Olivier Lherminier
email: olivier.lherminier@ifsttar.fr

Miquel Huguet
email: miquel.huguet-aguilera@egis.fr

Boumediene Nedjar
email: boumediene.nedjar@ifsttar.fr

Silvano Erlicher
email: silvano.erlicher@egis.fr

Lherminier Olivier

Huguet Miquel

Nedjar Boumediene

Erlicher Silvano

Argoul Pierre
email: pierre.argoul@ifsttar.fr

TIME-HISTORY AND PUSHOVER ANALYSES OF ASYMMETRIC STRUCTURES USING AN EFFICIENT NON-LINEAR REINFORCED CONCRETE MODEL ACCOUNTING FOR CRACKING

Keywords: Reinforced concrete, Cracking, Damage, Off-plane bending and shearing, Seismic margin assessment, Post-earthquake state, Non-linear constitutive model, Finite elements

Time-history and pushover analyses of asymmetric structures using a complex non-linear reinforced concrete model accounting for cracking.

Introduction

In many applications, RC structural analysis is usually realized by design offices using Finite Element (FE) models accounting for a structural linear elastic behaviour. However, in some cases (e.g. nuclear buildings), structural verifications have to be performed under extreme seismic solicitations; in this case, a non-linear behaviour is needed for RC cyclic calculations. Moreover, from a structural and earthquake-resistant point of view, when the bracing system of a structure essentially consists in shells connected to each other and to the slabs by heavily armed chaining, the contribution of RC slabs and walls have to be well represented.

The non-linear behaviour at the global scale of a RC element can be defined by the apparition and the evolution of different non-linear physical phenomena that dissipate energy. In this paper, the RC walls and slabs of the analyzed structures are modelled by GLRC HEGIS [START_REF] Huguet | Stress resultant nonlinear constitutive model for cracked reinforced concrete panels[END_REF] constitutive model. This thermodynamic admissible law accounts for four non-linear mechanisms: concrete cracking, concrete damage (or stiffness reduction), steel-concrete relative slip and steel yielding. It allows an efficient global modelling using a mono-layer shell FE, since the multiscale analysis has been performed analytically and the model implementation only accounts for the formulation at the global scale (macro-scale). A lot of information is available at the end of a FE calculation with GLRC HEGIS since many results of interest (as crack width, steel plastic strain...) are internal variables of the model. More details about this constitutive model are presented in chapter 2.

In this paper, the seismic action is taken into account by two different methods: nonlinear time-history and nonlinear pseudo-static pushover analyses. The basic (or classical) version of the pushover method is based on three main assumptions: (i) the structure has a plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the dynamic behavior is governed by a dominant mode of vibration (with high effective mass). Therefore, the basic pushover analysis cannot be applied for the assessment of global torsion, local effects or influence of high frequency modes, and asymmetric buildings cannot be analyzed. For that reason, in this paper the Enhanced Direct Vectorial Approach (E-DVA) [START_REF] Lherminier | Multi-modal pushover analysis for a multi-component earthquake: an operative method inspired by the Direct Vectorial Approach[END_REF] is used to take into account many modes of irregular buildings under a multi-component earthquake. The load pattern for the pushover analysis is defined as a linear combination of modal load patterns using the modal weighting factors (called α-factors), which are calculated using the elliptical response envelopes. The details of this pushover method are presented in chapter 3.

These two seismic nonlinear methods (time-history and pushover analysis) are compared with each other by application to two different structures in chapter 4. First, a four-story framed in-plane irregular asymmetric wall extracted from the CASH benchmark is analyzed in section 4.1. Then, the three-story RC building of SMART benchmark is considered in section 4.2, accounting for the nonlinear behavior of its RC walls and slabs. Comparisons are done at the global (force, displacements) and local (crack width, steel yielding...) scales to analyze the pertinence and the interest of each of these two different nonlinear methods for seismic structural analysis.

Constitutive model: GLRC HEGIS law for RC walls and slabs

An efficient and realistic material cyclic constitutive model is necessary for the comparison between the different seismic calculation approaches. Since the applications in chapter 4 are RC structures composed by walls and slabs, the GLRC HEGIS model [START_REF] Huguet | Stress resultant nonlinear constitutive model for cracked reinforced concrete panels[END_REF] is used for the material modelling. As shown in [START_REF] Huguet | GLRC HEGIS global constitutive model for RC walls and slabs for seismic nonlinear structural analyses[END_REF], this model is adapted to nonlinear seismic applications.

The model is implemented in the FE software Code Aster [START_REF]Electricité de France[END_REF] and allows an efficient global modelling and computation since it is implemented in mono-layer shell FE, accounting for an equivalent "reinforced concrete material". In order to obtain a stress-resultant model accounting for many nonlinear cyclic local phenomena which are at the origin of the nonlinear global behavior of RC elements, an analytical multi-scale analysis has been performed in [START_REF] Huguet | Stress resultant nonlinear constitutive model for cracked reinforced concrete panels[END_REF]. Therefore, there is no need of time-costly numerical multi-scale analysis at each Gauss point and at each load step. The resulting model is formulated in the framework of the Thermodynamics of Irreversible Processes; the detailed formulation can be found in [START_REF] Huguet | A homogenized nonlinear stress resultant constitutive model for cracked reinforced concrete panels[END_REF]. The four different local nonlinear cyclic mechanisms taken into account by GLRC HEGIS are the following ones:

• Concrete cracking is the development of concrete displacement discontinuities (or macrocracks) caused by tensile stresses. At each Gauss point, a constant average stabilized crack pattern characterized by the crack spacing s r (obtained with Vecchio and Collins [START_REF] Vecchio | The modified compression-field theory for reinforced concrete elements subjected to shear[END_REF] formula) and orientation θ r (perpendicular to the principal tensile strength) appears when tensile forces reach the concrete tensile strength f ct . After this cracking onset, these two parameters remain known and constant (fixed crack model), where only the normal (crack width) w n and tangential w t crack displacements evolve with the applied force by following the retained bridging stress and aggregate interlock local laws respectively. Four family of cracks are considered: for each layer (top and bottom) of the RC shells, the typical crack pattern of RC walls submitted to cyclic in-plane shear loading can be reproduced by two family of cracks characterized by two different crack orientations.

• Concrete damage is assumed to be associated with the onset and development of homogeneous diffuse micro-cracking, which results in a concrete stiffness reduction. This degradation of concrete stiffness only takes place at high strain levels, above the limit value in tensionf ct /E c . Therefore, concrete damage is supposed to be associated to compressive concrete behaviour. GLRC HEGIS considers concrete damage as isotropic and it is introduced as an internal damage variable d scalar (two values, defined for both top and bottom layers of the RC shell), positive, non-decreasing in time and which can evolve only at high stress states.

• Relative slip between concrete and steel bars originates bond stresses for each x and y and top and bottom steel reinforcement layers. As stresses are transmitted from steel to concrete between consecutive cracks, this phenomena is at the origin of the tension stiffening effect. GLRC HEGIS model uses an inelastic steel-concrete slip variable to limit the average tension stiffening effect to values given by the codes like [START_REF]Comité Européen de Normalisation[END_REF].

• Steel reinforcement yielding is supposed to be concentrated at the crack crossings due to the steel-concrete stress transfer by bond. GLRC HEGIS model considers that reinforcement bars only carry longitudinal forces and that the constitutive law is elastic-perfectly plastic characterized by a constant threshold equal to the steel yielding stress f sy .

3 Pushover method: the Enhanced Direct Vectorial Approach (E-DVA)

The pushover analysis is a seismic nonlinear calculation method based on the application of a static force field with constant pattern and increasing amplitude on a nonlinear structural model. In the basic versions, the pattern of the applied load is generally chosen as proportional to the deformed shape of the dominant vibration mode for a given earthquake component. Other conventional patterns are constant or triangular, or more complex when choosing the vector of the CQC (Complete Quadratic Combination) of the pseudo-accelerations for a given earthquake component. Some adaptive approaches exist, where the load pattern is updated to account for the effects of the non-linear phenomena.

As presented in section 1, the basic version of the pushover analysis does not reproduce accurately the seismic behavior of no-perfectly regular and no-perfectly symmetric structures. For that reason and for the numerical comparisons of this paper, more advanced pushover methods are needed in order to account for interesting and conclusive results. When doing a pushover analysis, the loading pattern selection is likely more critical than the accurate determination of the target displacement.

Several generalizations of the basic pushover analysis have been proposed in the past years, in particular by Chopra and co-workers [START_REF] Chopra | Capacity-demand-diagram methods based on inelastic design spectrum[END_REF][START_REF] Chopra | A modal pushover analysis procedure for estimating seismic demands for buildings[END_REF][START_REF] Chopra | A modal pushover analysis procedure to estimate seismic demands for unsymmetric-plan buildings[END_REF][START_REF] Goel | Evaluation of modal and FEMA pushover analyses: SAC buildings[END_REF], Fajfar and co-workers [START_REF] Faifar | A nonlinear analysis method for performance-based seismic design[END_REF][START_REF] Fajfar | The extension of the N2 method to asymmetric buildings[END_REF][START_REF] Fajfar | Torsional effects in the pushover-based seismic analysis of buildings[END_REF] and Penelis and Papanikolaou [START_REF] Penelis | Nonlinear static and dynamic behavior of a 16-story torsionally sensitive building designed according to Eurocodes[END_REF]. Some of these approaches take into account the possible multimodal structural behavior, but all assume that the earthquake is mono-component. The Direct Vectorial Addition (DVA) (Kunnath [START_REF] Kunnath | Identification of modal combination for nonlinear static analysis of building structures[END_REF], Lopez-Menjivar [START_REF] Lopez-Menjivar | Verification of a displacement based adaptive pushover method for assessment of 2-D reinforced concrete buildings[END_REF]) extends the pushover method to the case of multi-component earthquake by application of a load pattern obtained by a linear combination on the modes and earthquake directions.

The E-DVA pushover method is used in this work. It is based on the DVA approach and a rigorous definition of the weighting factors (α-factors) is provided, based on the notion of response envelopes of Menun and Der Kiureghian ( [START_REF] Menun | Envelopes for seismic response vectors. I: Theory[END_REF]). This definition for the load pattern was first proposed by Erlicher et al. [START_REF] Erlicher | Seismic design by the response spectrum method: a new interpretation of elliptical response envelopes and a novel equivalent static method based on probable linear combinations of modes[END_REF], which allows imposing an a priori chosen response of the structure. The pertinence of this pushover approach when comparing to time-history non linear analysis has been shown in [START_REF] Erlicher | A new approach for multi-modal pushover analysis under a multi-component earthquake[END_REF]- [START_REF] Huguet | The E-DVA pushover method for multi-modal pushover analysis with multi-component earthquake: analysis of two irregular buildings[END_REF].

The load pattern as a linear combination of modes

On the global axes (x, y, z) of the FE model of a structure, the mass M (assumed diagonal) and the stiffness matrix K are defined. It is supposed that the seismic input may have 1, 2 or 3 translational components, whose corresponding ground accelerations are named a g,x (t), a g,y (t) and a g,z (t), which act in the directions given by the influence vectors Δ k corresponding to the translation in the k = x, y, z direction.

The non-adaptative pushover analysis are defined by a nodal force vector q pushover (t) with constant shape and increasing amplitude:

q pushover (t) = c(t)Q (1)
where c(t) is a scalar increasing pseudo-time function and Q is the constant vector defining the pattern of the nodal force field (a displacement-driven is also equivalently possible). The E-DVA approach defines this load pattern as:

Q = nec � k=1 n � i=1 α i,k M • A max,i,k (2)
where α max,i,k is the linear combination factor and A max,i,k is the maximum pseudo-acceleration vector for the for the n retained modes i and n ec earthquake directions k:

A max,i,k = (2πf i ) 2 S d,k (f i , ξ i )γ i,k Φ i (3)
where S d,k (f, ξ) is the response spectrum, f i ,ξ i and Φ i are respectively the modal frequency, damping ratio and deformed shape of mode i, and γ i,k is the participation factor of mode i with respect to earthquake direction k.

Different pushover analyses for different load cases

It can be shown that any response vector any any time f (t) (vector containing forces and/or displacements and/or stresses...) can be written as a linear combination of modal responses with the weighting factors α i,k (t) [START_REF] Erlicher | Seismic design by the response spectrum method: a new interpretation of elliptical response envelopes and a novel equivalent static method based on probable linear combinations of modes[END_REF]. Actually, only some response vectors are of interest when comparing to time-history analyses, those that maximize the value of parameters of interest, e.g. that maximum force in the x direction at the basis of a building or the maximum displacement in the y direction of a point of the roof. These response vectors corresponding to the load cases that maximize the interest parameters can be obtained using the notion of elliptical responses, as done in [START_REF] Erlicher | A new approach for multi-modal pushover analysis under a multi-component earthquake[END_REF].

Once the response vector f (t) is known, the vector of modal combination α is calculated following Erlicher et al. [START_REF] Erlicher | Seismic design by the response spectrum method: a new interpretation of elliptical response envelopes and a novel equivalent static method based on probable linear combinations of modes[END_REF]:

α = H • R f • X -1 f • f (4)
where H is the modal coefficient correlation matrix, R f is the modal response vector matrix and

X f = R T f • H • R f
is the matrix which defines the elliptical domain of the concomitant values of f by:

f T • X -1 f • f ≤ 1 (5)
Finally, in Erlicher et al. [START_REF] Erlicher | The E-DVA method: a new approach for multi-modal pushover analysis under multi-component earthquake[END_REF] a method is proposed to choose several dominant modes to reach the searched response. As the total value of the response vector is f = R T f • α, the value of the parameter of interest of the response vector is compared to the cumulative contribution of each mode (and earthquake direction) by means of the sum of the products between α ik and the corresponding line of R f , for the column corresponding to the parameter of interest.

The equivalent seismic spectrum for multi-direction earthquakes

A difficulty exists when trying to define the response spectrum for an earthquake acting in the direction of the earthquake t, which is identified as the direction of the resultant of the load pattern Q. By considering the deformed shape U under Q load U = K -1 • Q, the participation factor of U in the t direction can be defined. In this direction, the structure vibrates with an equivalent frequency f * and damping ratio ξ * .

For a single-component earthquake, the maximum displacement can be easily calculated from the corresponding spectrum. For example, for single-component earthquake in direction k = x, one has γ U,t = γ U,x and the response spectrum is S d,x (f * , ξ * ). Analogous formulas can be written for earthquake components y and z. Based on the assumption of non-correlation between accelerograms in the x, y and z directions, the SRSS combination is used to define s max for a multi-component earthquake:

S d,t (f * , ξ * ) := 1 |γ U,t | � (γ U,x S d,x (f * , ξ * )) 2 + (γ U,y S d,y (f * , ξ * )) 2 + (γ U,z S d,z (f * , ξ * )) 2 (6)
4 Numerical Applications 4.1 Irregular wall from CASH : Benchmark on the beyond design seismic capacity of reinforced concrete shear walls CASH is an international benchmark organised by the OEDC-NEA (Nuclear Energy Agency). The main purpose is to evaluate the accuracy of tools and prediction methods used in civil engineering for the estimation of the seismic capacity of shear reinforced concrete walls in "beyond design" seismic situation (important seismic excitation). The benchmark study focuses on two different multi-storey shear walls representative of a real NPP building structure. The results presented in the article are those obtained for the irregular structure (Figure 1-b) and the following post-treatment results are not those presented to the benchmark but are only examined for the purpose this article. The structure represents the facade of a building with four floors, the studies are done in the plane (2D) of the wall. The height of the structure is 16m for 12m width and 0.40m thick. Slabs and out-of-plane walls are represented by beams and columns with strong depths. In-plane walls are modelled with shell elements using the GLRC HEGIS global constitutive law and beams and columns are modelled with multifiber beams elements using the MAZARS constitutive law [23] for concrete fibers and an elastic-plastic model (with kinematic hardening) for steel fibers.

Modal and spectral analyses

The purpose of this section is to evaluate the linear response of the considered irregular structure for a given pseudo-acceleration spectrum. First, the modal analysis is performed and the corresponding spectral values are calculated.

The results of the modal analysis performed on the FE model are summarized in Table 1. The 5 retained modes account for 99% of the total mass for x and z directions.

Pushover analysis

The objective of this analysis is to evaluate the non-linear response of the wall under an increasing horizontal load proportional to a specific profile. The E-DVA method procedure described in [START_REF] Erlicher | The E-DVA method: a new approach for multi-modal pushover analysis under multi-component earthquake[END_REF] is applied step by step. (b) The response matrix X f of Eq.( 5) defining the ellipse of the maximum seismic efforts F x , F z is obtained from the first and the third rows and columns of the matrix.

(c) The choice of the loading direction is done here in the plan X-Z in the directions of the global coordinate system +X and -X to maximize the global forces +F x and -F x .

(d) The corresponding α-vectors are computed using Eq. ( 4)

Direction +Fx -Fx F X (kN) 7571 -7571 f * (Hz) 4.92 4.92 ξ * (%) 2.0 2.0 γ U,X (m -1 )
237 237

[U ] j,X (mm) The procedure is applied to determine the dominant modes: based on the α i,k factors calculated at step (d),the products α i,X F T i,X are computed for the two load cases. The cumulative sum of the products according to the order defined in Table 3 is normalized according to the maximum response (second row of Table 2). For instance, when taking C d = 0.90 as suggested in [START_REF]ASCE-4-16, Seismic analysis of safety-related nuclear structure[END_REF] at chapter 4.3.1(b), the first ik max modes are dominant since their contribution to the response F = f T • b is 90% of the total response. Table 3 shows that only the first mode is needed to fulfill this condition. The application of incremental unidirectional loading for pushover analysis gives global force-displacement curves which can be analyzed to distinguish the evolution of the activated non-linear phenomena. First, in Figure 2, a linear segment describe the non-cracked phase (before the blue line), then there is creation of several cracks. When the crack pattern is stabilized, the crack width increase and the steel reinforcement can yield (purple line) and finally a "tension-stiffening" effect can be observed. As shown in Figure 2, the concrete ultimate limit in compression is reached for a displacement of +72 mm (red line) and corresponds to a strain level of � u = 3.5‰. It can be explained by the fact that the concrete developed too many microcracks in compression and can't bear more stress. The structure only reach its ultimate capacity in compression in the direction +Fx. Then, the coordinates of each target point are determined at the intersection of the capacity spectrum with the Acceleration Displacement Response Spectrum (ADRS) given by Eq. ( 6). The damping ratio ξ * of ADRS after iteration accounts for the hysteretic damping (Figure 3). The target point coordinates are shown in Table 4, with F X and V X corresponding to the obtained target global reaction and displacement of the structure, respectively.

Displacement [mm] Basis reaction [kN ]

Time history analysis

To evaluate the non-linear response of the irregular specimen under a horizontal seismic loading, a accelerogram whose spectrum corresponds to the one used in the pushover analysis is imposed to the structure. The chosen seismic input data is scaled to a P GA = 0.16g intensity earthquake.

Time [s] Displacement [mm] (a)

Comparison between time history and pushover analyses

The graphical comparison of Figure 5 (a) shows that the dynamic results (black lines) are mostly inside the envelope area defined by the obtained target points (red and blue) and that the calculated forces that are presented in Table 4 are well estimated by the pushover (Figure 5 (a)) compared to the time-history results. The pushover results given by the E-DVA approach provide a suitable and accurate envelope of the maximum roof displacements and global forces at the basis of the building.

In order to compare the obtained crack pattern, the crack opening values using GLRC HEGIS are plotted at the pushover target point. The results of Figure 5 (b) and(c) show that the crack patterns obtained by the pushover analyses are very close of the one obtained by time-history analysis showed in Figure 4 (b) and (c).

SMART: Seismic design and best-estimate Methods Assessment for Reinforced concrete buildings subjected to Torsion and non-linear effects

The experimental program SMART [START_REF] Richard | SMART 2013: Experimental and numerical assessment of the dynamic behavior by shaking table tests of an asymmetrical reinforced concrete structure subjected to high intensity ground motions[END_REF] was supported by the French companies Commissariat l � Energie Atomique et aux Energies Alternatives (CEA) and Electricite de France (EDF) and partially by the International Atomic Energy Agency (IAEA). The goals of the benchmark are to compare and to validate the used methods to evaluate the seismic responses of reinforced concrete structures under a seismic loading that induce 3D effects such as torsion and out-ofplane shear and to check the accuracy of prediction approaches of advanced calculation methods used in earthquake engineering.

Model description

The program concerns a 1/4 scale mock-up of a representative asymmetric RC multi-storey building in nuclear power plants. The experimental moke-up was tested under seismic loadings applied by the shaking table with 6 degrees of freedom AZALE at CEA Saclay. The tested structure corresponds to SMART 2013 international benchmarks [START_REF] Richard | SMART 2013: Experimental and numerical assessment of the dynamic behavior by shaking table tests of an asymmetrical reinforced concrete structure subjected to high intensity ground motions[END_REF], but the foundation conditions are not respected in this article and all the comparisons to experimental results are out-of-scope of this paper. The structure shown in Figure 6 Therefore, all the non-linearities are originated by the nonlinear response of the developed model. The full building is 3.650 m height for 3.100 m width, walls are 10 cm thick and beams and columns are 15 cm and 20 cm thick respectively. In order to check the performances of the constitutive law GLRC HEGIS, several studies were carried in parallel of the benchmark to compare the obtained results in the same way than those of the previous numerical application. Therefore, the shaking table was not taken into account here to save computation time but the benchmark will be fully conducted in a second time and the shaking table will be added.

For preliminary studies carried on the SMART building, several sets of seismic input data were generated. There particularity is that they all were generated from a unique aimed spectrum. Therefore, spectral, pushover and time-history results can be compared between each seismic input sets. The obtained pseudo-acceleration spectra were compared to only keep those which don't exceed a 10% error from the aimed spectrum, see Figure 7. All the generated accelerograms are different but the modes of the structure can be excited in a comparable way. The seismic intensity of the aimed spectrum is given by PGA= 2.45m/s 2 .

Modal and spectral analyses

First, the modal analysis is performed and the corresponding spectral values are calculated. The nine first modes are calculated for the structure. The results of the modal analysis performed on the FE model are summarized in Table 5. The 9 retained modes account for 83% of the total mass for x and y directions. The presented pushover method allows to choose along these modes which really need to be considered.

Pushover analysis

The E-DVA method procedure previously applied in section 4.1.3 is also applied to this 3D structure. The pushover directions are chosen here following 8 horizontal directions given by the Newmark combinations, as explained in [START_REF] Lherminier | Multi-modal pushover analysis for a multi-component earthquake: an operative method inspired by the Direct Vectorial Approach[END_REF].

Then, the coordinates of each target point are determined at the intersection of the capacity spectrum with the ADRS spectrum given by Eq. ( 6). The damping ratio ξ * of ADRS spectra 8). The target point coordinates are shown in Table 8, with F t and V t corresponding to the obtained target global reaction and displacement of the structure in the considered direction t.

Time history analysis

To evaluate the non-linear response of the irregular specimen under a horizontal seismic loading, accelerograms whose spectra correspond to those of Figure 7 used in the pushover analysis are imposed to the structure. The seismic input data are all scaled to a P GA = 2.45m/s 2 intensity earthquake. For the sake of brevity, only two time-history results are showed here. The roof displacements shown in Figure 9 (a) are characteristic of an asymmetric structure with a dominant torsion mode. In Figures 9 (b) and(c), the maximal values of the crack opening during two whole earthquakes are plotted and represent the obtained crack patterns. When analyzing the results, it can be observed that the cracks are localized near the openings. The structure is heavily cracked at its left basis corner and steel reinforcement yielded.

Comparison between time history and pushover analyses

In order to compare the obtain results, the pushover results are plotted at their target point steps. The graphical comparison of Figure 10-a shows that the dynamic results obtained by all performed time-history analyses are mostly inside the envelope area defined by the obtained target points. The results show that the calculated forces that are presented in Table 7 are well estimated (Figure 10-a). The pushover results given by the E-DVA approach provide a suitable and accurate envelope of the maximal global forces at the basis of the building. , the severally cracked left basis corner due to the torsion behaviour of the structure cannot be fully predicted by pushover analyses that maximize basis reactions but it can be interesting in another study to perform multi-modal and multi-component pushover analyses that maximize the torsion (global torsion moment of the building M zz ).

The GLRC HEGIS [START_REF] Huguet | Stress resultant nonlinear constitutive model for cracked reinforced concrete panels[END_REF] model for RC plates (walls and slabs) is implemented for shell finite elements in Code Aster [START_REF]Electricité de France[END_REF] software and is applied to incremental static pushover and transient dynamic structural analyses corresponding to the same seismic intensity level. The structures which have been studied in this paper consisting of RC walls and slabs and the possibilities offered by this thermodynamic admissible law accounting for non-linear mechanisms have been used to compare available crack patterns at the end of a FE calculation since many results of interest (as crack width, steel plastic strain...) are internal variables of the with GLRC HEGIS constitutive model.

In this paper, the seismic action has been taken into account by two different methods: nonlinear time-history and nonlinear pseudo-static pushover analysis. In this paper the Enhanced Direct Vectorial Approach (E-DVA) [START_REF] Lherminier | Multi-modal pushover analysis for a multi-component earthquake: an operative method inspired by the Direct Vectorial Approach[END_REF] is used to take into account many modes of irregular buildings under a multi-component earthquake. The load pattern for the pushover analysis has been defined as a linear combination of modal load patterns using the modal weighting factors (called α-factors), which have been calculated using the elliptical response envelopes. The results obtained by time-history and pushover analyses have been compared.

First, a four-story framed in-plane irregular asymmetric wall extracted from the CASH benchmark has been analyzed in section 4.1. Then, the three-story RC building of SMART benchmark has been considered in section 4.2, accounting for the nonlinear behavior of its RC walls and slabs. Comparison between obtained results shows a relatively good fitting both at the local (e.g. crack width) and global (structural behavior) scales. The capabilities of the model to show the evolution of variables (crack width, steel reinforcement plastic strain, energy dissipation...) fields at every load step, and to estimate in a relatively accurate manner the RC section strength, have been also demonstrated. Comparisons have shown that forces and displacements can be estimated by pushover analyses and that time-history analyses have given a lot of local results (crack width, steel yielding...) that show the interest of each of these two different nonlinear methods for seismic structural analysis.

Figure 1 :

 1 Figure 1: CASH Finite Element models on Code Aster

( a )

 a Based on the modal basis above, response-spectrum analysis and CQC coefficients are used to determine the response matrix of the six efforts f = [F x , F y , F z , M xx , M yy , M zz ] T at the basis of the structure, for the spectra of Figure1(c):

Figure 2 :

 2 Figure 2: Pushover curve (Force-Displacement) for (a) +Fx and (b) -Fx load cases

Figure 3 :

 3 Figure 3: (a) Spectra and graphical results in the ADRS plane for the cases (b) +Fx (c) -Fx

Figure 4 :Figure 5 :

 45 Figure 4: (a) Time-history roof displacement and obtained crack opening at (b) maximal displacement +Vx and (c) maximal displacement -Vx

  (a) represents a asymmetric 3 storey reinforced (a) (b)

Figure 6 :

 6 Figure 6: SMART (a) experimental moke-up and (b) used FE model on Code Aster

Frequency

  [Hz] Pseudo-acceleration [m/s 2 ] (a) Spectra at 5% damping Frequency [Hz] Pseudo-acceleration [m/s 2 ] (b) Spectra at 10% damping

Figure 7 :

 7 Figure 7: Chosen spectra associated to the seismic pseudo-acceleration inputs for the preliminary SMART studies

Figure 9 :

 9 Figure 9: (a) Time-history roof displacement and maximal obtained crack opening during (b) a first seismic input and (c) a second one

XFigure 10 :

 10 Figure 10: (a) Comparison of the capacity curves and obtained crack opening during the pushover analyses at (b) target point 12.9 • , (c) target point 168 • , (d) target point -167 • , (e) target point -57.6 • and (f) target point -12.5 •The crack patterns obtained the pushover analyses (Figure10-b-c-d-e-f) show that the crack opening are well estimated near the openings compared to the two time history crack opening pattern showed in Figure9-b-c. As the time history analysis is a cyclic loading, the phenomena of cracking and reclosing cannot be reproduced by monotonic pushovers therefore several pushovers are needed to reproduce the crack pattern. The maximum obtained crack opening values obtained with the pushover analyses (Figures 10) give a quite accurate localization and value of the maximal crack opening obtained by time-history analyses (Figures9). However, the severally cracked left basis corner due to the torsion behaviour of the structure cannot be fully predicted by pushover analyses that maximize basis reactions but it can be interesting in another study to perform multi-modal and multi-component pushover analyses that maximize the torsion (global torsion moment of the building M zz ).

  However

Table 1 :

 1 Modes Frequency Effective mass Effective mass S a,X Five first modes calculated for the irregular CASH specimen

	Damping

Table 2 :

 2 Equivalent SDOF parameters for the considered load cases

	5.42	-5.42
	0.00	0.00
	-0.550	0.550

Table 3 :

 3 Number of modes and corresponding percentage of the total response needed

(e)

Table 4 :

 4 Obtained target points for the considered load cases 4.1.

	Direction +Fx S a (m/s 2 ) 2.78 S d (mm) 7.79 ξ * (%) 12.6	-Fx 2.81 8.08 8.80
	5257 V x (mm) 10.18 F x (kN)	-5272 -10.25

Table 5 :

 5 Nine first modes of the SMART FE model

	Modes Frequency Effective mass Effective mass S a,X [Hz] in X in Y [%] [m/s 2 ] [m/s 2 ] factor [%] S a,Y Damping 1 8.47 52.6 8.19 6.77 6.77 2.81
	2	15.2	15.9	52.8	6.41	5.80	2.97
	3	29.8	13.2	7.48	3.78	4.10	4.49
	4	30.8	0.53	2.19	3.58	4.06	4.60
	5	32.5	0.05	0.39	3.45	4.04	4.81
	6	32.7	0.00	1.58	3.42	4.01	4.84
	7	35.5	0.56	0.46	2.79	3.74	5.17
	8	35.6	1.63	1.08	2.74	3.75	5.19
	9	37.1	0.31	0.00	2.57	3.86	5.37
	θ	12.9 •	51.9 •		122 •	168 •
	F θ (kN) F x (kN) F y (kN) f * (Hz)	222 216 49.6 9.06	197 121 155 12.3		198 106 -167 9.32	225 -219 48.6 8.79
	ξ * (%)	2.94	3.39		3.45	3.05
	γ U,t (m -1 )	496.1	1044		560.5	453.3
		2.01	0.919		1.30	-2.20
	[U ] j,t (mm)	-0.548 -0.059	0.210 0.001		-1.05 -0.080	0.959 0.086

Table 6 :

 6 Equivalent SDOF parameters for the considered load cases

		12.9 •		51.9 •		122 •		168 •
	Modes		Modes		Modes		Modes
	1	(54.1%)	2	(87.5%)	2	(22.9%)	1	(78.7%)
	2	(37.9%)	1	(5.97%)	1	(54.0%)	2	(5.93%)
	3	(5.68%)	10	(4.83%)	3	(14.4%)	3	(12.4%)
	10	(1.45%)	6	(0.794%)	10	(3.22%)	8	(1.08%)
	8	(0.399%)	4	(0.519%)	4	(2.22%)	10	(0.492%)
	4 modes are sufficient 4 modes are sufficient 7 modes are sufficient 6 modes are sufficient

Table 7 :

 7 Number of modes and corresponding percentage of the total response needed after iteration accounts for the hysteretic damping (Figure

Table 8 :

 8 Obtained target points for the considered load cases

	]			]									]
	a,t [m/s 2			a,t [m/s 2									a,t [m/s 2
	S			S									S
	(a)	S d,t [m]		(b)		S d,t [m]					(c)		S d,t [m]
	Figure 8: Capacity curves vs. spectrum in the ADRS plane for three of the load cases
	Direction 12.9 • S a (m/s 2 ) 6.50 S d (mm) 0.256 357 F t (kN) V t (mm) 8.14 ξ * (%) 3.37	51.9 • 6.80 0.146 395 7.92 3.39	122 • 5.02 0.260 428 7.89 7.11		168 • 5.26 0.211 374 8.03 2.41			-167 • 6.84 0.273 359 8.38 3.56	-128 • 6.68 0.149 383 8.02 3.39		-57.6 • -12.5 • 5.69 6.06 0.215 0.267 410 363 8.34 8.08 4.12 4.33
							Maximal Crack Opening (´ m)							Maximal Crack Opening (´ m)
				0.100	0.2	0.5	1	2	5	10	20	50	92.335	0.100	0.2	0.5	1	2	5	10	20	50	115.561
				(b)

X Roof displacement [mm] Y Roof displacement [mm] (a)


Özlem Lamontre-Berk

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Mingzhang Lin

Yuta Kumagai

Isabelle Lampre

F.-X Coudert

Yusa Muroya

Anne Boutin

Mehran Mostafavi
email: mehran.mostafavi@lcp.u-psud.fr

Yosuke Katsumura

François-Xavier Coudert

Temperature effect on the

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Introduction

Observed for the first time in aqueous solutions of carbonate salts, 1 the hydrated electron has been the subject of extensive works ever since. Its absorption spectrum was determined in this first study and appeared to be a broad, structureless band with a maximum around 715 nm in pure water. Because of the great interest of water in chemistry, biochemistry and physics, the structure of the hydrated electron remains a subject of intense research, both experimentally [2][3][4][5][6][7][8] and theoretically [9][10][11] . Several simulations of the hydrated electron were performed. [12][13][14][15][16] The properties of the solvated electron depend on several factors such as the solvent, the temperature, the pressure or the presence of salt in solution. For instance, at room temperature, the maximum of its absorption band is located around 525 nm in glycerol, 715 nm in water and 2300 nm in diethyl ether. The optical absorption band shifts to higher energies with increasing pressure up to 2000 bar; the shift is larger in primary alcohols than in water 17 or ethylene glycol. 18 A rise in the temperature induces a red shift of the solvated electron absorption spectrum. Pulse radiolysis experiments show that in water and several alcohols the maximum of the absorption band shifts from visible to the near IR. [19][20][21][22] For more than 35 years, the reactivity of the hydrated electron with different solutes, such as aliphatic, aromatic or heterocyclic compounds, and also anions and cations, has been widely studied mainly by pulse radiolysis. [23][24][25] The data about the reduction of metal ions have been compiled in 1988 and 1995. 26 Pulse radiolysis studies of aqueous solutions containing alkaline or earth alkaline metal ions have shown that the hydrated electron does not react with these metal ions but forms ion pairs. The first publication on the effect of non reactive metal cations on the absorption spectrum of the hydrated electron was published in 1965. 27 These pulse radiolysis measurements in very concentrated aqueous solutions of KF (12.2 M), MgCl2 (4.6 M), NaClO4 (10 M) and LiCl (15 M) showed that the absorption maximum of the solvated electron shifts from 720 nm in neat water to shorter wavelengths and that the shape of the absorption band remains similar. The origin of that blue shift was attributed to a contraction of the radius of the electron cavity due to the presence of the cation close to the electron. 28 Then, a few studies mentioned a blue shift of the absorption spectra of the solvated electron in concentrated alkaline salts solutions, in water, [29][30][31] in ethers and ammonia, [START_REF] Bockrath | Pulse radiolysis studies[END_REF][33][34][35] in alcohols 36 or in frozen aqueous solutions, 37 , 38 without giving a global explanation of the phenomena. They only reported an electrostatic effect of the cation on the ground and/or first excited state of the solvated electron due to the decrease of the electron cavity size. The first systematic study on the salt concentration effect on the hydrated electron absorption spectrum was done in very concentrated (0 -15 M) aqueous solutions of LiCl. 39 It has been shown that increasing the salt concentration induces a non-uniform blue shift explained by the formation of local microstructures, and that the absorption spectrum evolves differently in the low and high energy sides. In recent years, thanks to the development of ultrafast laser pump-probe setup, 40 a few publications 41 ,42 noted a blue shift of the absorption band of the hydrated electron in the presence of a strong concentration of NaCl and attributed it to a change in the hydration energy of the electron. In 1999, Krebs and co-workers resumed the work on LiCl aqueous solutions and showed that the blue shift increased continuously with the concentration without any change in the absorption band shape. 43 More recently a general study on the influence of various non-reactive metal cations on the absorption spectrum of the hydrated electron has been done. 44 The effect of the presence of a non-reactive metal cation upon the absorption spectra of the hydrated electron was measured in concentrated aqueous solutions of eight chloride and five perchlorate salts, with monovalent, divalent and trivalent non-reactive metal cations. A shift of the absorption band maximum toward shorter wavelengths that increases with the salt concentration but also with the cation charge has been observed. The spectral shift depends on the characteristics of the solution such as cation size (through charge densities) or dissociation degree of the salt (partial screening of the cation charge when incomplete dissociation). 45 Quantum simulations have indicated that the ground state of the hydrated electron is an s-like localized state and the excited states are three non-degenerate p-like states, also bound and localized, followed by a band of delocalised states; hence, the broad absorption band of the electron corresponds mostly to an s ® p transition with the contribution of a transition between the bound state to the continuum at high energy. 9,12,13,16 Recent three-pulses experiments on photoionization of water corroborated that attribution. 46,47 Lately, molecular dynamics simulations showed the possible formation of a contact cation-electron pair in the case of sodium cation. Spectral simulations of the pair revealed a blue shift of about 0.3 eV from the hydrated electron spectrum attributed to a destabilization of the p-like state in the close presence of the cation. 48 In the present paper, we depict the results obtained by pulse radiolysis measurements of deuterated water solutions containing different concentrations of Li + cations at various temperatures. As H2O absorbs in the near IR spectral domain, deuterated water was used for the measurements. To explain the shift of the absorption spectra of the hydrated electron due to the combined effects of temperature and salt concentration, mixed quantum classical molecular dynamics (QCMD) simulations of an excess electron in bulk water and in presence of a lithium cation at different temperatures have been performed.

Experimental Section

LiCl, LiClO4, tert-butyl alcohol and D2O (99.9 atom % D) were purchased from Wako Pure Chemical Industries, Ltd., and used as received. All the solutions were freshly prepared using D2O. The solutions were deaerated with high purity Ar before being loaded to the cell.

The pulse radiolysis experiments were carried out on the Linac electron accelerator of the Nuclear Professional School, the University of Tokyo. The energy and pulse duration of the electron beam were 35 MeV and 10 or 50 ns, respectively. The high-temperature/pressure flow cell was made of Hastelloy HC22 with sapphire windows. Details of the apparatus were described elsewhere. 20, 49 , 50 Here we give only some important parameters. The highest temperature and pressure for the flow cell guaranteed by the factory (Taiatsu Techno®) are 400 °C and 40 MPa, respectively. The optical path length is 15 mm. The flow system is composed of a pump, a preheater, a heater, a back-pressure regulator, and a power supply with a temperature control unit. Four thermocouples are used to monitor temperatures at the preheater and the heater; one of these thermocouples is placed inside the solution for monitoring the temperature of irradiated samples. Given the low solubility of metallic salts in water at very high temperature and the corrosion damage of the sapphire windows, the temperature was increased up to 300 ºC only. The pressure for all the measurements was 25 MPa.

For the measurements of absorption spectra, a pulsed Xenon lamp (SAX-100H lamp, SA-200F power supply, and an LB-5 inductor box, products of Nissin Electronics Co., Ltd.) with an output energy of 50 J/flash was used as analyzing light. Various blocking filters were used to cut the scattered and multiple orders light -a ultraviolet cut-off filter up to 340 nm was used for l < 520 nm, a cut-off filter till 520 nm for l= 520 -900 nm, and a IR transmitting filter above 850 nm was for l > 850 nm, respectively. The wavelength resolution of the detection system was ±10 nm in the UV-vis and ±20 nm in the near IR, respectively. Since the absorption spectrum of the hydrated electron is shifted to longer wavelength with increasing temperature, it is necessary to measure the absorption spectrum not only in the UV-vis domain (said l=300 -850 nm), but also in the near IR region (l> 850 nm). In order to measure the absorption spectrum under the same conditions, we used a removable mirror, two fixed monochromators and two photodiodes (a Si PIN photodiode Hamamatsu photonics, S1722-02 to measure from 400 to 960 nm and an InGaAs PIN photodiode, Hamamatsu photonics, G3476-05 to measure above 880 nm) in the experimental setup. The mirror was used during the measurements in the IR spectral region while it was taken away for the measurement in the UV-vis domain. The photodiodes were connected to an oscilloscope (Hewlett Packard, Tektronix, TDS3054B). The Linac and the Xenon lamp triggering, the wavelength changing and blocking filters, as well as the data acquisition from the oscilloscope, were controlled by a PC through GPIB interfaces. As already reported by Bartels et al. [START_REF] Cline | [END_REF] the secondary detector response introduces wavelength dependent distortions in transient kinetics signals. In our set-up, the kinetics measured with Si Pin photodiode are almost the same from 400 to 900 nm and those measured with InGaAs are also wavelength independent from 1000 to 1500 nm, but differ from the kinetics measured by Si photodiode (cf. supplementary materials). Nevertheless, in this study, we are only interested in the absorption spectrum at a given time and not in the time evolution of the absorption bands, so the absorbance obtained just after the pulse by the two photodiodes were corrected with the same factor determined in the overlapping region from 880-920 nm.

The dosimetry was done with an N2O-saturated 10 mM KSCN aqueous solution, taking Ge((SCN)2 •-) = 5.2 ´ 10 -4 m 2 /J at 475 nm. 52 We could not measure the dose pulse by pulse because of the use of full-metal high-temperature cell, but the dose fluctuation is less than 5% during a daylong experiment.

Results and Discussion

Figure 1 shows the normalized absorption spectra of the hydrated electron in D2O in the presence of 0.2 M tert-butyl alcohol at different temperatures. The inset shows the absorption spectra recorded just at the end of the electron pulse without normalization. As can be seen from the inset, the intensity of the absorption band decreases with increasing temperature. As the density decreases with temperature (from 1.1 at 25 °C to 0.82 g cm -3 at 300 °C), the deposited dose decreases. But the lowering of the signal intensity of the solvated electron cannot be explained only by this decrease and it is essentially due to the acceleration of solvated electrons reactions with temperature inducing a faster decay of solvated electron. For better comparison of the spectra, we normalize the maximum absorbance at each temperature to 1.0. Obviously there is a significant red-shift (shift to longer wavelength) with increasing temperature, as reported in previous work. 7,19, 20, 53,54, A careful comparison of the absorption maxima (Emax) and the spectral shapes using Gaussian-Lorentzian functions as proposed by Jou et al. 19 shows that these absorption spectra agree fairly well with those already reported. 19,7 That allows us to check the reliability of our experimental method and system. Figure 2 show examples of the temperature dependent absorption spectra obtained by pulse radiolysis of 1.0 M LiClO4, 1.0 and 4.0 M LiCl in D2O, respectively. Clearly, with increasing temperature, the absorption spectra of the hydrated electrons in these 3 solutions shift to the lower energy domain, similarly to those of the hydrated electrons in pure D2O. However, in the presence of Li + cation at room temperature, the absorption maximum (Emax) is shifted to lower energy. The amplitude of the shift depends on the concentration of Li + . The blue shift of the absorption spectrum of the hydrated electron in concentrated salt solutions has been reported by several groups. 27-31,38,39,41-45, Here, we compare Emax at room temperature in the presence of different concentrations of LiCl or LiClO4 with the data reported by Bonin et al., 45 as shown in Table 1. It is worth noticing that the data by Bonin et al. were measured in light water at slightly lower temperature (10 °C instead of 22 °C in D2O for this work) and for solutions of fixed molality (mol. kg -1 ) which deviates from concentration (mol. L -1 ) at high concentrations. Considering these differences the data obtained in this work agree well with the reported data. It is important to note that the isotope effect on the absorption spectra of the solvated electrons in water is very small. 19,7 As can be seen from Figure 2, the absorption spectra recorded in LiCl solutions, show an additional absorption band in the UV region compared to those observed at 1.0 M LiClO4. This band corresponds to the absorption of Cl2 •-anion radical with lmax = 340 nm (3.65 eV) and ε340nm = 8800 M -1 cm -1 55 formed according to the following fast reactions:

• OH + Cl -↔ ClOH •- (1)
ClOH •-+ H + → H2O + Cl • (2) Cl • + Cl -↔ Cl2 •- (3)
However, the absorption band of Cl2 •-is not broad at room temperature and the absorption coefficient is rather small (ε450nm~300 M -1 cm -1 ) as compared with that of hydrated electron (ε450nm > 3500 M -1 cm -1 ). Moreover, with increasing temperature, the spectral shift of the hydrated electron is much more significant than that of Cl2 •-. So, the absorption band of Cl2 •- does not affect the principal part of the spectrum of the hydrated electron. A previous study by Kreitus already demonstrated that the absorption of Cl2 •-had very little effect on the analysis of the spectrum of the hydrated electron even for concentrations of LiCl > 10 M. 39 In fact, according to the absorption spectra in Figure 2, the solutions containing 1.0 M LiCl and 1.0 M LiClO4 give the same values of Emax at corresponding temperatures and they present also the same spectral shape for l > 500 nm (2.48 eV). Although the use of LiClO4 gives more 'pure' absorption spectra of the hydrated electron, high concentration of perchlorate might be harmful to the sapphire windows and the tubing of flow system, especially at elevated temperatures. Therefore, we use LiCl instead of LiClO4 for high concentrations. In addition, the highest concentration in this work is limited to 4.0 M given the low solubility of LiCl at high temperatures and the safety of our experimental system, although a concentration as high as 14 M LiCl has been reported for experiments at room temperature in a previous study. 39 We observe also a change in the shape of the absorption spectrum with increasing temperature.

As an example, Figure 4 shows a comparison of the absorption spectra at room temperature and 250 ºC, obtained by pulse radiolysis of a solution containing 1.0 M LiCl. The absorbance maximum of the spectra has been normalized to 1.0 and shifted to the position at 25 °C. It is clear that with increasing the temperature the band broadens at lower energy and narrows at higher energy. Therefore, the width becomes slightly larger at high temperature.

We have performed mixed quantum classical molecular dynamics (QCMD) simulations of an excess electron in bulk water and in presence of a lithium cation. As there is no isotopic effect in such calculations, the calculations are done in H2O and not in D2O. The method and the simulation details are fully described elsewhere, 16,48 and the main features are summarized hereafter. The excess electron only was treated quantum mechanically, using the Born-Oppenheimer approximation. The forces acting on each classical degree of freedom were the Hellmann-Feynman forces as well as those arising from the empirical models used for the water [START_REF] Berendsen | Interaction models for water in relation to protein hydratation[END_REF] and the cation. [START_REF] Åqvist | [END_REF] The excess electron-water interactions were modelled using the pseudopotential developed by Turi and Borgis 59 and the electron-Li + pseudopotential was a one-electron semilocal pseudopotentials proposed by Durand and Barthelat 60 and optimized in previous work. 61 It has been proposed that cation concentration effects experimentally observed on systems containing a solvated electron and alkali cations are mainly due to the mean electron-cation distance. 61 Pursuing this approach, simulations of one electron and one Li + cation in bulk water were performed with additional constraints to allow the electron-cation distance d to fluctuate around certain equilibrium values, using the quantum umbrella sampling method. 62 To mimic the experimental effect of cation concentration, the simulations of the present study

This quantity and the position of the maximum of the absorption band, Emax, have similar trends, but Emean is subject to much smaller statistic uncertainty than Emax. The mean transition energy of the UV-Vis absorption spectrum, Emean, is reported in Table 2 for the electron in bulk water, as well as the {eaq -, Li + } systems with d ~ 2.5 Å and d ~ 4.0 Å. We observe that when the temperature is increased and the density is decreased, the absorption spectrum of the

( ) ( ) mean E I E dE E I E dE = ò ò
electron in the presence of a lithium cation is shifted to lower energies, but this shift is smaller than that of the electron in bulk water. Moreover, the closer the hydrated electron and the cation are, the smaller the shift is. In the case of Ag + , the ion is reduced by the solvated electron to yield a neutral Ag 0 atom in an excitonic state, 63 the spectrum of which exhibits very little temperature-or density-dependence. 64 Also presented in Table 2 the shifts:

ΔEmean(d) = Emean(eaq -,Li + ; d) -Emean(e -) (5)
between the absorption band in bulk water without cation and with the lithium cation at distance d, for a given temperature and density. These blue shifts are a measure of the influence of the cation on the hydrated electron, and it was experimentally observed that they grow with cation concentration. [43][44][45] The experimental dependence on cation concentration was shown to be related to the dependence on electron-cation distance observed in simulation.

We show here that this trend persists at temperatures higher than room temperature, in good agreement with the experimental results. We also show that, for a given electron-cation distance, higher temperatures lead to higher absorption spectrum shifts.

The evolution of Emax with temperature obtained by pulse radiolysis experiments (Figure 6 upper) is almost the same whatever the salt concentration. That means that the temperature effect on the absorption band is much larger than the salt effect. The shifts as a function of temperature of Emean calculated by QCMD simulations is also reported (Figure 6 bottom).

Obviously, the results are consistent.

Finally, the spectra of the hydrated electron at 2.5 Å of the Li + (Figure 5) exhibit a significantly larger Full Width at Half Maximum than that of the hydrated electron in bulk water under the same thermodynamic conditions (Table 2). The change in the shape of the spectrum and the existence of a shoulder are due to one of the three p-like excited states of the solvated electron (the one with Σ symmetry, its orbital pointing in the direction of the cation) being destabilized by core repulsion. This effect was previously shown in other systems. 61 The shoulder on the high-energy wing of the absorption spectrum is only obtained at room temperature. This result corroborates with the broadening of the spectrum reported in Figure 3.

The study of s → p transition energies for the three p excited states reveals that for temperatures higher than room temperature, there is a broadening of each individual s → p absorption band due to less structured water solvation shell. This broadening leads to higher overlap between the three bands and the absence of a high-energy shoulder on the resulting spectrum. Consequently, at high temperature and in the presence of metal cation, the shape of the absorption band changes while its width is roughly the same (Table 2). The experimental results reported on Figure 4 can be understood by that fact.

Conclusion

The increase in the temperature and the increase in the concentration of non-reactive metal cation have opposite effects. With temperature the absorption spectra of the solvated electron shifts to the red whereas in the presence of a salt it shifts to the blue. When both effects are present, the shift intensity and the shape of the absorption spectra are modified. However, the effect of the temperature on the absorption spectrum of the solvated electron is stronger than that of the presence of non-reactive metal cation even up to 4 M. QCMC simulations reveal that in the presence of the non-reactive metal cation, the width of the absorption band is broadened. The perturbation of the three s→p optical transitions by changing the solvation shell of the solvated electron accounts for such broadening.

Figure 3

 3 Figure 3 displays a comparison of the absorption spectra of solvated electrons at room temperature obtained by pulse radiolysis in a D2O solution containing 4.0 M LiCl and in pure D2O solution. The absorbance at lmax for the two spectra is normalized to 1.0 and the spectrum of pure D2O is shifted to overlap with that of 4.0 M LiCl solution at lower energy side. Apparently in the presence of 4.0 M LiCl, the absorption spectrum of solvated electrons broadens slightly but significantly. This spectral broadening becomes more and more pronounced with increasing LiCl concentration from 1.0 to 4.0 M. In inset of Figure 3, we report the absorption spectra after subtracting the contribution of Cl2 •-. We note that the

were performed for both d ~ 2 . 5 Å

 25 and d ~ 4 Å. Shorter distance simulates higher concentration of cation, and lower distance that of lower concentration of metal cation. The UV-Vis absorption spectra of the hydrated electron and a lithium cation in bulk water at different thermodynamic state points are shown in the lower panels of Figure 5, for a system where the hydrated electron is kept at a distance d ~ 2.5 and 4 Å from the Li + cation. The spectra of the hydrated electron without cation in bulk water at the same thermodynamic conditions are shown in upper panel of Figure 5 for comparison. To describe quantitatively the position of the UV-Vis absorption spectrum calculated from QCMD simulations, we have calculated the mean position of the absorption band by integrating over this band:

Figure 1 .

 1 Figure 1. Temperature dependence of the normalized absorption spectra of the hydrated electron in D2O. Inset: absorption spectra recorded just after the electron pulse. (■) 25, (□) 50, (•) 100, (○) 150, (▲) 200, (△) 250, and (◆) 300 ºC. Dose: 70 Gy ; optical path length : 15 mm.

Figure 2 .

 2 Figure 2. Normalized absorption spectra of the hydrated electron in D2O solutions containing 1.0 M LiClO4, 1.0 and 4.0 M LiCl as function of temperature. (■) 25, (□) 50, (•) 100, (○) 150, (▲) 200, (△) 250, and (◆) 300 ºC.

Figure 3 .

 3 Figure 3. Comparison of the normalized absorption spectrum of solvated electrons in 4.0 M LiCl (□, deuterated solution) with that in pure D2O (•) at room temperature. The spectrum in pure D2O is shifted to overlap that in 4.0 M LiCl solution at lower energy side. Inset: Same comparison but after subtraction of the contribution of Cl2 -. absorption. The Cl2 -. spectrum was obtained in the same experiment after complete disappearance of solvated electron.

Figure 4 .

 4 Figure 4. Normalized absorption spectra of the solvated electron in D2O solution containing 1.0 M LiCl at 25 °C (○) and 250 °C (■) (Absorbance maximum normalized to 1 and shifted

Figure 5 .

 5 Figure 5. UV-Vis absorption spectra of the hydrated electron in bulk water (upper panel) and in presence of a lithium cation at distance d ~ 2.5 (lower panel) and 4 Å (middle panel), at different thermodynamic state points (see Table2).

  ).

Figure 6 .

 6 Figure 6. Peak position of the absorption spectrum of the hydrated electron as a function of temperature. Top: Emax = f(T) experiments; Bottom: Emean = f(T); QCMD simulations.

Figure 1 .

 1 Figure 1.

Figure 3 .

 3 Figure 3.

Figure 5

 5 Figure 5

Table 1 .

 1 Peak positions of the absorption maximum of the hydrated electron in light and heavy water solutions containing LiCl and LiClO4 at different concentrations.

	Salt	Concentration	Emax [eV] at 22 ºC	Emax [eV] at 10 ºC
		[M]	(this work, in D2O)	(Bonin, et al. 45 * in H2O)
	LiCl	1.0	1.75	1.786
	LiCl	2.0	1.78	1.812
	LiCl	4.0	1.82	-
	LiCl	5.0	-	1.852
	LiClO4	1.0	1.77	1.812
	* The concentration unit used in Ref. 45 is mol/kg.

Table 2 .

 2 Main characteristics (mean transition energy and width in eV) of the UV-Vis absorption spectra of the electron at different thermodynamic state points, for the hydrated electron in bulk water and in presence of a lithium cation at distances d ~ 4 Å and d ~ 2.5 Å.

	T (K) r (g.cm -3 )	Emean	e -aq Width	e -aq,Li + (d ~ 4 Å) Emean DEmean Width Emean e -aq,Li + (d ~ 2.5 Å) DEmean Width
	298	1.00	1.97	0.72	2.05	0.08	0.72	2.10	0.13	0.87
	523	0.82	1.71	0.85	1.80	0.08	0.85	1.87	0.16	0.92
	623	0.63	1.53	0.77	1.62	0.09	0.77	1.74	0.21	0.85

Acknowledgments

We are grateful to Mr. T. Ueda and Prof. M. Uesaka for their technical assistance in pulse radiolysis experiments and encouragement. This work was partly entrusted by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japanese Government, as a "Fundamental R&D program on water chemistry of supercritical pressure water under radiation field".