DAM ENGINEERING-NEW CHALLENGES P. S. Pinto Professor of ...
DAM ENGINEERING-NEW CHALLENGES P. S. Pinto Professor of ...
DAM ENGINEERING-NEW CHALLENGES P. S. Pinto Professor of ...
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<strong>DAM</strong> <strong>ENGINEERING</strong>-<strong>NEW</strong> <strong>CHALLENGES</strong><br />
P. S. <strong>Pinto</strong><br />
<strong>Pr<strong>of</strong>essor</strong> <strong>of</strong> Geotechnical Engineering, University <strong>of</strong> Coimbra, Portugal<br />
President <strong>of</strong> International Society for Soil Mechanics and Geotechnical Engineering<br />
(ISSMGE)<br />
P. Simão<br />
Principal Research Engineer, National Laboratory <strong>of</strong> Civil Engineering (LNEC)<br />
ABSTRACT<br />
In this paper dam design criteria is addressed. Foundation studies for soil and rock<br />
materials are described. Alvito dam case study is analyzed. Lessons from dam behavior<br />
during earthquakes are presented. Analysis <strong>of</strong> dams stability during earthquakes by<br />
experimental and mathematical models is referred. Selection <strong>of</strong> design earthquakes by<br />
deterministic and probabilistic criteria is discussed. Las Cuevas Dam case study is presented.<br />
Hydrodynamic effects are discussed. Reservoir induced seismicity and prototype dynamic<br />
tests are treated. Ageing effects and rehabilitation <strong>of</strong> dams are discussed. Benefits and<br />
concerns <strong>of</strong> dams are referred. Some final considerations and topics for discussions are<br />
presented.<br />
“Where love is great, the littlest doubts are fear;<br />
Where little fears grow great, great love grows there.”<br />
(Love, Shakespeare, Hamlet)<br />
INTRODUCTION<br />
International Symposium on Geotechnical Engineering, Ground Improvement and Geosynthetics<br />
for Human Security and Environmental Preservation, Bangkok, Thailand<br />
Dam design criteria is addressed.<br />
Foundation studies for soil and rock materials are described.<br />
Alvito Dam case study is analysed.<br />
Lessons from dam behavior during earthquakes are presented.<br />
Analysis <strong>of</strong> dams stability during earthquakes by experimental and mathematical models is<br />
referred.<br />
Selection <strong>of</strong> design earthquakes by deterministic and probabilistic criteria is discussed.<br />
Las Cuevas Dam case study is presented.<br />
Hydrodynamic effects are discussed.<br />
Reservoir induced seismicity and prototype dynamic tests are treated.<br />
Ageing effects and rehabilitation <strong>of</strong> dams are discussed.<br />
Benefits and concerns <strong>of</strong> dams are discussed.<br />
Some final considerations and topics for discussions are presented<br />
63
<strong>DAM</strong> DESIGN CRITERIA<br />
Dam design requires the specification <strong>of</strong> all relevant conditions for “normal” and “unlikely<br />
but possible” behavior design. These sets <strong>of</strong> conditions are known as “utilization scenarios”<br />
and “hazard scenarios”, respectively (or simply “normal” and “extreme” conditions) (ICOLD,<br />
1988).<br />
Limit equilibrium analyses based in a safety factor do not provide any information on<br />
displacements.<br />
Finite element analyses considering soil nonlinear behavior give the designer information<br />
about the distribution <strong>of</strong> stress and displacements.<br />
Verification and Validation <strong>of</strong> Models<br />
The need <strong>of</strong> model and code validation is getting increased attention.<br />
Sargent (1990) has introduced the concepts <strong>of</strong> verification and validation and the relations<br />
established between the three entities: the physical problem; the conceptual model; and the<br />
computer model and its numerical implementation are illustrated in Figure 1.<br />
Verification intends to ensure that the computer program is correct and its represents<br />
faithfully the conceptual model and validation applies essentially to the conceptual model,<br />
and its ability to reproduce satisfactorily the physical phenomena.<br />
A slightly different terminology is adopted by ICOLD (1994a) that considers that the<br />
numerical modeling process for dams should be checked in order to avoid unreliable results<br />
considering the following aspects:<br />
Fig.1 Relations between physical problem, conceptual model and computer model (Sargent,<br />
1990)<br />
i) Justification <strong>of</strong> the whole modeling method ( the relevance to physical reality);<br />
64
ii) validation <strong>of</strong> the computer code;<br />
iii) quality assurance <strong>of</strong> the whole computation process.<br />
Foundations Studies<br />
The foundation properties for soil materials are estimated by geophysical tests (crosshole<br />
tests, seismic downhole tests and refraction tests), SPT tests, CPT tests, seismic cone and<br />
pressurometer tests (ICOLD, 2005a).<br />
For the analysis <strong>of</strong> rock mass discontinuities the following numerical techniques are used:<br />
finite elements, finite differences, boundary elements and discrete elements.<br />
To reproduce the opening <strong>of</strong> joints discrete element models are well suited for this type <strong>of</strong><br />
study, as they represent the dynamic behavior <strong>of</strong> the jointed rock medium. The spacing and<br />
orientation parameters <strong>of</strong> discontinuous cross-joints are defined by a mean value and a<br />
random deviation. A coupled hydro-mechanical analysis can be performed under the<br />
assumption that blocks are impervious and fracture flow is governed by the cubic law<br />
(Lemos, 1999b).<br />
Significant advances have been made in describing joint statistics and creating computer<br />
representations <strong>of</strong> rock masses with some measure <strong>of</strong> realism. The Veneziano polygonal<br />
model, which starts by generating lines by a Poisson process on each plane, where actual joint<br />
and rock bridge portions are then defined is shown in Figure 2.<br />
Dershowitz and Einstein (1988) described several joint system models, which are intended<br />
to characterize, in aggregate way, the various joint characteristics. Individual joints are<br />
idealized as disks or polygons, distributed in a 3D space, either randomly or according to<br />
some spatial criterion. This model illustrated in Figure 3 generates the planes by Poisson<br />
process first, then find the intersections in order to define the joint and rock bridge portions<br />
on each plane (Lemos, 1999a).<br />
To investigate the nonlinear dynamic soil-structure interaction <strong>of</strong> a plane-strain earth dam<br />
founded on elastic halfspace, subjected to transient vertically incident SV waves a couple<br />
finite element-boundary element formulation was applied (Abouseeda and Dakoulas, 1996).<br />
This formulation can also be used to assess the relative importance <strong>of</strong> the effects <strong>of</strong><br />
nonlinearity, soil structure-interaction, effect <strong>of</strong> a s<strong>of</strong>t foundation layer, type <strong>of</strong> excitation (P,<br />
S, Rayleigh waves) and other parameters affecting the response <strong>of</strong> the dam.<br />
The most dangerous manifestation concerning the dam stability and integrity is the surface<br />
fault breaking, intersecting the dam site.<br />
Following (ICOLD, 1998) an active fault is a fault, reasonably identified and located,<br />
known to have produced historical fault movements or showing geologic evidence <strong>of</strong><br />
Holocene (11 000 years) displacements and which, because <strong>of</strong> its present tectonic sitting, can<br />
undergo movements during the anticipated life <strong>of</strong> man-made structures.<br />
More recently it is recognized that gravelly material can liquefy.<br />
The behavior <strong>of</strong> Keenleyside dam with foundation composed <strong>of</strong> sands and gravel was<br />
investigated. Due may uncertainties in the assessment multiple methods both field tests (SPT<br />
65
tests, Becher Penetration tests, shear wave velocities) and laboratory tests (triaxial and<br />
permeability tests) were used (Yan and Lun, 2003).<br />
Alvito Dam Case Study<br />
Alvito dam in the south <strong>of</strong> Portugal is a 50 m high and 1 500 m long earth dam. A crosssection<br />
<strong>of</strong> the dam is shown in Figure 4. The core <strong>of</strong> the dam was constructed <strong>of</strong> clayed<br />
material and the shells <strong>of</strong> schist material. A chimney - filter located downstream <strong>of</strong> the core is<br />
composed <strong>of</strong> sand.<br />
A two dimensional plane strain analysis in total stresses <strong>of</strong> Alvito dam was done using<br />
hyperbolic stress - strain law. The construction stage was simulated in ten layers and the<br />
analysis <strong>of</strong> reservoir filling in three steps (<strong>Pinto</strong>, 1983).<br />
Also an incremental stress-strain relationship (modified cam-clay model that takes into<br />
account the consolidation <strong>of</strong> partly saturated clay soils with varying permeability and<br />
compressibility <strong>of</strong> the pore fluid was developed.<br />
The summary <strong>of</strong> parameters for the materials used in the analysis is given in Table 1<br />
(<strong>Pinto</strong>, 1987).<br />
The values <strong>of</strong> all the stress - strain parameters required for this model were obtained form<br />
the results <strong>of</strong> drained triaxial tests and one-dimensional consolidation tests performed on<br />
molded specimens. Special tests were conducted to quantity the variation <strong>of</strong> clay core<br />
permeability with degree <strong>of</strong> saturation, water content and void ratio.<br />
The values <strong>of</strong> the vertical and horizontal internal displacements observed at the end <strong>of</strong> the<br />
construction period (from USBR devices and inclinometers) are compared in Figure 5 with<br />
the values predicted by the two rheological models. There is a good agreement in the core<br />
zone and a slight deviation in the downstream shell considering the degree <strong>of</strong> accuracy to be<br />
expected in this type <strong>of</strong> analysis.<br />
LESSONS FROM <strong>DAM</strong> BEHAVIOR DURING EARTHQUAKES<br />
From a careful study <strong>of</strong> dam behavior during earthquakes occurrences the following failure<br />
mechanisms can be selected (<strong>Pinto</strong>, 2001):<br />
- Sliding or shear distortion <strong>of</strong> embankment or foundation or both<br />
- Transverse cracks<br />
- Longitudinal cracks<br />
- Loss <strong>of</strong> freeboard due to compaction <strong>of</strong> embankment or foundation<br />
- Rupture <strong>of</strong> underground conduits<br />
- Overtopping due to seiches in reservoir<br />
- Overtopping due to slides or rockfalls into reservoir<br />
66
Fig. 2 Veneziano polygonal model: a) 2D Poisson line process; b) marking <strong>of</strong><br />
polygonal joints; c) 3D Poisson plane process (after Einstein, 1993)<br />
Fig. 3 Dershowitz polygonal model: a) 2D Poisson plane process; (b) Poisson line process<br />
formed by intersections, c) marking <strong>of</strong> polygonal joints (Dershowitz and Einstein,<br />
1988)<br />
Fig. 4 Alvito dam cross-section<br />
67
Table 1 Summary <strong>of</strong> elasto-plastic Cam-Clay parameters for Alvito dam materials<br />
Paramet<br />
er<br />
Name Core material Shell material Filter material<br />
γt Total unit weight (kN/m 3 ) 20.0 22.5 18.4<br />
pb Pressure at juncture (kPa) 1000.0 1000.0 1000.0<br />
pr Reference pressure (kPa) 296..9 99.8 0<br />
p’r Reference pressure (kPa) 296..9 99.8 0<br />
k Slope <strong>of</strong> isotropic<br />
rebound curve<br />
0.0058 0.0058 0.0059<br />
Mr Strength parameter 0.79 1.17 1.55<br />
M’r Strength parameter 0.79 1.17 1.55<br />
eo Initial void ratio 0.5 0.40 0.45<br />
So Initial degree <strong>of</strong><br />
saturation (%)<br />
67 70 70<br />
Sf Threshold degree <strong>of</strong><br />
saturation (%)<br />
10 0.0 0.0<br />
Horizontal saturated 5 x 10 -7 10 -5 10 -4<br />
khs<br />
kvs<br />
permeability (m/s)<br />
Vertical saturated<br />
permeability (m/s)<br />
2 x 10 -8 10 -5 10 -4<br />
σt Tensile strength (kPa) 10.0 0 0<br />
avg avg avg<br />
po λ po λ po λ<br />
avg<br />
po - Average stress (po + σ3)/2(kPa) 432 0.026 299 0.0069 323 0.026<br />
λ - Slope <strong>of</strong> virgin isotropic<br />
consolidation curve<br />
747<br />
1329<br />
68<br />
0.068<br />
0.096<br />
671<br />
1278<br />
0.0272<br />
0.0581<br />
982<br />
1746<br />
0.044<br />
0.066<br />
p v p v p v<br />
p - mean effective stress (kPa)<br />
100<br />
300<br />
0.32<br />
0.37<br />
100<br />
300<br />
0.29<br />
0.33<br />
100<br />
300<br />
0.15<br />
0.32<br />
v - Poisson ratio 600 0.41 600 0.37 600 0.39<br />
ANALYSIS OF <strong>DAM</strong> STABILITY DURING EARTHQUAKES<br />
Introduction<br />
According to Aristotle (384-322 B.C.) in his book Meteorologica earthquakes were produced<br />
by the dried exhalations (spirits or winds) in caves inside the earth which trying to escape make<br />
the earth shake<br />
Martin Lister in England and Nicolas Lemery in France in 17 th century were the first to<br />
propose that earthquakes were produced by large explosions <strong>of</strong> inflammable material formed<br />
by a combination <strong>of</strong> sulfur, coal, niter and other products accumulated in the interior <strong>of</strong> earth<br />
(Udias and Arroyo, 2005). The explosive theory was also proposed by Newton`s Optics<br />
(1718).
Fig. 5 Values predicted by the two rheological models<br />
- Disruption <strong>of</strong> dam by major fault movement in foundation<br />
- Differential tectonic ground movements<br />
- Failure <strong>of</strong> spillway or outlet works<br />
- Piping failure through cracks induced by ground motions<br />
- Liquefaction <strong>of</strong> embankment or foundation.<br />
The damage modes listed are not necessarily independent <strong>of</strong> each other.<br />
In France the world was considered a good place in which everything that happened was<br />
viewed to be “for the best” and earthquake was considered with optimism. Voltaire in his<br />
novel Candide presented a hard attack to this optimistic view point. Also Kant and Rosseau<br />
defended the optimist position.<br />
Recent Earthquakes-Dam behavior<br />
During the Committee Seismic Aspects on Dams meeting in Seul, in 2004, the following<br />
reports were presented (ICOLD, 2004).<br />
D. Babbitt reported on the performance <strong>of</strong> dams during the San Simeon earthquake in<br />
California <strong>of</strong> December 22, 2003 (Magnitude 7.1). The maximum peak ground acceleration<br />
(PGA) estimated at the Las Tablas Creek embankment dam site was 0.36 g, which resulted in<br />
minor crest cracks and a spillway rock slide. At the 61 m high San Antonio embankment dam<br />
the seepage almost doubled after the earthquake and returned to normal in the following days<br />
(PGA ca. 0.25 g).<br />
M. Lino reported on the February 2004 earthquake the North <strong>of</strong> Morocco, magnitude 6.5,<br />
ca. 600 people killed. Two dams were affected by this earthquake, i.e. (i) a 30 m high CFRD<br />
built on a 30 m thick soil layer with epicentral distance <strong>of</strong> ca. 10 km experienced a PGA <strong>of</strong><br />
0.24 g; minor cracks were observed at the crest, and (ii) an RCC dam ‘built in a raw manner’<br />
and located at an epicentral distance <strong>of</strong> 30 km behaved well.<br />
N. Matsumoto reported on the M = 8.0 Tokachi-Oki earthquake <strong>of</strong> September 26, 2003 in<br />
Japan (epicenter ca. 60 km <strong>of</strong>fshore <strong>of</strong> Hokkaido island): PGA recorded at the ground surface<br />
69
(mainly alluvion) at epicentral distances <strong>of</strong> 100 to 150 km ranged from 0.2 to 0.8 g. At a<br />
depth <strong>of</strong> 50 to 100m (rock) the PGA was about ½ to 1/3 <strong>of</strong> that at the ground surface. 45 dams<br />
were inspected immediately after the earthquake but no major damage was found. At Takami<br />
dam two longitudinal cracks were found at the crest with a depth <strong>of</strong> less than 1 m, which were<br />
repaired.<br />
On May 2003 an earthquake <strong>of</strong> magnitude 6.8, with a depth <strong>of</strong> 10 km, occurred 40 km East<br />
Alger, provoking 2270 deaths. In Keddara rockfill dam, with 106m high, located 30 km from<br />
the fault, only 1 longitudinal crack and 3 transverse cracks were observed. A value <strong>of</strong> 0.34 g<br />
was recorded in rock and the dam was designed for a acceleration value <strong>of</strong> 0.25g. No damages<br />
were observed in the gallery (Benlala, 2003).<br />
Experimental Models<br />
Experimental methods are used to test predictive theories and to verify mathematical<br />
models. Nevertheless some limitations they are useful for physical modeling in geotechnique<br />
(Portugal, 1999).<br />
The most popular techniques for embankment dams are shaking table and centrifuge<br />
models.<br />
The existent equipments in LNEC are shown in Figures 6 and 7.<br />
Mathematical Models<br />
The following dynamic analysis <strong>of</strong> embankment dams is used (<strong>Pinto</strong> et. al, 1995):<br />
i) pseudo-static analyses;<br />
ii) simplified procedures to assess deformations;<br />
iii) dynamic analysis.<br />
The pseudo-static analyses assume a rigid or elastic behavior for the material (Ambraseys,<br />
1960) and have the limitation that the seismic coefficient acts in one direction for an infinite<br />
time.<br />
Fig. 6 Shaking table<br />
70
Fig. 7 Centrifuge equipment<br />
Simplified procedures to assess deformations were proposed by Newmark (1965), Sarma<br />
(1975) and Makdisi and Seed (1977) and have given reasonable answers in areas <strong>of</strong> low to<br />
medium seismicity.<br />
Newmark´s original sliding block model considering only the longitudinal component was<br />
extended to include the lateral and vertical components <strong>of</strong> earthquake motion by Elms (2000).<br />
The use <strong>of</strong> dynamic pore pressure coefficients along with limit equilibrium and sliding<br />
block approaches for assessment <strong>of</strong> stability <strong>of</strong> earth structures during earthquakes was<br />
demonstrated by Sarma and Chowdhury (1996).<br />
For large dams where strong earthquakes have occurred more sophisticated methods were<br />
used (Seed, 1979).<br />
Several finite element computer programs assuming an equivalent linear model in total stress<br />
have been developed for 1D (Schanabel et al., 1972), 2D (Idriss et al., 1973; Lysmer et al., 1974)<br />
and pseudo 3D (Lysmer et al., 1975).<br />
Since these models are essentially elastic the permanent deformations cannot be computed by<br />
this type <strong>of</strong> analysis and are estimated from static and seismic stresses with the aid <strong>of</strong> strain data<br />
from laboratory tests (cyclic triaxial tests or cyclic simple shear tests) (<strong>Pinto</strong>, 1999).<br />
71
To overcome these limitations, nonlinear hysteretic models with pore water pressure<br />
generation and dissipation have been developed using incremental elastic or plasticity theory.<br />
The incremental elastic models have assumed a nonlinear and hysteretic behavior for soil and<br />
the unloading-reloading has been modeled using the Masing criterion and incorporate the effect<br />
<strong>of</strong> both transient and residual pore-water pressures generated by seismic loading (Lee and Finn,<br />
1978; Finn, 1987).<br />
For the models based on the theory <strong>of</strong> plasticity two particular formulations appear to have a<br />
great potential for multidimensional analysis: the multi-yield surface model (Prevost, 1993) and<br />
the two-surface model (Mröz et al., 1979).<br />
Endochronic models have been refined by the inclusion <strong>of</strong> jump-kinematics hardening to<br />
satisfy Drucker's postulate and achieve closure <strong>of</strong> the hysteresis loops (Bazant et al., 1982).<br />
A modified cam-clay model for cyclic loading taking into account that when saturated clay<br />
is unloaded and then reloaded the permanent strains occur earlier than predicted by the camclay<br />
model was proposed by Carter et al. (1982). The predictions exhibit many <strong>of</strong> the same<br />
trends that have been observed in laboratory tests involving the repeated loading <strong>of</strong> saturated<br />
clays.<br />
For the definition <strong>of</strong> the constitutive laws the following laboratory tests are used for<br />
embankment dams: resonant column tests, cyclic simple shear tests, cyclic triaxial tests and<br />
cyclic torsional shear tests.<br />
Selection <strong>of</strong> Design Earthquakes<br />
The selection <strong>of</strong> seismic design parameters for dam projects depends on the geologic and<br />
tectonic conditions at and in the vicinity <strong>of</strong> the dam site (<strong>Pinto</strong>, 2004)..<br />
The regional geologic study area should cover, as a minimum, a 100 km radius around the<br />
site, but should be extended to 300 km to include any major fault or specific attenuation laws.<br />
The probabilistic approach quantifies numerically the contributions to seismic motion, at<br />
the dam site, <strong>of</strong> all sources and magnitudes larger than 4 or 5 Richter scale and includes the<br />
maximum magnitude on each source.<br />
The regional geologic study area should cover, as a minimum, a 100 km radius around the<br />
site, but should be extended to 300 km to include any major fault or specific attenuation laws.<br />
The dam should be designed for Design Earthquake (DE) and Maximum Design<br />
Earthquake (MDE). Both depend on the level <strong>of</strong> seismic activity, which is displayed at each<br />
fault or tectonic province (Wieland, 2003).<br />
For the OBE only minor damage is acceptable and is determined by using probabilistic<br />
procedures (SRB, 1990a).<br />
For the MDE only deterministic approach was used (ICOLD, 1983) but presently it is<br />
possible to use a deterministic and probabilistic approach. If the deterministic procedure is<br />
used, the return period <strong>of</strong> such an event is ignored, if the probabilistic approach is used a very<br />
long period is taken (ICOLD, 1989).<br />
72
Las Cuevas Dam – Case Study<br />
In general for embankment dams 2 D analyses are performed, but for narrow canyons<br />
where the ratio crest length to height L/H is less than 3, a 2 D model act as a kind <strong>of</strong> low pass<br />
filter in the frequency domain and the vibration in dam axis direction would induce the<br />
vibration in UD direction due to the 3D effect <strong>of</strong> valley (<strong>Pinto</strong> et al., 1992; Sato and Obnuchi,<br />
2000; Jafarzadeh, 2003).<br />
Las Cuevas dam is an earthfill embankment to be constructed in Venezuela, on the Doradas<br />
river, in a zone <strong>of</strong> very high seismicity. The dam is 100m high, 260m long at the crest, the total<br />
embankment volume will be 4.5 x 10 6 m 3 and will impound a reservoir <strong>of</strong> 1.2 x 10 9 m 3 . The cross<br />
section is shown in Figure 8 and the upstream slope will be 1:1.8 and the downstream slope 1:1.8.<br />
The dam has a sloped narrow core <strong>of</strong> clay material and two shells <strong>of</strong> silty-sand material. A chimney-filter<br />
located downstream <strong>of</strong> the core is composed <strong>of</strong> sand.<br />
The bedrock is composed from a sand-stone with high permeability and for this reason an<br />
extensive foundation treatment was recommended.<br />
Fig. 8 Las Cuevas dam cross-section<br />
Las Cuevas Dam is located close to active faults <strong>of</strong> Caparo and Bocono where generation <strong>of</strong><br />
very strong motions were recorded.<br />
The characteristics <strong>of</strong> the main sources <strong>of</strong> earthquakes are synthesized in Table 2.<br />
The first vibration mode is shown in Figure 9.<br />
Figure 10 presents the maximum acceleration response in both horizontal and vertical<br />
directions for selected points located in the upstream shell, core and downstream shell for the<br />
near earthquake.<br />
The shear stress time histories for six selected elements located at the upstream shell, core and<br />
down stream shell for the near earthquake are shown in Figure 11.<br />
Table 2 - Selection <strong>of</strong> design earthquakes<br />
73
Period <strong>of</strong> life<br />
(years)<br />
Probability <strong>of</strong><br />
exceeding the<br />
ground<br />
acceleration (%)<br />
Ground<br />
acceleration<br />
(gal)<br />
Duration <strong>of</strong><br />
earthquake (seg)<br />
Near Source Far Source<br />
100 100<br />
74<br />
10 10<br />
406 274<br />
21 41<br />
Fig. 9 2D first vibration mode<br />
The shear strain potential distribution is presented in Figure 12. It is clear that relatively high<br />
values <strong>of</strong> shear strain potential are concentrated near the surface <strong>of</strong> the upstream shell.<br />
Since, for dams in narrow canyons, the response <strong>of</strong> the structure is <strong>of</strong> a three-dimensional<br />
nature and as the crest length to height ratio L/H=2.6 a three dimensional analysis was performed.<br />
The computer program DYSE52 developed at LNEC was used and Figure 13 shows the<br />
finite element model. The structure was discretized in 555 isoparametric finite element (8<br />
mode cubic element and 6 mode prismatic element) with a total <strong>of</strong> 648 modal points.<br />
The materials that incorporate the dam were considered continuous and isotropic with the<br />
shear modulus and Poisson ratio obtained from the last iteration <strong>of</strong> the 2D dynamic analysis.<br />
A damping viscous coefficient <strong>of</strong> 10% was assumed.<br />
The first twenty vibration modes were determined with fundamental frequencies between 1Hz<br />
and 2Hz.<br />
The first vibration mode is shown in Figure 14.
A comparison between natural frequencies computed from 2D and 3D analyses has shown<br />
that for 3D analysis the fundamental natural frequencies were 25% higher than those computed<br />
from a plane strain analysis.<br />
It was found that a plane strain analysis <strong>of</strong> the maximum section gave values for the shear<br />
stresses that were 50% higher than those computed from a 3D analysis <strong>of</strong> the dam.<br />
Hydrodynamic Effects <strong>of</strong> Reservoir<br />
Seed, et al. (1985) have disregarded hydrodynamic effects <strong>of</strong> the reservoir water upon the<br />
concrete face considering that this effect is no important for earthfill dams where slopes are<br />
with 1(V): 3 (H). But for concrete faced rockfill dams (that will soon reach 200m height),<br />
located in high seismicity zones, where slopes are with 1 (V): 1.3 (H) and water pressures are<br />
applied directly to the concrete facing, these effects have deserved more attention (Bureau et.<br />
al., 1985).<br />
Both Westergaard method and Galerkin formulation were used to analyze reservoir<br />
interaction (<strong>Pinto</strong>, 1996b and Câmara, 1999).<br />
Hydrodynamic effects induced by the impounded water may have significant influence on the<br />
response <strong>of</strong> a dam subjected to earthquake excitation.<br />
Nevertheless the studies related with the dynamic analyses <strong>of</strong> embankment dams have been<br />
intensely developed the effects <strong>of</strong> water deserve more attention due the following reasons:<br />
The increasing interest in building concrete faced rockfill dams that will soon reach 200 m<br />
height.<br />
For concrete face rockfill dams where slopes are with 1(V): 1,3 (H) and water pressures are<br />
applied directly to the concrete facing, concentrating the loads in that area.<br />
Nevertheless the good observed behaviour <strong>of</strong> concrete face rockfill dams in areas <strong>of</strong> relatively<br />
low seismicity there is a lack <strong>of</strong> information about the behaviour <strong>of</strong> these dams in zones where<br />
strong earthquakes have occurred.<br />
Westergaard method employing the concept <strong>of</strong> added-mass and using a finite element<br />
analysis was used to study a concrete face rockfill dam with 100 m high (Figure 15).<br />
A mesh with 70 isoparametric <strong>of</strong> 8 nodes and 229 nodal points is presented in Figure 16. An<br />
interface element with thickness was considered between the concrete face and the rockfill<br />
material.<br />
The construction stage was simulated in 7 layers and the reservoir filling in six steps.<br />
The non-linear parameters for hyperbolic model were considered.<br />
The characteristics <strong>of</strong> design earthquakes are synthesized in Table 3.<br />
For the vertical component a value <strong>of</strong> 2/3 <strong>of</strong> horizontal component was assumed.<br />
The shear distribution at the end <strong>of</strong> reservoir filling is presented in Figure 16.<br />
A parametric study was done and the following parameters were analysed: (i) effect <strong>of</strong> the<br />
upstream concrete face; (ii) interaction <strong>of</strong> the reservoir; (iii) effect <strong>of</strong> the vertical component.<br />
75
Due to the lack <strong>of</strong> space only the main results are presented in Table 4.<br />
Table 3 Design earthquakes characteristiques<br />
Characteristics Near source<br />
Period <strong>of</strong> life (years) 100<br />
Probability <strong>of</strong> exceeding the<br />
ground acceleration (gal)<br />
76<br />
10<br />
Ground acceleration (gal) 406<br />
Duration <strong>of</strong> earthquakes 21<br />
From the study the following conclusions were obtained:<br />
Frequencies<br />
Fig. 10 Maximum accelerations responses
The frequencies related with the 1st vibration mode present the following variation: (i) they<br />
decrease when the two components <strong>of</strong> seismic acceleration are incorporated; (ii) they decrease<br />
with the effect <strong>of</strong> reservoir interaction; and (iii) they increase with the effect <strong>of</strong> the upstream<br />
concrete face.<br />
Shear stresses<br />
(i) The maximum shear stress values for the elements <strong>of</strong> upstream concrete face are located in<br />
the last third <strong>of</strong> the dam;<br />
(ii) The simultaneous occurrence <strong>of</strong> horizontal and vertical components <strong>of</strong> the earthquake<br />
provokes an increase <strong>of</strong> the maximum shear stresses;<br />
(iii) The maximum shear stresses increase with the effect <strong>of</strong> reservoir interaction;<br />
(iv) The effect <strong>of</strong> the upstream concrete face provokes a decrease <strong>of</strong> the maximum shear tresses<br />
values.<br />
The equivalent number <strong>of</strong> uniform cycles presents the following path; (i) it decreases when the<br />
two components <strong>of</strong> seismic acceleration are incorporated; (ii) it decreases with the effect <strong>of</strong><br />
reservoir interaction; and (iii) it increases with the effect <strong>of</strong> the upstream concrete face.<br />
Accelerations<br />
(i) The nodal accelerations increase from the base to the crest <strong>of</strong> the dam;<br />
(ii) The nodal accelerations increase when the two components <strong>of</strong> seismic acceleration are<br />
incorporated;<br />
(iii) The nodal accelerations increase with the effect <strong>of</strong> reservoir interaction;<br />
(iv) The effect <strong>of</strong> the upstream concrete face provokes a decrease <strong>of</strong> the acceleration values.<br />
Only some results will be presented here for analysis nº 8.<br />
The shear stress time histories for three selected elements located at upstream face (Figure 16)<br />
are shown in Figure 17.<br />
Figure 18 presents the maximum acceleration response in both horizontal and vertical<br />
directions for selected points located at the upstream face (Figure 15).<br />
RESERVOIR TRIGGERED SEISMICITY<br />
Man - made earthquakes caused by the filling <strong>of</strong> reservoirs have drawn the attention <strong>of</strong><br />
designers concerned with dam safety.<br />
The reservoir triggered earthquake (RTS) is linked to dams higher than about 100 m or to<br />
large reservoirs (capacity greater than 500 x 10 6 m 3 ), rate <strong>of</strong> reservoir filling and to new dams<br />
<strong>of</strong> smaller size located in tectonically sensitive areas. This means that the causative fault is<br />
already near to failure conditions and so the added weight stresses and pore pressures<br />
propagation due to reservoir impounding, can trigger the seismic energy release.<br />
77
Fig. 11 Shear stress time histories<br />
Fig. 12 Shear potential distribution<br />
78
Fig. 13 3D finite element mesh<br />
Fig. 14 3D first vibration mode<br />
Fig. 15 Concrete face rockfill dam section<br />
79
Fig. 16 Finite element mesh<br />
Fig. 17 Shear stress – time story for finite elements nº 13, 33 and 53<br />
80
Fig. 18 Horizontal and vertical accelerations for nodal Nº 61, 121 and 181<br />
The earthquakes that have occurred around the few dams by mere accident cannot<br />
definitely be attributed to dam or water load, which is insignificant, compared to the earth<br />
mass.<br />
The detection <strong>of</strong> reservoir induced seismicity may be performed in two phases (ICOLD,<br />
1999): (i) phase 1 includes on historical seismicity and surveys <strong>of</strong> reservoir and surrounding<br />
geological structures, aiming at identification <strong>of</strong> possible active faults; and (ii) the second<br />
phase is carried out starting at least one or two years prior to the impounding with the<br />
installation <strong>of</strong> a permanent network <strong>of</strong> seismometers and other measures such as precise<br />
levelling, use <strong>of</strong> instrumentation to detect active fault movements, and reservoir slope<br />
stability studies.<br />
Seismological observations established at Bhakra, Pong and Ramanga dams in the<br />
Hymalayan terrain have not registed any increase in seismicity due to impounding <strong>of</strong> waters.<br />
Table 5 presents some examples <strong>of</strong> dam sites where induced earthquakes with magnitude<br />
higher than 5 in the Ritcher scale have occurred (<strong>Pinto</strong>, 1996b).<br />
The question <strong>of</strong> maximum magnitude to be ascribed to reservoir triggered seismicity is<br />
difficult to clarify but it seems in the range <strong>of</strong> 6 to 6.3.<br />
An interesting overall picture is shown in Figure 19 taken from USSD Report (1997).<br />
81
Table 4 Parametric study<br />
Without upstream membrane<br />
With upstream membrane<br />
Ex. Acceleration Analyse<br />
Without reservoir<br />
With reservoir<br />
Without reservoir<br />
With reservoir<br />
nº<br />
Frequence<br />
(Hz)<br />
H 1 1.64<br />
H + V 2 1.58<br />
H 3 1.57<br />
H + V 4 1.52<br />
H 5 1.74<br />
H + V 6 1.69<br />
H 7 1.69<br />
H + V 8 1.64<br />
Element Maximum<br />
9<br />
25<br />
41<br />
9<br />
25<br />
41<br />
9<br />
25<br />
41<br />
9<br />
25<br />
41<br />
13<br />
33<br />
53<br />
13<br />
33<br />
53<br />
13<br />
33<br />
53<br />
13<br />
33<br />
53<br />
82<br />
shear stress<br />
(kPa)<br />
219.8<br />
252.5<br />
173.8<br />
273.4<br />
278.8<br />
192.4<br />
328.3<br />
299.7<br />
206.8<br />
363.0<br />
331.6<br />
242.8<br />
187.4<br />
203.7<br />
106.5<br />
213.7<br />
209.1<br />
122.5<br />
224.9<br />
221.3<br />
114.3<br />
259.2<br />
220.3<br />
142.1<br />
Uniform<br />
number<br />
<strong>of</strong><br />
cycles<br />
31<br />
29<br />
31<br />
22<br />
22<br />
27<br />
15<br />
24<br />
31<br />
14<br />
18<br />
21<br />
39<br />
24<br />
23<br />
32<br />
22<br />
15<br />
31<br />
23<br />
15<br />
22<br />
26<br />
12<br />
H - horizontal acceleration V - vertical acceleration<br />
Nodal<br />
points<br />
53<br />
105<br />
157<br />
53<br />
105<br />
157<br />
53<br />
105<br />
157<br />
53<br />
105<br />
157<br />
61<br />
121<br />
181<br />
61<br />
121<br />
181<br />
61<br />
121<br />
181<br />
Horiz.<br />
accel.<br />
(m/s 2 )<br />
4.2<br />
4.4<br />
7.2<br />
5.1<br />
5.9<br />
7.4<br />
8.4<br />
7.8<br />
8.9<br />
8.6<br />
9.1<br />
10.0<br />
1.1<br />
1.7<br />
4.6<br />
2.9<br />
5.4<br />
6.0<br />
6.3<br />
6.1<br />
7.3<br />
Vert.<br />
accel.<br />
(m/s 2 )<br />
0.44<br />
1.8<br />
4.6<br />
3.1<br />
6.0<br />
8.6<br />
0.76<br />
2.0<br />
5.2<br />
3.2<br />
9.1<br />
10.0<br />
Monitoring the RTS activity is recommended for large dams and reservoirs (Oliveira,<br />
1988). In order to distinguish between background seismicity and RTS monitoring before<br />
impounding is recommended. For obtained reliable epicentral locations and hypocentral<br />
depths, a local array <strong>of</strong> stations is required (ICOLD, 2005c).<br />
61<br />
121<br />
181<br />
6.7<br />
7.8<br />
7.5<br />
1.1<br />
1.7<br />
4.6<br />
2.9<br />
5.4<br />
8.0<br />
1.5<br />
2.4<br />
5.4<br />
2.7<br />
7.5<br />
9.1
Table 5 Examples <strong>of</strong> dams with induced seismicity.<br />
<strong>DAM</strong> Country Type<br />
Height<br />
(m)<br />
83<br />
Reservoi<br />
r volume<br />
(x 10 6<br />
m 3 )<br />
Year<br />
<strong>of</strong><br />
impou<br />
nding<br />
Induced<br />
seismicity<br />
M year<br />
Prior<br />
seismicity<br />
Marathon Greece gravity 63 41 1930 5 1938 moderate<br />
Hoover U.S.A. Arch-gravity 221 36703 1936 5 1939 ---<br />
Kariba<br />
Haifengki<br />
g<br />
Zimbabwe<br />
/Zambia<br />
arch 128 160368 1959 5,8 1963 low<br />
China buttress 105 10500 1959 6,1 1962 aseismic<br />
Koyna Índia gravity 103 2708 1964 6,5 1967 low<br />
Kremasta Greece embankment 165 4750 1965 6,3 1966 moderate<br />
Roi<br />
Constantin<br />
e<br />
Greece embankment 96 1000 1969 6,3 moderate<br />
Oroville U.S.A. embankment 236 4298 1967 5,7 1975 moderate<br />
Nurek Tajikistan embankment 330 11000 1972 5 1977 moderate<br />
Tarbella Pakistan embankment 143 14300 1974 5,8 1996 low<br />
Aswan Egypt embankment 111 163000 1974 5.3 1981 aseismic<br />
PROTOTYPE DYNAMIC TESTS<br />
Full scale and man-made vibration tests accompanied by appropriate geophysical<br />
measurements can provide vital information regarding the dynamic properties <strong>of</strong> the materials<br />
(<strong>Pinto</strong>, 1991).<br />
These tests play a fundamental role, providing reliable reference data on the seismic<br />
behavior <strong>of</strong> a dam, but the stress level is always very low with respect to that induced by an<br />
earthquake. So these tests can not reproduce adequately the non linear behavior <strong>of</strong> the dam.<br />
For concrete dams forced vibration tests still maintains an important role for the validation<br />
<strong>of</strong> the analytical model.<br />
Table 6 lists the dams, which were subject to one or more types <strong>of</strong> dynamic excitation.<br />
The dam response to such vibrations was recorded on seismometers placed at various<br />
locations <strong>of</strong> the dam. By analyzing the recorded motions, natural frequencies and associated 3<br />
D mode shapes, as well as damping ratios were obtained.
Fig. 19 Scattergraph <strong>of</strong> RTS cases (after USSD, 1997)<br />
Table 6 lists the dams, which were subject to one or more types <strong>of</strong> dynamic excitation.<br />
The dam response to such vibrations was recorded on seismometers placed at various<br />
locations <strong>of</strong> the dam. By analyzing the recorded motions, natural frequencies and associated 3<br />
D mode shapes, as well as damping ratios were obtained.<br />
84
Table 6 List <strong>of</strong> dams subjected to dynamic excitation<br />
Nº Name Type Country Height (m) Type <strong>of</strong> Recorded Vibrations<br />
1 Santa Felicia ED U.S.A. 83<br />
Seismic, ambient, forced,<br />
hydrodynamic<br />
2 Brea ED U.S.A. 27 Seismic<br />
3<br />
Carbon<br />
Canyon<br />
ED U.S.A. 33 Seismic<br />
4 Bouquet ED Yugoslavia 60 Forced<br />
5 Mavroro ED Japan 56 Forced<br />
6 Kisenyama RD Japan 95 Seismic, ambient, forced<br />
7 Shimokotori RD Japan 119 Seismic, ambient, forced<br />
8 Nikappu RD Japan 103 Seismic, ambient, forced<br />
9 Talaragi RD Japan 65 Seismic, ambient, forced<br />
10 Sannokai ED Japan 37 Seismic<br />
11 Ainono ED Japan 41 Seismic<br />
12 Ushino RD Japan 21 Seismic<br />
13 Kamishiba AD Japan 110 Forced<br />
14 Mainadisauro AD Italy 136 Forced<br />
15 Pacoima AD USA 128 Forced<br />
16 Cabril AD Portugal 136 Forced<br />
17 Aguieira MAD Portugal 89 Forced<br />
ED - earth dam RD - rockfill dam AD - arch dam MAD - multi arch dam<br />
AGEING EFFECTS<br />
Ageing is defined as a class <strong>of</strong> deterioration associated with time-related changes in the<br />
properties <strong>of</strong> the materials <strong>of</strong> which the structure and its foundation are constructed in normal<br />
conditions. And so these deteriorations occur more that 5 years after the beginning <strong>of</strong><br />
operation (ICOLD, 1993b).<br />
Inspection, testing and monitoring <strong>of</strong> the works are the methods used to obtain the<br />
knowledge required to exercise control. A direct evaluation <strong>of</strong> ageing is possible by<br />
monitoring changes in structural properties, and indirect evaluation is available by monitoring<br />
the effects and consequences <strong>of</strong> these changes and <strong>of</strong> the actions causing them.<br />
Piping in the foundation and in the body <strong>of</strong> fill dams has caused a number <strong>of</strong> failures.<br />
The progress in safety <strong>of</strong> dams is due the improvements <strong>of</strong> design and construction, but<br />
possibly even more to maintenance and monitoring and in particular to proper visual<br />
inspections and careful follow-up <strong>of</strong> increases in leakage that have prevented many failures<br />
and reduced the consequences <strong>of</strong> others.<br />
85
REHABILITATION OF <strong>DAM</strong>S<br />
Due to ageing effects and retr<strong>of</strong>it <strong>of</strong> dams this topic is getting an increasing attention.<br />
Anastassopoulos et al. (2004) describe the behavior <strong>of</strong> Thissavros rockfil dam, with 172m<br />
high and 480m long, constructed in Greece. The bedrock is composed by gneiss, partially<br />
schistose, granitic gneiss and layers <strong>of</strong> mica schist.<br />
Based on morphological criteria the project assumed the existence <strong>of</strong> several large dormant<br />
landslides at the dam site.<br />
Two areas <strong>of</strong> instability developed at the site: (i) right bank slide where a monitoring<br />
system composed by inclinometers, piezometers and survey monuments was installed to<br />
assess the remedial measures that have included major excavation, removing <strong>of</strong> unstable<br />
mass, toe buttressing and drainage by a system <strong>of</strong> galleries; and (ii) left bank where jet<br />
grouting and toe load berm were used.<br />
Perlea et al. (2004) conducted numerous seismic retr<strong>of</strong>it solutions to reinforce the strength<br />
<strong>of</strong> a liquefiable sand deposit in the foundation <strong>of</strong> a major embankment dam with 42 m high<br />
and 1650m long.<br />
The following methods <strong>of</strong> foundation soil stabilization were evaluated: (i) removal and<br />
replacement <strong>of</strong> liquefiable material; (ii) dynamic compaction (heavy tamping); (iii)<br />
densification by vibrocompaction; (iv) compaction grouting; (v) jet-grouting; (vi) soil mixing,<br />
(vii) densification by stone columns; (viii) gravel drains; (ix) enlargement embankment; and<br />
(x) foundation seepage cut<strong>of</strong>f<br />
The authors have considered that the best alternative solution for stabilization <strong>of</strong> the<br />
upstream slope was jet grouting from a platform built on the lower portion <strong>of</strong> the slope and<br />
for stabilization <strong>of</strong> the downstream slope was deep soil mixing.<br />
The use <strong>of</strong> geomembranes for the rehabilitation <strong>of</strong> dams is a topic <strong>of</strong> great interest. Following<br />
ICOLD (1991) more that 70 dams located in 24 countries have used geomembranes.<br />
The causes <strong>of</strong> dam deterioration are related with irregular settlement <strong>of</strong> the fill or foundation,<br />
poor concrete quality and shrinkage cracks.<br />
The following agents are related with the dangers to which the geomembranes are<br />
exposed:<br />
-falling rock at mountain site<br />
-blows from heavy floating objects<br />
-ultraviolet radiations<br />
-willful damage.<br />
BENEFITS AND CONCERNS OF <strong>DAM</strong>S<br />
The benefits <strong>of</strong> dams are demonstrated with the multipurpose uses <strong>of</strong> dams for water<br />
supply, irrigated agriculture, electric energy generation, flood control, recreation and other<br />
usages.<br />
86
Importance to the environmental and social aspects <strong>of</strong> dams and reservoir is increasing.<br />
Construction <strong>of</strong> dams is no longer acceptable without a careful analysis <strong>of</strong> mitigation and<br />
adverse impacts. It is important to build dams in harmony with the environment and therefore<br />
economic development and environmental protection must proceed hand in hand.<br />
Social and economic impacts <strong>of</strong> large dam projects vary greatly in different geographic,<br />
political, and economy contexts (ICOLD, 1992). Social and economic considerations must be<br />
brought into the planning process early to permit major process layout and design elements.<br />
In the Stcokholm Conference on World Environmental held in 1972, hunger and poverty<br />
were identified as the major reasons for environmental degradation. Inadequate and uneven<br />
distribution <strong>of</strong> rainfall, drought and floods, lower irrigation intensity and instability <strong>of</strong><br />
agricultural, poor health status are all factors contributing to hunger and poverty.<br />
One <strong>of</strong> the predominant concerns about reservoirs is re-settlement. Following ICOLD<br />
(1997) involuntary settlement must be handled with special care, managerial skill and<br />
political concern based on comprehensive social research and sound planning for<br />
implementation.<br />
The implementation <strong>of</strong> resettlement planning needs to take into account: (i) opinion<br />
surveys and talks to people about resettlement rights; (ii) identification <strong>of</strong> entitled families;<br />
(iii) site selection; (iv) allocation <strong>of</strong> funds, (v) preparation <strong>of</strong> agricultural land; (vi) road<br />
construction, provision <strong>of</strong> water supply and other infrastructure; (vii) tendering <strong>of</strong> bids for<br />
resettlement housing construction; (viii) transportation <strong>of</strong> settlers, (ix) training and<br />
agricultural extension services; and (x) rehabilitation programs.<br />
A study carried out in respect <strong>of</strong> a number <strong>of</strong> major dams built for multipurpose projects<br />
indicates that the population displaced on account <strong>of</strong> construction <strong>of</strong> dams varies between<br />
0,5% to 4% <strong>of</strong> the population benefited by the irrigation facilities and a tiny fraction <strong>of</strong> the<br />
percentage <strong>of</strong> those benefited by electricity (Naidu, 1999). The rate <strong>of</strong> beneficiaries to<br />
affected persons is better than 200:1.<br />
Statistical analysis <strong>of</strong> a number <strong>of</strong> major projects also indicates that forest area submerged<br />
is just 1-2% <strong>of</strong> the area to be irrigated by those projects.<br />
A detailed listening <strong>of</strong> over 80 potential impacts on the natural renvironment (flora, fauna<br />
and aquatic fauna), social economic and cultural aspects, land, dam construction activities,<br />
sedimentation <strong>of</strong> reservoirs, downstream hydrology, water quality, tidal barrages, climate and<br />
human health was presented by Veltrop (1998).<br />
Technical feasibility and economic justification <strong>of</strong> new dam projects are now second to<br />
social, political and environmental considerations and requires cooperation among engineers,<br />
scientists, environmentalists and stakeholders.<br />
FINAL REMARKS AND TOPICS FOR DISCUSSION<br />
In spite <strong>of</strong> the impressive progress that has been made in the last years on dam engineering<br />
there is still space for questions that remain without a definitive answer. Some questions that<br />
deserve further discussion are outlined below.<br />
87
The floor discussions that we hope lively will give us the unique opportunity to share our<br />
experience and will also contribute to the advancement <strong>of</strong> the knowledge.<br />
i) The complexity <strong>of</strong> computer codes demands validation <strong>of</strong> models. What is the best<br />
approach?<br />
ii) It seems that the criteria to select the recurrence periods for MCE and OBE are not<br />
well defined. Are the ICOLD suggestions well accepted?<br />
iii) The use <strong>of</strong> discrete element models to reproduce the opening <strong>of</strong> joints rock medium<br />
during earthquakes.<br />
iv) Interplay between ageing effects and maintenance and monitoring related with the<br />
safety <strong>of</strong> dams.<br />
v) The use <strong>of</strong> geomembranes for dam rehabilitation related with: limitation <strong>of</strong> specific<br />
height <strong>of</strong> dam, the use <strong>of</strong> a second watertight barrier in large structures and the risks <strong>of</strong><br />
leaving the geomembranes uncovered;<br />
vi) Co-operation among engineers, scientists, environmentalists and stakeholders for new<br />
dam projects due the important role <strong>of</strong> social, political and environmental factors;<br />
vii) Continuing education is highly recommended to follow the very fast developments <strong>of</strong><br />
earthquake geotechnical engineering and particularly <strong>of</strong> dam engineering (Sêco e<br />
<strong>Pinto</strong>, 2000).<br />
In dealing with these topics we should never forget the memorable lines <strong>of</strong> Hippocrates:<br />
- “The art is long<br />
- -and life is short<br />
- experience is fallacious<br />
- -and decision is difficult”.<br />
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Anastassopoulos, K., Hoek, E., Milligan, V. and Riemer, W. (2004) Thissavros Hydropower<br />
Plant managing geotechnical problems in the construction”. Session II “Dams,<br />
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Bazant, Z. P. and Zrizek R. J. (1976) Endochronic constitutive law for liquefaction <strong>of</strong> sand.<br />
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88
Bureau, G., Volpe, R. L. Roth, W. H. and Udaka, T. (1985) Seismic analysis <strong>of</strong> concrete face<br />
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Caldeira, L., Pimenta, L. and Silva Gomes, A. (2005) Framework <strong>of</strong> risk analysis and their<br />
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thesis (in Portuguese), LNEC.<br />
Carter, J. P., Booker J. R. and Wroth, C. P. (1982) A Critical State Soil Model for Cyclic<br />
Loading. Soil Mechanics Transient and Cyclic Loads Constitutive Relations and<br />
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Dershowitz, N. S. and Einstein H. H. (1988) Characterization rock joint geometry with joint<br />
system models, Rock Mechanics and Rock Engineering., Vol. 21, No. 1, pp. 21 - 51.<br />
Elgamal, A.W., Zeghal, M. and E. Parra (1995) Identification and modeling <strong>of</strong> earthquake<br />
ground response. Proceedings <strong>of</strong> the First International Conference on Earthquake<br />
Geotechnical Engineering, Japan.<br />
Elms, D. (2000) Refinements to the Newmark sliding block model. Paper No. 2132.<br />
Proceedings <strong>of</strong> 12 th WCEE, Auckland, New Zealand.<br />
Finn, W.D.L. (1987) Finite Element Handbook - Chapter 3 - Geomechanics. Mc. Graw-Hill<br />
Editors H. Hardestuncer, .<br />
ICOLD (1983) Seismicity and Dam Design. Bulletin No. 46.<br />
ICOLD (1988) Dam Design Criteria. The Philosophy <strong>of</strong> their Selection. Bulletin No. 61.<br />
ICOLD (1989) Selection Seismic Parameters for Large Dams - Guidelines. Bulletin No.72.<br />
ICOLD (1991) Watertight Geomembranes for Dams. State <strong>of</strong> the Art. Bulletin No. 78.<br />
ICOLD (1992) Dams and environment, Socioeconomic Impacts. Bulletin No. 86 .<br />
ICOLD (1993a) Rock Materials for Rockfill Dams. Bulletin No. 92 .<br />
ICOLD (1993b) Ageing <strong>of</strong> Dams and Appurtenements Works. Bulletin No. 93 .<br />
ICOLD (1994a) Computer S<strong>of</strong>tware for Dam. Validation. Bulletin No. 94 .<br />
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