domain: sde spi

text:
M Zribi

A Gorrab

N Baghdadi

A new soil roughness parameter for the modelling of radar backscattering over bare soil

Keywords: Soil, Roughness, Moisture, Zg, Radar, Backscattering coefficient, Model

A newsoil roughness parameter for themodelling of radar backscattering over bare soil

Mehrez Zribi, Azza Gorrab, Nicolas

Introduction

Soil moisture and roughness parameters play a key role in hydrological and climate studies. In recent years, various efforts have been devoted to the analysis of the backscattering characteristics of bare soils. Initially, different backscattering models (theoretical, semiempirical and empirical) were developed [START_REF] Ulaby | Microwave Remote Sensing Active and Passive[END_REF][START_REF] Fung | Backscattering from a randomly rough dielectric surface[END_REF][START_REF] Oh | An empirical model and an inversion technique for radar scattering from bare soil surfaces[END_REF][START_REF] Dubois | Measuring soil moisture with imaging radars[END_REF][START_REF] Chen | Emission of rough surfaces calculated by the integral equation method with comparison to three-dimensional moment method simulations[END_REF][START_REF] Zribi | A method for soil moisture estimation in Western Africa based on ERS Scatter meter[END_REF]. More recently, several studies have proposed various approaches for the improvement of roughness descriptions [START_REF] Oh | Condition for precise measurement of soil surface roughness[END_REF][START_REF] Mattia | Backscattering properties of multi-scale rough surfaces[END_REF][START_REF] Zribi | Validation of a rough surface model based on fractional brownian geometry with SIRC and ERASME radar data over Orgeval site[END_REF], Davison et al., 2000[START_REF] Li | A generalised Power Law Spectrum and its Applications to the Backscattering of soil surfaces Based on the Integral Equation Model[END_REF][START_REF] Callens | Parameterization of tillage-induced single-scale soil roughness from 4-m profiles[END_REF][START_REF] Verhoest | On the soil roughness parameterization problem in soil moisture retrieval of bare surfaces from Synthetic Aperture Radar[END_REF], Bretard et al., 2013), which are essential to the accurate analysis and interpretation of backscattering behaviour and soil moisture estimation [START_REF] Lievens | Error in SAR-derived soil moisture due to roughness parameterization: An analysis based on synthetical surface profiles[END_REF]). An analysis based on a fractal representation has been proposed (Rouvier et al., 1997;[START_REF] Zribi | Validation of a rough surface model based on fractional brownian geometry with SIRC and ERASME radar data over Orgeval site[END_REF] allowing a multi-scale description, which is not limited to the use of a single scale based on the correlation length parameter. [START_REF] Zribi | Validation of a rough surface model based on fractional brownian geometry with SIRC and ERASME radar data over Orgeval site[END_REF] introduced fractal and Brownian approaches to describe the correlation function, whereas [START_REF] Li | A generalised Power Law Spectrum and its Applications to the Backscattering of soil surfaces Based on the Integral Equation Model[END_REF] proposed a general power law description of roughness spectra. [START_REF] Fung | Microwave Scattering and Emission Models and their Applications[END_REF], [START_REF] Shi | Estimation of Bare Surface Soil Moisture and Surface Roughness Parameter Using L-Band SAR Image Data[END_REF] and [START_REF] Zribi | Evaluation of a rough soil surface description with ASAR-ENVISAT Radar Data[END_REF] have proposed different types of analytical correlation function, used to fit the experimental data. Although all of these studies have led to improvements in the direct backscattering simulations, the availability of a limited number of radar configurations makes it generally impossible to retrieve the volumetric soil moisture with all of the roughness parameters. In this context, [START_REF] Zribi | A new empirical model to retrieve soil moisture and roughness from Radar Data[END_REF] introduced a description based on the parameter Zs = s 2 /l, where s is the rms surface height and l is the correlation length (Bretard et al., 2013[START_REF] Lawrence | Evaluating the Semiempirical H -Q Model Used to Calculate the L-Band Emissivity of a Rough Bare Soil[END_REF]. [START_REF] Baghdadi | Semiempirical calibration of the IEM backscattering model using radar images and moisture and roughness field measurements[END_REF][START_REF] Baghdadi | Calibration of the Integral Equation Model for SAR data in C-band and HH and VV polarizations[END_REF][START_REF] Baghdadi | Semi-empirical calibration of the Integral quation Model for SAR data in C-band and cross polarization using radar images and field measurements[END_REF] proposed an empirical correlation length, computed as a function of the rms height, radar frequency, incidence angle and polarization, in order to obtain a better fit between Integral Equation Model [START_REF] Fung | Backscattering from a randomly rough dielectric surface[END_REF] simulations and radar observations. [START_REF] Lievens | Effective roughness modelling as a tool for soil moisture retrieval from C-and L-band SAR[END_REF] show that roughness parameters differ between SAR acquisitions, as they are related to the observed backscatter coefficients and variations in local incidence angle. A statistical model was thus developed, to allow the effective roughness parameters to be estimated from microwave backscattering observations. Despite these contributions, the influence of roughness is still poorly modelled in currently known inversion techniques.

In the present study, a new surface description is proposed, in which the analysis uses the moment method to numerically simulate the backscattering integral equations. Our paper is organised into five sections, of which Section 2 presents the principles of the numerical backscattering simulations, Section 3 discusses the influence of roughness on the backscattering simulations and introduces the new roughness parameter, Zg. Section 4 describes the potential of this parameter, through the use of experimental analyses based on different types of ground and radar measurements. Finally, our conclusions are presented in Section 5.

Numerical backscattering simulations -methodology

A numerical backscattering model based on the moment method is used to simulate radar signals over bare soils [START_REF] Harrington | Field Computation by Moment Method[END_REF][START_REF] Chen | Computer simulation of wave scattering from a dielectric random surface in two dimensions cylindrical case[END_REF][START_REF] Johnson | Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data[END_REF][START_REF] Davidson | On the characterisation of agricultural soil roughness for radar remote sensing studies[END_REF][START_REF] Soriano | Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations[END_REF][START_REF] Zribi | Numerical backscattering analysis for rough surfaces including a cloddy structure[END_REF]. With this approach, the computations are made using simulated surfaces, with various roughness and soil moisture characteristics. The first step in this process thus involves the generation of soil roughness profiles.

Roughness profile generation for different types of correlation function

In this section, it is proposed to generate soil surfaces with different correlation functions

                    l x x exp
, in which the parameter  can range between 1 and 2 [START_REF] Li | A generalised Power Law Spectrum and its Applications to the Backscattering of soil surfaces Based on the Integral Equation Model[END_REF], with these extremes corresponding to exponential and Gaussian functions, respectively [START_REF] Fung | Numerical Simulation of Scattering from Simple and Composite Random Surfaces[END_REF]. The approach described by [START_REF] Fung | Numerical Simulation of Scattering from Simple and Composite Random Surfaces[END_REF] is used as follows:

The surface heights are written as:

) ( ) ( ) ( k i X i W k h M i M i       (1)
where X(i) is a Gaussian random variable N(0,1), and W(i) is the weighting function given by

      i C F F i W 1 ) (  
, in which C(i) is the correlation function and F[] denotes the Fourier transform operator. In the numerical simulations, a Fast Fourier Transformation (FFT) is used to compute the corresponding values of W(i).

Fig. 1 shows three soil profiles generated using different values of  (=1,  =1.5 and  =2).

In this case, the rms surface height is equal to 0.6 cm and the correlation length is equal to 6 cm. It can be clearly seen that a decrease in the value of  leads to an increase in the presence of high frequency structures.

Moment Method simulations

In this section, a limited description of the moment method, used to compute radar backscattering over generated surfaces, is proposed. The analyses presented here make use of two-dimensional simulations, which are adequate for the purposes of the present study, and are based on the use of isotropic surfaces only (Chen et al., 1994[START_REF] Fung | Microwave Scattering and Emission Models and their Applications[END_REF]. The

backscattering computation is based on the numerical resolution of integral equations, in which the medium is considered to be air [START_REF] Chen | Computer simulation of wave scattering from a dielectric random surface in two dimensions cylindrical case[END_REF]:

' . 2 1 ) ( 1 1 1 1 0 dl G j J G K J G j n K r E n c i                            ' . 2 1 ) ( 1 0 1 1 1 dl G j K G J K G j n J r H n c i                            (2)
When the medium is soil rather than air, the corresponding integral equations are:

' . 2 1 0 2 2 2 2 0 dl G j K G K J G j n K c                         ' . 2 1 0 2 2 2 2 0 dl G j K G J K G j n J c                         (3)
where μ 0 is the permeability of air, ε 1 and ε 2 are the dielectric constants of air and soil, respectively, and n  is the unit outward normal to the surface.

H n J     
is the equivalent surface electric current density, and

E n J      
is the equivalent surface magnetic current density.

The Green functions are defined in cylindrical coordinates, by the zeroth order Hankel function of the second kind, as:

  2 , 1 , ' 4 ) 2 ( 0     i k H j G i i     (4)
In this paper, we present integral equations and method of resolution only for horizontal polarisation. For vertical polarisation, the approach is similar with just minor modifications [START_REF] Chen | Computer simulation of wave scattering from a dielectric random surface in two dimensions cylindrical case[END_REF].

For the horizontal polarisation, the incident electric and magnetic fields are written as:

) cos sin ( 1   z x jk i e y E      ) cos sin ( 1 ) sin cos ( 1      z x jk i e z x H        (5) With ) (l J y J    
and then 0 .   J 

The integral equations could be written as:

  l d G K J G j n K r E n c i           1 1 0 2 1 ) (          l d G K J G j n K c          2 2 0 2 1 0      (6) where: 2 , 1 , ) '. ( ) ' (            i G n E G E n G K i i i     
The integral equations can then be simplified to:

  l d G n E J G j E E c y y y i y       ) '. ( ) ( 2 1 ) ( 1 1 0         l d G n E J G j E c y y y       ) '. ( ) ( 2 1 0 2 2 0     (7)
These equations can then be rewritten in the form of a matrix system:

                         0 22 21 12 11 i y y y E J E Q Q Q Q (8)
The details of the different terms in these matrices are described in (Chen et al., 1989).

The solution for this system allows the electric field and electric field density to be estimated over the studied surface. The backscattered field can then computed as:

  ' ) '. ( 1 1 0 dl G n E J G j E c y y s y         (9)
This leads to the following expression for the backscattered signal:

                P j P j s j s j eff E P E PL 1 2 1 2 0 1 2  (10)
Where eff L is the effective illumination length of Gaussian antenna pattern.

On the basis of the outcome of several convergence tests, the profile length was set to 1 m and the number of profiles as taken to be 100. For each profile, the size of the cells was taken to be /10, where  is the wavelength of the radar signal.

Analysis of simulated radar backscattering as a function of roughness

Influence of roughness on the backscattering simulations

In order to study the influence of the soil roughness parameters on radar signal backscattering, Moment Method (MM) simulations were run in the HH and VV polarizations, at 20 and 40° incidence angles, and at three different values of soil moisture: 10%, 20% and 30%. The results shown in Figs. 2, 3, 4 and 5 were computed at a 40° incidence angle, since the radar signals are known to be more sensitive to roughness at higher incidence angles [START_REF] Fung | Microwave Scattering and Emission Models and their Applications[END_REF][START_REF] Zribi | Backscattering behavior and simulation comparison over bare soils using SIRC/XSAR and ERASME 1994 data over Orgeval[END_REF]. Various surface parameters were used: rms heights s=0.4 cm, s =0.6 cm, s =0.8 cm, s =1 cm, s =1.2 cm, s =1.4 cm, s =1.6 cm; correlation lengths l=4 cm, l =6 cm, l =8 cm and l =10 cm;  parameter =1,  =1.25,  =1.5 and  =1.75. The latter range (for the parameter ) was based on the values retrieved during various experimental campaigns [START_REF] Zribi | Evaluation of a rough soil surface description with ASAR-ENVISAT Radar Data[END_REF].

Fig. 2 shows the simulated backscattered signal, for the HH polarization, assuming volumetric moisture conditions of 10% and 30% in the C and X bands at 40° incidence, for all of the above roughness configurations, plotted as a function of the rms surface height. These simulations show that the backscattered signal is moderately well correlated with the rms surface height (in the C band, R 2 is equal to 0.65 and 0.66, and in the X band it is equal to 0.58 and 0.51, for volumetric moistures of 10% and 30%, respectively). This outcome is influenced, in particular, by the correlation length, which is not taken into account in the above relationships. Fig. 3 plots the simulated backscattered radar signals for the HH polarization, for volumetric moistures of 10% and 30%, in the C and X bands at 40°

incidence, for all of the above roughness configurations, plotted as a function of the parameter Zs. Since the latter parameter is defined as Zs = s 2 /l [START_REF] Zribi | A new empirical model to retrieve soil moisture and roughness from Radar Data[END_REF], it combines the influence of both the soil's rms height and its correlation length: it is in effect given by the product of the rms height s, which is related to the power of the surface height variations, and the ratio s/l, which represents the local slope of the soil. The underlying motivation for the introduction of Zs was to introduce the influence of slope, which is an important soil feature in the estimation of °. It can clearly be seen that the simulated backscattering is more strongly correlated with Zs (R 2 = 0.82, 0.81 in the C band, and R 2 = 0.71, 0.62 in the X band, for volumetric moistures of 10% and 30%, respectively), than with the rms height. When the exponential correlation function is considered alone, the correlation between Zs and the simulated backscattered signal is very high (R 2 >0.9). When different function shapes are considered, corresponding to different values of  (1, 1.25, 1.5 and 1.75), the correlation coefficient decreases, as shown in Fig. 3. This outcome could be explained by the influence of the slope component (s/l) on backscattering, which depends on the shape of the correlation function.

Generating the Zg parameter

The parameter Zs was initially proposed for use with an exponential correlation [START_REF] Zribi | A new empirical model to retrieve soil moisture and roughness from Radar Data[END_REF], and weaker correlations are observed between Zs and the simulated backscattering when other correlation function shapes are considered. However, with agricultural and natural soils, differing correlation function shapes are retrieved during the same period. In practice, new tillage is often associated with an exponential function, whereas rain-eroded and ploughed soils are often found to have correlation functions with a shape lying between that of an exponential and a Gaussian function [START_REF] Zribi | Backscattering behavior and simulation comparison over bare soils using SIRC/XSAR and ERASME 1994 data over Orgeval[END_REF][START_REF] Zribi | Evaluation of a rough soil surface description with ASAR-ENVISAT Radar Data[END_REF]. For these reasons, the use of a single roughness parameter, with an rms height, correlation length and correlation function shape, could be very useful for inversion studies based on the analysis of radar measurements, which generally make use of a small number of radar configurations.

Since the contribution of the ratio s/l must be different from one correlation shape to another, as a result of differences in the high frequency spectrum of the soil profile, we propose to introduce a new parameter, which is a global representation of the Zs parameter, written as:

   g l s s Zg         (11)
where g() is a power function accounting for the influence of the ratio (s/l) on Zg, and  is the power of the correlation function.

In the following, it is assumed that g() can be written as:

  b a g    
where a and b are constants.

All of the backscattering simulations made in the C-and X-bands, using three values of volumetric moisture (10%, 20% and 30%), a large range of values of rms height (from 0.4 to 1.6 cm), correlation length (from 4 cm to 10 cm), and  (from 1 to 1.75), were reviewed. The best correlation between the global roughness parameter Zg and the simulations was determined by least squares regression. This is obtained when the function g is written as:

     g (12)
such that (from Eq. 11):

   l s s Z g  (13)
In [START_REF] Zribi | A new empirical model to retrieve soil moisture and roughness from Radar Data[END_REF], it was proposed to use a roughness parameter Zs = (s.s/l), in the case of simulations corresponding to the special case of an exponential correlation function (=1). to large values of Zg [START_REF] Zribi | Backscattering behavior and simulation comparison over bare soils using SIRC/XSAR and ERASME 1994 data over Orgeval[END_REF][START_REF] Zribi | Evaluation of a rough soil surface description with ASAR-ENVISAT Radar Data[END_REF]. Firstly, it can be seen that the simulated backscattering increases with Zg, and that there is a strong correlation between the backscattering and Zg, equal to 0.97 and 0.97 for 10% and 30% volumetric moistures in the C-band and equal to 0.97 and 0.93 for 10% and 30% volumetric moistures in the X-band. A high dynamic range can be observed at small values of Zg, and near saturation can be seen when Zg reaches approximately 0.3-0.35. The highest values of  produce the weakest backscattering. From this initial result, Zg appears to be a useful parameter for the characterization of surface roughness, in the case of a given (fixed)

radar configuration. This result can be explained by the fact that Zg takes the influence on radar backscattering behaviour of s, l and the correlation function shape into account.

Table 1 provides a summary of the correlations determined from backscattering simulations, using different roughness parameters (s, Zs and Zg), for all combined conditions of incidence angle, moisture, polarisation, and frequency. It can be seen that under almost all conditions of radar transmission, the strongest correlations are obtained with the parameter Zg, rather than with s or Zs. This conclusion is not completely verified in the C-band, in the case of a 20° incidence angle, for which the empirical logarithmic relationship can be seen to less well correlated.

To simplify the combination of backscattering simulations made at different radar frequencies, the former were considered as a function of electromagnetic roughness, written in the form: k.Zg (k: radar wave number). Fig. 5 plots the simulated backscattered signals as a function of k.Zg, in the HH and VV polarizations, at a 40° incidence angle, and with the volumetric moisture equal to 10% and 30%, thus allowing all roughness conditions and Cand X-band simulations to be combined.

A least squares approach was then used to establish an empirical relationship between k.Zg and the backscattered signals, taking the form:

  Zg k e         1 0 (14)
where   is expressed in dB, k in cm -1 , and Zg in cm.

The backscattered signals can be seen to be strongly correlated with k.Zg.

Experimental analysis

In this study, we use data acquired over agricultural watersheds, during the course of three experimental campaigns (Orgeval'94, Pays de Caux'94, Villamblain'2003) (Fig. 6). For each of these campaigns, radar data (SIRC, ERASME, ASAR/ENVISAT) was acquired with different configurations (Table 3). Simultaneously to the radar acquisitions, ground measurements were carried out in a large number of test fields: the soil moisture was measured within the top 5 cm soil using a gravimetric method and/or a TDR probe, and roughness measurements were made using a pin-profiler (total length equal to 2 m, resolution equal to 10 mm).

Description of the database  Orgeval'94

The Orgeval watershed is located to the East of Paris (France). An experimental campaign was conducted during the SIRC/XSAR mission in April 1994 [START_REF] Zribi | Backscattering behavior and simulation comparison over bare soils using SIRC/XSAR and ERASME 1994 data over Orgeval[END_REF]. The soil texture is relatively constant over the whole basin: clay 17%, silt 78%, sand 5%. Ground measurements (roughness and moisture) were made in 5 fields.

 Pays de Caux'94

This

 Soil moisture measurements

The mean volumetric moisture (Mv) was estimated for each test field, within the top 5 cm, and using a gravimetric method. As a result of relatively rainy winters, this parameter remained high and nearly constant (approximately 0.3 cm 3 /cm 3 ), at all three sites.

 Soil roughness measurements

Roughness measurements were made using a pin profiler (with a total length of 2 m and a resolution of 1 cm). Ten surface profiles were taken for each test field, in order to ensure that roughness parameters were determined with sufficient statistical accuracy. For each profile, we computed the correlation function (Ogilvy, 1991), as well as the two statistical parameters, the rms height (s) and the correlation length (l). The parameter corresponding to the shape of the correlation function, is computed for the first scales up to the correlation length from experimental functions, using a least squares optimisation approach. In general, the value of  is found to be close to 1 for smooth soils, and higher for ploughed soils. This type of relationship was also observed by [START_REF] Zribi | Evaluation of a rough soil surface description with ASAR-ENVISAT Radar Data[END_REF]. The measured values of Zg (Fig. 7-b) ranged between 0.01 and 0.03 for smooth soils. In the case of cloddy soils, Zg ranged between approximately 0.04 and 0.2, and for ploughed soils it ranged between 0.2 and 0.62 [START_REF] Zribi | Evaluation of a rough soil surface description with ASAR-ENVISAT Radar Data[END_REF].

Comparing backscattering simulations with radar signal data

In Figs. 8-a and 8-b, the results derived from the moment method simulations made in two dimensions are compared with real radar data, for the HH and VV polarizations, respectively.

Two-dimensional (rather than three-dimensional) simulations were used, since the analysed experimental fields had very little directional structure. For each individual test field, ground measurements (rms height, correlation length,  parameter, soil moisture) were used as input for the radar backscattering simulations. Fig. 8-a shows the HH polarization data obtained from several different configurations: C and X bands, and five different incidence angles: 20°, 25°, 30°, 35° and 44°, whereas Fig. 8-b shows VV polarization results for the same set of configurations. In the HH polarization, the simulations can be seen to deviate from the radar measurements, with an RMSE equal to 3.34 dB. In the VV polarization, a good agreement can be observed, with an RMSE equal to 1.62 dB. These results illustrate some of the limitations encountered, particularly in the HH polarization, when the MM model is used to simulate all surface conditions. This is probably due to the greater sensitivity of HH polarization to soil roughness [START_REF] Fung | Microwave Scattering and Emission Models and their Applications[END_REF][START_REF] Zribi | Backscattering behavior and simulation comparison over bare soils using SIRC/XSAR and ERASME 1994 data over Orgeval[END_REF]. In the following section, it is proposed to use empirical relationships to express the backscattered radar signals as a function of the surface parameters.

Analysis of the relationship between roughness and radar data

All of the ground data analysed in the present study was acquired under very similar soil moisture conditions (close to 30%). Fig. 9 shows the radar signals measured over the test fields, as a function of kZg, for various configurations (both polarizations and several incidence angles). As in the case of the simulations described in section 3, the radar signals are characterized by a high dynamic range at small values of kZg, and near saturation can be observed when kZg reaches approximately 0.3-0.35.

Figs. 9a, 9b, 9c, 9d, 9e, and 9f correspond to observations made at the Pays de Caux site, using the ERASME airborne FM-CW scatterometer. This data was acquired in the HH and VV polarizations, in the C-and X-bands at 20°, 25°, 30° and 35° incidence. In both polarizations, the roughness parameter kZg and the radar measurements are strongly correlated. These radar measurements are also found to be strongly correlated with kZg. Empirical relationships can be used to express the backscattered radar signals as a function of k.Zg, for various multi-incidence and polarization configurations. These are written:

  Zg k p p p p e             1 0 ( 15
)
where the coefficients   p ,   p and   p are adjusted using a least squares optimisation, p is the polarization and  is the incidence angle. analysed in this study.

Table 5 indicates the general improvement found in the statistical parameters (R 2 and RMSE) when k.Zg is used, rather than k.Zs, in the same empirical model. Only the last configuration (HH polarization at 44°) leads to better results with the parameter k.Zs.

From the empirical relationships established for the nine radar configurations, a general empirical model is proposed, in which the radar signal is expressed as a function of kZg,  and the radar polarisation:

                    Zg k g f e p p p p p p p p e d c b a      2 1 0 (16)
This model is found to be valid when  lies between 20° and 44°.

The values of the parameters used in Eq. 16 are listed, for the HH and VV polarizations, in Table 6.

In Fig. 10, the radar signal levels predicted by the model are compared with the measured data, over the full range of experimental incidence angles. The modelled and measured signals are found to be strongly correlated, with R 2 equal to 0.79 and 0.88 and the RMSE equal to 1.42 dB and 1.19 dB, in the HH and VV polarizations, respectively.

Conclusion

It is very difficult to separately estimate the influences of rms height (s), correlation length (l) and correlation function shape, on the backscattering behaviour of a rough soil surface. In practice, the availability of only a limited number of radar configurations can make it impossible to retrieve all of these parameters with soil moisture.

In the present study, a new approach is proposed for the description of surface roughness and its influence on the backscattering behaviour of radar signals. The resulting expressions make use of a numerical backscattering algorithm based on the moment method, applied to synthetically generated surfaces and assuming a correlation function described by

                    l x x exp
. The correlation between the simulated and measured rms soil heights is weak, as a consequence of influences related to the correlation length of the surface roughness and the shape of the correlation function. These influences must be accounted for, in order to retrieve accurate surface roughness or moisture estimations. The parameter Zs, which allows the influence of soil surface height and slope to be taken into account, can be used to improve

  For a fixed value of , small values of Zg correspond to small values of s and/or large values of l, whereas large values of Zg correspond to large values of s or small values of l. In the case of a fixed correlation length, small values of Zg correspond to small values of s and/or large values of , whereas large values of Zg correspond to large values of s or small values of . A smooth soil surface (without clods) is generally characterised by a small value of s and a medium to large value of l, thus to a small value of Zg. Ploughed soil, corresponding to new tillage, is generally associated with a large value of s, a medium to large value of l, and a value of  close to 1, and thus to a large value of Zg. Ploughed surfaces, corresponding to eroded soils, are often characterised by a large value of s, a medium to large value of l and a value of  close to 2, thus to a medium value of Zg. Even when its rms height (s) is small, a cloddy soil is characterised by a very small value of l and a value of  close to 1, thus leading

Fig. 4

 4 Fig. 4 shows a plot of simulated backscattered signals as a function of Zg, for various ranges of roughness and four correlation function shapes (=1,  =1.25,  =1.5,  =1.75), in the C and X bands and for the HH polarization, with volumetric moisture values of 10% and 30%.

Fig. 7 -

 7 Fig. 7-a plots the parameter corresponding to the correlation function shapes retrieved for

Fig. 9g corresponds

  Fig. 9g corresponds to data acquired by SIR-C and ASAR-ENVISAT over the Orgeval and

  the correlation strength. Nevertheless, the simulated radar signals are still affected by strong fluctuations, resulting from variations in the shape of the correlation function. By introducing a new roughness parameter (Zg), written in the form of the rms surface height, the slope of the soil surface, and a third parameter  related to the shape of the correlation function, can be taken into account. A very good correlation is then observed between k.Zg and the simulated radar signals in the C and X bands, with R 2 equal to 0.93 and 0.9 at 40° incidence for the HH and VV polarizations, respectively. Empirical functions are proposed to describe these relationships. The usefulness of this new parameter is demonstrated through the analysis of radar signal data acquired at three experimental sites in France (Orgeval, Pays de Caux and Villamblain). In the case of smooth soils, Zg is found to range between 0.01 and 0.03. In the case of cloddy soils, Zg lies between approximately 0.04 and 0.45, and in the case of ploughed soils, it ranges between 0.2 and 0.62. A high correlation (R 2 >0.7 and RMSE<1.54 dB) is observed between kZg and the experimental radar signals acquired in the C and X bands, at incidence angles ranging between 20° and 44°. An empirical model is proposed for the relationship observed between the measured radar signals and kZg, , and the polarization parameters. This is found to be in excellent agreement with the radar measurements, with the RMSE equal to 1.42 dB and 1.19 dB in the HH and VV polarizations, respectively. These results are particularly useful for the improvement of empirical or semi-empirical inversion models used in soil moisture estimations. In the past, these models were often based on the rms height roughness parameter only, leading to a high level of noise and a lower accuracy in the soil moisture estimation, resulting from the influence of the correlation length and shape of the correlation function.

Figures captions Fig. 1 :Fig. 2 :Fig. 3 :Fig. 4 :Fig. 5 :

 captions12345 Figures captions

Fig. 8 :

 8 Fig. 8: Numerically simulated radar signals as a function of measured radar signals, a) HH pol

Fig. 9 :

 9 Fig. 9: Relationship between kZg and measured radar signals, for: a) HH polarization at 20°

  Fig. 1

  Fig.2

  Fig. 6

Table 2

 2

	lists the

  test site corresponds to the Blosseville watershed, located in the Pays de Caux in Northern France (49°47' N; 0°50' W). The loamy soils of the northern European loess belt are sensitive mainly to soil structure degradation, and are commonly exposed to erosion caused

	by concentrated runoff. The site's soil is characterized by a very homogenous loamy texture
	(13% clay, 65% loam, and 22.5% sand). ERASME FM-CW scatterometer airborne
	measurements were recorded in 1994, over 10 large test fields.
	 Villamblain'2003
	This site is located approximately 80 km west of Paris (48°10'N; 01°48'E), and is
	characterized by large agricultural fields, which are mainly bare soil fields with a
	homogenous soil composed of approximately 60% loam, 30% clay and 10% sand.

Simultaneously to the radar measurements acquired by the ASAR-ENVISAT radar in 2003, ground measurements were made over a large number of bare soil test fields.

  Table 2 lists the values of

  p ,   p and   p , together with the statistical parameters R 2 and RMSE, for the nine configurations

Table 4 :

 4 Values of ,   p and   p (parameters of Eq. 15) together with the statistical parameters R 2 and RMSE, for the nine configurations analysed in this study.

	  p 	  p 	  p 	R 2	RMSE (dB)
	HH-20° -14.11	12.63	35.95	0.77	1.29
	VV-20° -12.41	12.22	32.16	0.83	1.16
	HH-25° -12.85	10.91	22.45	0.76	1.4
	VV-25° -12.61	11.55	21.03	0.85	1.1
	HH-30° -12.68	10.08	15.68	0.76	1.38
	VV-30° -11.98	10.11	11.32	0.75	1.45
	HH-35° -12.56	9.41	12.05	0.7	1.54
	VV-35° -12.88	10.14	11.72	0.86	1.02
	HH-44° -10.28	5.63	4.62	0.7	0.89

  p

Table 5 :

 5 The statistical parameters R 2 and RMSE, corresponding to the use of different relationships between the radar data and the parameters kZs and kZg.

	kZs		KZg
	R 2	RMSE	R 2	RMSE
		(dB)		(dB)
	HH-20° 0.67	1.5	0.77	1.29
	VV-20° 0.79	1.21	0.83	1.16
	HH-25° 0.65	1.69	0.76	1.4
	VV-25° 0.77	1.39	0.85	1.1
	HH-30° 0.67	1.6	0.76	1.38
	VV-30° 0.67	1.69	0.75	1.45
	HH-35° 0.65	1.66	0.7	1.54
	VV-35° 0.8	1.2	0.86	1.02
	HH-44° 0.86	0.6	0.71	0.86

Table 6 :

 6 values of the parameters used in Eq. 16 for the HH and VV polarizations

		a p	b p	c p	d p	e p	f p	g p
	HH	0.046	-12.81 -0.026 10.55	0.05	-4.38	97.99
	pol
	VV	-0.089 -9.88	-0.062 12.63	0.109	-7.346 134.61
	pol

Acknowledgements

This study was funded by three projects: ASCAS and CFOSAT (the TOSCA/CNES program) and AMETHYST (ANR-12-TMED-0006-01). The authors wish to thank the BRGM, IRSTEA and LATMOS teams for their logistical support during the field campaigns.

Tables:

Table 1: The statistical parameter R 2 , computed for different backscattering simulations, as a function of the rms height (s), the parameters Zs and Zg, and various different values of soil moisture, incidence angle and polarisation.


Michael Piotrowski

Natural Language Processing for Historical Texts

Reviewed by Laurent Romary Inria & Humboldt University Berlin

The publication of a scholarly book is always the conjunction of an author's desire (or need) to disseminate his experience and knowledge and the interest or expectations of a potential community of readers to gain benefit from the publication itself. Michael Piotrowski has indeed managed to optimise this relation by bringing to the public a compendium of information, which I think has been heavily awaited by many scholars having to deal with corpora of historical texts. The book covers most topics related to the acquisition, encoding and annotation of historical textual data, seen from the point of view of their linguistic content. As such, it does not address issues related, for instance, to scholarly editions of these texts, but conveys a wealth of information on the various aspects where recent developments in language technology may help digital humanities projects to be aware of the current state of the art in the field.

Still, the book is not an encyclopedic description of such technologies. It is based on the experience acquired by the author within the corpus development projects he has been involved in, and reflects in particular the specific topics on which he has made more in-depth explorations. It is thus written more as a series of return on experience than a systematic resource to which one would want to return after its initial reading.

The book is organized as a series of 9 short chapters, which I describe below.

In the first two (very short) chapters, the author presents the general scope of the book and provides an overview of the reasons why NLP has such an entrenched position in digital humanities at large and the study of historical text in particular. Citing several prominent projects and corpus initiatives that have taken place in the last few decades, Piotrowski defends the thesis, which I share, that a deep understanding of textual documents requires some basic knowledge of language processing methods and techniques. Chapter 2 in particular ("NLP and digital humanities") could be read as an autonomous position paper, which, independently of the following chapters, presents the current landscape of infrastructural initiatives and scholarly projects that shape this convergence between the two fields.

Chapter 3 ("Spelling in historical texts"; pp. 11-23) describes the various issues related to spelling variations in historical text. It shows how difficult it may be to deal with both diachronic (e.g. in comparison to modern standardised spellings) and synchronic variations (degree of stabilisation of historical spellings), especially in the context of the uncertainty brought about by the transcription process itself. This is particularly true for historical manuscripts and Piotrowski goes deeply into this, showing some concrete examples of the kind of hurdles that a scholar may fall into. This is the kind of short introduction I would recommend for anyone, in particular students, wanting to gain a first understanding in the domain of historical spelling.

Chapter 4 is the longest chapter in the book "Acquiring historical texts"; pp. 25-52) and covers various aspects of the digitization workflow that needs to be set up for creating a corpus of historical texts. The chapter is quite difficult to to read as one single unit because of its intrinsic heterogeneity. Indeed, it covers quite a wide range of topics: presentation of existing digitisation projects worldwide, technical issues related to scanning, comparison of various optical character recognition systems for various types of scripts, the potential role of lexical resources, crowd-sourcing for OCR postprocessing, manual or semi-automatic keying. Getting an overview of the various topics is even more difficult because of the way the author has followed his own personal experience, and alternates between general considerations and in-depth presentations of concrete results. Pages 34-40 for instance is one single subsection on the comparison of OCR outputs that goes into so much detail that it breaks out the continuity of the argument although in itself this subsection could be really interesting for a specialized reader. As we shall see in the conclusion, this chapter illustrates that the content of this book would benefit from being published on a more modern and opened setting.

Data representation aspects are covered in chapter 5 ("Text encoding and annotation schemes"; pp. 53-68), which tackles two specific issues, namely character and document encoding. On these two, the author presents what could be considered best practices. For character encoding, the book rightly focuses on the advantages that the move towards ISO 10646/Unicode has brought to the community. The corresponding subsection actually covers three different aspects: it first makes an extensive presentation of the history of character encoding standards (from ASCII/ISO 646 to Unicode/ISO 10646), provides insights into the current coverage and encoding principles (e.g. UTF-8 vs. UTF-16) of ISO 10646, and finally focuses on the specific difficulties occurring in historical texts both from the point of view of legacy ASCII based transcription languages and the management of characters that are not present in Unicode. Although well documented, these three topics should have been more clearly separated so that readers interested in one or the other could directly refer to it. This is a typical case where, given the great expertise of the author in the subject, I could imagine the corresponding texts being published online as separate entries in a blog. The second half of the chapter focuses on the role of the TEI guidelines for the transcription and encoding of historical text. It covers the various representation levels that may be concerned (metadata, text structure, surface annotation) and insist on the current difficulty of linking current NLP tools to TEI encoded documents. While this is indeed still an issue in general, it might have been interesting to refer to standards (ISO 24611-MAF) and initiatives (Textgrid core encoding at the token level; the TXM platform for text mining) that have started to provide concrete sustainable answers to the issue.

The following chapter ("Handling spelling variations"; pp. 69-84), provides a series of short studies describing possible methods for dealing with OCR errors or spelling variation as described in chapter 3. Independently from the fact that I find it strange to see the two chapters quite far from one another, the present one distinguishes itself with its profound heterogeneity. While several sections do have the most appropriate level of details and topicality for historical texts (in particular those on canonicalization), some sections seem to be completely off-topic (section 6.2, "Edit Distance", describes what I would consider as background knowledge for such a book). It is all the more disappointing that the author shows here a very high level of expertise and as in the case of chapter 3, I would strongly recommend the reading of the relevant sections to newcomers in the field.

In contrast with the previous chapter, chapter 7 ("NLP tools for historical languages"; pp. 85-100) is more coherent and focused. It mainly addresses the morpho-syntactic analysis of historical text and presents, through concrete deployment scenarios, possible methods to constrain the appropriate parsers, in a context where hardly any existing tools can be simply re-used. The chapter is very well documented and refers to most of the relevant initiatives in the domain of morphology for historical text, at least on the European scene. This focus may also be misleading since recent work on named entity recognition on historical texts are not at all mentioned and are probably, to my view, one of the most promising direction for enhanced digital scholarship.

The last chapter ("Historical corpora"; pp. 101-116) is a compendium, sorted by language, of the major historical corpora available worldwide. It shows the dynamic that currently exists in the community and is an essential background resource to both understanding who is active in maintaining historical corpora and discerning the most relevant resources. The chapter as a whole provides an interesting "historical" perspective on the progress made by most text-based projects in using the TEI guidelines as their reference standard. It seems quite difficult now to imagine an initiative which would not take TEI for granted, and would not build inside the TEI framework. On another issue, namely copyright, Piotrowski also provides an interesting analysis on the difficulty of re-using old editions which have been recently re-edited on paper, and thus fall into some publisher's copyright restrictions. The conclusion could have been a little tougher here though, and probably should have recommended putting a hold on any paper publication of historical sources by a private publisher, unless it is guaranteed that the electronic material can be used freely, under an appropriate open license.

As a whole, the book leaves the reader with a mixed feeling of enthusiasm and disappointment. Enthusiasm, because the content is so rich that it should serve as background reference (and indeed be quoted) for any further work on the creation, management and curation of historical corpora. Still, I cannot help thinking that the editorial setting as a book is not the most appropriate setting for such content. The variety of topics that are addressed as well as the heterogeneous levels of details provided through the different chapters would benefit from a more fragmented treatment. Indeed, this would be the perfect content for a series of blog entries (for instance in a scholarly blog such as those on the hypotheses.org platform) which in turn would allow an interested reader to discover exactly the topics he wants information about and cite the corresponding entries. With the bibliography in Zotero and relevant pointers to the corresponding online corpora or tools, I could imagine the resulting content soon becoming one of the most cited online resources. I am sure the author would gain more visibility in doing so than having the material hidden on a library shelf or behind a paywall. Not knowing the exact copyright transfer agreement associated with the book, I cannot judge if it is too late for the author to think in these terms, but this could be a lesson for scholars who are now planning to write such an introductory publication. Is the book still the best medium?

This book review was edited by Pierre Isabelle Laurent Romary is Directeur de Recherche at Inria, France, and guest scientist at the Humboldt University in Berlin. He has been involved for many years in language resource modeling activities and in particular in standardization initiatives in the TEI consortium and ISO committee TC 37/SC 4 (language resource management). He is the director of the European DARIAH digital infrastructure in the humanities. email: laurent.romary@inria.fr.


N Essaidi

B Samet

S Baklouti

# S Rossignol
email: sylvie.rossignol@unilim.fr

THE ROLE OF HEMATITE IN ALUMINOSILICATE GELS BASED ON METAKAOLIN

Keywords: Hematite, Kaolin, Polycondensation reaction, Natural clay, Infrared spectroscopy

This paper investigates the role of iron oxide in natural clay and its contribution to polycondensation reactions. Iron oxide was added to pure kaolin in the same proportion as Medenine clay with different amounts of potassium hydroxide. The physicochemical and structural properties of these materials were determined by infrared spectroscopy, scanning electron microscopy, thermal analyses (DTA-TG) and X-ray diffraction. The amorphous character seen in the diffractograms obtained from the materials and the displacement of the IR wavenumber are indicative of a polycondensation reaction. The representative characterization of the microstructure of different samples using electron microscopy highlights the nonreactivity of iron exhibited during consolidation. In general, the contribution of iron oxide seems to be small under the conditions described here.

INTRODUCTION

Tunisia is among the countries that have signiicant deposits and quantities of clay as a part of its geology. However, research on the development of this resource is limited. Few authors (A. Chakchouk et al., 2006) [1] have tested Tunisian clay that has been calcined at different temperatures for use as pozzolanic materials. Other studies have been conducted on the use of Tunisian clays in ceramics [2], despite containing minerals such as iron oxide, as is the case for Medenine clay. Recently, these natural clays have been proposed as raw materials for the synthesis of a new class of building materials called geopolymers [3]. The production of these geopolymeric materials provides an obvious economic and environmental advantage via a reduction in energy consumption and in 80 % of CO 2 emissions.

Geopolymers are dense "gels" of amorphous silicoaluminates, obtained by mixing an alkaline silicate solution and an aluminosilicate source, such as metakaolin or ly ash. Because geopolymers possess attractive material properties, they are presently used in several applications, such as thermal insulation, refractory materials, and anti-corrosion coatings; however, their main use today is in construction. Among the different families of geopolymers, there are some that contain iron oxide (hematite) added in small quantities [4] (without the presence of aluminum). The resultant material is insoluble in water. X-ray analysis of these materials show a broad amorphous peak centered near 25 -20° that is indicative of short range ordering. The material formed is composed of a tetrahedral network occupied by silicates or iron in a primarily octahedral orientation. The addition of iron to a metakaolin based geopolymer was studied in detail by DS Perera et al. [5]. The basic approach was to introduce ferric iron, either as a soluble salt or as an (oxy) hydroxide precipitate. In this study, metakaolin was mixed in a solution of sodium silicate, and iron was added later as a minority phase. Under these conditions, the rapid formation of the aluminosilicate does not leave enough time for the iron to participate in the geopolymerization reaction. From X-ray diffraction and electron microscopy, it was concluded that in as-cured geopolymers the Fe was present in octahedral sites, either as isolated ions in the geopolymer matrix or as oxyhydroxide aggregates which had not reacted with the starting geopolymer components. According to these authors, iron can be a major component of mining wastes and it can exist in many forms, but it would be more likely to affect the kinetics and overall chemistry of geopolymer formation if the iron was relatively soluble form. Choi et al. [6] discussed the effect of the addition of Fe 2 O 3 on the physical properties of geopolymeric materials based on raw materials containing CaO. They showed a difference of compressive strength caused by Fe inhibition to geopolymerization reaction and form of C-S-H gel.

Others works [7] have studied the solubility of hematite in alkaline solutions and proven that the solubility increases with temperature and the concentration of the alkali metal hydroxide, even though the solubility is still considered very low. The solubility of hematite changes signiicantly, depending on the nature of the alkali metal hydroxide (KOH < NaOH). It has been shown [8] that the dissolved silicates can adsorb onto the surface of various iron oxides with different afinities, such as hematite (Fe 2 O 3 ). Additionally, the adsorption of dissolved silicates on iron oxides occurs over a wide pH range [8][START_REF] Pialy | Etude de quelques matériaux argileux du site de Lembo (Cameroun) : minéralogie, comportement au frittage et analyse des propriétés d'élasticité[END_REF][START_REF] Manoharan | [END_REF]. A thermal analysis of clay containing iron oxide shows fewer mass losses than clay not containing iron oxide or experiencing dehydration phenomena, dehydroxylation and recrystallization [START_REF] Pialy | Etude de quelques matériaux argileux du site de Lembo (Cameroun) : minéralogie, comportement au frittage et analyse des propriétés d'élasticité[END_REF][START_REF] Manoharan | [END_REF]. However, the shift in the observed peak is attributed to the structural reorganization of metakaolinite at low temperatures for samples containing iron. [START_REF] Soro | Inluence des ions fer sur les transformations thermiques de la kaolinite[END_REF] In conclusion, the presence of iron oxide does not inhibit the formation of a geopolymer, but it does inluence the characteristics of the obtained material.

The aim of this work is to understand the role of iron oxide in the geopolymerization reaction of natural clay. In this approach, a geopolymer mixture is synthesized with the same composition as clay. To accomplish this, kaolin or metakaolin are mixed with iron oxide and different amounts of KOH. These various materials are characterized in-situ or after consolidation using different methods.

EXPERIMENTAL

Raw minerals and consolidated materials

The reference clay in this study is a Tunisian clay from the south of Medenine. It is characterized by its composition (SiO 2 = 67.5 %, Al 2 O 3 = 18 %) [START_REF] Essaidi | [END_REF].

The consolidated materials were prepared from a solution containing kaolinite supplied by IMERYS, iron oxide (Fe 2 O 3, particle size < 5 µm, 99 % purity) and KOH pellets (85.7 % purity) dissolved in potassium silicate, as described in Figure 1. Two different methods were used to synthesize the consolidated materials from a mixture of either (kaolin/Fe 2 O 3 ) or (metakaolin/Fe 2 O 3 ).

The materials were prepared by irst dissolving potassium hydroxide in potassium silicate and then adding the clay/hematite mixture to the alkaline solution and mixing until the resulting paste was homogenous, according to the procedure established by Prud'homme et al. in 2010 [13].

After mixing, the paste specimens were poured into plastic containers (Ø = 15 mm, H = 35 mm) and cured at 70°C for 24 hours, followed by 7 days at ambient temperature.

The samples are identiied by Fe T G KOH , where Fe is the mass of Fe 2 O 3 (g), T is the calcination temperature and KOH is the mass of KOH contained in 1 g of the mixture (kaolin and Fe 2 O 3 ).

The designation [(K -Fe) ca ] means that the raw materials are composed of a mixture of kaolin and iron oxide calcined together; whereas [MK-Fe] means that the raw materials are composed of a mixture of metakaolin and iron oxide.

As an example, the compound 0.12Fe G 0.18 is obtained from a mixture of kaolin and Fe 2 O 3 calcined together at T = = 700°C and contains 0.12 g of iron oxide and 0.18 g of potassium hydroxide.

Technical characterization

The mineral phases were identiied by powder X-ray diffraction (XRD) with a BRUKERAXSD8 Advance powder diffractometer using CuK α radiation (λ Kα = 0.154186 nm). The analytical range used was between 5° and 70° with a step size of 0.04° and an acquisition time of 2 s. JCPDS (Joint Committee Powder Diffraction Standard) iles were used for phase identiication.

The particle size distributions of these raw materials were measured using a laser particle size analyzer (Mastersizer 2000). The mixture contained 1 g of clay in 20 ml of water, mixed by ultrasound to eliminate any aggregation. The dispersant used was water. The measured particle sizes are in the range 0.05 -880 microns. Additionally, the concentration of the solution should not be too large (obscuration < 35 %).

Powder BET surface areas were determined by N 2 adsorption at -195.85°C using a Micrometrics Tristar II 3020 volumetric adsorption/desorption apparatus. Prior to the measurement, the samples were degassed at 200°C under vacuum for 24 h.

The wetability, expressed in cm 3 /g, corresponds to the volume of water that can be absorbed by one gram of powder to saturation.

Differential thermal analyses (DTA) and thermogravimetric analyses (TG) were performed with the samples held in a Pt crucible between 25°C and 1200°C using a SDTQ600V20.9. The samples were heated at a rate of 20° C min -1 in a dry air low.

The FTIR spectra were obtained from a Thermo Fischer Scientiic 380 infrared spectrometer (Nicolet) (MK-Fe) or (MK-Fe) ca using the attenuated total relection (ATR) method. A drop of the geopolymer reactant mixture was deposited on the instrument's diamond crystal and protected with a small bell from any environmental pollution during the spectrum acquisition process, which was performed regularly until the end of the geopolymerization process. The IR spectra were gathered between 500 and 4000 cm -1 at a resolution of 4 cm -1 . The commercial software OMNIC (Nicolet Instruments) was used for data acquisition and spectral analysis. The spectra were recorded every 10 min for 13 h to permit the superposition of 72 raw spectra [14]. Measurements were carried out at different times.

The morphology of the inal products was observed using a Philips XL 30 scanning electron microscope (SEM) at 15 kV coupled with an EDX spectrometer. Prior to observations, a thin layer of Au/Pd was deposited on the samples.

The shrinkage per unit volume of samples is determined using (Equation 1):

(1) where V = (Π × Φ × H)/4, H is the height of the sample and Φ is the diameter of the sample.

RESULTS

Precursor mixtures

The properties of the geopolymer materials are strongly inluenced by the raw materials used during fabrication. The various raw materials used in the preparation of the geopolymer, such as the Imerys kaolin and iron oxide, are characterized using several different methods of physicochemical analysis. Physicochemical data, such as the speciic surface, D 50 (particle size) and wettability of the precursors, are shown in Table 1. The speciic surface area of the powders is similar for iron oxide (4 m 2 /g) and metakaolin (8 m 2 /g). These values do not change signiicantly during alkaline attack. The data analysis shows that the iron oxide particle size has a D 50 of approximately 0.1 µm, which is considered small. The metakaolin (M I ) has a D 50 of approximately 7.5 µm, which is slightly greater than the D 50 of kaolin (K I ). The (K I + Fe) no ca , (K I + Fe linitic phase without impurities. Calcination at 700°C leads to the dehydroxylation of the kaolinite, which is characterized by the amorphous nature of the metakaolin compound (M I ).

The diffractogram of the (K I + Fe) no ca mixture indicates the presence of kaolinite and iron oxide peaks. The diffractograms of the (K I + Fe) ca and (M I + Fe) mixtures show a disappearance of the kaolinite phase and the persistence of hematite after calcinations is completed. Therefore, the diffractograms of the (K I + Fe) ca and (M I + Fe) mixtures are similar to the original product due to the presence of the iron oxide peaks (Fe 2 O 3 ) (hematite). Mixing iron oxide into metakaolin or calcining the (K I + Fe) mixture provides no substantial structural modiication. This result is likely explained by no interaction taking place between the clay phases and the iron oxide at this temperature [15]. In comparison, the diffractogram of the Medenine clay (Figure 2g) is characterized by the presence of impurities (illite, quartz), unlike the precursors, which are based on kaolin and hematite. For the calcined samples, the presence of hematite and an amorphous clay phase may be favorable for the formation of geopolymerization reactions.

The thermograms of the K I, (K I + Fe) ca and (K I + Fe)

no ca samples are shown in Figure 3. An analysis of the sample K I thermogram (Figure 3a) reveals the presence of two endothermic peaks located at 120°C and 400°C, respectively. The irst peak corresponds to the loss of the physisorbed water molecules, and the second is related to the loss of the structural water. The exothermic peak at 984°C may be attributed to the nucleation of mullite [16] . The mass losses associated with these peaks agree within 1 % and 14 % of the pure kaolin peaks. An analysis of the (K I + Fe) no ca (Figure 3b) mixture reveals the presence of the same endothermic and exothermic phenomena, namely dehydration, dehydroxylation and recrystallization. The mass loss from the (K I + Fe) no ca mixture is calculated to be approximately 10 %. This loss, compared to the kaolin (14 %), is consistent with the addition of 5 % iron oxide. The thermogram of the (K I + Fe) ca mixture (Figure 3c) shows only the presence of a very low endothermic peak assigned to dehydration and an exothermic peak related to recrystallization.

The SEM pictures of the different precursors are shown in Figure 4. The characteristics of the hematite particles are < 1 micron in size, which agrees with the value for D 50 , which is very low (approximately 0.1 µm). Furthermore, these particles and the agglomerated hexagonal shape have a speciic surface area of approximately 4 m 2 /g (Table 1), which is consistent with this morphology [START_REF] Acebal | [END_REF]. The (K I + Fe) no ca mixture reveals the presence of layers of kaolinite and hematite particles. After calcination, the mixture is characterized by the presence of hematite particles and non-dehydroxylated sheets characteristic of kaolinite and metakaolin particles. Autef et al. [START_REF] Autef | Inluence of metakaolin purities for the potassium geopolymer formulation: existence of several networks[END_REF] observed the presence of partially dehydroxylated kaolin platelets. Both photos of the (M I + Fe) and (K I + Fe) ca SEM samples may be obtained in-situ or ex-situ because both mixtures have the same morphologies. This result is explained by the nonreactivity exhibited between the iron oxide and the clay material when treated at 700°C, as mentioned above.

These data show that the addition of 5 % Fe 2 O 3 does not affect the behavior of kaolin at this temperature, and therefore, there is no interaction between the Fe 2 O 3 and kaolin. This inding agrees with the literature [START_REF] Castellein | Inluence de la vitesse du traitement thermique sur le comportement d'un kaolin : application au frittage rapide[END_REF], which shows that these compounds are stable in the temperature range considered here.

Consolidated material feasibility

The raw materials precursors were used to synthesize consolidated material from a mixture of potassium silicate and potassium hydroxide. The different samples were placed in an oven at 70°C for 2 h in a closed mold.

To learn more about the geopolymerization reaction, volume shrinkage values are reported in Figure 5 that depend on the Si/K molar ratio of the sample. The data show two families of materials, one with a Si/K ratio greater than 0.99 and one with a Si/K ratio less than 0.99. The use of untreated kaolin provides materials with a drawal < 0.99, regardless of the value of the Si/K ratio. These cannot be considered geopolymer samples [20]. The use of calcined kaolin (M I ) produces two types of materials, one with a shrinkage of 1 and the other with a shrinkage of less than 0.99. The difference is due to the KOH content. A very large amount of KOH in the alkaline solution has the effect of bringing the different species together without a geopolymerization reaction, in agreement with the work performed by Gao et al. [21]. The addition of iron oxide (M I +Fe) creates a material with a shrinkage of less than 0.99. For low amounts of KOH in the alkaline solution, this phenomenon is minimized. It appears that the presence of iron oxide acts as a dispersant that limits the coating effect. These data are explained in further detail in the following sections.

Consolidated materials

The different samples were characterized during consolidation by IR spectroscopy and, after 7 days, by XRD, SEM and TGA /DTA.

Monitoring the progress of the geopolymerization reaction is performed using FTIR spectroscopy by following the displacement of the Si-OM band versus time (Figure 6). For different consolidation reactions, this displacement relects the formation of bonds characteristic of a speciic type of network [22,23]. The spectrum of the composition 0 G 0.18 synthesized with a small amount of KOH exhibits a displacement of approximately 9 cm -1 versus a displacement of approximately 6 cm -1 for large amounts of KOH. These two values are considered a low shift from the high initial wave number of 1003 cm -1 . For the samples containing only metakaolin ( 0 G 0.18 , 0 G 0.38 ), the displacements are recorded (28 cm -1 , 25 cm -1 ), and the initial values for the wave numbers are 998 cm -1 and 978 cm -1 . The spectra of the compositions 0.12Fe G 0.18 , 0.12Fe G 0.38 in the presence of iron show displacements of 30 approximately cm -1 and 35 cm -1 , respectively. For the composition 0.12Fe G 0.18 and 0.12Fe G 0.38 , the recorded displacements are 24 and 32 cm -1 , respectively. When using kaolin (K I ) in the presence of different quantities of KOH for the compositions ( 0 G 0.18 , 0 G 0.38 ), the observed shift is very small. In this case, it is very dificult to form stable Si-O-Al bonds, and the observed difference in terms of the amount of KOH is insigniicant because it lies within the uncertainty of the measurements. These results are consistent with the volume shrinkage, which shows that the samples are only consolidated and are not geopolymeric materials. The compositions ( 0 G 0.18 , 0 G 0.38 ) show a shift from an initial displacement, depending on the alkaline solution. When potassium is added, the number of non-bridging oxygen bonds increases the effect of reducing the initial value of the Si-OM band. In the presence of high quantities of KOH, the predominant silicate species are different. Indeed, for large amounts of KOH, there is a monomer depolymerization for Q 0 [24]. The decrease in the shift is important and proves that a polymerization reaction has taken place. The addition of iron to the mixtures 0.12Fe G 0.18 , 0.12Fe G 0.38 provides some information on the origin of this decreasing rate, which also depends on the initial amount of KOH in the solution and a similar shift (30 and 36 cm -1 , respectively). For samples containing (K I + Fe) ca , the same phenomena are observed. It appears that when the calcination of kaolin occurs in the presence of Fe 2 O 3 , the Si-O-Al or Si-O-K bonds form faster for the corresponding geopolymer without iron oxide. In this case, a geopolymer network forms, and the iron oxide particles are dispersed. For the three groups of samples investigated here, it seems that there are polycondensation reactions due to this shift that are consistent with the dimensional changes that were observed previously. The diffractograms of these samples (Figure 7) are characteristic of an amorphous dome located at 30°. However, a broad peak near 28° (2θ) was also formed and is similar to what has been observed in aluminosilicate systems [25]. The consolidated samples ( 0Fe G 0.18 , 0Fe G 0.18 ) contain a lot of water and have not been studied using X-ray diffraction. The formation of the amorphous dome is a characteristic feature of geopolymerization. However, in the presence of a larger amount of KOH, the intensity of the amorphous dome increases. This result may be due to additional phase dissolution in the presence of high concentrations of KOH [26] The SEM photos representative of the microstructure for the different synthesized samples are shown in Figure 8. The observed microstructures are characteristic of material consolidation in all of the compositions [27]. The noticeable presence of iron on the different samples suggests that the corresponding oxide did not react during the consolidation process. A comparison of a sample of 0.12Fe G 0.18 and the geopolymer synthesized based clay Medenine ( 0.18 G 0.5 )shows no difference in the microstructure. However, the detected particles highlight the unresponsiveness of iron during these consolidation stages at the microscopic level.

The main results based on these various formulations evidenced that the hematite addition don't modify the nature of the inal network due to polycondensation reaction. In effect, these compounds do not contain the iron as network formatter as evidence by Kriven et al [START_REF] Dileep | Collection of papers presented at the 33 rd international Conference on advanced Ceramics and composites[END_REF]. Indeed, in this work, the iron element was introduced in the form of magnetite. Nevertheless, the modiication of the slope, deduced from IR results, can be correlated to the coating of iron oxide particles with alkaline solution. In addition, the microstructure of different samples highlights the non-reactivity of iron during these stages of consolidation. In general, the contribution of iron oxide seems to be inactive in these conditions.

The thermograms of the various compositions are shown in Figure 9. The thermograms of the kaolin based samples 0Fe G 0.18 , 0Fe G 0.38 exhibit mass losses (36 % and 34 %) associated with the loss of the water in the mixture and the transformation of kaolin into metakaolin dehydroxylation at T = 500°C. The amount of KOH introduced does not affect these curves.

For the other six samples containing metakaolin, the mass loss is between 10 and 15 %, suggesting that these compounds are preferred for polycondensation reactions that may lead to geopolymerization [START_REF] Duxon | [END_REF]. No matter which sample is examined, the irst endothermic peak has at least two contributors, one at 80°C and the other at 180°C. This result suggests that the water is physisorbed and eliminated during the heat treatment. The endothermic peak at 450°C may be attributed to an aluminosilicate compound that forms via different reactions in a basic environment [30]. Indeed, phase-type zeolites may be formed. In this case, the concentrations of [Si] and [K] are, respectively, 22 and 9 g mol -1 for the sample of 0.12Fe G 0.18 in the zeolite formation zone, as determined by Prud'homme et al. [31]. However, in the presence of a large amount of KOH, the formation of this compound is less common. We also consider the presence of iron, which may change the formation of these phases by changing the reaction medium. It has been proven that there is no interaction between the iron oxide and the potassium hydroxide. The silicate species containing KOH remains around the particles of hematite [8].

Geopolymer with Fe admixture show low values of mechanical properties (Table 1) because of the friable character of these materials display different networks aluminosilcates in agreement with the results of Cheol et al., 2012 [6]. They have showmen that the addition of Fe 2 O 3 in geopolymer systems decreased the mechanical properties. Indeed, as example, the addition of 5 % of Fe 2 O 3 leads to a decreasing from 70 to 32 MPa.

DISCUSSIONS

The materials obtained from polycondensation reaction were amorphous. Their formation could be described by the silicate solutions containing KOH remains around the particle of hematite and interacting with metakaolin evidencing the presence of different networks. So to investigate the various networks formed, it is important to study the reactivity of the mixture determined by FTIR measurements and the temperature stability of the samples by thermal analysis.

The evolution of the band shift of the Si-OM depending on the slope reduced the amount of water contained in the solution SiK [START_REF] Gouny | Nouveau système constructif multi matériaux bois/liant géopolymères/brique de terre crue: formulation, caractérisation et transfert d'échelle[END_REF] for all samples is reported in Figure 10. From these data, it is possible to deine the existence of various types of materials depending on their chemical composition and their rate of silicon by reactive surface as established by the work of Gouny [31]. Indeed, for a value of between 0 and 22 cm -1 , it had preferentially polycondensation reactions between siliceous species leading to gel formation, whereas for above 22 cm -1 value, the formation of different aluminosilicate networks is preponderant. From these data, the samples (K I ), present low values of displacement, are composed of at least a binder phase that maintains a partial cohesion. In this case, the formed materials are simply agglomerated with alkaline solution and drying. Conversely, the other samples (M I , M I -Fe, K I -Fe) with different rate of KOH, have respectively values of displacement (28, 35, 32 cm -1 : Si/K = 0.2). Their slopes values are low not exceeding -0.1 cm -1 /s. Consequently, there is formation of different networks consist in geopolymer binder phase type, aluminosilicate phase and/or a platelet adhesion unaltered by excess solution [START_REF] Autef | Formulation géopolymère: inluence des rapports molaires Si/K et Si/Al sur les réactions de polycondensation au sein de gels aluminosilicatés[END_REF].

The evolution of the band shift of the Si-OM according to the water mass loss (Table 2) of the different samples in [200 -500°C] is shown in Figure 11. The compositions of K I in the presence of different levels of KOH ( 0Fe G 0.18 , 0Fe G 0.38 ) show low weight loss justifying their brittle character. For compositions containing iron oxide, such as ( 0.12Fe G 0.18 , 0.12Fe G 0.38 , 0.12Fe G 0.18 , 0.12 G 0.38 ), the calculated weight loss increases as the FTIR shift decreases. With the exception of the M I and K I based samples, only a slight decrease in the mass loss is recorded with increasing displacement.

It is noted that for all compositions containing iron oxide, the amount of water increases as the displacement decreases.

These results agree with the formation of geopolymer consolidated materials. In effect, the compounds containing (K I -Fe), (M I -Fe) and M I have molar compositions corresponding to the geopolymers or stratiied compounds identiied by Gao et al. in ternary Si-Al-K-O [21].

Finally, the data obtained on the reactivity of the raw materials, the behavior of the reaction mixture, the inal structure of materials, allow the proposal of the model of reactivity during synthesis presented in Figure 12. The potassium silicate solution was placed in the presence of different sources of aluminosilicates that causes formation of different networks: (i) metakaolin (M I ) leads to the formation of a geopolymer gel phase and a rich siliceous species (ii) kaolin (K I is simply agglomerated with the alkaline solution by drying (iii) mixtures of (Fe + K I ) ca or (M I + Fe) leads to the formation of a compound consisting of a solid network geopolymer in interaction phase with an aluminosilicate coating solution.

CONCLUSIONS

In this work, we have discussed consolidated materials obtained from kaolin or metakaolin mixed with iron oxide. These materials were characterized in-situ and after consolidation using different characterization methods.

The analysis of the precursor materials reveals that regardless of the calcined precursors utilized in this study, they are characterized by the presence of hematite and an amorphous phase derived from the clay components. The existence of an amorphous dome on the diffractograms of the consolidated materials and the shift of the Si-O-R + band are characteristic of a polycondensation reaction. It appears that when the kaolin is calcined and iron oxide is present, Si-O-Al or Si-O-K bonds form faster in the consolidated material than without iron oxide. The presence of a higher concentration of KOH may inluence the formation of consolidated materials.

Representative characterization by electron microscopy of the microstructure of different samples highlights the non-reactivity of iron during these stages of consolidation.

The role of iron in geopolymerization has not been adequately explored. The presence of iron oxide modiies the formation of geopolymer compounds leading to the formation of consolidated materials. In fact, these materials contain different speciic networks with geopolymer binder. The interactions between various networks inhibit mechanical properties.

Figure 1 .

 1 Figure 1. Synthesis protocol of consolidated materials.

  ) ca and (M I + Fe) mixtures have D 50 values of approximately 5, 7 and 7 µm, respectively. These values demonstrate the effect of powder agglomeration during calcination. The diffractograms of the different precursors used in this study are shown in Figure 2. The Imerys kaolin (K I ) precursor has a diffractogram characteristic of a kao-Vf = Vi final volume of sample after 2 h its removal from the oven initial volume of sample

Figure 2 .

 2 Figure 2. X-Ray patterns of a) kaolin, b) calcined kaolin, c) Fe 2 O 3 , d) (K I +Fe) ca , e) (M I +Fe), f) (K I +Fe) no ca and g) Medenine clay calcined at 700°C precursors (JCPDS Files: K: kaolinite (00-003-0059), H: hematite (04-008-7624), Q: quartz (04-012-0490), I: illite (00-002-0462), M: muscovite (04-012-1956).

Figure 3 .

 3 Figure 3. Weight loss and heat low curves for a) K I , b) (K I + + Fe) no ca and c) (K I +Fe) ca . c) (K I + Fe) ca

Figure 4 .Figure 5 .

 45 Figure 4. SEM micrographs Fe 2 O 3 (a), (K I + Fe) no ca (b), (K I + Fe) ca (c) and (M I + Fe) (d) of various precursors. c) (K I + Fe) ca

Figure 6 .Figure 7 .

 67 Figure 6. Evolution of Si-O-R + band shift versus the time of reaction of polycondensation. a)

  700 (K I -Fe) ca 700 (K I -Fe) ca

Figure 8 . 5 b

 85 Figure 8. MEB photos of consolidated materials. c) 0.38 G 0.5

Figure 8 .Figure 9 . 18 c

 8918 Figure 8. MEB photos of consolidated materials. g) 0.18 G 0.5

Figure 10 .

 10 Figure 10. Evolution of shift versus slope for various samples.

Figure 11 .

 11 Figure 11. Evolution of shift versus water loss (mole number) for various samples.

Figure 12 .

 12 Figure 12. Schema of the various steps leading to K I , M I , (K I + Fe) ca and (M I + Fe) settings materials.

Table 1 .

 1 Various data of raw and consolidated materials.

		Si/K	Si/Al	SBET (m 2 /g)	D 50	Wetting (cm 3 /g)	Compressive strengh (MPa)
	K I	-	1	6	7.0	1.50	-
	M I	-	1	8	7.5	1.40	-
	Fe 2 O 3	-	-	4	0.1	0.96	-
	(K I + Fe) non ca	-	1	6	5.0	1.15	-
	(K I + Fe) ca	-	1	7	7.0	1.25	-
	(M I + Fe)	-	-	7	7.0	1.18	-
	0.12Fe G 0.18	2.28	1.17	-	-	-	1.0
	0.12Fe G 0.38	1.39	1.17	-	-	-	3.0
	0.12Fe G 0.18	2.28	1.17	-	-	-	1.0
	0.12Fe G 0.38	1.39	1.17	-	-	-	2.0
	0Fe G 0.18	2.55	1.15	-	-	-	1.0
	0Fe G 0.38	1.56	1.15	-	-	-	3.0
	0Fe G 0.18	2.24	1.18	-	-	-	1.0
	0Fe G 0.38	1.38	1.18	-	-	-	2.0

Table 2 .

 2 Moles number determined by thermal analysis of samples.

	Samples	Number of moles of water (10 -5 ) [25 -200°C] [200 -500°C] [< 500°C]
	0.12Fe G 0.18 700 M I -Fe 0.12Fe G 0.38 700 M I -Fe 0.12Fe G 0.18 700 (K I -Fe) ca 0.12Fe G 0.38 700 (K I -Fe) ca 0Fe G 0.18 700 M I 0Fe G 0.38 700 M I 0Fe G 0.18 25 K I	4.19 9.22 6.35 10.15 13.02 9.14 6.55	1.51 1.26 2.83 1.69 4.55 4.57 0.428	1.35 2.44 1.03 2.07 3.01 0.15 -
	0Fe G 0.38	5.70	1.026	-

Ceramics -Silikáty 58 (1)1-11 (2014)


Didier Bertil

Agathe Roullé

Gildas Noury

Claude Prepetit

Ronaldine Gilles

Rochenel Sylvain

Julio Jean-Philippe

AN IBC APPROACH FOR SEISMIC MICROZONING AT CAP-HAÏTIEN (HAÏTI)

A seismic microzoning was performed for Cap Haitien city in Haiti. This city is as much exposed to seismic hazard as Port-au-Prince struck by the January 2010 earthquake. Many complementary investigations in geology, geophysics and geotechnics were needed to define areas of homogeneous soil response. The cross-analysis of this information allowed us to distinguish five soil classes with lithological site effects. The soil columns responses were simulated through a 1D nonlinear analysis using CyberQuake software. Design response spectra were produced with the shape defined for ASCE 7-05/IBC(2009) code and specific amplification factors Fa and Fv. The seismic microzoning highlight that the majority of the urban area is located on soft soil or very soft soil with strong lithological site effects over large areas.

INTRODUCTION

The magnitude 7.1 earthquake that struck Haiti on January 12, 2010, caused great damage and over 230,000 casualties in the metropolitan area of Port-au-Prince in the southern part of Haiti. This earthquake is one of the deadliest known after those of Tangshan in China in 1976 and Sumatra in Indonesia in 2004.

Haiti is located at the western part of Hispaniola Island lying along the boundary between the North American and Caribbean plates. Geodetic studies (i.e., [START_REF] Demets | Effect of recent revisions to the geomagnetic reversal timescale on estimates of current plate motions[END_REF] showed that the Caribbean plate moves eastward at about 20 mm/year with respect to the North American plate. In Haiti, this motion is mainly partitioned between two major strike-slip fault systems, the Enriquillo Plantain Garden fault (EPGF) in the south and the Septentrional fault (SF) in the north (Figure 1). The 2010 event had an epicenter close to the trace of the EPGF.

In the Northern coast, Cap-Haitien is the second largest city of Haiti with similar tectonic settings to Port-au-Prince: it is close to the Septentrional Fault system and very long time has passed since the last highly destructive earthquake. The city was completely destroyed by the M8 earthquake of May 8, 1842.

Following the 2010 earthquake, a program of seismic microzoning for the most vulnerable cities of the country was initiated by the Haitian government. These studies are conducted in partnership between LNBTP, BME for Haiti and BRGM for France. In the North, those microzonings are part of a United Nation Development Program started in 2012: "The Seismic risk reduction plan for northern Haiti".

The seismic microzoning of Cap-Haitien covers an area of 40 km 2 for its extension until Quartier Morin at East. It assesses topographic and lithological site effects, liquefaction and landslide hazards. This paper focuses on lithological site effects.

METHODOLOGY

To take into account lithological site effects, microzoning aims at defining specific soil classes based on a cross analysis of geological, geotechnical and geophysical information collected on the studied area. Regional hazard is not redefined but is based on the works of [START_REF] Frankel | Documentation for Initial Seismic Hazard Maps for Haiti[END_REF] representing the seismic hazard for rock conditions and a probability of exceedance of 2% in 50 years (return period of 2475 years). We follow the recommendation of the future Haitian seismic code CNBH2012 which advocates the use of these maps in the current state of knowledge.

This zoning is performed following several steps:

mapping of surficial geological formations; -compilation / analysis of geological, geophysical, geotechnical existing data; -geophysical and geotechnical surveys to supplement existing data; -cross-analysis of geological, geophysical and geotechnical information; -identification of homogeneous areas in terms of seismic response; -definition of one or more 1D representative soil columns for each zone; -calculation of seismic responses for each soil column; -fusion of areas with equivalent seismic responses. Expected ground motions are very strong. [START_REF] Frankel | Documentation for Initial Seismic Hazard Maps for Haiti[END_REF] found pga=0.35g for 475-y return period and pga=0.60g for 2475-y return period on rock site. Soils consist mostly of recent colluvium and very soft alluvium. In this context, a non-linear behavior is expected for some kind of soils and must be taken into account for seismic response spectra calculation.

The seismic design response spectrum of each class of soil is based on those described in ASCE 07-5/IBC(2009) building code on which the CNBH2012 will rely in the future. For our specific soil classification, we choose to keep the same shapes for design response spectra but considering specific amplification factors Fa for short period (0.2s) and Fv for mid-period (1.0s).

MAPPING OF SUPERFICIAL FORMATIONS

The most precise available geological map was produced by BME (Bureau des Mines et de l'Energie) at 1 / 250 000 scale [START_REF] Boisson | Carte géologique à 1/250 000 de la République d'Haïti. Feuille Nord-Est (feuille[END_REF], for North East of Haiti) and is not detailed enough to be usable for the microzoning (Figure 2). The boundary between rock and recent sediment formations is too imprecise. Sedimentary facies of the Quaternary are grouped into a single unit. A re-assessment of geological mapping was performed at the scale of the urban agglomeration to improve our understanding of superficial deposits [START_REF] Monthel | Cartographie géologique des villes de Cap-Haïtien, Fort-Liberté et Ouanaminthe (République d'Haïti)[END_REF], Figure 2). 14 superficial formations are described. This new geological mapping shows that the historical city center (labeled as "Cap Haïtien" in figure 2) is located on colluvium at the foot of a Cretaceous mountain and that the new districts at East extend over thick Quaternary alluvial deposits in the plain and coastal zones.

Figure 2. Geological map reassessed for the project at a 1: 25 000 scale. On top left, the geological map at 1:250 000 from [START_REF] Boisson | Carte géologique à 1/250 000 de la République d'Haïti. Feuille Nord-Est (feuille[END_REF]. The studied area is represented by the red line.

GEOPHYSICAL AND GEOTECHNICAL DATA

The existing data collection brought together 23 georeferenced geotechnical drilling profiles unevenly distributed over the area and more concentrated around the historical city center. Geophysical data (H/V, MASW) concern only some isolated point. Those data were completed by a geophysical and geotechnical campaign operated by the LNBTP in order to refine our knowledge on mechanical properties of superficial deposits and to improve the spatial distribution of the data. These new data consist in: MASW profiles at 31 sites, H/V measurements at 54 sites and 12 geotechnical drillings with CPT or SPT values and laboratory tests (Figure 3).

CROSS-ANALYSIS OF INFORMATION

Figure 4 shows geophysical interpretations superimposed with the superficial formations map. Recent alluvium of the coastal plain are characterized by H/V peaks between 0.5 Hz and 1.2 Hz and VS 30 values between 130 and 250 m/s. Colluvium of the historical center (Northern area) and to the west along the foot of the mountain also show strong H/V peaks but with higher frequencies 3-5 Hz and higher Vs30 values (350 to 600 m/s).

On some sites, geotechnical and geophysical information can be confronted directly. Figure 5 shows MASW, H/V spectrum and SPT profiles at point A located on superficial colluvium. We see a soft soil on the first 8 meters then stiff soil. The seismic bedrock is reached at 25 m. At point B on a site of the alluvial plain (Figure 6), the thickness of very soft soil is at least 30 m A B . A cross analysis of all available data is performed to define homogeneous zones in terms of geology, resonance frequency and mechanical properties. Then, for each zone, representative soil columns are defined to perform 1D seismic response simulations. For each layer of the soil columns, the following parameters are defined: thickness of the layer, geological interpretation, Nspt from SPT drillings, shear waves velocity Vs from MASW profiles, material property (either sand, clay or gravel behavior), density h, plasticity index IP The coherence between the resonance frequency derived from H/V measurements and the characteristics of the soil column was also checked before simulations. Figure 7 shows the cross-analysis realized for soil class 3 dominated by superficial colluvium and the resulting soil column. The alluvial plain is characterized by very soft soils and spectra with a very broad constant acceleration branch (0.19-0.95s for class 2) and with a low acceleration plateau spectrum. Class 3, 4 and 5 correspond to a transition between the outcropping rock of the mountain and the alluvial plain. They are characterised by increasing amplification for low-period (Fa 1.2-1.7) and for mid-period (Fv from 1.5 to 2.5) when getting closer to the alluvial plain.

Amplication factors Fa and Fv are then compared to those proposed by ASCE 07-5/IBC(2009) for soils with equivalent Vs30 and the same level of rock site acceleration (Figure 10). As for IBC, Fv increases when Vs30 value decreases. But no such correlation is seen for Fa.

In this study, we choose to keep the simplified shapes of the design spectra proposed by ASCE 7-05/IBC(2009) and to represent the specific classes of soils only by modifying Fa and Fv factors. In that way, microzoning results are easily usable by engineers familiar with IBC. Secondly, it allows a partial decoupling of the local hazard due to soil response and the regional hazard. Provided that the acceleration levels do not change a lot in the future updates of the regional hazard assessment, design spectra could be reproduced without modification of the study. We have noted, however, that the very simplified forms of design spectra do not fit perfectly with the spectra output from 1D simulations and require compromises in the choice of Fa and Fv.

Fa and Fv are different than those proposed with the standard classification in ASCE 7-05/IBC(2009). This justifies the implementation of microzonings on the basis of crossing geological, geotechnical and geophysical information instead of a simple characterization of the VS30 velocity.

CONCLUSIONS

The level of local seismic hazard knowledge for this region of Haiti is low. Geology and tectonics need to be updated at a scale compatible with an urban area scale. Lack of seismic monitoring involves great uncertainty about the regional hazard. The site effects microzoning presented here required numerous additional geological, geophysical and geotechnical investigations to characterize the different kind of soils of the studied area.

Five specific soil classes were defined with amplification factors Fa and Fv globally higher than those proposed in the IBC code for similar values of VS 30 . Short period amplification factor Fa is particularly high on the west side of the area where we have soft shallow formations and where the substratum is shallower. In the alluvial plain, very soft soil is present at great depth and low bearing capacity of foundation soil is expected. An aggravating factor is a high liquefaction hazard that has not been detailed here.

Cap Haitien is then heavily exposed to seismic risk, because of its proximity to seismic sources, of its great seismic vulnerability of buildings, its high concentration of population but also because of the very poor soil quality. The seismic microzoning highlight that the main part of the urban area is located on soft soils or very soft soils with strong lithological site effects over large areas.

Figure 1 .

 1 Figure 1. Seismotectonic setting of Hispaniola from Douilly et al. (2013). The January 2010 earthquake is shown with a blue star and black focal mechanisms. Cap-Haitien is displayed as a yellow square. The city is on the vicinity of the Septentrional Fault (red line named SF) and has been totally destroyed by the M8 earthquake of 1842. Other main historical earthquakes are shown (years in black and red focal mechanisms)

Figure 3 .

 3 Figure 3. Main data used for site effect zoning. See the legend of Figure 2 for geological background. H/V spectral ratios, MASW and SPT profiles for the sites A (cité administrative) and B (centre éducatif Suzanne Flon) are illustrated on Figure 5 and Figure 6.

Figure 4 .

 4 Figure 4. Joint interpretations of geological and geophysical measurements.

Figure 5 .

 5 Figure 5. MASW profile, SPT profile and H/V curves for Point A

Figure 7 .

 7 Figure 7. Column of soil for the colluvium area (part of class 3 of the final microzoning) and examples of H/V peaks, MASW profiles and NSPT profiles.

Table 1 .Figure 9 .

 19 Figure 9. Elastic response spectra for the 6 soil classes. Spectrum for outcropping bedrock (Class 0) is represented in green.

Figure 10 .

 10 Figure 10. Comparisons of amplification factors Fa (left) and Fv (right) found for this microzoning (MZ) and proposed in IBC code.

Seismic Risk Unit, BRGM, Orléans-France, d.bertil@brgm.fr

LNBTP, Port-au-Prince, Haïti, claudeprepetit@hotmail.com

BME, Port-au-Prince, Haïti

CALCULATION OF SEISMIC RESPONSES

Seismic responses are first estimated using CyberQuake software [START_REF] Modaressi | Computer aided seismic analysis of soils[END_REF] through 1D non-linear simulation. The input bedrock motions consist in 4 accelerograms (2 are real ones and 2 are modified from real ones) with response spectra close to the design spectrum for rock sites. Seismic responses were first simulated for 9 initial zones. After calculations, results were compared and similar seismic response zones were grouped to obtain finally 5 specific soil classes to complement the outcropping rock class 0 (Figure 8). Five-percent-damped design spectra are constructed on basis of 1D response spectra simulations with the same shapes as those recommended by IBC ( 2009). The design ground motion parameters are the ordinate values S DS and S D1 that equal to accelerations at short periods and 1 second period respectively. S DS defines the plateau of the design spectrum between periods T0 and TS. Between TS and TL the constant velocity branch is given by S D1 /T and beyond TL the constant displacement branch is given by S D1 TL / T 2 . TL is considered to be higher than 4.0 as defined for U.S. in NEHRP.

S DS and S 1 are derived from S S and S 1 , the spectral accelerations of the hazard maps of [START_REF] Frankel | Documentation for Initial Seismic Hazard Maps for Haiti[END_REF] for Haiti from PSHA at 2475-y return period and from individual amplification coefficients Fa (low-period) and Fv (mid-period) defined for each class of soil.

The seismic design response spectra are represented in Figure 9 and associated parameters in Table 1.