Time dependent earthquake modeling of an earth dam

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1 Available online at ScienceDirect Procedia Engineering 00 (2016) st International Conference on the Material Point Method, MPM 2017 Time dependent earthquake modeling of an earth dam Eric Antoinet a, *, Hadrien Buffiere b, Kristina Kovalcikova a a Antea Group, 803 Bd Duhamel du Monceau, Olivet, , France b Antea Group, Rue des finances - Morne Notre Dame, Les Abymes, , France Abstract In accordance with new French regulations, new dams in seismic areas have to be justified for earthquake solicitation by coupled poro-mechanical modeling. Allowable displacement thresholds are thus given by these regulations. This paper presents the first phase of a real time dependent modeling using a finite difference software for an earth dam in Guadeloupe (French West Indies) for a 7.5 magnitude earthquake The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of the 1st International Conference on the Material Point Method. Keywords: earth dam; seismic sollicitations; dynamic modeling; displacements. 1. Introduction Water supply for agriculture activities in Guadeloupe (French West Indies) requires the construction of several new dams all around Basse-Terre Island. These dams are generally made with earth, using the local clayey material which covers the hilly areas at the base of the volcano chain. As the region is highly seismic due to the subsidence of the Atlantic plate under the Caribbean plate, dam design has to take into account earthquake solicitations. Different methods exist for this design but the French Authorities request that the new project dams are justified with poro-mechanical coupled modeling. The use of time-dependent modeling based on real accelerogram is thus needed. This paper will present the modeling of a dam in such geotechnical conditions. Computations are made using FLAC software [1], which uses the explicit finite difference method. * Corresponding author. address: eric.antoinet@anteagroup.com The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of the 1 st International Conference on the Material Point Method.

2 2 E. Antoinet et al. / Procedia Engineering 00 (2016) Description of the geotechnical context and the project 2.1. Geotechnical context At this time, two geotechnical surveys were carried out on the site with different types of boreholes and measurements: core sampling, CPT, DPT, PMT and laboratory tests. The geological and geotechnical analysis allows to define five main strata below the ground level: H1 - muddy clay in the valley axis. This compressible material will be totally removed; H2 - ocher silty clay; H3 - grey silty clay (volcanic ashes), found as a lens below a half part of the dam; H4- weathered conglomerate at a depth of about 10 m; H5 - conglomerate (thickness potentially higher than 100m). The material H2 will be used for the backfilling but there is still a huge uncertainty about the water conductivity k h and k v of this material after compaction and thus its availability for an impervious core. Table 1. Geotechnical parameters. Parameters Stratigraphy ρ h E dyn n C u f u C f k h k v (g/cm 3 ) (MPa) (kpa) ( ) (kpa) ( ) (m/s) (m/s) Filling E -7 1.E -7 H2 ocher silty clay E -6 5.E -7 H3 grey silty clay E -6 5.E -7 H4 weathered conglomerate E -5 1.E -5 H5 - conglomerate E -8 1.E -8 The stratigraphy and soil parameters are given in Table 1. Computations under dynamic solicitation are done with drained parameters for the dam filling (non saturated soils) and undrained shear strength for the foundation (saturated soils), using Plastic-Hardening (PH) model Dam User-defined Groups H5 H4 H2 Wall Embankment H3 Fig. 1. Lithology of the dam used for modelling. Considering the natural topography of the valley, the dam will be 20m high and 400m long. The upstream and downstream slopes are about 19 (3H for 1V). The crest width is 5m. As described before (see Table 1), the lack of material with low hydraulic conductivity (k h m/s) generates a specific design with an upstream sealing using a geomembrane (black dotted line) and a slim grouted curtain wall in the foundation (yellow area in Figure 1) Design thresholds In accordance with French recommendations [2, 3], two different types of earthquake have to be taken into

3 E. Antoinet et al. / Procedia Engineering 00 (2016) account in the design, depending on their depth sources and their magnitudes: Operating basis earthquake which can be identified as a Service Limit State load case; Safety assessment earthquake which can be viewed as an Ultimate Limit State load case. For this dam project in Guadeloupe, crustal earthquakes are the most energizing and the longest earthquakes. They are used for the computation as ULS load cases. For this type of earthquake, the magnitude reaches 7.5. The following thresholds of deformation and displacement have to be respected for ULS earthquakes: Deviatoric deformation: 5% on a line from upstream to downstream; Horizontal displacement: 1/3 of the dam height (i.e. 0.66m); Settlements: 1/3 of the height but no more than 1m (i.e. 0.66m) Static behavior of the model The construction of the dam is simulated as a successive setting up of the layers with a width of 1.5m. A delay of 2 weeks is taken considered between the constructions of subsequent layers, in order to take into account the evolution of the pore pressure in the soil during the raising of the dam. The settlement of the dam immediately after construction is assessed to be close to 50cm (Fig. 2). Slope factor stability (F S ) in static conditions is very good with a value higher than 1.3 with partial safety factors (F S 1). It is very important to note that a good static design is required for an earthquake proof design. Y-displacement contours -4.50E E E E E E-02 Contour interval= 5.00E-02 Fig. 2. Settlements of the dam immediately after end of construction Dynamic properties: modulus reduction and soil damping The damping properties of the embankment material and of soil strata were determined from the Hardin and Drnevich model [1,5] and from cyclic triaxial tests carried out for a previous dam project in Guadeloupe (Moreau dam) using similar materials (see Fig. 3). The calculations were finally carried out with the curves that approach the laboratory tests from the Moreau dam (the red dashed lines). Fig. 3. Damping ratio and G/G max curve for the material of the embankment.

4 4 E. Antoinet et al. / Procedia Engineering 00 (2016) Dynamic boundary conditions The bottom of the model is procured with a quiet (or absorbing) boundary condition [1]. The seismic source is applied along the base of the mesh, using this compliant base. The compliant base absorbs the refracted waves coming from the surface or from interfaces inside the model [1]. The lateral sides of the model are treated as free-field boundaries. The free field grid supplies conditions that are identical to those of an infinite model. The boundaries have non-reflecting properties, so the outward waves from the inside of the model are properly absorbed and the plane waves propagating upward suffer no distortion at the boundary Input signal As the Guadeloupe Island has not been hit by a large earthquake since the installation of dynamic sensors (~20 years ago), it is not possible to use local acceleration records. Thus the acceleration records are issued from the Valparaiso earthquake from March 3 rd Its magnitude was 7.8 and the epicentral distance from the recording station Pichilemu was about 138 km. A spectral adjustment was needed before it could be used for the modeling. Adjusted acceleration records are presented in the Fig. 4. Fig. 4. Horizontal and vertical component of the acceleration record from the Valparaiso earthquake, after spectral adjustment Treatment of the input signal In addition, before introducing them into the model, the records were treated as follows: Frequency cutoff at 12 Hz the significant frequencies of the signal are in the range of 0-12 Hz. The size of individual zones in the mesh limits the propagation of high frequencies, so it was set up according to the frequency content of the original input record, and the redundant frequencies cut off the signal. Reduction of the records to 30s in the time domain - the analysis of Arias intensity shows us that 90% of energy is contained between 7 th and 30 th seconds of the records [4]. The analysis allows us to optimize the time of calculation. Thereby the records were cut off after the 30 th second. To avoid further modifications of the signal due to incoherencies of the resultant velocity, the first 7 seconds were kept Implementation of the input signal To be coherent with the compliant base boundary condition at the bottom of the model, the dynamic input is applied as a stress history at the base. For the purpose, the velocity record is converted into a stress record using the following formulae:

5 E. Antoinet et al. / Procedia Engineering 00 (2016) s n = 2(r C p ) v n (1) s s = 2(r C s ) v s (2) where s n = applied normal stress, s s = applied shear stress, r = mass density; C p = speed of primary wave propagation in the medium; C s = speed of secondary wave propagation in the medium; v n = input from normal particle velocity record; v s = input from shear particle velocity record Phasing of the calculation The following stages were used to execute the dynamic analysis: Mechanical initialization of the earth dam construction with elastic properties; Hydraulic initialization of the earth dam (reservoir supposed totally filled); Mechanical equilibration of the earth dam with plastic-hardening model properties; Reset of the displacements and the velocities to zero; Application of the seismic solicitation at the base of the model during 30s. The dynamic and the hydraulic calculations are coupled during the dynamic modeling in order to assess the increase of pore pressure Results of the dynamic analysis Fig. 5 illustrates the variation of the pore pressure due to the earthquake. A small increase of the pore pressure in the dam is visible after the earthquake which is very favorable for stability issues. Fig. 6 presents the horizontal displacement of the dam at the end of the calculation. Pore pressure contours 0.00E E E E E E E E+02 Contour interval= 5.00E+01 Pore pressure contours 0.00E E E E E E E E+02 Contour interval= 5.00E+01 Fig. 5. Pore pressure in the model before (left) and after (right) earthquake calculation (kpa). X-displacement contours 0.00E E E E E E E-01 Contour interval= 2.50E (*10^2) Fig. 6. Dam horizontal displacements at the end of the earthquake (meters).

6 6 E. Antoinet et al. / Procedia Engineering 00 (2016) Fig. 7 displays frequency analysis of three acceleration records: Input signal at the base of the model; Recorded signal at the top of the dam; Recorded signal at the free surface of the model, which is 20 m away from the dam, so called free field. Its position is detailed in Fig. 8. The amplitudes of the acceleration in the frequency analysis are normalized, such as the maximal amplitude of the input signal is equal to 1. Fig. 7 shows the amplification effect by the dam. Fig. 8 presents the evolution of the horizontal displacements of the model in three monitored points the top of the dam, the middle of the slope of the dam, and the so-called free field point. The increase of displacement is almost linear with time during the most energizing earthquake phase (see figure 8). Normalized acceleration (/) Top of the dam Free field Input on the base Frequency (Hz) Fig. 7. Frequency analysis of input acceleration record (base of the model), the acceleration at the top of the dam and the free field acceleration. -01 (10 ) Top of the dam Middle of the slope Free field Middle of the slope Displacement(m) Top of the dam Free field Time (s) 3. Conclusions Fig. 8. Record of horizontal displacement in three observed points top of dam, middle of the slope and free field (in meters). The modeling presented in this paper has to be considered as preliminary computations for the dam design. Complementary computation will be carried out during the next stages of the dam design. However, after this first modeling phase, the following points will have to be highlighted: contrary to static computations, dynamic computations are very difficult to debug, due to a huge number of parameters and difficulty to visualize the evolution in the displacements and stresses during the computation. A small mistake in the modeling hypothesis or parameter could have a huge impact on the results. Thus, it is necessary to be careful and validation tests must be carried out very precisely;

7 E. Antoinet et al. / Procedia Engineering 00 (2016) Complementary data have to be acquired from in situ and laboratory tests, in order to determine the behavior parameters, mainly deformability and damping, in relation with strain level. The analysis of the modeling results helps to define the real needs of data and mechanical parameters. That is why the computation have to be started early in the design process; Feedback from the behavior of existing dams under recorded earthquakes will be necessary in order to calibrate the modeling. To obtain this data, an existing dam in Guadeloupe is being fully monitored. References [1] Itasca Consulting Group. Fast Lagrangian Analysis of Continua. Minneapolis: Itasca Consulting Group Inc, [2] Comité Français des Barrages et Réservoirs - Recommandations pour la justification de la stabilité des barrages et des digues en remblai Octobre 2015 [3] Report of a working group from the French Ministry«Risque Sismique et Sécurité des Ouvrages Hydrauliques, October 2014, [4] Stafford PJ, Berrill JB, Pettinga JR (2008). New predictive equations for Arias intensity from crustal earthquakes in New Zealand. Journal of Seismology, Springer Verlag, 13(1):31-52, January doi: /s [5] Zhang J, Andrus RD, Juang CH (2005). Normalized Shear Modulus and Material Damping Ratio Relationships. J Geotech Geoenviron Eng, 131(4): , April doi: /(asce) (2005)131:4(453)