51687 Reims, Cedex 2, France. ABSTRACT

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1 Effct of Tmpratur-dpndnt Sorpton Charactrstcs on th Hygrothrmal Bhavor of a Hmp Concrt Buldng Envlop Submttd to Ral Outdoor Condtons Anh Dung Tran L 1, Drss Samr², Mourad Rahm 1, Omar Douzan 1, Goffry Proms 1, Chad Maalouf 3, Mohammd Lach 3, Thrry Langlt 1 1 Laborator ds Tchnologs Innovants (LTI), Unvrsté d Pcard Juls Vrn Avnu ds Facultés, Amns, Cdx 1, Franc 2 Crm Drcton trrtoral Sud-Oust, Ru Prr Ramond CS Sant Médard n Jalls Cdx, Franc 3 Laborator d Thrmomécanqu (LTM), GRESPI, Unvrsté d Rms, Faculté ds Scncs, Mouln d la Houss, Rms, Cdx 2, Franc. Emal: anh.dung.tran.l@u-pcard.fr ABSTRACT Hmp concrt has bn usd mor and mor n buldng constructon bcaus hmp s a rnwabl plant, rcyclabl and dos not dgrad wthn tm. Up to now, many smulaton tools us th sorpton sothrms that dscrb th rlatonshp btwn rlatv humdty of ar and th mostur contnt to prdct th humdty n porous matrals. Howvr, th sorpton capacty of matral dpnds on tmpratur. Th objctv of ths papr s to study th mpact of th tmpratur dpndncy of th sorpton curvs on th hygrothrmal bhavor of a hmp concrt buldng nvlop. Numrcal modls to dscrb th coupld hat and mass transfr n porous matrals ar prsntd and valdatd aganst xprmntal data. In addton, th ffct of tmpratur-dpndnt sorpton on th hygrothrmal profls of a hmp concrt wall submttd to outdoor ral condtons has bn conductd. Th rsults show that takng th nflunc of tmpratur on th sorpton charactrstcs nto account s ncssary for bttr prdcton of th hygrothrmal bhavor of a hmp concrt buldng nvlop. Kywords: hygrothrmal bhavor; tmpratur-dpndnt sorpton; hmp concrt NOMENCLATURE C P Spcfc hat at constant prssur D T Mass transport coffcnt assocatd to a tmpratur gradnt D T,v Vapor phas transport coffcnt assocatd to a tmpratur gradnt D θ Mass transport coffcnt assocatd to a mostur contnt gradnt D θv Vapor phas transport coffcnt assocatd to a mostur contnt gradnt h M Mass transfr convcton coffcnt Hat transfr convcton coffcnt h T L v T θ ρ 0 ρ l ρ v φ Hat of vaporzaton Tmpratur Mostur contnt Mass dnsty of dry matral Mass dnsty of watr Mass dnsty of watr vapor Rlatv humdty 1. Introducton Tmpratur and rlatv humdty ar mportant paramtrs nfluncng prcvd ndoor ar qualty and human comfort. Hgh mostur lvls can damag constructon and nhabtant s halth. Hgh humdty harms matrals, spcally n cas of condnsaton and t hlps moulds dvlopmnt ncrasng allrgc rsks. Consquntly, svral rsarchrs hav studd

2 th us of varous hygroscopc matrals to modrat ndoor humdty lvls. Th matral that absorbs and dsorbs watr vapor can b usd to modrat th ampltud of ndoor rlatv humdty and thrfor to partcpat n th mprovmnt of th ndoor qualty and nrgy savng (Hamury 2005; Olalkan t Smonson 2006; Woloszyn t al.2009; Tran L t al. 2010; Sha t al. 2013; Maalouf t al. 2014). Vgtal fbr matrals ar an ntrstng soluton as thy ar co matrals and hav low mbodd nrgy. Hmp concrt s on of ths matrals whch s mor and mor rcommndd by th co-buldrs for ts low nvronmntal mpact. Th physcal proprts of hmp concrt has bn masurd by many authors (Crzo 2005; Collt t al. 2008; Evrard 2008; Rahm t al. 2015). It s hghlghtd that th on prsnts hgh mostur buffrng capacty and a good comproms btwn nsulaton and nrta matrals. To nvstgat th hygrothrmal bhavor of buldng nvlop, a smulaton should b don bcaus t s chapr and mor dtald than th tst n stu. For ths to b don, many smulaton tools hav bn dvlopd. Hygrothrmal proprts ar rqurd for all Hat, Ar and Mostur transfr (HAM) modls. Many modls and smulaton tools for prdctng th hygrothrmal bhavor of buldng nvlop ar rprsntd n th Annx 41 of th Intrnatonal Enrgy Agncy s (IEA). For th buldng nvlop, th man dffrnc n HAM-transfr modlng s mad by th dmnson of rprsntd phnomna and thy can b classd by th granularty and complxty (Annx 41). A dtald paramtrc study of hygrothrmal bhavour of a wall mad of hmp concrt submttd to hygrothrmal shock has bn carrd out and showd that tmpratur and rlatv humdty varatons n a wall ar vry snstv to thrmal proprts, mostur transport coffcnt and sorpton sothrm (Tran L t al. 2014). Up to now, most hygrothrmal tools hav usd th sothrmal sorpton curvs that xprss th qulbrum btwn th mostur contnt and rlatv humdty n th rprsntatv lmntary volum at a constant tmpratur. Howvr, fw works studd th ffct of tmpratur on hygrothrmal bhavour of a buldng nvlop (Carstn and Clorus 2004; At Oumzan 2014). Ths artcl ams to study th ffct of th tmpratur-dpndnt sorpton on th prdcton of hygrothrmal bhavor of a hmp buldng nvlop submttd to a varaton of tmpratur and rlatv humdty. Frst, th dtals for th mathmatcal modl ar shown. Th modls ar laboratd and mplmntd n th Smulaton Problm Analyss and Rsarch Krnl (SPARK), whch s adaptd to th complx problms (Sowll and Havs 2001; Wurtz t al. 2006; Mndonça t al. 2002; Tran L t al. 2009). Thn, th smulaton tools ar valdatd wth xprmntal rsults obtand from th tst wall ralsd n our laboratory. Aftr bng valdatd, th ffct of non-sothrmal condtons on th tmpratur and rlatv humdty profls wll b dscussd. In th nxt part, th mathmatcal modl for th coupld hat and mostur transfr n buldng matrals wll b prsntd. 2. Mathmatcal modls 2.1 Hat and mostur transport n porous buldng matrals Mchansms of mostur transport n a sngl porous buldng matral hav bn xtnsvly studd (Phlp and D Vrs 1957; Cunnngham 1988; Bar and Bachmat. 1990; Pdrsn 1992, Kunzl 1995, Mnds t al. 2003). Most of th modls hav narly th sam orgn; th man dffrnc among thm s rlatd to partcular assumptons usd. In ths artcl, th modl that taks nto account mostur (lqud and vapor phass) transport s usd (Mnds t al. 2003). Forms of mostur transport dpnd on th por structur as wll as on th nvronmntal condtons. Th lqud phas s transportd by capllarty whras th vapor phas s du to th gradnts of partal vapor prssur. Wth ths consdratons, th mass consrvaton quaton bcoms: T DT D (1) t x x x x Wth th followng boundary condtons rspctvly for th xtrnal (x=0) and ntrnal (x=l) surfacs of th wall: T l D T D hm, v, v, s, x x x0, (2) T l D T D hm, v, s, v, x x xl, (3) whr th subscrpt a rprsnt th adjacnt ar and s th sold surfac of th matral, whl th subscrpts and corrspond rspctvly to th xtrnal and ntrnal nghborng nvronmnt (a) or sold surfac (s). On dmnson of th nrgy consrvaton quaton wth coupld tmpratur and mostur for a porous mda s consdrd and th ffct of th adsorpton or dsorpton hat s addd. Ths quaton s wrttn as: T T T 0Cpm Lv l DT, v t x x x x D, v (4) x x whr C Pm s th avrag spcfc hat whch taks nto account th dry matral spcfc hat and th contrbuton of th spcfc hat of lqud phas. CPm l CP0 CPl (5) 0

3 s thrmal conductvty dpndng on mostur contnt. Not that th mor porous a mda s, th mor th ffctv thrmal conductvty would b on th thrmal conductvty of th watr contnt (Sadoun t al. 2012). Outdoor condtons Convctv hat and mass transfr φ ray,o φ m,o φ T,o Hat and mass transfr φ ray, φ m, φ T, Indoor condtons Convctv hat and mass transfr Fg. 1. Schmatc rprsntaton of hat and mostur transfr through th wall. Fg. 1 shows th boundary condtons that tak nto account convctv hat transfr, radatv hat transfr and hat assocatd to phas changs, as xprssd n th rght sd of Eqs. (6) and (7) for th xtrnal and ntrnal surfacs rspctvly. T T Lv l DT, v D, v ht, T Ts, x x x x0, L vh M, v, v, s, (6) T Lv l D x T L vh M, v, s, v, T, v D, v ht, Ts, x x xl, (7) T In th cas lackng a data bas of mostur transport coffcnts, smplfd modls should b usd. Th us of smplfd mathmatcal modls has varyng ffcts on accuracy and has bn dscussd n (Mnds t al. 2003). In ths study, th ffct of tmpratur gradnt on mostur transport s nglctd whch s gnrally accptd. Th mostur dffuson coffcnt rlatd to mostur contnt gradnt s valuatd as: D P vs T l (8) Th quatons contan svral paramtrs that ar thmslvs functon of th stat varabls. Th spcal ntrsts of th modl ar th dpndncs of mostur contnt, mostur transport coffcnt, thrmal conductvty tc. upon th rlatv humdty and tmpratur. Ths maks possbl to tak nto account th tmpratur-sorpton dpndnc nto th modl, whch wll b prsntd n th nxt subscton. 2.2 Effct of tmpratur on th sorpton charactrstcs Up to now, many studs hav bn carrd out to masur th gnral shap of th sothrmal sorpton charactrstc. Howvr, th physcs rlatd to th sothrmal sorpton curvs ar stll dsputd. Th rsarchs showd that th sorpton capacty of matrals dpnds on th tmpratur (Carstn and Clorus 2004; At Oumzan 2014; Nav and Hrgr 2005). Incrasng tmpratur wll ntal that th sostrc mostur contnt b rachd n qulbrum wth a hghr rlatv humdty. Th study of ts ffct on th hygrothrmal bhavor for th bo-basd matrals s nw (Carstn and Clorus 2004). Concrnng th hmp concrt, At Oumézan (2014) showd that takng nto account ts nflunc s ncssary. In ths artcl, w us two modls dscrbng th rlaton btwn sorpton charactrstcs at dffrnt tmpraturs: Mlly's modl (Mlly 1982) and Poyt's modl (Poyt and Charls 2009). Mlly's modl s basd on th ffct of tmpratur on th ntrnsc proprts of watr to stablsh th sorpton curvs. Th tmpratur dpndnt sorpton charactrstcs ar xprssd as: C 2(, T2 ) 1 T 1( C ( T2 T1 ), T1 ) (9) (10) Howvr, Poyt and Charls (2009) showd that ths consdraton s not suffcnt to wll prdct th hygrothrmal bhavor of concrt. Thus, th authors propos on anothr modl basd on th dffrntal hat of sorpton, whch s wrttn as: 2 T, T, 2 ( T ) ( T ) M l T 2 T1 R T1T st sat P P q (11) sat 2 whr: M l : molar mass of watr [kg.mol -1 ]; R: dal gas constant [J.mol -1.K -1 ]; q st : sostrc hat [J.kg -1 ], whch s calculatd from two sorpton sothrms at two dffrnt tmpraturs (T 1 and T 2 ). In ordr to solv th prvous quaton systm, th numrcal soluton s basd on th fnt dffrnc tchnqu wth an mplct schm. To solv ths systm of quatons, w usd th Smulaton Problm Analyss and Rsarch Krnl (SPARK) whch s spcally sutd to solv ffcntly dffrntal quaton systms. 3. Modl valdaton 3.1 Exprmnt and smulaton condtons Ths scton concrns th valdaton of th numrcal modl by comparng th smulaton rsults wth xprmntal ons. For ths to b don, an xprmntal faclty has bn dvlopd at "Ecol Natonal ds Travaux Publcs d l'etat (ENTPE)" n

4 Tmpratur ( C) Journal of Appld Flud Mchancs, Vol. 9, Spcal Issu-1, pp. x-x, 200x. Franc. Th xprmntal stup conssts of an clmat chambr to smulat outdoor clmat condtons, a tst wall and snsor for masurng th tmpratur and th rlatv humdty. Mor dtals of ths faclty can b found n (Samr 2008). On sd of tstd wall was submttd to varous outdoor condtons of tmpratur and rlatv humdty usng a clmat chambr, whl othr sd of th wall was n contact wth th laboratory ambnt whr tmpratur and rlatv humdty ar rlatvly constant. Th tst wall was nstrumntd wth snsors, whch ar connctd to an acquston systm to masur th hygrothrmal profls. It conssts of a hmp concrt wall wth 30 cm of thcknss. Th wall was subjctd to cyclc stp-changs n rlatv humdty and tmpratur: 20 C/50% RH durng 24h followd of 10 C/80% RH durng 24h; 40 C/45% RH durng 24h and fnally fnshd wth 20 C/50% durng 24h (s Fg. 2). Fg. 2 : Exprmntal procdur : Stp-changs n rlatv humdty and tmpratur. Tabl 1: Hygrothrmal proprts of hmp concrt (At Oumzan, 2014). Dnsty Thrmal conductvty Spcfc hat capacty Watr vapor prmablty kg/m 3 W/(m.K) J/(kg.K) Kg/(m.s.Pa) Th hygrothrmal proprts of hmp concrt masurd by (At Oumzan, 2014) ar usd for th smulaton. Som basc hygrothrmal data of hmp concrt s gvn n Tabl 1. It s notcd hr that som authors hav valdatd thr modls wth constant coffcnts usng th rsults of ths xprmntal cas (Tran L t al., 2014; Samr, 2008). Howvr, th fact that a valu of about (m²/s) of mass transport coffcnt assocatd to a mostur contnt gradnt was usd for thr valdatons s not ralstc. Thrfor, ths artcl focuss on a mor compltd modl that taks nto account th ffct of th tmpratur-dpndnt sorpton charactrstcs on th hygrothrmal rspons of hmp concrt wall. Th smulaton has bn ralzd for two followng modls: Isoth: Usng th sothrmal sorpton charactrstcs n th smulaton Non-Isoth: Takng nto account th ffct of tmpratur on th sorpton curv by usng th Poyt's modl or Mlly's modl In addton, to tst th ffct of usng th dffrnt sorpton curvs, for ach modl, thr cass hav bn consdrd: Adsorpton curv Dsorpton curv Man sorpton curv obtand from th avrag btwn adsorpton and dsorpton. In ths papr, th sostrc hat adsorpton of hmp concrt has bn dtrmnd by usng th sorpton sothrms at 10 and 23 C (At Oumzan, 2014). For th both ndoor and outdoor surfacs, th hat and mass transfr coffcnts ar 9 W.m -2.K -1 and m.s -1, rspctvly. Th tm stp s 240 sconds and th wall was dscrtzd nto 25 nods accordng to on snstv study conductd by (Tran L t al. 2009). In ordr to facltat th nvstgaton, only th rsults obtand n th mddl of th wall (pont C) wll b prsntd. 3.2 Isothrmal hygrothrmal bhavor of hmp concrt wall: Isoth modl Th comparson btwn th varaton of tmpratur and rlatv humdty at pont C obtand from th smulaton usng th Isoth modl and th on from th xprmntal masurmnt s prsntd n Fg. 3 and Fg T at C Tstng T at C Smulaton_Adsorpton T at C Smulaton_Man curvs T at C Smulaton_Dsorpton T outsd Tm (h) Fg. 3 : Varaton of tmpratur at pont C Isoth modl and xprmntal masurmnt. On can obsrv that th varaton of tmpratur s vry smlar for th thr studd cass (adsorpton,

5 Rlatv humdty (%) Rlatv humdty (%) Tmpratur ( C) Journal of Appld Flud Mchancs, Vol. 9, Spcal Issu-1, pp. x-x, 200x. dsorpton and avrag curv). Th modl gvs a qut satsfactory prdcton of tmpratur wthn th wall, dspt som dscrpancy btwn xprmntal and prdctd valus. Concrnng th varaton of rlatv humdty, th computd rsults dd not ft to th xprmntal on. Ths should b xpland by th fact that th studd modl nglctd th ffct of tmpratur on th mostur sorpton capacty of th matral, n whch ncrasng tmpratur rsults n ncras of th rlatv humdty at gvn watr contnt. Thrfor, th dpndncy of sorpton charactrstc on tmpratur has bn takn nto account n th physcal modl and th rsult wll b prsntd n th followng subscton. RH at C Tstng RH at C Smulaton_Adsoprton RH at C Smulaton_Man curvs RH at C Smulaton_Dsorpton RH outsd Tm (h) Fg. 4: Varaton of rlatv humdty at pont C Isoth modl and xprmntal masurmnt. 3.3 Non-sothrmal hygrothrmal bhavor of hmp concrt wall: Non-Isoth modl As mntond abov, both Mlly's modl and Poyt's modl hav bn usd to study th mpact of nonsothrmal condtons on th hygrothrmal bhavor of hmp concrt. Bcaus th rsults obtand from th Mlly's modl ar vry clos to thos from Isoth modl, thy ar not dpctd hr. Ths subscton focuss only on th rsults obtand by usng Poyt's modl and on th comparson btwn ts rsults and xprmntal data whch ar shown n Fg. 5 and Fg T at C Tstng T at C Smulaton_Adsorpton T at C Smulaton_Man curvs T at C Smulaton_Dsorpton T outsd Tm (h) Fg. 5: Varaton of tmpratur at pont C Non-Isoth modl and xprmntal masurmnt. 100% As can b sn from Fg. 5, th numrcal rsults ar n accordanc to th xprmntal rsults. In addton, thy ar vry clos to thos obtand by usng th Isoth modl (by comparng Fg. 5 wth Fg. 80% 3). Fg. 6 showd that compard to th fnal on, th Non-Isoth modl rsults n sgnfcantly bttr prdcton of th rlatv humdty varaton n th 60% tstd wall. Concrnng thr cass studd, th rsults ar dpndnt on whch th sorpton curv s usd for th smulatons. Th rsults calculatd wth th adsorpton allow a bttr prdcton of th rlatv 40% humdty varaton than thos for th modl that uss dsorpton curv or an avrag sorpton curv btwn adsorpton and dsorpton. Th maxmum dffrnc btwn th computd rsults for th modl that uss adsorpton curv and th xprmntal ons s 3% RH. Ths valu s small compard to th accuracy of snsor nsrtd n th tstd wall, whch s qual to ±1.5% of RH. 100% 80% RH at C Tstng RH at C Smulaton_Adsoprton RH at C Smulaton_Man curvs RH at C Smulaton_Dsorpton RH outsd 60% 40% Tm (h)

6 Tmpratur ( C) Tmpratur ( C) Pv (Pa) Radaton (W/m²) Journal of Appld Flud Mchancs, Vol. 9, Spcal Issu-1, pp. x-x, 200x. Fg. 6: Varaton of rlatv humdty at pont C Non-Isoth modl and xprmntal masurmnt. It can b drawn a concluson that t s ncssary to tak nto account th non-sothrmal condtons on th sorpton curvs n ordr to wll prdct th hygrothrmal bhavor of th wall submttd to th dynamc condtons of tmpratur and rlatv humdty. 4. Hygrothrmal bhavor of a hmp concrt buldng nvlop submttd to ral outdoor condtons Th applcaton cas dals wth th ffct of tmpratur-dpndnt sorpton on th prdcton of hygrothrmal bhavour of a hmp concrt wall submttd to outdoor ral condtons. Schmatc llustraton of boundary condtons of studd hmp concrt wall wth 30 cm of thcknss s shown n Fg. 7. Th ndoor tmpratur and rlatv humdty ar consdrd constant and qual to 25 C and 50%, rspctvly. Th Marsll (n Franc) wathr data s usd for th outdoor condton. Smulatons usng Isoth and Non-soth modls ar run for thr months n summr. Th hat transfr coffcnts for th outdoor surfac (h T, ) and for ndoor surfac (h T, ) ar 16 W/m 2.K and 9 W/m 2.K, rspctvly. Th mass convcton coffcnts wr calculatd by usng th Lws rlaton by consdrng th Lws numbr quals to 1. Th long-wav mssvty and th shortwav absorpton coffcnts ar qual to 0.9 and 0.4. Th wall s dscrtzd nto 25 nods and th tm stp s 240 s. Fg. 8 shows th outdoor tmpratur and outdoor rlatv humdty for thr months n summr n Marsll. It s notcd that durng th nght th outdoor tmpratur droppd down and th outdoor rlatv humdty could ncras to 90 %. Th solar radaton on a south-facng vrtcal wall s gvn n Fg. 9, n whch th radaton flux can rach 445 W/m². Also, th outdoor and ndoor watr vapor prssurs wr dpctd n ths on. Not that th drcton of watr vapor flow s from hgh vapor prssur to low vapor prssur whch dpnds on both th rlatv humdty and th saturaton watr vapor prssur Outdoor Pv Indoor Pv Solar radaton Tm (days) 1000 Fg. 9: Outdoor and ndoor watr vapor prssurs and solar radaton on a south-facng vrtcal wall T_Non-Isoth T_Isoth Outdoor T Tm (day) Fg. 7: Schmatc llustraton of boundary condtons of studd wall Outdoor T 100% 80% 60% % Tm (day) Fg. 8: Outdoor tmpratur and outdoor rlatv humdty. RH Fg. 10: Tmpratur dstrbuton n th mddl of th wall (x=15 cm) obtand from Isoth and Non- Isoth modls. Fg. 10 shows th tmpratur dstrbuton n th mddl of th wall ovr a prod of 5 days for clarr prsntaton. Frstly, t can b sn that th tmpratur varaton n th mddl of th wall s sgnfcantly dampnd compard wth th xtrnal tmpratur. Scondly, th rsults obtand from both modls ar vry clos whch s n accordanc wth prvous rsults. Rgardng hat-dampnng ablty, th tmpratur profl n th mddl of th wall shows a rducton n ampltud of about 88% and 8 hours of tm shft compard to varaton of th outdoor tmpratur. Thrfor, th us of hmp concrt

7 Rlatv humdty (%) Journal of Appld Flud Mchancs, Vol. 9, Spcal Issu-1, pp. x-x, 200x. contrbuts to avod ovrhatng n summr. Th sam conclusons hav bn drawn from th xprmntal study on a hmp concrt wall conductd by (Colnart t al. 2013; Collt and Prtot. 2014; Samr t al. 2014). Concrnng th rlatv humdty profl n th mddl of th nvstgatd wall, t s prsntd n Fg. 11. In contrast wth th RH profl obtand from th Isoth modl, th on from th Non-soth modl shows a notcabl daly varaton ampltud whch can rach 7% of RH. Th rsults ar n accordanc wth th masurmnts conductd by Samr t al.(2014), n whch th n stu montorng of th hygrothrmal profls n buldng and a hmp concrt buldng nvlop hav bn carrd out. In addton, th authors confrmd that th WUFI modl that not taks nto account th tmpratur-dpndnt sorpton cannot rproduc th varaton and tndncs of th rlatv humdty profl n th mddl of a hmp concrt wall whch s submttd to ral outdoor condtons. Ths on s n accordanc wth th rsults obtand from th Isoth modl n th prsnt study. 70% 65% 60% 55% RH_Non-Isoth 50% Tm (days) RH_Isoth Fg. 11: Rlatv humdty dstrbuton n th mddl of th wall (x=15 cm) obtand from Isoth and Non-Isoth modls. 5. Conclusons Ths artcl focuss on th dvlopmnt and th us of a numrcal modl that taks nto account th ffct of tmpratur on th sorpton charactrstcs n th transnt modlng of coupld hat and mass transfr n porous matrals. In ordr for ths to b don, two modls (Isoth and Non-Isoth that uss th approachs proposd by Mlly and Poyt) hav bn carrd out and mplmntd n th smulaton nvronmnt SPARK whch s sutd to solv ffcntly dffrntal quaton systms. To valdat th prsntd modl, th numrcal rsults wr thn compard to th xprmntal ons. Fnally, th applcaton cas, whch dals wth a hmp concrt wall submttd to outdoor ral condtons has bn carrd out. Th rsults showd that takng th nflunc of tmpratur on th sorpton curvs nto account s ncssary for bttr prdcton of th hygrothrmal bhavor of a hmp concrt buldng nvlop. Both Isoth and Non-Isoth modls prdctd wll th varaton of tmpratur. Howvr, only Nonsoth modl that uss th Poyt's approach s adaptd to study th varaton of th rlatv humdty n th wall. REFERENCES At Oumzan, Y (2014). Evaluaton ds prformancs hygrothrmqus d'un paro par smulaton numérqu: applcaton aux paros n béton d chanvr. Thès d doctorat, INSA d Rnns, Bar, J. and Bachmat, Y (1990). Introducton to modlng of transport phnomna n porous mda. Dordrcht, Nthrlands: Kluwr Acadmc Publshrs. Carstn, R. and Clorus, C.O (2004). Modlng of mostur transport n wood wth hystrss and tmpratur dpndnt sorpton charactrstcs," n Prformanc of Extror Envlops of Whol Buldngs IX. Intrnatonal Confrnc, Clarwatr, Flord Crzo, V. (2005). Proprétés mécanqus, thrmqus t acoustqus d un matérau à bas d partculs végétals : approch xpérmntal t modélsaton théorqu. Thès d Doctorat, INSA & ENTPE d Lyon. Colnart, T., Glouannc, P., Prr T, Chauvlon,P., Magurss., A (2013). Exprmntal study on th hygrothrmal bhavor of a coatd sprayd hmp concrt wall. Buldngs, 3 (2013), pp Collt, F. and Prtot, S (2014). Exprmntal hghlght of hygrothrmal phnomna n hmp concrt wall. Buldng and Envronmnt, 82 (2014), pp Collt, F., Bart, M., Srrs, L., Mrl, J (2008). Porous structur and watr vapour sorpton of hmp-basd matrals. Constr. Buld. Matr, vol. 22, pp Cunnngham, M.J. (1988). Th mostur prformanc of framd structurs: a mathmatcal modl. Buldng and Envronmnt, 23, pp Evrard, A. (2008). Transnt hygrothrmal bhavour of Lm- Hmp matrals. Thès d doctorat d scncs d l ngénur, Ecol polytchnqu d Louvan Unté d Archtctur.

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