Jean-Charles Coulon

Amulets and Talismans in the Earliest Works of the Corpus Bunianum

The thirteenth-century Sufi shaykh al-Būnī is the putative author of an important corpus dealing with occult sciences in the Islamicate world, known in Western scholarship as the corpus bunianum.* The best-known of these magical texts attributed to him is The Great Sun of Knowledge (Shams al-maʿārif al-kubrā), and another of the more famous works in this corpus is the Source of the Foundations of Wisdom (Manbaʿuṣūl al-ḥikma), a compilation of four epistles. It has now become clear, however, that the works that al-Būnī actually authored have more to do in nature with Sufi theory and practice rather than strictly magical purposes. His limited corpus nevertheless became the basis of an important magical tradition especially through the extensive commentaries by later esoterists. While al-Būnī's earliest books were seminal in feeding the later magical tradition, the information they contain about amulets and talismans per se, is in fact limited. In this paper, I will analyse the vocabulary, processes and figures related to amulets and talismans in the ancient core of the corpus bunianum.

1

Al-Būnī, the Putative Key-Author for the Analysis of Islamic Amulets and Talismans

Al-Būnī (d. 622/1225 or 630/1232) holds a special place in the understanding of magical practices in the Islamicate world, both medieval and contemporary. During the colonial period, Orientalist scholars and colonial authorities (administrative and military) produced numerous discussions of amulets and talismans that they encountered in local museum collections or acquired during their missions. In the context of colonialist and Orientalist works, the first studies dealing with al-Būnī did not demonstrate any historical perspective.

To the contrary, al-Būnī was considered as the actual author of the Shams al-maʿārif, in accordance with the Islamic tradition, and the starting point of Islamic talismanic tradition. The colonial administrator Edmond Doutté,1 for example, connected Islamic talismans and magical practices to the Shams al-maʿārif, Ibn al-Ḥājj al-Tilimsānī's (d. 930/1524) Shumūs al-anwār, and al-Suyūṭī's (d. 911/1505) Kitāb al-Raḥma fī al-ṭibb wa-l-ḥikma.2 Thus, he introduced these texts to European Orientalist scholarship, with lasting consequences. Later, particular attention was brought to the problem of magic squares, especially in relation to apocryphal texts circulating under al-Būnī's name.3

The works of Tawfik Canaan also drew attention to al-Būnī. Canaan was a Palestinian physician in the Ottoman army, and a skilled Orientalist involved in Orientalist and local interests in preserving "traditional" aspects of Palestinian culture.4 Hence, he wanted to preserve Palestinian traditions and popular culture. He wrote a number of papers dealing with such traditions. At the same time, he gathered a collection of artefacts, among which were several talismanic bowls. He analysed these "fear cups" in two papers, and went on to produce an influential study entitled "The decipherment of Arabic talismans".5 In this article, he supported his decipherment with the Shams al-maʿārif and the Manbaʿ uṣūl al-ḥikma, two works falsely attributed to al-Būnī also by Canaan. Curiosity about al-Būnī has generally been driven by the desire to understand the Islamic talismanic tradition as a way to decipher talismans,6 as well as what was considered as the "margins" of Muslim religious practices, especially "practical" Ṣūfīsm.7

However, all these works are based upon the corpus bunianum,8 a themebased collection supposedly produced by one author, in this case al-Būnī. In fact, recent research has pointed out that both Shams al-maʿārif al-kubrā and Manbaʿ uṣūl al-ḥikma are later works falsely attributed to al-Būnī.9 Even the "short version" of the Shams al-maʿārif is an apocryphal compilation.

On the other hand, we must add that astral and natural magic works of the ninth-tenth centuries were not taken in account for the decipherment of Islamic amulets and talismans. Indeed, the most famous book in this tradition, Maslama al-Qurṭubī's (d. 353/964) Ghāyat al-ḥakīm,10 contains a lot of instructions for the making of talismans or magical objects (ṭilasm, nīranj, nushra, etc.), and introduces itself as a book on magic (siḥr). However, despite its firmly established reputation, it was not considered as a valuable source to analyse Islamic amulets and talismans. The obvious reason is that the Ghāyat al-ḥakīm does not contain a lot of instructions based upon the Arabic alphabet, the divine names, the Qurʾanic verses or the magic squares.

sance, ed. Alain de Surgy (Paris: L'Harmattan, 1997), 129-160; Constant Hamès, "Taktub ou la magie de l' écriture islamique. Textes soninké à usage magique," Arabica 34, no. 3 (1987): 305-325; Constant Hamès, "Entre recette magique et prière islamique," Fétiches ii. Puissance des objets, charme des mots, Systèmes de pensée en Afrique noire 12 (1993): 187-223; Constant Hamès, "L' usage talismanique du Coran," Revue de l'Histoire des Religions 218, no. 1 (2001): 83-95; Constant Hamès, "Problématiques de la magie-sorcellerie en islam et perspectives africaines," Cahiers d'études africaines 189-190 (2008) To the contrary, in the corpus bunianum, we can find that the earliest works by al-Būnī seem to ignore the magical objects terminology that can be found in the Ghāyat al-ḥakīm, although later works in the same corpus in the 16th century seem to rehabilitate these words. Hence, we might ask which elements of the Islamic talismanic tradition can be truly related to al-Būnī. Do al-Būnī's own genuine works deal with amulets and talismans, or is this topic a later development in the apocryphal corpus bunianum works?

A Brief History of the Corpus Bunianum

First of all, we need to introduce the outlines of the constitution of the corpus bunianum.11 Who was al-Būnī? Al-Būnī was a ṣūfī master. During the Mamluk and Ottoman era, hagiographical notices described him as "the source (zamzam) of secrets, the mine of lights, the master of miracles, glorious stations," and he is known as one whose prayers are granted (mujāb al-daʿawāt).12 He was probably born in Annaba (Būna in the Middle Ages, hence his nisba al-Būnī, it is located in Algeria On the other hand, al-Būnī often cites his own works in the four texts mentioned above, but in al-Lumʿa al-nūraniyya there is no mention of al-Būnī's other works. This casts doubt upon the authenticity of this work, but it is in my opinion not sufficient at this stage to prove that it was not written by al-Būnī. Whatever its authorship, al-Lumʿa al-nūrāniyya is certainly among the oldest works of the corpus bunianum.

The second work whose relationship to the historical core is unclear is Shams al-maʿārif wa-laṭāʾif al-ʿawārif. Indeed, in my doctoral thesis, I demonstrated that the text usually known under its shorter title, Shams al-maʿārif, and often considered as authentically composed by al-Būnī does in fact not belong to the historical core. The text contains many anachronisms.16 However, the four above mentioned works do quote a book entitled Shams al-maʿārif, which makes it likely that al-Būnī did indeed write a text with that title. The solution to this apparent contradiction came with the discovery of a unique manuscript in the National Library of Damascus whose title is Shams al-maʿārif.17 The content of this work is totally different from that which was previously identified by that title. The Damascus manuscript is a cosmological Ṣūfī work and all quotations of the Shams al-maʿārif in the four works authored by al-Būnī previously mentioned perfectly match the content of this text. Another point that supports al-Būnī as the author of this text is that he calls ʿAbd al-ʿAzīz al-Mahdawī his master-indeed al-Mahdawī was al-Būnī's teacher.18 Finally, the content and style of the text perfectly match the themes and style of the historical core of al-Būnī's oeuvre. It was therefore possible to finally reject the attribution to al-Būnī of the magical Shams al-maʿārif, and affirm that the Ṣūfī cosmological text of the same name may be the one authored by al-Būnī.

The next major step in the composition of the corpus bunianum and the development of al-Būnī's reputation was due to an Ottoman scholar and adīb named ʿAbd al-Raḥmān al-Bisṭāmī (d. 858/1454). This author bears primary responsibility for al-Būnī's fame in the Ottoman era. He wrote commentaries wa-najm al-ihtidāʾ. I defended the same idea concerning Tartīb al-daʿawāt fī taḫṣīṣ al-awqāt ʿalā iḫtilāf al-irādāt and Qabs al-iqtidāʾ ilā wafq al-saʿāda wa-najm al-ihtidāʾ based upon philological arguments and a comparison with the other Būnian works, however, although we cannot definitely prove that al-Lumʿa al-nūrāniyya is a genuine work by al-Būnī, I also think that there is not enough convincing evidence at this stage to consider this work out of the core. See Coulon, "La magie islamique," 1, 451-461; on the works of al-Būnī, adding much information on talismanic uses and recipes to al-Būnī's original treatises in the process. For instance, his Rashḥ adhwāq al-ḥikma al-rabbaniyya written in 815/1413 is an extensive commentary on al-Lumʿa al-nūrāniyya, in which he included instructions for the creation of amulets in the addenda. Finally, the last major step in the development of the corpus bunianum is the composition of the Shams al-maʿārif al-kubrā (The Great Sun of Knowledge). Indeed, this apocryphal huge compilation, based upon some authentic works by al-Būnī, some apocryphal works attributed to him-particularly the Shams al-maʿārif-and some of ʿAbd al-Raḥmān al-Bisṭāmī's works, has been wide spread in the Ottoman high society. Lithographical reproductions also contributed to its success in the nineteenth and twentieth centuries. The Shams al-maʿārif al-kubrā is a magical encyclopaedia, containing a few hundred recipes and formulas. Although this work contains a lot of anachronisms with regard to al-Būnī's days, it has been considered as al-Būnī's major work.

In his authentic works, al-Būnī himself never used terms such as ṭilasm,19 nushra, tamīma,20 ḥijāb,21 or other words with similar meanings. However, he did describe practices that could subsequently be used in the confection of amulets and talismans. This is what I would like to introduce now.

Amulets and Talismans in Laṭāʾif al-Ishārāt

Laṭāʾif al-ishārāt is a ṣūfī cosmological work. Indeed, the first part of this treatise deals with cosmology and God's creation of the world. The second part is an esoteric commentary on the Arabic letters. In light of this text, it is not surprising that later scholars considered al-Būnī as the master of the science of letters and magic squares (ʿilm al-ḥurūf wa-l-awfāq). The author of the magical Shams al-maʿārif indeed copied a number of sections from the Laṭāʾif al-ishārāt.

19

The word ṭilasm, from the Greek telesma, was used in the ninth and tenth centuries mainly for talismans referring to Greek authorities. A lot of monumental buildings of the Antiquity were depicted as ancient talismans settled to protect countries and cities. However, the term is used in the Shams al-maʿārif al-kubrā for any kind of written talisman. See for example Coulon,La Magie,[92][93][94][95][96][97][98] Nushra and tamīma are two words often used for anteislamic amulets. We can find these terms in later Arabic literature for protective objects. See for example Coulon,La Magie,[48][49][50][51] This latter word appears in al-Būnī's works, but exclusively in a ṣūfī meaning, i.e. a veil that the ṣūfī path enables to raise to see the world as it is. To the contrary, the term ḥijāb is used in the Shams al-maʿārif al-kubrā as a synonym of protective talisman. Some later talismans called ḥijāb refer to al-Būnī although his authentic works do not use the word in this meaning. In the Laṭāʾif, al-Būnī sketched out creation in a cosmological perspective, and for this reason it contains many schematic drawings, but these must not be confused with magical drawings per se. Indeed, some of these drawings can be both considered as a representation of a kind of knowledge and magical item as well, but a lot of them are only added for a mnemonic purpose or to help the reader to figure organized data.22 For example, the following diagram represents the hierarchy of the spheres and introduces the creation.

This image is, however, taken from a late and anonymous manuscript on occult sciences partly based upon some chapters of the Shams al-maʿārif and now kept in the collections of the bulac (Bibliothèque des Langues et Civilisations).23 This diagram representing the cosmos which originally appeared in al-Būnī's Laṭāʾif al-ishārāt, became so popular that it was subsequently taken up by the compiler of Shams al-maʿārif and many other writers.

In fact, the greater part of the Laṭāʾif deals with ṣūfī cosmological theory. Before we get into the text itself, it should be reiterated that we do not find references to words describing amulets or talismans such as nushra, tamīma, ṭilasm, ḥirz, ḥijāb, etc. in the Laṭāʾif al-ishārāt. Nevertheless, the use of such objects can well be deduced from the text, but al-Būnī did not use these words himself.

There are, however, some instructions for certain praxes, as well as allusions and references to the utilisation of written elements, especially Arabic letters and magic squares, and, although al-Būnī was celebrated at his time as a ṣūfī master, these occult elements were the basis of commentaries and magic oriented additions and development, which finally made al-Būnī more famous as a "theurgist" than a ṣūfī master. Indeed, al-Būnī describes the esoteric properties (khawāṣṣ) of the letters. The instructions to use the properties for a material gain usually indicate that the letter has to be written on a specific material (parchment, paper, etc.), sometimes with a specific ink (rosewater, orange blossom water, etc.), in specific conditions to produce a specific effect (taʾthīr). Al-Būnī developed the idea that each letter has a shape (shakl, pl. ashkāl) which synthesises its occult properties and esoteric meaning. These ashkāl are mainly magic squares and circles.

For example, in the section on the letter ḥāʾ, we can read:

And for this reason, he who writes this letter on a seal eight times with the four names mentioned above is preserved by God's praise against all diseases. If he puts it in water and gives it to sick people to drink, they This diagram can be found in a lot of manuscripts. We chose this one particularly because the bulac freely and kindly allows the use of its manuscripts for scholarly publication purposes.

will experience relief. If they continue to drink this water and to refresh themselves with it, it will cure all sickness. It is also beneficial for wrathful men among those who suffer from yellow bile. He who wears this seal, if he lives a long life, he will not be often confused. Among its properties (are that) it removes the inclination for sexual intercourse. If one is a young man, it is better to hide this seal and not to wear it on Saturday nor on Monday, but one may wear it on any other day. [This seal] ensures that the one who holds it will not experience thirst and be able to drink water copiously. If it is suspended in a garden, it makes the fruit grow and flourish, if God-exalted be He!-so wishes.24 For this letter, an offensive utilisation exists, but it is not possible to mention it here. We have introduced the religious benefits leading to God-exalted be He!-by the secret of the Oneness. He who writes it on a parchment, when the moon is in the rays [of the sun] in the hour of Mercury, and who is summoned by a sultan or a tyrant, God makes their inner thoughts removed from mentioning him and He distracts them from him with another. He [must] wear it directly on his bare head and cover his head over this [object], and leave it until he is no longer afraid. This frees prisoners.

He who writes it with sūrat al-Mulk in a cup and drinks [water poured in it] after an eight days' fasting, God improves his memory and his ability to concentrate to complete matters. He preserves him from anything that harms him-I mean the complete figure that will follow-if Godexalted be He!-wants.

In the same way, he who engraves in a circle (mustadīr) [made] of silver eight [times the letter] ḥāʾ and the four names and suspends it upon his heart and firmly believes in God cools his heart for worldly desire or what is hidden in his will, and [if he does] this in the hour of the moon while the moon is in an auspicious conjunction ( fī al-suʿūd), or in the hour of Venus while the moon is in an auspicious conjunction (masʿūd), and suspends it while he is pure, fasting and remembering God-exalted be He!-and does not approach it when he is [already] close: if he does [all of] this, God removes the fear and the terror from his heart of hearts. This may also be a protection (litt. "cause") against the loss of understanding from his heart and the tyranny of forgetting; consider it carefully. This is its drawn and marked figure : The figure consists of a lozenge in a circle accompanied by writing. This figure is not only a cosmological drawing but a talismanic figure that can be used in the creation of talismans. The cosmological meaning of the figure is evident in the writing: the sentence surrounding the circle states that "this is the circle (dāʾira) of the ḥāʾ which surrounds the isthmus of life (al-ḥayāt al-barzakhiyya) which binds the natural world and which surrounds the fourth sphere of the ether from the [celestial] Globe. In [this circle] is the secret of the natural dissecting (al-tafṣīl al-ṭabīʿī). The essence of Ādam was completed by [this circle] in the first growth." This sentence expresses the esoteric meanings of the letter ḥāʾ, which is supposed to refer to life (ḥayāt) since it is the first letter of this word in Arabic. The circle is then divided in four parts by the diagonals of the lozenge. The four parts of the circle contain four sentences dealing with the successive steps of the Creation, and the four parts of the lozenge contain four sentences, each associated with the Aristotelian natural properties. Thus, the four sentences of the circle explain that "God created you by the secret of life in the world of the Tablet, which is the world of life," that "He then placed you in your world through the descent of the secret of science and spiritual inspiration into the World of the Pen (ʿālam al-qalam wa-l-waḥy al-rūḥī)," that "He then makes you live by the secret of the cold and the moist in the World of the Throne (ʿālam al-kursī), the Representation (al-taṣwīr) and the Spheres (al-aflāk)," and finally that "He then makes you die by the secret of the cold and the dry in the world of the lower globe and the essences of the world which surround it." The four sentences of the lozenge explain that they represent "the world of the hot and the dry, which is the place of the soul (maḥall al-nafs) by the secret of the thought (sirr al-fikra)," "the world of the hot and the moist, secret of the representations (sirr al-ṣuwar), place of the heart (maḥall al-qalb)," "the world of the cold and the moist, secret of the celestial representation (al-ṣūra al-ʿuluwiyya)," and "the world of the cold and the dry of the ḥāʾ, which are four for each essence (rukn)." The sentences in the diagonals are "This is the secret of the whole human world" and "asking help for life (istimdād al-ḥayāt)." Therefore, each quarter of the figure corresponds both to a stage of the Creation and a humour. It should be noted that the numerical equivalent of the letter ḥāʾ is eight, and the lozenge divides the circle in eight parts.

This kind of circle-shaped figure is common in the Laṭāʾif al-ishārāt. However, the second important kind of talismanic figure in this treatise is the magical square (wafq, pl. awfāq).

Here is an example of the four-based magic square, as introduced by al-Būnī:

He who makes a table of four by four squares and puts in it numerical relation (nisba ʿadadiyya), must do it on a Monday, which is the birthday of the Prophet, the day of his mission and the day of his death. Know that the letters are efficient by their own properties: no particular moment is required, it is a choice to be made by the one who desires it. The numbers are efficient by nature: they depend on the auspicious celestial moments by God's wisdom, the One who does what He wants. Do it when the Moon is in exaltation, without any evil influence, during the hour of the Moon. Write it after achieving ritual purity through ablutions using the Throne Verse (Q: 2:255), and [the verse] "Say: He is God, the One" (Q112:1) a hundred times on a blank/pure parchment. God will allow its wearer memory, understanding and access to wisdom, He will increase his power over the lower world in its entirety, he will free the prisoners, defeat the enemy in any controversy, and so many things that it is not possible to describe them. Here is the figure: As for the secret of this letter-square, it too is wonderful. Put the letters instead of the numbers and perform this operation after two weeks of fasting. During this period of fasting, you must eat only bread, stay pure and invoke God. You should take a moon-plate (i.e. a plate made of silver) and engrave on it the above-mentioned numbers (sic) and face the qibla. Do this on Thursday during the hour of Jupiter. The moon must be in conjunction with the Sun, and Jupiter and the Gemini should be in the ascendant. You must burn mastic and white aloe each Thursday. God will make the one who wears the seal love what concerns religion, God will make easy for him acts of obedience [to God], and He will give him the power over "the causes" ( fī al-asbāb).26 God will bless anything he attempts. He who writes it on a blank paper at the same time and wears it in the seam of his coat will be safe, with God's power, against thieves and all appalling things. Take care not to put it in any impurity or to put it in a dirty place. Here it is. Consider it carefully. This is the first product of the secrets of the even numbers:27

A Ḥ Y.Ā Y.D Y.B Y.J B Ḏ W J Y.W Ṭ Y.H Y H D 26
That is, the principles of causation which will enable him to achieve his desired results. 27

Coulon, "La magie islamique," 1, 962-964; 4, 81-82; Laṭāʾif al-ishārāt, fol. 14a-15a.

The compilator of the Shams al-maʿārif borrowed this introduction to the four by four magic square, which led to its spread in magical treatises.28 We also find in the Laṭāʾif al-ishārāt: -two 3×3 magic squares (Coulon,"La magie islamique," 4,85;Laṭāʾif alishārāt,fol. 17a;and Coulon,4,174;fol. 62a), -another 4×4 square (Coulon,4,149;, -a 5×5 square (Coulon,4,(119)(120), -two 6×6 squares (Coulon,4,(155)(156)fol. 55a;and Coulon,4,172;, -a 7×7 square (Coulon,4,170;, -two 8×8 squares (Coulon,4,(83)(84)(85)and Coulon,4,(112)(113), -a 9×9 square (Coulon,4,144;, -a 10×10 square (Coulon,4,(133)(134), -an 11×11 square (Coulon,4,(175)(176)fol. 63a). This list clearly shows that magic squares are not peripheral in al-Būnī's work. But they are not the primary subject itself, rather they are used as a seal, i.e. as a way to represent the esoteric meaning and properties of a letter (or number) although it also makes it inunderstandable for a non-initiated individual.

What was the place of the magic square during al-Būnī's era? The most famous magic square was obviously the three by three magic square. This probably originated from China, where it was known as the Lo-Shu.29 The first mention of this magic square in an Arabic text is in ʿAlī al-Ṭabarī's (fl. 9th century) Firdaws al-ḥikma. This physician prescribed a recipe based upon the properties of the three by three magic square to help women in labour. A similar use with slightly different recipes can be found in (pseudo-)Jābir b. Ḥayyān's Kitāb al-Mawāzīn al-ṣaghīr (probably dating to the fourth/tenth century), in the Rasāʾil Ikhwān al-Ṣafāʾ (fl. 4th/10th century) and in Maslama al-Qurṭubī's Ghāyat al-ḥakīm. Mathematicians also wrote treatises exclusively devoted to the mathematical aspects of magic squares; these include Abū al-Wafāʾ al-Buzjānī (d. 997-998) Laylat al-qadr is the 27th night of the month of Ramaḍān. In the Qurʾan, laylat al-qadr is depicted as the moment the Qurʾan was sent down and as "better than a thousand months" (Q: 97, 1-3). As yawm ʿArafa, it is the ninth day of Dhū l-ḥijja and the second day of the pilgrimage (ḥajj). It commemorates Muhammad's last sermon.

This treatise deals particularly with invocations, prayers (duʿāʾ) and dhikr. But the book also reveals some talismanic uses of the Beautiful Names, and some of their uses in a written or engraved form to produce various effects upon the world. We may note a few examples here.

In the section for the prayer of the first hour of Sunday ( yawm al-aḥad), the related names of God are listed as follows:

Among the Beautiful Names [related to this prayer] there are the King, the Light (al-Malik al-Nūr). He who recites this Qurʾanic verse the aforementioned number of times in a dark house with closed eyes, he will see wonderful lights filling up his heart. If he continues to do so, [the lights] take shape in the sensory world, and this dhikr is beneficial for the masters of concentration (arbāb al-himam) and the masters of ascetic retreats (arbāb al-khalawāt). He who writes and wears it will see for himself increases in the forces of his soul, contrition for his enemy and opponent as he could never have seen before. And it is possible to cure with it diseases of the head, especially the cold. This effect (taʾthīr) exists in its moment.35

This extract is very typical of the other sections about the prayers. It begins with an oral use of the names by means of prayers and invocations (duʿāʾ and dhikr). Then, the written use is introduced. There is no precise word used to refer to this kind of amulet: they are introduced as undefined written objects. Moreover, the recipe is not necessarily as precise as in the Laṭāʾif al-ishārāt. Indeed, in the current case, we have only the indication of what should be written, and that it must be worn. There are no indications for a specific moment or astral compilation at which the writing should take place, for a suitable writing material, for a peculiar ink or colour, etc.

In the paragraph of the invocation for the second hour of Sunday, we can find a reference to another practice: He who "breaks" His name the Generous (al-Bāsiṭ wa-l-Jawwād) and wears His names himself, no-one will see him without loving him and opening his heart to him, thanks to the property of this prayer, the name and the Qurʾanic verse. This dhikr is good for the masters of contrition among the masters of the ascetic retreats.36 coulon

Ā Ḥ D Th L Ā Th W N Th M Ā N W N Th L Ā Th W N Ā Ḥ D Ā R B ʿ W N Th M Ā N W N Ā Ḥ Ds
The verb "to break" (kassara) appears in other passages. For example, about the invocation for the third hour:

He who breaks His name the Fast (al-Sarīʿ), the Heart Turner (al-Muqallib = muqallib al-qulūb) and maintains it, God will make anything he wants happen quickly and he will know what is far from him.37 "To break" (kassara) refers here to the taksīr operation. The tafṣīl, the taksīr and the basṭ are the names of three operations within the "science of the letters and the magic squares" (ʿilm al-ḥurūf wa-l-awfāq) aiming to deconstruct letters in order to increase their esoteric properties. The tafṣīl is the operation which consists in writing a letter with the name of the letters of its own name. Thus, alif would be written Ā-L-F. In a sense, the taksīr is the tafṣīl of the result of the tafṣīl. Thus, the taksīr of alif is Ā-L-F (alif ) L-Ā-M (lām) F-Ā ( fāʾ). Finally, the basṭ consists in converting the taksīr in the numeric equivalent, and then, in doing the tafṣīl of the name of each number. Table 9.1. sums up the three operations for the letter alif. Concerning a divine name, we may take the example of al-Ḥayy, and the taksīr would be Ā L F M Ḥ Y, as shown in table 9.2.

These operations are not explained by al-Būnī in al-Lumʿa al-nūrāniyya, and so we may infer that these techniques were already known to its readership. Although the process seems simple, the text presupposes specific skills and knowledge by the practitioner.

L Ḥ Y Alif Lām Ḥāʾ Yāʾ Ā L F L Ā M Ḥ Ā Y Ā Ā L F M Ḥ Y
The section Anmāṭ is devoted to the Beautiful Names of God. As in the previous section on invocations, similar instructions are given. Here is the second namaṭ:

Second namaṭ among the names. Al-Wāḥid al-Aḥad al-Ṣamad al-Faʿʿāl al-Baṣīr al-Samīʿ al-Qādir al-Muqtadir al-Qawī al-Qāʾim. Those ten names are one path in the approach to the dhikrs (invocations). In this section are the dhikrs of those who walk upon the path, depending (litt. "hanging") upon the secrets of Oneness. And their dhikr is al-Aḥad al-Wāḥid.

As for al-Ṣamad, this is a good dhikr, especially for starving people. The one who does dhikr with this name do not feel any pain of starvation unless he introduces another dhikr. You must understand! Al-Faʿʿāl is a name for those who are dominated by thoughts, evil whispers, an overabundance of ideas and affliction in the heart because of these. The one of this description who practices dhikr will have his thoughts turned to what is for him joy and happiness.

As for al-Baṣīr and al-Samīʿ, it is a good dhikr especially for those who are persistent in praying (duʿāʾ). This may make an answer come more quickly to them.

As for al-Qādir al-Muqtadir al-Qawī al-Qāʾim, it is a dhikr good for those with burdens and the heavy letter. If one who suffers from a burden knows its secret and perseveres, he will not feel the burden or the exhaustion in anything he does. If someone engraves it on a seal and wears it on his finger, it will work in a moment. And if one who is weak for some reason wears it ("hangs it upon himself") and does dhikr with it, he will strengthen himself at once.38 coulon This second namaṭ is also very typical of the structure of this section. The Beautiful Names of God are used as dhikr, a well-known ṣūfī practice. We know that al-Būnī was a ṣūfī master, had a group of disciples, and may have conducted dhikr sessions when he was still living in al-Qarāfa area in Cairo.39 However, another practice appears here: the making of rings. Indeed, he prescribes the engraving of the divine name on a seal. In this second example, the instructions are also very brief: no mention of a proper moment when the writing of the seal should take place or of astral influence on the action, of the need to use a peculiar material, etc. This seal aims to help the ṣūfī disciple to practise dhikr, as it is indicated.

Lastly, we must add that a final section is entirely devoted to the construction of magic squares. This final section may be a kind of appendix, or even an interpolation. Indeed, a sentence explains that this passage was added in order to explain the method of constructing magic squares.40 This method was distributed as a booklet entitled Sharḥ al-ism al-aʿẓam (The Commentary of the Greatest Name), later analysed by Bernard Carra de Vaux.41 This method of construction is based upon the game of chess and is especially simple, appropriate for readers who might not be mathematicians. Although al-Lumʿa al-nūrāniyya does not explain in detail the magical uses of the squares, the presence of this section suggests that this work was intended for readers who might want to make amulets.

Conclusion

Although al-Būnī's works are in general Sufi cosmological treatises, the descriptions of the occult properties of the letters, the Beautiful Names of God, and the Qurʾanic verses take a very important place in his works. Can we speak about amulets and talismans in the Laṭāʾif al-ishārāt and al-Lumʿa al-nūrāniyya? Al-Būnī only wrote about the "properties of letters" (khawāṣṣ al-ḥurūf ), which included their use in a written form and how these could be used to protect the bearer of the written form or the one orally expressing the names or phrases. Al-Būnī never calls these practices in his work by the regularly used words for talisman or amulet. It is these elements in his work, however, that turned al-Būnī into the expert on amulets and talismans. Indeed, al-Būnī's descriptions of the esoteric properties was easily applied in the creation of protective objects, and he gave instruction to make objects we can depict as amulets and talismans, but he carefully avoided to use the words that can relate those effective objects to amulets and talismans. It is these properties which explain why al-Būnī has long been considered as the author of a huge corpus of texts about magic, and why he remains up to today the main reference in the analysis of Islamic amulets and talismans. Indeed, building on al-Būnī's supposed expertise and reputation in this domain, subsequent authors embellished and expanded on the descriptions by adding more instructions on making amulets and even ascribed to him entire treatises on amulets and talismans that he did not write. Thus, ṭilasm, ḥijāb or other words are clearly used in the late Shams al-maʿārif al-kubrā for any recipe designed to produce protective objects. The different attitude towards this vocabulary choice can be explained by a slow evolution in the field of occult sciences. Indeed, words such as ṭilasm, nīranj or nushra are mainly used for objects based upon the natural occult properties known since Antiquity. However, they are common words in treatises such as Maslama al-Qurṭubī's Ghāyat al-ḥakīm which clearly assumes to deal with magic (siḥr) as the ultimate knowledge or nature. Of course, al-Būnī had to clearly differentiate his speech about the occult properties of Arabic letters and divine names from the natural properties. However, as the later commentators of al-Būnī's works added a lot of astrological and natural data for the fabrication of protective objects, they appropriate the rich vocabulary of amulets and talismans.

Bibliography

  figure 9.1 The hierarchy of the spheres. ms Paris, bulac, ara.572, fol. 37b © bulac

  figure 9.2 The circle of the letter ḥāʾ. Adapted from ms Paris, BnF, Arabe 2637, fol. 40a

  : 81-99; Karl R. Schaefer, Enigmatic Charms: Medieval Arabic Block Printed Amulets in American and EuropeanLibraries and Museums (Leiden: Brill, 2006), 19.

		Brill,
		2007), 183-199.
	9	See Jean-Charles Coulon, "La magie islamique et le corpus bunianum au Moyen Âge" (PhD
		diss. Université de Paris iv Sorbonne, 2013): vol. 1, 479-499, 544-552 and 552-564; Jean-
		Charles Coulon, La Magie en terre d'islam au Moyen Âge (Paris: cths, 2017), 219-229; Noah
		Gardiner, "Forbidden Knowledge? Notes on the Production, Transmission, and Reception
		of the Major Works of Aḥmad al-Būnī," Journal of Arabic and Islamic Studies 12 (2012):
		81-143.

7 Pierre Lory, "Magie et religion dans l' oeuvre de Muhiy al-Dîn al-Bûnî," Horizons maghrébins 7-8 (1986): 4-15; Pierre Lory, "La magie des lettres dans le Šams al-maʿārif d'al-Būnī," Bulletin d' Études Orientales 39-40 (1987-1988): 97-111. 8 On this concept, see Jan Just Witkam, "Gazing at the Sun: Remarks on the Egyptian Magician al-Būnī and His Work," in O Ye Gentlemen: Arabic Studies on Science and Literary Culture in Honour of Remke Kruk, eds. Jan P. Hogendijk and Arnoud Vrolijk (Leiden: 10 On the Ghāyat al-ḥakīm, see, among many others, Coulon, La Magie en terre d'islam, 143-169; and Liana Saif, "From Ġāyat al-ḥakīm to Šams al-maʿārif : Ways of Knowing and Paths of Power in Medieval Islam," Arabica 64, no. 3-4 (2017): 297-345.

  Coulon, La Magie en terre d'islam, 221.

16 About these anachronisms, see Coulon, "La magie islamique," 1, 482-483; Coulon, La Magie en terre d' islam, 227-229; Gardiner, "Forbidden Knowledge?" 102-103. 17 About this manuscript and hypothetically authentic version, see Coulon, "La magie islamique," 1, 484-491; Coulon, La Magie en terre d' islam, 227-229. 18 Coulon, "La magie islamique," 1, 488; Coulon, La Magie en terre d'islam, 227-228.

4 Amulets and Talismans in al-Lumʿa al-Nūrāniyya Al

  , ʿAlī b. Aḥmad al-Anṭākī (d. 987) and Abū ʿAlī al-Ḥasanb. al-Haytham (d. 1041).30 However, there is another scholar who might have had some influence in the development of the esoteric properties of the magic squares, namely Abū Isḥāq al-Zarqālī (d. 493/1100). In his treatise, he associated a planet with each magic square.31 Al-Zarqalī's treatise was well-known in al-Andalus, and so one might postulate that al-Būnī could have known this text and used it.32 -Lumʿa al-nūrāniyya was one of al-Būnī's most widely-known works. Many commentaries and addenda were written on it during the Middle Ages and in the Early Modern period, and these added many additional magical elements. However, originally the work was a kind of book of prayers with a section entitled al-Anmāṭ, the purpose of which was to facilitate the learning of the ninety-nine Beautiful Names of God. These Anmāṭ were so famous that Lisān al-Dīn b. al-Khaṭīb (d. 776-1375) and Ibn Khaldūn (d. 809/1406) considered them as a separate treaty.33 After the Anmāṭ, the next section concerned the invocations of the different thirds of the nights, and the next the prayers that one could perform during the Night of Destiny (laylat alqadr) or the Day of ʿArafa.34 The last part discussed the composition of magic squares.Al-Qanṭara 30, no. 1 (2009): 137-169. 32 Since the writing of this paper, a major contribution on the history of magic squares has been published and must be pointed out here, as it renewed our knowledge of the magic squares in the first centuries of Islam: Bink Hallum, "New Light on Early Arabic Awfāq Literature," in Islamicate Occult Sciences in Theory and Practice, eds Liana Saif, Francesca Leoni, Matthew Melvin-Koushki, and Farouk Yahya (Leiden-Boston:

		Brill,
		2020): 57-161.
	33	Lisān al-Dīn b. al-Ḫaṭīb, Rawḍat al-taʿrīf bi-l-ḥubb al-sharīf, ed. ʿAbd al-Qādir Aḥmad ʿAṭāʾ
		(Cairo: Dār al-fikr al-ʿarabī, n.d.): 330-331; Ibn Khaldūn, Shifāʾ al-sāʾil li-tahdhīb al-masāʾil,
		ed. Muḥammad b. Tāwīt al-Ṭanjī (Istanbul: Osman Yalçin matbaasi, 1957): 67-68; La voie
		et la loi, French transl. René Pérez (Paris: Actes Sud, 2010): 190-191; and Ibn Khaldūn,
		Muqaddimat Ibn Ḫaldūn, ed. Étienne Marc Quatremère (Paris: B. Duprat, 1858): 3, 142;
	28	Coulon, "La magie islamique," 2, 180-187. Les prolégomènes, French transl. William Mac Guckin De Slane (Paris: Imprimerie impé-
	29	Schuyler Cammann, "The Magic Square of Three in Old Chinese Philosophy and Religion," riale, 1863-1868): 3, 194; The Muqaddimah. An Introduction to History, English transl. Franz
		History of Religions 1 (1961): 37-80; Schuyler Cammann, "Old Chinese Magic Squares," Sino-Rosenthal (New York: Bollingen Foundation, 1958): 3, 177.
	34

logica 7 (1962): 14-53; Schuyler Cammann, "Islamic and Indian Magic Squares," History of

Religions 8, no. 3-4 (1969): 180-209, 271-299. 30

All of these authors are introduced in Jacques Sesiano, Les carrés magiques dans les pays islamiques (Lausanne: Presses polytechniques et universitaires romandes, 2004), 10-12. coulon 31 Sesiano, Les carrés magique, 14; Marcè and Rosa Comes, "Los cuadrados mágicos matemáticos en al-Andalus: El tratado de Azarquiel,"

table 9

 9

	.1 Tafṣīl-taksīr-basṭ
				Alif
	tafṣīl	Ā (alif )			L (lām)		F ( fāʾ)
	taksīr Ā	L	F	L	Ā	M	F	Ā
	1	30	80	30	1	40	80	1
	(aḥad) (thalāthūn)	(thamānūn)	(thalāthūn) (aḥad) (arbaʿūn) (thamānūn) (aḥad)
	basṭ

table 9

 9

	.2 Example for a letter
	al-Ḥayy
	Ā

Primary Sources al

  -Bisṭāmī, ʿAbd al-Raḥmān. Shams al-āfāq. ms Paris, BnF, arabe 2689. al-Būnī, Laṭāʾif al-ishārāt, ms Paris, BnF, arabe 2637 (compared to ms Paris, BnF, arabe 2658), edited in Coulon, "La magie islamique." al-Būnī, al-Lumʿa al-nūrāniyya fī al-awrād al-rabbāniyya, Damascus, BnA, 3679 and 18554; Paris, BnF, arabe 1225 and arabe 1226; Princeton, Princeton University Library, 1895, fol. 1b-48b; Dublin, Chester Beatty, 4284; Istanbul, Aya Sofya, 1870, fol. 43a-84a and Sehid Ali Pasa, 2764, edited in Coulon, "La magie islamique." Ibn Khaldūn. Shifāʾ al-sāʾil li-tahdhīb al-masāʾil. Edited by Muḥammad b. Tāwīt al-Ṭanjī. Istanbul: Osman Yalçin matbaasi, 1957. Ibn Khaldūn. La voie et la loi. French transl. By René Pérez. Paris: Actes Sud, 2010. Ibn Khaldūn. Muqaddimat Ibn Khaldūn. Edited by Étienne Marc Quatremère. Paris: B. Duprat, 1858.

Jean-Charles Coulon -9789004471481 Downloaded from Brill.com05/10/2022 12:45:26PM via BULAC

For whom see Alain Messaoudi, "Carra de Vaux," in Dictionnaire des orientalistes de langue française, ed. François Pouillon (Paris: iismm and Kharthala,

2008), 310-312. 2 Edmond Doutté, Magie et religion dans l' Afrique du Nord (Alger: Typographie Adolphe Jourdan, 1909). 3 Wilhelm Ahrens, "Studien über die "magischen Quadrate" der Araber," Der Islam 7 (1917): 186-250; and Wilhelm Ahrens, "Die "magischen Quadrate" al-Būnīs," Der Islam 12 (1922): 157-177; Bernard Carra de Vaux, "Une solution arabe au problème des carrés magiques," Revue d' histoire des sciences 1 (1948): 206-212. 4 Marcela Probert, "Exploring the Life of Amulets in Palestine. From Healing and Protective Remedies to the the Tawfik Canaan Collection of Palestinian Amulets" (PhD diss., Leiden University, 2021). 5 For the bowls, see Tawfik Canaan, "Ṭâsit er-radjfeh (fear cup)," Journal of Palestine Oriental Studies 3 (1923): 122-131; Tawfik Canaan, "Arabic Magic Bowls," Journal of Palestine Oriental Studies 16 (1936): 79-127. For talismans, see Tawfik Canaan, "The Decipherment of Arabic Talismans," Berytus 4 (1937): 69-110 and 5 (1938): 141-151. Reprinted in Magic and Divination in Early Islam, ed. Emilie Savage-Smith (Aldershot and Burlington: Ashgate and Variorum, 2004), 125-177. 6 Georges Chehata Anawati, "Trois talismans musulmans en arabe provenant du Mali (marché de Mopti)," Annales islamologiques 11 (1972): 287-339; Constant Hamès, "Le Coran talismanique, De l' Arabie des origines à l' Afrique occidentale contemporaine, Délimitation et inventaire des textes et des procédés linguistiques utilisés," in Religion et pratiques de puis-Jean-Charles Coulon -9789004471481 Downloaded from Brill.com05/10/2022 12:45:26PM via BULAC

Coulon, "La magie islamique," 3,[7][8]

 Coulon, 3,[13][14] Jean-Charles Coulon -9789004471481 Downloaded from Brill.com05/10/2022 12:45:26PM via BULAC


A Allaoui

P Evesque

J B Bai

Effect of aging on the reinforcement efficiency of carbon nanotubes in epoxy matrix

Keywords: Polymer Matrix-Composites, Carbon Nanotubes, Mechanical Properties, Aging, Payne Effect

The reinforcement efficiency of carbon nanotubes (CNTs) in epoxy matrix was investigated in the elastic regime. Cyclic uniaxial tensile tests were performed at constant strain amplitude and increasing maximum strain. Post-curing of the epoxy and its composite at a temperature close to the glass transition temperature allowed us to explore the effect of aging on the reinforcement efficiency of CNT. It is found that the reinforcement efficiency is compatible with a mean field mixture rule of stress reinforcement by random inclusions. It also diminishes when the maximum strain increased and this effect is amplified by aging. The decrease of elastic modulus with increasing cyclic maximum strain is quite similar to the one observed for filled elastomers with increasing strain amplitude, a phenomenon often referred as the Payne effect.

The reinforcement of polymer matrices with carbon nanotubes (CNTs) has been the subject of a prolific literature, especially with epoxy as the matrix. Depending on the preparation method, the reinforcement potential of CNTs (theoretical Young modulus of 1 TPa) was partially [START_REF] Zhu | Reinforcement epoxy polymer composites through covalent integration of functionalized nanotubes[END_REF][START_REF] Allaoui | Mechanical and electrical properties of a MWNT/epoxy composite[END_REF] or fully exploited [START_REF] Moniruzzaman | Increased flexural modulus and strength in SWNT/epoxy composites by a new fabrication method[END_REF]. A review [START_REF] Du | The present status and key problems of carbon nanotube based polymer composites[END_REF] has been published on the subject. However, to our knowledge, the effect of aging has never been explored. In this paper, the elastic properties of CNT reinforced epoxy composites and the effect of aging on the reinforcement efficiency of CNT were investigated by means of cyclic uniaxial tensile tests at increasing maximum strain and constant strain amplitude.

Multiwall carbon nanotubes (MWNT) with diameters in the range of 10-150 nm and average length of 10 m, were produced by the CVD method [START_REF] Bai | Influence of ferrocene/benzene mole ratio on the synthesis of carbon nanostructures[END_REF]. A low viscosity diglycidyl ether of bisphenol-A (DGEBA) epoxy resin ( ~ 0.7 Pa.s) with triethylenetetramine (TETA) hardener (Epofix, Struers) was used. The stochiometric ratio was 100:12 (w/w) epoxy resin:hardener. Carbon nanotubes were dispersed in ethanol using magnetical agitation for 3 days. CNTs were filtered with a vacuum pump and then heated until complete removal of the solvent. The CNT powder was dispersed in epoxy resin using mechanical mixing for half an hour. The hardener was added and the mixture was mixed for another 5 min, vacuum pumped and cast into silicon moulds. The samples were cured at room temperature for 3 days followed by post-cure at 80 °C for 24 h. The dogbone samples (width ~6 mm, length ~30 mm, thickness ~2-3mm) were polished in order to eliminate the surface flaws. Six unfilled epoxy resin samples and seven composites epoxy + 0.5 wt.% MWNT were prepared.

Cyclic uniaxial tensile tests were performed at constant strain amplitude with an electromechanical testing stage (Instron 4505) equipped with a 1000 N force cell and an extensometer with 12.5 ± 2.5 mm gage length. A 10N pre-stress was applied to all samples. The strain amplitude was fixed to 0.1 % and the maximum strain was increased from 0.2 to 0.5 % to stay in the ''elastic'' regime. The crosshead speed was set to 0.5 mm/min. The elastic modulus was taken as the average slope of the stress-strain curve over three cycles at each maximum strain (0.2, 0.3, 0.4, and 0.5%). The samples were tested 3 days after their fabrication and tested again 1 month later to evaluate the effect of aging.

The elastic modulus of the unfilled epoxy and the composites tested after 3 days and after 1 month are plotted, respectively, in Fig. 1a andb. Physical aging allowed local rearrangement of the polymer chains leading to an increase of the modulus of the unfilled epoxy after 1 month. The decrease of the elastic modulus with increasing maximum cyclic strain is clearly much more marked in the case of the composite compared to the unfilled resin. This phenomenon is very similar to the substantial decrease of the modulus of carbon black filled rubbers with the increasing cyclic strain amplitude, which is often referred as the Payne effect [START_REF] Payne | The dynamic properties of carbon black-loaded natural rubber vulcanizates[END_REF].

We could expect the modulus to reach a plateau at small enough cyclic strain.

However, this plateau is not observed yet in Fig. 1. In our case, the polymer was in the glassy state and the increase of the maximum strain at constant strain amplitude led to the decrease of the elastic modulus. It is worth noting that this softening was enhanced by aging as the modulus drop is higher after 1 month. Kraus [START_REF] Kraus | Mechanical losses in carbon-black-filled rubbers[END_REF] proposed a phenomenological model to describe the Payne effect as breakage and recovery of some weak physical bonds during strain oscillations.

The model led to the following expression of the strain dependent elastic modulus  is a characteristic strain at which the reinforcement drops to half of its initial value and m an adjustable parameter related to the filler aggregate structure and connectivity. In the original model,  is the strain amplitude. In our case, the strain amplitude is constant, we thus considered  as the maximum cyclic strain and fitted our data. A good agreement was found with m equal to 1. The set of fitted parameters for the composites tested after 3 days and after 1 month are summarized in Table 1. The effects of physical aging were manifested by the increase of  E , corresponding to the increase of the unfilled epoxy modulus associated to rearrangement of the polymer chains, and the shift of the characteristic strain to lower values indicating an amplification of the modulus drop. To evaluate the CNT reinforcement efficiency, the rule of mixture with an orientation factor (with a value of 1/5 [START_REF] Krenchel | Theoretical and practical investigation of the elasticity and strength of fibrereinforced material[END_REF])

to take into account the random orientation of the CNT in the matrix was used.

The CNT reinforcement efficiency was thus calculated, under a mean-field homogenization assumption with random distribution of fiber orientation, as

 

with E composite and E epoxy are the elastic modulus of, respectively, the composite and the unfilled epoxy, and p is the volume fraction of CNT. In the case of an effective reinforcement of CNT, the reinforcement efficiency should give an estimation of the average CNT Young modulus. The CNT reinforcement efficiency is plotted as a function of the maximum strain (Fig. 2). The reinforcement efficiency decreased with the maximum strain and this decrease was amplified by aging. The reinforcement efficiency at the lowest maximum strain applied gave a valuable evaluation of the average Young modulus of CNT around 580 GPa. A lower value than the theoretical 1 TPa is expected for CVD synthesized nanotubes due the presence of defects on this type of tubes. Cooper et al. [START_REF] Cooper | Investigation into the deformation of carbon nanotubes and their composites through the use of Raman spectroscopy[END_REF] used the rule of mixture with an orientation factor to estimate the Young modulus of CNT from measured Raman band shift on strained CNT/epoxy composite films. They evaluated the modulus of SWNT to be around 1 TPa while they found a lower estimate for MWNT in the order of 0.3 TPa. The fitting parameters of the Kraus model provide the lower (  E ) and the upper bond ( 0 E ) of the modulus. 0 E should correspond to the modulus of the composite with the maximum reinforcement achievable and  E to the modulus of the un- reinforced epoxy. The epoxy modulus was found to slightly decrease so that the zero-strain modulus was obtained using a linear fit. The zero-strain reinforcement efficiency can be evaluated using 0 E as the composite modulus and the extrapolated zero-strain epoxy modulus. It is worth noting that the reinforcement efficiency obtained is lower than the theoretical 1 TPa before aging and higher than this value after aging. This suggests that they could be an additional reinforcement effect after aging or a larger plateau modulus at sufficiently low cyclic strain. The explanation of this observation is still unclear. Further investigations may help to point out possible additional reinforcement due to CNT entanglement effect or polymer chains reduced mobility at the vicinity of CNT.

In this study, the reinforcement efficiency of CNTs fillers in epoxy matrix was assessed along with the influence of aging through cyclic tensile tests at constant strain amplitude and increasing maximum strain. The modulus of the composites was found to decrease with increasing maximum cyclic strain in a similar manner to the Payne effect in filled rubbers; that is the modulus decrease with increasing strain amplitude. The exponent of the Kraus model was found to be m=1. At sufficiently low strain, the reinforcement was effective and the average tensile modulus of these CVD CNTs can be deduced using the mixture law to be around 580 GPa. At higher strains, the CNT reinforcement efficiency diminished and this tendency was amplified by aging.

Figure 1 -

 1 Figure 1 -Elastic modulus of unfilled epoxy and composites tested after a) 3 days and b) 1 month as a function of maximum cyclic strain. Solid lines are fits to Kraus model.

Figure 2 -

 2 Figure 2 -CNT reinforcement efficiency as a function of maximum cyclic strain before and after aging.

Table 1 -

 1 Values of the parameters of the Kraus model fitted to the experimental tests performed on the composites after 3 days and after 1 month.

LIST OF CAPTIONS

Table 1 -Values of the parameters of the Kraus model fitted to the experimental tests performed on the composites after 3 days and after 1 month.


Duc Toan Pham
email: ductoan.pham@cstb.fr

Nicolas Pinoteau

Mingguan Yang

Patrick De Buhan

Pierre Pimienta

Romain Mège

Full-scale fire test on a high-rise RC wall

Keywords: full-scale test, fire loading, high-rise wall, large deflection, reinforced concrete

This paper describes a full-scale test carried out on a high-rise reinforced concrete wall subjected to fire loading conditions in the special Vulcain furnace (very large and modular gas furnace) at CSTB, France. The test sample was designed to represent a slender wall with a very large height/thickness ratio. The experimental results showed a large deflection of the high wall in fire conditions (almost equal to the wall height/24) even for a fire exposure time of 90 min. Such a deflection was significantly higher than the maximum value recommended by design codes (about the wall height/30 for 120 min of fire exposure). Furthermore, other test results (full-field displacements in the 3 directions, residual deformed shape after the heating and cooling phases) may also provide additional useful experimental data for validating available or future models (which are usually based on some specific assumptions).

In addition, the measurements of thermal-induced deformed shape of the wall are compared to

INTRODUCTION

A great amount of tests has been carried out after about a century of investigations on the fire resistance of structures under standard conditions. One may quote, among many others, the experiments performed by Lie and Woollerton [START_REF] Lie | Fire Resistance of Reinforced Concrete Columns: Test Results[END_REF]; Dotreppe et al. [START_REF] Dotreppe | Experimental research on the determination of the main parameters affecting the behaviour of reinforced concrete columns under fire conditions[END_REF]; Franssen and Dotreppe [START_REF] Franssen | Fire tests and calculation methods for circular concrete columns[END_REF]; Kodur and Mcgrath [4], who more specifically focused their attention on the fire resistance of reinforced concrete (RC) columns exposed to fire; the fire tests on unbonded and bonded post-tensioned concrete slabs of Bailey and Ellobody [START_REF] Bailey | Fire tests on unbonded post-tensioned one-way concrete slabs[END_REF][START_REF] Bailey | Fire tests on bonded post-tensioned concrete slabs[END_REF] or the experimental work of Crozier and Sanjayan [START_REF] Crozier | Tests of load-bearing slender reinforced concrete walls in fire[END_REF] on slender RC walls. However, even though results of these standard fire tests provide useful experimental data for validating theoretical and numerical models, they are still limited to the situations where the dimensions of the tested structural components should remain compatible with those of conventional furnaces (furnace height is about 3 m, while furnace width may reach 4 m). In this context, any attempt to perform a fullscale test on a high-rise structural element requires the use of a higher (and wider) furnace such as the test of Lahouar et al. [START_REF] Lahouar | Fire design of post-installed bonded rebars: Full-scale validation test on a 2.94×2×0.15 m 3 concrete slab subjected to ISO 834-1 fire[END_REF]. On the other hand, the large-scale non-standard structural fire testing (see for example Troxell [START_REF] Troxell | Fire resistance of a prestressed concrete floor panel[END_REF], Rubert and Schaumann [START_REF] Rubert | Structural steel and plane frame assemblies under fire action[END_REF]; British Steel [START_REF] Steel | The behaviour of multi-storey steel frame buildings in fire[END_REF], Bailey and Lennon [START_REF] Bailey | Full scale fire tests on hollow core slabs[END_REF], or quite recently Santiago et al. [START_REF] Santiago | Experimental investigation of the behaviour of a steel sub-frame under a natural fire[END_REF]) may present an interesting alternative (Bisby et al. [START_REF] Bisby | A contemporary review of large-scale non-standard structural fire testing[END_REF]), but its reproducibility remains questionable.

With an increasing use in industrial buildings, the evaluation of fire behaviour of high-rise RC walls which are larger than the dimensions of conventional experimental test furnaces, requires a more sophisticated approach than for conventional, i.e. smaller size structures. Indeed, important out-of-plane (horizontal) displacements due to thermal-induced deformations induce an eccentricity of the vertical load (self-weight) with respect to the initial vertical plane of such the slender wall. Therefore, bending moments are generated in the wall in addition to the pre-existing compressive axial force distribution due to the wall self-weight, which is usually known as a second order (or P-delta) effect (Bazant and Cedolin [START_REF] Bazant | Stability of structures: elastic, inelastic, fracture and damage theories[END_REF]). Moreover, it is well known that elevated temperatures lead to local degradation of the stiffness and strength properties of both concrete and steel materials, which may accentuate the wall deformations still further.

Based on a simplified one-dimensional (1D) modelling of the problem, a yield designbased approach (Salençon [START_REF] Salençon | Yield design. Great Britain and the United States[END_REF]) has been developed for evaluating the potential failure of high-rise RC walls exposed to fire (see Pham [START_REF] Pham | Yield design based analysis of high rise reinforced concrete walls in fire[END_REF] or Pham et al. [START_REF] Pham | Interaction diagrams of reinforced concrete in fire: a yield design approach[END_REF][START_REF] Pham | Yield-design based of high rise concrete walls subjected to fire loading conditions[END_REF] for more details).

These studies have shown that the equilibrium deformed shape of the wall and the corresponding out-of-plane displacements due to thermal loading, may strongly increase with an even relatively slight increase of its height. On the other hand, the maximum value of 1/30 th for the deflection to height ratio (corresponding to a fire exposure of 120 min) recommended in design codes seems to be too conservative for high-rise RC walls. To provide a validation of the previously mentioned theoretical work, a full-scale fire test has therefore been carried out on an 8.4m-high RC wall in the very large and modular furnace Vulcain at CSTB, France.

In the present experimental study, the chosen configuration is the following. The wall is hinged at both ends and the top support can move vertically. This corresponds to a real technological system developed for constructing industrial buildings (see for example CIMbéton [START_REF] Cimbéton | Conception des bâtiments d'activités en béton : Murs séparatifs coupe-feu et façades à fonction d'écran thermique en béton[END_REF]). It is obvious that the results obtained in such a configuration, are on the safe side when compared to other configurations, where for instance the bottom of the panel would be clamped instead of simply supported.

According to the tabulated data of EN 1992-1-2 [START_REF]EN1992-1-2. Eurocode 2: Design of concrete structures-Part 1 2: General rules-structural fire design[END_REF] for non-load-bearing partition walls, the ratio of height of wall to wall thickness should be lower than 40 in order to avoid excessive thermal deformation and subsequent failure of integrity between wall and slab. In the context that such a proposed value was typically based on conventional fire tests (carried out on common structural elements), and in order to extend the specified limits of validity of such design aids for further high-rise walls, the test has been carried out on a slender wall with a very large height/thickness ratio (40% higher than the maximum value recommended in EN 1992-1-2 [START_REF]EN1992-1-2. Eurocode 2: Design of concrete structures-Part 1 2: General rules-structural fire design[END_REF]). Such a heavy and sophisticated fire test may help to reproduce the large deflection and the desired (P-delta) effect associated with the large vertical size of the structure, providing thus useful experimental data for validating available or future predictive models (which are usually based on some specific assumptions).

In this paper, the characteristics of the RC wall specimen, the test setup related to its thermal loading and the instrumentation are first described. It would be interesting to note that, in order to gather full-field displacements (in the 3 directions) of the wall during the fire test, a Stereo Digital Image Correlation technique (DIC) was used in addition to classical linear variable differential transformer sensors (LVDTs). The experimental results are then reported and discussed with reference to the equilibrium deformed configuration of the high wall in relation with thermal loading. Finally, the measurements of the thermal-induced deformed shape of the wall are compared to those predicted by an analytical solution derived from a simplified 1D beam model previously mentioned (Pham [17] or Pham et al. [START_REF] Pham | Interaction diagrams of reinforced concrete in fire: a yield design approach[END_REF][START_REF] Pham | Yield-design based of high rise concrete walls subjected to fire loading conditions[END_REF]) as well as to those obtained with non-linear finite-element simulations (with 2D plate elements), in order to assess the validity of these models.

TEST PROCEDURE

Characteristics of the test wall

The RC wall was 2.6m-wide, 8.4m-high and 0.15m-thick, the height being equal to three times the width and the height/thickness ratio being equal to 56. Table 1 presents the concrete formulation which was used. In order to prevent spalling of concrete due to fire, polypropylene fibers were included in the concrete. After 90 days of curing in ambient laboratory conditions, the concrete presented a compressive strength of fc = 36.1 MPa (determined from compressive tests performed on 150×150×150 mm 3 cubes) and a tensile strength of ft = 2.75 MPa (determined from splitting tests on 160×320 mm² cylinders). The wall was reinforced by two symmetrical layers of 9 mm diameter hot rolled steel reinforcing bars of yield stress fy = 480 MPa, ultimate strength fr = 533 MPa and Young modulus's Es = 210 GPa, with a spacing of 100 mm (Fig. 1). The steel bars were arranged in two orthogonal arrays and placed with 25 mm of concrete cover at both the top and the bottom parts of the wall thickness.

Test setup

The boundary conditions were such that both ends of the wall were articulated (no deflection but free rotation) as shown in Fig. 2. The bottom end of the wall was kept fixed in vertical and transversal translations, while its top end was free to translate vertically. The lateral sides of the wall were stress free. To ensure such boundary conditions, the main part of the wall (8m-high) was connected at the top and the bottom to two concrete blocks of 0.3×0.3×2.6 m 3 which were reinforced in order to resist to concentrated local stresses and connected to the main wall by reinforcing bars. These reinforcing bars were welded to the steel frames (diameter 9 mm) inside the wall. These two concrete blocks were casted before the main wall. A rough surface on the concrete was realized at the interface between the main wall and the concrete blocks (Fig. 3). The concrete block at the bottom (Fig. 3(b)) was equipped with a steel plate (20 mm-thick) that was connected to the concrete during casting with steel bars. At mid-width, this plate was equipped with a welded steel cylinder to ensure the boundary condition at the bottom of the wall (free rotation). The total mass of the sample (main wall and 2 concrete blocks) was around 8 tons. The whole wall was positioned inside a concrete frame for transportation (including retrieving the sample after the test) to place the sample in front of the furnace. This concrete frame (with the sample inside) was used to close the furnace while exposing the sample on one side. Between the sample and the frame, insulating material was positioned to prevent any thermal action on the lateral sides of the wall. This isolation was placed with a fold so as to allow large deflections of the wall without ripping the insulation.

The concrete frame was also used to position the outer mechanical systems ensuring the boundary conditions. At the top, two U-shaped steel devices allowed the steel cylinder to slide vertically (ensuring translation and rotation-Fig. 3(a)). At the bottom, a steel plate notched at mid-width along the entire length allowed the bottom cylinder to be maintained in position (ensuring the rotation -Fig. 3(b)).

In addition, a steel frame was bolted onto the concrete frame. This steel frame (composed of 2 vertical HEA160 and 10 horizontal HEA100) was used for safety purposes in order to maintain the sample in case of collapse. Flexible steel wires were bolted to the wall samples and connected to the steel frame to prevent the wall from falling in case of failure during the test. The wires were left loose enough (600 mm) to avoid disturbing the deflection of the wall during the test. Finally, the steel frame was used to fix the displacement LVDTs, serving as reference for all the displacements that were measured.

During the fire test, the inner inside surface of the wall was exposed to ISO 834-1 fire (EN 1991-1-2 [START_REF]EN1991-1-2. Eurocode 1: actions on structures-Part 1-2: General actions[END_REF]) for 90 min. The special 9m-high furnace presented a maximal power around 12 MW. The ISO 834-1 curve was conventionally controlled by using 24 plate thermometers positioned at 100 mm from the exposed surface of the test sample. Furnace temperatures were recorded during the test.

Instrumentation and measurements

The temperatures (across the wall thickness -Fig. 4) of concrete material were measured with thermocouples positioned at different locations (T1 to T8 : Fig. 5). These thermocouples were placed in the central area of the wall as well as in the areas near the lateral sides, as shown in Fig. 5. In order to avoid edge effects, thermocouples and LVDTs were all placed with a minimum distance of 500 mm from the vertical sides of the wall (see Fig. 5). In addition, the displacement fields in the 3 directions of the wall during the fire test were recorded with a Stereo Digital Image Correlation technique (DIC). The image correlation was carried out using 2 cameras with a resolution of 2.3 MPixels and positioned 7.5 m away from the wall.

These two cameras were calibrated to recognize spatial positions by triangulation. To identify displacements, a speckle (composed of black dots presenting a non-uniform distribution and a

given diameter) was painted on the non-exposed side of the wall sample.

TEST RESULTS AND DISCUSSIONS

Thermal loading

The ambient temperature at the beginning of the fire test was recorded with the average values around 13°C. The evolution of the average furnace temperatures in comparison with the ISO 834-1 temperature-vs-time curve (EN 1991-1-2 [START_REF]EN1991-1-2. Eurocode 1: actions on structures-Part 1-2: General actions[END_REF]) is presented in Fig. 6, showing that the applied temperature on the interior surface of the wall closely followed the target ISO 834-1 curve, except for an overshoot in the early stages of the test. Figure 7 shows the average temperature profiles across the thickness of the wall, corresponding to 30, 60 and 90 min fire durations. Slightly higher temperatures can be observed in the central zone (thermocouples from T1 to T4) with respect to those in the lateral zone (thermocouples from T5 to T8). For the steel reinforcing bars, since their diameter was small, their temperature could be considered as corresponding to that of the concrete located at the same position (EN 1992-1-2 [START_REF]EN1991-1-2. Eurocode 1: actions on structures-Part 1-2: General actions[END_REF]).

1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 1 T 5 T 2 T 3 T 7 T 4 T 6 T 8 T 8.

Live viewing of the wall deflected configuration

During heating, the deformation of the high wall under the combined action of thermal loading (thermal curvature and thermal expansion) and the wall self-weight was clearly visible. Figure 8 displays the out-of-plane deflected shape of the wall after 90 min of fire exposure time. Large displacements were observed, with the maximum value up to 350 mm in the middle-height of the wall. This leads to a deflection/height ratio equal to 1.25/30 which is 25% higher than the value quoted in design codes, even for a fire exposure time of only 90 min (value of deflection/height around 1/30 for a fire exposure time of 120 min). However, despite such relatively large deflections, no lateral instability or damage of the structure has been observed. Values recorded by the three LVDTs D7 to D9 were lower and very close since they are placed near the top edge of the wall. Moreover, the edge was connected to the concrete block (Fig. 3(a)) and simply supported, thus preventing out-of-plane displacement at the top edge.

Figure 10 shows the evolution of the vertical displacement measured by LVDTs V (placed at the top of the test wall -Fig. 5) as a function of the fire exposure time, positive displacements corresponding to a downwards movement. As can be seen from this figure, the top of the wall is first moving upwards due to thermal expansion, then after 15 min moves in the opposite direction (i.e. downwards) as the thermal curvature and related out-of-plane displacements increase. From Fig. 11, it can be immediately seen that distribution of displacements is almost symmetrical with respect to the mid-height as well as to the mid-width of the wall, with the maximum values appearing in the central zone. The curvatures seem to be slightly decreasing from the central area of the wall to its top and bottom horizontal edges. Moreover, an estimated one third of the wall surface does not seem significantly affected by the conditions on these horizontal end supports (where the out-of-plane displacements were kept equal to zero during the test). This may be due to the fact that, the width of the wall (2.6 m) is equal to one-third of its height (8.4 m) that is enough to neglect the influence of the two top and bottom edges, while the lateral sides of the wall are stress free.

3D deformed shape obtained by image correlation technique

Figure 12 presents the horizontal displacement profiles along the height near the midwidth of the wall, while figure 13 shows the horizontal displacement profiles along the width at mid-height of the wall, as functions of fire exposure time. Values recorded about 24 h after the end of the thermal loading are also given in these two figures (blue lines). During this cooling phase, the horizontal displacement was reduced to about one-third of the maximum recorded value (110 mm) and did not return to zero (initial vertical plane). This implies that non negligible irreversible plastic deformations have been generated during the fire test. This residual deformed configuration of the wall thus provides additional information on the final equilibrium of the structure after the entire heating and cooling cycle.

COMPARISON WITH AN ANALYTICAL SOLUTION DERIVED FROM A SIMPLIFIED ONE-DIMENSIONAL (1D) BEAM MODEL

In this section, experimental results are compared to those obtained from a simplified onedimensional (1D) beam model of the high-rise wall, represented as an initially straight vertical beam of height H and thickness h, articulated at both ends as shown in Fig. 14.

A fully detailed description of the theoretical model, with the associated assumptions and the proposed iterative calculation procedure may be found in Pham [START_REF] Pham | Yield design based analysis of high rise reinforced concrete walls in fire[END_REF] or Pham et al. [START_REF] Pham | Interaction diagrams of reinforced concrete in fire: a yield design approach[END_REF][START_REF] Pham | Yield-design based of high rise concrete walls subjected to fire loading conditions[END_REF]. The geometric configuration of the high-rise wall is determined from a thermo-elastic iterative calculation accounting for geometrically non-linear second order effects. This calculation is carried out until convergence of the sequence of computed transversal displacements is observed. As it has been shown in Pham [START_REF] Pham | Yield-design based of high rise concrete walls subjected to fire loading conditions[END_REF], such an iterative procedure, which could appear time consuming, remains however quite simple since the deformed shapes corresponding to the second and the third iterations are almost coincident with the converged solution. By carrying out 2 iterations of the iterative procedure proposed in these studies, the following closed-form expression of the solution of the final equilibrium deformed configuration of the wall, characterized by the out-of-plane displacement u at any point x, may be obtained:

2 2 1 1 ( ) ( ) 120960 ( ) u x w f x EI θ θ χ = (1)
f x x H x x x H x H x H H x H x H = - - + - - + + (2)
is a polynomial function of degree 8, w denotes the constant linear density of the wall selfweight while χθ and (EI)θ are the constant curvature of the wall and the wall section flexural stiffness under pure bending, respectively. These quantities may be easily calculated for any prescribed thermal gradient across the wall thickness (see Pham [START_REF] Pham | Yield design based analysis of high rise reinforced concrete walls in fire[END_REF] or Pham et al. [START_REF] Pham | Interaction diagrams of reinforced concrete in fire: a yield design approach[END_REF][START_REF] Pham | Yield-design based of high rise concrete walls subjected to fire loading conditions[END_REF] for more details).

For numerical applications of the proposed model, the thermal gradients across the wall thickness were introduced by the use of the temperatures in the central zone provided in Fig. 7. Since the temperature dependencies of the thermal-mechanical properties of concrete as well as steel materials were not directly measured in this work, material properties were considered to be temperature dependent according to Eurocode 2-Part 1-2 (EN1992-1-2 [START_REF]EN1992-1-2. Eurocode 2: Design of concrete structures-Part 1 2: General rules-structural fire design[END_REF]).

Besides, in order to include the majority of encountered normal strength concretes and limit the effects of some uncertainties concerning the material properties due to lack of extra characterization tests, material properties of concrete with both siliceous and calcareous aggregates are used for comparison. As a direct result, performing calculation with siliceous aggregates concrete is on the safe side, thus providing an upper bound estimate of the out-ofplane displacement. On the other hand, calculations with calcareous aggregates concrete lead to lower bound estimates.

The results of both experiments and theoretical predictions are illustrated in Fig. 15,

showing a rather good agreement between them. As expected, the experimental measurements are located between two corresponding theoretical predictions (lower and upperbounds). This comparison represents a first preliminary validation of the simplified 1D beam model and the associated closed-form expression of the equilibrium deformed configuration, even in the absence of extra characterization tests of material properties of concrete as functions of temperature increase. Besides, the deflection values predicted with siliceous aggregates concrete are higher than those resulting from the use of calcareous aggregates concrete (the relative difference between the maximum deflections is about 20%). This suggests that the results of the theoretical model are quite sensitive to the variation of the thermal expansion with temperature, εc(θ), as well as to the coefficient kc(θ) quantifying the decrease of stiffness and strength properties of the concrete material as a function of temperature increase (see Pham [START_REF] Pham | Yield design based analysis of high rise reinforced concrete walls in fire[END_REF] and Pham et al. [START_REF] Pham | Yield-design based of high rise concrete walls subjected to fire loading conditions[END_REF] for more details).

Fig. 15.

Comparison of experimental results with theoretical predictions (note that the abscissa scale is strongly dilated)

COMPARISON WITH THE RESULTS OF NUMERICAL SIMULATIONS WITH 2D PLATE ELEMENTS

The main limitation of the simplified 1D beam model presented above lies in the fact that the horizontal curvature as well as the vertical displacement of the wall top edge could not be directly evaluated. Indeed, the wall was hinged along the bottom edge, but it was not hinged along the top edge. In fact, two U-shaped steel devices allowed the outer parts of the steel cylinder of the concrete block at the top of the wall to slide vertically (in order to ensure the free rotation and vertical translation -see Fig. 3(a) for more details). Moreover, the thickness of the two concrete blocks which was twice the thickness of the main wall, may have some influence on the final out-of-plane displacements field. For these reasons, two numerical simulations using a dedicated finite element software (Marc finite-element code -MSC Software Corporation [START_REF]User documentation of MSC Marc[END_REF]) of the same problem have been performed. These simulations differed from each other by the top and bottom end conditions as summarized in Tab. 2. The numerical calculation is performed in the context of a thermo-elastic behaviour (see Pham [START_REF] Pham | Yield design based analysis of high rise reinforced concrete walls in fire[END_REF] for a detailed description of the specific features of the simulation). For illustrative purpose, the results of the non-linear finite-element simulation for the first wall (wall 1without concrete blocks and hinged along two top and bottom edges) are presented in Fig. 16, in the form of the contours of the out-of-plane as well as vertical displacements experienced by the wall for 90 min of fire exposure (values in meters). As expected, the displacements distribution is symmetrical with respect to both the mid-height and the mid-width of the wall, with the maximum value in the central part of the wall.

Tab

The corresponding maximum out-of-plane deflections and vertical displacement of the top wall of the simplified 1D and 2D plate models are reported in Tab. 3. It confirms that the influence of both the concrete blocks and the 2 points support on the final maximum out-ofplane displacement is negligible. Besides, the results of the simplified 1D model seems to be on the safe side and accurate enough for a preliminary engineering design of this kind of structure.

CONCLUSIONS

The purpose of this experimental study was to investigate the influence of temperature increase on the thermal-induced change of geometry of a high-rise reinforced concrete (RC)

wall. The full-scale fire resistance test has been successfully carried out on an 8.4m-high wall.

The experimental results have shown some specific features of such a full-scale fire test which might affect current design practices as follows:

• The maximum value of 40 relating to the height to thickness ratio of the wall indicated in the design codes (EN 1992-1-2 [START_REF]EN1992-1-2. Eurocode 2: Design of concrete structures-Part 1 2: General rules-structural fire design[END_REF]) seems to be too much restrictive as regards the application of these codes to very slender walls. This is probably due to the fact that the additional horizontal displacement due to further elastic bending associated to the self-weight eccentricity, remains negligible in the case of walls of normal heights.

When the ratio of height of wall to wall thickness is higher than 40, geometrically non-linear second order effects should be taken into account.

• The evolution of the deflection of the high wall as a function of the fire exposure time appears to be almost linear. This deflection could reach a much higher value than that indicated by design codes for walls of normal heights (experimental value around wall height/24 even for a fire exposure time of 90 min compared to a value of wall height/30 for a fire exposure time of 120 min). As a consequence, such a value should be revised for the case of high-rise walls.

• Contrary to walls of normal heights, the top of the high-rise wall is not always moving upwards due to the axial thermal expansion of the concrete material. The wall top edge appeared to be moving downwards as soon as the deflection exceeded a specific value (of the order of the wall thickness (after about 35 min) in the present test). This was due to the fact that the effect of transversal displacement (which is directly linked to the thermal curvature) became more important than that of in-plane displacement (vertical displacement) which was related to the axial thermal expansion.

• At the end of the total heating-coolingcycle, the wall did not return to its initial vertical configuration, which is probably due to irreversible plastic deformations induced by the fire test. Even for only 90 min of fire exposure, the residual out-ofplane deflection may remain important (two thirds of the wall thickness in the present test).

In addition, comparisons have also been made on the deformed shape predicted by a simplified 1D beam model, in which particular importance was attributed to the degradation of material properties under fire-induced thermal loading, as well as by a non-linear finiteelement simulation (with 2D plate elements) of the same problem, in order to assess their practical validity. Such comparisons show a reasonably good agreement between experimental and theoretical/numerical predictions, thereby validating the theoretical and numerical models. It confirms that the simplified 1D model provides results on the safe side and accurate enough for a preliminary engineering design of this kind of structure. For the more realistic 2D plate models, displacement distributions may not be significantly affected by the boundary conditions prescribed along the top and bottom edges (with or without concrete blocks, hinged along the top edge or simply supported on 2 points) if the wall is high enough (the wall height should be three times higher than the width). On the other hand, the results of this unprecedented test may provide useful experimental data for validating available or future models based on some specific assumptions.

Fig. 1 .

 1 Fig. 1. Sample formwork and reinforcement layout of the test wall

Fig. 2 .

 2 Fig. 2. Positioning of the test sample in front of the furnace

Fig. 3 .

 3 Fig. 3. (a) Top and (b) bottom concrete blocks before casting of the main wall

Fig. 4 .

 4 Fig. 4. Thermocouples positioned at different depths across the wall thickness

Fig. 5 .

 5 Fig. 5. Positions of thermocouples and LVDTs

Fig. 6 .

 6 Fig. 6. Average furnace temperatures and ISO 834-1 temperature curve

Fig. 7 .

 7 Fig. 7. Average temperature distributions across the wall thickness for different fire exposures

Fig. 8 .Fig. 5 )Fig. 9 .

 859 Fig. 8. Deformed shape of the wall after 90 min of fire exposure time

Fig. 10 .

 10 Fig. 10. Evolution of vertical displacements (counted positive downwards) measured by LVDTs at the

Figure 11 (

 11 Figure 11(a) shows the contours of the out-of-plane (horizontal) displacements of the wall

Fig. 11 .

 11 Fig. 11. Contours of the wall horizontal displacements (in mm): (a) front view and (b) 3D deflected

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Horizontal displacement profiles along the height near the mid-width of the wall as function

Fig. 14 .

 14 Fig. 14. Schematic diagram of thermal and equilibrium deformed shapes of the wall under fire loading

  where

Fig. 16 .

 16 Fig. 16. Face views of contours of the wall out-of-plane (left) and vertical displacements (in meters)

  . 2. Difference between two numerical simulations (with 2D plate elements)

		Simulation 1	Simulation 2
	Boundary conditions at the bottom edge	Hinged	Hinged
	Boundary conditions at the top edge	Hinged	Simply supported on 2 points
	Concrete blocks at the bottom and top edges	Not simulated	Simulated

Table 3 .

 3 Comparison between maximum displacements obtained by the simplify 1D beam model

	and the 2D plate models

ACKNOWLEDGMENT

Authors wish to thank all members of experimental team of the Mechanical and Fire Resistance division at CSTB: Philippe Rivillon, Romuald Avenel, Stéphane Charuel, Jean-Francois Moller, for their help to make the test successful.