Evaluation of Existing Arch Dam Design Criteria in Lieu of

ANCOLD Guidelines
Marius Jonker and Dr Radin Espandar
GHD Pty Ltd

This paper provides a summary of the current state of practice for arch dam design criteria that have been
adopted by some international dam organizations, and where relevant, compares that with the criteria
provided in the updated ANCOLD Guidelines on Design Criteria for Concrete Gravity Dams, with the view
to provide a basis for consistent and unified design criteria for arch dams in Australia.
The paper draws on the authors’ experience with arch dams, including recent experience with a number of
arch dam safety reviews in Australia, their past experience with arch dams over 200 m height, as well as
their involvement with the development of the mentioned updated ANCOLD Guidelines.
Since the last arch dam was constructed in Australia, a number of international publications have been
released on arch dam design practices, providing general information and guidance for the design of new
dams and evaluation of the safety and structural integrity of existing arch dams. This paper compares these
publications and proposes criteria that are aligned with the ANCOLD gravity dam guidelines.
Keywords: Arch dams; Design Criteria

Introduction Key concepts of arch dams

The ANCOLD register includes 43 arch dams constructed Concrete arch dams are complex three-dimensional shell
between 1857 and 1974, ranging from about 15 m to structures that are thinner but have more redundancies
140 m in height. Although there have been no new arch than gravity dams. They carry load both in a vertical
dams constructed in Australia for many years, the safety plane by cantilever action into the base foundation, as
of existing arch dams are required to comply with various well as horizontally by arch action into the abutments.
state dam safety regulatory requirements, which often Arch dams thus resist the water pressure and other loads
refer to, or are aligned with, the ANCOLD guidelines. by self-weight and by transmitting the load by arch action
into the valley walls or into concrete gravity thrust blocks.
ANCOLD has developed guidelines to enhance the ability
Typically the arch action reduces the bending (cantilever)
of dam organizations to assure that adequate safety
stresses and adds load carrying capacity. The abutments
programs and practices are in place. However, only three
guidelines cover particular types of dams, whilst the and foundations must therefore be of sufficient strength to
others deal generally with flood capacity and earthquake support the arch thrust.
design, and dam safety and environmental management Arch dam structures are curved towards upstream with
practices. Except for limited information regarding either single curvature (curved only in plan) or double
earthquake design in ANCOLD (1998), and selected curvature (curve both in plan and section). An arch-
information in ANCOLD (2013), none of them deals gravity dam or curved-gravity dam has the characteristics
specifically with arch dams design criteria. In the absence of both an arch dam and a gravity dam, but can be thinner
of a single recognized guideline covering the various than the pure gravity dam.
design aspects of arch dams, there is currently
An arch structure has to be monolithic to achieve
inconsistency in the underlying principles in the review
successful arch action, i.e. no structural discontinuities,
processes of arch dams in Australia. such as open joints or cracks, should exist at the time the
Since the last arch dam was constructed in Australia, a water load is applied.
number of international publications have been released
The shape and curvature of an arch dam, its contact with
on arch dam design practices, e.g. by the US Bureau of the foundation and the stability of the foundations are the
Reclamation (1977, 2006), USACE (1994) and FERC most important design features in providing stability and
(1999). These publications provide general information
favourable stress conditions. The desired stresses and
and guidance on the design of new arch dams, and for the
stability is achieved most economically by proper shaping
evaluation of the safety and structural integrity of existing
and the use of both horizontal and vertical curvature,
arch dams, including design criteria, material properties,
rather than by adding to the thickness of the dam.
loads and load combinations and evaluation procedures.
The ideal arch shape depends on the valley shape, with
This paper provides a summary of the current state of
typically a high degree of horizontal curvature in
practice for arch dam design criteria that have been
relatively narrow valleys, and poly-centred, parabolic or
adopted by these international dam organizations, and
elliptically shaped arches in wider sites.
compares that with the criteria provided in the updated
ANCOLD Guidelines on Design Criteria for Concrete Arch dams provide redundant load carrying capacity, i.e.
Gravity Dams (2013), with the view to provide a basis for if one part of the structure is overstressed, the load can be
consistent and unified design criteria for arch dams in transferred to other parts of the structure and transmitted
Australia. by arch action to the abutments. Where necessary to
reduce stresses in the rock, the thickness of the dam near Typical failure modes
the foundation can be increased by using a fillet, or
variable thickness arches, or abutment thrust blocks. Before considering the design criteria for arch dams, it is
useful to review some case histories and understand
Based on Reclamation (1977) arch dams are generally typical failure modes. Case history on arch dam failures
classified as a thin arch dam if the base thickness to or incidents is limited but available in various
height (b/h) ratio is 0.2 or less, a medium-thick arch dam publications. Tables 1 and 2 below provide a summary of
if the b/h ratio is between 0.2 and 0.3, and a thick arch some known failures and incidents, while ICOLD Bulletin
dam if the b/h ratio is 0.3 or greater. 120 (2001) contains more extensive lists of dams which
experience strong seismic ground motion.
Note 1
Table 1 Incident and failures of arch dams during normal operation and flood events

Name Completion Country Height When What happened

Lake Hodges 1918 USA 41 m 1918 Dam body damaged by cracked piers but did not completely fail.
Gleno 1923 Italy 44 m 1923 Dam failed when nine arches fell due to a poor masonry base.
Manitou Unknown USA 15 m 1924 Portion of the dam body failed due to deterioration of the concrete.
Moyie River 1923 USA 16 m 1926 Spillway erosion completely washed out one of the abutments. The
(Eileen) abutment was replaced and the dam is still in use.

Lake Lanier 1925 USA 19 m 1926 One of the abutments (cyclopean masonry) washed out as a result of the
failure of soft rock in the abutment. The remainder of the dam was
unharmed
Vaughn Creek 1926 USA 19 m 1926 The dam failed during first filling as a result of seepage and poor materials
in the dam.
Alla Sella Zerbino Unknown Italy 12 m 1935 The dam failed as a result of overtopping and sliding on its foundation.
Le Gage 1955 France 46 m 1955 The dam developed extensive cracking on both faces after first filling,
which worsened for the next 6 years. After the failure of Malpasset Dam,
Le Gage Dam was abandon and a new thicker arch dam was constructed
upstream.
Malpasset 1954 France 66 m 1959 The dam failed due to movement of the left abutment, thought to be due to
sliding on a rock wedge formed by intersection of a fault with gneissic
foliation in the rock.
Idbar 1959 Yugoslavia 38 m 1960 The dam failed during first filling as a result of piping and erosion of the
foundation.
Vajont 1959 Italy 276 m 1963 A huge landslide-generated wave overtopped the dam wall by an estimated
100 m. The dam suffered little damage, but the reservoir was a total loss.
Arequipa Unknown Peru Unknown 1965 The dam body failed as a result of fractures caused by a vibrating penstock
which passed through the dam.
Matilija 1949 USA 50 m 1965 The dam was judged to be unsafe as a result of deterioration of the
concrete due to expansive aggregate and poor foundation conditions. The
dam was decommissioned.
Zeuzier 1957 Switzerland 156 m 1978 The dam began to deflect upstream due to riverward movement of the left
abutment.
Koelnbrein 1979 Austria 200 m 1981 Cracks and substantial leakage appeared in the lowest foundation gallery
when the reservoir was 80% full two years after first filling. Full uplift
pressure was observed over the entire base in the central portion of the
dam. Major repair was undertaken between 1989 and 1994.
Meihua (Plum) 1981 China 22 m 1981 The experimental dam failed shortly after filling as a result of structural
failure due to excessive uplift movement along a peripheral joint. Evidence
was observed of sliding both in the arch and downstream direction. The
scheme was abandoned after failure.
Leguaseca 1958 Spain 20 m 1987 The dam body failed structurally, apparently due to deterioration due to
both aging and the effects of freezing and thawing.
El Fraile Unknown Peru 61 m Unknown The dam experienced a major slide on one of the abutments during filling.
The dam did not collapse. A concrete thrust block abutment was
constructed and the dam was saved.
Tolla 1960 France 90 m Unknown The dam experienced severe cracking and was buttressed in response.
Cracking may have been the result of large temperature stresses.
Note 1: Data obtained from FERC (1999) & ICOLD (2001)
 Note 1
Table 2 Incident and failures of arch dams during strong motion shaking

Earthquake Magnitude &

Name Completion Country Height Effects
Event Acceleration
Gibraltar 1920, 1990 USA 52 m Santa Barbara 6.3 (>0.3g) No damage resulted. The dam was modified
(1925) in 1990 with RCC.
Pacoima 1929 USA 113 m San Fernando 6.6 (0.6-0.8g) No damage resulted in the arch, but it
(1971) opened a joint between the arch and the
thrust block.
Northridge 6.8 (0.53g, >2.3g at It opened the joint (50 mm) between the arch
(1994) the crest) and thrust block.
Ambiesta 1956 Italy 59 m Gemona- 6.5 (0.36g at right No damage resulted.
Friuli (1976) abutment)
Rapel 1968 Chile 111 m Santiago 7.8 (0.31g) Damage resulted to the spillway and intake
1985 tower.
Maule 2010 8.8 (0.302g)
Techi 1974 Taiwan 185 m Chi Chi 1999 7.6 (0.5g at the base No damage resulted in the arch, with local
and 0.86g at the crest) cracking of the curb at the crest.
Maina di Sauris 1976 Italy 136 6.5 No damage
Shapai RCC 2003 China 132 m Wenchuan 8.0 (0.25 to 0.5g) No damage resulted.
2008
Note 2: Data obtained from Nuss et al (2012)

An arch dam may potentially fail as a result of: are cases of damage that did not result in dam failure.
• structural failure within the dam body due to Four cases involving dam body failure resulted from poor
overstressing of the concrete, or during earthquake construction materials or concrete material deterioration.
events due to excessive contraction joint opening Charlwood and Solymay (1995) reported 32 cases of
combined with cantilever tensile cracking, alkali aggregate reaction (AAR) in concrete arch dams.
• sliding along the dam-foundation interface, or Most of these dams were constructed prior to or while the
• movement of the abutment rock wedges formed by understanding of the AAR processes were still emerging.
rock discontinuities. A large number of arch dams subjected to AAR have
continued to function adequately, but in some cases
The above conditions could be the result of static loading
strengthening measures were required (Stewart Mountain,
during normal and flood conditions, and additional
Churchill and Gmued Dams), or partial replacement
dynamic loading during earthquake events.
(Matilija Dam), or complete replacement (Drum Afterbay
It is evident from Table 1 that concrete arch dams that Dam).
have performed well under normal operating conditions
As shown in Table 2 there are no known arch dam
will likely continue to do so unless something changes.
failures as a result of earthquake shaking. There is thus no
No arch dams are known to have failed statically within
direct empirical evidence to indicate how an arch dam
the dam body after five years of successful operation
would structurally fail under this type of loading. Payne
having reached its normal operating reservoir level,
(2002) conducted shaking table model studies to gain
although four incidents are shown where severe cracking
some insight as to how an arch dam might fail under
required remedial works.
earthquake shaking. In these tests:
Changes could result from plugging of drains leading to • failure initiated by horizontal (cantilever) cracking
an increase in foundation uplift pressures, possible across the lower central portion of the dam,
gradual creep that reduces the shear strength on potential • followed by diagonal cracking parallel to the
sliding surfaces, or degradation of the concrete from abutments,
alkali-aggregate reaction, freeze-thaw deterioration, or
• then cracking propagated through the model forming
sulphate attack.
isolated blocks within the dam, and
Under earthquake loading concrete arch dams will • eventually, the isolated blocks rotated and swung
respond according to the level and frequency of the downstream releasing the reservoir.
shaking, and the reservoir level at the time of shaking.
Unlike gravity dams, the most critical case for earthquake Vertical contraction joints possess very little or no tensile
loading of an arch dam might not be the reservoir full resistance and might repeatedly open and close during
scenario. A more severe overstress condition could result intense earthquake shaking. As postulated by Ghanaat
with the reservoir empty or partially filled. (2004), the contraction joint opening releases tensile arch
stresses but increases tensile cantilever stresses. The
Structural failure within the dam body increased cantilever stresses may exceed tensile strength
As shown in Table 1, there are no cases of failure within of the concrete or lift joints, causing horizontal cracks.
the arch dam bodies due to load overstressing, but there The resulting partially-free blocks bounded by the opened
contraction joints and cracked lift joints may become foundation. Sliding in the foundation typically occurs
unstable and cause failure of the dam (see Figure 1). along a single failure plane (plane sliding) or along the
line of intersection of two of these planes (wedge sliding).
To be kinematically capable of failure, the direction of
sliding surfaces must intersect or "daylight" a free surface
downstream from the dam. While it might be capable of
bridging a small unstable foundation block at the bottom,
large, unstable wedges of rock in the abutments could
endanger the safety of the arch dam.
For thin arch dams, sufficient movement may be
generated in the foundation during the shaking to cause
rupture of the dam body. Even if movement initiates but
does not cause dam failure, water forces acting on the
block planes may still increase as a result of the
movement. Stability analyses simulating post-earthquake
conditions are thus required to assess the likelihood of
post-earthquake instability.
Overtopping failure
Figure 1 Rotation of blocks caused by cracking and
opening of contraction joints (Ghanaat, 2004)
During large floods the arch wall could be subject to
overtopping and erosion of the abutments. Table 1
Dam-foundation interface failure includes one such case where overtopping erosion at the
contact zone resulted in sliding failure.
The dam-foundation interface includes the concrete-rock
contact, the concrete immediately above up to about the Although no arch dams are known to have failed statically
first lift joint, and the foundation rock typically 1 to 2 m due to overstressing within the dam body, a possibly more
immediately below the contact. serious condition occurs when there is an abutment
foundation block upon which the dam rests, that could
There are three types of potential sliding instability cases erode due to overtopping flows, or become unstable under
at the dam-foundation interface, i.e. sliding along the increased loading due to the flood conditions.
contact between the dam concrete and foundation rock,
within the concrete along lift joints, and along planes The loss of part of the abutment and foundation near or at
immediately below the contact. the toe of the arch wall could enable plane or wedge
sliding by exposing (daylighting) sliding planes, by
Sliding instability for the first two cases are less likely removing passive resisting rock, or by changing the
because of the wedging produced by arch action and deformations of the dam and redistribution of stress state
embedment of the structure into the rock. However, arch at the region and applying more forces to the wedge.
dams with relatively flat abutment slopes, or arch dams
with abutment thrust blocks supported by rock It is important to perform abutment stability analyses
foundations with inadequate shear strength, could be under flood loading considering the increase in dam thrust
susceptible to sliding along the foundation contact or on the foundation blocks and the increased hydrostatic
along planes immediately below the contact, in either or forces on the block bounding planes.
both the arch and downstream directions. Existing design references
Severe earthquake shaking could break the bond between A number of internationally recognised design guidelines
the dam and foundation, or cause movement along planes and manuals applicable to arch dams have been published
below the contact, especially if the foundation was not since 1953, as listed below. This list is not exhaustive and
excavated to radial lines and the excavation surfaces dip several other guidelines and manuals could be applied to
downstream on sections cut radial to the dam axis. arch dams, e.g. regarding site investigations, spillways,
Resulting sliding and rotation at the base could lead to outlet works and dam safety management practices.
loss of arch action and subsequently to instability.
United States Bureau of Reclamation
Foundation failure • Guide for Preliminary Design of Arch Dams (1977)
Actual arch dam failures have resulted from foundation • Design of Arch Dams (1977)
deficiencies, which included sliding of large blocks • Design Criteria for Concrete Arch and Gravity Dams
bounded by geologic discontinuities within the foundation (1977)
and abutments, or along planes of weakness (three failure
• Guidelines on Foundation and Geotechnical Studies
cases and three incidents shown in Table 1).
for Existing Concrete Dams (1999)
Although no arch dam foundations are known to have • State-of-Practice for the Nonlinear Analysis of
failed because of earthquake shaking, they have not been Concrete Dams at the Bureau of Reclamation (2006)
subjected to unprecedented seismic design loads.
United States Army Corps of Engineers
The most critical mode of foundation instability involves
• Arch Dam Design, EM 1110-2-2201 (1994)
sliding on discontinuities (joints, faults, shears, bedding
planes, foliation, clay seams, shale beds etc.) within the
• Response Spectra and Seismic Analysis for Concrete distributions in concrete dams and foundations, to
Hydraulic Structures, EM 1110-2-6050 (1999) establish ranges of shear and tensile strengths and
• Time-History Dynamic Analysis of Concrete cohesion values typical of concrete (parent concrete,
Hydraulic Structures, EM 1110-2-6051 (2003) bonded and unbonded joints), and concrete to rock
• Stability Analysis of Concrete Structures, interfaces (EPRI, 1992). In the absence of site specific
EM 1110-2-2000, (2005) testing, this document provides valuable information.
• Earthquake Design and Evaluation of Concrete The determination of the condition of the lift joints and
Hydraulic Structures, EM 1110-2-6053 (2007) the overall strength of the dam based on limited available
testing remains a challenge for dam engineers. Over the
Reclamation and USACE have also prepared the last 50 years Reclamation has performed strength and
following joint publication: frictional tests on numerous concrete dams of different
• Best Practices in Dam and Levee Safety Risk ages, with construction dates ranging from 1905 to 1993.
Assessment, Chapter 21 – Risk Analysis for Concrete Dolen (2011) processed the data of these tests and
Arch Dams, (2010) reported on the strength and frictional properties of parent
United States Federal Energy Regulation concrete and lift joints, grouping the results by dam ages.
Commission In the absence of site specific information this data
provides valuable information to understanding the joint
• Engineering Guidelines for the Evaluation of
strength in relation to construction practices over the
Hydropower Projects, Chapter 11 – Arch Dams (1999)
years.
ANCOLD Dolen presented ratios of bonded to unbonded lift joints
ANCOLD has no publications specifically for arch dams; for dams of different ages. A practical approach to
however ANCOLD (1998) contains guidance related to account for the portion of lift joints that are not bonded in
earthquake design of arch dams, while ANCOLD (2013) the global lift strength properties, as proposed by Dolen,
contains information that could be applied to materials consists of reducing the average test values based on the
and load conditions for concrete dams in general. estimated fraction of bonded lift joints.
The remainder of this paper draws to a large extent on the
Loads
information provided in the above references.
General
Material parameters
Reclamation, USACE, FERC and ANCOLD all have the
Reclamation, USACE, FERC and ANCOLD all have same design loads and generally the same definitions,
similar approaches in defining material properties and although some of the references define the load types in
they often refer to the same past studies and reports for more detail.
typical values.
Arch dams are designed for the same loads as gravity
The material parameters for both the dam wall and dams with the exception of the temperature load which
foundations are project and site specific. Due to limited has a significant influence in arch dam design.
space this paper cannot discuss this topic in sufficient
detail and the reader is therefore referred to the extensive The loads for which arch dams must be designed can be
coverage of this topic in the design references listed in the categorized as static or dynamic loads. Static loads are
previous section. However, it is emphasised that a sustained loads that do not change, or change very slowly
thorough knowledge must first be gained on a dam's compared to the natural periods of vibration of the
original design and its performance history and records, to structure, e.g. dead load, hydraulic load, loading from silt
provide a basis for evaluation and any further studies and and backfill materials, dynamic forces from flowing water
investigations that might be required. changing direction, uplift, forces from ice expansion or
impact, and stresses caused by temperature changes.
The dam and foundation material parameters should be
determined on the basis of field and laboratory Dynamic loads are transitory in nature and typically
investigations. In assigning strength and stiffness seconds in duration, e.g. earthquake-induced forces, blast-
parameters for the foundations, it is essential to firstly induced forces, fluttering nappe forces, or forces caused
derive a proper geological model for the foundations. This by the impact of ice, debris, or boats. Because of the
should be undertaken by a geologist with assistance where speed at which they act, the inertial and damping
appropriate, by a rock mechanics expert. In most cases, characteristics of the dam as well as its stiffness affect the
the required parameters will be determined by rock dam's behaviour.
defects rather than by the rock mass. Dead load
Where the field or laboratory determination of certain Dead load includes the weight of both the concrete and
material parameters is neither cost effective nor appurtenant structures (gates, bridges, and outlet works).
conclusive, the parameters can be estimated by existing The dead load is normally imposed on cantilever
correlation relations or using the same parameters in monoliths prior to the grouting of the contraction joints
similar projects. In these cases, their effects on the dam (no arch action) and should be taken into account when
response should be evaluated by parameter sensitivity analysing an arch dam, which is different to applying the
analyses. The USA Electric Power Research Institute self weight of a gravity dam. The weight of appurtenances
investigated the factors that influence uplift pressure is typically negligible compared to the dam itself;
however, massive outlet works and overflow ogee weir analysis for simplicity (FERC, 1999). However, if
spillways may have noticeable effects on the static and tailwater affects uplift pressure on a failure plane on
dynamic stresses. which sliding stability is being analysed, tailwater uplift
should still be considered.
Temperature load
Temperature loading is the most important difference Uplift and pore water pressures
between gravity and arch dams analysis. The temperature Uplift or pore water pressures develop when water enters
load in arch dams results from the differences between the the spaces and cracks within the body of an arch dam, as
closure temperature and concrete temperatures in the dam well as in the foundation joints, cracks, and seams.
during its operation.
During static loading conditions the effect of pore water
The closure temperature is the concrete temperature at the pressure is to reduce normal compressive stresses within
time of grouting of the contraction joints. It can also be the concrete and to increase the corresponding normal
considered as the stress-free temperature, i.e. there will tensile stresses should they exist. Considering the
not be any thermal stresses in the dam as long as the cumbersome process to include pore pressures in finite
temperature of the dam remains at the closure element models, combined with the relatively minor
temperature. However, once the average concrete change in stress, pore pressures and their effects within
temperature through the thickness exceeds the closure arch dams have often been ignored in the absence of any
temperature, the resulting positive temperature loading cracks. McKay & Lopez (2013) proposed a practical
will cause compressive stresses in the arches, which in methodology for including uplift and pore pressures.
turn will result in deflection into the reservoir. The
According to FERC (1999) uplift does not need to be
opposite happens when in the winter the concrete
considered in the stress analysis for thin arch dams. Uplift
temperature drops below the closure temperature and the
should always be considered in the sliding stability
arches experience tension which causes downstream analysis and be applied as external loads on both faces of
deflection. tensile cracks at the dam-foundation interface. In the
There are two ways which are generally adopted for absence of field data and seepage analysis, uplift can be
defining the internal concrete temperature causing loading represented as described in ANCOLD (2013).
and thermal stress: conduct steady state temperature
Silt load
calculations based upon water and air face temperatures
(such as USACE (1994) or Stucky and Derron (1957) for The need to apply silt pressure in arch dam analysis
nonlinear distribution of temperature through the dam depends on the sediment depth. According to FERC
thickness), or assume a cyclic variation of ambient (1999) for U-shaped and broad base arch dams, sediment
temperature with respect to time (seasonal variations) and depth of less than 0.25 of the dam height produces
conduct a harmonic temperature analysis, with due regard negligible deformations and stresses, and thus their effects
being given to the time dependant temperature condition may be ignored. For V-shaped dams the effects of silt
of the reservoir water. pressure may be ignored if the depth of sediment is less
than 0.33 of the dam height.
In the case of old arch dams where construction
methodology, vertical joint treatment and construction Ice load
timing are unknown, a practical approach is to adopt the Although uncommon in Australia, ice can produce
average ambient temperature as the closure temperature. significant loads against the face of an arch dam and must
However, it would be advisable to undertake a sensitivity be considered where reservoir freezing can be expected.
analysis using the average summer and average winter Static ice loads is produced by the ice in contact with the
temperatures as the closure temperature. dam when the reservoir is completely frozen, and
Further details about temperature loading are contained in dynamic ice loads by sheets of ice colliding with the dam.
USACE (1994) and Stucky and Derron (1957). Hydraulic loading of spillways
Hydrostatic hydraulic loads Forces produced by discharge through a spillway located
Reservoir and tailwater loads on an arch wall are usually insignificant and typically
ignored. USACE (1992) provides methods for
Water loads include hydrostatic pressures on the dam determining spillway pressures if hydrodynamic forces
faces resulting from the reservoir and tailwater during the
could affect the dam.
normal and flood conditions. Unlike a gravity dam for
which higher reservoir levels would result in more critical Arch dams with overflow spillways can also be subject to
cases, an arch dam may experience higher tensile stresses forces produced by a fluttering nappe, which is caused by
on the downstream face under low reservoir levels. resonance between air trapped in the cavity between the
nappe and the downstream face of the dam, as well as by
As tailwater acts in the opposite direction than the
spillway gates that transfer dynamic loading to the top of
headwater, it reduces the deformations caused by the
the dam. Such vibrations could be of importance to the
headwater and thus reduces both tensile and compressive
safety of tall and thin arch dams. The phenomenon, and
stresses below the tailwater levels. This effect is methods to prevent such vibrations, is thoroughly
negligible when the tailwater depth is less than 20% of the described in ICOLD (1996).
dam height. Below this level it is generally considered
conservative to then ignore tailwater loads in the stress
Hydrodynamic hydraulic loads ANCOLD (1998) guidelines) is the highest adopted
magnitude the dam is required to withstand. The dam is
As the dynamic interaction that occurs between the
allowed to respond nonlinearly and suffer significant
reservoir and the dam during an earthquake can have a
damage, but without a catastrophic failure. The SEE to be
significant effect on the earthquake response of the dam,
it must be considered in the dynamic analysis. Because used in the analysis of arch dams is defined in ANCOLD
the inertia force of a structure is a function of acceleration (1998), which is currently under review.
and mass, hydrodynamic interaction has a larger influence For preliminary linear response spectra analysis, site-
on thinner, less massive dams. There are three specific response spectra of earthquake ground motions
formulations for modelling hydrodynamic interaction: should be developed by experienced seismologists. The
• use of lumped mass (e.g. determined using the spectra should be developed for 5% damping, and
relationships or factors provided to obtain response
Generalised Westergaard theory of added mass to
spectra for higher damping ratios (as high as 10%) if
model incompressible fluid);
required for the analysis. These relationships or factors
• incompressible fluid finite element equivalent added may be based on a documented site-specific study;
mass; and alternatively, the relationships presented by Newmark and
• compressible fluid added mass, added damping and Hall (1982) may be used.
added forces with and without reservoir absorption.
For more detailed linear and non-linear time-history
Westergaard’s theory of added mass, as developed in
analysis, acceleration time histories of ground motions
1931, is reasonably appropriate only when assuming
should be developed consistent with the latest guidelines
incompressible reservoir acting on a rigid straight gravity
as for example contained in FERC (1999) and USACE
dam perpendicular to a wide valley, and with a vertical
(2003). Acceleration time histories should be developed
upstream face. For curved surfaces like arch dams, a
for three components of motion (two horizontal and one
Generalized Westergaard Method accounts for dam
vertical). Time histories may be either (a) recorded or
curvature and dam flexibility (Kuo, 1982). This method
simulated-recorded time histories or (b) response
assumes that the hydrodynamic pressure at any point on
spectrum matched time histories. For recorded or
the upstream face is proportional to the total acceleration
simulated-recorded time histories, a minimum of three
acting normal to the dam at that point. The application of
sets of recordings should be used.
the Generalised Westergaard method is described in more
detail in FERC (1999) and Reclamation (2006). Recorded earthquake ground motions at Pacoima Dam
during the 1994 Northridge earthquake indicated that the
Incompressible fluid formulations ignore the
seismic input for arch dams might vary along the dam
compressibility of water and assume the reservoir floor
foundation interface. At present time scarcity of data
and the upstream extent of the reservoir are rigid and
prevents a realistic definition of such non-uniform free-
ignore accelerations at these locations. Thus, the pressures
field motions for arch dams, even though procedures for
induced on the dam from accelerations applied to the
handling non-uniform input have been developed. In view
reservoir bottom are ignored.
of these difficulties, the use of standard uniform seismic
Modern finite element analysis (FEA) software input is currently still acceptable.
incorporates compressible water effects, which model the
interaction between dam and reservoir and the proper Loading Combinations
transmission of pressure waves in the upstream- Arch dams are designed for two groups of loading
downstream direction. The use of compressible water combinations. The first group combines all the static
effects is described in USACE (1999 & 2003) and loads and the second group takes into account the effects
Reclamation (2006). of earthquake. In addition, depending on the probability
Fluid elements are used to model the reservoir-dam and of occurrence of the cases in each group, they are
reservoir-foundation interaction more accurately. A three- categorised as Usual, Unusual, and Extreme loading
dimensional mesh of fluid elements is developed to combinations.
represent the reservoir. The use of fluid elements is Table 3 on the next two pages presents a summary of the
described in Reclamation (2006). static and dynamic loading combinations used by
Earthquake load Reclamation, USACE, FERC and ANCOLD, including
the loading combination categories. Although having a
Arch dams are expected to respond linearly under the similar approach, they differ with regard to categorising
Operational Basis Earthquake (OBE), assuming certain loading combinations. The designer should
continuous monolithic action along the entire length of however assess each load case to ensure that it is
the dam. If damage did occur, it should be possible to applicable to the project and that it is properly classified
repair it while the dam remains operational. under one of the three categories.
The SEE (Safety Evaluation Earthquake, to replace
Maximum Design Earthquake in the update of the
 Note 1
Table 3 Summary of loading combinations

USACE (1994) Reclamation (1977 & 2006) FERC (1999) ANCOLD (1998) Note 2 ANCOLD (2013) Note 2 Proposed for arch dams

Static Usual
D + Tw + Hx + U Reclamation (2006): D + Tw + Hx + S + I + U D + Tw + Hn+ S/B + I + U D + Hn+ S/B + U + I D + Tw + Hx + S/B + U + I
D + Ts + Hx + U D + Hn+ Tw + U D + Ts + Hx + S + U D + Ts + Hn+ S/B + U D + H50 + S/B + U D + Ts + Hx + S/B + U
D + Hn+ Tx + U D + Hn+ Ts + U PQ: D + Hn+ S/B + U + I (If Hx is uncertain, check for Hl and Hf.)
Reclamation (1977): D + H50 + Tx + S/B + U
D + Tw + Hx + S + I + U D + Hn+ Tx + S/B + U + I
D + Ts + Hx + S + U
D + Hn+ Tx + S + I + U
D + Hl + Tx + S + I + U
Static Unusual
Note 3 Note 4
D + Hs + Tx + U Reclamation (2006): D + Hl + Tx + S + U D + Tw + Hf + S/ B + U D + H500-H2000 + S/B + U D + H500-H2000 + Tx + S/B + U
D + Hl + Tx + U Note 4 D + Hl + Ts + U Note 4 D + He + Tx + S + U Note 4 D + Ts + Hf + S/B + U PQ: D + H50 + S/B + U PQ: D + H50 + Tx + S/B + U
D + He + Tx + U Note 4 D + Hf + Tw + U D + Ts + Hf + S + U D + H100 + S/B + Ubd D + H100 + Tx + S/B + Ubd
Reclamation (1977): D + Tw + Hf + S + I + U D + H100 (1 gate closed) + S/B + U D + H100 (1 gate closed) + Tx + S/B + U
D + Hf + Tx + U D + Tx + Hf + S + I + U D + H100 + S/B + U + Wind seiche D + H100 + Tx + S/B + U + Wind seiche
and wave action and wave action
D + Hl / He + Tx + S/B + U Note 4
Static Extreme
D + Hf + Tx + U D + Hf + S/B + U + I D + Hf + Tx + S/B + U + I
D + H100(>1 gate closed) + S/B + U D + Hf + Tw + S/B + U + I
D + Hlw + S/B + U D + Hf + Ts + S/B + U + I
D + H100(>1 gate closed) + Tx + S/B + U
D + Hlw + Tw + S/B + U
Dynamic Unusual
OBE + D + Hn+ Tx + U OBE + D + Tw + Hn+ S/B + I + U OBE + D + Hc + S/B + U OBE + D + Hn+ Tw + S/B + U
OBE + D + He + Tx + U OBE + D + Ts + Hn+ S/B + U OBE + D + Hn+ Ts + S/B + U
OBE + D + Tw + He+ S/B + I + U OBE + D + He / Hl + Tw + S/B + U
OBE + D + Ts + He+ S/B + U OBE + D + He / Hl + Ts + S/B + U
Table 3 continued

USACE (1994) Reclamation (1977 & 2006) FERC (1999) ANCOLD (1998) Note 2 ANCOLD (2013) Note 2 Proposed for arch dams

Dynamic Extreme
SEE + D + Hn + Tx + U Reclamation (2006): SEE + D + Tw + Hx + S + I + U SEE + D + Hc + S/B + U SEE + D + Hn+ S/B + U SEE + D + Hn+ Tw + S/B + U
SEE + D + Hn + Tc + U SEE + D + Ts + Hx + S + U SEE + D + Hn+ Ts + S/B + U
SEE + D + Hn + Tw + U SEE + D + He / Hl + Tw + S/B + U
SEE + D + Hn + Ts + U SEE + D + He / Hl + Ts + S/B + U
Reclamation (1977):
SEE + D + Tw + Hx + S + I + U
SEE + D + Ts + Hx + S + U
SEE + D + Hn + Tx + S + I + U
SEE + D + Hl + Tx + S + I + U

Hn: Usual (normal) reservoir level with associated tailwater level H50: 1in 50 AEP reservoir level with associated tailwater level Tx: Temperature at the time D: Dead load including appurtenances
Hx: Reservoir level at the time with associated tailwater level H100: 1in 100 AEP reservoir level with associated tailwater level Ts: Summer temperature U: Uplift
Hl: Lowest operating reservoir level with associated tailwater level H500: 1in 500 AEP reservoir level with associated tailwater level Tw: Winter temperature Ubd: Uplift with blocked drains
He: Empty reservoir level with no tailwater level H2000: 1in 2000 AEP reservoir level with associated tailwater level S: Silt (if applicable)
Hc: Critical reservoir level with associated tailwater level B: Backfill against dam (if applicable)
Hf: Maximum flood reservoir level with associated tailwater level I: Ice (if applicable)
Hlw: Landslide generated wave reservoir level with normal tailwater level PQ: Post earthquake

Notes:
1. This table contains a collation of loading combinations proposed by the respective publications. Not all the cases would apply to a specific dam and the design should use judgement in selecting the
combinations and categorising them.
2. The combinations for ANCOLD (1998) and ANCOLD (2013) were developed for gravity dams and are included here with the view to achieve proposed combinations for arch dams that are reasonably
consistent with these ANCOLD guidelines.
3. This case applies only to dams that are normally at a low level or empty, such as flood retention dams.
4. For flood retention dams these cases should be considered under Usual Static.
5. Uplift should be determined by the reservoir level and tailwater level taking into account any foundation drains.
6. Silt, backfill against the dam and ice should be included only if applicable.
Table 4 Summary of factors of safety
USACE Reclamation ANCOLD ANCOLD Proposed for
Parameter FERC (1999) Range
(1994) (1977 & 2006) (1998) Note 1 (2013) Note 1 arch dams
Static Usual
3.0-not more
Compression 4.0 than 10.3 MPa 2.0 4.0 3.3 2.0-4.0 3.3
(4.0) Note 2
Not more than
Tension 1.0 1.0 1.0 1.0 1.0 1.0
1.03 MPa
Sliding 2.0 3.0 1.5 (2.0) Note 3 1.5 – 2.0 1.5 / 2.0 / 3.0 Note 4 1.3-3.0 1.5 / 2.0 / 3.0 Note 4
Static Unusual
2.0 not more
Compression 2.5 than 15.5 MPa 1.5 2.7 2.0 1.5-2.7 2.0
(2.7) Note 2
Not more than
Tension 1.0 1.0 1.0 1.0 1.0 1.0
1.55 MPa
Sliding 1.3 2.0 1.5 1.3 – 1.5 1.3 / 1.5 / 2.0 Note 4 1.3-2.0 1.3 / 1.5 / 2.0 Note 4
Static Extreme (maximum flood condition only)
Note 5 Note 5 Note 5
Compression 1.5 1.3 1.3-1.5 2.0
Note 5 Note 5 Note 5
Tension 1.0 1.0 1.0 1.0
Note 5 Note 5 Note 5
Sliding 1.1 1.1 / 1.3 / 1.5 Note 4 1.1-1.5 1.3 / 1.5 / 2.0 Note 4
Dynamic Unusual (cases including OBE)
2.0 not more
Compression 2.5 than 15.5 MPa - 2.7 2.0 2.0-2.7 2.0
(2.7) Note 2
Not more than
Tension 1.0 - 1.0 1.0 1.0 1.0
1.55 MPa
Sliding 1.3 2.0 - 1.3 – 1.5 1.3 / 1.5 / 2.0 Note 4 1.3-2.0 1.3 / 1.5 / 2.0 Note 4
Dynamic Extreme (cases including SEE)
Compression 1.5 1.0 (1.3) Note 2 1.1 1.3 1.3 1.1-3.0 1.3
Tension 1.0 1.0 1.0 1.0 1.0 1.0 1.0
Sliding 1.1 1.0 1.1 1.2 – 1.4 1.1 / 1.3 / 1.5 Note 4 1.0-1.5 1.1 / 1.3 / 1.5 Note 4
Notes:
1. These guidelines were developed for gravity dams.
2. Values in brackets are for the foundations.
3. Value in brackets is for internal shear.
4. Factors are for “Residual strength c’ and ’ well-defined” / “Peak strength c’ and ’ well-defined” / “Peak strength c’ and ’ not well-defined”
(refer ANCOLD (2013) for further explanation of these conditions).
5. These references included maximum flood in the static unusual category.
6. The factor of safety for allowable tensile strength should be applied to the concrete under consideration, i.e. either the parent or lift joint strength.

Acceptance criteria first. The tensile strength of the concrete is however an

important consideration, particularly in estimating seismic
The structural integrity of an arch dam is maintained and safety of concrete arch dams.
it is considered safe if overstressing, sliding and other
possible modes of failure will not occur. As discussed by Gillan et al (2011) the general stress-
strain behaviour of concrete can be characterized in four
Reclamation, USACE, FERC and ANCOLD differ stages:
slightly in the values assigned to determine the allowable
stresses and the factors of safety against sliding. • In the first stage the stress-strain curve is considered
to be linear elastic, i.e. there would be no permanent
Table 4 presents the factors of safety used by each of the deformation. According to ACI (1996) mass concrete
organisations for the allowable stresses and stability. This material behaves linearly up to approximately 35 % of
table also includes the factors suggest by the authors of the ultimate strength.
this paper when assessing arch dams in accordance with
• In the second stage the stress-strain curve consists of
ANCOLD guidelines, as further discussed below.
some inelastic behaviour (cracking). The load would
Allowable stress result in minor permanent deformations and strains in
The ultimate load-resisting capacity of an arch dam is the material. According to ACI (1996) the growth of
determined by the compressive strength of the concrete, internal microcracks commences in the concrete at
unless foundation or another mode of failure occurred
 loads equal to approximately 35 to 50 % of the In Table 4 for all the cases the factor of safety for
ultimate strength. allowable tensile stress is unity. The intent of any design
• The third stage consists of large inelastic strains, so should be to minimize or limit tensile stresses to localized
that there is a noticeable change in deformation. In areas by reshaping and / or redesigning the dam. A dam
this stage there is stable crack growth in the concrete, designed with high tensile stresses in too many areas,
meaning that cracks will form but not initiate failure. even though within the allowable limits, might exceed the
• The fourth stage is the fracture stage where compressive limits under one or more loading
deformations are great enough to produce unstable combinations. When the tensile strength of the concrete is
crack grow and eventual failure of the concrete. exceeded and cracking occurs, the uncracked portion of
the cantilever would tend to carry more compression
The above mentioned concrete behaviour was considered while also increasing the balance of the loads carried by
when comparing the factors of safety given in the existing the arches. If the cracking becomes widespread, too much
references and suggesting factors to be adopted for arch of the load would have to be carried by the arches. The
dams. For load combinations in the Static Usual category uncracked portion of the cantilevers could exceed the
it is assumed that the concrete behaviour is limited to the compressive strength of the concrete and cause crushing
linear elastic first stage and a factor of safety for failure of the concrete. Subsequent joint opening and
compressive strength of 3 would be appropriate, with 3.3 cracking and load redistributions might eventually
adopted in ANCOLD (2013). Compared to the factors exhaust the capacity of the concrete, or might form
used provided in the references by USACE, Reclamation surfaces along which partial sliding could occur.
and FERC, the same factors as used in ANCOLD (2013) Therefore, since compression is the dominant mode of
is suggested for arch dams. failure of an arch dam, and since the other concrete
For the less frequent load combinations in the Static properties are a function of the compressive strength, a
Unusual, Static Extreme and Dynamic Unusual categories more conservative approach is taken in establishing the
it is assumed that the concrete behaviour is limited to the allowable compressive stresses compared to the allowable
second stage, which can result in microcracking and tensile stresses.
minor permanent deformations and strains in the concrete Pursuant to the above, one of the objectives in arch dam
that would not affect the operation of the dam. Therefore, design is minimizing the magnitude and the locations of
a factor of safety for compressive strength of 2 to 3 would tension in the dam. Tensile stresses are however inherent
be appropriate, with 2.0 adopted in ANCOLD (2013). to most arch dams and therefore require further
Compared to the factors provided in the references by consideration.
USACE, Reclamation and FERC, the same factors as
used in ANCOLD (2013) is suggested for arch dams, Arch dams typically exhibit tensile stresses at the
except for the Static Extreme category, as discussed in the downstream face along the foundation under the low
second paragraph below. reservoir – high temperature conditions, which includes
the construction period. This condition is regarded as a
For the rare load combinations in the Dynamic Extreme significant problem as long as the stability of the
category (SEE) it was assumed that the concrete cantilevers is not in question. Even if some cracking has
behaviour is limited to the third stage. This assumes that occurred, the additional hydrostatic load and the resulting
the concrete may crack and experience permanent downstream deflection will cause the cracks to close.
deformations and damage due to the load, but not enough Tension at the upstream face of the dam however requires
to cause failure. A factor of safety for compressive more careful consideration, due the possibility of a
strength of 1.1 would be appropriate, with 1.3 adopted in seepage path through the dam if cracks were to develop
ANCOLD (2013). Compared to the factors provided in and extend through the thickness of the dam. Cracked
the references by USACE, Reclamation and FERC, the cantilevers do not necessarily imply a dam failure, as
same factors as used in ANCOLD (2013) is suggested for loads carried by the cantilevers before cracking will be
arch dams. transferred to the arches and adjacent cantilevers. A
ANCOLD (2013) adopted only one set of criteria for the nonlinear analysis is required to ensure that the
Extreme category, which includes both the maximum compressive stresses of the remaining uncracked section
design flood and the maximum safety evaluation of the cantilever and the other arches and cantilevers
earthquake, although they relate to the static and dynamic remain within the allowable concrete stresses.
strength parameters respectively. This implies that for the As already mentioned the current engineering guidelines
flood load condition concrete behaviour is allowed recommend a factor of safety of 1.0 to determine the
beyond the second stage, i.e. in the third stage which allowable tensile stresses. The authors believe that this
includes cracking and permanent deformation. Whereas factor should be used with caution and only be used when
the SEE loading is a cyclic loading, the extreme flood extensive testing has been undertaken so that sufficient
condition is a sustained loading. The authors believe that statistical data is available to estimate the existing tensile
the factors in ANCOLD (2013) for the flood loading strength with confidence.
condition (Static Extreme) may be too low and the
allowable behaviour of the concrete should be limited to In the absence of tensile strength data of the concrete,
the second stage for which the factor of safety for Chopra (1994) suggested that the tensile-compressive
compressive strength of 2 to 3 would be appropriate. strength relationships determined by Raphael (1984)
could be used if sufficient compressive strength data is
available.
When assessing existing dams with insufficient or no in the analysis to provide a more realistic idealisation of
construction records, the number of tensile strength tests the structural system.
are usually limited and insufficient to make reliable
Method of analysis
statistical correlations. This could lead to overestimating
the existing tensile strength of the concrete when applied Three-dimensional finite element analysis is preferred for
to the entire dam. It is therefore deemed appropriate to the static and dynamic analysis of arch dams. The trial
apply a strength reduction factor and assume a lower and load method is considered outdated, but may still be used
more conservative tensile strength for the entire dam. for preliminary static stress analysis only if the dam has a
simple geometry and uniform material parameters can be
The ACI Building Code (ACI, 2008) states that one of the assumed for the concrete and for the foundation rock in a
reasons for strength reduction factors is to account for low hazard area. Other mathematical formulations and
potential understrength members due to variations in
approaches can also be employed, but the accuracy of
material strengths and dimensions. In plain (mass)
such methods should be verified by comparison with the
concrete, since both flexural tension strength and shear
finite element analyses
strength depend on the tensile strength characteristics of
the concrete, with no reserve strength or ductility possible With the development of the finite element method, the
due to the absence of reinforcement, equal strength advances in dynamic analysis procedures and the
reduction factors for both bending and shear are availability of high capacity computers, the older
considered appropriate. Consequently, ACI suggests a traditional methods of analysis have been abandoned. The
strength reduction factor of 0.6 for bending and shear, use of the finite element analysis technique, with its
based on reliability analyses and statistical studies of versatility and capability to deal with structural,
concrete properties, as well as calibration against past geotechnical and fluid aspects, allowing a more realistic
practice. A practical approach is therefore to apply the analysis of virtually any type of dam, has become the
strength reduction factor of 0.6, as suggested by ACI for standard practice for dam design and analysis.
tensile strength in plain concrete, to determine the Different elements have been used in the past to model
existing tensile strength of the concrete when only limited arch dams, including shell elements and solid elements.
testing has been undertaken. The factors of safety for Shell elements (with five or six degrees of freedom) are
tension as given in Table 4, are then applied to the consistent with the behaviour of the dams; however they
reduced tensile strength in order to estimate the allowable are unable to accurately model stress distribution through
tensile strength. the dam thickness. Therefore, three dimensional
Stability of cantilevers during construction brick/solid elements (with three degrees of freedom) are
now routinely used for the analysis.
As arch dams are constructed in monoliths, because of the
vertical curvature, the monoliths may be unstable against Evaluation for static loading
overturning prior to the grouting of the monolith joints Idealization of the dam and an appropriate portion of the
and the filling of the reservoir. When assessing the foundation rock as an assemblage of finite elements is the
construction phase dam empty case, the stability of the first step in a typical finite element static analysis. Each
cantilevers must be assessed to assure that each cantilever individual static load case as explained in the previous
is stable at different stages of construction. sections is applied to the model separately and the results
Dynamic loading should be obtained and reviewed to facilitate examination
of the consistency of the results. The load cases are then
Establishing the acceptability of performance of arch
combined based on proposed load combinations and
dams under dynamic load cases is a complicated process
finally the system is solved to determine displacements at
which cannot be summarized in a table and is discussed in
nodal points of the assembled structure, stresses computed
the next section under “Analysis methods and at various locations (such as the Gauss integration points)
evaluation”. The factors of safety given in Table 4 are
and arch thrusts and shears exerted on the dam abutments
only the first step in determining the safety criteria and
and / or thrust blocks.
should not be regarded as absolute limits. These factors
should be applied to the test results for the appropriate At each nodal point, three displacement components
rate of loading as indicated by the dynamic analysis, or as corresponding to a global system of axes are computed.
determined for the static analysis and modified according The magnitudes and deflected shapes of the resulting
to the approach discussed by Raphael (1984). displacements provide important data that can be used to
visually evaluate the overall behaviour of an existing dam
Analysis methods and evaluation (or acceptability of a new design), although the
Concrete arch dams are complex three-dimensional shell magnitudes of the resulting deformations are not directly
structures that rely on both cantilever action (on vertical used in safety evaluation of arch dams. The deflection
planes) and arch action (on horizontal planes) for patterns should vary smoothly from point to point and are
transferring the loads to the foundation, which is deemed used to evaluate the adequacy of the design/analysis by
to include the entire length of concrete rock interface. visual means.
Hence, two dimensional analyses cannot provide realistic Since maximum stresses in an arch dam usually occur at
results and the three dimensional geometry of the dam, the faces of the structure, normal stresses resolved into
foundation and reservoir (if required) has to be considered arch, cantilever and principal stresses at the upstream and
downstream faces of the dam are the primary stresses
used for the evaluation of the analysis results. However, be interpreted as being positive (e.g. tensile stress) or
shear stresses induced in the body of the dam by bending negative (e.g. compressive stress). In the response-
and twisting moments should also be examined to assure spectrum method, total stresses are estimated by linear
that they are within the allowable limits. The evaluation combination of the dynamic stresses with static stresses
of the safety of an existing dam involves comparing the due to the usual loading combination and compared with
maximum computed stresses with the allowable the allowable values. This method requires a qualitative
compressive and tensile strengths of the concrete. The judgement of how stresses will be redistributed during
largest compressive and tensile stresses should be less joint opening and cracking. This evaluation is done in lieu
than the corresponding allowable strengths of the concrete of more prolonged time-history analysis. This approach is
considering the factors of safety established in Table 4 for not sufficient for some situations and a more detailed
each particular loading combination. analysis using time-history techniques may be required.
Whenever the overall stresses in the structure are below The evaluation criterion for time-history analysis is more
the allowable values as specified in the previous sections, involved than simple stress checks. As described by
the design is considered to be adequate or the existing Ghanaat (2004), a systematic interpretation and
dam is safe from stress distribution through the dam wall evaluation of these results in terms of the stress demand-
point of view. A well-designed arch dam will develop capacity ratios, cumulative overstress duration, spatial
only compressive stresses under the static loads and these extent of overstressed regions, and other considerations
are generally much smaller than the allowable form the basis for an approximate and qualitative estimate
compressive strength of the concrete. of damage (see Figure 2). This evaluation is applied to the
damage control range of strains. If the estimated level of
The stress results produced by the linear finite element
analysis usually indicate some areas of tensile stress in the damage falls below the acceptance threshold for a
particular dam type, the damage is considered to be low to
dam. Whilst tensile strength of the parent concrete could
moderate and the linear time-history analysis would
be high, it should be kept in mind that a typical arch dam
suffice. Otherwise the damage is considered to be severe,
is made of concrete blocks divided by lift joints and
requiring a non-linear time-history analysis to determine
vertical contraction joints, with lower tensile and shear
strengths than the parent concrete (or even a pre-existing whether or not it would lead to failure of the dam.
crack with no tensile strength). Therefore it is not Horizontal lift joints and vertical contraction joints should
appropriate to evaluate the indicated tensile stresses of a be assumed to crack when subjected to tensile stresses
finite element model in terms of allowable tensile stress exceeding their tensile strengths. The dam may be
for the parent concrete alone. considered safe for the SEE if, after the effects of crack
If the compressive or tensile stresses in some locations of and joint opening have been accounted for, it can be
shown that the concrete is not over-compressed and free
the dam predicted by linear elastic analysis exceed the
cantilevers do not topple.
allowable strengths, they may not reliably predicted the
extent of the cracking (damage) or the true behaviour of
the dam. For these cases, nonlinear response of concrete
dams can be employed to provide a more accurate
response of the dam and the damaged region of the dam.
However, the predictions of the extent of the damage
obtained from these analyses are quite sensitive to the
assumed nonlinear properties of concrete or joints.
Evaluation for seismic loading
There are no codes and regulations which are universally
applicable to the earthquake resistant design of concrete
arch dams. The performance criteria, therefore, should be
discussed on a case-by-case basis.
The earthquake response of an arch dam is assessed
through a staged approach. Usually, the linear response-
spectrum mode-superposition method is used as first
approach, but if maximum stresses exceed the allowable
values, a time-history analysis is required to assess the Figure 2 Illustration of seismic performance and
severity of joint opening and tensile cracking. The basic damage criteria (Ghanaat, 2004)
results of a response-spectrum analysis consist of the
maximum nodal displacements and element stresses. Post-earthquake safety
Because the response to the three earthquake components
(two horizontal plus vertical) are developed A post-earthquake safety evaluation is required to assure
independently, the maximum dynamic responses due to the safety of the dam if a damaging SEE should occur, or
the earthquake components are further combined by the the predicted performance of the dam due to a postulated
SRSS method to include the effects of all three SEE should indicate substantial damage. This evaluation
components. It is notable that the resulting dynamic should consider the effects of static loads as well as
responses obtained in this manner have no sign and may
severe aftershock earthquakes that invariably occur after Chopra, A.K. 1994. Earthquake analysis, design and
any major quake. safety evaluation of concrete arch dams. Proceedings of
the 10th World Conference on earthquake engineering.
Sliding stability
Balkema, Rotterdam.
To assure safety against sliding along identified feasible
Dolen, T.P. 2011. Selecting strength input parameters for
failure planes in the dam, at the dam-foundation interface,
structural analysis of aging concrete dams. Proceeding of
or in the foundation, the shear friction factor of safety
the 31st Annual USSD Conference, San Diego, California.
should higher than those given in Table 4 for normal,
unusual and extreme loading. These safety factors assume EPRI. 1992. Uplift pressures, shear strengths, and tensile
that stability has been evaluated with respect to strengths for stability analysis of concrete gravity dams.
conservative shear strength parameters. For major dam TR-100345 Volume 1. Prepared by Stone and Webster
structures subjected to severe seismic loading, time- Engineering Corporation, Denver, Colorado, for Electric
history analyses should be considered for abutment and Power Research Institute, Palo Alto, California.
foundation stability instead of the usual pseudostatic FERC. 1999. Engineering Guidelines for the Evaluation
analyses. In time-history analyses, the factor of safety of Hydropower Projects, Chapter 11 – Arch Dams. US
varies with time and may become less than 1.0 for one or
Federal Energy Regulation Commission, Washington DC.
more cycles provided that the resulting cumulative sliding
displacement is very small and can be tolerated. Gillan, C.; Lund, G.; Weldon, J. 2011. Three predominant
failure modes for thin arch dams. Proceedings of the 31st
Stability analyses of foundation blocks typically involve Annual USSD Conference. San Diego, California.
uncoupled analyses whereby loading from the dam is
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separate rigid block foundation analysis. When time- evaluation of dams. Proceedings of the 13th World
history rigid block analyses are performed and the factor Conference on Earthquake Engineering. Vancouver.
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permanent displacement could be estimated using the Dams, Bulletin 102. International Commission on Large
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Acknowledgement
UCB/EERC-82/09. University of California Earthquake
The authors which to acknowledge Mr Brian Cooper, who Engineering Research Center, Berkeley, California.
reviewed this paper also from the perspective as a
McKay, M.; Lopez, F. 2013. Practical methodology for
member of the Working Group that is updating the
inclusion of uplift and pore pressures in analysis of
ANCOLD (1998) guidelines, and commented as follows:
concrete dams, Proceedings of the NZSOLD/ANCOLD
“I am in general agreement with the principles and 2013 Annual Conference, Rotarua, New Zealand.
concepts presented in this paper. They are consistent with
Newmark, N.M.; Hall, W.J. 1982. Earthquake Spectra
what has been written to date, in the revised ANCOLD
and Design; Engineering monographs on earthquake
earthquake guidelines which covers earthquake analysis
criteria, structural design, and strong motion records -
of all concrete dams. There may be some minor
Vol. 3: Earthquake Engineering Research Institute,
differences in the factors of safety but these will be
University of California, Berkeley, California.
worked out as the revised guidelines are further
developed. The revised guidelines are less cook-book and Nuss, K.N.; Matsumoto, N.; Hansen, K.D. 2012. Shaken
more guidelines – more along the lines of this paper.” but not stirred – earthquake performance of concrete
dams. Proceedings of the 32nd Annual USSD Conference.
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