Numerical Simulation of Triaxial Comreion Stre Path Tet for Unaturated Soil Dong Jian-jun Key Laboratory Of Mechanical Reliability For Heavy Equiment And Large Structure of Hebei Province, Yanhan Univerity, Qinhuangdao 664, China; College of Civil Engineering & Machenic, Yanhan Univerity, Qinhuangdao 664, China e-mail: dongjianjun@gmail.com ABSTRACT With reect to aturated oil, the tudy of triaxial comreion tre ath for unaturated oil under uction-controlled condition i more comlex. With the continuou develoment of unaturated oil contitutive theory, the reult of abundant academic and tet reearche indicate that, the trength and deformation behaviour of unaturated oil can be aroximately decribed by elato-latic contitutive model of unaturated oil. Therefore, it i an effectual academic reearch method adoting elato-latic contitutive model of unaturated oil that numerically imulate three tye of triaxial comreion tre ath tet for unaturated oil under uction-controlled condition. Uing Barcelona model can well numerically imulate uch exeriment, and the reearch reult demontrate that, under uction-controlled condition, the tre ath which in the triaxial comreion tre tate have imortant influence on trength and deformation behaviour of unaturated oil. KEYWORDS: Stre ath; unaturated oil; elato-latic; triaxial comreion; numerical imulation. INTRODUCTION A a tye of comlicated engineering material, the mechanical behavior of oil i not only deendent on the current tre tate, but alo aociated with oil tye, tre hitory and tre ath [, 2]. Stre ath method rovide a reaonable method that tudie the trength and deformation behavior of oil under different loading condition. Currently, the tre ath tudy for aturated oil ha got abundant exerimental data and etablihed academic model, while, due to the limitation of tet mean, the tre ath tudy for unaturated oil ha not een extenive develoment. It ha made great achievement in the tudy that contitutive model for unaturated oil over the lat forty year. The main rereentative work focued on nonlinear elatic model, elato- - -
Vol. 8 [23], Bund. A 2 latic model and tructural model [3]. Fredlund et al. [4] have ut forward the nonlinear model for unaturated oil in 976. Alono et al. [5] came u with the yield urface elato-latic model, that i Barcelona elato-latic model. Chinee cholar Yang Dai-quan, Shen Zhu-jiang and Chen Zheng-han alo rooed their own model. The trength and deformation behavior of unaturated oil can be reflected by thee model in different degree. The reult of academic and tet reearche alo how that, the elato-latic contitutive model can aroximately decribe the trength and deformation behavior of unaturated oil. It lay theoretical bae that tudy the effect of tre ath on trength and deformation behavior of unaturated oil. Barcelona elatolatic model i one of outtanding rereentative in thee unaturated oil contitutive model, and get a good alication in engineering ractice. The Author alying Barcelona elato-latic model imulate contant-uction triaxial comreion tet of unaturated oil under different tre ath. The influence of tre ath on trength and deformation behavior of unaturated oil wa tudied and dicued under uction-controlled triaxial comreion tre tate. BARCELONA ELASTO-PLASTIC MODEL Model Etablihment Baed on claic Cam-Clay model, Barcelona elato-latic model rooed by Alono et al. i a unified elato-latic contitutive model that introduced uction comonent in tre ace, according to the concet that critical tate for aturated oil, aiming at non-welling oil and weak welling oil in the generalized tre ace ( q,, ). [5] In which q,,, reectively, the hear tre q, the average net tre = σ ii ua and the uction = u w 3 a u ; u a and u w mean ore air reure and ore water reure reectively. The model degenerate into modified Cam-Clay model when the oil i in aturated tate. Wheeler and Sivakumar demontrate the LC yield line in (, ) lane uggeted by Alono, Gen and Joa, which i exitence by uction-controlled triaxial tet. Cui conider that ellie yield line with a major axi of η = K tre ath in (q,, =Contant) lane i exitence through abundant uction-controlled triaxial tet, thereunto, η = q /. On the bai of exerimental data and energy equation, yield function in generalized ( q,, ) ace which i imilar to Cam-Clay model i derived by Karube et al. In accordance with the concet that equivalent effective tre, Kohgo et al. etablihed an ellie ingle yield urface model and it ha been alied to the analyi for ideal earth dam [6]. The Barcelona elato-latic model i exreed imly a follow: For yield urface, two kind of yield function can be defined according to the following tre variable: = ( σ + 2σ 3 ) / 3 u a () q = σ σ 3 (2) = u a u w (3) The firt kind of yield function:
Vol. 8 [23], Bund. A 3 where 2 2 f (, q,, ) q M ( + )( ) = (4) = k (5) [ λ () k ] /[ λ ( ) k ] = ( ) c c (6) λ ( ) = λ()[( r)ex( β) + r] (7) Thereinto, equation (6) i LC (after loading-collae) yield urface function, and are re-conolidation tree which reectively correond to uction and aturated condition. The econd kind of yield function: f, ) (8) 2 ( = The equation rereent SI yield curve (after uction increae), i the maximum uction in the hitory of oil. For flow rule: Platic train increment ( dε, dε ) i aociated with yield urface f. v dε v = μn (9) dε = μnq () In the above equation, n = () n = 2 2qα / M (2 + )] (2) q [ In equation (9), α i a contant that can be ought by calculating the latic train increment direction of no lateral deformation. q d ε dε SI LC dε v
Vol. 8 [23], Bund. A 4 q CSL(>) M CSL(=) M > = - SI LC k - Figure : Yield urface of q ace dε dε v { /[ k / ()]} = ( 2 / 3) λ (3) In order to imlify the formula, condition i determined: Equation (2) ~ (4) how that, e dε ha been aumed to be. The tre tate to meet K ( q / + ) = 3( K ) /( + 2K ) (4) M ( M 9)( M 3) α = { /[ k / λ()] } (5) 9(6 M ) To yield urface of f 2, the aociated latic train vector i ( dε v,). In the formula, μ and μ 2 are obtained by latic conitency condition. For hardening law: d ε = μ 2 (6) v The develoment of yield urface i controlled by hardening arameter deend on the total latic volume train increment dε v. and. They
Vol. 8 [23], Bund. A 5 d v = dε v (7) λ() k d v (8) = dε v + ) λ k ( at For elatic train: The volumetric elatic train and hear elatic train are contituted by the following formula. e k d k d dε v = + (9) v v ( + at ) dε e = (/ 3G) dq (2) Determination of Model Parameter There are 2 arameter need to be determined for Barcelona elato-latic model. Including c,, λ (),κ, r, β,, λ, κ, G, M and k. All the arameter can be gained through the following three ort exeriment: () The arameter c,, λ (),κ, r and β can be determined by iotroic comreion drainage comreion tet(loading and unloading) under different contant-uction condition. (2) Drying and wetting cycle exeriment under given average net tre can determine the arameter, λ andκ. (3) The data rovided by hear trength tet under different contant-uction can define G, M and k. In order to acquire thee arameter, unaturated oil triaxial tet aaratu mut be able to meet: () Control matric uction, namely, control ore air reure and ore water reure reectively in the tet roce. (2) Volume change and moiture change of amle can be meaured indeendently. NUMERICAL SIMULATION OF TEST Stre Path There are mainly three tye of tre ath in triaxial comreion tet which are hown in Figure 2, and can be exreed in ~q lane: ()Conventional triaxial turbocharging comreion tet (CTC: conventional triaxial comreion): Δ>,Δq>; (2)Triaxial comreion tet of average rincial tre i contant (PTC: =contant triaxial comreion): Δ=,Δq>; (3)Conventional triaxial reduced comreion tet (RTC: reduced triaxial comreion): Δ<, Δq>.
Vol. 8 [23], Bund. A 6 q CSL PTC CTC RTC Figure 2: Stre ath of ~q urface The author alying Barcelona elato-latic model imulate the three kind of triaxial comreion tre ath tet for unaturated oil under uction-controlled condition. Selection of Model Parameter The author conduct the numerical imulation calculation that triaxial comreion tre ath tet for unaturated oil under uction-controlled condition, and the model arameter adoted in calculation are hown in table. Table : Parameter of Barcelona model [8] Parameter name Parameter value determined by tet Unit λ ().22 - κ. - β 7.89 MPa - r.2 - c.36 MPa G 8.8 MPa M.982 - k.324 -.4 MPa Reult and Analyi of Numerical Simulation Generalized hear tre q = σ σ 3 and average net tre = ( σ + 2σ 3 ) / 3 ua of CTC tet, PTC tet and RTC tet when uction =5kPa are gained by the reult of numerical imulation. Relation curve of generalized hear tre q and average net tre, generalized tot hear tre q and total hear train ε a well a ecific volume v = + e and total hear train ε are hown in Figure 3, Figure 4 and Figure 5. tot
Vol. 8 [23], Bund. A 7 2 generalized hear tre q / kpa 5 5 PTC CTC CSL RTC - -5 5 5 2 average net tre / kpa Figure 3: Stre ath of ~q ace It can be een by relation curve that generalized hear tre q and average net tre, the reult of numerical imulation are anatomotic with theoretical form of tre ath, and the coincidence degree with exerimental reult need to be further verified. 2 generalized hear tre q / kpa 8 6 4 2 CTC PTC RTC 5 5 2 total hear train ε tot / % Figure 4: Curve of q ~ ε tot under =5kPa
Vol. 8 [23], Bund. A 8 ecific volume v=+e 2.2 2.8 2.6 2.4 2.2 2. 2.8 2.6 2.4 2.2 2. 5 5 2 Figure 5: Curve of total hear train ε tot / % v = + e ~ ε tot under =5kPa The numerical imulation reult how that, the three ort triaxial comreion tre ath tet under uction-controlled condition(=5kpa), from which it can be acquired the morhology tot of relation curve between generalized hear tre q and total hear train ε are imilar, tretrain curve reent nonlinear tre hardening tye; the morhology of relation curve between ecific volume v = + e and total hear train ε tot are alo imilar, both of them howed hrinkage reducing deformation; However, due to tre ath are different, the change range of eak trength and ecific volume v = + e are obviou difference. Among three tye of tre ath tet, the eak trength value i larget in CTC tet, while leat in RTC tet, and middle in PTC tet. A for ecific volume v = + e, the change range i bigget in CTC tet, econdly i PTC tet and RTC tet i lat. Therefore, tre ath have ignificant effect on hear trength and hear hrinkage deformation. CONCLUSION Elato-latic contitutive model for unaturated oil can be aroriately ued to imulate the triaxial comreion tre ath tet of controlled uction for unaturated oil. And the reult are anatomotic with theoretical form of tre ath. The reult of numerical imulation indicate that, under the ame uction condion, tretrain curve morhology i imilar in three ort tre ath tet, all reent nonlinear train hardening tye. Curve morhology of ecific volume alo i baic conitant with total hear train, both aear hrinkage reducing deformation. However, becaue of different tre ath, the change range of eak trength and ecific volume are obviou difference, it i bigget in CTC tet, and then i PTC tet and RTC tet i lat. Alying Barcelona elato-latic model imulate tre ath tet for unaturated oil a a mean of theoretical reearch, the reliability of the reult till need to be further verified through exeriment. CTC PTC RTC
Vol. 8 [23], Bund. A 9 ACKNOWLEDGEMENT The tudy reented here i uorted by Hebei Provincial Deartment of Education Scientific Reearch Program of Hebei Province College & Univeritie Natural Science Reearch Youth Fund Project, China (Q229). REFERENCES. Huang Wenxi. Engineering roertie of oil[m]. Beijing: Water Reource and Electric Power Pre, 983. (in Chinee) 2. Zheng Yingren, Shen Zhujiang, Gong Xiaonan. Generalized Platic Mechanic-Princile of Platic Mechanic for Geotechnique [M]. Beijing: China Architecture and Building Pre, 22. (in Chinee) 3. Shen Zhujiang. Theoretical Soil Mechanic [M]. Beijing: China Water Power Pre, 2. (in Chinee) 4. Fredlund D G, Rahardjo H. Soil Mechanic for Unaturated Soil[M]. Tranlated by Chen Zhongyi. Beijing: China Architecture and Building Pre, 997. (in Chinee) 5. Alono E E, Gen A, Joa A. A contitutive model for artially aturated oil [J]. Geotechnique, 99, 4(3): 45-43. 6. Alono E E, Gen A, Joa A, Yang Daiquan. Elatolatic modeling for the tre and train behavior of unaturated oil [J]. Chinee Journal of Geotechnical Engineering, 995, 7(6):42-5. (in Chinee) 7. Li Guangxin. Advanced oil mechanic [M]. Beijing: Tinghua Univerity Pre, 24. (in Chinee) 8. Emir Joe Macari, Laureano Rene Hoyo, Pedro Arduino. Contitutive modeling of unaturated oil behavior under axiymmetric tre tate uing a te/uctioncontrolled cubical tet cell [J]. International Journal o f Platicity, 23, 9:48-55. 23, EJGE