Modeling the Dilatancy of Overconsolidated Clay

Transcription

1 oeling the Dilatany of Oeronsoliate Clay Zhiwei Gao * an Jiong Zhao Deartment of Ciil an Enironmental Engineering, Hong ong Uniersity of Siene an Tehnology, Clearwater Bay, owloon, Hong ong gzwe@ust.hk Summary. The ilatany of lay has long been onsiere as a funtion of the urrent stress state ineenent of the loaing history. Exerimental eiene, howeer, iniates the ilatany behaior of oer-onsoliate (OC) lay bears lose orrelation with the oeronsoliation ratio (OCR) of the soil. This aer resents a simle ilatany relation for OC lays base on the moifie Cam-lay (CC) moel. The ilatany relation is integrate into a bouning surfae moel to reit the behaior of OC lays. With only three extra arameters ae to the CC moel whih an be easily alibrate by triaxial omression tests, the new moel is shown to offer goo reitions for the exerimental ata. eywors: Oeronsoliation, lay, ilatany, bouning surfae moel. 1 Introution The term ilatany was first use by Reynols [1] to esribe the ifferent behaior of olumetri hange obsere in ense an loose granular assemblies subjete to shear. Dilatany has been regare key to the haraterization of strength an eformation of soils. Base on raine shear tests on san, Taylor [2] has shown that there are two soures attributable to the eak strength of san, one being the inter-artile frition an the other the ilatany (or interloking). Later, Rowe [3] eeloe his seminal stress-ilatany theory highlighting the imortant ontribution of ilatany to soil strength an the mobilize frition in the loaing roess. Not uniuely tagge to san only, stress ilatany has been isusse for lay as well (e.g., [4]). In this stuy, a simle ilatany relation for OC lay will be roose base on the CC moel [5]. The new relation an be easily use in onjuntion with either the bouning surfae or the subloaing surfae moels for OC lay. A emonstratie bouning surfae moel is eeloe with the imlementation of this ilatany relation. * Corresoning author. Q. Yang et al. (Es.): Constitutie oeling of Geomaterials, SSGG, sringerlink.om Sringer-Verlag Berlin Heielberg 213

2 542 Z. Gao an J. Zhao 2 A Simle Dilatany Relation for OC Clay In seeral stuies on OC lay using bouning surfae, the ratio R = rr has been use as a key ariable to haraterize the egree of oeronsoliation, where r an r enote the istanes of the urrent an image stress oint from the maing enter, resetiely. Smaller R orresons to higher egree of oeronsoliation. By aoting the origin of the lane as the maing enter, this R will be emloye as a esritor for the egree of oeronsoliation, where an enote the mean an eiatori stress, resetiely. Base on this efinition of R, we roose the following ilatany relation for OC lay where ε D = = (1) ε 2η m = R (2) where η ( = ) is the stress ratio; is the ritial state stress ratio in triaxial omression an m is a non-negatie material onstant. The ilatany relation exresse aboe has the following features: (a) For Normally onsoliate (NC) lays with the stress state on the bouning surfae, Euation (2) is reoere to the ilatany relation of the CC moel as = ; (b) As the egree of oeronsoliation inreases, R ereases, so o an D. This iniates that the resonse of a lay with higher egree of oeronsoliation woul be more ilatie at the same stress ratio η [6]; () At the ritial state, the lay beomes NC an the stress state lies on the bouning surfae ( R = 1 ) with D =. η =, an thus, 3 A Bouning Surfae oel for Oeronsoliate Clay Base on the ilatany euation in Euations (1) an (2), a bouning surfae moel for OC lay is eeloe here. We will use the α γ yiel surfae roose by Collins [7] as the bouning surfae with the assumtion of α = γ, ( α 2) ( ) + f = + 1= α α 2 1 α + α 2 (3)

3 oeling the Dilatany of Oeronsoliate Clay 543 where enotes the size of the bouning surfae; an are resetiely the mean stress an eiatori stress at the image oint. Following Dafalias an Herrmann [8], the same isotroi harening law as in the CC moel is assume for, 1+ e ε = (4) λ κ where λ an κ are the omression an swelling inies, resetiely; ε is the lasti olumetri strain inrement. An assoiate flow rule in the eiatori lane will be emloye, ε where L is the loaing inex; f = L (5) ε is the lasti eiatori strain inrement; are the Cauley brakets. The lasti moulus at the image stress oint, is exresse as ( e) ( e) R= 1 ( ) f f f = D = λ κ λ κ 2η (6) The exression for the lasti moulus at the urrent stress state assume to be of the iential form of eak stress ratio, where = ( 1 ) is relate to R aoring to by simly relaing ( ) + e f f λ κ 2η is simly by a irtue (7) n = R (8) where n is a non-negatie moel arameter. For OC lay, is eenent on the ifferene between the urrent stress ratio η ( = η ) from the irtue eak stress ratio attainable at the urrent egree of oeronsoliation efine by R. Sine R 1, the irtue eak stress ratio in Euation (11) is a ereasing funtion of R an thus an inreasing funtion with the egree of oeronsoliation [6].

4 544 Z. Gao an J. Zhao 4 oel Verifiation Shown in Fig. 1 is the omarison between our moel reitions with the test ata on the Boston blue lay (ata from [6]). Goo agreement an be obsere. In the figures, ε is the axial strain an is the maximum onsoliation ressure. a The moel arameters are liste in Table 1, where ν is the Poisson ratio an Γ is the oi ratio at the referene mean stress on the normal onsoliation line. r Table 1. oel arameters for Boston blue lay λ κ ν Γ ( r (kpa)) α m n (3) (a) (b) Fig. 1. Comarison between the moel simulation an test results on Boston blue lay (ata from Pestana et al. (22)): (a) the ε a relations an (b) the effetie stress aths 5 Conlusion A simle ilatany relation for OC lay is roose an use in a reitie bouning surfae moel. The moel has been emonstrate to reit the behaior of OC lays well as omare to test ata. Future work will be one on moeling the behaior of struture soils (e.g., [9]). Aknowlegements. This work was suorte by Researh Grants Counil of Hong ong (uner grant no ).

5 oeling the Dilatany of Oeronsoliate Clay 545 Referenes [1] Reynols, O.: On the ilatany of meia omose of rigi artiles in ontat. With exerimental illustrations. Phil. ag. 2, (1885) [2] Taylor, D.W.: Funamentals of soil mehanis. Wiley, New York (1948) [3] Rowe, P.W.: The stress-ilatany relation for stati euilibrium of an assembly of artiles in ontat. Pro. Roy. So. Lonon A269, (1962) [4] Shofiel, A.N.: The ohr-coulomb error. In: Pro. Sym. on ehanis an Geotehnis, LS Eole Polytehniue, Paris, ol. 23, (1998) [5] Rosoe,.H., Burlan, J.B.: On the generalize stress-strain behaior of wet lay. In: Engineering Plastiity, Cambrige Uniersity Press, Cambrige (1968) [6] Pestana, J.., Whittle, A.J., Gens, A.: Ealuation of a onstitutie moel for lays an sans: Part II lay behaiour. Int. J. Numer. Anal. eth. Geomeh. 26, (22) [7] Collins, I.F.: Elasti/lasti moels for soils an sans. Int. J. eh. Si. 47, (25) [8] Dafalias, Y.F., Herrmann, L.R.: Bouning surfae lastiity II: Aliation to isotroi ohesie soils. J. Eng. eh. 112(12), (1986) [9] Gao, Z.W., Zhao, J.D.: Constitutie moeling of artifiially emente san by onsiering fabri anisotroy. Comuter an Geotehnis 41, (212)