frequency of the reservoir but below this
frequency the boundary condition did not perform very well, especially when it was applied in close distances
from the dam.
Jiang et.al.(2011) carried out a study on Seismic Damage assessment and performance levels of reinforced
concrete members. A modified damage model of the Park-Ang model was studied. The combined coefficient in
the modified damage model was calibrated by using the experimental database from a large number of RC
member tests. The damage indices at principle damage states of flexure-dominant RC members in the same
database were calculated by the modified damage model. The limit values of damage index classifying the
seismic performance levels were proposed on the basis of the statistical analysis results.
Fujun et. al. (2012) carried out a study on Simulation analysis of crack cause of concrete overflow dam for
Hadashan Hydro Project by 3-D FEM. A 3-dimensional finite element method (3-D FEM) was developed for
simulation analysis of the temperature and thermal stress distribution in the concrete overflow dam during the
construction period. The variables used was average temperature of construction area, concrete material
properties and the actual pouring temperature of concrete. It was found that cracks developed in the dam body
due to this temperature field. Cracks were found to be formed during both the heating and cooling phases of the
Ali et. al. (2012) carried out a study on Comparison of design and analysis of concrete gravity dam. A high
concrete gravity dam was designed based on U.S.B.R. recommendations in seismic Zone-II of Bangladesh and its
stability and stress conditions were analyzed using analytical 2D gravity method and finite element method.. It was
found that the factor of safety against sliding was satisfied at last than other factors of safety, resulting huge dam
section to make it safe against sliding.
Li et. al. (2012) carried out a study on Three-Dimensional nonlinear strain-stress analysis of gravity dam base. An
integrated three-dimensional calculus model was set up, and the geological structure of the concrete gravity dam of
a hydroelectric station in Yunnan province was simulated. The strain-stress relationship of the bedrock was
simulated by the elastic-plastic constructive model and Mohr-Coulomb yield criterion. It was found that the largest
compression stress and tensile stress distributed on the heel of dam and dam site, and the largest displacement
takes place at the top of dam. The yielding zone of the face of the constructive base was enlarged from the heel of
dam and dam site to the inner part of the dam till the plastic deformation connecting the upper and lower reaches
appears and the bearing capacity of the whole structure was lost.
Teng-fei et. al. (2012) carried out a study on Stability analysis of concrete gravity dam foundation based on
catastrophe model of plastic strain energy. A catastrophe model of plastic strain energy based on strength
reduction factor was established and applied to the sliding stability analysis of a concrete gravity dam. A two-
dimensional finite element model of the dam had been built by using MSC Marc software and Energy dissipation
process of gravity dam and dam foundation system was analyzed. The catastrophe model was found more
accurate than that of the displacement catastrophe criterion based on displacement curves. Anti-sliding stability
safety coefficient of the simulated dam was accurately determined to be 1.4.
Zhang et. al. (2013) carried out a study on Seismic cracking analysis of concrete gravity dams with initial cracks
using the extended finite element method. Extended finite element method (XFEM) approach was used to
evaluate the seismic crack propagation of the concrete gravity dam with single and multiple initial cracks. Two
meshes with different densities were utilized to examine mesh-sensitivity of the model. It was found that the
crack propagation change the vibration period of the dam, and a lengthening vibration period was found which
implied that the rigidity of the dam is gradually decreased due to concrete softening.
Jiang et. al. (2013) carried out a study on Failure analysis of a cracked concrete gravity dam under earthquake.
They used a dynamic contact model for simulating the interaction of two surfaces divided by a dam crack, and a
simplified reinforcing steel constitutive model for simulating the effect of earthquake-resistant reinforcement on a
cracked dam was developed. It was found that the cracked dam maintains a large safety margin, and the curving
crack was found beneficial to the improvement of earthquake resistance. It was also found that commonly applied
steel reinforcement can effectively decrease the sliding displacement and the joint opening of the cracked dam.
Su and Wen (2013) carried out a study on Interval risk analysis for gravity dam instability. Risk analysis and
fuzzy mathematics were conducted to evaluate the stability problems of gravity dams. The fuzziness of both the
design parameters and failure criterion were accordingly eliminated through a transformation by use of the
concept of the Level Set. Corresponding analysis procedures were then provided to calculate the fuzzy risk and its
probability of the stability failure for gravity dams. It was found feasible to apply the present method to analyze
the fuzzy risk of stability failure for gravity dams. The obtained risk (interval value) was found more reasonable
and more accord with engineering practice.
Paggi et. al. (2013) carried out a study on A multiscale approach for the seismic analysis of concrete gravity dams.
The problem of cracking in concrete gravity dams subjected to seismic loadings was examined under a multi-scale
perspective. The size-scale effects on the mechanical parameters entering the nonlinear constitutive models of the
interface crack were discussed. It was found that the material tensile strength, the fracture energy, the friction
coefficient and the concrete compressive strength are strongly size-scale dependent. The size-scale effects on
tensile strength and fracture energy of concrete was found useful to characterize the behavior of the interface up to
Khosravi and Heydari (2013) carried out a study on Modelling of concrete gravity dam including dam-water-
foundation rock interaction. A hybrid meta-heuristic optimization method was introduced to efficiently find the
optimal shape of concrete gravity dams including dam-water-foundation rock interaction. A 2-D finite element
model including dam, reservoir and foundation was provided in APDL (Parametric Design Language) language
programming. The model was verified for 4 different cases.Very small percentage of error showing excellent
accuracy of the proposed model for dam-reservoir-foundation system was found. Maximum value of main
frequency was obtained when the reservoir was empty and foundation was rigid while, minimum value of main
frequency was obtained when the reservoir was full and foundation was flexible (dam-water-foundation rock
Zhang et. al. (2013) carried out a study on Numerical simulation of failure modes of concrete gravity dams
subjected to underwater explosion. A numerical simulation of antiknock performance and failure modes of
concrete gravity dams under blast loading was performed. The pressure and impulse produced by underwater
explosion were calculated and the numerical results were verified by comparing with analytical expressions in
different scaled distances. The influence of the dam height, standoff distance and the upstream water level on the
antiknock performance of the dam was investigate. The accuracy of numerical results was found strongly
dependent on the mesh size used in the analysis. The lateral deflections of the dam rise with the increase of the
dam height but the maximum peak values of the maximum principal stresses for the dam heel zone gradually
decrease with the increase of the dam height. The failure of concrete gravity dams subjected to underwater
explosion was caused by compressive crushing, spalling and punching of concrete materials. Lowering the water
level in the reservoir was found as an effective defense measure to reduce the risk of the dam failure subjected to
Seghir et. al.(2013) carried out a study on Coupling FEM and symmetric BEM for dynamic interaction of dam–
reservoir systems. A numerical model coupling boundary and finite elements suitable for dynamic dam–reservoir
interaction was presented. The performance and the accuracy of this model were examined by comparing its results
to those obtained from three other numerical models. The unbounded reservoir domain was found to be effectively
idealized without any treatment of the infinite part. The model produced results were found similar to those of a
complete finite element modelling of both the dam and the reservoir subdomains.
Yuan et. al. (2013) carried out a study on Static and dynamic analysis of anti-sliding stability of gravity dam under
united form between dam and plant. The limit equilibrium method and strength accumulation coefficient method
was used to analyze the deep and shallow anti-sliding stability of gravity dam under united form between dam and
plant for the Jin’anqiao hydropower riverbed dam sect. 2D and 3D finite element model was established in order
to detail the united action between dam and plant for various kinds of rock. Earthquake case was found to be the
control case of anti-sliding stability. Adopting united form between dam and plant was found to provide improved
anti-stability in Jin’anqiao hydropower plant sect.
Problem of Study: Design of a Concrete Gravity Dam and its seismic analysis.
Proposed site of dam.
OBJECTIVES OF THE PRESENT STUDY
Hydrology and Hydraulic Engineering Aspects:-
a) Identification of catchment area.
b) Collection and analysis of hydro-meteorological data like rainfall, evaporation temperature, flow etc.
c) Estimation of design flood.
d) Water availability studies for power generation– flow duration curve.
Structural Engineering Aspects:-
a) Stability analysis of concrete gravity dam section, for toppling, sliding, compression, tension modes of failure.
b) Finite Element Analysis of non-overflow section of the diversion dam.
HYDROLOGY AND HYDRAULIC
Catchment boundary definition for the dam site
= 38*40/100 =15.2
Hence, from above table required dependable rainfall = (1532+1433)/2= 1482.5 mm.
Here if we design the reservoir for 819mm rainfall then eventually the reservoir will be filled up every year with
a dependability of 100% but if we design the reservoir foe 3057 mm rainfall then eventually the reservoir will be
filled up only once in 38 years with a dependability of 2.63%.Hence we need to design the reservoir for a suitable
dependability percentage (say 40%).
1. Water supplied for daily uses:-
As per Indian standards, For rural areas, per capita water demand = 135 liters.
Hence, total yearly water demand for a population of 3 lakhs= 300000*135*365
= 14.79 M. m3
2. Water supplied for irrigation purpose:-
Total irrigated area as per map = 5350 Km2
Major crops in Uttarakhand is:-
Total water required for irrigation purpose = 120+40+45+22.5=227.5 cm
Average annual rainfall in the area= 205.1cm
Additional water required= 227.5-205.1= 22.4cm
Total water to be provided annually= 5350* .224= 672 M. m3
Assuming efficiency of irrigation system =80%
Total water to be supplied= 672/.80= 840 M. m3 (annually)
3. Water passed from the reservoir to satisfy the prior water rights/obey the agreements between various sharing
states through which the river is passing:-
Assume water to be released everyday = 350000 m3 satisfy the prior water rights.
Hence, total water to be released annually = 350000*365 =127.75 M. m3
Total outflow required annually= 14.79+840+127.75= 982.54= 983 M. m3 (Say)
RESERVOIR AND RESERVOIR CAPACITY
The capacity of reservoir is the storage needed to accommodate the given inflow minus the given outflow.
Assume available area for reservoir = 100 Km2
Required Reservoir capacity= annual inflow- annual outflow =4080.5 – 983
= 3097.5 M.m3=3100 M.m3 Approx. (live storage)
Dead storage: - assume rate of silting = 300 (Reference; - Example 18.4 Garg SK “Irrigation Engineering &
Hydraulic Structures” Khanna Publishers, Delhi, 1999)
Assume life of reservoir= 100 years.
Dead storage = 300 *2943=88.29 M.m3
Or dead storage = 20% of live storage = 0.2 *3100= 620 M.m3
Hence, dead storage = 620 M.m3
Now, Gross storage required= dead storage+ live storage= 3720 M.m3
Structural Engineering Aspect
Design of gravity dam
1) Rock formations at the dam-site are available and are capable of carrying the loads transmitted by the dam with
(2) The dam is thoroughly bonded to the foundation rock throughout its contact with the canyon.
(3) The concrete in the dam is homogeneous, uniformly elastic in all directions, and strong enough to carry the
applied loads with stresses below the elastic.
(4) Contraction joints that are keyed and grouted may be considered to create a monolithic structure, and loads may
be transferred horizontally to adjacent blocks by both bending and shear.
(5) Horizontal and vertical stresses vary linearly from the upstream face to the downstream face.
(6) Horizontal shear stresses have a parabolic variation from the upstream face to the downstream face.
Dead storage level= dead storage/ reservoir area= 620/100= 6.2m.
Normal reservoir level = gross storage/ reservoir area=3720/100= 37.2m
Highest flood level= design maximum flood/ catchment area
= 10107.635/100 = 101.07m= 102m (say)
Hence maximum reservoir level= 102+37.2= 139.2m
Using Gravity Method or two Dimensional Stability Analysis:-
The practical profile of dam will have a free board of about 3 to 4% of dam height. Assume 4% of height as free board=
139.2*4/100=5.57m (since wave ht. etc are note given)
Total Ht. of dam= 145m (say)
R.L. of top of dam = 245m
Again Ht. of low gravity dam H1 =
Therefore, it is a high gravity dam.
Hence, the dam from RL 245 to RL 245-117.64=127.36m shall be designed as low gravity dam and the remaining bottom
ht. of dam from RL 127.36 to RL 100 shall be designed on the principles of high gravity dam.
Designed section of dam from RL 127.36m to RL 245m (Not
Designed section of dam from RL 127.36m to
RL 100m (Not scaled)
STABILITY ANALYSIS OF DESIGNED
Stability against overturning:
a.) Total overturning moment about toe (clockwise)
b.) Total resisting moment about toe (anti- clockwise)
Factor of safety against overturning=
Hence, F.O.S. = 2.8 > 2.5 (Ok)
Stability against sliding:-
Assuming coefficient of friction between dam base and rock foundation is 0.45
a.) Total sliding force = 97298.66 KN
b.) Total resisting force = 243072.49 KN
Factor of safety against sliding =
4517890.54oM KN m
12723019.84rM KN m
Hence, F.O.S. = 2.49 > 1.5 (Ok)
Stability against compression or crushing:-
p [1 ]
X = 81.59m (C.G. of vertical forces)
e = ( B
) = 19.84m
Hence, pmax = 2479.86 KN/m2 < 4000 KN/m2 (Ok)
Pmin = 45.455 KN/m2 < 4000KN/m2 (Ok)
Stability against tension:-
Since e < B
Hence no tension will be there. (Ok)
SIMULATION IN STAAD PRO
The geometry of the designed gravity dam section was drafted using AutoCAD and imported to STAAD Pro
The geometry of the dam was divided into small parts to know more accurate value of actual stresses on the section
due to different loads (i.e. dead loads, earthquake loads etc.)
OPTIMIZATION OF MESHING
Stress values for load1 (design flood).
1. Sections with 28 horizontal and 15 vertical positions (28 * 15 = 420 elements)
Stress values for load1 (design flood)Section with 28 horizontal and 20 vertical partition
2. Section with 28 horizontal and 20 vertical partition (28 *20 = 560 elements)
Stress values for load1 (design flood)Section with 28 horizontal and 25 vertical partition
3. Section with 28 horizontal and 25 vertical partition (28 *25 = 700 elements)
Stress values for load1 (design flood)Section with 37 horizontal and 25 vertical partition
4. Section with 37 horizontal and 25 vertical partition (37 *25 = 925 elements)
OPTIMIZATION OF MESHING
Here, it is clear that after case (b.) (i.e. 28 horizontal and 20 vertical partition or 560 elements) there is no significant
change in stresses with decrease in mesh size. Therefore, optimum no. of elements for this section is 560 with 28
horizontal and 20 vertical partition.
As per IS-6512:1984, Gravity dam design should be based on the most adverse load combination A, B, C, D, E, F
or G given below using the safety factors prescribed. Depending on the scope and details of the various project
components, site conditions and construction program one or more of the following loading combinations may not
be applicable may need suitable modifications:
Load Combination ‘A’ (Construction Condition) - Dam completed but no water in reservoir and no tail water.
Load Combination ‘B’ (Normal Operating Condition) - Full reservoir elevation normal dry weather tail water,
normal uplift; ice and silt (if applicable).
Load Combination ‘C’ (Flood Discharge Condition) - Reservoir at maximum flood pool elevation, all gates
open, tail water at flood elevation, norma1 uplift, and silt ( if applicable ).
Load Combination ‘D’ - Combination A, with earthquake.
Load Combination ‘E’ - Combination B, with earthquake but no ice.
Load Combination ‘F’ - Combination C, but with extreme uplift (drains inoperative).
Load Combination ‘G’ - Combination E, but with extreme uplift (drains inoperative).
Again, ice pressure is not applicable here. And the uplift pressure intensities at the heel and the toe should be
taken equal to their hydrostatic pressures and joined by a single line.
LOAD COMBINATION ‘A’
(Construction Condition) - Dam completed but no water in reservoir and no tail water. (i.e. only self-weight)
Stresses on the section due to load case 1
LOAD COMBINATION ‘B’
(Normal Operating Condition) - Full reservoir elevation normal dry weather tail water and normal uplift pressure.
Stresses on the section due to load combination B
LOAD COMBINATION ‘C’
(Flood Discharge Condition) - Reservoir at maximum flood pool elevation, all gates open, tail water at flood
elevation and normal uplift pressure
Stresses on the section due to load combination C
LOAD COMBINATION ‘D’
Combination A, with earthquake.
Stresses on the section due to load combination A+ EQX Stress on the dam section due to Load Combination A-EQX
LOAD COMBINATION ‘E’
Combination B, with earthquake but no ice.
Stresses on the section due to load combination B+ EQX Stress on the dam section due to Load Combination B-EQX
LOAD COMBINATION ‘F’
Combination C, but with extreme uplift (drains inoperative).
Stresses on the section due to load combination F
LOAD COMBINATION ‘G’
Combination E, but with extreme uplift
Stress on dam section due to load Combination
B +EQX (with extreme uplift)
Stress on dam section due to load Combination
B -EQX (with extreme uplift)
RESULTS AND DISCUSSIONS
Various stages involved in design of a concrete gravity dam was discussed in detail. And its seismic analysis was
done using FEM in STAAD Pro software. Conclusions of the study are:-
1. The dam section was analyzed for different load combinations as per recommended by Indian standards. The
section was found safe and stable against all load conditions.
2. Maximum stress was developed in the dam section at points where there is sudden change of slopes. The points on
the section where there is sudden change in slope were found more critical.
3. When the dam section was analyzed with FEM using 15 vertical and 27 horizontal division, the value of minimum
and maximum stress found was equal to the theoretically calculated value. But when the mesh size was decreased
this stress increased. Hence, we may say that Optimization of meshing in FEM give us more correct and reliable
4. In future the crack will be initiated at the point of slope change on the U/S face. Large slope changes in the dam
section should be avoided.
5. Stress contours spread outwards from U/S face to D/S face.
Future scope of the study: -
1. Effect of reservoir bottom on earthquake response of concrete dams should be studied.
2. Thermal stress developed during the mass concreting should be studied.
3. Power plant should be designed of suitable capacity for electricity generation.
Garg SK “Irrigation Engineering & Hydraulic Structures” Khanna Publishers, Delhi, 1999.
W. G. Bligh “ DAMS AND WEIRS” American Technical Society Chicago- 1915.
United States Department of the Interior (Bureau of Reclamation) “DESIGN OF GRAVITY DAMS” – Design
manual for concrete gravity dam by - 1976.
Sudip S. Bhattacharjee, and Pierre Leger, “Application of NLFM models to predict cracking in concrete gravity
dams” Member, ASCE – 1994.
P. Leger and M. Leclerc, “ Evaluation of earthquake ground motions to predict cracking response of gravity dams”
Department of Civil Engineering, Ecole Polytechnique, University of Montreal Campus, Canada- 1995