Ngoc Phuong Pham

A Toumi
email: toumi@insa-toulouse.fr

Anaclet Turatsinze

N-P Pham

Effect of an enhanced rubber-cement matrix interface on freeze-thaw resistance of the cement-based composite

Keywords: Rubber aggregates, rubber-cement matrix interface, rubber coating, freezethaw resistance, durability factor, strain capacity

Introduction

Rubber aggregates (RA) addition into cementitious mixtures was reported to improve resistance of cement-based composites to freeze-thaw action [START_REF] Benazzouk | Durability of cement-rubber composites under freeze thaw cycles[END_REF][START_REF] Paine | Use of crumb rubber to achieve freeze/thaw resisting concrete[END_REF][START_REF] Al-Akhras | Properties of tire rubber ash mortar[END_REF][START_REF] Topçu | Durability of rubberized mortar and concrete[END_REF][START_REF] Turgut | Physico-mechanical and thermal performances of newly developed rubber-added bricks[END_REF][START_REF] Paine | Research on new applications for granulated rubber in concrete[END_REF][START_REF] Richardson | Freeze/thaw protection of concrete with optimum rubber crumb content[END_REF][START_REF] Gesoglu | Abrasion and freezing-thawing resistance of pervious concretes containing waste rubbers[END_REF]. Benazzouk et al. [START_REF] Benazzouk | Durability of cement-rubber composites under freeze thaw cycles[END_REF] studied the frost behaviour of cement-rubber composites in which RA contents were ranging from 0% to 40%. The authors reported a reduction in both mass loss and relative dynamic modulus loss of the materials containing 30% and 40% of RA by volume, demonstrating an improvement in frost resistance of the composites. According to Paine et al. [START_REF] Paine | Use of crumb rubber to achieve freeze/thaw resisting concrete[END_REF], 6% volume of RA incorporation was suitable to improve frost durability in terms of resisting scaling phenomenon and of limiting a decrease in relative dynamic modulus. However, due to bond defects at rubber-cement matrix interface, performance of rubberized concrete under freeze-thaw conditions appeared less impressive than that of the one manufactured with a high content of air entrained [START_REF] Paine | Use of crumb rubber to achieve freeze/thaw resisting concrete[END_REF]. Al-Akhras et al. [START_REF] Al-Akhras | Properties of tire rubber ash mortar[END_REF] investigated relative dynamic modulus of elasticity during freeze-thaw actions and reported that, compared to the control mortar, the ones incorporating rubber ash (size 0.15 mm) as natural sand replacement at two distinct levels of 5% and 10% by weight exhibited higher durability factor, which was determined according to ASTM C666/C666M standard [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF]. It should be noted that relative dynamic elastic modulus is defined as a variation in the dynamic modulus of the specimens.

The detrimental effect of RA addition on freeze-thaw resistance of rubberized cementbased composites was also reported. Karahan et al. [START_REF] Karahan | Fresh, mechanical, transport, and durability properties of self-consolidating rubberized concrete[END_REF] partially replaced natural sand in self-consolidating concretes with RA (size 4.75-0.15 mm) at different RA contents of 0%, 10%, 20% and 30%, by volume. Their experimental results showed some spalling on surface of rubberized concrete specimens, and a gradual loss in flexural strength and mass was observed with an increase of rubber content. Similarly, acording to investigations of Savas et al. [START_REF] Savas | Freeze-thaw durability of concrete with ground waste tire rubber[END_REF], increasing rubber volume would decrease the freeze-thaw durability of rubberized concrete, which was measured according to ASTM C666/C666M standard [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF] using procedure A. Among previous studies, Richardson et al. [START_REF] Richardson | Freeze/thaw protection of concrete with optimum rubber crumb content[END_REF] found that washing RA before adding them to cementitious mixtures led to a composite with lower pulse velocity but reduced weight loss under freeze-thaw conditions. As reported by Si et al. [12], resistance of rubberized concrete to freeze-thaw environments appeared more significant in composites incorporating 15% by volume of sodium-treated RA replacing fine aggregates (rubber size 1.44 -2.83 mm and 40-minute sodium treatment with the concentration of 4%), especially in terms of preventing both mass loss and relative dynamic elastic modulus reduction.

As briefly summarized above, there is still no consensus about the role of RA in cementitious mixtures against freeze-thaw conditions. Also, all previous studies have only evaluated durability of rubberized cement-based composites to frost actions thanks to mass loss and changes in relative dynamic modulus of elasticity. Moreover, no investigations have been assessed on bond effects between RA and cement matrix on freeze-thaw durability of the composites. This study therefore aims to characterize freeze-thaw resistance of two rubberized mortars, one of them incorporating polymer-coated RA, as demonstrated by Pham et al. [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF], to obtain an enhanced RA-cement matrix interfacial transitional zone. The mass loss, changes in ultrasonic pulse velocity and relative dynamic modulus of elasticity, residual mechanical properties (compressive and flexural strengths), durability factor, and especially length change of these mortars under freeze-thaw actions were investigated and compared to the ones of control mortar.

Materials and methods

Materials and mix proportions

As mentioned earlier, control mortar and two rubberized ones were investigated. Materials used for making these mortars include cement CEM I (52.5 R), natural sand (0-4 mm), RA (similar size as sand), and water. It should be noted that, in these rubberized mortars, only 30% volume of sand was replaced by RA. Compared to higher specific gravity (2.62) and significant water absorption (1.9%) of sand, RA have a lower density of 1.2 and are hydrophobic materials. These characteristics can explain a reduction in workability and segregation phenomena of rubberized cement-based mixtures. Hence, superplasticizer and viscosity agent were used to maintain workability and to make sure homogeneity of the composite, respectively. It is worth recalling that hydrophobic nature of RA is a main reason of higher porosity in rubberized cement-based composites due to air-entrapment effect when RA are in contact with mixing water. Obviously, bond defects at untreated rubber-cement matrix interface also contribute to such property. The difference in size distribution between RA and sand used in this work is described in Fig. 1.

Three mortars studied (control, untreated and coated rubberized ones) and their mix proportions are presented in Table 1. It should be noted that acronyms UR and CR denote Untreated Rubber and Coated RA, respectively; letter P stands for coPolymer, which is as bonding material to enhance the interfacial zone between RA and cement matrix. The rubber-cement matrix enhancement demonstrated in Fig. 2 was obtained using a coating method [START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF]. Firstly, RA were required to precoat with styrene-butadiene-type copolymer (2% mass of RA). The processed RA were then maintained in a conditioned room fixed at 20 • C temperature and at 50% relative humidity for 1 hour. This step is necessary for copolymer's condensation and stabilization on RA surface. Finally, pre-mixed cementitious mixture was prepared for a light and short mixing with coated RA.

Prismatic mortar specimens (40 mm x 40 mm x 160 mm) were prepared for freeze-thaw test. For monitoring length change, during mould preparation and casting process, two steel pinholes were embedded at the center of two head ends of mortar specimens.

Then 24 hours after casting, the specimens were demoulded and placed in the curing room maintained under controlled atmosphere (20 • C temperature and 95% relative humidity) for 27 days before starting freeze-thaw cycles.

Freeze-thaw test programme

The freeze-thaw resistance test of control and rubberized mortars was carried out according to NF P18-424 standard [START_REF] Nf P | Concrete -Freeze test on hardened concrete -Freeze in water -Thaw in water[END_REF] in combination of ASTM C666/C666M-15 standard -Procedure A [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF]. An environmental chamber is used to simulate freeze-thaw cycles. It is able to induce the highest and lowest temperatures, namely 150 • C and -40 • C.

In order to induce frost actions, temperature inside the chamber can be controlled by either a chamber sensor or the one embedded in the core of a specimen (Fig. 5). In this work, freeze-thaw cycles were established in accordance with the latter case. Actual temperatures in the chamber and at the core of a mortar specimen were recorded during the test. The temperature-controlled specimens illustrated in Fig. 3 were made of untreated rubberized mortar (30UR). The authors' experience showed that during casting and hardening process or under freeze-thaw actions, the thermal sensor embedded at the center of the temperature-controlled specimen can fail, stop to work and need to be replaced by another specimen. Hence, to prevent these hazards, several temperature-controlled specimens were prepared and placed in the chamber as tested specimens. The curing pro-cess of such specimens was similar to the one of tested mortars. One should notice that the connecting systems including electronic wire lines and the sensor connectors must be protected under high moisture condition of curing. Fig. 4 shows the temperature cycle set-up for the freeze-thaw test. The black, red, green colors indicate the target freeze-thaw temperature, and the ones of the chamber and at the core of the control specimen, respectively. The actual core temperature was

dropped from 4 ± 2 • C to -18 ± 2 • C for around 3.0 hours, kept at -18 ± 2 • C for 0.5 hour, raised from -18 ± 2 • C to 4 ± 2 • C
for other 2.0 hours, and kept at 4 ± 2 • C for 0.5 hour. The duration of a freeze-thaw cycle was 6 hours. It therefore allowed 4 cycles per day to be conducted. This core temperature cycle obtained was quite adapted to the requirement of standards [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF][START_REF] Nf P | Concrete -Freeze test on hardened concrete -Freeze in water -Thaw in water[END_REF]. Indeed, it was difficult to set up the core temperature of the controlled specimen close to the one inside the chamber due to requirement of thermal conductivity time into mortar specimens.

The arrangement of mortar specimens in the chamber is shown in Fig. 5. Before transferring the specimens into the chamber, the initial length, mass, and ultrasonic pulse velocity of prismatic mortar specimens were measured. Compressive and flexural tests were also carried out in order to determine initial strengths. It should be noted that the specimens were required to dry carefully using a sponge to remove only surface water before weight measurement. In general, the freeze-thaw test is continuing until the mortar specimens have been subjected to 300 cycles or terminated earlier if the relative length change overpasses 500 µm/m [START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF] or 1000 µm/m [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF]; or the relative dynamic modulus of elasticity falls below 60%, as recommended in standards [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF][START_REF] Nf P | Concrete -Freeze test on hardened concrete -Freeze in water -Thaw in water[END_REF]. In this study, the test was finalized when the expansion of mortar specimens exceeds 0.1% (1000 µm/m) of its original dimension.

After a given number of freeze-thaw cycles, length change, mass loss, ultrasonic pulse velocity were measured. Flexural and compressive tests on the prismatic mortar specimens were only performed at 130 cycles and at the test end. Details of necessary tests are described as below.

Mass loss and length changes

During the freeze-thaw test, the specimen mass was simply measured by weighing the surface-dried specimens using a scale with an accuracy of 0.01 g. The mass loss is determined according to Eq. [START_REF] Benazzouk | Durability of cement-rubber composites under freeze thaw cycles[END_REF], where m o and m i are weights before starting freeze-thaw test and after i cycles of freezing and thawing, respectively. A length sensor with a precision of 1 µm was used for determining the length of mortar specimens. Length gain (dimensional expansion) is then calculated according to Eq. ( 2), where L 1 , L i are the readings on the length sensor at the beginning of the test and at the i th freeze-thaw cycle, respectively; and L 0 is the initial distance between two steel pinholes (specimen length of 160 mm). The average mass loss and length change from three specimens of each mortar were reported.

M ass loss

(%) = m 0 -m i m 0 . 100 (1)
Length gain

(µm/m) = L i -L 1 L 0 (2)

Ultrasonic pulse velocity test

The ultrasonic pulse velocity was determined according to NF EN 12504-4 standard [START_REF]Testing concrete. Part 4: Determination of ultrasonic pulse velocity[END_REF].

The tester used mainly consists of a control unit (an electrical pulse generator, an amplifier, and an electronic timing device) and a pair of transducers. The devices with a frequency of 54 kHz are used to generate an ultrasonic pulse to travel on the path length of 160 mm from the transmitting transducer to the receiving one. The apparatus must be calibrated at every testing time using a calibration bar. The time duration for acoustic wave to propagate through the longitudinal direction of the specimen and the ultrasonic pulse velocity were recorded. Three specimens of each mortar type and at least five measurements for each specimen were taken to make sure that the variation between the measured transit time on single tested specimen should be within ± 1 % of the mean value of these three measurements. Note that the specimen surface contacted with transducers must be smooth enough by coating a quick-setting epoxy resin, especially when mortars are subjected to damage after a given number of freeze-thaw cycles.

From values of ultrasonic pulse velocity, a relative dynamic modulus of elasticity (P c ) is calculated as Eq. ( 3) [START_REF] Pleau | Durability of concrete in cold climates[END_REF], where v c and v o are ultrasonic pulse velocities at the c th cycle of freezing and thawing and at time right before starting freeze-thaw test, respectively.

The durability factor (DF) is finally determined at the end of freeze-thaw test using Eq.

(4), as recommended by ASTM C666/C666M-15 standard [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF].

P c (%) = v 2 c v 2 0 . 100 (3)
DF = P.N M (4)
where P (%) is relative value of dynamic elastic modulus at N th cycle; N is the number of freeze-thaw cycles at which P drops to the minimum value for terminating the frost test (60% as required by standards [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF][START_REF] Nf P | Concrete -Freeze test on hardened concrete -Freeze in water -Thaw in water[END_REF]) or the selected number of freeze-thaw cycles when

frost actions are to be ended (whichever is less); and M is the specific number of cycles at the end of freeze-thaw test.

Flexural and compressive tests

The flexural and compressive tests were carried out on prism mortar specimens according to NF EN 1015-11 standard [START_REF] Nf En | Methods of test for mortar for masonry[END_REF]. Firstly, three point-bending tests were carried out on prismatic mortar specimens to get load-bearing capacity. The two rollers of the flexural tests were spaced at a distance of 100 mm. Two parts of specimens obtained after the bending tests were then compressed on an area of 40 mm x 40 mm to obtain the compressive strength. The loading rates of flexural and compressive tests were 0.05 kN/s and 0.5 kN/s, respectively.

3 Results and discussion

Mass loss

Fig. 6 shows mass loss versus number of freeze-thaw cycles for three types of mortars.

The untreated rubberized mortar specimens were observed to increase slightly in mass for the first 50 cycles of freezing and thawing. It is due to the higher air-void density of this mortar, which still absorbs water to reach a critical degree of saturation [12]. The mass of the control mortar specimens started to decrease quickly since the 160 th cycles of freezing and thawing, and to become severely deteriorated at approximately 200 cycles compared to other rubberized mortar specimens (Fig. 7). A slight difference in mass loss was also observed between rubberized mortar using untreated RA and the one incorporating copolymer coated RA.

Length gain

The expansion of all mortar specimens under the freeze-thaw action is illustrated in Fig. 8. It can be clearly seen that the length gain of control mortar is much higher than the one of rubberized mortars. The smaller length change of rubberized mortar specimens exposed to freeze-thaw cycles can be explained as below:

(i) As demonstrated from Scanning Electron Microscope (SEM) observations and air permeability values from the same composites [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF], incorporation of RA in cementitious mixture induces high porosity not only at the poor rubber-cement matrix interface, but also especially high density of air pores in the core of cementitious matrix. It means that many escape spaces are formed in rubberized mortars. As explained by Mehta et al. [START_REF] Mehta | Concrete: Microstructure, properties, and materials[END_REF], much lower temperature was required to freeze water in capillary pores than the one in gel pores. Higher energy state in gel pores forces water to transport to the capillary ones in order to balance the energy between these pores. Therefore, such escape spaces in rubberized cement-based composites play an important role to reduce energy gradient, leading to a decrease in expansion of rubberized mortars. Normally, spacing factor, a parameter associated with the distance from the periphery of an air void to adjacent ones in cementitious matrix measured on microscopic scanning pictures of air-void system according to ASTM C457/C457M [START_REF]Standard test method for microscopical determination of parameters of the air-void system in hardened concrete[END_REF] is used to estimate whether the cement-based composites are resistant to freeze-thaw actions [21]. However, due to unexpected problems related to polishing procedure of rubberized mortar specimens, spacing factor is therefore difficult to qualify accurately [START_REF] Savas | Freeze-thaw durability of concrete with ground waste tire rubber[END_REF]. Additional voids would be generated due to low stiffness of RA and bond defects available at untreated rubber-cement matrix interface.

(ii) It is necessary to recall that low stiff RA should help in absorbing energy induced by a given damage process [START_REF] Ho | Effects of rubber aggregates from grinded used tyres on the concrete resistance to cracking[END_REF]. Hence, compared to the control mortar, high amount of energy from freeze-thaw actions in rubberized composites is assumed to be released.

(iii) Low water porosity and capillary absorption of rubberized cement-based composites compared to the control one can reduce the volume change due to ice formation.

Moreover, high water absorption of natural aggregates (sand) is also detrimental to the durability under freeze-thaw performance than RA that do not absorb water.

(iv) According to Sahmaran et al. [START_REF] S ¸ahmaran | Assessing the durability of engineered cementitious composites under freezing and thawing cycles[END_REF], tensile strain capacity and strain-hardening behaviour were also important to prevent damage from freeze-thaw actions. As demonstrated by previous authors [START_REF] Turatsinze | Mechanical characterisation of cementbased mortar incorporating rubber aggregates from recycled worn tyres[END_REF][START_REF] Turatsinze | Positive synergy between steel-fibres and rubber aggregates: Effect on the resistance of cement-based mortars to shrinkage cracking[END_REF][START_REF] Turatsinze | On the modulus of elasticity and strain capacity of self-compacting concrete incorporating rubber aggregates[END_REF], low stiffness property of RA is beneficial to improve strain capacity, the deformation at failure of rubberized cement-based composites, and to result in higher residual post-peak tensile strength. Hence, freeze-thaw resistance of rubberized mortars was consequently improved.

The difference in length change between rubberized mortar incorporating untreated RA and the one using coated RA was also observed. Rubberized mortars incorporating coated RA exhibited a slightly higher expansion. It can be explained by the fact that rubber coating resulted in an improved rubber-cement matrix bond and a partial reduction in gel and capillary pores in the composite. The frost resistance of mortar specimens can be evaluated through the total number of freeze-thaw cycles at which the relative length change exceeds 500 µm/m [START_REF] Nf P | Concrete -Freeze test on hardened concrete -Freeze in water -Thaw in water[END_REF] or 0.1% of the original length [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF]. As illustrated in Fig. 8 and Table 2, it can be concluded that rubberized mortars are more resistant to freeze-thaw environments in term of length change due to a tolerance towards a greater number of freeze-thaw cycles.

Ultrasonic pulse velocity

The ultrasonic pulse velocity of mortar specimens over a freeze-thaw test period is presented in Fig. 9. The initial ultrasonic pulse velocities of rubberized mortars after 28 days in the curing room were lower than the one of control mortar. Higher density of pores in the cement matrix due to air entrapment phenomenon during casting process of rubberized cementitious mixtures, bond defects at untreated rubber-cement matrix interface, and low density of the composite are qualified explanations why the transmitting time of ultrasonic pulse waves in rubberized mortars is delayed, leading to low pulse velocity of rubberized mortars.

Under frost actions, the pulse velocity of all mortar specimens remained similarly as original values over the first 50 cycles of freezing and thawing. After this period, while pulse velocity of rubberized mortars seemed to be still constant, the one of control mortar decreased gradually and reached the value lower than the one of rubberized mortars after approximately 180 cycles of freezing and thawing. This is a consequence of damage induced by ice pressure inside the control mortar. On the contrary, presence of RA can absorb energy induced by volumetric expansion during phase change of water. Therefore, control mortar was less durable than the rubberized mortars, which highlighted the greater relevance of the pores induced by presence of RA in the composites. Coating RA with copolymer seemed to have no specific effect on a change of pulse velocity during a 200 freeze-thaw cycle testing period.

Based on ultrasonic pulse velocity, cement-based materials can be classified as excellent, good, questionable, poor and very poor qualities [START_REF] Malhotra | Testing hardened concrete: Nondestructive methods[END_REF]. One found that initial pulse velocity values of all control and rubberized mortars were greater than 3660 m/s and less than 4575 m/s, thus classifying them as good mortars. At the end of freeze-thaw test, while rubberized mortars still remained their original classification, the control mortar dropped to a lower standard, a questionable one.

The number of freeze-thaw cycles where relative dynamic modulus of elasticity falls below 60% is also considered as a parameter to express the frost resistance of mortar/concrete [START_REF]Standard test method for resistance of concrete to rapid freezing and thawing[END_REF]. Fig. 10 presents the relative dynamic modulus of elasticity over a period of 200 cycles of freezing and thawing. It can be clearly seen that none of control mortar specimens was freeze-thaw resistant after 200 cycles. On the contrary, rubberized mortar specimens exhibited a very good performance under frost action. Durability factor (DF) determined at the test end for three types of mortars is compared in Table 2. Based on durability factor values, Hansen [START_REF] Hansen | Recycling of demolished concrete and masonry[END_REF] reported that freeze-thaw resistance of cement-based composites can be classified as follows: Nonresistance to freeze-thaw actions (DF ≤ 40%), doubtful frost resistance (40% <DF ≤ 60%), acceptable frost resistance (60% <DF ≤ 80%), and frost resistance (DF > 80%). Therefore, it can be concluded that incorporating 30% volume of RA (0 -4 mm) to cementitious mortars as a sand replacement produced "frost resistance" of rubberized mortars compared the "doubtful frost resistance" of the control one.

Loss of compressive and flexural strengths

The The enhanced bond between RA and cement matrix was observed to maintain mechanical properties (flexural and compressive strengths) with increasing the number of freeze-thaw cycles. It is explained by Sahmaran et al. [START_REF] S ¸ahmaran | Assessing the durability of engineered cementitious composites under freezing and thawing cycles[END_REF] that, in addition to the air-void system, other parameters such as high tensile strain capacity and strain-hardening behaviour of cement-based composites are important for resisting cycles of freezing and thawing. As reported by Pham et al. [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF], coating RA with copolymer before mixing them with cementitious mixture was demonstrated to improve strain capacity and residual post-peak tensile strength compared to the untreated one. Therefore, the coated rubberized mortar was still durable under freeze-thaw cycles regardless of a slight length gain as reported above.

Conclusions

Freeze-thaw resistance of rubberized mortars were investigated and compared to the one of control mortar. From experimental results, the following conclusions can be drawn:

• Rubberized cement-based composites were more resistant to frost environments than the control one. It was especially validated based on the length change.

• Durability of rubberized mortars under freeze-thaw conditions can be attributed to high energy absorption and hydrophobic nature of RA and to lower water capillary absorption, high strain capacity and better residual post-peak performance of the composites.

• Rubber coating to enhance rubber-cement matrix interface led to a slight increase in length change of coated rubberized mortar under freeze-thaw actions, but the composite was still more durable than the control mortar under frost environment.

  residual compressive and flexural strengths after 130 freeze-thaw cycles and at the test end are presented in Figs. 11 and 12, respectively. One should note that zero values of such mechanical properties of the control mortar at the test end because of a serve deterioration on the surface of the specimens. At the 130 th cycle of freezing and thawing, compressive and flexural strengths of the control mortar were decreased by 33% and 31%, respectively. Despite low expansion and insignificant change in pulse velocity of untreated rubberized mortar specimens, a slight reduction in compressive and flexural strengths of this type of mortar was still observed. It can be attributed to the additional water absorption of untreated rubberized mortar during the first period of freeze-thaw action.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Difference in size distribution between sand and RA

Figure 4 :

 4 Figure 4: Freeze-thaw temperature cycle set-up

Figure 5 :Figure 6 :

 56 Figure 5: Specimen arrangement in freeze-thaw chamber (unit: mm)

Figure 7 :

 7 Figure 7: Degradation of mortar specimens at test end

Figure 8 :

 8 Figure 8: Length changes versus number of freeze-thaw cycles

Figure 9 :Figure 10 :

 910 Figure 9: Changes of ultrasonic pulse velocity versus freeze-thaw cycles

Figure 11 :

 11 Figure 11: Compressive strength versus freeze-thaw cycles

Figure 12 :

 12 Figure 12: Flexural strength versus freeze-thaw cycles

Table 2 :

 2 Frost resistance of mortar specimens

	Mix name

List of Tables


Valérie Canals
email: valerie.canals@univ-montp3.fr

Claude Diebolt
email: cdiebolt@unistra.fr

Magali Jaoul-Grammare
email: jaoulgrammare@beta-cnrs.unistra.fr

Charlotte Le Chapelain
email: charlotte.le-chapelain@univ-lyon3.fr

Education, Defense Spending and Economic Growth in Japan: 1868-1940. Understanding the Time Series Dynamics

Keywords: JEL Classification: C32, H50, N15, O53 Cliometrics, Time Series Analysis, Economic Growth, Education, Military Expenditures, Japan, Outliers. Éducation, depenses militaires et croissance economique Cliométrie, Croissance économique, Dépenses militaires, éducation, Japon, Outliers, Séries temporelles

published or not. The documents may come

Introduction

No economic research can present a monistic explanation of growth. Indeed, the effects of many variables overlap to create a favourable texture for economic expansion. Military investment is perhaps an important factor but it can only have an effect if it is supported by a combination of political, economic and social circumstances. Analysis of socio-economic activity in Japan from the viewpoint of military investment does not therefore give any prior decisive importance to this factor at the expense of the other structural variables. However, given the fundamental role played by military expenditure in the country's economic growth, we consider that it is important to stress this impact. But is there a connection between the level of development in Japan and the level of military expenditure? The reply seems obvious. Nevertheless, the question of knowing whether military expenditure is the cause or in contrast the result of economic development is far from having been settled by the specialists and the two hypotheses are still opposed!

The pattern of development of Japan's military expenditure clearly shows growth over a long period and threshold effects. This would seem to strengthen Wagner's law of growth of public expenditure (1904,1913) in which public expenditure increases with economic growth. Furthermore, relatively high growth rates are observed periodically, followed by a period of low growth rates. This definition corresponds to growth in stages consisting of alternate highs and lows. In their study of federal expenditures in the United States, [START_REF] Kendrick | A Century and a Half of Federal Expenditures[END_REF] outline this phenomenon without providing theoretical explanation for it. In a study published in 1961, Peacock and Wiseman refer to the same type of development in stages in the United Kingdom as the 'displacement effect'. The amount of resources likely to be produced by the fiscal system (but without causing discontent) determines the amount of public expenditure. They considered that the displacement effect was a direct result of the war.

As was put forward by Von [START_REF] Ciriacy-Wantrup | Agrarkrisen und Stockungsspannen. Zur Frage der langen Welle in der wirtschaftlichen Entwicklung[END_REF], the greatest changes seem to be those caused by wars and revolutions through the economic, institutional and population changes that they necessarily cause. According to this analysis, the long periods of good times are basically caused by the vast governmental expenditures relating to preparation for war and the war itself, while the periods of chronic hard times, on the other hand, are caused by the difficult readjustments incident to the sharp decrease of war expenditures. The best case for this thesis can probably be made with respect to the first long wave (1793/1797-1847/1850). During the long period of the Napoleonic wars, vast government's expenditures gave a stimulus to economic expansion and hastened the changes in the economic system ushered in by the Industrial Revolution. There is little doubt that the impact of these wars played a very considerable role. Similarly, the sharp decrease of expenditures, together with the necessary readjustments to a peacetime basis after the whole of western Europe had for a quarter of a century adjusted itself to war conditions, goes far toward explaining the difficulties of the long period of chronic hard times from 1817 to the end of the 1840s. More recently, [START_REF] Goldstein | Long Cycles. Prosperity and War in the Modern Age[END_REF] established a link between the turning points in long cycles of the economy and the periodic outbreak of wars.

Starting from this point, the aim here is to study the nature and importance of the links that may exist between the structural dynamics of military expenditure and that of the socioeconomic system (economics, demography, etc.). Does the dynamic of the socio-economic system impulse military development or might it rather be the evolution and change in military financing that changed the economic and social system in Japan before World War 2? Following previous causality analysis [START_REF] Diebolt | Les dépenses militaires, moteur de la croissance économique japonaise? Une analyse cliométrique: 1868-1940[END_REF], we investigate here a dynamic analysis (outliers methodology) in order to determine if the socio economic context and especially the conflict context influences the Japanese economy.

The article is in three parts. A succinct description of the state of the art is followed by a description of our database. We then discuss the results of our cliometric tests.

STATE OF THE ART

The economic role of military expenditures can't be limited to their volume. Defence economic is related to many economic sectors and the analysis of the impact of military expenditures implies to examine the whole economic system. From a macroeconomic point of view, military expenditures appear as a part of public expenditures and consequently as a part of the "autonomous demand". However, other mechanisms have been integrated to this Keynesian explanation. If their results don't converge, all of them underline the dynamics related to military expenditures.

From a theoretical point of view, many models try to explain the causes and consequences of military expenditures. Added to the econometric analysis, there are two main approaches in defence economics: the models of "arms race" [START_REF] Richardson | Generalized foreign politics[END_REF][START_REF] Richardson | Arms and Insecurity[END_REF] and the models of public economy. The first ones generally used game theory in order to analyse the behaviour of many countries; the second ones applied mathematical optimization in order to explain coalition between countries (Matelly, 1997).

At the empirical level, if it is impossible to analyse all papers which deal with the influence of military expenditures on economic growth, it appears that the model -keynesian or neo classical-and the length of the time period studied, influence the results. Indeed, a keynesian model generally underlines short term negative effects of the military expenditures on economic growth [START_REF] Huang | Defence expenditures and economic growth: the externality effects[END_REF][START_REF] Batchelor | Military spending and economic growth in South Africa[END_REF], on employment [START_REF] Dunne | Military expenditure and employement in South Africa[END_REF]. Other studies show a positive effect of military expenditures on economic growth [START_REF] Atesoglu | Defence spending and economic growth[END_REF][START_REF] Nair | Growth and defence : pooled estimates for the NATO alliance, 1951-1988[END_REF][START_REF] Diebolt | Les dépenses militaires, moteur de la croissance économique japonaise? Une analyse cliométrique: 1868-1940[END_REF] while [START_REF] Jacques | Relations causales entre les dépenses militaires et leur environnement macroéconomique : tests partiels pour la France et les Etats-Unis[END_REF] don't find any relationship between economic growth and defence spending. Finally, many studies underline a causal relationship between military expenditures and economic growth without providing insight about the sign of this relationship [START_REF] Joerding | Economic growth and defence spending: Granger causality[END_REF]Chowdury, 1991;[START_REF] Kollias | Defence expenditure and economic growth in the European Union: A causality analysis[END_REF][START_REF] Yildirim | Military expenditure and economic growth in Middle Eastern countries: A dynamic panel data analysis[END_REF].

In their panel data analysis on European Union, [START_REF] Kollias | A panel data analysis of the nexus between defence spending and growth in the european union[END_REF] highlighted a positive feedback between growth and military expenditures in the long run and a positive impact of the military expenditures on growth in the short run. Their results are in line with those of [START_REF] Lee | Do defence expenditures spur GDP? A panel analysis from OECD and non-OECD countries[END_REF] on 27 OECD countries and 62 non-OECD countries. They underlined different effects according to the fact that the country is part of OECD or not: they distinguished a positive causal effect from GDP to military expenditures for OECD countries whereas for non-OECD ones, there is a negative causal effect from military expenditures to GDP.

The influence of military expenditure has also been examined by numerous papers about the development of the Asian economies. At this stage, no clear-cut role has been brought to light. For example, Benoit was the first in 1973 to test empirically a model aimed a priori at demonstrating that the slowing of the growth in developing countries results from the scale of the resources devoted to defense. Nevertheless, the author's results showed the opposite. This work was fairly surprising, revealing a positive correlation. Indeed, the countries that had borne the largest expenditure were those with the fastest growth. According to Benoit, expenditure on defense might therefore have favourable effects on growth that are strong enough to make up for the negative effects. He also considers that military expenditure creates a reassuring context that is favourable for investment and hence for growth.

Other authors such as [START_REF] Dunne | Economic Effects of Military Expenditure in Developing Countries: A Survey[END_REF], [START_REF] Ram | Defense Expenditure and Economic Growth[END_REF], [START_REF] Deger | Military Expenditure and Developing Countries[END_REF] and then [START_REF] Caro | Croissance et dépenses de défense dans les pays de l'Asean[END_REF] subsequently discussed the question. All these studies tend to show that military expenditures do not have one particular effect on growth but that the effect varies in time and space. According to Deger and Sen, for example, only two of the nine channels by which expenditures on defense can influence growth display a positive impact: Benoit's positive externalities channel and the Keynesian channel of support for overall demand. According to [START_REF] Ram | Defense Expenditure and Economic Growth[END_REF], although empirical studies do not reveal a positive effect of military expenditure on growth, they do not make it possible to conclude that it has a negative impact. He considers that this indecision results, on the one hand, from econometric weaknesses (related to the problem of the measurement and imprecision of the series) and, on the other hand, from the heterogeneity of the countries studied. For [START_REF] Looney | Arms Races in the Middle East: A Test of Causality[END_REF], economic production has a significant positive influence on defense spending. Finally, [START_REF] Caro | Croissance et dépenses de défense dans les pays de l'Asean[END_REF], in his analysis of the ASEAN countries from 1967 to 1993, highlights the importance of the positive externalities of military expenditure for 'the coherence of the growth strategy' of these countries. Nevertheless, numerous authors continue to attribute the rapid growth of the Japanese economy (during the post-war period) to the low level of military expenditure (1% of GNP). Concerning other countries, [START_REF] Dunne | Military Spending and Economic Growth in the Peripherical Economies of Europe: A Causal Analysis for Greece, Spain and Portugal[END_REF] suggest a positive impact of military burden on growth for Greece and, on the contrary, a negative effect for Spain, while for Portugal, there is no evidence of any causal links. They also show [START_REF] Dunne | Military Spending, Investment and Economic Growth in Small Industrialising Economies[END_REF]) that military spending does not have a positive effect on growth in the long run, but would appear to have a clear negative short run effect.

DATABASE AND METHODOLOGY

A triple base of original data drawn from the work of [START_REF] Ohkawa | The Growth Rate of the Japanese Economy since 1878[END_REF][START_REF] Ohkawa | National Income (Volume 1: Estimates of Long-Term Economic Statistics of Japan since 1868[END_REF], [START_REF] Taeuber | The Population of Japan[END_REF] and [START_REF] Diebolt | Accounting Expenditures on Education. Japan from the Meiji Restoration to the Second World War[END_REF] is used to analyse the evolution of the Japanese economy before World War 2.

The following indicators are considered between 1881 and 1940:

-total expenditure on education (DEDUC); -military expenditure (DMILI); -capital expenditure (DCAP); -gross national product (GNP); -total government expenditure; -national income; -national debt; -price index;

As an extension to the causality pattern [START_REF] Diebolt | Les dépenses militaires, moteur de la croissance économique japonaise? Une analyse cliométrique: 1868-1940[END_REF], we introduce here an alternative econometric technique for shock analysis: the outliers methodology. 5 Our basic assumption is to say that the regular shocks we observe for the Japanese socioeconomic development are superposed by irregular shocks, which appear rarely. Through this approach, we ask whether the long-term economic development of Japan is caused by such extraordinary shocks and wars especially. If this was the case, economic growth could probably not be explained as a systematic process but would have to be traced back to specific historical events.

«Outliers represent sudden temporary or permanent shifts in the level of a time series.

There are several methods for the detection of outliers based on intervention analysis as originally proposed by [START_REF] Box | Intervention Analysis with Applications to Economic and Environmental Problems[END_REF]. An often used procedure is that of [START_REF] Tsay | Outliers, Level Shifts, and Variance Changes in Time Series[END_REF]. This method was also used by [START_REF] Balke | Large shocks, small shocks, and economic fluctuations: Outliers in macroeconomic time series[END_REF], althought with some modifications. Here we will use an improved algorithm by [START_REF] Chen | Joint estimation of model parameters and outlier effects in time series[END_REF], which is readily available, with slight modifications, in the computer program TRAMO developed by [START_REF] Gómez | Programs TRAMO and SEATS: Instructions for the user[END_REF]Maravall (1997, 2001) ». 6 In this paper, we analyse three main outliers: AO, LS and TC.

Consider a univariate time series * t y which can be described by the ARIMA(p, d, q) model:

t t a B y B B ) ( ) ( ) ( *     ( 7
)
where B is the lag operator, at is a white noise process,

) ( ), ( ), ( B B B   
are the lagged polynomials with orders d, p, q, respectively.

The outliers can be modelled by regression polynomials as follows:

   I t i i t t I B y y ) ( ) ( *    (8) where * t y is an ARIMA process, ) (B i 
is the polynomial characterizing the outlier occurring at time t = , i  represents its impact on the series and

) ( t I
is an indicator function with the value 1 at time t =  and 0 otherwise. In this paper, three 7 main outliers are classified as:

-Additive Outliers (AO) that affect only a single observation at some points in time series and not its future values. In terms of regression polynomials, this type can be modelled by setting:

1 ) ( 1  B  .
-Level Shifts (LS) that increase or decrease all the observations from a certain time point onward by some constant amount. In this case, the polynomial:

) 1 ( 1 ) ( B B i    .
-Temporary Changes (TC) that allow an abrupt increase or decrease in the level of a series which then returns to its previous level exponentially rapidly. Their speeds of decay depend on the parameter

) 1 ( 1 ) ( B B i    
, where 0<<1.

It is considered that AOs are outliers, which are related to an exogenous and endogenous change in the series, respectively, and that TCs and LSs are more in the nature of structural changes. TCs represent ephemeral shifts in a series whereas LSs are more the reflection of permanent shocks.

An ARIMA model is fitted to * t y in (7) and the residuals are obtained:

) 9 ( , ) ( t t Y B â   where ... 1 ) ( ) ( ) ( ) ( 2 2 1      B B B B B B      
For the three types of outliers in (8), the equation in (9) becomes:

AO: ) ( ) ( 1    t t t I B a â   TC: ) ( ) 1 ( ) ( 2     t t t I B B a â          LS: ) ( ) 1 ( ) ( 3    t t t I B B a â          7
There is a fourth main outlier that is not detected in this analysis: the innovative outlier (IO) that affects temporarily the time series with the same dynamics as an innovation. The polynomial is then

) ( / ) ( ) ( B B B i     .
IOs will have a relatively persistent effect on the level of the series.

These expressions can then be viewed as a regression model for t â , i.e.,

t t i i t a x â   ,  With:
for all i and t < : 0 ,  t i x for all i and t = :

1 ,  t i x for t >  and k  1: (LS). 1 ; (TC) ; (AO) 1 , 3 1 1 , 2 , 1                 k j j k t k j k j j k k k t k k t x x x      
The test statistics for the types of outliers are given by: AO:

  2 / 1 2 , 1 1 1 ) ( ) ( ˆ         n t y a x       TC:   2 / 1 2 2 2 , 2 ) ( ) ( ˆ         n t a t x       LS:   2 / 1 2 , 3 3 3 ) ( ) ( ˆ         n t t a x            n t y i n t t i t i x x â     2 , , ) ( ˆfor i = 1,

Cliometric results

The outliers methodology clearly shows that the dynamic of the process that led to economic growth and development in Japan was dependent of political events, especially the Sino-Japanese and the Russo-Japanese Wars (Annex 1).

National income

No outlier

In order to explain the importance of the influence of various outliers, we consider the two main events which influence both military expenditures and others variables: the Sino Japanese War and the Russo Japanese War.

The Sino-Japanese War broke out in 1894. There may be several explanations for this war. Among these, mutually related factors such as the need to find new markets is probably a crucial one! The war resulted in provoking further nationalism, stimulating national unification, and gradually changing the industrial structure. The victory is also the result by superior spirit and equipment, which may be ascribed to the development of education and the foundation of the industrialisation since the early Meiji period. From a purely economic perspective, the Sino-Japanese War enlarged the domestic financial and capital market through rising military expenditures based on public loans, stimulated military technology and general industry (by the distribution of military expenses). The war also reinforced the foundation for the development of light industry by assuring it connection with the Chinese market, and provided a foundation for the growth of heavy industry. The experience of the 8 The demographic time series is excluded from our test for the main reason that growth and change in the population dynamics rarely have an instantaneous effect.

war was immediately related to demands for domestic steel production, extending railways, reinforcement of the number of vessels, promotion of shipbuilding etc. Responding to such progress in industrialisation, secondary and higher education began to be consolidated. It is also significant that the Gold Standard was established in 1897 as a result of the reparations paid to Japan after the war. In addition to the influence on military expenditures (1894; 1896), this event also has an impact on educational expenditures (1895). In line with our previous paper [START_REF] Diebolt | Les dépenses militaires, moteur de la croissance économique japonaise? Une analyse cliométrique: 1868-1940[END_REF], a causal relationship from the military expenditures to the educational expenditures seems to be verified. So, historical events seem to affect first the military sector and then influence the rest of the economy and especially the educational sector.

Within only ten years after the Sino-Japanese War, the Russo-Japanese War started. The competitive invasion into China stimulated the Boxer Rebellion in 1899. In 1901, the Peking Protocol was concluded, but during the process, opposition arose between Russia and the United States and England. In 1902, the Anglo-Japanese Alliance was formed and the Russo-Japanese War started in 1904. This event was far larger in scale then the Sino-Japanese War in military expenditures, the number of mobilised military forces and the duration of the war. The scale of the war influenced education as well as the whole economy. The Ministry of education summarised the influence of the war upon school children and parents in the following account: the war made them realise the importance of education and academic skills, and stimulating their ambitions for learning; world and nationalistic concepts were clarified, and knowledge of economics, geography, science, military affairs etc. was provided; the war offered an opportunity for cultivation of the virtues of patriotism, public spirit, chivalry, sympathy, obedience, self-respect and progressiveness; the war made them realise the importance of business; the war made the parents and communities accept the necessity of the establishment of schools as basic assets. This war, in contrast to the Sino-Japanese War, was developed in an abnormal situation. Japan was inferior in the number of soldiers and arms, but was superior in the quality of the soldiers. Before country acquired a decisive victory either politically or militarily, the Peace Treaty was conducted through Roosevelt's mediation during the 1905 Revolution in Russia. This victorious war was the turning point for Japanese politics and its economy, initiating its rapid conversion to imperialism! As for the Sino Japanese War, according to [START_REF] Diebolt | Les dépenses militaires, moteur de la croissance économique japonaise? Une analyse cliométrique: 1868-1940[END_REF], a causal relationship appears for the Russo-Japanese War. This war affected military expenditures (1904), education expenditures (1905) and the national debt (1906).

How can we explain the role of the military expenditures?

There are, at least, three hypotheses to explain state's motives of increasing the defence spending [START_REF] Castillo | Military Expenditures and Economic Growth[END_REF]:

-Ambition: military expenditures vary with the economic power. This suggests that military spending is a positive function of economic growth. This relation can occur through another variable like capital expenditure [START_REF] Diebolt | Les dépenses militaires, moteur de la croissance économique japonaise? Une analyse cliométrique: 1868-1940[END_REF].

-Fear: military expenditures are a function of the state's insecurity. "The greater the level of threat to a state's security, the higher the level of military spending" (Castillo & al., 2001, p. 53). This reason has been modeled by [START_REF] Looney | Arms Races in the Middle East: A Test of Causality[END_REF] following the work of [START_REF] Richardson | Arms and Insecurity[END_REF] who thought that military expenditures of a country depend on military expenditures of another one. [START_REF] Castillo | Military Expenditures and Economic Growth[END_REF] also analyzed this possibility: they include US military expenditures in order to explain Japanese military expenditures and showed that there is a significant effect.

-Legitimacy: States use aggressive foreign policies and high levels of military expenditures to deflect domestic troubles.

Contrary to the two first hypotheses which refer to an international system, the latter one refers to a domestic determination of the level of the military expenditures. Concerning Japan, we suggest three main hypotheses in order to explain the increase of the military expenditures (Table 2). During the period 1870-1890 Japan begins its period of modernisation with the Meiji Restoration. The country knew an economic takeoff and military expenditures increased rapidly but economic growth didn't imply an expansionist foreign policy so that the ambition hypothesis cannot explain this period. However, fear appears to be the principal motivation of the period of Meiji Restoration.

During the period 1891-1913, military expenditures were driven by territorial expansion. The increase in economic growth pushed up military spending as well as more ambitious foreign policy. However the willingness to extend territory can also explain a feel of fear. So the two hypotheses can explain this period.

The last period is characterised by the three hypotheses: fear (growth of the Russian military capabilities and a possible conflict with the Soviet union over a territory in China), legitimacy (willingness to build a Japanese empire despite scarcity resources) and ambition (between 1934 and 1938, Japanese GDP grew from 30$ billion to 55$ billion and spurred military spending in an ambitious way to expend territory). Whatever the reason of the increase on the military expenditures, their role seems to have a lagged effect on the economy. Indeed, the influence on the education sector is lagged of one year and the effect on national debt (for the Russo Japanese war) is lagged of two years. In order to verify this lagged influence, we calculate on the one hand, correlation coefficients and on the other hand, we estimate with ordinary least squared, a single equation explaining (1) the education expenditures in function of lagged (-1) military expenditures and (2) the national debt in function of lagged (-2) military expenditures. The correlation coefficient between education expenditures and lagged (-1) military expenditures equals 0,69 and the single equation shows a significant influence of the lagged military expenditures on educational expenditures (t-stat = 7, 33; R²=0,48). Between national debt and lagged (-2) military expenditures, the correlation coefficient equals 0,71 and the single equation also shows a significant influence (t-stat=7,57; R²=0,61).

Conclusion

This paper has investigated the impact of defense spending on Japanese long-term development. Military expenditures can therefore be considered as driving forces behind the economic growth process of the country. Our analysis also shows that the amount of military expenditures governs those of education and capital expenditures. This being so, even if the level of the former is a direct cause of the level of economic growth, it is clear that although the level of capital expenditures encourages economic growth it is initially governed by the initial growth level. Chronologically, Japan therefore seems to have developed its military and education sectors, enabling a certain degree of growth, and this favoured capital expenditures. The latter then played the determinant role of driving force behind growth. This conclusion has important lessons for current topics in policy, especially for the question of the sources of growth. The subject is of renewed interest since the early 1980s. The so-called 'endogenous' growth theories have been used to extend and go beyond the traditional 'exogenous' growth model [START_REF] Aghion | Endogenous Economic Growth[END_REF]. The main factors of endogenous growth, that may or may not generate externalities, are the accumulation of knowledge, public infrastructure and human capital. In addition, there is inquiry into how the economic effects of education may derive directly from individuals and indirectly, through their descendants (the legacy effect) and via other individuals, as well as into how economic activity affects education systems and the types and levels of education offered. After the initial contributions, the themes investigated were different: models based on human capital accumulation insist more on social inequalities or on the relationship between inequalities and growth; models based on R&D insist more on the Schumpeterian issue of destructive creation and its impact on the labour market as well as nations' specialisation or persistent development gaps. Taken as a whole we feel rather confident that there are historically important effects of education and knowledge on growth. We are less confident that the effects of education on growth are as large as is claimed by the growth theories [START_REF] Diebolt | Education, Knowledge and Economic Growth. France and Germany in the Nineteenth and Twentieth Centuries[END_REF].

Future studies may investigate more systematically the role of military policy, wartime periods and defense expenditures as a main engine for growth. Wars are special moments in the metamorphosis of economic structures. They take the form of stages during which the economic sphere has to change under the weight of political issues. They deform probably part of reality, but are not just milestones marking the turning points of history. They exist as facts of considerable importance for past, present and future economic growth of many countries.

Future works must also take into account the phenomenon of terrorism in the models of defense economics [START_REF] Fontanel | Les fondements (avoués et non avoués) de l'évolution des dépenses militaires depuis[END_REF] and especially the rationality of the actors and the asymmetrical information. Indeed, with terrorism, the amount of defense expenditures will not be directly linked to the quantity of the military expenditures of an unfriendly state but it will more depend on the detection of a threat. The 1904 peak was caused by the Japanese attack of the Russian installations at Port Arthur. The Russian-Japanese war (won by Japan) was the first conflict between major powers since 1870. The phase of strong increase in defense expenditure that began in 1937 corresponds to Japan's invasion of China.

  Time Series Regression with ARIMA Noise, Missing Observations, and Outliers) the critical value is determined by the number of observations in the series based on simulation experiments. The different test statistics at time t =  are compared in order to identify the type of outlier. The one chosen has the greatest significance such as

			2, 3.
	where	1 ˆ  )( ( i	) 3
	An outlier is identified at time t =  when the test statistics	( ˆ 	)	exceeds a critical
									i
	value. In TRAMO () ( max ˆ   i max  . When an outlier is detected, we can adjust the observation	t Y at time t =  to
	obtain the corrected * t Y via (8) using the	i  ˆ, i.e.	t Y		t Y		t * i i ) (   I v	. Finally, the procedure is
	repeated until no outlier is detected. A multiple regression on * Y is performed on the various
									t
	outliers detected to identify spurious outliers.

i  

denotes the estimation of the outlier impact at time t = , and a ˆ is an estimate of the variance of the residual process.

Table 1 Outlier detection 8

 1

		Total educational expenditure
	Year	Type	Value	T-stat	Event
	1896	LS	0,1546	5,83	Sino Japanese War
	1905	AO	-0,069934 -5,01	Russo japanese War
	1916	LS	0,24798	9,45	WW1
		Military expenditure
	Year	Type	Value	T-stat	Event
	1894	TC	1,254	11,13	Sino Japanese War
	1896	AO	-0,38199	-5,4	Sino Japanese War
	1904	TC	0,83041	11,23	Russo Japanese War
	1937	LS	0,60083	5,85	Japan's Invasion of China
			National debt
	Year	Type	Value	T-stat	Event
	1906	LS	1,0622	4,97	Russo Japanese War
	Capital expenditure	No outlier
	Price index	No outlier
	GNP	No outlier
	Total Gov Exp	No outlier

Table 2 . The possible explanations of the increase of the military expenditures

 2

	Period	Hypotheses	Events
	1870-1890 Fear		Meiji Restoration and Satsuma Rebellion
	1891-1913 Ambition and Fear	Sino and Russo Japanese Wars
	1919-1939 Ambition, Fear and Legitimacy Japan's Invasion of China

For the reader interested in the complete mathematical and statistical presentation of the outlier methodology, please cf.Darné and Diebolt, 2004, 2006.

 Darné and Diebolt, 2004, p. 1452.