3 4. El Centro earthquake acceleration as a function

3 ANALYIS AND DISCUSSIONThe lower San Fernando dam has a height of 44m.The upstream slope is 1H: 2.5V and the downstreamslope is 1H: 4.5V.

A finite elements mesh comprising510 elements as well as 551 nodes was used. Fig. 1gives a presentation of shape of the analyzed dam.

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3.1 Static analysisThe static limit equilibrium analysis based onMorgenstern and Price approach gave a factor of safetyof 2.389. Fig 2 shows the most critical failure surfaceunder static loading. Keeping all data constant andchanging the cohesion from 30 kPa to 120 kPaincreases the safety factor from 1.45 to 2.

55, whileincreasing the friction angle from 10 deg to 40 deg(with cohesion =0), the safety factor increases from 2.0to 3.5.16743.2 Pseudo Static analysisThe critical failure surface gives a lower factor ofsafety with increasing acceleration factor k. However,these factors of safety remain greater than 1 tillreaching an acceleration factor k of 0.412(corresponding to amax= 0.412g) with a factor of safetyequal to 1.

This acceleration is called the yieldacceleration. Fig. 3 shows the variation of yieldacceleration with cohesion. The yield accelerationbecomes higher with increasing values of soil cohesion;hence, the value of yield acceleration is very sensitiveto soil cohesion. Soil cohesion is difficult to measureunless we have undisturbed samples. This explains thesignificance of measuring correctly soil properties.

El 349El 333El 338UpstreamDownstreamFig. 1. Cross section of the analyzed dam.

2.389El 349El 333El 338UpstreamDownstreamDistance – m0 25 50 75 100 125 150 175 200 225 250 275 300 325 350E l e v a t i o n – m290300310320330340350Fig. 2. Most critical surface under static loading conditions.Fig.

3.Yield acceleration of the slope as function of cohesion.3.3 Dynamic analysisA detailed dynamic finite element analysis is carriedout with the aim of understanding the effect of anearthquake on embankment dam. For the analysis, theEl Centro accelerogram shown in Fig. 4 is used.One of the objectives of the present study is toexamine the soil behavior on the crest. Fig.

5 shows thecrest maximal acceleration as a function of maximumacceleration on rock. Again, soil properties play amajor role in determining soil response to earthquakeloading. It is obvious that the highest amplification(ratio of crest acceleration to base rock acceleration) ismeasured in the case of small rock accelerations(Rahhal and Lefebvre, 2006b). Fig 6 gives themaximum crest displacement as a function of maximumrock acceleration. It is observed that beyond anacceleration of 0.

1g, higher displacements are obtained.Fig. 4.

El Centro earthquake acceleration as a function of time.0.000.050.100.150.

200.250.300.350 0.1 0.

2 0.3 0.4a max crest (g)a max rock (g)amax crest= f(amax rock)Fig.

5. Maximum acceleration at the crest as a function ofmaximum acceleration on the rock.16750.000.020.

040.060.080.100.120.140.160.

180 0.1 0.2 0.3 0.

4d max crest (m)a max rock (g)dmax crest= f(amax)Fig. 6. Maximum displacement at the crest as a function ofmaximum acceleration on the rock.Another aspect that was studied in this paper is thedynamic factor of safety. In fact, this dynamic factor ofsecurity is measured during the earthquake loading andis not constant. This is the importance of using adynamic approach because the dynamic factor of safetymay be monitored and one may detect at what timeduring the loading, the safety is at the lowest level. Thisis an advantage when comparing with the pseudo-staticmethod where the factor of safety is approximate andapplied safely in the case of low accelerations.

Fig.7shows that for accelerations greater than 0.2g, thedynamic approach should be considered because is itmore conservative, and smaller factors of safety aremeasured. Fig. 8 shows the variation of the dynamicfactor of safety with the crest displacement.

Rahhal(2014) investigated the relevance of the dynamic factorin a slope stability analysis.00.511.

522.50.1 0.

15 0.2 0.25 0.3 0.

35 0.4 0.45FSa max (g)FS dyn =f(a max)FS pseudo =f(a max)Fig. 7.

Dynamic and pseudo-static factor of safety as a functionof acceleration.00.511.

522.50 0.04 0.

08 0.12 0.16 0.2 0.24FS dyn = f (dmax meters )Fig. 8. Dynamic factor of safety as a function of displacement.As far as the acceleration response spectra isconcerned, different rock accelerations were tested tosee how the crest acceleration response spectra changeddepending on the level of earthquake loading.

As it maybe seen from Fig. 9, the highest amplifications areobtained in the presence of higher rock accelerations.The two different peaks identified in the responsespectra correspond to the first and second mode ofresonance of the analyzed embankment.In the same framework, different shear wavevelocities were used to measure the soil response toearthquake loading. Shear wave velocities were chosenconsidering a homogeneous embankment and valuesbetween 200 m/s and 500 m/s.

The value of Vsindicates the state of rigidity of the soil. Fig. 10 showsthat higher amplifications in the crest accelerationresponse spectra are obtained in the presence of highershear wave velocities. The peaks appear to bepositioned for the same periods as the ones in Fig. 9.00.

511.522.533.50 0.

5 1 1.5 2Sa (g)T(s)amax=0.1gamax=0.2gamax=0.

3gamax=0.4gamax=0.45gFig. 9. Crest Response Spectra for different rock accelerations.167600.511.

522.533.540 0.

5 1 1.5 2Sa (g)T (s)Vs= 200m/sVs=300m/sVs=350m/sVs=400m/sVs=500m/sFig. 10. Crest Response Spectra for different shear wavevelocities Vs.

Finally, an attempt was made by the authors toexplain the relevance of using correct G/Gmax curves asa function of the induced cyclic shear strain. It is knownthat small stain shear modulus is of upmost importancein characterizing soil behavior under earthquakeloading. The value of Gmax is related to soil rigidity, thesame way the value of shear wave velocity Vs does.Relations between Gmax and Vs have been presented byLefebvre et al.

(1994). But in the presence of severeearthquakes, the value of Gmax diminishes as a functionof the induced cyclic shear strain. The curves giving therelations between G/Gmax and cyclic shear strain havebeen proposed by Rahhal and Lefebvre (2004, 2006a).A special attention is given to the threshold cyclic shearstrain (TCSS), a value below which the G/Gmax is equalto unity or 100%. When the cyclic shear strain becomesgreater than the TCSS, the shear modulus decreasesrapidly. The decrease in Gmax takes place at smallerTCSS in the case of sands than in the case of clays(Rahhal and Lefebvre, 2004 and 2006a).

And in thecase of clays, the plasticity index controls the decreaseof G/Gmax: the more plastic the clay is, the higher theTCSS and the smaller the decrease G/Gmax. Fig. 11 and12 show the relation between crest acceleration anddisplacement with G/Gmax.When the ratio G/Gmax remains equal to unity forhigher cyclic shear strain, the soil starts losing itsrigidity at higher deformations and this may explainedwith the higher displacements measured. As far as crestacceleration is concerned, lower accelerations aremeasured when G/Gmax has already diminished,implying that acceleration amplification may be veryimportant in the case where the shear modulus does notlose its value until reaching high cyclic shear strainslevels.

At this point, we may emphasize that crestacceleration and displacement will be much higher inthe soils where the threshold cyclic shear strain has amore significant value. This is the case of highly plasticclays. Actually, these clays are prone to accelerationamplifications during earthquakes. This fact has beenevidenced during many earthquakes especially the veryfamous Mexico earthquake in 1985.00.10.

20.30.40.50.

60.70.80.910.9 0.92 0.94 0.96 0.

98 1a max (g)G/GmaxFig. 11. Maximum crest acceleration as a function of G/Gmax.

00.010.020.030.

040.050.060.070.080.

9 0.92 0.94 0.96 0.98 1d max (m)G/GmaxFig. 12.

Maximum crest displacement as a function of G/Gmax.What is interesting to observe in the abovementioned results is that a 10% decrease in shearmodulus (G/Gmax dropping from 100% to 90%) yieldscrest acceleration decreasing from 0.85g to 0.35g, andcrest displacement decreasing from 0.

075 m to 0.050 m.1677These observations are to be related with earlierobserved results in this paper where higher spectralaccelerations were measured in the presence of highershear wave velocities in the embankment. The analysisbrings to light the importance of having laboratory andin situ data including shear modulus Gmax values as wellas G/Gmax ratio behavior with induced cyclic shearstrain in the soil.