MINISTRY OF REGIONAL DEVELOPMENT
AND PUBLIC ADMINISTRATION
GOVERNMENT OF ROMANIA
1. ------IND- 2013 0045 RO- EN- ------ 20130220 --- --- PROJET
ORDER
No.……… of..…….2013
for the approval of technical regulation “Normative document for the seismic design,
construction and assessment
of water engineering structures used in dam facilities”, Code NP 076-2012
In accordance with the provisions of Article 10 and Article 38(2) of Law No 10/1995 on quality in
constructions, with its subsequent amendments, of Article 2(3) and (4) of the Regulation regarding the
types of technical regulations and costs relating to regulatory activities in the field of constructions, town
planning, land development and habitat, approved by Government Decision No 203/2003, with its
subsequent modifications and supplementation,
on the grounds of Article 4(II)(d) and Article 12(7) of Government Decision No 1/2013 concerning
the organisation and operation of the Ministry of Regional Development and Public administration,
the Ministry of Regional Development and Public Administration hereby issues the following
ORDER:
Article 1. – The technical regulation “Normative document for the seismic design, construction and
assessment of water engineering structures used in dam facilities, code NP 076-2012”, revision NP0762002, drawn up by the Technical University of Civil Engineering of Bucharest, Faculty of
Hydrotechnics, stipulated in the annex that is an integrated part of the present order, is hereby approved.
Article 2. - This order shall be published in the Official Journal of Romania, Part I and shall come
into force 30 days after its date of publication.
Article 3. - On the date this order comes into force, Order No 1709/2002 of the Ministry of
Transport, Constructions and Tourism for approval of the technical regulation “Normative document for
the seismic design, construction and safety assessment of water engineering structures used in dam
facilities, code NP 076/2002*) shall cease to be applicable.
This technical regulation was adopted in accordance with the notification procedure No RO/..............
of ...................... stipulated in Government Decision No 1016/2004 regarding measures for organising
and carrying out the exchange of information in the field of technical standards and regulations, as well
as the rules regarding information society services between Romania and the EU Member States, as well
as the European Commission, with its subsequent modifications, published in the Official Journal of
Romania, Part I No 664 of 23 July 2004, which transposes Directive 98/34/EC of the European
Parliament and of the Council of 22 June 1998 laying down a procedure for the provision of information
in the field of technical standards and regulations, published in the Official Journal of the European
Communities L 204 of 21 July 1998, amended by Directive 98/48/EC of the European Parliament and of
the Council of 20 July 1998, published in the Official Journal of the European Communities L 217 of 5
August 1998.
DEPUTY PRIME-MINISTER,
*)
The technical regulation “Normative document for the seismic design, construction and assessment of water engineering structures used in
dam facilities, code NP 076/2002”, was approved by Order No 1709/2002 of the Ministry of Constructions and Tourism, and was published
in the Constructions Journal No 19/2003 edited by the National Institute for Research and Development in Constructions and Building
Economics – INCERC.
1
MINISTER
Nicolae-Liviu DRAGNEA
Annex
to MDRAP Order No________/___.___.2013
Normative document
for the seismic design, construction and assessment of
water engineering structures used in dam facilities
Code NP 076-2012
- Revision NP 076-2002 -
2
Contents
1.
2.
3.
Scope of the normative document........................................................................................4
Seismicity and seismic parameters ......................................................................................5
Seismic design and calculation of water engineering structures used in dam
facilities. Structure-reservoir-foundation ground interaction ............................................13
4.
Seismic calculation of dams made of concrete and local materials ...................................20
5.
Seismic calculation of auxiliary water engineering structures used in dam facilities .......26
5.1
Introduction.................................................................................................................. 26
5.2
Design calculation of high-water spillways ................................................................. 27
5.3
Water carrier pipes, sluice gates and valves ................................................................ 27
5.4
Intake towers. Funnel spillways .................................................................................. 28
5.5
Navigation locks .......................................................................................................... 28
6.
Seismic calculation of tailings dams and dykes .................................................................30
7.
Construction of dams in seismic zones. Anti-seismic structural measures .......................31
8.
Surveillance and monitoring of dam engineering structures built in seismic zones ..........33
9.
Restoration works for water engineering structures affected by earthquakes ...................34
10. Reference documents .........................................................................................................35
Anexa A - Glossary of terms ......................................................................................................39
Anexa B - International seismic criteria and regulations ...........................................................45
Anexa C - Calculation relationships used in the pseudo-static method .....................................47
Anexa D - Assessment of hydrodynamic pressures due to earthquakes ....................................48
Anexa E - Assessment of the seismic pressures due to the foundation ground .........................52
Anexa F - Seismic analysis of a gravity dam .............................................................................60
Anexa G - Seismic analysis of an earthfill dam .........................................................................87
3
1.
Scope of the normative document
1.1.
The normative document includes provisions regarding the seismic design, construction
and safety assessment of water engineering structures used in dam facilities (dams, dykes, dam power
stations, locks, auxiliary structures).
(1) Therefore, the following chapters specify the seismicity and seismic parameters, anti-seismic
design principles, the seismic calculation and safety assessment of water engineering structures used in
dam facilities, the construction of such structures in seismic zones, anti-seismic structural measures,
surveillance and monitoring, as well as works for the restoration of any water engineering structures
used in dam facilities which have been affected by earthquakes.
(2) The provisions are applicable to both the actual dam and the other water engineering
structures used within the dam facility: dam power plants, water inlets, spillways, hydromechanical
equipment, locks, abutments and connecting walls, etc.
(3) The seismic safety of the structures shall depend on their response to the combinations of
loads compatible with the seismic action. Therefore, the seismic action cannot be dissociated from other
types of loads or the state and specific conditions of the respective structure.
(4) Although the normative document only refers to aspects that are directly related to the
seismic action, the person responsible for ensuring the safety of these structures shall have to take into
consideration all of the structural and non-structural factors involved that comply with the practice
principles applicable in the field.
(5) Since the normative document generally reflects current engineering practice, the document
will need to be periodically revised and supplemented with the new practices developed in the field of
seismic engineering of water retention structures.
1.2. This normative document provides specialists responsible for designing or constructing
water engineering structures for dam facilities with the necessary theoretical and practical (structural)
elements relating to the calculation methodologies to be used and the seismic behaviour of these
structures.
(1) This normative document mainly refers to technical prescriptions relating to the fundamental
requirements applicable to structures and aims to harmonise the applicable specific technical regulations
in the field with those agreed nationally and internationally, namely the Seismic Design Codes No P1001 and P100-3, EUROCODE 8, ICOLD Bulletins and conferences, as well as the publications of the
European ICOLD Club.
1.3. The provisions of this normative document shall apply to dam engineering structures located
on sites whose geological conditions, determined by means of geological, hydrogeological, geotechnical
and geophysical surveys, are accepted by the practice in the field.
(1) Normally, sites located in zones with high tectonic activity, with faults that have a high risk
of relative sliding between adjacent faces, which are affected by landslides, caving-in or karst processes,
shifting sands or sands that pose the risk of liquefaction, massifs containing soluble materials (salt,
gypsum), or recent unconsolidated fillings shall not be accepted for water engineering structures used in
dam facilities.
1.4. The normative document refers to structures that are being designed, as well as existing
structures that are to undergo expert examination or verification, in accordance with the applicable
specific legislation in force.
(1) This normative document is to be used by all parties involved in the investment process:
planners, planning assessors, certified technical experts, contractors, technical managers responsible for
the construction works, investors, owners, administrators and users, personnel responsible for operating
4
the facilities, operators/companies working in the field of water engineering, as well as public
administration authorities and inspection bodies.
1.5. The normative document shall be supplemented by the following annexes:
Annex A - includes a glossary with the terminology used in this normative document;
Annex B - contains the main international regulations in the field of seismic safety of dams;
Annexes C, D, E - provide, as a recommendation, calculation relationships to be used in the
pseudo-static method, as well as when determining the hydrodynamic pressures due to earthquakes and
the seismic pressure developed in the foundation ground;
Annexes F, G - contain applications for the seismic analysis of a gravity dam and a rockfill dam,
respectively.
2.
Seismicity and seismic parameters
2.1. The strength of an earthquake can be described by its magnitude or its intensity.
(1) Magnitude is a measure of the energy released by the earthquake and, therefore, each
earthquake is characterised by a single magnitude.
(2) Intensity is a measure of the destructive effects of an earthquake in a certain zone and,
consequently, the intensity of an earthquake varies depending on the zone being analysed.
(3) The strength of an earthquake can be assessed by either determining its effects on people,
buildings or the environment, or by carrying out instrumental recordings at seismic stations.
(4) The most frequently used magnitude scale is Gutenberg-Richter (M), which includes nine
degrees of magnitude (1-9). The best known intensity scales are the Modified Mercalli (MM) scale,
which has twelve degrees of intensity (I - XII), and the Medvedev Sponheur and Karnic (MSK) scale,
which has ten degrees of intensity (I - X), in the MSK-64 and MSK-76 versions. The EMS 98 scale has
been developed in the European Union.
(5) Figure 2-1 shows correlations between various earthquake strength scales. For intensity
scales, the comparison refers to the epicentral intensity of the earthquake.
(6) In Romania, in accordance with STAS 3684 regarding the “Seismic intensity scale”, the
degree of seismic intensity is expressed in degrees on the international MSK-64 scale (MedvedevSponheur-Karnik scale).
5
ENERGY
MAGNITUDE
M
ergi
EPICENTRAL
ACCELERATI
ONS
M.M.
M.S.K.
JAPANESE
SCALE
CLASS
E
CLASS
D
CLASS
C
CLASS
B
CLASS
A
M - Gutenberg, Richter - 1956
MM - Modified Mercalli - 1931
MSK - Medvedev, Sponheur, Karnik - 1964
Figure 2.1 Correlations between various seismic scales
2.2. The peak value of the seismic horizontal ground acceleration (ag) within a site shall
correspond to a mean recurrence interval (MRI) of 225 years (exceedance probability of 20 % over 50
years) for the zones that are mainly influenced by the Vrancea subcrustal seismic source and the Banat
crustal sources, or a mean recurrence interval of 100 years (exceedance probability of 40 % over 50
years) for the rest of Romania, in accordance with Regulation P100-1 (Figure 2-2).
(1) A primary seismic action can usually be defined by two parameters:
ag - peak seismic horizontal ground acceleration for earthquakes whose mean recurrence interval
MRI complies with Paragraph 1(2.2);
Tc - the control (corner) period characteristic to the spectral composition diagram of the seismic
movement within the site, representing the limit between the maximum value zone in the absolute
acceleration spectrum and the maximum value zone in the relative velocity spectrum (Figure 2-3).
(2) Figure 2.4 shows the normalised elastic response spectra for horizontal accelerations at
foundation level, depending on the corner periods (Tc). The normalised spectra shall be obtained using
the elastic response spectra for absolute accelerations, by dividing the spectral ordinates by the peak
ground acceleration ag.
6
ESRI, ArcMap 8.3
Scale
Kilometres
Figure 2.2 Zoning of Romania according to the design peak ground acceleration ag with an MRI=225
years and an exceedance probability of 20 % over 50 years (red line), and an MRI=100 years and an
exceedance probability of 40 % over 50 years (blue line), respectively.
Scale
Kilometres
7
Figure 2.3 Zoning of Romania as a function of the corner period (Tc) of the
response spectrum.
(3) The absolute acceleration elastic response spectra [Sa(T)] for the horizontal components of
the seismic action shall be obtained from the normalised spectra [β(T) Figure 4] corrected by the peak
values of the ground acceleration ag:
Sa(T) = ag β(T)
(2.1)
(4) The relative velocity response spectra [Sv(T)] or relative displacement response spectra
[Sd(T)] shall be obtained from Sa(T) in accordance with the relationships between the elastic response
spectra:
Sd(T) = Sv(T)/ω = Sa(T)/ω2 where ω=2П/T
8
(2.2)
Period T, s
Period T, s
Period T, s
Figure Normalised elastic response spectra for horizontal accelerations at foundation level, depending
on the corner periods (Tc).
9
(5) The response spectra calculated in accordance with relationships (2.1) and (2.2) shall be used
in the calculations carried out to assess the safety of water engineering structures used in dam facilities
(SEE).
(6) The spectra shall be applied for seismic actions that are horizontal in the most unfavourable
structural response direction(s) specified in the following chapters for various water engineering
structures used in retention facilities.
(7) For water engineering structures used in retention facilities that are located in the relative
vicinity of earthquake epicentres, verifications shall also be carried out for the vertical component of the
seismic action. The peak acceleration for the vertical component avg shall be determined with
relationship (2.3), unless otherwise recommended:
avg = 0.5 ag
(2.3)
(8) The acceleration elastic response spectrum for the vertical component of the seismic action
[Sv,a(T)] shall be determined with the following relationship:
Sv,a(T) = avg β(T)
(2.4)
(9) Figure 2.5 shows the zones of seismic hazard due to crustal earthquakes in Romania. If
response spectra specific to these zones are created, which are certified by official documents, these
spectra shall be used in the design calculations.
Figure 2.5 Territory of Romania, showing the zones of seismic hazard due to crustal earthquakes.
(10) In the dynamic calculation of water retention structures, the seismic action shall be
described by accelerograms. These can be artificial, generated based on an elastic response spectrum
created as a function of ag and Tc within the site, or can be recorded accelerograms scaled to the values
of ag within the site, providing that the frequency content is compatible with the local conditions.
10
(11) The level of seismic hazard determined in accordance with the above relationships is the
minimum level that must be taken into consideration when designing water retention structures.
2.3. For dams or dam engineering structures (which create water retention) belonging to
importance classes I or II (STAS 4273-83) or importance categories A, B for new works (for the design
stage) (NTLH-021), the level of seismic hazard within the site (ag, Tc) shall be determined by means of a
special seismicity survey of the site based on thorough geological, hydrogeological and geophysical
studies, as well as statistical seismological research and studies.
2.4. The site seismic survey shall be drawn up in order to create a detailed seismic zoning and
micro-zoning of the region where the water engineering structure is located and determine the basic
earthquake parameters.
This survey must include the following data:
(1) A description of the structural and seismotectonic geological conditions present within the
region where the water engineering structure is located, at regional scale (100–300 km), represented on
maps and geological cross-sections, as well as geological, tectonic and electrometric block diagrams.
(2) A description of the local geomorphological and geophysical conditions present within the
site of the water engineering structure, represented on geological and geophysical profiles based on
drilling and geophysical tests relating to the seismic wave velocities (Vs and Vp) and strata density.
(3) The geotechnical characteristics of the superficial ground strata (longitudinal “Ed” and
transverse “Gd” longitudinal dynamic moduli of elasticity, propagation velocities “Vs” and “Vp”,
damping “υ”) and their stress-related variation.
(4) A description of the local seismic conditions, as well as the seismotectonic zones which
affect the site, specifying the focus points and epicentres, their seismic characteristics (maximum
accelerations, intensity, earthquake frequency, magnitude-frequency relationship, seismic degree of the
site), as well as the seismic intensity coefficients of the design earthquakes (cg=ag/g where g is the
gravitational acceleration) of the water engineering structure for the operating basis earthquake (OBE)
and the maximum credible earthquake (MCE).
(5) Primary historical data obtained by direct observation and by recording strong, medium and
weak earthquakes at the seismic stations installed within the region or zone being studied, or in areas
with similar geological and geodynamic properties:
a) maximum acceleration, velocity and displacement amplitude;
b) spatial characterisation of the seismic movement (ratio between the acceleration amplitudes in
different directions, spatial correlation characteristics);
c) the historical envelope of the movement over time, for the two body waves (P and S) and the
surface waves;
d) total duration of the seismic event: duration of the significant part of the movement and the
number of significant cycles;
e) the periods of the two main phases of the seismic movement (Tp and Ts);
f) the interval of time lapsed from the beginning of the phase until the maximum value is
reached, for the two types of waves (DoS, DoP).
(6) The spectral composition of a strong seismic movement within the site being studied shall be
predicted based on the following data:
a) a determination of the natural periods of the ground structure; the natural periods of the
ground under low stresses will significantly increase in the event of a strong earthquake, due to ground
damage; for non-rocky terrain, the quantitative assessment method used to determine the increase in the
natural periods shall be based on the variation curves of the transverse ground deformation modulus
“Gd” as a function of the specific angular deformation “γ”;
b) recordings of strong earthquakes that occurred within the area;
c) data from specialist literature.
11
(7) The seismic survey must take into consideration the risk of seismic phenomena occurring due
to the storage reservoirs created by water retention facilities, as well as the modification of certain
seismic parameters during the reservoir filling and operating periods.
2.5. In accordance with the international terminology, the earthquakes that are frequently taken
into consideration in the seismic analysis of water engineering structures used in dam facilities are MCE
(Maximum Credible Earthquake), SEE (Safety Evaluation Earthquake) and OBE (Operating Basis
Earthquake). Other typical earthquakes included in the international terminology are defined in Annex
A.
(1) MCE is the earthquake that would cause the highest possible level of ground movement
within the site, depending on the geological conditions.
(2) A SEE is an earthquake which generates the highest level of ground movement for which a
catastrophic rupturing of the dam does not occur. A SEE can be, at the limit, equal to the MCE or a
certain proportion of the MCE, or can be determined as a function of the return period of earthquakes of
a certain intensity within the site.
(3) OBE is an earthquake which is likely to occur, on average, no more than once throughout the
expected service life of the structure (but not less than 100 years, depending on the service life of the
water engineering structures used in the dam facilities). Under the action of an OBE, the dam and its
auxiliary structures must remain operational, but could need repairs.
(4) The ground movement can be characterised by the peak or effective acceleration, velocity or
displacement values.
(5) The peak ground acceleration (PGA) is the maximum free-field acceleration occurring in any
horizontal direction during an earthquake. The peak acceleration lasts for an extremely short period of
time, since it usually occurs in one or two of the high-frequency seismic oscillations and, therefore,
contains a small amount of energy. The engineering meaning of PGA is subject to debate. In general, a
parameter based on the evaluation of the earthquake energy which, in most cases, is 0.5 PGA can be
accepted as a parameter of the seismic acceleration.
(6) The effective peak acceleration is the peak acceleration after the seismic movement recording
(accelerogram) has been filtered in order to remove ultra-high-frequency oscillations which only have a
small influence on the structural response.
2.6. The design earthquake of a water engineering structure shall be determined as a function of
the peak ground acceleration (ag) and the class or category of importance of the respective structure.
(1) For water engineering structures belonging to the importance classes III, IV or V or the
categories of importance C and D, a single intensity level shall be established for the design earthquake,
namely the operating basis earthquake (OBE).
(2) For water engineering structures belonging to the importance classes I or II or the categories
of importance A and B, two intensity levels shall be established for the design earthquakes, namely: the
operating basis earthquake (OBE) and the safety evaluation earthquake (SEE).
(3) Table 2-1 gives the maximum seismic acceleration values for the operating basis earthquake
(anOBE) as a function of the peak ground acceleration (ag) within the site, in accordance with regulation
P100-1 and depending on the class or category of importance of the water engineering structure.
12
Class or category of importance
of the water engineering structure
I or A, for new structures
II or B, for new structures
III or C, for new structures
IV or D, for new structures
V
Table 2-1
Maximum seismic acceleration for
OBE (anOBE)
0.28 ag but not less than 0.12g
0.28 ag but not less than 0.10g
0.28 ag but not less than 0.08g
0.24 ag but not less than 0.06g
0.24 ag but not less than 0.05g
(4) The maximum seismic acceleration of the design OBE earthquake shall be determined by
taking into consideration the highest value resulting from the two determinations (based on the
importance class and based on the importance category, respectively).
(5) The maximum seismic acceleration of the design OBE earthquake for dam engineering
structures belonging to importance classes I or II or the categories of importance A and B, which are
located in zones where the peak ground acceleration (ag) within the site is, in accordance with regulation
P100-1, equal to or higher than 0.35g, shall also be determined based on additional analyses so that the
values given in Table 2-1 can be increased if necessary.
2.7. For water engineering structures belonging to importance classes I or II or categories of
importance A and B for which two intensity levels of the design earthquake are established, the
maximum acceleration of the safety evaluation earthquake (SEE) shall be determined in accordance with
P 100-1 or based on a site seismic survey, in accordance with Table 2-2.
Table 2-2
Class/category of importance of the
water engineering structure
I or A, for new structures
II or B, for new structures
3.
SEE
Maximum seismic acceleration
ag in accordance with P 100-1 or
the
maximum
acceleration
in
accordance with the site seismic survey
Seismic design and calculation of water engineering structures used in
dam facilities. Structure-reservoir-foundation ground interaction
3.1. The seismic design of water engineering structures used in dam facilities consists of creating
structural shapes which, together with the foundation and surrounding environment, help meet the
following performance criteria under the most economical conditions:
a) a satisfactory structural and functional behaviour, without any significant degradation under
the action of various stresses, including seismic stresses, whose occurrence throughout the service life of
the structure is considered normal;
b) acceptance of certain structural and functional deteriorations which do not generate
uncontrolled water discharges from the storage reservoir or catastrophic ruptures, and do not jeopardize
structural safety under conditions of exceptional stress.
(1) The degradations that can be tolerated in the case of dams made of concrete, rolled concrete
or stabilised ballast include small (limited) remnant displacements, limited surface fissures and certain
increases of the infiltration rates. In the case of rockfill dams, any settling areas occurring at crest level
must be smaller than the safety guards, any potential fissures must not lead to concentrated infiltrations
accompanied by damping of the internal erosion phenomenon, and the increased water pressure in the
13
pores in the saturated areas within the body or foundation of the dam must not lead to the occurrence of
liquefaction (cyclic mobility) phenomena or the loss of stability of the overall dam-foundation ground
assembly.
3.2 The seismic assessment of water retention structures should include risk management and
risk analysis. These methods can be used as support in the following situations:
a) prioritising on safety assessments when a large number of dams are taken into consideration;
b) assessing the benefits of various alternative restoration measures;
c) selecting the loading levels and assessing the structural response.
Risk management and risk analysis can also be used as part of general seismic evaluations to
help make final decisions.
3.3 The seismic design aims to limit the level of degradation and damage, as well as to prevent
the collapse of structural and non-structural elements, equipment and installations, in order to:
a) prevent personal injuries or the loss of human lives;
b) avoid the discontinuation of any activities and services which are essential in order to
maintain the continuity of social and economic life during and immediately after an earthquake;
c) prevent the destruction or degradation of certain highly-valuable cultural and artistic assets;
d) prevent the release of certain dangerous substances (toxic, explosive, etc.);
e) limit any material damage.
3.4 The calculation methods used in the structural seismic analyses shall be chosen in correlation
with the class and category of importance of the dam structure and the entry data available
(seismotectonic data, parameters of the free-field seismic movement, on-site investigations). The degree
of accuracy of the analyses shall increase progressively, the initial analysis being based on the simplest
conservative methods which correspond to the problem. Highly accurate structural analyses must take
into consideration data obtained by carrying out specific on-site investigations, and not values taken
from literature.
3.5 The measures which ensure the anti-seismic protection of water engineering structures used
in dam facilities shall be taken into consideration during all construction stages of these structures:
design, construction, operation.
(1) The following measures shall be taken during seismic design:
a) choosing sites which are favourable in terms of the seismic behaviour of the structure-ground
system and avoiding building the foundation on unfavourable terrain; if a problematic site cannot be
avoided, measures shall be taken to improve the foundation conditions on the basis of special surveys;
b) ensuring that the overall design of the structure enables it to have favourable behaviour during
earthquakes, as well as the creation of a clear calculation model;
c) constructing the supporting structure so that it meets the strength, stability, rigidity and
ductility parameters, in accordance with the provisions stipulated in this normative document.
(1) The following measures shall be implemented during the construction of the structures:
a) using building materials/products whose quality parameters are similar to those stipulated in
the design engineering documents, in accordance with the provisions of the applicable specific
legislation in force;
b) using suitable building technologies;
c) making sure that the structural details stipulated in the design are complied with on site.
(1) When operating the structures, constant attention shall be paid in order to:
a) adopt operating and maintenance measures which comply with the operating rules and help
the structure retain its entire strength;
14
b) monitor the technical condition of the structure over time so that any potential damage can be
detected early and the causes and consequences of such damage can be removed;
c) intervene promptly on the structure or its operating conditions, as necessary.
3.6 The seismic design of water engineering structures aims to:
(1) Provide suitable overall design of the structure, by:
a) choosing favourable structural shapes, both in plane and in elevation, avoiding any gross
discontinuities and ensuring the harmonious distribution of the masses and rigidities, corresponding to
the functions of the water engineering structure;
b) ensuring the correct layout and conformation of the structural elements and overall structure,
the non-load-bearing components as well as all equipment and installation housed inside the building;
c) avoiding any uncontrolled interactions with potential unfavourable effects between the system
components, between the structural and non-structural elements (downstream dam and plant) and
between components with very different rigidities;
d) correctly locating and configuring the auxiliary structures which ensure the operation and
safety of the system (water inlets, spillways, pipes, galleries).
(2) Ensure a sufficient level of rigidity that can restrict all absolute and relative displacements
occurring due to interaction with the other system components to permissible values.
(3) Obtain favourable structural mechanisms for dissipating energy (seismic isolators,
plasticising mechanisms, earthquake-absorbing components) under high intensity seismic actions. This
objective implies:
a) guiding the zones that are likely to undergo stresses within the post-elastic range mainly in
zones or elements which, due to the nature of the stress, display constant level of ductility or whose
rupture would not pose a threat to the overall stability of the structure and which can be repaired without
excessive technical effort and costs;
b) when the occurrence of post-elastic range deformation stresses in elements or zones which do
not belong to the above-mentioned category cannot be avoided, these stresses must be removed to
prevent the risk of structural collapse or the risk of any degradation that would incur significant
expenses for the repair works;
c) choosing a size and/or structural layout that prevents premature brittle ruptures;
d) the structure of the potential plastic zones must ensure a sufficient post-elastic deformation
capacity and the most stable hysteretic behaviour possible;
e) special attention shall be paid to the post-elastic analysis of the foundation ground and groundstructure contact zone, especially the concrete-rockfill contact zone, which can have a significant
influence on the behaviour and safety of the system.
3.7 Seismic actions manifesting through ground oscillations belong to the category of
exceptional actions and produce the following types of loads:
(1) inertial forces due to the mass of the structure, as well as the masses connected to the
structure which are produced due to permanent gravitational loads (technological and net loads);
(2) hydrodynamic pressures (in addition to hydrostatic pressures) due to the oscillation of the
liquid mass inside the reservoir and the hydroelastic interaction with the structure, which oscillates and
undergoes elastic deformation;
(3) dynamic thrust of the ground and rockfill.
3.8 The seismic calculation methods recommended in this normative document are, in general,
applicable to all types of water engineering structures.
(1) The object of the calculations is the unitary structure-reservoir-foundation ground system,
both from a sizing point of view and from a verification point of view.
15
(2) In general, seismic calculations require the use of specific calculation programmes validated
by engineering practice; the normative document is mainly focusing on this, and the calculations are
usually based on the finite element method.
(3) The entry data needed in order to carry out seismic calculations are the following:
a) the geometrical elements of the structure;
b) geological, hydrogeological and morphological data about the site;
c) the static and dynamic physico-mechanical characteristics of the materials;
d) the design seismic parameters of the site.
3.9 The seismic calculations shall mainly consist of:
a) strength calculations (stress and deformation state);
b) sliding or overturning stability calculations.
(1) The sliding stability calculations shall be carried out using the limit equilibrium method and
the finite element method based on the stress state.
(2) For rockfill dams, the calculations shall also focus on assessing the liquefaction risk and the
remnant seismic displacements.
3.10 The seismic calculations can be carried out using one or more of the following analysis
methods:
a) pseudo-static;
b) spectral analysis (modal analysis using seismic response spectra);
c) a modal analysis which integrates uncoupled equations;
d) a dynamic analysis which uses numerical time integration;
(1) The pseudo-static methods and the modal analysis methods shall be used for the linear elastic
behaviour of the system being analysed; non-linear spectra can also be used in the spectral method; the
numerical time integration method can be used both in the elastic and the non-elastic linear behaviour
range, on the basis of structural behaviour laws of the materials compatible with the calculation method
and programme.
3.11 The pseudo-static analysis method can be used in strength and stability calculations using
the limit equilibrium method:
(1) for structures belonging to importance classes I and II or importance categories A and B, the
method can only be used for preliminary assessments during the initial stages of the project (prefeasibility, feasibility);
(2) for structures belonging to classes III, IV and V or importance categories C and D, the
method can be used during any stage of implementation of the project.
(3) for sliding stability calculations, the method can be used during all stages of implementation
of the project, regardless of the importance class or category of the structure, simultaneously with other
analysis methods.
3.12 The pseudo-static analysis method implies major simplifications during calculation,
accepting that the seismic acceleration at the base of the structure remains constant for the entire height
of the structure.
(1) In the calculations, the inertial forces induced by the earthquake from the structural mass and
the hydrodynamic forces shall be considered static loads unlimited over time. The analysis also takes
into account the rigid body motion of the dam, as well as the incompressible water. The dam-foundation
rock interaction or the absorbing effect of the materials in the bottom or banks of the reservoir shall not
be taken into consideration. The inertial forces shall be calculated using the ground accelerations in
corresponding directions (upstream-downstream or valley-valley horizontal direction, vertical direction)
and shall then be applied to the centres of gravity of the volumes in which the structure was digitised.
16
(2) The hydrodynamic forces shall be estimated using the Westergaard and Zangar relationships,
or other equivalent relationships. The sliding stability of the dam shall be verified for the hypothesis that
the maximum design horizontal and vertical accelerations (if taken into consideration) occur
simultaneously.
(3) The pseudo-static analysis method is conservative for the following hypotheses:
a) the seismic load is continuous (unlimited over time);
b) the damping is ignored;
c) the energy absorption through the dam, foundation ground, bottom and banks of the reservoir
is ignored;
d) the maximum horizontal and vertical accelerations (if taken into consideration in the
calculation) are applied simultaneously.
(4) The method is non-conservative due to the fact that the amplification of the response
accelerations along the height of the structure (in elevation), which can be significant even for lowheight dams, is not taken into consideration.
3.13 The pseudo-static method shall only be used to assess the stability and strength of dam
engineering structures under the action of an OBE (operating basis earthquake).
3.14 The spectral analysis method (a modal analysis using seismic response spectra) has the
following general and specific elements:
(1) the calculations are carried out in the linear elastic range;
(2) the method is based on probabilistically adding up the maximum structural responses in each
significant natural mode of vibration, for an earthquake compatible with the site and represented by the
seismic response spectrum;
(3) the normalised spectra scaled to the site acceleration in accordance with P 100-1 shall be used
for water engineering structures used in dam facilities, in accordance with the provisions stipulated in
Chapter 2 of this normative document. For water retention structures belonging to importance classes I
and II or importance categories A and B, the calculation spectra can be obtained by means of a seismic
site survey, in which case the smoothed spectral envelope shall be used.
The spectral analysis requires the following entry data:
(1) the geometry of the structure, with the significant data (from the point of view of its rigidity);
the finite element model of the structure;
(2) the site ground morphology, with details which could influence the response of the system
(e.g. ravines, crests, overhangs, protuberances);
(3) the dynamic physico-mechanical characteristics of the dam materials, namely: Ed, µd; the
volumetric weight of the structural materials; damping as a fraction or percentage of the critical damping
(υ); since υ can only be determined experimentally “a posteriori”, values shall be taken from literature or
experience accumulated during other similar works and shall be used during the design stage; in the
absence of such data, the values given in Table 3-1 can be used:
System being analysed
Concrete dam
Dam made of local materials
Foundation ground
Table 3-1
Fraction of critical damping (υ)
OBE
SEE
0.02 - 0.05
0.04 - 0.07
0.05 - 0.12
0.07 - 0.15
0.05 - 0.12
0.08 - 0.20
(4) for concrete, in the absence of determinations carried out on laboratory samples or in situ, the
values accepted for Ed shall be within the range 265 000–370 000 daN/cm2 (corresponding to the static
17
values 200 000–250 000 daN/cm2), whilst the values of the dynamic Poisson factor (µd) shall be within
the range 0.22–0.26 ;
(5) for materials used for the earth fill, in the absence of any laboratory or on-site determinations,
the data obtained by simulating the construction (non-linear static calculation) can be used, providing
that they are corrected (multiplied) by coefficients which take into account the dynamic nature of the
stress; the mean dynamic modulus can also be used if determined by geophysical methods;
(6) for structures belonging to importance classes I and II or importance categories A and B,
indicative data (Ed, µd) can only be used for the pre-feasibility and feasibility phases; the next phases
require specific on-site and laboratory studies to be carried out in order to determine the data to be used
for calculation;
(7) the foundation ground shall only be entered in the calculations through its rigidity, and its
masses shall be considered null.
3.15 The direct numerical time integration method consists in the successive, step-by-step
temporal assessment of the response of the structure to the seismic action introduced as a discreet time
function (usually accelerations occurring at very short intervals of time).
(1) The direct numerical time integration method shall be equally applicable for the linear and
non-linear elastic behaviour of the materials.
(2) Linear elastic calculations, which are particularly applicable to concrete or metallic structures
founded on normal or rigid ground, require the following entry data:
a) the digitisation of the finite element model;
b) the dynamic elastic characteristics of the materials making up the system (dam, foundation
ground, etc.), as well as the dynamic modulus of elasticity (Ed), the dynamic Poisson ratio (µd), the
damping that can be determined from the damping rate (υd) for various natural modes using the Rayleigh
model;
c) volumetric weights for materials;
d) additional masses calculated from hydrodynamic pressures and concentrated in the nodes of
contact with the liquid, with components in the directions of the global system axes;
e) the directions of action of the accelerogram;
f) the artificial (synthetic) or recorded accelerogram that is compatible with the site, scaled to the
level required for calculation, which can be OBE/SEE;
g) the accelerogram can be given on the surface of the base rock or at ground level; the
accelerogram corresponding to the base of the foundation ground modelled in the calculation,
determined for the finite element model, as well as for statistical calculation. The ground level
accelerogram shall be deconvoluted through the foundation ground so that it can be assessed at the base
of the digitisation of the foundation ground.
3.16 The structure-liquid interaction in the spectral analysis method shall be determined in
accordance with the principle of additional masses, which means accepting the hypothesis of the ideal
and incompressible liquid. In the direct numerical integration method, the structure-liquid interaction
can be determined both in accordance with the principle of additional masses and by using the
subsystem analysis method. The structure-liquid-foundation ground interaction should be determined
using the subsystem analysis method.
(1) The subsystem analysis method implies the digitisation of each subsystem (dam, storage
reservoir, foundation ground) of the unitary structure-liquid-foundation system using specific numerical
methods (finite elements, finite differences, boundary elements), as well as an analysis of the seismic
behaviour of the subsystem according to its own behaviour laws.
(2) Some particular subsystems can be approached analytically. The unity of the system shall be
obtained by implementing the requirements regarding the simultaneous temporal equality of the
18
response from various subsystems in the connection nodes located between them. The working method
is iterative and shall be applied as part of the numerical time integration method.
19
4.
Seismic calculation of dams made of concrete and local materials
4.1 The most significant safety problems occurring in concrete dams stressed by earthquakes are
generated by excessive cracking, which can lead to potential instability due to sliding or overturning
(dislocation). Sliding can occur on existing, less resistant surfaces within the body or foundation of the
dam, or surfaces created as a result of excessive cracking of the concrete or concrete-foundation
interface due to earthquakes. In arch dams, sliding instability is more likely to occur at the outlets, in the
area where the dam is supported into the slopes.
4.2 The seismic safety of rockfill dams shall mainly depend on the level of crest settling induced
by earthquakes, which must not lead to the overflowing and erosion of the dams and the occurrence of
transversal cracks (fissures) that could cause concentrated infiltrations and erosion of the dam body.
4.3 The seismic calculation of dams made of concrete and local materials can employ all the
seismic calculation methods presented in Chapter 3, as well as other methods specific to different types
of dams (remnant displacements, liquefaction analyses, etc.).
(1) The calculation method shall be chosen depending on the class or category of importance of
the dam, as well as its completion or existence stage (studies, design, operation, post-earthquake) and
the type of the dam. Figures 4.1 and 4.2 show block diagrams of the calculations that must be carried out
during the anti-seismic design of concrete and rockfill dams.
4.4 The direction of action of the design earthquake shall normally be horizontal, upstreamdownstream. For dams located in relative vicinity to seismic focus points (DE ≤ 1.5 HF, where DE is the
distance between the dam site and the focus point epicentre, and HF is the depth of the focus point), the
vertical component of the earthquake shall also be taken into consideration; this shall be equal to 50 %
of the horizontal component.
(1) For buttress or arch dams, the valley-valley horizontal component (perpendicular to the axis
of the valley) shall also be taken into consideration and shall be equal to the upstream-downstream
horizontal component (along the valley).
(2) If several directions of action of an earthquake on the same dam are taken into consideration,
the earthquake components shall be considered to act separately, if a spectral analysis or pseudo-static
calculation method is used. In these situations, the response of the structure to each component shall be
analysed independently and shall not be added up.
(3) In the direct numerical time integration method, the components of a design earthquake
which occur in several directions (accelerograms, tachograms, seismograms) can also be applied
simultaneously.
20
Assessment of the
behaviour under static
loads
Collection of properties of the materials used
in the dam-foundation ground system
Dynamic
analysis
The criterion is
not fulfilled
Fulfilment of the
permissible stress
criterion
The dam profile must
be redesigned
The criterion is
fulfilled
The criterion is
not fulfilled
Fulfilment of the
stability criterion
The dam profile must
be redesigned
The criterion is
fulfilled
The criteria are
not fulfilled
Fulfilment of the criteria for
auxiliary structures, the reservoir
banks and the foundation
The dam-foundation ground
system must be redesigned
The criteria are
fulfilled
All criteria are fulfilled
STOP
Figure 4.1 Block diagram regarding the analyses required to design concrete dams in seismic zones.
4.5 The seismic calculations must be carried out for the “full reservoir” hypothesis, considering
that the water level in the reservoir is at the normal retention limit (NRL). In justified situations, the
calculations shall also be carried out for the hypotheses of an “empty reservoir” or for intermediary
water levels in the reservoir, between empty and full.
(1) In the linear elastic calculations, the seismic response shall be added to the response to the
other loads (static, dynamic) in accordance with the combinations of loads established by specific
regulations. In the non-linear calculations, the response to all the loads in the respective combination,
including the seismic action, shall be assessed taking into account the history of the loads over time.
21
Gathering geological and geotechnical data about
the materials used in the dam-foundation ground
system
Determination of the
pressure increase
potential of the water in
the pores due to the
seismic action
The criterion is
fulfilled
The criterion is not fulfilled
Analysis of the water pressure
increase in the pores due to
the seismic action
Sliding is possible
Stability analysis
No sliding occurs
Stability analysis, taking into
consideration the water
pressure increase in the pores
due to the seismic action
The criterion is fulfilled
STOP
Sliding is possible
The displacements are too
large
Displacement analysis
The displacements are
within the permissible
limits
The dam profile
must be redesigned
The criterion is fulfilled
STOP
Displacement analysis,
taking into consideration
the water pressure increase
in the pores due to the
seismic action
The displacements are
within the permissible
limits
The criterion is fulfilled
STOP
Figure 4.2 Block diagram regarding the analyses required to design rockfill dams in seismic zones.
4.6 Normally, the seismic action shall be considered to be a synchronous action (in all the
digitisation nodes where the seismic action is considered to be applied, it shall be simultaneously
identical, which means that the seismic wave propagation speed is infinite). For dams which belong to
importance classes I, II or importance categories A, B and stretch over large areas (crest length Lc ≥ 500
m or base width B ≥ 300 m), the asynchronous nature of the seismic waves should also be taken into
consideration (the hypothesis of the finite seismic wave propagation speeds within the site).
4.7 The seismic safety of dams and other structures used in dam facilities shall be calculated for
the action of OBE (operating basis earthquake) regardless of their importance class or category. The
seismic safety of dams belonging to importance classes I, II or importance categories A, B, which are at
technical design stage or are in operation as part of an expert assessment in order to obtain an
authorisation for safe operation, shall also be checked under the action of SEE (safety evaluation
earthquake).
22
4.8 Rectilinear dams (except for hollow gravity dams and buttress dams) constructed in relatively
large valleys (ratio between the valley aperture at the crest Lc and the height of the dam HB, Lc / HB ≤ 3–
4) shall undergo seismic analysis in their transversal profile (two-dimensional analysis), usually for the
maximum height profile.
(1) Hollow gravity and buttress dams shall also be analysed under the action of a longitudinal
earthquake upon the dam, parallel to the axis of its crest.
(2) Due to their specific configuration, arch dams shall only undergo a three-dimensional
analysis.
(3) A three-dimensional analysis should also be used to assess the seismic behaviour of concrete
and rockfill dams constructed in relatively narrow valleys (Lc / HB ≤ 3–4), in order to determine the
effect of the slopes on the structural response.
4.9 The seismic response to OBE shall be calculated using the pseudo-static method for dams
belonging to importance classes III, IV, V or importance categories C, D regardless of their stage of
completion (design) or existence (in operation, under survey, post-earthquake analysis).
(1) The seismic response to OBE of concrete dams belonging to importance classes I, II or
importance categories A, B shall be calculated using the pseudo-static method for the initial phases (prefeasibility, feasibility) of the dam construction process only. For concrete dams that are at the technical
design stage, or during the survey and post-earthquake analysis of existing dams, the OBE response
shall be calculated using the spectral analysis or direct numerical time integration methods. For rockfill
dams belonging to importance class I, II or importance categories A and B, the pseudo-static method can
be used regardless of the stage of completion or existence of the respective dams.
(2) The seismic response of concrete dams to SEE shall only be calculated using the spectral
analysis or direct numerical time integration methods using, as much as possible, non-linear spectra in
the spectral analysis method or non-linear elasto-plastic laws for the behaviour of the materials in the
direct numerical integration method.
(3) For dams made of local materials, the seismic response to SEE shall be calculated both using
the spectral analysis or step-by-step numerical time integration methods, as well as specific procedures
for determining the remnant seismic displacements, the liquefaction risk and the sliding stability of the
banks.
(4) For dams with a maximum height of over 80 m, the risk of seismicity occurring on site due to
the storage reservoirs shall be taken into consideration, and the respective dams shall undergo a
technical survey.
4.10 Statistical or simplified relationships for determining the natural fundamental periods of
dams, according to their type, or auxiliary structures of such dams are given in Table 4-1. The values are
given for guidance only, to help select the natural modes that have significant response effects in the
spectral analysis method or help choose the calculation step (Δt) in the direct numerical integration
method.
Table 4-1
Type of
structure
Gravity dams
Fundamental periods
T1 (s)
T1  (1,695 ...1,637 )
H b2
B
Notations
Hb- height of the dam
B - profile base width
b - volumetric weight of the concrete
Eb
- modulus of elasticity of the concrete
g - gravitational acceleration, 9.81 m/s2
12  b
Eb g
23
Buttress dams
Arch dams
Rockfill dams
Upstreamdownstream
direction
Direction
perpendicular to
the valley
Vertical direction
Earthfill dams
Intake towers,
Funnel spillways
T1  4 D
b
Eb
D - buttress width on the upper side
Eb
- modulus of elasticity of the concrete
ρb- density of the concrete
T1 - fundamental period when the reservoir is
full
Hb- height of the dam
T1g - fundamental period when the reservoir
is empty
T1=0.1+0.2 x (Hb / 100),
T1g= 0.5 x T1
T1 = 0.5 x Hb / 100
T1 = 0.45 x Hb / 100
Hb- height of the dam
T1 = 0.36 x Hb / 100
T1 = 2.62 x Hb / VS
Hb- height of the dam
VS
- secondary wave velocity
through the filling
M - mass concentrated in the centre
of gravity
K - bending rigidity of the
structure
Mh - additional mass of the water
T1 = 2 (M/K)0.5
T1 = 2 ((M + Mh)/K)0.5
(1) The natural modes selected when using the spectral analysis method should be those whose
participation coefficients are at least 0.05 in one of the directions of the dynamic degrees of freedom
taken into consideration. Normally, this requirement can lead to the selection of 10–20 natural modes for
rockfill or concrete gravity dams, and 20–50 natural modes for arch dams.
(2) When using the direct numerical integration method, the calculation step (Δt) must not
exceed 0.10–.0.12 of the value of the shortest natural period of the dam which is considered to have a
significant influence on the response. This requirement shall lead to guidance values of the calculation
steps Δt = 0.01–0.02 s for concrete dams, and Δt = 0.02–0.10 s for rockfill dams.
4.11 The structure-liquid interaction occurring in concrete dams should be determined in
accordance with the principle of additional masses used for OBE analysis.
(1) The effect of the hydrodynamic pressures on the seismic response of rockfill dams is
insignificant and can be ignored.
(2) The (active/passive) dynamic pressures created in the foundation ground can also be
modelled as additional masses attached to the joint structure-foundation ground nodes, projected in the
directions of the degrees of freedom in the respective nodes.
(3) Annexes C, D and E provide examples of the calculation relationships to be used in the
pseudo-static method (Annex C), as well as the relationships used to determine the hydrodynamic
pressures induced by earthquakes (Annex D) and the seismic pressures developed in the foundation
ground (Annex E). These are given as a recommendation only.
(4) Also, the examples of seismic analyses given in Annexes F and G are intended to help users
implement the normative document.
4.12 The basic seismic calculations required for an OBE action are those presented in Article 4.9.
For concrete dams, the sliding stability and deformation-stress state shall be analysed. For rockfill dams,
24
the sliding stability and permanent displacements (settling) caused by an earthquake shall have priority
during analysis. The analysis shall also be extended to include the sliding stability of the foundation and
slopes of the dam, as well as the reservoir basin.
(1) The response parameters recommended for evaluation in the event of an SEE action are as
follows:
a) for concrete dams: the risk of developing cracks (fissures) which, at the limit, would penetrate
the cross-section of the dam and dislocate elements from the dam body, opening (fissuring) of the
injected joints of arch dams and, eventually, fracturing of the overhanging elements, dislocation of the
slopes, cracking of the areas where sudden changes in rigidity (gallery corners, cavities in the dam body,
dam-foundation contact surface, etc.) occur, and relative sliding between the rock areas in the dam
foundation, which are separated by faults activated by the earthquake.
b) for rockfill dams: the risk of crest settling (dislocations) that exceeds the safety guards, which
would lead to spillage of the dam and its destruction by erosion, the risk of cracks occurring, in
particular cracks that run transversally through the dam, which would lead to uncontrolled water
discharges from the lake and, eventually, erosion of the dam, sliding-dislocation of the banks and slopes
located on faults activated by the earthquake.
4.13 Earthfill dams which are founded on waterlogged sandy soils or are made of granular noncohesive materials with grain sizes of 0.02–2.00 mm or created by hydraulic sedimentation must be
calculated for liquefaction, both under an OBE action and an SEE action.
(1) Liquefaction is a phenomenon in which waterlogged sandy granular materials lose their loadbearing capacity under the action of cyclic dynamic loads due to a water pressure increase in the pores.
(2) The main factors which influence liquefaction are: the granulometric curve of the material,
the relative density and the initial stress state.
(3) The analyses shall be carried out using specific calculation programmes validated by
engineering practice and shall be based on laboratory tests regarding the number of cycles in which
liquefaction occurs and/or standard ground penetration tests.
a) In the first instance, the sliding stability of the dam or the dam-foundation ground system, as
applicable, shall be determined using the limit equilibrium method; the stability calculations shall be
carried out in post-earthquake conditions, for static loads; in zones where the materials are expected to
undergo liquefaction, the shear strength of these materials shall be considered in the calculations to be
equal to the residual strength in undrained conditions.
b) If the stability factors determined in accordance with the recommendations given in Point (a)
are subunitary, the stability shall be determined using the complete dynamic method for time integration
of the coupled equations for non-linear motion and transient pressure evolution regimen of the water in
the pores; the dam stability shall be estimated as a function of the induced remnant deformations.
4.14 The calculations must confirm that the dams being analysed meet the performance criteria
depending on the combinations of loads considered. In the event of an OBE action, slight damage
(fissures, small remnant displacements, slight increases in the level of infiltrations) that could require
repairs at no significant cost shall be permitted, but the dam must remain operational. In the event of an
SEE action, damage that that requires repairs shall be permitted, provided that it does not lead to
uncontrollable discharges of water from the reservoir or yielding of the dam.
(1) The basic criteria that help evaluate the performance of concrete dams under the action of
design earthquakes are the following: the permissible flexural compressive and tensile strength values
must not be exceeded; the safety coefficients obtained by means of sliding stability calculations must be
super-unitary.
(2) The permissible flexural compressive strength of the concrete under dynamic (seismic) loads
Rcd shall be considered to be 50 % higher than the permissible equivalent strength of the concrete under
static loads Rcs; however, it must exceed 20 MPa:
25
Rcd = min (1.50 Rcs, 20 MPa)
(3) The permissible flexural tensile strength of the concrete under dynamic loads (Rid) shall be
considered to be 10 % of Rcd
Rid = 0.10 Rcd
(4) The sliding safety coefficients for the critical sliding surfaces (which are the most exposed to
sliding) should be within the 1.00–1.05 range.
(5) The basic criteria that help evaluate the performance of rockfill dams under the action of
design earthquakes are the following: the safety coefficients obtained by means of sliding stability
calculations must be super-unitary; any crest settling caused by earthquakes must not exceed the safety
guards.
(6) The basic performance criterion for earthfill dams or sites with the potential of undergoing
liquefaction shall be to prevent liquefaction under the action of an OBE. For an SSE, the performance
criterion shall be determined in accordance with the provisions stipulated in 4.13(a) and (b).
(7) The sliding safety coefficients for the critical sliding surfaces (which are the most exposed to
sliding), both in the body of a rockfill dam and the foundation, should be within the 1.00–1.10 range.
(8) The maximum crest settling caused by design earthquakes must not exceed 80 % of the size
of the safety guards provided.
(9) If the depth of the sliding surfaces is smaller than the face of rockfill dams (superficial sliding
surfaces), subunitary safety coefficients shall also be permitted, providing that they are not smaller than
0.90.
4.15 Local and isolated exceedance of the permissible stresses in the calculations carried out
using the finite element process in spectral analysis method or the method of direct numerical
integration within the linear elastic behaviour range of the materials shall be permissible if the excess
stresses can be redistributed to the neighbouring zones or the cracks that they could generate would not
have a significant effect on structural safety. These shall be accepted by means of a practical engineering
analysis of their consequences, based on historical cases and existing experience.
4.16 The seismic analyses stipulated in this normative document shall only use specialised
calculation programmes verified by engineering practice.
5.
Seismic calculation of auxiliary water engineering structures used in dam
facilities
5.1 Introduction
(1) The destruction of auxiliary water engineering structures used in dam facilities, such as highwater spillways, water inlets, bottom discharge conduits, forced pipes, gates and navigation locks can
lead to uncontrolled water discharges into the tailwater pool. Therefore, the seismic safety of such
auxiliary water engineering structures must be carefully analysed.
(2) The most important factor in determining the degree of anti-seismic protection of auxiliary
water engineering structures used in dam facilities shall depend on the consequences that the destruction
of such a structure would have, i.e. whether its destruction would lead to an uncontrolled discharge of
the water from the storage reservoir.
26
(3) The traditional seismic analysis methods — pseudo-static, spectral, numerical time
integration — presented in Chapter 3 shall also apply to auxiliary water engineering structures used in
dam facilities. If retaining functionality is essential, such as in the case of mechanical and electrical
equipment, seismic qualification through testing is necessary.
(4) Regardless on the analysis method chosen, the final assessment of the seismic safety should
be based on engineering judgement and the experience of similar structures, given the fact that each
structure and its environment are unique.
5.2 Design calculation of high-water spillways
(1) Normally, high-water spillways are structures made of reinforced concrete. Usually, the
seismic loads belong to most unfavourable load combinations that condition the design of such
structures. A high-water spillway is made up of three main types of structures: the intake (circular front
weir), the transport structure (channel, case, gallery) and the end structure (energy dissipation basin, end
weir sill, counter-slope pool, take-off).
(2) The combination of loads that includes the seismic load shall also include: the hydrostatic
and hydrodynamic loads corresponding to the normal retention limit (NRL) in the reservoir, the
temperature loads experienced during the extreme months (February, July) but which correspond to the
multi-annual average air and water temperatures, the dynamic pressure of the soil used in the
embankments adjacent to the structures.
(3) In calculations, the fraction of critical damping (damping rate) should be considered to have
values between 2–5 %.
(4) The local safety factors of hydraulic structures shall be determined by comparing the
effective maximum stresses with the limit stresses, both for the concrete and the reinforcements. When
the seismic load is considered, the permissible stresses can be 50–80 % higher than the normal stresses
permitted for fundamental load combinations.
(5) When determining the seismic loads, the safety factors used to carry out sliding and/or
overturning stability verifications should be between 1.00–1.15.
(6) The load-bearing components of high-water spillways whose destruction could lead to
uncontrolled water discharges from the reservoir must undergo verification at SEE. In all other
situations, the load-bearing components of high-water spillways shall be subject to verification at OBE.
The safety factors determined by comparing the maximum effective stresses with the stresses
permissible for the sluice gates used in weirs should be at least 1.1 for SEE and at least 1.5 for OBE. The
sluice gates must also undergo verification at limit deformations, to prevent them from getting stuck in
the weir fields.
5.3 Water carrier pipes, sluice gates and valves
(1) Water carrier pipes, such as conduits, forced pipes, galleries and low pressure water outlets
must be reliable and ensure the quick and controlled drainage of the reservoir should it be necessary.
The design of the water carrier pipes must not cause ruptures or compromise the normal operation of the
dam or its foundation. In addition, for reservoirs used to supply drinking water to populated areas, the
operating safety of the system of pipes, sluice gates and valves shall be an essential factor in the supply
of drinking water and the delivery of water for putting out fires and other post-seismic recovery
activities.
(2) The experience accumulated in tunnels subjected to large earthquakes has shown that these
have very good behaviour. Even tunnels built in soft ground behaved very well if provided with a certain
degree of flexibility and joints along their structure. The most frequent failures occurring in tunnels
affected their portals.
27
(3) If the failure of water carrier pipes, sluice gates or valves does not lead to uncontrolled water
discharges from the reservoir, these shall undergo a seismic OBE verification using the permissible
stress criterion. The provisions stipulated in normative document P100-1 should be applied.
(4) The anti-seismic design of sluice gates and valves shall take into account the amplification of
the seismic movement along the height of the dam, as well as the connections with the mechanical and
electrical equipment. Therefore, certain differentiated displacements caused by seismic vibration must
be accepted on the foundation-equipment interfaces and between various components of the mechanical
and electrical equipment. This equipment must remain operational even if the earthquake has caused
certain residual permanent displacements. The emergency power supply units and switchboards must be
installed on foundations or strong walls that can resist the design earthquake.
(5) In zones with a very high level of seismicity, automatic systems should be provided to close
the flow control valves or sluice gates of the systems used to carry (discharge) water from the reservoir.
5.4 Intake towers. Funnel spillways
(1) In general, intake towers consist of the following structural elements: the actual intake tower,
the water carrier tunnel (pipe) or gallery, the end structure and the bridge that enables access to the
tower. Funnel spillways with tall towers contain the same structural elements as intake towers and
comply with comparable anti-seismic design requirements.
(2) Towers which are buried in the body of earthfill dams interact dynamically with the material
in which they are embedded. Most towers are immersed, for much of their height, in the water in the
reservoir. The effects of the hydrodynamic interaction are very important. Sometimes, water can also be
found inside the towers, which also affects the seismic response.
(3) The seismic analysis of intake towers shall depend on their natural vibration characteristics.
Outlet towers that have low height, relatively large diameters and thick walls (fundamental frequency f1
≥ 33 Hz) behave like quasi-rigid bodies and their seismic response can be conveniently assessed using
the pseudo-static method. The fundamental period of tall or flexible towers shall normally be within a
range where maximum spectral amplifications occur, which require the implementation of a dynamic
analysis method (spectral analysis or numerical time integration).
5.5 Navigation locks
(1) Navigation locks used in dam facilities have the following essential components: upstream
and downstream waiting ports, upstream and downstream ends, lock chamber, hydraulic filling and
emptying systems which include sluice valves, upstream and downstream gates, the hydromechanical
and electrical control system. In general, modern locks are structures made of reinforced concrete.
(2) During seismic calculation, the working chamber of the lock (lock chamber) can be
considered equivalent to a rectangular basin filled with water. This way, the dynamic seismic calculation
methods used for rectangular water storage basins can also be used for lock chambers.
(3) The issue posed by the structure-liquid interaction is important. Both types of hydrodynamic
pressures — impulsive pressures generated by the acceleration response and convective pressures
generated by the displacement response — must be taken into consideration during the design stage.
(4) The structure-liquid interaction for the acceleration response (impulsive mass) can be
determined in accordance with the principle of additional masses. Once the additional masses have been
determined, the analysis can be continued using the spectral analysis or direct numerical integration
method. For the displacement response (convective mass), the analysis can only be carried out using the
numerical time integration method.
(5) Calculation procedures that are similar to those used for metallic structures can also be used
for the seismic calculation of lock gates. The gates can be considered similar to flat slabs or bars with
suitable supporting conditions.
28
(6) Because the electromechanical equipment of the lock (sluice valves, hydraulic circuits,
electric switchboard) is essential for the operation of the lock, it must be seismically qualified. The
equipment must be suitably anchored onto the floor or walls and must resist the design seismic loads.
29
6.
Seismic calculation of tailings dams and dykes
6.1 The behaviour of downstream and centreline tailings dams and dykes is similar to the
behaviour of rockfill dams used for water storage. Upstream tailings dams are the most vulnerable to
seismic action.
6.2 The main factors which influence the seismic behaviour of tailings dams and dykes are:
a) the epicentral distance and magnitude of the earthquake. The stresses can be highly amplified
if the dominant periods of the earthquake that are filtered through the ground coincide with the natural
frequencies of the dam or its foundation;
b) the embankment slopes;
c) the position of the infiltration curve for the body and shoulders of the dam;
d) width of the layer of deposited materials which separates the dam from the clarified water on
the surface after the waste has settled;
e) the characteristics and degree of consolidation of waste with a granular content similar to
sands;
f) the frequency content, the number of high acceleration peaks and the duration of the
earthquake.
(1) The presence or absence of a small pond (pool) on the surface of the deposits shall reduce the
risk of the dam yielding and minimise the level of downsteam destruction caused should the dam yield.
(2) Lowering the position of the dam body infiltration curve by using adequate drainage systems,
increasing the degree of consolidation of the deposits, and the potential increase of the shear strength of
the materials within the storage basin-dam due to ageing are factors which improve the seismic
performance of tailings dams and dykes.
6.3. Any analysis of the seismic behaviour of tailings dams and dykes must include:
a) an assessment of the remnant horizontal displacements and settling caused by the seismic
action;
b) a calculation of the water pressure increase in the pores and the risk of liquefaction;
c) an assessment of the oscillations of the water lingering on the surface of the storage basin
and/or any unconsolidated waste;
d) a calculation of the profound and superficial sliding stability of the banks;
e) an assessment of the risk of internal and external erosions (due to discharge);
f) an assessment of the increase in the infiltration volumes;
g) an assessment of the floods caused by gaps occurring in the body of the dam.
6.4 All tailings dams and dykes shall be calculated for the operating basis earthquake (OBE).
AOBE,TD shall correspond to the highest resulting value between 0.4 ag (identical to aOBE for dams used
for water storage facilities), the earthquake with an exceedance probability of 10 % for a period of 50
years and the earthquake with an annual exceedance period of 1 to 475, respectively. Tailings dams and
dykes must remain operational after an OBE, and only superficial failures that do not require costly
interventions shall be permitted.
6.5 Tailings dams and dykes belonging to importance classes I and II or importance categories A
and B shall also be calculated for the safety evaluation earthquake (SEE). aSEE,TD shall correspond to the
highest resulting value between ag and the maximum acceleration determined by carrying out on-site
seismic surveys, which are compulsory in such situations. In the event of the action of an SEE, certain
failures shall be permissible providing that the dam retains its stability and integrity, and uncontrolled
discharges of water or runny (unconsolidated) waste into the tailwater pool are prevented.
30
6.6 For tailings dams with a height of more than 80 m, which are constructed on sites with large
tectonic disturbances (faults, fissures, breccias, etc.), the risk of occurrence of seismic phenomena due to
the storage of waste shall be assessed.
6.7 It is permissible to use the pseudo-static method to analyse the seismic stability of tailings
dams and dykes made of riprap, cohesive soils or well-compacted dense sands (Dr ≥ 0.8), which suffer
small strength losses when exposed to seismic action. The remnant displacements caused by earthquakes
can be assessed using the Newmark method (1965).
6.8 Tailings dams and dykes with medium density sands (Dr < 0.8) in the body or foundation of
the dam shall require special thorough analyses, which progress from simpler to more refined analyses
depending on the importance of the structure and the results obtained during the successive analysis
stages. These analyses can be, in ascending order of their costs and complexity, as follows:
a) stability analyses carried out based on the limit equilibrium and the pseudo-static method;
b) simplified seismic stability analysis;
c) seismic stability analysis using the finite element process.
(1) As part of these analyses, special attention shall be paid to the risk of the dam (dyke) losing
its stability due to total (partial) liquefaction of certain zones within the dam-foundation ground-waste
storage basin system.
7.
Construction of dams in seismic zones.
Anti-seismic structural measures
7.1 All construction works shall be carried out in accordance with the provisions stipulated in the
technical documentation — technical design and work plan details — and the applicable specific
normative documents in force. During the execution stage, any changes to the technical solutions
stipulated in the technical designs, which could affect the mechanical strength, stability or operating
safety of the structure, shall only be permitted on the basis of amending construction change
notices/work plan details drawn up by the design engineer and verified by a certified project inspector,
in accordance with the law and with the prior written consent of the investor/beneficiary.
7.2 After carrying out topsoil stripping and excavation works, the beneficiary shall take all
necessary steps to arrange for a final “visual” re-verification of the seismo-tectonic conditions present
within the site, to determine whether they correspond to the conditions predicted during the previous
investigation stages. Sites which display faults with high risks of activation due to seismic action, which
could pose a threat to the safety of the structure, shall be able to be eliminated even during this stage.
7.3 The actual construction works (concreting, filling) shall only be resumed after the site and
foundation ground of the respective structure have been accepted by an acceptance committee made up
of the beneficiary’s representative, a geologist, the design engineer and the contractor’s technical quality
control specialist. The acceptance shall be recorded in a site acceptance report, which shall be added to
the Instructions Book of the Structure.
(1) The beneficiary’s representatives and the contractors shall continuously monitor the quality
of the works, in accordance with the specifications and the applicable specific normative documents in
force, and shall draw up reports for any concealed works found.
(2) The concrete components of the dam body shall be made of strong, waterproof and frostproof
concrete that has no pouring imperfections (gaps, segregation). The quality of the concrete from the
point of view of the types of tests (laboratory and in situ) and their frequency shall be checked in strict
compliance with the legal provisions.
31
(3) Lamellas shall only be concreted under the supervision of the technical manager and the
beneficiary’s representative, who shall record the way in which the works are carried out in the lamella
concreting sheet.
(4) When carrying out filling works, the granulometric composition and degree of compaction
stipulated shall be ensured in accordance with the filling compaction and advancement technology. The
quality control of the materials shall be carried out by the contractor by taking samples on a systematic
basis, in accordance with the specifications. The progress of the construction works shall be documents
in daily data sheets that constitute documents to be included in the Log Book of the structure.
(5) All metallic structures shall only be installed in accordance with the installation design drawn
up by a specialist company, which shall include: the main elevation heights of the structure (control
heights), the order in which the various components must be installed and the order in which the joints
must be made, the devices and equipment used, etc.
7.4 The personnel working in water retention structures located in seismic zones shall receive
special training on how to act in the event of major seismic events. The emergency action plan shall also
stipulate the situation generated by a major seismic event.
7.5 The anti-seismic structural measures can be grouped into general measures and specific
measures.
(1) General measures shall include the procedures for choosing the site and type of dam, as well
as the processes implemented in order to ensure very good quality of the above-mentioned construction
works.
7.6 The specific anti-seismic structural measures shall largely depend on the type of dam being
built.
(1) The shapes selected for concrete dams shall be as harmonious as possible, making sure to
avoid sudden changes in the face slopes, geometries or rigidities. The galleries and cavities inside the
dam body shall be reduced in number and in terms of cross-sectional surface areas, and their corners
shall be rounded.
(2) The centre of gravity of the transverse profile of gravity dams should be as low as possible,
which can be achieved by suitable optimisation of the cross-section, to reduce the overturning moments
caused by the seismic inertial forces developed within the mass of the dam.
(3) The special structural measures adopted for buttress dams must lead to an increase in the
longitudinal stability of the dam. Therefore, the following measures can be taken: closing the buttresses
downstream, founding the buttresses on independent sole plates placed next to each other, installing
buttons adjacent to the toe of the buttresses, encasing the buttresses, installing longitudinal wind bracing
diaphragms or girders.
(4) Arch dams are hyperstatic structures with very good behaviour under seismic stress. The
specific structural measures adopted for these types of dams include the provision of special dissipative
elements consisting of shrinkage joints that are partially non-injected and tied together at the crest with a
reinforced concrete girder, as well as the pre-stressing of certain zones of the dam body, the closing
abutments in the banks and the banks, in order to limit the risk of cracking.
(5) The specific measures adopted for rockfill dams are designed to retain the functionality of the
sealing elements, which are vital for the safety of the dams. Cracking of the sealing elements can lead to
uncontrolled water losses and the initiation of severe erosion phenomena. The reinforced concrete
guards can be made of several layers with staggered joints. Cores made of clayey materials should have
high plastic qualities and be relatively thick to prevent their perforation due to cracking.
(6) The sliding stability of rockfill dams can be improved by reducing the declivity of the faces,
fragmenting the embankments using stabilising berms, partially or fully ballasting the embankments
32
with dry masonry made of blocks of rock, and installing stabilising benches at the heel and toe of the
dam.
(7) To prevent the dam from overflowing due to excessive crest settling caused by earthquakes,
the crest safety guards of rockfill dams located in zones with high seismicity shall be increased by 25–
50 %.
(8) In general, liquefiable materials cannot be used in the foundation or body of rockfill dams. If
removing such materials is too costly, their degree of packing shall be increased (Dr ≥ 0.8, Dr - relative
density) using adequate constructive measures.
(9) The design of the new rockfill dams shall stipulate the use of seismic isolators and seismoabsorbing layers. These structural elements have the role of absorbing a higher portion of the earthquake
energy, whilst reducing the earthquake energy which acts upon the body of the dam.
(10) Other specific structural measures that can be taken for auxiliary water engineering
structures used in dam facilities were presented in Chapter 5.
8.
Surveillance and monitoring of dam engineering structures built in
seismic zones
8.1 Dams belonging to importance classes I and II and importance categories A and B, which are
built on sites with an MSK degree of seismic intensity equal to or higher than VIII, shall be equipped
with seismic monitoring equipment that operates continuously, in order to gather information about the
seismic response of these structures.
8.2 The operating safety, including the seismic safety, of the water engineering structures used
for dams belonging to importance classes I and II and importance categories A and B shall be assessed
on a periodic basis, at intervals of no more than 7 years, by taking into consideration the ageing of the
structure, the structural and non-structural modifications that have occurred since the last assessment, as
well as the progress registered with regard to the seismic safety assessment methods and methodologies.
(1) The seismic safety shall be assessed both by using calculation models and by carrying out onsite dynamic measurements (free vibration characteristics, damping, elastic wave velocities, dynamic
stress response).
(2) The operating safety, including the seismic safety of all other water engineering structures
used in dam facilities shall be assessed at maximum intervals of 10 years. The operating safety,
including the seismic safety of tailings dams and dykes shall be assessed at maximum intervals of 5
years.
8.3 Dam engineering structures that have been subjected to an earthquake with an intensity of at
least V MSK degrees shall be inspected in the period immediately after the earthquake, in order to
determine the effects of the respective earthquake on the structures and whether repair-consolidation
measures are required.
8.4 Throughout the entire service life of the dam engineering structures, no structural or
functional modifications shall be permitted if these have a negative influence on the strength, stability,
safety or functionality of the respective structure. Any technical intervention on the dam engineering
structures shall only be designed and implemented by suitably qualified personnel, in accordance with
the specific applicable technical regulations in force with regard to the tracking of the behaviour of
structures over time.
8.5 The structural (strength) elements and non-structural elements (partition walls, secondary
elements), as well as the equipment and installations used in dam engineering structures shall be
rigorously analysed to prevent their destruction or damage due to earthquakes. All objects, equipment,
33
installations and network systems whose displacement or falling could lead to functional disturbances or
even the loss of human life shall be anchored to secured fixed elements in a suitable manner.
8.6 The emergency warning-alarm plans drawn up for water retention structures, when these
structures are located in zones with a seismicity of at least VII MSK, shall also include the measures that
must be taken during and immediately after high intensity seismic events.
9.
Restoration works for water engineering structures affected by
earthquakes
9.1. The restoration works carried out for water engineering structures affected by earthquakes
are intended to return the structures being restored to safety levels close to those that they had before
they were affected by the earthquakes.
(1) A simple, quick and non-destructive method of checking the efficiency of the restoration
works is to carry out on-site measurements of the free vibration characteristics (natural periods + natural
shapes) of the structure being restored. The first natural modes (natural periods + natural shapes) of the
structure being restored must be as similar as possible to the ones the structure had before the
earthquake.
(2) The latter are known due to the dynamic identification carried out during the operation of the
respective structure in accordance with Article 8.2 of this normative document.
9.2 The decision to restore certain dam engineering structures affected by earthquakes shall be
taken on the basis of the conclusions drawn and recommendations issued in the technical survey report.
If the required costs would be too high and economically non-justified, water engineering structures that
have been severely affected by earthquakes could be demolished (decommissioned).
9.3 There is a large variety of restoration works, depending on the type of damage suffered by
the structure. The most frequent restoration works are specified below.
(1) Excessive infiltrations that occur in rocky foundations shall be reduced by means of sealing
injections of cement slurry or other verified substances, after the main infiltration routes have been
determined using specific procedures.
(2) If any fissures occurring in the body of concrete dams or the auxiliary concrete structures of
rockfill dams pose a threat to the safety of the dam or generate functional disturbances (infiltrations),
they shall be injected with epoxy resins or other substances that will increase the strength (shear, tensile)
on the respective fissure, at the level within the concrete mass. The solutions adopted for large fissures
(cracks), especially horizontal fissures occurring in the upper region of concrete dams, shall ensure precompression in the direction perpendicular to the surface of the fissures, using prestressed anchors.
(3) Any rock areas that have become dislocated or have slid from the banks shall be removed by
ripping or shall be anchored, if the second solution is more economical and provides a suitable level of
safety.
(4) The sliding stability of gravity dams can be improved by reinforcing the toe of the dam. The
longitudinal stability of buttress dams can be improved by installing foundation mats or diaphragms,
placed next to each other, at buttress level.
(5) The sliding stability of the banks of rockfill dams can be improved by softening their slope,
as well as by installing additional berms or stabilising benches at the base of the bank.
(6) Any rockfill zones that have slid or have become dislocated shall be removed and the riprap
shall then be restored using a suitable technology.
(7) The drying of certain zones of the body of rockfill dams by reducing the elevation height of
the infiltration curve can be achieved by carrying out special drainage works in the area of the toe
(drainage galleries, drainage pipes, deep counter conduits in the area adjacent to the toe of the dam, etc.).
34
(8) The sealing elements, such as sealing guards, used in rockfill dams which have lost their
functionality due to cracking, can be restored by applying a leaktight membrane made of synthetic
materials on the upstream face. The same solution can also be used for concrete or rolled concrete dams
that have been severely fissured and experience an excessive level of infiltration.
9.4 For dam engineering structures or their reinforced concrete or metallic structural elements
that can be assimilated to the structures or structural elements stipulated in normative document P100-3,
all restoration works carried out after an earthquake shall comply with the provisions stipulated in this
normative document.
10. Reference documents
(1) This normative document shall be enforced in correlation with the provisions of the
normative documents in the field of water engineering, environmental protection, constructions and land
improvement, as well as the applicable specific technical regulations in force, as follows:
Ite
m
No
1.
Standards
SR EN 1998-1:2004
SR EN 1998-1:2004/AC:2010
SR EN 1998-1:2004/NA:2008
SR EN 1998-2:2006
SR EN 1998-2:2006/AC:2010
SR EN 1998-2:2006/A1:2009
Name
Eurocode 8: Design of structures for earthquake resistance
Part 1: General rules, seismic actions, and rules for buildings
National annex
Eurocode 8: Design of structures for earthquake resistance.
Part 2: Bridges
Eurocode 8: Design of structures for earthquake resistance.
Part 2: Bridges. Amendment 1.
National Annex
SR EN 1998-2:2006/NA:2010
SR EN 1998-3:2005
SR EN 1998-3:2005/AC:2010
SR EN 1998-3:2005/NA:2010
SR EN 1998-4:2007
Eurocode 8: Design of structures for earthquake resistance.
Part 3: Assessment and retrofitting of buildings
National Annex
Eurocode 8: Design of structures for earthquake resistance.
Part 4. Silos, tanks and pipes
National Annex
SR EN 1998-4:2007/NB:2008
SR EN 1998-5:2004
Eurocode 8: Design of structures for earthquake resistance.
Part 5: Foundations, support structures and geotechnical
aspects. National Annex.
SR EN 1998-5:2004/NA:2007
SR EN 1998-6:2005
Eurocode 8: Design of structures for earthquake resistance.
Part 6: Towers, masts and chimneys. National Annex.
SR EN 1998-6:2005/NB:2008
2.
STAS 4273-1983
Water engineering structures. Classification into importance
classes
35
Ite
m
No
Normative documents
Publication
1.
Seismic design code - Part I - Provisions for the design of
buildings”, code P 100-1/2012
2.
Seismic design code. Part III. Provisions for the seismic
evaluation of existing buildings”, code P 100-3/2008,
approved by MDRL Order No 704/2009
draft technical regulation notified to
the European Commission with
numbers 2012/679/RO,
2012/682/RO, 2012/683/RO,
2012/684/RO
Official Journal of Romania, Part I,
No 674 and No 674 bis of 1 October
2009
3.
Law No 10/1995 regarding quality in constructions, with its
subsequent modifications
Official Journal of Romania, Part I,
No 12 of 24 January 1995
4.
Government Emergency Ordinance No 195/2005 regarding
environmental protection, with its subsequent modifications
and supplementation
Official Journal of Romania, Part I,
No 1196 of 30 December 2005
5.
6.
7.
8.
9.
10.
11.
Water Law No 107/1996, with its subsequent modifications
and supplementation
Methodology for determining the importance categories of
dams - NTLH-021, approved by MAPM/MLPLT Order No
115/288/2002
Government Decision No 766/1997 for the approval of
certain regulations concerning quality in constructions, with
its subsequent modifications and supplementation
Government Decision No 273/1994 for approval of the
Acceptance Rules for building works and their related
installations, with its subsequent modifications and
supplementation
General rules for fire protection, approved by Order No
163/2007 of the Ministry of Administration and Interior
Government Emergency Ordinance No 244/2000 regarding
dam safety, republished
Rules for the management of emergency situations generated
by floods, dangerous weather phenomena, accidents occurring
at water engineering structures, accidental pollution of water
courses and sea pollution in the coastal region, approved by
MMP/MAI Order No 1422/192/2012
36
Official Journal of Romania, Part I,
No 244 of 8 October 1996
Official Journal of Romania, Part I,
No 427 of 19 June 2002
Official Journal of Romania, Part I,
No 352 of 10 December 1997
Official Journal of Romania, Part I,
No 193 of 28 July 1994
Official Journal of Romania, Part I,
No 216 of 29 March 2007
Official Journal of Romania, Part I,
No 96 of 4 February 2002
Official Journal of Romania, Part I,
No 649 of 12 September 2012
B. General bibliographical references
1.
2.
5.
3.
4.
5.
6.
7.
8.
x X x An engineering guide to seismic risk to dams in the United Kingdom, 1990.
ICOLD Bulletin No 52 Earthquake Analysis Procedures for Dams. State of the Art., Paris, 1986.
ICOLD Bulletin No 72 Selecting Seismic Parameters for Large Dams. Paris, 1989.
ICOLD Bulletin No 112 Neotectonics and Dams, Paris, 1998.
ICOLD Bulletin No 113 Seismic observations of dams - Guidelines and case studies, Paris, 1999.
ICOLD Bulletin No 120 Design features of dams to resist seismic ground motion, Paris, 2000.
ICOLD Bulletin No 122 Computational procedures for dam engineering, Paris, 2000.
x X x USBR – Design of Gravity Dams. Denver-Colorado, 1983
x X x ICOLD European Club Final Report of Working Group on Guidelines for the Seismic
Assessment of Dams. Co-ordinator: N. Reilly (United Kingdom), Madrid, 2004.
37
Notations. Abbreviations
I - XII
1...9
M
MM
MSK
TB,TC,TD
-
Ed
µd
Gd
υ
Vp
Vs
OBE
MCE
SEE
MDE
DBE
PGA
PGV
KOBE
β
-
A, B, C, D
DE
HF
Δt
Rcd
Rcs
Rid
Dr
ag
MRI
T
-
Degrees of seismic intensity;
Degrees of seismic intensity;
Gutenberg-Richter magnitude scale;
Modified Mercalli intensity scale;
Medvedev-Sponheur-Karnik intensity scale;
corner periods specific to the spectral composition diagrams of the horizontal
seismic movement occurring within a site;
dynamic modulus of elasticity;
dynamic Poisson ratio;
dynamic shear deformation modulus;
damping rate (fraction of the critical damping);
primary seismic wave velocities
secondary seismic wave velocities;
operating basis earthquake;
maximum credible earthquake;
safety evaluation earthquake;
maximum design earthquake;
design basis earthquake;
peak ground acceleration of an earthquake;
peak ground velocity of an earthquake;
seismic intensity coefficient of OBE (operating basis earthquake);
non-dimensional dynamic amplification factor equal to the ratio between the
maximum response acceleration of the oscillator and the maximum ground
acceleration;
- importance categories of water engineering structures
distance between the site where the dam is located and the epicentre of the focus
point of an earthquake;
depth of the focus point of an earthquake;
calculation step (seconds) used in the direct numerical time integration method;
flexural compressive strength of the concrete under dynamic loads;
flexural compressive strength of the concrete under static loads;
flexural tensile strength of the concrete under dynamic loads;
relative density of a granular material;
design peak ground acceleration;
reference mean recurrence interval of the seismic action, corresponding to the
calculation at SEE (ultimate limit state in P 100-1);
natural period of the oscillator (seconds);
38
Annex A
GLOSSARY OF TERMS
Absorption: a process in which the energy of a seismic wave heats the medium through which it
propagates.
Effective peak acceleration: see Peak (maximum) ground acceleration.
Peak ground acceleration (PGA1): the maximum free-field acceleration produced during an earthquake
in any horizontal direction. It is usually expressed in relation to the gravitational acceleration.

The effective peak ground acceleration is the peak acceleration obtained after filtering high
frequencies, which have a small influence on the structural response.
Accelerogram: a recording of the vibrating movement, representing the acceleration over time.
Accelerograph: an instrument used for measuring acceleration during vibrating movements.
Focal depth: the radial (vertical) distance between the epicentre and the focus point (hypocentre) for a
certain earthquake.
Damping: a vibration damping phenomenon occurring due to energy absorption.
 Critical damping: the minimum damping at which the free oscillation of a structure within a
system with a single degree of dynamic freedom becomes aperiodic.
 Fraction of critical damping (damping ratio, ): the ratio between the damping value and the
critical damping value.
 Quality factor (Q): Q = 1/(2).
 Damping factor: 1/Q.
Amplification: increasing the parameters for the source movement from the base stratum to the upper
strata due to a lower level of consolidation of these strata, as well as due to the response of an existing
structure.
Amplitude: the maximum deviation from the median or the central reference line of a wave.
Pseudo-static analysis: a limit equilibrium stability analysis in which the effect of the earthquake is
represented by an acceleration ag, where a is the seismic intensity factor and g is the gravitational
acceleration. In the simplest forms, ag shall be considered to act horizontally, producing an inertial force
equal to aW, where w is the weight of the mass that has the potential of sliding. This force is applied
statically, not dynamically.
Attenuation: the loss of amplitude and modification of the frequency content of the seismic waves over
a certain distance due to scattering, dissipative phenomena, energy absorption, etc. It also represents (1)
the reduction in signal magnitude during transmission and (2) the loss of amplitude or energy with or
without changing the shape of the waves.
Free field: regions of the environment which are not influenced by artificial structures, or an
environment which does not contain such structures (also refers to those regions where the boundary
1
PGA = Peak Ground Acceleration, in English.
39
conditions do not significantly influence the behaviour of the environment).
Earthquake: vibrations of the Earth’s crust due to excessive deformations occurring inside it. For study
purposes, the parameters corresponding to the design or safety assessment analyses (e.g. acceleration)
can be defined. When analysing the seismic behaviour of dams, the following types of earthquakes can
be defined:
 Design basis earthquake (DBE2): represents the earthquake that may occur, on average, no more
than once throughout the expected service life of the structure (usually no less than 100 years) and
during which no significant damages should occur (see OBE).
 Maximum credible earthquake (MCE3): an earthquake which could produce the highest level of
ground movement within the site being studied and which appears to be possible from the point of
view of the on-site geological conditions.
 Maximum design earthquake (MDE4): an earthquake which produces the maximum level of
ground movement for which a certain dam is being designed or analysed.
 Operating basis earthquake (OBE5): an earthquake that is possible to occur, on average, no more
than once throughout the expected service life of the structure (usually at least 100 years), and
during which the dam and its auxiliary structures would remain operational but could require
repairs (see DBE).
 Safety evaluation earthquake (SEE6): an earthquake that produces the most severe level of ground
movement for which the dam safety requirements must be complied with in the event of
catastrophic yielding (it can be an MCE, a fraction of MCE, or can be determined depending on
the return period).
Epicentre: the point on the Earth’s surface which corresponds to the radial (vertical) projection of the
focus point (hypocentre) of an earthquake.
Quality factor (Q): see Damping.
Safety factor (F): it can be defined in any convenient way, as long as it is applied consistently. For
example, it can represent the factor by which the strength must be reduced to “bring” the structure to a
limit equilibrium state.
Fault: a fracture or fractured area of the Earth’s crust along which relative movements of the adjacent
fragments have occurred.
 Active fault: a fault known to have produced historic earthquakes and which, due to the tectonic
conditions, can undergo movement in the foreseeable future.
 Capable fault: a fault which has the potential of undergoing future surface movements. A fault
shall be considered to be capable if it displays at least one of the following characteristics:
1. had one movement during the period of time elapsed since the Quaternary period up until the
present
2. was accompanied by macro-seismic activity
3. is in a structural relationship with another capable fault, so that the movement of one of them
can initiate the movement of the other.
 Normal fault: a fault in which the main component of the relative displacement was vertical.
 Tectonic fault: an inclined fault along which the rocks located above the area of discontinuity have
2
DBE = Design Basis Earthquake, in English.
MCE = Maximum Credible Earthquake in English.
4
MDE = Maximum Design Earthquake in English.
5
OBE = Operating Basis Earthquake in English.
6
SEE = Safety Evaluation Earthquake in English.
3
40
raised compared to the rocks located below the area of discontinuity.
Focus point: see Hypocentre.
Frequency: number of cycles as a ratio of the time unit (measured in Hertz [Hz] or cycles per second).
Natural frequency: a property of the elastic system undergoing a free vibration movement. The free
vibration will naturally occur at a discrete frequency, when an elastic system vibrates under the action of
the internal forces, in the absence of an exterior force.
Resonant frequency: a frequency at which resonance occurs.
Geophone: a sensitive device for the electronic measurement of the speed at which the sound or waves
produced by a known source propagate through the ground.
Tectonic geology: the study of the global arrangement of the main plates on the Earth’s surface, as well
as the origin and evolution of the vertical and horizontal movements which have led, over time, to this
arrangement.
Hazard: a situation that has the potential of leading to the injury or death of people and/or destruction of
goods.
Hypocentre: the point inside the Earth which is the source of an earthquake and the origin of the elastic
waves associated with it.
Acoustic impedance: it is numerically equal to the product between the velocity of the seismic wave
and the density of the propagation environment.
Intensity: a numerical indicator which describes the effects of an earthquake on people, structures and
the ground.
Spectral intensity: the surface below the diagram of the velocity response spectrum between the periods
of 0.1–2.5 seconds. It represents a measurement of the intensity of the ground vibrations, which is useful
in engineering studies.
Liquefaction: a temporary loss of shear strength, which makes the ground behave similar to fluids.
Loose sandy soils are the most vulnerable to the liquefaction induced by the occurrence of earthquakes.
Magnitude: a quantity which characterises the total energy released following the occurrence of an
earthquake. There are several types of magnitudes, calculated in different ways and using different
instruments.
 ML is based on the maximum amplitude of the local waves, measured by a Wood-Anderson
seismometer.
 MS is based on the amplitude of the surface waves.
 mb is based on the amplitude of the body waves.
 M0 (seismic moment) measures the size of an earthquake based on the energy it releases, in
accordance with the formula M0 = GAD, where G is the shear modulus of the environment
(usually considered to be 3x1011 dyne/cm2); A is the size of the displacement surface or the fault
(fracture) surface; D is the average backlash on the respective surface.
 MW (magnitude moment) is derived from the seismic moment:
 MW = (2/3) log M0 - 10.7, where M0 is the seismic moment (dyn.cm)
41
The Richter magnitude must be strictly applied for ML although, in practice, it can also be used for MS.
The relationships between MS, ML and mb are not unique and various versions, sometimes inconsistent,
have been published. Ambraseys proposes the following formulas:
MS = 0.93 ML + 0.09
MS = 1.05 mb – 0.8
Near-field movement: a ground movement registered in the vicinity of a fault, over a region on whose
radium the intensity on the Modified Mercalli scale is higher than V.
Strong movement: a ground movement whose amplitude is sufficiently high to allow it to be
considered significant, from an engineering point of view, in assessing the destruction caused by an
earthquake.
Shear modulus (G): the ratio between the shear stress and the specific shear deformation.
G = 0.5 E / (1+)
where E is the Young modulus and  is Poisson’s ratio.
The shear modulus of a soil depends on the specific shear deformation and decreases as the
deformation increases. Gmax is the shear modulus of the soil in the presence of very small cyclic shear
deformations (10-6).
Gmax = VS2 where  is the mass density of the soil and VS is the shear wave velocity.
Moment: for the seismic moment (M0), see Magnitude.
Return period: the average interval of time elapsed between the occurrence of certain events, which
exceeds a certain level within a given site. It is the reverse of the annual exceedance probability.
According to the definition, earthquakes are considered to be independent stochastic events, which does
not fully match reality. The probability Pr that an event with a return period of at least T years will occur
at least once in the next r years can be expressed with the following relationship:
Pr / 100 = 1 – (1–1/T)r
Period: the time interval of a vibration cycle.
Exceedance probability: the probability (in percentages) that an earthquake will generate a level of
ground movement above a certain limit, calculated over a time interval.
Aftershocks: secondary seismic movements produced after the main shock of an earthquake.
Resonance: the amplified response of one of the natural modes of vibration of a dynamic system excited
at a frequency close to the natural frequency.
Risk: the probability that a certain undesirable event or hazard will occur within a certain time interval.
Seismic: relating to earthquakes.
 Seismic intensity factor. The ratio between the maximum acceleration of the earthquake and the
gravitational acceleration.
 Seismic moment: see Magnitude.
Seismogram: a recording of the ground movement or vibrations of a structure, produced by a perturbing
cause (e.g. an earthquake). See Accelerogram.
42
Seismograph: a system which amplifies and records the signals transmitted by seismometers.
Seismometer: an instrument used to transform the seismic wave energy into voltage. Most
seismometers are velocity detectors and the values they measure are proportional to the velocity of the
inertial mass in respect with the seismometer casing (which is proportional to the ground movement
velocity). Under natural frequencies, the response of most geophones will decrease linearly with
frequency, therefore these geophones will function as accelerometers.
Response spectrum The maximum response of an infinite number of harmonic oscillators with various
natural periods of vibration and damping, which are subjected (mathematically) to a seismic action.
Design spectra spectra used for anti-seismic design. The design spectra are obtained by modifying
families of historical earthquake spectra to take into account the particular characteristics of a certain
region or site. The design spectra will not include the effects of the interaction between the ground and
the structure.
Fourier transform: mathematical formulas which transform a function from the time range (waveform,
seismogram, etc.) into a function in the frequency range and vice versa.
Rayleigh wave: see Seismic waves.
Seismic wave: an elastic wave generated by an earthquake or explosion which only cause a temporary
displacement of the medium; the return to the initial position is accompanied by ground vibrations. Body
waves are of two types:
 compression or longitudinal waves (P), for which the direction of movement of the medium
particles coincides with the direction of propagation of the wave. The velocity of propagation is
noted with VP.
 shear or transverse waves (S), for which the direction of movement of the medium particles is
perpendicular to the direction of propagation of the wave. The velocity of propagation is noted
with VS.
Surface waves propagate near the surface of the crust and are of two types:
 Rayleigh waves, which cause the medium particles to move along an elliptical and retrograde
trajectory in a vertical plane formed with the direction of propagation. The velocity of propagation
is noted with VR.
 Love waves, which cause the medium particles to move in a direction perpendicular to the
direction of propagation, without any movement in the vertical plane.
Body waves: see Seismic waves; for the magnitude of the body waves (mb) see Magnitude.
Forced vibrations: vibrations which occur if the response is forced by an excitation. If the excitation is
periodical and continuous in terms of its duration, the oscillation shall take place in a stationary state.
Free vibration: a vibration which occurs in the absence of a perturbing force.
Viscoelastic: a stress-deformation relationship containing terms that are proportional to both the specific
deformation and its increment. It can lead to seismic wave attenuation laws that are frequencydependant.
Effective peak velocity: see Peak (maximum) ground velocity.
43
Peak ground velocity (PGV7): maximum free-field ground velocity produced during an earthquake.
 The effective peak ground velocity represents the peak velocity obtained after the filtration of high
frequencies.
Shear wave velocity (VS): see Seismic wave.
Seismotectonic zone: see Tectonic zone.
Tectonic zone: a zone characterised by homogeneity of the geological and seismic structure.
Seismic zoning: summary of the seismic information within a territory, which is used to delimit the
zones with the same seismic risk. The seismic micro-zoning highlights the influence of the local natural
conditions on the seismicity of a limited area (e.g. a town).
7
PGV – Peak Ground Velocity, in English.
44
Annex B
INTERNATIONAL SEISMIC CRITERIA AND REGULATIONS
Eurocode 8 for the design and construction of civil engineering buildings and structures in
seismic zones does not include references to large dams. However, the Eurocode has an influence on the
way the seismic safety assessment of dams is carried out. It presents the national regions classified into
seismic zones, based on their general tectonic characteristics and previous seismic activity. The peak
(maximum) ground acceleration is considered to be a suitable parameter to characterise each zone.
Eurocode 8 states: “For regular structures located in zones with very low seismicity, the general
sturdiness requirements could be sufficient to guarantee a suitable level of (anti)seismic protection.”
The International Association for Earthquake Engineering (IAEE) has published a collection of
codes and regulations applicable in countries located in seismically active regions around the world.
Most of these regulations are not intended to cover the field of dam engineering. The Australian
standard for anti-seismic protection of buildings explicitly excludes dams. However, both the Indian
standard “Criteria for the anti-seismic design of structures” (IS: 1893-1975) and the Japanese “Standards
for seismically-resistant civil buildings” include dams. It must be noted that the safety assessment
standards in force for existing dams do not have to be the same as those in force for newly designed
dams.
In India, an initial standard was published in 1962 and revised in 1966. The 1966 standard
includes the necessary factors for a much more rational seismic zoning. The clauses referring to concrete
and masonry dams were amended to take into account the dynamic behaviour of these dams during
earthquakes. Depending on the problem, one of the following two methods can be used to determine the
seismic forces:
a) the seismic coefficient method;
b) the response spectrum method.
The map of India is divided into five seismic zones. Each of these zones is allocated a basic
horizontal seismic coefficient and a seismic zone factor. When designing concrete and masonry dams,
the seismic force is considered in addition to the hydrodynamic pressures created by the storage
reservoir; the seismic coefficient method is used for dams with a height of up to 100 m, whereas the
response spectrum method is used for dams higher than 100 m. The effect of the vertical seismic
acceleration is also taken into consideration.
In 2005, a document including guidelines for the seismic design of earthfill dams and
embankments was drawn up by the Indian Institute for Technology in Kanpur and the Disaster
Management Authority in Gujarat state. The guidelines were revised in 2007.
The criteria for choosing the anti-seismic protection measures for water supply systems,
established by Japan Water Works Association, also include dams. These criteria use the seismic
coefficient method. The Japanese National Committee for Large Dams has also issued design criteria for
dams. These criteria also use the seismic coefficient method. The seismic coefficient depends on the
region, type of terrain, type of dam and importance of the dam.
In the US, most federal and state agencies use seismic zone maps when they decide to include
seismic factors in the design of dams. The Body of Engineers uses the following seismic coefficients:
45
Seismic zone
0
1
2
3
4
Minimum coefficient
0
0.05
0.10
0.15
0.20
The Federal Guidelines for Dam Safety were published in 2005 and provide complete
information about the design and assessment of dams located in seismic zones.
In the UK, the Building Research Establishment has drawn up an “Engineering guide to seismic
risk to dams in the United Kingdom”.
The European Club formed by some European countries that are ICOLD members, which
Romania has joined, published a guide in 2004 which summarises all the regulations applicable to the
seismic design and assessment of dams, in force in several European countries.
Several bulletins drawn up by specialist ICOLD committees are relevant for highlighting the
international views on the seismic safety assessment of dams. The numbers of these ICOLD Bulletins
are: 27 (1975) 46 (1983) 52 (1986) 59 (1987), 61 (1988), 62 (1988), 72 (1989), 112 (1998), 113 (1999),
120 (2000), 122 (2000). The years given in brackets is the year when these ICOLD Bulletins were
published. One of the four themes on the agenda of the ICOLD Congress held in Montreal in 2003
referred to seismic aspects of dams.
46
Annex C
CALCULATION RELATIONSHIPS USED IN THE PSEUDO-STATIC METHOD
The pseudo-static method assumes that the seismic acceleration at the base of a structure shall
remain constant for the entire height of the structure. This method shall only be used to determine the
seismic response to an OBE (operating basis earthquake).
The earthquake generates inertial forces due to the structural mass, whose direction and
orientation are opposite to the seismic acceleration, as well as hydrodynamic pressures due to the
reservoir, with a direction opposite to the seismic acceleration and an orientation perpendicular to the
surface on which they are applied.
The inertial forces (Fi) corresponding to a structural mass (Mi) shall be calculated with the
following relationship:
Fi  K C ,OBE g M i
(1)
where Kc, OBE is the corrected seismic intensity factor of OBE and g is the gravitational
acceleration. The force Fi shall apply to the centre of gravity of the mass Mi.
The hydrodynamic pressures applied on a vertical rectilinear face (pz,v) that is subjected to a
horizontal earthquake can be calculated with the Westergaard relationship:
p z, v  0.875 KC, OBE  a ( H l z) 0,5
(2)
where γa is the volumetric weight of the water, Hl is the depth of the reservoir upstream from the
dam, and z is the depth of the point where the hydrodynamic pressure is calculated.
The hydrodynamic pressure on an inclined rectilinear face (pz, α) that is subjected to a horizontal
earthquake shall be determined with the following relationship:
p z,   p z, v cos 2 
(3)
where α is the angle between the vertical direction and the direction of the dam face. The
pressure pz, α is perpendicular to the dam face.
The inertial and hydrodynamic forces shall be applied statically to the structure, without a time
limit.
47
Annex D
ASSESSMENT OF HYDRODYNAMIC PRESSURES DUE TO EARTHQUAKES
During an earthquake, water engineering structures have to bear a hydrodynamic pressure in
addition to the hydrostatic pressure; this additional pressure is applied on the face that is in contact with
the water, perpendicular to the contact surface, due to the liquid-structure interaction.
The value of the hydrodynamic pressure manifested in a point of contact with the water shall
depend on the depth of the water column, the gradient formed by the surface with the vertical axis, the
planar shape of the surface, the ground morphology, the rigidity of the reservoir bottom and the direction
of the seismic acceleration.
The hydrodynamic pressures shall be perpendicular to the surface on which they are applied,
similarly to hydrostatic pressures, and shall have a direction opposite to the seismic acceleration
(reversed phase).
The hydrodynamic pressures shall be determined for two hypotheses relating to the liquid,
namely: non-compressible liquid (the frequently-accepted situation) and compressible liquid; there can
be significant differences between the two situations.
This annex refers to the non-compressible liquid situation.
The analyses carried out for very important structures should also include the compressible
liquid hypothesis.
In the spectral analysis or numerical time integration method, as well as for the non-compressible
water hypothesis, the effect of the hydrodynamic pressures and structure-liquid interaction on the
seismic response is usually modelled using additional masses. The additional masses are virtual masses
equivalent to the effect of the hydrodynamic pressures on the response of the water engineering
structure. They shall be calculated from the hydrodynamic pressures and attached to the natural masses
of the structure. In the particular situation in which the direction of the hydrodynamic forces
(perpendicular to the surface to which they are applied), the direction of the earthquake and the direction
of the dynamic degrees of freedom are identical, the matrix of additional masses[Mh] shall be
determined with the following relationship:
Px   M h  a x 
where {Px} is the vector of the hydrodynamic forces and {ax} are the total accelerations along
the perpendicular to the water contact nodes in the system digital representation. The additional masses
shall be positive and, in general, depend on the direction of the earthquake and the directions of the
dynamic degrees of freedom.
The calculations carried out as part of the pseudo-static method shall directly use the
hydrodynamic forces, considered similar to static loads.
When the ratio between the free length of the reservoir and the aperture of the valley at the site is
higher than 3, the hydrodynamic pressures applied to the planar surfaces of the dam facilities shall be
calculated using the following relationships:
For the vertical upstream face (α = 0)
a) For horizontal seismic acceleration (Figure D.1):
p x ( y )  0.743  K s   a  R ( y )  h
48
Px  0.544  K s   a  h 2
h'  0.597  h
m x  0.544   a  h 2
where
px (y) is the hydrodynamic pressure at the depth y (kPa);
Px
- resultant of the hydrodynamic pressures (kN/m);
γa - volumetric weight of the water (kN/m3);
ρa - water density (t/m3);
h
- reservoir depth (m);
h'
- water depth at the point where the resultant of the hydrodynamic pressures is applied
Ks - factor of seismic intensity;
mx - additional mass in direction x;
R (y) - non-dimensional function in accordance with Table E.1
R ( y) 
y/h
R(y)
0.00
0.00
00
0.10
0.31
29
0.20
0.48
10
1
2
0.30
0.61
21
 y

 h
y

2   
h

0.40
0.72
00
0.50
0.81
80
y
y  
2  
h
h  
0.60
0.87
83
0.70
0.93
20
0.80
0.96
99
Table D.1
0.90 1.00
0.99 1.00
25
00
b) For vertical seismic acceleration
In the case of vertical seismic acceleration, the hydrodynamic pressures shall have a linear
distribution in accordance with the following relationships:
p x ( y )  K s, v   a  y
Px 
1
 K s ,v   a  h 2
2
2
xh
3
1
mx   a  h 2
2
h' =
where Ks,v is the vertical seismic intensity factor and the other notations have been explained
above.
The case of an inclined upstream face which forms angle α with the vertical axis.
c) For horizontal seismic acceleration (Figure D.2):
p (, y )  K ()  K S   a  R ( y )  h
where: p (α, y) is the hydrodynamic pressure perpendicular to the face, at depth y;
K (α) - non-dimensional coefficient as a function of the angle α, in accordance with Table D. 2.
The other notations have been explained above.
49
α
K (α)
0°
0.743
15°
0.612
30°
0.511
40°
0.448
60°
0.292
75°
0.168
Table D.2
90°
0.000
d) For vertical seismic acceleration
In the case of vertical seismic acceleration, the hydrodynamic pressures shall have a linear
distribution in accordance with the following relationships:
p (  y )  K s, v   a  y
1
h2
P ()   K s, v   a 
2
cos 
2
h ' ( )  h
3
1
Px ( )   K s, v   a  h 2
2
1
Py ( )   K s, v   a  h 2  tg 
2
where: Px (α) is the horizontal hydrodynamic force and Py (α) is the vertical hydrodynamic force. The
other notations have been explained above.
For arch dams, the approximate calculation of the hydrodynamic pressures can be carried out in
accordance with the following relationships:
e) For horizontal seismic acceleration along the valley (Figure D.3a)
7
p ( , y )   K s   a  h  y  cos 
8
where y is the water depth and α is the angle between the direction of the earthquake and the
perpendicular to the surface of the arch, at the point where the hydrodynamic pressure is calculated. The
other notations have been explained above.
f) If the horizontal seismic acceleration is perpendicular to the valley (Figure D.3,b)
2x
p ( , y )  K s   a  h  y 
L
where the lengths x and L are marked on Figure D3.b, and the other notations have been explained
above.
50
Figure D.1.
Hydrodynamic pressures on the vertical
rectilinear face due to a horizontal earthquake
Figure D.2.
Hydrodynamic pressures on the inclined
rectilinear face due to a horizontal earthquake
Figure D.3.
Hydrodynamic pressures applied to arch
dams.
a - horizontal earthquake along the valley;
b - horizontal earthquake perpendicular to the valley
51
Annex E
ASSESSMENT OF THE SEISMIC PRESSURES DUE TO THE FOUNDATION GROUND
In addition to the inertial seismic forces applied by the dead load of the structure, the calculations
carried out to determine the seismic stability of partially or fully buried structures (abutments, galleries,
underground structures, dams, plants) shall also take into consideration the additional active or passive
seismic earth pressure.
Normally, the seismic earth pressure applied to abutment-type structures is determined for a
horizontal earthquake, whereas the seismic ground pressure applied to the dome (roof slab) of buried
(underground) water engineering structures is determined for a vertical earthquake.
The active seismic pressure can be assessed in the following two situations:
a. The active seismic earth pressure acting on the structure-foundation system when only elastic
deformations occur in the ground;
b. The active seismic earth pressure when plastic ground deformations occur in the structurefoundation system.
The passive seismic earth pressure shall only manifest when plastic ground deformations occur
in the structure-foundation system.
Active seismic earth pressure.
a. Elastic ground deformations.
In abutment-type structures, when the limit equilibrium state has not been reached yet, the active
earth pressure shall be determined with relationships (1) (Figure 6.1 a): The limit equilibrium state shall
correspond to the situation in which the sliding safety coefficient for the foundation is 1.0.
p a ( y )  K s    z  h  R ( y ,  )
21  16tg
Ma 
 K s   z  h3
48
3  2tg
Pa 
 K S   z  h2
4
1 15  8tg
ha'  
h
12 3  2tg
 1  y    y  2
 y      y 
R ( y,  )  1    10   9   3   1     tg
 h      h 
 4  h    h 
where:
Ks - factor of seismic intensity;
a - active pressure coefficient;
h - total height of the embankment near the abutment (m);
 - angle of the embankment (surface) behind the abutment;
γz - volumetric weight of the ground (kg/m3);
pa (y) - intensity of the active seismic pressure at level (y) (kPa);
Pa - resultant of the active seismic pressure (kN/m);
52
(1)
h'a - position of the resultant with respect to axis x (m);
Ma - bending moment in the section at the base of the abutment (ymax = h) (kNm/m);
R (y,) - non-dimensional function (in accordance with Table E.1)
Ψ - reduction coefficient for the active pressure Ψ = 0.75;
Values of function R (y,)
Table E.1
R (y, )
20°
°
0°
10°
15°
y/h
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1. 00
1. 0000
0.9450
0.9200
0.9100
0.9000
0.8750
0.8200
0.7200
0.5600
0.3250
0. 000
1.1763
1.1037
1.0611
1.0334
1.0058
0.9632
0.8905
0.7729
0.5953
0.3426
0. 000
1.2679
1.1862
1.1344
1.0976
1.0608
1.0090
0.9272
0.8004
0.6136
0.3518
0. 000
1.3640
1.2726
1.2112
1.1648
1.1184
1.0570
0.9656
0.8292
0.6328
0.3716
0. 000
25°
1.4663
1.3647
1.2930
1.2364
1.1798
1.1082
1.0065
0.8599
0.6533
0.3716
0. 000
30°
1.5774
1.4646
1.3819
1.3141
1.2464
1.1637
1.0509
0.8932
0.6755
0.3827
0. 0000
35°
2. 0000
1.8450
1.7200
1.6100
1.5000
1.3750
1.2200
1.0200
0.7600
0.4250
0. 000
The active seismic pressure determined this way shall only be the active pressure resulting from
seismic action; therefore, the action of the static active earth pressure must also be taken into
consideration when checking the stability of the structure.
b. Plastic ground deformations
In this situation, for abutment-type structures, it shall be considered that plastic ground
deformations have also occurred. For this hypothesis, the active earth pressure shall be determined as
total pressure, obtained directly by adding up the static pressure and the seismic pressure.
The resultant of the total active earth pressure (Pa) shall be calculated first, followed by the
resultant of the active static pressure (Pa,st). In the end, the active seismic earth pressure (Pa,d) shall be
obtained from the difference between Pa and Pa,st (Figure F1.b).
Pa , d  Pa  Pa , st
(2)
The calculation relationships are the following:
1
Pa   K a   z  h 2
2
3
K a  K as
ha, 
h
6 Ka
1
 K as   z  h 2
2
2
ha' , st   h
3
Pa , st 
53
(3)
1
 K a  K as    z  h 2
2
1
ha' , d   h
2
Pa , d 
cos 2     
Ka 
cos   cos
K as 
2

  cos    1 

sin    sin      

cos    cos     
2
cos    
2

sin    sin     
cos   cos   1 

cos    cos    

2
2
where:
the angle with the tangent line equal to Ks  Ψ where
Ks - is the seismic intensity factor and Ψ = 0.75 is an active pressure reduction coefficient;
a - active pressure coefficient;
h - total height of the embankment near the abutment;
 - angle of the slope of the embankment surface behind the abutment;
 - angle formed by the abutment face with the vertical axis at the point of contact with the
embankment;
ϕ - angle of internal friction of the embankment (in degrees);
 = the friction angle at the point of contact between the abutment and the embankment
 is
1
2
 or    );
2
3
Ka - non-dimensional function which defines the total active pressure (sum) of the embankment
(static + seismic);
Kas - non-dimensional function which defines the static active pressure of the embankment
Kas = Ka for Ks = 0
( 
Pa - resultant of the total active pressure, static + seismic, of the ground (kN/m);
Pa,st - resultant of the static active earth pressure (kN/m);
Pa,d - resultant of the seismic active earth pressure (kN/m);
ha' , st ; ha' , d , ha' - y coordinates of the position of the resultant of the static active, seismic
(dynamic) and total earth pressure (Figure E1 b)
Passive seismic earth pressure
The passive earth pressure shall only be calculated for the limit equilibrium state with plastic
ground deformations, represented by the total static + seismic (dynamic) passive pressure.
In successive steps, the total passive earth pressure (Pp) shall be calculated first, followed by the
resultant of the static passive pressure (Pp,st), where the difference between the two shall be the passive
seismic pressure (Pp,d)
Pp,d = Pp - Pp,st
(4)
54
The calculation relationships are the following:
K p  K p, st
h' p 
3 Kp
Pp 
1
K p   z  h2
2
Pp, st 
1
K p, st   z  h 2
2
h 'p, st 
2
h
3

(5)

1
K p  K p, st   z  h 2
2
1
h 'p, d   h
3
Pp, d 
Kp 
cos 2     

sin    sin      
cos   cos   cos      1 

cos    cos      

2
2
K p, st 
cos 2    

sin    sin     
cos   cos      1 

cos    cos     

2
2
where
is the angle whose tangent line is Ks  Ψ where Ks is the seismic intensity factor and Ψ = 0.75 is
a passive pressure reduction coefficient;
p - passive earth pressure coefficient;
Kp - non-dimensional function which defines the total passive earth pressure (static + dynamic);
Kp,st - non-dimensional function which defines the static passive earth pressure;
Kp = Kp,st for Ks = 0

Pp,st; Pp,d; Pp - resultants of the static, dynamic and total earth pressures (Figure E.2);
h 'p, st ; h 'p, d ; h 'p - y coordinates of the position of the resultant of the static passive, dynamic and
total earth pressure (Figure E.2)
If there is water in the pores of the ground behind the abutment, this shall have an influence by
increasing the active and passive seismic earth pressure. The active and passive inertial seismic
pressures shall be calculated by taking into consideration the volumetric weight of the saturated
ground (  'z ) instead of the dry volumetric weight (  z ), in accordance with the following
relationship:
 'z =  z + n  a
55
where:
 z is the volumetric weight of the dry ground (Kg/m3); n - porosity;
 'z - is the volumetric weight of the saturated ground (Kg/m3 and  a - is the volumetric weight
of the water (Kg/m3);
When the hydrostatic and hydrodynamic pressures due to ground water are considered separately
in the calculations, the earth pressures shall be calculated for the submerged volumetric weight.
Additional active seismic earth pressure applied by useful loads to the surface of the
embankment behind the abutment.
In the case of abutments, bank reinforcements, etc., high intensity useful vertical loads also
develop on the free surface of the embankments, which apply additional active seismic pressures to the
vertical face of the abutment, at the point of contact with the embankment.
In accordance with Figure E.3, an abutment of unlimited length along axis z shall be considered,
with the uniformly distributed vertical load, q, acting on the surface of the ground behind the abutment.
The intensity of the horizontal active seismic pressure pa(x,y) and the resultant of this pressure
Pa(x), as well as the position of this resultant shall be determined using the following relationships (the
calculation shall be carried out for the unitary length of the abutment l=1):
p  Ks    q
(6)
  y   y  2  y 3 
p a ( x, y )  p  a x   1          
  h   h   h  
from where max pa (x,y) = p  a(x) for y = 0
5
5
Pa ( x)   max pa  h   p  a x  h
12
12
'
h'a  0.28 h (see Figure F.3)
1  x
a x   1   
60  h 
for 0 
2

 x  x 
25  39    8   
 h   h  

x
 3 (Figure F.4) where:
b
a is the coefficient used for the active seismic pressure;
x,y,z - three-dimensional Cartesian coordinates;
h - total height of the embankment behind the abutment (m);
h a' - position of the resultant of the active seismic pressure (m);
l - length of the abutment along axis (z); the formulas are given for l = 1 (m);
Ks - factor of seismic intensity;
Ψ - reduction coefficient for the active pressure Ψ = 0.75;
q - constant-intensity useful vertical load at the distance (x) from the edge of the abutment
(Figure E.3) (kN/ml);
p - constant-intensity horizontal inertial load which acts on the free surface of the embankment at
the distance (x) from the edge of the abutment (Figure E.3) (kN/ml);
pa(x,y) - intensity of the horizontal active seismic pressure acting on the abutment face at the
point with the coordinates (x,y) (kN/m2);
56
max pa - maximum intensity of the horizontal active seismic pressure acting on the abutment face
at the point y = 0 (kN/m2);
Pa(x) - resultant of the horizontal active seismic pressure (kN/ml);
a(x) - non-dimensional function representing the influence line for max pa and Pa(x),
respectively, due to the action of the useful load qi at the distance xi from the abutment.
0  xi  3 h ; Figure E.4 and Table E.2
x/h
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
a(x)
1.0000
1.0353
1.0584
1.0701
1.0712
1.0625
1.0448
1.0189
0.9856
0.9457
0.9000
x/h
a(x)
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2. 00
0.8493
0.7944
0.7361
0.6752
0.6125
0.5488
0.4849
0.4216
0.3597
0.3000
x/h
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
Table E.2
a(x)
0.2433
0.1904
0.1421
0.0992
0.0625
0.0328
0.0109
-0.0024
-0.0064
0. 000
The process of determining the total active seismic pressure applied to the abutment wall (max pa
and Pa(x)) due to the simultaneous action of different vertical useful loads using the influence line a(x)
shall be carried out in accordance with the following relationships (Figure E.5):
p1  K s    q1
max pa 
p2  K s    q2
p3  K s    q3
3

i 1
pi a ( x i )
for y = 0
x4
max p a  p1 a ( x1 )  p 2 a ( x 2 )  p3
 a ( x ) dx (7)
x3
Pa ( x ) 
5
 max p a  h
12
ha'  0.28  h
57
  0.75
Figure E.1. Evaluation of active seismic earth pressures
a - for elastic ground deformations;
b - for plastic ground deformations
Figure E.2. Evaluation of passive seismic earth pressures
Figure E.3. Evaluation of additional seismic active pressures
58
max.
Figure E.4. Variation of function a (x)
max.
Figure E.5. Evaluation of additional active seismic pressures
59
Annex F
SEISMIC ANALYSIS OF A GRAVITY DAM
A seismic analysis of the transverse profile of the gravity dam shown in Figure B1 under the
action of an OBE (Operating Basis Earthquake) must be carried out in accordance with Regulation NP
076/2002.
The following shall be taken into consideration in addition to the geometrical elements shown in
the figure:
The mechanical properties of the concrete used for the dam body:
Eb = 24 000 MPa, µ = 0.16, γb = 24 kN/m3
The structure shall be considered to have 3 dynamic degrees of freedom in the horizontal direction.
The seismic interaction between the dam and the reservoir shall be determined using the additional
masses method.
The dam belongs to importance class II (STAS 4273-83) and importance category B (NTLH021).
In accordance with regulation P100-1, the dam is located in a seismic zone characterised by the
peak value of the site ground acceleration ag = 0.24g and corner periods TB = 0.1 s, TC = 1.0 s. The
special seismic survey of the site has confirmed the values given in P100-2006.
The earthquake is applied in a horizontal direction, perpendicular to the dam.
The seismic response spectrum is shown in Figure F2.
If using the pseudo-static method, anOBE = 0.40 ag but not less than 0.1g.
If using the spectral analysis method, anOBE = 0.40 ag but not less than 0.1g.
If using the finite element analysis, Ed = 1.35 Eb,s = 1.35 x 2 400 = 3 240 MPa and µd = 0.22
υ = 0.05 (υ - fraction of the critical damping).
The concrete-rock sliding friction coefficient when considering a seismic action is f = 0.70
Maximum permissible flexural compressive/tensile stresses when the seismic action is
considered – 200 kPa / +3 000 kPa (+ compressions).
The seismic analysis shall be carried out for the hypothesis of a full reservoir, where the water
level is at the normal retention limit (NRL), and the hypothesis of an empty reservoir.
Figure F1 Geometrical elements and digitisation diagram of the profile of a gravity dam.
60
β - Spectral amplification
T - Natural period of the oscillator
(s)
Figure F2 Normalised elastic response
spectrum in accordance with P 100-2006
A. Analysis of the free vibrations
the following notations were used: d = 15 m, b = 6 m, λ = 0.80
a. The net masses and the additional masses shall be calculated by breaking them up into simple
geometrical elements:
The calculations shall be carried out for a distance of 1 m in the longitudinal direction of the dam.
Calculation of the net masses:

1 
d 
d 1
6
  2.45   6  7.5  2.5   119.438 t
m1 =
 b  b
g  2 2
d 
15 





5 
1

d
d
 W  d 1
d 6  
d d 1 
d
m2 =
 b  b 
 b        b     d  3

g  2 2
2 d  
2 2 2 
2
2




1
12.5
1
5

 2.45   6  7.5   6.7.5 
 12  7.5   12  15    450.427
2
15
2
15 

2
1
d
d
W 
d d 1 
d
d 1 
d
3
3
m3 =
b        b     d 
 2 d      b     d 
g 
2 2 2 
2
2
2 2 
2
2
1
10
1
5

= 2.45  12  7.5   12  15   24  7.5   12  15    882 t
2
15
2
15 

2
d
W
d 1 
d
1
10 

3
membedment =
 2 d      b     d 
 2.45   24  7.5   12  15  
g
2 2 
2
2
2
15 

= 588 t
Mass matrix [M] for the hypothesis of an empty reservoir:
 W 
0
0 
119.438

M    0
450.427
0  t
 0
0
882.000
Calculation of the additional masses:
61
7 W

Hl  z
8 g
where  W is the volumetric weight of the water  W  10 kN/m3
g - gravitational acceleration g  9.81 m/s2
7 
7 10
mad1 =  W  H l  d  H b  H l   
40  10  17.845 t/m2
8 g
8 9.81
7 
7 10
mad2 =  W  H l  2d  H b  H l   
40  25  28.215 t/m2
8 g
8 9.81
7 
7 10
mad3=  W  H l  H b  H b  H l   
40  40  35.690 t/m2
8 g
8 9.81
Concentrated additional masses:
2
 d  H b  H l 
2
mc1 =  mad1  d  H b  H l  5
 31.725 t
3
d
2
d   d  H b  H l 
2
d
d 1
5
mc2 =  mad1  d  H b  H l 
 mad1   mad 2  mad1   
3
d
2
2 3
= 247 006 t
d
d 2
d
d 1
mc3 = mad1   mad 2  mad1     mad 2   mad 3  mad 2    = 415 993 t
2
2 3
2
2 3
d
d 2
mc embedment = mad2   mad 3  mad 2     2 248 989 t
2
2 3
mad 
Verification:
2
 H l  mad 3 = 951 735 t
3
mad 3 mc incastrare
embedmen = 943 712 t
Total surface area of the parabola:
m
c
 mad1  mad 2
t
The sum of the concentrated additional masses shall be different from the total surface area of
the parabola, since the concentrated additional masses were calculated by breaking them up into simple
geometrical shapes (rectangles and triangles); therefore, the following correction must be applied:
4
 31 714 t
15
11
1
mc2 = 118.927   133.792  83.588  = 248 868 t
15
3
2
1
mc3 = 133.792  83.588   211.54  58.223   420 465 t
3
3
2
membedment = 211.54  58.223   250 355 t
3
mc1 = 118.927 
Verification:
 mc  31.725  248.868  420.465  250.35  951 413 t
Additional mass matrix:
62
0
0 
31.714

M h    0
248.868
0 
 0
0
420.465
b. Calculation of the net and additional masses by direction integration:
The profile of the dam is defined by the following function:
Bsite
   H b  h   b  36 045 m
ampriza
area

y p z   Bsite
ampriza
area    i f z  H b, H b , z, H b  h

Calculation of the centres of mass:
cm1 =
cm2 =

Hb
2d


y p z   z dz
Hb
2d
2d
y p z   z dz
d
cm3 =
y p z  dz

2d
d
y p z   z dz
d

 2d  6.499 m
y p z  dz
0

d
0
y p z  dz
 d  6.667 m
 d  7.00 m
Calculation of the net masses:
Hb
c 
mc1 = m1  b   y p z  dz  119.399 t
d g 2d
2d
d  cm1  b Hb
c

mc2 =
   y p z  dz  m 2  b   y p z  dz  450.245 t
2
d
d
d
g
d g
d
d  cm 2  b 2 d
c

mc3 =
   y p z  dz  m3  b   y p z  dz  882.136 t
d
g d
d g 0
d  cm 3  b d
mc embedment =
   y p z  dz  588.091 t
d
g 0
Verification:
 mc  mc1  mc2  mc3  mc embedmen
incastare  2 039 871 t
Mdam =
b
g

Hb
0
t
y p z  dz  2039.872 t
Mass matrix [M] for the hypothesis of an empty reservoir:
0
0 
119.399

M    0
450.245
0  t
 0
0
882.136
Calculation of the additional centres of mass:
63
7 W

 H l  z  z dz
8 g
cm1 = d  H b  H l  
 4.00 m
d  H b  H l  7 
W

 H l  z dz
0
8 g
2 d  H b  H l  7 
d Hb Hl  8  gW  H l  z  z dz
cm2 = 2d  H b  H l  
 6.952 m
2 d  H b  H l  7 
W
d Hb Hl  8  g  H l  z dz
Hl
7 
2d Hb Hl  8  gW  H l  z  z dz
cm3 = H l 
 7.210 m
Hl
7 W
2d Hb Hl  8  g  H l  z dz
Concentrated additional masses:

d  H b  H l 
0
cm1 d  Hb  Hl  7  w

  H l  z dz  31.725 t
d 0
8 g
2 d  H b  H l  7 
c
 c  d  H b  H l  7  w
mc2s = 1  m1   

 H l  z dz  m 2  
 w  H l  z dz
0
d


H

H

b
l
d 
8 g
d
8 g

= 250 056 t
Hl
c
7 w
 c  2 d  H b  H l  7  w
mc3s = 1  m 2   

 H l  z dz  m 3  

 H l  z dz
d  d  H b  H l  8 g
d 2 d  H b  H l  8 g

= 419 898 t
7 w
 c  Hl
mc embedment s = 1  m3   

 H l  z dz  250 056
d  2 d  H b  H l  8 g

mc1s =
Verification:
2
 H l  mad 3 = 951 735 t
3
 mc embedmen
incastrares  951 735 t
Total surface area of the parabola:
m
p
 mc1s  mc 2 s  mc3s
t
Additional mass matrix:
0
0 
31.725

M h    0 250.056
0  t
 0
0
419.898
Net + additional mass matrix for the hypothesis of a full reservoir:
0
0
151.123



M  M h    0
700.302
0

 0
0
1302.034
Calculation of the flexibility matrix:
64
 f11
F    f 21
 f 31
b
fi j  
f12
f 22
f 32
f13 
f 23 
f 33 
mi  m j  dz
EI z 
 1.2
b

ti  t j  dz
GA( z )
E
24000
G

 10 345 MPa
2(1   b ) 2(1  0.16)
a
a
Figure F3. Diagrams of bending moments and shear forces due to unitary loads applied in the direction
of the degrees of freedom.
h z 2  dz
H
 b
0
h
b3
f11  
f 22  
Hb
f 33  
Hb
f12  
Hb
f13  
Hb
f 23  
Hb
d
2d
d
2d
2d
Eb 

z 2  dz
  z 3

h 12  dz
H 12  dz
 1.2 b
 2.480  10 6
0 G b
h G    z 
 1.2 

Eb
12
12
2
Hb
( z  d )  dz
12  dz

1
.
2
 3.641  10 7
3

d
G

(


z
)
  z 
Eb 
12
Hb
( z  2d ) 2  dz
12  dz
 1.2 
 7.498  10 8
3
2 d G  (  z )
  z 
Eb 
12
Hb
z ( z  d )  dz
12  dz
7

1
.
2
d G  (  z)  5.811  10

  z 3
Eb 
12
Hb
z ( z  2d )  dz
12  dz

1
.
2
 1.292  10 7
3

2 d G  (  z )
  z 
Eb 
12
2
H b 1  dz
( z  d )  z  2d  dz
 1.2 
 1.021  10 7
3
2 d G  (  z )
  z 
Eb 
12
65
2.480  10 6 5.811  10 7
F   5.811  10 7 3.641  10 7
1.292  10 7 1.021  10 7

1.292  10 7 

1.020  10 7 
7.489  10 7 
Calculation of the rigidity matrix [K] by reversing the flexibility matrix [F]:
F 1
 6.544  10 5

 K    1.178  10 6
 4.762  10 5

 1.178  10 6
6.563  10 6
 6.908  10 6
4.762  105 

 6.908  10 6 
2.192  10 7 
Calculation of the natural periods and shapes for the EMPTY RESERVOIR hypothesis:
K    M  A    0 
2
i
6.544  10 5  119.398   2
 1.178  10 6
4.762  10 5
 1.178  10 6
6.563  10 5  450.245   2
 6.908  10 6
4.762  105
 6.908  10 6
0
7
2
2.192  10  882.136  
The solutions of the characteristic equation are the following:
12  2531.648 rad / S 2  22  9664.959 rad / S 2 32  32415.466 rad / S 2
1  50.315 rad / S 2  2  99.824 rad / S 3  180.043 rad / S
2
T1 
 0.125 s
T2  0.063 s
T2  0.035 s
1
Evaluation of the natural shapes:
Fundamental natural shape:
352148  A11  1178040  A21  476289  A31  0
 1178040  A11  5424020  A21  6908160  A31  0
476289  A11  6908160  A21  19690100  A31  0
A
31  0.094
11  11  1
21  0.337
A11
Natural shape number 2:
 525379  A12  1178040  A22  476289  A32  0
 1178040  A12  2077200  A22  6908160  A32  0
476289  A12  6908160  A22  13133000  A32  0
A
31  0.350
12  12  1
22  0.596
A12
66
Natural shape number 3:
 3215942  A13  1178040  A23  476289  A33  0
 1178040  A13  8031040  A23  6908160  A33  0
476289  A13  6908160  A23  6671450  A33  0
A
23  1.904
33  2.043
13  13  1
A13
Calculation of the natural periods and shapes for the FULL RESERVOIR hypothesis:
6.544  10 5  151.123   2
 1.178  10 6
4.762  10 5
 1.178  10 6
6.563  10 6  700.301   2
 6.908  10 6
4.762  10 5
 6.908  10 6
0
7
2
2.192  10  1302.034  
The solutions of the characteristic equation are the following:
12  1858.845 rad / S 2  22  6974.608 rad / S 2 32  21707.679 rad / S 2
1  43.114 rad / S
 2  83.414 rad / S 3  147.335 rad / S
T1  0.146 s
T2  0.075 s
T2  0.043 s
Evaluation of the natural shapes:
Fundamental natural shape:
373508  A11  1178040  A21  476289  A31  0
 1178040  A11  5262130  A21  6908160  A31  0
476289  A11  6908160  A21  19503100  A31  0
A
31  0.103
11  11  1
21  0.359
A11
Natural shape number 2:
 399602  A12  1178040  A22  476289  A32  0
 1178040  A12  1679550  A22  6908160  A32  0
476289  A12  6908160  A22  12842200  A32  0
A
12  12  1
31  0.281
22  0.453
A12
Natural shape number 3:
 2626110  A13  1178040  A23  476289  A33  0
 1178040  A13  8638050  A23  6908160  A33  0
476289  A13  6908160  A23  6340740  A33  0
67
13 
A13
1
A13
33  1.738
23  1.526
Figure F.4 Natural modes for the hypothesis of an empty reservoir.
Figure F.5 Natural modes for the hypothesis of a full reservoir.
B. Solution obtained with the finite element method, using the SAP 2000 programme:
The profile of the dam is digitised into PLANAR finite elements with incompatible modes. The
calculations are carried out for the hypothesis of a planar deformation state.
Click FILE and Select a New Model.
Choose the measurement units: kN, m, C
Select a Template: Grid only
Set the following data in New Coord/Grid System:
Number of Grid Lines: X direction 13
Y direction 1
Z direction 13
Grid Spacing: X direction 3
Y direction 1
Z direction 3.75
In the plane view quadrant, select Set X-Z view.
Click Define →Materials –Add New Materials.
In Material Property Data, enter:
Material Name: Concrete
Type of Design: Concrete
In Analysis Property Data, enter:
68
OK!
Mass per unit Volume: 2.45
Weight per unit Volume: 24
Modulus of Elasticity: 24000000
Poisson’s Ratio: 0.16
In Type of Material, choose Isotropic
The programme is calculating the Shear Modulus 10344828 OK! OK!
Click Define /Area Section.
In Select Section Type to Add, select Plane.
Click on Add New Section.
In Plane Section Data, in Section Name, enter Dam.
In the Type section, select Plane-Strain and Incompatible Modes.
In Material Name, select Concrete.
In the Thickness section, enter 1.
OK! OK!
Click on Set Select Mode.
Click on Draw/Draw Poly Area. In Properties of Object in Section click on ASEC1 and choose
Dam.
Use the resulting grid to draw the digitised profile of the dam, made up of rectangular or triangular
elements.
The nodes of a finite elements are drawn in a clockwise direction (i, j, k, l). The digitisation
diagram contains 79 PLANAR elements and 94 nodes.
Close Property of Object.
Set Select mode(Pointer).
Select the nodes at the base of the profile (click on each node).
Click on Assign/Joint/Restraints.
In Joint Restraints, in the Restraints section, in Joint Local Direction cancel the 3 translations
and the 3 rotations by clicking the corresponding boxes.
Select all profile nodes except for those located at the base for which total restrictions have
been enforced (3 translations + 3 rotations).
Click on Assign/Joint/Restraints.
In Joint Restraints, in the Restraints section, in Joint Local Direction cancel translation 2 and
rotations 1, 2 and 3.This way, each of the selected nodes will display two degrees of translation freedom
in the local directions 1 and 3, corresponding to the global axes X and Z. OK!
Click on Define/Mass Source.
In Define Mass Source, in the Mass Definition section, check that From Element and
Additional Masses is selected.
OK!
Select node 1 (x = 0, z = 45).
Click on Assign/Joint/Masses.
In Joint Masses, in the Coordinate System section, select Global.
In the Masses section, in Global Directions in Direction X, enter 31 714
In the Options section, select Add to Existing Masses. OK!
Select node 14 (x=0, z=30).
Repeat the operations carried out for node 1 and enter 248 868 in Direction X OK!
Select node 40 (x=0, z=15).
Repeat the operations carried out for node 1 and enter 420 465 in Direction X OK!
At this stage, all the data required to calculate the natural modes for the FULL RESERVOIR
hypothesis have been entered.
Click on Analyze/Set Analysis Cases to Run/Run Now.
The screen will display Save Model File As/Save in: My Document.
In File Name, enter, for example, Problem 2.10 Full Reservoir → Save.
69
Check the results displayed on the screen.
The results show that the digitised profile contains 94 nodes and 79 SOLID-2D elements. In total,
the digitised system has 162 degrees of translation freedom in directions X and Z.
Initially, a static analysis is carried out for the load applied due to the dead load, followed by an
analysis of the free vibrations. The first 12 natural modes (natural periods + the corresponding natural
shapes) are determined.
OK!
Click on Display and select the results you wish to view, save, store, print.
If the analysis is carried out for the EMPTY RESERVOIR hypothesis, cancel the additional
masses in nodes 1, 14 and 40 by selecting each node in turn and cancelling the corresponding mass.
Number of the natural
period
Hypothesis
Empty reservoir
Full reservoir
1
2
3
0.1201
0.1446
0.0535
0.0684
0.0426
0.0452
Table F.1. Natural periods (s).
4
5
6
0.0304
0.0419
0.0207
0.0259
0.0192
0.0215
Figure F.2 shows the profile discretisation diagram. Figures F.3 and F.4 show the geometric
configurations of the first 4 natural shapes for the empty reservoir and the full reservoir hypotheses.
In this calculation, the system has a total of 162 dynamic degrees of freedom (81 translations in
direction X and 81 translations in direction Z).
It can be observed that the free vibrations (natural periods, natural shapes) calculated in situation
A (a system with 3 degrees of freedom) can be found amongst the natural modes calculated for the
hypothesis of the system being digitised into finite elements (situation B). The natural shapes 1 and 2
have identical geometric configurations in situations A and B. For the empty reservoir hypothesis, the
natural mode 3 in situation A is replicated in the natural mode 4 of situation B. In situation B, the natural
mode 3 develops mainly in direction Z (vertical), which was blocked in situation A (the system had only
3 degrees of horizontal translation freedom).
For the full reservoir hypothesis, the natural mode 3 in situation A is replicated in the natural mode
3 of situation B. The additional masses introduced in the horizontal direction (X) caused the natural
mode 3 to develop mainly in direction X and the natural mode 4 to develop mainly in direction Z.
Figure F.6. Profile digitisation diagram.
70
T1=0.1201 s
T2=0.0535 s
T3=0.0426 s
T4=0.0304 s
Figure F.7. Geometric configurations of the first 4 natural shapes for the empty reservoir hypothesis.
T1=0.1446s
T2=0.0684 s
T3=0.0452 s
T4=0.0419 s
Figure F.8 Geometric configurations of the first 4 natural shapes for the full reservoir and empty
reservoir hypotheses
B. Pseudo-static method
This method shall only apply when carrying out preliminary determinations for dams belonging
to class II and importance category B (pre-feasibility and feasibility studies).
anOBE = 0.40 x 0.24 g = 0.096 g, considering that anOBE =0.1 g
aOBE = 0.1 x 9.81 = 1 m/s2
anOBE – the maximum design earthquake acceleration shall be considered constant along the entire
height of the dam
71
Figure F.9 Loads manifested in the profile of a gravity dam and stresses σv for the full
reservoir hypothesis (a) and the empty reservoir hypothesis (b), calculated using the
pseudo-static method.
Name of load
Force size kN
Vertical
Horizontal
19.440
540
8000
-3880
1944
54
876.84
16.100
10874.84
G1
G2
Ph
S
Fi,1
Fi,2
Pc
 b = 24 kN/m3
8.17
Cp =
7.75  H 
1
 
10 6  T 
2
Arm
m
6.00
14.00
13.33
4.93
15.00
42.50
16.00
Bending moments
+
116640
7560
106640
19128.4
29160
2295
14029.4
171252.8
124200
 a = 10 kN/m3
8.17
kN
kN

 8.22
7.75
m3
m3
1
 40 2
10 6
Stability and strength calculations under static stresses (without taking into consideration the seismic
action)
- Full reservoir
8000
tg  
 0.497
19440  540  3880
0.70
 1.408
csig =
0.497
16100 1568.4
full plin
 vlac
v,

 439.961 kN / m 2
reservoir
, am
36
216
upstream
full plin
16100 1568.4
 vlac

 454.483 kN / m 2
reservoir
, av v, 
downstream
36
216
- Empty reservoir
There are no horizontal loads and negative pressure
empty
reservoir
gol 19980 124200
 vlac


 1130 kN / m 2
v,, am

36
216
19980 124200


 20 kN / m 2
36
216
upstream
empty
lac
golv,
reservoir
vdownstream
,aval
Calculations for the full reservoir hypothesis:
 H ef  8000  1944  54  876.84  10874.84  0.675
tg  
19440  540  3880
16100
Vef
f
0.70

 1.037
csig =
tg  0.675
tg  - sliding coefficient of the structure
72
csig - sliding safety coefficient
Af = 1 x 36 = 36 m2
1 . 36 2
Wf =
 216 m3
6
full
V   M  16100  47052.8  229.38 kN
plin
reservoir
 vlac

,
am
v,
Af
Wf
36
216
m2
upstream
full reservoir
V   M  16100  47052.8  665.06 kN
v, plin
 vlac

,av
downstream
Af
Wf
36
216
m2
Calculations for the empty reservoir hypothesis
The more dangerous situation occurs when the direction of the seismic acceleration is from upstream to
downstream.
1944  54
tg  
 0.10  0.70
19440  540
empty
lac
gol 19980 ( 116640  7560  29160  2295)
 vreservoir

 1275.62 kN / m 2
v,,am
upstream
36
216
empty
golv,
reservoir
 vlac

,av
downstrea
m
19980 (116640  7560  29160  2295)

 165.62 kN / m 2
36
216
Conclusion: The seismic response parameters (csig, σv,am, σv,av) are within the permissible limits
due to the data used in the seismic calculation carried out in accordance with the pseudo-static method.
C. Spectral analysis
anOBE = 0.40 x 0.24 g = 0.096 g, where it is considered that anOBE = 0.1g anOBE = 0.1 x 9.81 =
1.0 m/s2
Natural periods of the full reservoir:
T1 = 0.146 s
T2=0.075 s
Natural periods of the empty reservoir:
T1 = 0.125 s
T2=0.063 s
T3=0.043 s
T3=0.035 s
Spectral amplifications as a function of the period of the oscillator
Full reservoir
T1 Sa.1 l p = 2.750 x 1. = 2.750 m/s2
T2
Sa.2 l p = 2.312 x 1. = 2.312
m/s2
T3
Sa.3 l p = 1.752 x 1. = 1.752
m/s2
Empty reservoir
T2
T3
T1 Sa.1 l g = 2 750  x 1. = 2 750
Sa.2 l g = 2 102 x 1. = 2 102
m/s2
Sa.3 l g = 1 612 x 1. = 1 612
m/s2
m/s2
Calculation of the shape coefficient matrix [E]
 ei K   i  TK [M ] r
 K
 TK [M ] K
where the index i refers to the degree of freedom of the structure and the index k refers to the
natural shape.
73
C1. Full reservoir hypothesis
Calculation of the coefficients of matrix [E] for the full reservoir hypothesis:
151.123
 1

 1
1 0.359 0.103 
700.302

1

1302.034 1

ei 1  0.359
151.123
 1 
0.103

 1 0.359 0.103 
 0.359
700.302





1302.034 0.103
151.123
 1

 1
1  0.453  0.281 
700.302

1



1302.034 
1
 ei 2   0.453
151.123
 1 
 0.281

 1  0.453  0.281 
  0.453
700
.
302






1302.034  0.281

151.123
 1
 1
1  1.526  1.738 
700.302

1


1302.034 1


ei 3   1.526
151.123
 1 
 1.738

 1  1.526 1.738 
  1.526
700.302





1302.034  1.738 
 2.103  1.338 0.235 
[E] = 0.755 0.606  0.359


0.217 0.376
0.409 
n

Verification condition for [E]:
k 1
3
 e1, k
k 1
3

k 1
ei , k  1
 2.103  1.338  0.235  1
3

e2, k  1.002
k 1
e3, k  1.002
Calculation of the maximum inertial forces {Fi}k, max in various natural modes in the directions of
the degrees of freedom for the full reservoir hypothesis:
 Fi k
max
i=1,2...n
 M
 ei k
S a i k  k ,  k 
i=1,2...n
i=1,2...n
74
 Fi 1 max
max
 151.123




700.302


1302.034 
 2.103


 0.755  2.750 
 0.217


 873.982 


1454.002 kN
 776.988 


 Fi 2
 151.123
   1.338
 467.493






kN

700.302
max
  0.606   2.312   981.174 
max





1302.034   0.376 
 1131.874 
 Fi 3
 151.123
  0.235 
 62.221 






kN

700.302
max
max
   0.359 1.752   440.468





1302.034   0.409 
 932.996 
Figure F.10. Graphical representation of the inertial forces in kN, in various
natural modes for the full reservoir hypothesis.
Calculation of the spectral vertical stresses in various natural modes at the base of the profile:
upstre
am
 Fi k di
 v,vam

,
av
max
down k , max
W
strea
i=1...n
m
873.982  45  1454.002  30  776.988  15
upstre
am
 vam

  437 982 kN/m2
,av 1,max
2
max
v,
1.36
down
strea
6
m
upstre
upstre
kN
am

  16.578
 vam
  117.482 kN/m2
am
am
v
,
av
, av 2,max
3
max
v,
v,
m2
down
down







strea
m

strea
m
Calculation of the spectral shear forces in various natural modes at the base of the profile
75
FT k

 Ft i k
n
i 1
F T 1,max
 873.982  1454.012  776.988  3104.972 kN
max
F T 2,max
F T 3,max
max  554.749 kN
max   1645.555 kN
Calculation of the spectral vertical stresses and spectral shear forces at the base of the profile, in
accordance with Rosenblueth formula (RSS):
 
am
upstre
v ,iav max
am
max
v, iav


am
upstream
v , max, av RSS
v,max,
upstream
F T
base,max
baza, max


RSS
2
1
2
n
ups
am 2 
   vtre
, i , Kav 
 k 1 am 
437.892 2  117.482 2  16.578 2  453.768
kN
m2
 2 3104.972 2  1645.555 2  554.749 2  3557.590
kN
m2
Stress regimen σv due
to static loads for the
full reservoir
hypothesis
Spectral stresses σv
due to seismic action
for the full reservoir
hypothesis
Figure F11 Combining of stresses σv due to static loads with the spectral stresses
due to seismic action.
Verification of the stress regimen and sliding stability — full reservoir hypothesis:
8000  3557.590
 0.717
16.100
0.7

 0.976
0.717
tg  
csig
sig
The maximum flexural compressive/tensile stresses that take into consideration the seismic
action are within the permissible limits.
For the hypothesis of a seismic action, the profile does not meet the sliding stability requirement.
The foundation of the dam should be inclined in an upstream direction, or the slopes of the profile faces
should be softened.
76
Calculation of the maximum displacements caused by the seismic action within various natural
modes in the directions of the degrees of freedom.
 i k
  ei k S d  k , k 
max
i=1...n
i=1...n
S
S
Sd = v  a2
 
Sd, Sv, Sa - spectral values in relative displacements, relative velocities and absolute
accelerations, respectively
2
6.28
rad
rad
rad
1 

 43.01
.... 2  83.73
3  146.05
T1 0.146
s
s
s
0.00345


 0.00125
0.00036

m
 i 1 max
max
 i 2 max
max
0.000497


 0.000225
0.000140

m
 i 3 max
max
 0.000022 


  0.000034
 0.000039 

m
Calculation of the maximum upstream-downstream crest displacement, full reservoir hypothesis


max,
crest RSS
max, coron
 0.3482  0.0497 2  0.0022 2  0.351 cm
The displacements caused by the earthquake are very small due to the high rigidity of the dam
profile.
C2. Empty reservoir hypothesis
Calculation of the coefficients of matrix [E] for the empty reservoir hypothesis:
1.985  1.181 0.196 
[E]empty reservoir = 0.669 0.704  0.373


0.187 0.413
0.400 
Verification of the accuracy of coefficients ei k from matrix [E]:
3
e
k 1
1, k
1
3
e
k 1
2 ,k
1
3
e
k 1
3, k
1
Calculation of the maximum inertial forces {Fi}k, max in various natural modes in the directions of
the degrees of freedom for the empty reservoir hypothesis
 651.981
 Fi 1 max   828.674.kN
 453.568


 Fi 2
 Fi 3
  296.500


  666.547 .kN
max
max
 765.687 


max
 37.740 


   270.830.kN
 568.714 


77
Figure F12. Graphical representation of the inertial forces in kN, in various
natural modes for the empty reservoir hypothesis.
Calculation of the spectral vertical stresses in various natural modes at the base of the profile, for
the empty reservoir hypothesis:
upstr
eam
am
max, empty
vv,, av 1, max,
lac gol
down reservoir
strea
m
upstr
am
eam
max, empty
v , av 3, max, lac gol
v,
reservoir
down
strea
m
 
 282.421
kN
m2
 
 9.741
kN
m2
upstr
eam
am
v,
max, empty
v , av 2 , max,
lac gol
down
reservoir
strea
m
 
 83.978
kN
m2
Calculation of the spectral shear forces in various natural modes at the base of the profile, for the
empty reservoir hypothesis:
F T 1,max
  max  1135.734
max  1934.223 kN F T 2 , max
kN F T 3,max
max  335.624 kN
Calculation of the spectral stresses and spectral shear forces at the base of the profile, in
accordance with Rosenblueth formula (RSS):
 
F T 
v , max
v,
max RSS
max
max RSS
kN
m2
 2267.985 kN
 294.813
78
Stress regimen σv due
to static loads for the
empty reservoir
hypothesis
Spectral stresses σv
due to seismic action
for the empty reservoir
hypothesis
Figure F13 Combining of stresses σv due to static loads with the spectral stresses
due to seismic action.
Verification of the stress regimen and sliding stability for the empty reservoir hypothesis:
2267.985
 0.113
19980
0.70

 6.19
0.113
(tg  ) lac
reservoir
gol 
empty
empty
reservoi
(csig
sig )rlac gol
There are no sliding stability issues for the empty reservoir hypothesis. In the toe region, the
vertical flexural tensile stresses (σv) exceed the permissible stresses but, given the fact that the empty
reservoir hypothesis only occurs during the construction of the dam, they can be accepted.
Calculation of the maximum displacements caused by the seismic action within various natural
modes in the directions of the degrees of freedom:
 i 1 max
max
0.00241


 0.00081
0.00023

m
 i 2 max
max
 0.000283


  0.000170 
 0.000099 

m
 i 3 max
max
 0.000011 


  0.000022
 0.000023 

m
Calculation of the maximum upstream-downstream crest displacement, empty reservoir
hypothesis:


max,
max, coron
crest RSS
 0.243 cm
The displacements caused by the earthquake are very small due to the high rigidity of the dam
profile.
C3. Spectral analysis via the finite element method using SAP 2000
79
The instructions given for the analysis of free vibrations using the finite element method (Point
A2 - page 77) is continued.
The seismic response spectrum is defined in accordance with P100-2006 (Figure F2).
Click on Define / Functions / Response spectrum.
In Define Response Spectrum Functions, in Choose Function Type to Add – Choose User and
enter P100-2006Medium in Response Spectra.
Click on Add New Function.
In Response Spectrum Function Definition, P100-2006 Medium will appear in the Function
Name box
Enter 0 in Function Damping Ratio.
In Define Function, enter the following table:
Period
0
0.1
1
1.5
2
2.5
3
3.5
4
5
7
10
Acceleration
1.
2.75
2.75
1.833
1.375
1.1
0.517
0.673
0.516
0.330
0.168
0.09
OK!
OK!
Click on Define / Load Pattern
In Define Load Pattern, click on Add New Load Pattern
In the Load Pattern Name column, enter WaterForce
In the Type column, select OTHER
In Self Weight Multiplier, enter 0.
OK!
Click on Define / Load Cases
Click on DEAD and Modify / Show Load Case
In Load Case Data - Load Case Name DEAD
In Loads Applied, column Load Type, write Load Pattern; in column Load Name, write DEAD;
in column Scale Factor, enter 1.
OK!
Click on MODAL and Modify/Show Load Case
In Load Case Data / Load Case Name MODAL
Check in Stiffness to Use – Zero Initial Conditions
in Type of Model – Eigen Vectors
in Number of Modes – Maximum Number of Modes 12
Minimum Number of Modes 1
Allow Automatic Frequency Shifting
OK!
Click on Add New Load Case
80
In column Load Case Name, write WaterForce1; in Load Case Type, write Linear Static
Click on Add New Load Case
In the column Load Case Name, write Spectral Analysis; in Load Case Type, write
ResponseSpectrum.
Click on WaterForce1 – Modify / Show Load Case
In Load Case Data – Load Case Name WaterForce1
In Load Applied, column Load Type, write Load Pattern; in column Load Name, write
WaterForce; in column Scale Factor, enter 1.
OK!
Click on Spectral Analysis – Modify /Show Load Case
In Model Combination, choose CQC; GMC f1 1.; GMC f2 0.;
Periodic+Rigid Type SRSS
In Directional Combination, choose SRSS
In Model Load Case, choose MODAL
In Loads Applied, column Load Type, choose Accel; in Load Name, choose U1; in Function,
select P100–2006Medium; in column Scale Factor, enter 1. OK! OK!
Click on Define / Load Combinations
In Define Load Combinations, in Load Combinations, write EarthquakeDWH.
Click on Modify/Show Combo
In Load Combination Data/EarthquakeDWH, in Load Combination Type, select Linear Add.
In Define Combination of Load Case Results, select the data from the following table:
Load Case Name
Spectral Analysis
DEAD
WaterForce1
Load Case Type
Response Spectrum
Linear Static
Linear Static
Scale Factor
1.
1.
1.
OK!
In Define Load Combinations, in Load Combinations, write Full Reservoir.
Click on Modify/Show Combo
In Load Combination Data/ Full Reservoir in Load Combination Type, select: Linear Add.
In Define Combination of Load Case Results, select the data from the following table:
Load Case Name
DEAD
WaterForce1
Load Case Type
Linear Static
Linear Static
Scale Factor
1.
1.
OK!
OK!
To carry out a spectral analysis for the full reservoir hypothesis, the hydrostatic pressure shall be
introduced, with the water in the lake at level  40.00 m, by applying hydrostatic forces in the nodes of
the upstream face.
Click on Select / Select Pointer Window
Click on node 7 (X = 0., Z = 37.50)
81
Click on Assign / Joint Loads / Forces
In Joint Forces / Load Pattern Name, select WaterForce
In Coordinate System, select GLOBAL
In Loads, in Force Global X, enter 101 56
In Options, select Replace Existing Loads.
The operations specified for node 7 shall be repeated for the other nodes of the upstream face of
the digitised profile on which hydrostatic forces are applied, in accordance with the following table:
Node number
in digitisation
10
14
19
25
32
40
49
59
70
Coordinate
X
m
0.
0.
0.
0.
0.
0.
0.
0.
0.
Coordinate
Force in direction X
Z
m
kN
33.75
234.375
30
375.
26.25
515.625
22.50
656.25
18.75
796.875
15.
937.5
11.25
1078.125
7.50
1218.75
3.75
1359.375
Verification: Total hydrostatic force 1/2 x 10 x 402 = 8 000 kN
The resulting force in direction X in node 82 (blocked), with the coordinates (X=0, Z=0), is
equal to 733 43 kN
11
 i Fi, X 101.56  234.375  ....  733.43  8006.86 kN
1
Click on Analyze / Set Load Cases to Run
Column 1 Case Name will display the four Load Cases:
MODAL, DEAD, Spectral Analysis and WaterForce1.
In Analysis Monitor Options, select Always Show
Click on Run Now
Click on Display and successively choose to have the analysis results displayed on the monitor.
The calculation results obtained for the load combinations (FullReservoir, EarthquakeDWH) will appear
directly in Display.
The type of analysis used corresponds to a gravity dam with a foundation of infinite rigidity.
This simplification influences, to a certain extent, the analysis results.
Figure F14 shows the lines of equal stress σv (or σz) and τxz due to the dead load + hydrostatic
pressure of the reservoir at the normal retention limit (NRL) (  40 m). It can be determined that,
throughout the entire dam body (except for one local crest zone), the stresses σv are compressions and
the stresses τxz are manifested in a downstream to upstream direction. The maximum compressive stress
reaches the value of 662 kPa on the contact surface between the dam and the foundation, in a zone near
the heel of the dam.
82
Figure F14. Lines of equal stress σz and τxz due to the dead load and the
hydrostatic pressure of the reservoir at the normal retention limit (NRL) (  40
m).
The sliding stability of the contact surface between the dam and the foundation shall be checked
by integrating the stresses σz (vertical stresses) and τxz on the contact surface (see Figure F17), in
accordance with the following relationship:
tg α =

 Vef
H ef
S

 s

xz d A
 z dA  S
s
where tg α is the sliding coefficient of the structure and S – the force applied to the contact
surface by the resultant of the negative pressures.
The sliding safety coefficient (k) is determined with the following relationship:
k=
f
tg 
where f is the sliding friction coefficient of the contact.
83
For the full reservoir hypothesis, the result is:
7460
tg  
 0.50
18802  3880
Kfull
lac plin 
reservoi
r
0.70
 1.40
0.50
Figure F15. Lines of equal stress σz and τxz obtained by carrying out a spectral analysis for a horizontal
earthquake of 0.1 g, considered to comply with the P100-2006Medium spectrum.
Figure F15 shows the lines of equal stress σz and τxz, calculated by carrying out a spectral
analysis for a horizontal earthquake of 0.1 g, in accordance with the P100-2006Medium spectrum.
In the analysis, the degrees of translation freedom were considered in the nodes of the digitised
profile in both planar directions (horizontal and vertical), resulting in a total of 162 degrees of freedom
and 12 natural modes.
The degrees of vertical freedom had a significant influence on the response; therefore the stresses
σz are of a tensile nature throughout the entire dam body, reaching 840 kPa at the heel.
The following table presents the response participation factors of the natural modes. It can be
noted that modes 3 and 4 have significant participation factors in the vertical direction (z).
Modal participation factors
Number of the
natural mode
1
2
3
4
5
6
7
8
9
10
11
Period
seconds
0.1445
0.0684
0.0452
0.0418
0.0259
0.0215
0.0206
0.0190
0.0148
0.0144
0.0137
84
Ux
Uz
38.82
-26.64
17.21
-0.47
9.15
-7.32
-11.04
3.71
5.16
-3.12
5.34
5.08
-19.8
-17.43
-30.16
7.93
6.44
-7.32
-13.42
2.01
-5.16
-4.29
12
0.0122
2.95
-2.73
Figure F16. Lines of equal stress σz and τxz due to the dead load + the hydrostatic pressure of the
reservoir at the normal retention limit (NLR) + a horizontal earthquake of 0.1g, in accordance with the
P100-2006Medium spectrum.
Figure F16 shows the lines of equal stress σz and τxz due to the dead load + the hydrostatic
pressure at the normal retention limit (NLR) + a horizontal earthquake of 0.1 g applied in accordance
with the P100-2006Medium spectrum. It can be noted that the stresses σz occurring in the profile body
are usually compressive stresses (maximum stress 601 kPa), except for a zone on the upper half of the
upstream face, where tensile stresses occur (maximum stress 249 kPa).
The diagrams of the stresses σz and τxz manifested on the contact surface between the dam and
the foundation due to the loads applied by the dead load + the hydrostatic pressure at the normal
retention limit (NLR) and by the dead load + the hydrostatic pressure at the normal retention limit
(NLR) + a horizontal earthquake of 0.1g applied according to the P100-2006 Medium response
spectrum, respectively, are shown in figure F17.
Stresses due to the dead load + hydrostatic pressure
Stresses due to the dead load + hydrostatic pressure + earthquake 0.1 g
compressions
upstream orientation
85
Figure F17. Diagrams of the stresses τxz and σz due to the dead load + the hydrostatic pressure at the
normal retention limit (NLR) and the dead load + the hydrostatic pressure at the normal retention limit
(NLR) + a horizontal earthquake of 0.1g, in accordance with the P100-2006Medium spectrum.
To determine the sliding stability coefficient for the contact surface between the dam and the
foundation for the hypothesis of a seismic action, the corresponding diagrams σz and τxz shall be
integrated on the contact surface, using the relationships given above. The result is that:
tg  
3678
3678

 0.737
8856  3880 4976
Csig.0.1g =
0.70
 0.95
0.737
The sliding safety coefficient when an OBE earthquake (0.1 g) is considered is subunitary and
the profile must be corrected to meet the sliding stability requirement (the sliding safety coefficient must
be within the 1.00–1.10 range). The same conclusion was drawn from the pseudo-static analysis.
86
Annex G
SEISMIC ANALYSIS OF AN EARTHFILL DAM
A seismic analysis of the transverse profile of the earthfill dam shown in Figure G1 under the
action of an OBE (Operating Basis Earthquake) must be carried out in accordance with Regulation NP
076/2002.
Base stratum: MARL
Figure G1. Profile of an earthfill dam with geometrical elements and zoning of the materials
The following shall be taken into consideration in addition to the data provided in the figure:
The dam belongs to importance class II (STAS 4273-83) and importance category B (NTLH021).
In accordance with regulation P100-2006, the dam is located in a seismic zone characterised by
the peak value of the site ground acceleration ag = 0.24g and corner periods TB = 0.1 seconds and TC =
1.0 seconds. The seismic survey of the site has confirmed the values given in P100-2006.
The seismic response spectrum was shown in Figure F.2. (Annex F).
If using the pseudo-static method, anOBE = 0.40g but not less than 0.1g.
If using the spectral analysis method, anOBE = 0.40 g but not less than 0.1 g.
The seismic analysis shall be carried out for the hypothesis of a full reservoir, where the water
level is at the normal retention limit (NRL). The infiltration curve for the dam body is shown in Figure
G1.
The vertical component of the earthquake acceleration shall not be taken into consideration.
A. Pseudo-static method
This method shall only apply when carrying out preliminary determinations for dams belonging
to class II and importance category B (pre-feasibility and feasibility studies).
anOBE = 0.40 x 0.24 g = 0.096  1 m/s2
(G-1)
anOBE – the maximum design earthquake acceleration shall be considered constant along the
entire height of the dam. In the seismic analysis of the stability of the downstream bank, the upstream
direction of the horizontal earthquake which produces downstream inertial response forces is the
dangerous direction that must be taken into consideration.
87
Sliding surfaces shall be successively traced for the upstream and downstream faces, and
calculation strips shall be determined (i=1…n). The sliding safety coefficient (FS) shall be calculated for
each sliding surface using the following relationship:
n
 i (Gi cos  i  U i  Fi sin  i ) tg i
FS = 1
(G-2)
n
 i (Gi sin  i  Fi cos  i  ci li )
1
where Gi is the weight of the strip; in the zone underneath the infiltration curve,  sat   u  n  w ( sat 
the saturated volumetric weight,  u - the dry volumetric weight, n – porosity and  w  the volumetric
weight of the water shall be taken into consideration;
αi - the angle between the normal line in the middle of strip i of the sliding surface and the
vertical axis;
Ui – resultant of the infiltration water pressure on strip i;
Fi – inertial force produced by the earthquake on strip i;
φi - angle of friction of the sliding surface on strip i;
ci - cohesion of the sliding surface on strip i;
li – length of the sliding surface along strip i.
Distribution of the
response accelerations in
elevation
Marl
Figure G2. Calculation diagram using the Fellenius method of the sliding safety factor for a sliding
surface in the pseudo-static method.
88
The following table presents the calculations carried out for the sliding surface shown in Figure G2.
No
of the
strip
i
cos 
1
2
3
4
5
6
7
8
9
63°
54°
42°30'
32°30'
23°
14°
6°
-2°
-10°
0.45399
0.58779
0.73728
0.84339
0.92050
0.97030
0.99452
0.99939
0.98481
sin  i
Gi
kN
Gi
Gi cos sin  i
 i kN kN
Fi
kN
0.89101 22.05 10.01 19.65 2.20
0.80902 577.50 339.45 467.21 57.75
0.67559 918.75 677.38 620.70 91.87
0.53730 1023.75 863.42 550.06 102.37
0.39073 1063.65 979.09 415.60 106.36
0.24192 971.25 942.40 234.96 97.12
0.10453 813.75 809.29 85.06 81.37
-0.03490 551.25 550.91 -19.23 55.12
-0.17365 236.25 232.66 -41.02 23.62
Fi
sin  i
kN
1.96
46.72
62.07
55.00
41.56
23.49
8.50
-1.92
-4.10
Fi
cos
i
kN
1.00
33.94
67.73
86.34
97.90
94.24
80.92
55.09
23.26
Ui
kN
Ci
kN/m
62.50
100.0
100.0
50.00
0
0
0
0
0
0
0
0
0
Table G-1
li
tg i
m
2
9
7
6
5.75
5.50
5.25
5
5.60
0.67451
0.67451
0.67451
0.67451
0.67451
0.60239
0.55431
0.55431
0.55431
The following is obtained on the basis of relationship (G-2) and the data given in Table (G-1) FS
for the sliding surface shown in figure G2:
FS 
5.43  197.449  415.033  545.288  632.374  515.885  388.454  251.008  103.523
20.65  471.15  688.43  636.40  513.50  329.20  165.98  35.86  17.76
3054.44
FS 
 1.074
(G-3)
2843.41
The minimum safety factor (FSmin) shall be determined by carrying out determinations of this
factor for other sliding surfaces, using the same methodology.
The calculations should be carried out using computer programmes.
B. The pseudo-static method using the GeoStudio programme
Height [m]
The stability calculation of the earthfill dam profile shall be carried out using the GeoStudio
programme, namely the Slope and Seep modules for two-dimensional calculation.
The Seep module is used to determine the position of the infiltration curve for the structure
digitised into finite elements of the “Structured Quad - Integration order 4” type (Figure G3).
Distance [m]
Figure G3. Digitisation diagram and position of the infiltration curve.
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In GeoStudio, each drawn region was allocated a type of material. The data entered are in SI
units. The regions were digitised in the “Region Properties” window (Figure G4) so that each region
contains convex quadrilateral elements with angles that are very close to a right angle and the sides ratio
is approximately unitary.
Figure G4. Window for establishing the characteristics of the materials.
In the Seep module, the unknown quantities in the nodes are the piezometric levels. The
boundary conditions on the upstream face of the dam and the bottom of the reservoir corresponded to
the equivalent piezometric levels of the full reservoir at the normal retention limit (NRL), whereas
downstream, the piezometric levels were considered at ground height.
The hydraulic conductivity of the materials was considered to be constant and the thermal
influence was ignored (Figure G5).
Figure G5. Window with the hydraulic conductivity characteristics.
This helped determine the position of the infiltration curve and the volume of water infiltrated
(Flux Sections) through the watertight diaphragm and luting shield.
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In the Slope module, the behaviour of the material (Mohr-Coulomb) and the characteristics of
the material were determined for each region (Figure G6).
Figure G6. Slope module with the characteristics of the materials, per region.
The calculation was carried out using the pseudo-static method, with a seismic acceleration of
0.1g in the horizontal direction (Figure G7).
Figure G7. Window with the characteristics of the seismic action.
The Slope programme calculates the minimum sliding safety coefficients of the banks using
various methods, for the hypothesis of the pseudo-static method (Figure G8).
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Figure G8. Sliding stability coefficients for a horizontal earthquake of 0.1 g.
Height [m]
Figures G9 and G10 show the sliding surfaces of the upstream and downstream faces
corresponding to the minimum safety coefficients for the action of a horizontal earthquake of 0.1 g,
determined using the Jambu method.
Distance [m]
Figure G9. Sliding surface of the downstream bank, corresponding to the minimum safety coefficient
determined using the Jambu method (earthquake of 0.1 g)
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Height [m]
Distance [m]
Figure G10. Sliding surface of the upstream bank, corresponding to the minimum safety coefficient
determined using the Jambu method (earthquake of 0.1 g)
The seismic analysis using the pseudo-static method, carried out with the GeoStudio programme,
has led to subunitary safety coefficients (k=0.910) in the event of sliding of the downstream bank, which
requires the profile to be redesigned to ensure that the coefficients are within the 1.00–1.10 range.
C. Spectral analysis via the finite element method, using SAP2000
The instructions for carrying out the spectral analysis are similar to those stipulated in Annex G
and will not be repeated.
The digitisation diagram of the earthfill dam-foundation ground assembly in the Y-Z plane is
shown in Figure G11. The dam body is digitised into 35 PLANAR elements with incompatible modes,
which are also included in the hypothesis of the planar deformation state. The foundation ground up to
bedrock level is digitised into 34 PLANAR elements similar to those in the body of the dam. The nodes
located at the lateral and lower limits of the digitised representation of the foundation ground were
blocked.
The system has 127 degrees of translation freedom.
The characteristics of the materials used in the earthfill dam-foundation ground assembly are
given in the table below:
Name of
material
Earth1
Earth2
Face
Cutoff
m
kN/m3
21
24
-
E
kPa
µ
40000
250000
24000000
21000000
0.3
0.3
0.2
0.2
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Position
of the material
Dam body
foundation ground
reinforced concrete
diaphragm
luting shield
(diaphragm wall)
Figure G11. Finite element digitisation diagram.
The punctual additional masses (mhi) for the hypothesis of the full reservoir with water levels
equal to the normal retention limit (NRL) (  16.00 m) were calculated from the hydrodynamic pressures
(phi) determined with Westergaard’s formula for inclined faces:
mhi = k
7 w H z
8
g
(G – 4)
where k = 0.226 is a coefficient which takes into consideration the gradient of the face (1:2.50);
 w - volumetric weight of the water; g – gravitational acceleration; H – depth of the reservoir;
z - depth of the point where the punctual additional mass is calculated.
The additional masses concentrated in the nodes have the same orientation as the corresponding
hydrodynamic forces and are given in the table below:
Node
number
Mass concentrated in
direction Y
1
7
13
21
33
1.72
6.25
9.01
11.12
6.16
Mass concentrated in
direction Z
t
t
4.30
15.62
22.50
27.80
15.40
The following table presents the hydrostatic forces developed in the nodes, calculated for the full
reservoir hypothesis (NRL  16.00 m)
Node
number
1
7
13
21
33
Hydrostatic force in
direction Y
kN
26.67
160.
320.
480.
293.33
Hydrostatic force in
direction Z
kN
-66.67
-400.
-800.
-1200
-733.33
The first six natural periods of the earthfill dam profile for the full reservoir and empty reservoir
hypotheses are presented in the following table. Figure G12 shows the first four natural modes for the
full reservoir hypothesis.
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Natural period
number
Hypothesis
Empty reservoir
Full reservoir
T1
T2
T3
0.3245
0.3260
0.2302
0.2308
0.1958
0.1984
Natural periods in seconds
T4
T5
T6
0.1696
0.1721
0.1532
0.1552
0.1443
0.1483
The result is that the natural periods for the full reservoir have the same values as the natural
periods for the empty reservoir.
- Mode 1 - Period 0.32603
- Mode 2 - Period 0.23082
- Mode 3 - Period 0.19843
- Mode 4 - Period 0.17215
Figure G12. First four natural modes for the hypothesis of a full reservoir.
Figure G13 shows the lines of equal stress σz (vertical stress σv) and τxz due to the dead load +
hydrostatic pressure when the level of the water in the reservoir at the normal retention limit (NRL). The
vertical stresses throughout the entire dam body are compressive stresses and reach maximum values of
361 kPa at the point of contact with the foundation, under the crest. The shear stresses τxz have small
values, the highest of them occurring on the surface of contact with the foundation and being equal to 37
kPa.
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Figure G13. Lines of equal stress σz and σy due to the dead load and the hydrostatic pressure of the
reservoir at the normal retention limit (NRL) (  +16.00 m).
Figure G14 shows the lines of equal stress σy; σz and τxz calculated by carrying out a spectral
analysis for a horizontal earthquake of 0.1 g, in accordance with the P100-2006Medium response
spectrum. The stresses σy can reach up to 79 kPa on the downstream face of the dam. The stresses σz are
small and do not exceed 7.4 kPa in the central zone, on the dam-foundation contact surface. The
maximum stresses τxz of 64 kPa also occur in this zone.
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Figure G14. Lines of equal stress σy; σz and τxz determined by carrying out a spectral analysis under the
action of a horizontal earthquake of 0.1 g, in accordance with the P100-2006Medium seismic response
spectrum.
The following table presents the response participation factors of the natural modes.
Modal participation factors - full reservoir hypothesis
Number of the
Uy
Uz
natural mode
1
44.814
-1.2521
2
-1.8120
-34.3772
3
0.5785
-3.6721
4
0.3347
-21.2649
5
-1.2424
-14.0669
6
6.1946
-2.3458
7
-2.2439
-11.2281
8
-7.3944
5.5837
9
1.8995
-2.0417
10
-1.0033
-6.0747
11
-2.9392
-2.5874
12
-1.1047
-5.3454
The result is that the natural modes 1 and 6 have mainly horizontal participation factors, whilst
modes 2, 4, 5 and 7 have mainly vertical participation factors.
Figure G15 shows the lines of equal stress σz and τxz due to the dead load + hydrostatic pressure
at the normal retention limit (NRL) + a horizontal earthquake of 0.1g applied in accordance with the
P100-2006Medium seismic response spectrum. The stresses σz are compressive stresses which can reach
maximum values of 341 kPa in the central area of the dam-foundation interface. The upstream face
displays a local zone at the crest where small tensile stresses σz with maximum values of up to 12 kPa
occur. The stresses τxz can reach maximum values of up to 61 kPa on the contact surface between the
dam and the foundation, in the upstream vicinity of the zone below the crest.
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Figure G15. Lines of equal stress σz and τxz due to the dead load + the hydrostatic pressure of the
reservoir at the normal retention limit (NLR) + a horizontal earthquake of 0.1 g, in accordance with the
P100-2006 Medium spectrum.
The level of stress developed in the dam-foundation ground assembly under the action of a
horizontal earthquake of 0.1g shall be within permissible limits. The stress spectra σz and τxz can be used
to determine the sliding stability coefficients for various sliding surfaces of the dam [2].
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