Seismic Response of a Zoned Earth Dam (Case Study) Antonio Brigante Department DIGA, University of Naples Federico II, Naples, Italy
[email protected]
Stefania Sica Department of Engineering, University of Sannio, Benevento, Italy
[email protected]
ABSTRACT The Conza Dam is a rare case in literature of a zoned earth dam that during the construction stage (started in the 1979 and finished in 1988) was subjected to a very strong earthquake in almost near-source condition: the Irpinia earthquake (main shock on November 23, 1980; Richter magnitude of 6.9 and duration up to 80s). Settlements, pore water pressures and accelerations measured during different stages of the dam lifetime have been collected and interpreted. The effects of the 1980 earthquake on measured settlements of the dam embankment have been elucidated. By using a coupled dynamic approach based on the u-p formulation of the Biot consolidation theory, solved numerically with the finite element method, a numerical study has been performed in order to: (i) reproduce the observed permanent settlements of the dam embankment due to the 1980 Irpinia earthquake and (ii) predict the dam response to different seismic scenarios.
KEYWORDS:
Earth dam, Permanent settlement, Finite Element Analysis,
Earthquake
INTRODUCTION Seismic analysis of earth dams should be aimed at verifying to what extent seismic actions could affect the main task of these structures, that is, ensuring water tightness (Fanelli et al., 1998; Pagano et al., 2010; Pagano et al., 2012). Earthquakes may induce negligible effects or decrease dam water tightness; the amount of such a decrease mainly depends on earthquake characteristics, dam vulnerability. Seismic induced effects are also significantly related to development of asynchronous motions during the earthquake, which partly compensate inertial forces (Bilotta et al., 2010; Bilotta & Siervo, 2012). In the case of earth dams, the suitable theoretical approaches should predict damage typologies (and related physical quantities) which could affect dam water tightness (Sica et al., 2008; Sica and Pagano, 2009). These damage typologies may be derived from past experience, collecting the effects induced by strong earthquakes to earth dams (Sica & Pagano, 2009; Fontanella et al., 2012), or may be argued recalling some typical mechanisms related to the operational stages (Pagano et al., 2006, 2010). Global sliding mechanisms, freeboard loss due to permanent settlements (e.g., Resendiz et al., 1982; Ozkan, 1998; Fujii et al., 2000; Paoliani, 2001, Singh et al., 2005; Sica & Pagano,
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2009), fractures of the watertightness elements (e.g., Paoliani, 2001) followed by erosion phenomena, and liquefaction of the embankment (e.g., Seed, 1979; Fujii et al., 2000; Singh et al., 2005) or foundation soils are the most feared seismic-induced phenomena which could significantly affect dam water tightness. All the above phenomena require predictions in terms of permanent settlements, stress states and pore water pressures for all seismic scenarios expected at the dam site. The prediction of the permanent settlement at the dam crest, typically carried out in plane strain conditions, may be adopted for checking freeboard loss and also (in its meaning of medium vertical strain) as an effective indicator of dam performance with respect to other damage mechanisms that are very difficult to simulate (e.g., vertical fractures of the embankment due to differential settlements among different cross-sections, fractures at the contact between the embankment and structural elements). Permanent settlement at the dam crest is also a suitable indicator of structure performance to characterize dam mechanical response under different seismic scenarios (Sica et al., 2008). Such indicator, if reliably and promptly predicted, may result effective for the mitigation of environmental risks by the implementation of an early warning system, in line with the mitigation approaches increasingly followed in different fields of civil engineering for both static (Pagano et al., 2008, 2010; Rojas et al., 2008; Toll et al., 2011; Rianna et al., 2012) and seismic problems (Iervolino et al., 2011). The paper accounts for the methodology followed to evaluate the seismic performance of a real case: the Conza Dam. This dam is a rare case in literature of a zoned earth dam subjected during the construction stage to a strong earthquake occurred very close to the dam site: the Irpinia earthquake, whose main shock on November 23, 1980 was characterized by a Richter magnitude of 6.9 and duration of 80s. Settlements, pore water pressures and accelerations measured during different stages of the dam lifetime have been collected and interpreted. The effects of the 1980 earthquake on the measured settlements of the dam embankment have been elucidated. Details are later provided on the experimental procedures to characterize soil parameters required by the selected model; the definition of the expected seismic scenarios at the dam site is accounted for; the seismic performance of the dam is finally discussed on the basis of the computed results.
MATERIALS AND METHODS The Conza dam The Conza dam (Figures 1 and 2) is a zoned earth dam located in the Irpinia region (around 300 Km SE of Rome) in the core of the Apennine chain (Italy), i.e. the part of the Italian peninsula from which the latest strong earthquakes were generated (Lanzo et al., 2011). It is characterized by a maximum height H equal to 46 m. The vertical core is made of clayey silt of medium plasticity (average properties are: plasticity index PI=20%, water content wopt and dry density γs at the optimum of Proctor standard are 21.7% and 1.68 g/cm3, respectively; -8 permeability k=10 cm/s). The filters are made of sand with gravel (permeability k ≈ 4.5x103 cm/s). The shells consist of sandy gravel ( γs =2.3g/cm3 ; wopt=3% ; k=10-3 cm/sec). The dam is founded on a grey-azure clay formation (wL=44%-77%; PI=27%-50%) which is typical of the river Ofanto valley. A 5 meter thick alluvial layer lies upon the clay formation. The shells constituting the dam were obtained from the alluvial soils transported by the Ofanto River and common throughout the river valley. Below the cofferdam an impermeable cutoff reaches the clay formation crossing the alluvial layer. The maximum water storage of the reservoir is of about 77 million m3. - 2496 -
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Figure 1: Main cross section of the Conza Dam. Material zones: (1) core; (2) filters; (3) shells; (4) alluvial layer and (5) clay foundation. The original (A) and actual (B) cross sections are indicated by dashed and continuous lines, respectively
Figure 2: View of the Conza Dam The dam was built between May 1979 and July 1988. The construction was interrupted for almost five years starting from the occurrence of the Irpinia earthquake (main shock dated November 23, 1980) up to June 1985. The 1980 Irpinia earthquake strongly jeopardized the part of the embankment already built. As shown in Figure 3, at that time the shells and the core had reached elevation 420 m a.s.l and 415 m a.s.l., respectively. The maximum height foreseen in the original project was equal to 45m (elevation 440.95m a.s.l.). Huge damage was observed in the embankment soon after the earthquake (permanent settlements, fractures) and construction was stopped.
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Figure 3: Part of the embankment built at the time of the 1980 Irpinia earthquake The initial project of the dam, which was carried out without accounting for seismic actions, was completely reviewed in light of a new law in-force at that time (D.M. 14/03/1982) and seismic classification of the site. The following modifications to dam geometry were carried out: • • •
the slope of the upstream shell was decreased from 2.25/1 to 2.5/1; the slope of the downstream shell was modified from 1.5/1 to 2/1 between the crest (441.95 m a.s.l.) and the upper berm at elevation 429.80 m, and from 1.75/1 to 2/1 between elevations 429.8 and 419.8 m a.s.l. The eight of the dam was changed from 45m to 46m.
Monitoring data During the second stage of construction the dam was very well instrumented to measure internal core settlements (cross-arms placed in 6 different cross-sections of the dam), pore pressures and vertical total stresses. Figure 4 represents the settlements measured during the construction stage in correspondence to the core vertical located in the cross section n. 2. The monitoring data, here selected, cover the period June 1980 May 2000, in order to enhance the effects exerted by the Irpinia earthquake.
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Figure 4: Settlements measured in the Conza Dam core from June 1980 to May 2000 Settlement profiles measured during the construction stages (Figure 4) preceding the 1980 earthquake, arise with the typical symmetrical shape characterizing most of the observed responses in zoned earth dams (Pagano et al., 1998 and 2001). The seismic event makes settlements increasing linearly versus dam elevation with a maximum permanent settlement of 43,5cm at the maximum elevation reached by the embankment at that time (corresponding to a core height of 17.82m) and with a vertical strains equal to 2.4% on average. The settlement profiles observed during the post-seismic construction stages arise asymmetrical due to the contribution of the permanent settlements induced by the Irpinia earthquake.
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Figure 5: Three fault mechanisms activated during the 1980 Irpinia earthquake
The mathematical-numerical model The approach adopted to predict the response of Conza Dam is based on the u-p version of the Biot generalized consolidation theory, where u represents the displacement vector of the solid phase and p the pore water pressure. The field equations characterizing the boundary value problem consist of overall dynamic equilibrium, water equilibrium, water continuity, compatibility, constitutive law and generalized Darcy’s law. The u-p formulation consists of neglecting fluid acceleration terms and convective terms of this acceleration so that the unknown variables remain the displacement of the solid u and the pressure of the water p. As further simplifications, soil grain compressibility is assumed to be null. Under such hypotheses the set of governing equations is: 1) Overall equilibrium for the soil-fluid mixture ..
ST σ − ρ u+ ρb = 0
(1)
2) Equilibrium of the water + flow conservation equation (and generalized Darcy’s law) . .
p ∇ k ( −∇ p + ρ f b ) + m ε + =0 Q
(2)
dσ' = Ddε
(3)
dε = Sdu
(4)
T
3) Constitutive law
4) Compatibility
The boundary conditions imposed on the field variables u and p complete the problem. The equations to be solved by finite elements are the variational form of the above equation set. They are solved using a finite difference technique time integration scheme of the Newmark- 2500 -
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type. For the scheme to be unconditionally stable, the following integration parameters were adopted: γ=0.5 and β = 0.25 + (γ + 0.5) 2 = 0.25 . The constitutive law adopted to model the soil skeleton behaviour of the dam soils is the socalled Hujeux model (Aubry et al., 1982; Aubry & Modaressi, 1996) developed at the Ecole Centrale de Paris (France). The model is developed in the framework of the incremental elastoplasticity and is characterized by both isotropic and kinematic hardening. It decomposes the total strain increment into elastic and plastic parts. Whilst the elastic response is assumed to be isotropic, the plastic behaviour is considered anisotropic by superposing the response of three plane-strain deviatoric plastic mechanisms (k=1, 2, 3) and one purely isotropic (k=4). With these assumptions, the total plastic strain increment dε 3
d ε = dε + dε = dε p
p d
p v
dεdp
is written as:
4
+ dε vkp
p dk
k =1
where
p
(5)
k =1
p
and dεv represent, respectively, the total deviatoric and volumetric plastic strain
increments. The former is given by the contributions, dε dk , of the three deviatoric mechanisms, p
the latter by the contributions of all four mechanisms. In the Hujeux model, the shape of the loading function is controlled by the parameter b, that, in its range of variability, may provide a Mohr Coulomb (b=0) or Cam-Clay (b=1) type yield criterion. Both yield criteria have been modified in order to include a deviatoric hardening parameter, represented by the degree of mobilized friction rk , and a volumetric hardening parameter, represented by the volumetric plastic strain
ε vp .
In the Hujeux model, the elastic response is assumed to be isotropic and non-linear with the bulk (K) and the shear moduli (G) functions of the mean effective stress according to the relations:
p K = K ref p ref
n
p G = Gref p ref
n
(6)
where K ref and Gref are respectively the bulk and shear modulus at the mean reference effective pressure p ref . During a monotonic loading process the primary yield function associated with the generic mechanism k, has the following expression:
f k (q k , p k , ε vp , rk ) = q k − p k sin ϕ (1 − b log where the following variables have been introduced:
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pk ) rk pc
(7)
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σ 'ii −σ ' jj q k = 2
2502
2
+ (σ 'ij )2 , the radius of the Mohr circle in the plane of the generic →
deviatoric mechanism of normal e k . Here i, j, k ∈ {1,2,3} ; i = 1 + mod(k ,3) and j = 1 + mod(k + 1,2) with mod(k, j ) representing the residue of the division of k by j; •
pk =
(σ 'ii +σ ' jj )
, the centre of the Mohr circle in the plane of the deviatoric mechanism of
2 →
normal e k ; •
pc, the critical pressure that is linked to the volumetric plastic strain ε vp by the relation
pc = pc0 exp(βεvp ) , where p c 0 represents the initial critical pressure and β the plastic compressibility of the material in the isotropic plane (Lnp’, ε vp ). • •
ϕ , the soil friction angle at perfect plasticity; b, a numerical parameter which controls the shape of the loading function (b=0 for Mohr Coulomb surface type; b=1 for Cam Clay surface type). • rk , degree of mobilized friction of the deviatoric mechanism k. The last variable is linked to the plastic shear strain ε dp k by the following hyperbolic function:
rk = r
el k
dε κ dt + a + dε κ dt p d
p d
(8)
where a is a parameter which regulates the deviatoric hardening of the material. It varies between a1 and a2 such that:
a = a1 + (a2 − a1 )α k (rk )
(9)
where:
α k (rk ) = 0
r −r ) (r ) = ( k r mob − r hys hys
αk
if
rk < rkhys
if
rkhys < rk < rkmob
if
rkmob < rk < 1
m
k
α k (rk ) = 1
(10)
rkel defines the elastic limit while rkhys and rkmob designate the extend of the domain where hysteretic degradation occurs. In the model an associated flow rule is assumed for each deviatoric mechanism in the relative plane while a non-associated Roscoe type dilatancy law is assumed for the volumetric plastic strain of each deviatoric mechanism:
∂ε vkp q = α (rk )(sinψ − k ) p ∂ε dk pk
(11)
with ψ representing the dilatancy angle. It should be noted that no volumetric plastic strain is generated before rkhys thus its value can be estimated with respect to the volumetric strain threshold.
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Whenever a stress reversal occurs, the primary yield function (7) is abandoned and the cyclic surface becomes active. The latter is defined by the function:
f kc (q k , p k , ε vp , rkcyc , c k ) = [q k − c k ] − p k sin ϕ (1 − b log where
cyc k
r
=r
el k
dε κ dt + a + dε κ dt p d
p d
p k cyc )rk pc
(12)
(13)
represents the mobilization degree during the cyclic loading process and c k is a kinematic hardening parameter, which depends on the stress ratio in the plane of the mechanism k at the moment of the stress reversal. Whenever a reversal of loading occurs, the variables rkcyc and c k are discontinuously updated [9]. The model takes into account plastic volumetric and deviatoric strains developed during unloading-reloading processes, linking the amount of these strains to the level of the stress ratio from which loading reversal takes place such as observed from experimental data. This model has been already adopted to reproduce the behaviour of other earth dams (Sica et al., 2008 and 2009; Bilotta et al., 2010) and road embankments (Pagano et al., 2009). It resulted effective in reproducing the observed dam behaviour during both static operational and seismic stages (Sica et al., 2008).
The Input Motion The Irpinia earthquake was characterized by three main sub-events, associated to three distinct phenomena of fault rupture. The first event was characterized by a bilateral propagation, the second and the third by a unilateral propagation (Bernard & Zollo, 1989). The third fault line, triggered 40 s after the first rupture, was located very close (15 km) to Conza dam. To carry out the dynamic analysis of the Conza Dam the accelerogram recorded in Calitri during the 1980 Irpinia earthquake was adopted (Table 1). The Calitri seismic station is close to the dam site and from a seismological point of view (Festa G., 2010) the signal recorded there may be considered representative of the seismic actions experienced by the Conza dam. Once calibrated the numerical model with the seismic scenario actually occurred during the 1980 Irpinia earthquake, further parameter analyses were carried out to investigate the seismic response of the Conza Dam to different input motions. These events were selected from the European Strong Ground Motion Database (Ambraseys et al., 2000) – Calitri (1980, ENEL record), Valnerina (1979), Montenegro UH and PH (1979) - and from the Japanese Kyoshin Network database: JapanKGS 005 (1997) and JapanMYG 010 (2003). The basic parameters of the selected earthquakes (Peak Ground Acceleration, PGA; total duration; Arias Intensity, Ia, and peak frequency fp derived from the Fourier spectrum of acceleration) are summarized in Table 1. All the reference events are characterized by significant energy content between 1 and 8 Hz. The maximum values of the recorded accelerations range between 0.17g and 0.53 g. The original signals were scaled in amplitude to evaluate the seismic response of the dam to more severe seismic actions (it was avoided a scaling ratio higher than 2 with respect to the original peak acceleration of the record to avoid also frequency scaling).
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Table 1: Main features of the original signals adopted for the parametric dynamic analyses. input signal Calitri (1980) Valnerina (1979) Mont PH (1979) JMYG (2003) JKGS (1997)
PGA (g) 0.17 0.20 0.45 0.25 0.53
duration (s) 80 17.9 21.8 29.9 10
Ia (m/s) 1.036 0.195 4.435 0.991 1.371
fp (Hz) 1 4.49 2.17 0.903 3.95
RESULTS AND DISCUSSION The back-analysis of the construction stages carried out by adopting the above described model, proved successful in reproducing dam settlements observed before and after the occurrence of the Irpinia earthquake (Figure 6). The back-analysis, along with results of laboratory tests (oedometric and triaxial) carried out during the construction stages on the core material and in situ tests (cross-hole), allowed all parameters of the model to be quantified. The calibrated model was subsequently adopted to predict dam seismic performance under the seismic events listed in Table 1. Dam seismic performance was represented in terms of the maximum permanent settlement of the crest (that also corresponds to the dam freeboard loss), assumed to effectively synthesize the dam response in light of the modern performance-based design/verify philosophy.
Figure 6: Measured and computed settlements (core axis - cross-section 3) at the end of dam construction accounting for the 1980 Irpinia earthquake In Figure 7 the permanent settlements of the crest have been plotted versus the Arias intensity Ia of the input motions. The Arias intensity has been preferred to other ground motion synthetic parameters as it reflects three important ground motion characteristics: amplitude, frequency - 2504 -
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content and duration (Kramer, 1996). It can be observed that the permanent settlements of the dam crest increase with the Arias intensity of the input motions and that settlement values are contained in a very thin range (less than 20 cm) for each Ia value. Computed displacements should be compared with threshold values assumed tolerable for the dam. Hynes-Griffin and Franklin (1984) recommended 1 meter of permanent displacement as a possible upper limit, admitting (questionable) that such a value is tolerable in most dams without threatening integrity of the reservoir, although serious damage could be observed. On the basis of the observed seismic-performance of earth dams during past earthquakes, it can be argued that earth dams did not suffer important damage (with respect to water tightness) when the permanent settlement at the dam crest was lower than 1% of the maximum embankment height H. This value can be, hence, adopted as a plausible limit threshold to assess dam performance and for the Conza dam it corresponds to 46 cm. This value is predicted for a Ia approximately equal to 4, i.e. four times as high as that characterizing the Irpinia earthquake, which represents the strongest earthquake expected at the dam site. This indicates a satisfactory performance of the structure.
Figure 7: Crest settlement vs. Arias Intensity of the input signals of Table 1, scaled at different PGAs The computed permanent settlement at the dam crest can be also considered a representative indicator of global instability phenomena, in the sense that below the above threshold global sliding is not likely to occur.
CONCLUSION After detecting the objectives related to the seismic verification of earth dams the paper accounts for the steps followed to accomplish the seismic verification of a real case study by performance-based criteria. A complex and powerful theoretical tool was adopted in accordance with the structure importance and the need to predict several physical quantities to assess dam performance. The selected theoretical tool proved to be very effective in providing a comprehensive picture of the dam response both under static and seismic loading conditions. Worth pointing out is that if a seismic event really occurs at the dam site, the availability of refined theoretical predictions should be only intended as an additional support to monitoring that - 2505 -
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always remains the main tool to check dam safety. Measurement of accelerations, permanent displacements, pore water pressures, total stresses and, over all, leakage have to be promptly collected and reinterpreted to evaluate the dam post-seismic safety conditions.
ACKNOWLEDGMENTS We would like to thank Prof. Luca Pagano who has managed the research projects concerning the development of a seismic early warning system for the Conza Dam. We would like to thank A. Modaressi and F. Lopez-Caballero of ECP (France) for their contributions on numerical aspects of the research. G. Di Trapani as engineer in charge of the Conza Dam safety, is also gratefully acknowledged for providing all required monitoring data.
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