A structured Cam Clay model

Transcription

1 1313 A tructured Cam Clay model M.D. Liu and J.P. Carter Abtract: A theoretical tudy of the behaviour of tructured oil i preented. A new model, referred to a the Structured Cam Clay model, i formulated by introducing the influence of oil tructure into the Modified Cam Clay model. The propoed model i hierarchical, i.e., it i identical to the Modified Cam Clay oil model if a oil ha no tructure or if it tructure i removed by loading. Three new parameter decribing the effect of oil tructure are introduced, and the reult of a parametric tudy are alo preented. The propoed model ha been ued to predict the behaviour of tructured oil in both compreion and hearing tet. By making comparion of prediction with experimental data and by conducting the parametric tudy it i demontrated that the new model provide atifactory qualitative and quantitative modelling of many important feature of the behaviour of tructured oil. Key word: calcareou oil, clay, fabric, tructure, contitutive relation, platicity. Réumé : On préente une étude théorique ur le comportement du ol tructuré. On formule un nouveau modèle auquel on réfère comme le modèle Cam Clay tructuré en introduiant l influence de la tructure du ol dan le modèle Cam Clay modifié. Le modèle propoé et hiérarchique, i.e., il et identique au modèle de ol Cam Clay modifié i un ol n a pa de tructure ou i a tructure et éliminé par chargement. Troi nouveaux paramètre décrivant le effet de la tructure du ol ont introduit et le réultat d une étude paramétrique ont également préenté. Le modèle propoé a été utilié pour prédire le comportement de ol tructuré dan le eai de compreion et de ciaillement. En faiant de comparaion de prédiction avec de donnée expérimentale et en conduiant un étude paramétrique, il et démontré que le nouveau modèle fournit une modéliation qualitative et quantitative de pluieur caractéritique importante du comportement de ol tructuré. Mot clé : ol calcareux, argile, fabrique, tructure, relation de comportement, platicité. [Traduit par la Rédaction] Liu and Carter 1332 Introduction Soil in itu uually poe natural tructure, which enable them to behave differently from the ame material in a recontituted tate (e.g., Burland 1990; Leroueil and Vaughan 1990; Cuccovillo and Coop 1999). Recently, there have been important development in formulating contitutive model incorporating the influence of oil tructure, uch a thoe propoed by Gen and Nova (1993), Whittle (1993), Wheeler (1997), Rouainia and Muir Wood (2000), and Kavvada and Amoroi (2000). In thi paper a new contitutive model for tructured clay i propoed. The main objective of thi new formulation i to provide a contitutive model uitable for the olution of boundary value problem encountered in geotechnical engineering practice. It i intended therefore, that the new model hould be relatively imple and hould have few parameter, each of which ha a clear phyical meaning and can be conveniently identified. The model hould alo be relatively eay to undertand and apply. Received 30 October Accepted 8 April Publihed on the NRC Reearch Pre Web ite at on 6 November M.D. Liu 1 and J.P. Carter. Department of Civil Engineering, The Univerity of Sydney, NSW 2006, Autralia. 1 Correponding author ( m.liu@civil.uyd.edu.au). The Modified Cam Clay model (Rocoe and Burland 1968) i widely referenced and ha been widely ued in olving boundary value problem in geotechnical engineering practice (e.g., Gen and Pott 1988; Yu 1998; Pott and Zdravkovic 1999), although it wa developed originally for recontituted clay. Becaue of ome familiarity with the model by the geotechnical profeion and becaue it capture well the eential behaviour of recontituted oil, the Modified Cam Clay model wa choen a the bai for the current reearch. A new model ha been formulated by introducing the influence of oil tructure into the Modified Cam Clay model. A parametric tudy demontrating the capabilitie and limitation of thi new model i preented. The model ha alo been ued to predict the behaviour of a variety of tructured natural oil in both compreion and hearing tet, allowing for a reaonably comprehenive evaluation. It i demontrated that the propoed new model i uitable for decribing the behaviour of a variety of natural clay and cemented oil. Generalization of Modified Cam Clay The Modified Cam Clay model wa propoed by Rocoe and Burland (1968) and a decription and ytematic tudy of the model can be found in the text by Muir Wood (1990). Formulation of thi model uitable for ue in finite element analyi can alo be found in variou text (e.g., Britto and Gunn 1987; Pott and Zdravkovic 1999). In thi paper, the Modified Cam Clay model i employed a a bai for Can. Geotech. J. 39: (2002) DOI: /T02-069

2 1314 Can. Geotech. J. Vol. 39, 2002 formulating a hierarchical model for tructured clay, which i referred to a the Structured Cam Clay model. It i aumed that the behaviour of oil in a recontituted tate can be decribed adequately by the Modified Cam Clay model. The term oil tructure i ued here to mean the arrangement and bonding of the oil contituent, and for implicity it encompae all feature of a oil that are different from thoe of the correponding recontituted oil. Following the uggetion of Burland (1990), the propertie of a recontituted oil are called the intrinic propertie, and are denoted by the ymbol * attached to the relevant mathematical ymbol. Hence, under all tre condition, the influence of oil tructure can be meaured by comparing it behaviour with the intrinic behaviour. The formation and development of oil tructure often produce aniotropy in the mechanical repone of oil to change in tre. Detructuring uually lead to the reduction of aniotropy. To concentrate on introducing the phyical concept of the framework and to avoid unneceary complexity of mathematical detail, only the iotropic effect of oil tructure are included in the propoed theoretical framework. The extenion required to include the influence of oil aniotropy hall be a future reearch topic, however, it i noted that other have previouly conidered thi feature of oil behaviour, e.g., Dafalia (1987), Whittle and Kavvada (1994), Wheeler (1997), and Rouainia and Muir Wood (2000). It hould alo be noted that coaxiality between the principal axe of the platic train increment and thoe of tre i aumed in the propoed framework. The tre and train quantitie ued in the preent formulation are defined a follow. Variable σ ij and ε ij are the Carteian component of effective tre and of train, repectively. The implified form for tre and train condition in conventional triaxial tet are alo lited, where σ 1 (or ε 1 ) and σ 3 (or ε 3 ) are the axial effective tre (train), and the radial effective tre (train), repectively. The mean effective tre p, deviatoric tre q, and tre ratio η are given by σ + σ + σ [1] p = σ + σ = for conventional triaxial tet [2] q = ( σ σ ) + ( σ σ ) + ( σ σ ) + ( σ + σ + σ = ( σ1 σ3 ) for conventional triaxial tet q [3] η= p 2 The correponding (work-conjugate) volumetric train increment, dε v, and deviatoric train increment, dε d, are defined by [4] dεv = dε11 + dε22 + dε33 = dε1 + 2dε3 for conventional triaxial tet and 2 31 ) [5] d ε d = ( dε dε ) + ( dε dε ) + ( dε dε ) + 6( dε dε31 ) + dε + = 2( dε1 dε3) 3 for conventional triaxial tet Influence of oil tructure on virgin iotropic compreion The work by Liu and Carter (1999, 2000) i employed here a a tarting point for including the effect of oil tructure in the model. The material idealization of the iotropic compreion behaviour of tructured clay i illutrated in Fig. 1. In thi figure e repreent the void ratio for a tructured clay, e* i the void ratio for the correponding recontituted oil at the ame tre tate during virgin yielding, p y,i i the mean effective tre at which virgin yielding of the tructured oil begin, and e, the additional void ratio, i the difference in void ratio between a tructured oil and the correponding recontituted oil at the ame tre tate. Hence, the virgin iotropic compreion behaviour of a tructured oil can be expreed a [6] e = e* + e The following equation wa propoed by Liu and Carter (2000) to decribe the volumetric behaviour of natural clay during virgin iotropic compreion: [7] e e e p = + y,i * i p b where e i i the additional void ratio at p = p y,i, where virgin yielding of the tructured oil begin (Fig. 1), and b i a parameter quantifying the rate of detructuring and i referred to here a the detructuring index. The value of b depend on oil type and tructure and generally b 1 for oft tructured clay and b < 1 for tiff clay. For the 30 different

3 Liu and Carter 1315 Fig. 1. Idealization of the iotropic compreion behaviour of recontituted and tructured oil. clay tudied by Liu and Carter (1999, 2000), it wa found that generally 0 b 30. For clay ample of a given mineralogy and with imilar geological tre hitory but different depth below the urface, it i found that b depend mainly on the liquidity index. Yield urface for tructured clay In the propoed Structured Cam Clay model the behaviour of clay i divided into virgin yielding behaviour and elatic behaviour by it current yield urface, which i dependent on oil tructure a well a tre hitory, i.e., the tructural yield urface i defined by the current tre tate, void ratio, tre hitory, and oil tructure. Similar to the original propoal by Rocoe and Burland (1968), the yield urface of a tructured oil in p q pace i aumed to be elliptical and to pa through the origin of the tre coordinate (Fig. 2). The apect ratio for the tructural yield urface i M*, the critical tate tre ratio of the recontituted oil. One axi of the ellipe coincide with the p axi.the value of the p coordinate where the ellipe again interect the axi, p, repreent the ize of the tructural yield urface. The yield urface i thu given by the yield function f, where [8] f q = 0.5M* p 2 2 p 0.5p p 1= 0 Volumetric deformation for virgin yielding along general tre path A illutrated in Fig. 1, virgin yielding and the elatic behaviour of recontituted clay, i.e., a clay where tructure i completely removed, are both linear in e lnp pace, with gradient λ and κ, repectively. The iotropic virgin compreion line for the recontituted oil, i.e., ICL*, i given by [9] e* =e IC * λ lnp where e IC * i the void ratio of the recontituted oil when p = 1 kpa during virgin iotropic compreion. We eek now to generalize eq. [9] for a oil that poee tructure. Fig. 2. The yield urface for tructured oil. Conider loading where the current tre tate tay on the yield urface, and the ize of the current yield urface i denoted a p. For monotonic loading, virgin yielding occur if p p y,i. Under the aumption that the hardening of tructured oil i dependent on the platic volumetric deformation, the yield urface for a tructured oil i defined by all tre tate that have the ame accumulation of abolute platic volumetric train. In uch a model, the platic volumetric deformation i dependent on the change in ize of the yield urface only. If the elatic deformation for a tructured oil i aumed to be the ame a that of the recontituted oil, any change in the additional void ratio due to oil tructure mut alo be aociated with platic volumetric deformation, and therefore i alo dependent on the ize of the yield urface. Conequently, the variable p in eq. [7] may be written in term of the ize of the current yield urface p. On ubtituting eq. [9] into eq. [7], the following expreion for the variation of the void ratio i obtained: p [10] e = e + e y,i IC * i λ ln p for p p p b where p y,i i the value of the mean effective tre at the initial yield point for an iotropic tre tate and i numeri- y,i

4 1316 Can. Geotech. J. Vol. 39, 2002 cally equal to the ize of the initial yield urface aociated with the initial oil tructure. According to Schofield and Wroth (1968), during compreion along a general tre path the volumetric deformation of a recontituted oil i defined by λ ln p, which can be divided into two part. The elatic part i defined by κ ln p, which i dependent on the current mean effective tre, and the platic part i given by (λ κ )ln p, which i dependent on the ize of the yield urface. The void ratio for a tructured oil during virgin compreion along a general tre path may therefore be expreed a p [11] e = e + e y,i IC * i ( λ* κ )lnp κ lnp p b The general compreion eq. [11] tate that void ratio for a tructured oil during virgin compreion i compoed of two part; an elatic part which i dependent on the current mean effective tre and a platic part which i dependent on the ize of the current yield urface. The platic part i further ubdivided into two part; the part aociated with the intrinic propertie of the oil and that aociated with the oil tructure. Differentiating eq. [11] and noting eq. [6] and [7], the total volumetric train increment for compreion along a general tre path i obtained a follow dp d d [12] dε v = λ κ κ + + p + + p ( * *) b e ( 1 ep ) ( 1 ep ) ( 1+ e) p The lat part of the expreion for the total volumetric train increment, i.e., the lat term on the right hand ide of eq. [12], i aociated with elatic deformation. Hence [13] dε e v and furthermore dp = κ* ( 1 + ep ) p d p [14] dε v = λ κ + + dp ( * ) b e ( 1 ep ) ( 1+ ep ) Conidering the mechanim of hearing, it i rational to aume that detructuring and the aociated platic volumetric deformation hould be dependent on both the change in ize of the yield urface and the magnitude of the current hear tre. Therefore, a modification of eq. [14] i made o that the effect of hear tre on detructuring i alo conidered, i.e., p d p [15] dε v = ( λ* κ ) ( 1 + ep ) η dp + b e 1 + M* η ( 1 + ep ) where η i the hear tre ratio defined in eq. [3]. It may be een from eq. [15] that the effect of detructuring, which i decribed a the reduction of the additional void ratio, increae with the value of the current tre ratio. For a recontituted oil, e 0, and the volumetric behaviour predicted by the Modified Cam Clay model i recovered. Equation [15] can be rewritten a p dp d [16] dε v = λ κ + + M* p ( * ) b e ( 1 ep ) η M* ( 1+ ep ) Becaue of the modification made in proceeding from eq. [14] to eq. [15], the new hardening rule for a tructured oil i no longer dependent only upon the platic volumetric deformation. It alo depend on the hear tre ratio, η. In ummary, tructured clay i idealized here a an iotropic hardening and detructuring material with elatic and virgin yielding behaviour. It i aumed that during virgin yielding the yield urface include the current tre tate and expand iotropically cauing detructuring of the material. Flow rule In the Modified Cam Clay model aociated platic flow i aumed. Thu the yield urface i alo the platic potential and the flow rule i given a p dε [17] d 2η = p dε M* 2 η 2 v The tructure of oil alo ha an influence on the flow rule. It i oberved that a tructured clay with poitive e generally ha a lower value for the train increment ratio p p dε d /dε v than the correponding recontituted oil at the ame virgin yielding tre tate (e.g., Olon 1962; Graham and Li 1985; Cotecchia and Chandler 1997). The following equation i therefore propoed a a flow rule for tructured clay: p dε [18] d 21 ( ω e) η = p 2 2 dε M* η v where ω i a new model parameter that decribe the influence of oil tructure on the flow rule. The modifier hould not be negative; otherwie the platic train increment vector will alway be directed inide the yield urface. Hence, baed on the need to meet thi condition at all time, including the tart of virgin yielding, the following contraint i impoed [19] 0<1 ω e i 1 and therefore [20] 0 ω 1 e i Equation [18] implie a nonaociated platic flow rule for the new model. Thi feature ha important conequence for numerical olution cheme employing the model to olve boundary value problem. In particular, it generally reult in the governing equation being nonymmetric. Stre train relationhip Elatic deformation For tre excurion within the current yield urface, only elatic deformation occur. The elatic deformation of a tructured oil i aumed to be independent of oil truc-

5 Liu and Carter 1317 Fig. 3. Influence of parameter b on iotropic compreion behaviour. Table 1. Model parameter. Parameter M* λ* κ* e* IC ν* Value ture. According to the Modified Cam Clay model, the elatic train increment can be expreed a [21] d [22] d εv e εd e κ = * 1 + e dp p 21 ( + v*) κ = * 91 ( 2v*) 1+ e dq p where ν i Poion ratio. The aumption of a contant Poion ratio lead to a nonconervative repone to cyclic loading but i a common feature of the Cam Clay model. Virgin yielding For tre tate on the yield urface and with d p >0, virgin yielding occur. Baed on the platic volumetric deformation, i.e., eq. [16], the flow rule given by eq. [18], and conidering the elatic deformation, the following tre and train relationhip for virgin yielding are obtained: dp d [23] dε v = κ λ κ + + p * ( * *) ( 1 ep ) ( 1 + ep ) [24] d ε d M* dp + b e M* η ( 1 + ep ) 21 ( + v*) κ d η ω = * q ( 1 e) 2 ( v*) e p ( M* η 2 ) M* dp ( λ* κ*) + b e M* η ( 1 + ep ) Softening Soil i regarded a an elatic material for loading inide the yield urface. When the current tre tate reache the virgin yield urface at a point with d p > 0, virgin yielding occur. If the oil reache the yield urface with η > M*, oftening occur if the boundary condition allow appropriate adjutment of the tre tate. Otherwie, catatrophic failure will be predicted. During the oftening proce, the oil tructure will be broken down, and the yield urface hrink with the current tre tate alway remaining on it. In uch cae, the yield urface contract until the oil reache a critical tate of deformation where the tructure of the oil i completely removed. It follow, therefore, that the oftening behaviour of a oil hould be decribed by virgin yielding equation. The platic volumetric train increment given by eq. [16] i valid for the oftening proce. It may be noticed that becaue the yield urface hrink, the volumetric deformation aociated with intrinic oil propertie i negative, i.e., expanive. However, the volumetric deformation aociated with the detructuring i determined by e, becaue both the term (M* η) and dp are negative. For example, for a tructured clay with poitive e, the volumetric deformation aociated with detructuring will be poitive, i.e., compreive. Conequently, unlike a recontituted clay, oftening of tructured clay can be accompanied by either overall volumetric expanion or overall volumetric compreion. The occurrence of compreive volumetric deformation for clay both naturally and artificially tructured ha been widely reported by everal reearcher, including Lo (1972), Nambiar et al. (1985), Georgiannou et al. (1993), Burland et al. (1996), and Carter et al. (2000).

6 1318 Can. Geotech. J. Vol. 39, 2002 Fig. 4. Influence of detructuring index b on the hearing behaviour of oil. (a) Stre path in the e ln p pace. (b) Stre and train relationhip. (c) Deviatoric tre and train relationhip at different cale.

7 Liu and Carter 1319 Fig. 5. Influence of the ize of the initial yield urface on imulated oil behaviour. (a) Deviatoric tre and train. (b) Deviatoric and volumetric train. The expreion for the platic deviatoric train increment contained within eq. [24] i thu modified to accommodate oftening a follow: p M* [25] dε d = 21 ( ω e) ( λ* κ*) b e M* η η dp 2 ( M* η 2 ) ( 1 + ep ) In thi cae, only the ign of the platic deviatoric train aociated with detructuring ha been changed, o that the train increment vector will point outide the yield urface. The elatic part of the deformation can be calculated by eq. [21] and [22]. The total train increment during oftening are thu fully determined. A oftening i a trainedcontrolled proce, the change in the tre tate can be decided from the ize of the current tructural yield urface. When the condition η = M* i reached, the tructure of the oil i uually completely detroyed with e = 0, and there-

8 1320 Can. Geotech. J. Vol. 39, 2002 Fig. 6. The influence of parameter ω on imulated oil behaviour. (a) Deviatoric tre and train. (b) Deviatoric and volumetric train. fore the tructured clay ha reached the critical tate of deformation. It may be noticed that for both virgin yielding and oftening behaviour the oil may reach a tate with η = M* but with e 0. A pecific example i the cae where a oil reache critical tate by loading entirely inide the yield urface. In thi cae virgin yielding commence once the yield urface i reached and, according to eq. [23] and [24], the oil i alo in a tate where it can be ditorted continuouly p p at contant volume (dε v = 0 and dε v ). Hence, the propoed model predict that under pecial tre path a oil may reach a critical tate of deformation with it tructure having not been removed completely. Conequently, in uch cae the oil tate will not be on the critical tate line defined in e p pace. If there i evidence that the tructure of a oil i detroyed completely after the oil reache the critical tate of deformation, then detructuring could be decribed by the platic ditortional train intead of the current tre ratio. However, thi poibility ha not been purued here. Parameter determination Eight parameter define the propoed model, i.e., M*, e IC *, λ, κ, ν, b, p y,i, and ω. The firt five parameter, denoted by the * ymbol, are intrinic oil propertie and are inde-

9 Liu and Carter 1321 Fig. 7. Behaviour of Leda clay in an oedometer tet (tet data after Yong and Nagaraji 1977). Table 2. Model parameter for Leda clay. Parameter M* λ* κ* e* IC b σ vy,i (kpa) Value Table 3. Model parameter for weathered Bangkok clay. Parameter M* λ* κ* e* IC b σ vy,i (kpa) Value pendent of oil tructure. Thee five intrinic parameter are the ame a thoe adopted in the Modified Cam Clay model (Rocoe and Burland 1968). The influence of thee parameter will not be invetigated in thi paper ince tudie of them are well documented (e.g., ee Muir Wood 1990). Three new parameter, i.e., b, p y,i and ω have been introduced to decribe the influence of tructure on the oil mechanical behaviour. The value of the detructuring index, b, indicate the rate of detructuring during virgin yielding (Fig. 1), and p y,i repreent the ize of the initial yield urface for a tructured oil (Fig. 1). The value of thee two parameter can be determined directly from an iotropic compreion tet on an intact (unditurbed) oil pecimen. Parameter ω wa introduced to decribe the influence of oil tructure on the flow rule (e.g., ee eq. [18]), and it value can be determined by applying the flow rule to the train meaured in a hearing tet on an intact pecimen provided that the elatic propertie of the oil are known. The value of the model parameter e IC *, λ*, κ*, b, and p y,i can be determined from iotropic compreion tet. The value of parameter λ *, κ *, and b can be determined directly from any compreion tet with contant η, wherea the value of e IC * and p y,i can only be determined directly from iotropic tet. In geotechnical engineering practice, oedometer tet on oil are much more widepread than iotropic compreion tet. Therefore, approximate method for obtaining the parameter e IC * and p y,i from oedometer tet are alo uggeted. The approximate method i baed on the aumption that the behaviour of recontituted clay obey the principle of critical tate oil mechanic (e.g., ee Muir Wood 1990 for detail) and an empirical equation uggeted by Jacky (1944) for one-dimenional compreion. Detail of thi analyi can be found in a report by Liu and Carter (2002), from which the following approximate expreion have been derived: 2 c [26] p y,i = 2 3 in 1 inϕ c ϕ inϕ c and [27] e* = e* + ( λ* κ*) IC ID σ vy,i inϕ c ln 1 inϕ 1 + c 3 6 4inϕ c where ϕ c i the critical tate friction angle meaured from a triaxial compreion tet, σ vy,i i the value of the vertical effective yield tre, and e ID * i the value of the void ratio at p = 1 kpa in an oedometer tet on a recontituted oil.

10 1322 Can. Geotech. J. Vol. 39, 2002 Fig. 8. Compreion behaviour of Leda clay with different value of η (tet data after Walker and Raymond 1969). Fig. 9. Iotropic compreion behaviour of weathered Bangkok clay (tet data after Balaubramanian and Hwang 1980). Feature of the model The influence of the three new parameter b, p y,i, and ω, and ome feature of the new Structured Cam Clay model are decribed in thi ection. Example calculation have been made uing the new model, and the value of the intrinic oil propertie adopted are lited in Table 1. Baed on thee value, it i found that e c * = 2.1, where e c * i the wellknown parameter defining the poition of the critical tate line in e p pace. Parameter b The influence of the detructuring index b i demontrated by the imulation hown in Fig. 3 and 4. The following value of parameter for the oil tructure were employed in thee calculation: p y,i = 100 kpa, and ω = 1. Six different value of b were aumed and they are 0, 0.25, 0.5, 1, 5, and 100. The initial tre tate wa defined by p = 100 kpa and q = 0, and the initial value of the additional void ratio wa e i = 0.8. It can be een in Fig. 3 that the rate of reduction in the additional void ratio maintained by oil tructure increae with the magnitude of b. Forb = 0, the virgin compreion line for a tructured oil and that for it correponding recontituted oil are parallel in the e ln p pace. Theoretically, in thi cae no detructuring take place during the virgin yielding and the value of e remain unchanged. The imulated hearing behaviour of a tructured oil with different value of the detructuring index b i hown in Fig. 4. The effective tre path imulated follow thoe in a

11 Liu and Carter 1323 Fig. 10. Compreion behaviour of weathered Bangkok clay (tet data after Balaubramanian and Hwang 1980). Table 4. Model parameter for a natural calcarenite Parameter M* λ* κ* e* IC ν* b ω p y,i (kpa) Value Fig. 11. Iotropic compreion tet on calcarenite (tet data after Lagioia and Nova 1995). conventional drained triaxial tet. Except for the unlikely ituation with b = 0, the final tate for a tructured oil under monotonic hearing i independent of oil tructure and correpond to the critical tate of deformation. At thi tate the oil tructure ha been completely removed. Where the initial tre tate, void ratio, and the loading path are exactly the ame, the final tate for all even cae fall onto the ame point on the critical tate line (Fig. 4a), and the final value of the deviatoric tre and the volumetric train are the ame (Fig. 4b and 4c), indicating that parameter b ha no influence on the final tate of the oil under monotonic hearing if b >0. It may alo be noticed in Fig. 4b and 4c that for oil with high b value, uch a the cae for b = 100, the hear tiffne may be non-monotonic. Thi i becaue for high value of b, oil tructure i detroyed rapidly when virgin yielding commence, and hence the tiffne of the oil i low during the early tage of loading. After the tructure of the oil ha eentially been removed, the behaviour of the original tructured oil i almot the ame a that of the cor-

12 1324 Can. Geotech. J. Vol. 39, 2002 Fig. 12. Shearing behaviour of calcarenite at σ 3 = 25 kpa (tet data after Lagioia and Nova 1995). (a) Deviatoric tre and train relationhip. (b) Volumetric train and deviatoric train relationhip. Table 5. Revied value of model parameter for a natural calcarenite. Parameter M* λ* E* (kpa) e* IC ν* b ω p y,i (kpa) Value a a Apect ratio of the yield urface i reponding recontituted oil and the tiffne of the oil then i uually higher. Thi phenomenon ha been oberved experimentally (Lagioa and Nova 1995; Arce et al. 1998). Parameter p y,i To illutrate the influence of the ize of the initial yield urface defined by p y,i, the oil parameter lited in Table 1, together with b = 1 and ω = 1, were adopted. Four different value of p y,i were aumed and they are 100, 200, 500, and 1000 kpa. The influence of parameter p y,i on the imulation i hown in Fig. 5. The effective tre path imulated follow thoe in a conventional drained triaxial tet in which the axial loading only i increaed. The initial tre tate for all ix cae wa the ame, with p = 100 kpa and q = 0, and the initial void ratio wa e i = For thi initial oil tate and the given intrinic oil propertie, the initial yield urface for

13 Liu and Carter 1325 Fig. 13. Shearing behaviour of calcarenite at σ 3 = 900 kpa (tet data after Lagioia and Nova 1995). (a) Deviatoric tre and train relationhip. (b) Volumetric train and deviatoric train relationhip. the correponding recontituted oil i p o = 100 kpa. Therefore, for the particular ituation with p y,i = 100 kpa the oil i in a recontituted tate and ha no tructure. The oil i tructured for ituation with p y,i > 100 kpa. Thu, thi et of computation imulate the development of tructure for oil at contant void ratio and the ame tre tate. The following feature of oil behaviour have been predicted: (1) The final tate of a tructured oil under monotonic hearing i independent of the ize of the initial yield urface. (2) Unlike a recontituted oil, the peak trength of a tructured oil i dependent on oil tructure a well a on the initial tre tate, void ratio, and the tre path. (3) If oftening occur the peak trength of a tructured oil reduce to the critical tate trength more rapidly than for a recontituted oil. Thi i becaue the oftening of a tructured oil may be attributed to two factor, detructuring and volumetric expanion. (4) The repone pattern uually labeled dry behaviour (Schofield and Wroth 1968) may not be oberved for a tructured oil, i.e., volumetric expanion may not occur when the oftening proce tart. It i een that for the cae with p y,i = 500 kpa there i a continuou volumetric compreion accompanying the oftening proce. For the imulation with p y,i = 1000 kpa, volumetric expanion, although

14 1326 Can. Geotech. J. Vol. 39, 2002 Fig. 14. Shearing behaviour of calcarenite at σ 3 = 1300 kpa (tet data after Lagioia and Nova 1995). (a) Deviatoric tre and train relationhip. (b) Volumetric train and deviatoric train relationhip. Table 6. Model parameter for natural Corinth marl. Parameter M* λ* κ* e* IC ν* b ω p y,i (kpa) Value oberved, tart only after a coniderable amount of oftening ha occurred. Parameter ω Figure 6 how the influence of the parameter ω. Value of the oil parameter lited in Table 1 were adopted for thee imulation, together with b = 1 and p y,i = 100 kpa. The initial tre tate i defined a p = 100 kpa and q =0, and the initial value of the additional void ratio wa e i = 0.8. Three different value of ω were aumed, i.e., ω =0, 0.625, and 1.25 (the correponding value of ω e i are 0, 0.5, and 1, repectively). Baed on the tudy of the three parameter decribing oil tructure, it can be concluded that the final tate of a tructured oil under monotonic hearing predicted by the propoed model for ituation with b > 0 i the critical tate of deformation, which i independent of oil tructure. The exitence of the critical tate of deformation for geomaterial and the implication that their mechanical propertie are independent of material tructure have been widely oberved feature of oil behaviour (e.g., Been and Jefferie 1985; Ihihara 1993; Novello et al. 1995; Carter et al. 2000). Model evaluation The validity and utility of the propoed model were evaluated by making comparion between the model prediction and experimental data. The compreion behaviour of two

15 Liu and Carter 1327 Fig. 15. Shearing behaviour of calcarenite at σ 3 = 3500 kpa (tet data after Lagioia and Nova 1995). (a) Deviatoric tre and train relationhip. (b) Volumetric train and deviatoric train relationhip. Table 7. Model parameter for a natural clayhale. Parameter M* λ* E* (kpa) e* IC ν b ω p y,i (kpa) Value different clay ha been conidered; natural Leda clay and weathered Bangkok clay. The hearing behaviour of three other tructured oil, i.e., natural calcarenite, Corinth marl, and a clay hale, have alo been conidered. Further detail of thee particular comparion may be found in a report by the author (Liu and Carter 2002), together with more detailed explanation of how the model parameter were determined in each cae. Compreion behaviour of two clay Two et of compreion tet on different oil were imulated and for thee tet only the volumetric deformation ha been computed. A can be een from eq. [23], the volumetric deformation i not influenced by the value of parameter ν and ω. Hence, for the preent purpoe there i no need to determine or pecify value for thee parameter. Leda clay The firt group of tet data include five compreion tet on natural oft Leda clay performed by Yong and Nagaraj (1977) and Walker and Raymond (1969). The two oedometer tet on the natural and recontituted Leda clay reported by Yong and Nagaraji (1977) were ued to identify oil parameter, and their value are lited in Table 2. The initial tate of the tructured oil i defined by σ v =20kPa and e = A hown in Fig. 7, the compreion behaviour of Leda clay i well imulated by the model. Three tet performed by Walker and Raymond (1969) were ued to evaluate the model prediction. Although all

16 1328 Can. Geotech. J. Vol. 39, 2002 Fig. 16. Iotropic compreion behaviour of Corinth marl (tet data after Anagnotopoulo et al. 1991). of the pecimen teted by both Yong and Nagaraji (1977) and Walker and Raymond (1969) were Leda clay, they were obtained from different location in the ame area. It i aumed that thee pecimen differed only in the ize of the initial yield urface, i.e., the different Leda clay ample poeed the ame mineralogy and type of tructure but may have had different degree of tructure. The three compreion tet were with η = 0, 0.63, and 1, repectively. The experimental data for the tet with η = 0 were ued to identify the ize of the yield urface, and it wa found that p y,i = 265 kpa. The predicted compreion behaviour of the Leda clay i hown in Fig. 8. It i een that the propoed model give an approximate but reaonable decription of the compreion behaviour of natural Leda clay. Bangkok clay The econd group of tet data include the reult of five compreion tet on weathered Bangkok clay performed by Balaubramanian and Hwang (1980). Value of the model parameter are lited in Table 3. The one-dimenional compreion curve for the recontituted oil type wa etimated by the empirical method uggeted by Burland (1990), upon which the parameter λ and e IC * were etimated. The imulated behaviour of Bangkok clay i hown in Fig. 9. It may be noticed that the compreion behaviour of the Bangkok clay i well imulated in thi cae. The predicted compreion behaviour of Bangkok clay with η = 0.16, 0.43, 0.6, and 0.75 i hown in Fig. 10. A may be een in the inet in Fig. 9, ome difference in the initial oil tructure exit among the ample ued for the five tet. The tet pecimen were obtained from the field and ome variation in the pecimen would normally be expected. It can be een that the initial oil tate for the five pecimen may be divided into three group, i.e., the tet with η = 0, the tet with η = 0.16, and tet with η = 0.43, 0.6, and It i aumed in the imulation that the difference in the initial tate of the oil can be repreented adequately by the difference in the ize of the initial tructural yield urface. It may be een from the compreion curve that the initial tre tate for the tet with η = 0.16 i on the yield urface, i.e., p y,i = 67.6 kpa. The ize of the initial yield urface for the other three pecimen i 45 kpa (the tet with η = 0.43 i ued to identify the value of thi parameter). Overall, it i een that the propoed model give a reaonably good approximation of the compreion behaviour of weathered Bangkok clay. Behaviour of a natural calcarenite The reult of experimental work carried out by Lagioia and Nova (1995) on a natural calcarenite have been compared with the model prediction. The natural calcarenite wa formed by marine depoition. It i a coare-grained material with a high degree of uniformity and calcareou interparticle cement. An iotropic compreion tet on the cemented oil wa ued to identify oil parameter and their value are lited in Table 4. The meaured and imulated iotropic compreion behaviour of the calcarenite i hown in Fig. 11. The value of parameter e IC * λ*, κ*, b, and p y,i were obtained directly from the experimental data. The value of Poion ratio wa aumed. The critical tate trength for the natural calcarenite wa reported by Lagioia and Nova (1995) a M* = The initial tate for the tructured oil i defined by p = 147 kpa and e = 1.148, and o the initial value of the additional void ratio due to oil tructure i e i = The value of parameter ω wa etimated by auming 1 ω e i = 0.5 baed on the contraint condition eq. [19]. By uing the value of the model parameter lited in Table 4, the behaviour of the natural calcarenite under conventional drained triaxial tet wa predicted. In all, eight tet were conidered with the confining preure σ 3 ranging from 25 to 3500 kpa. A comparion between tet reult and the prediction for four tet are hown in Fig For the tet with σ 3 = 3500 kpa, the initial tre tate i much larger than the ize of the initial tructural yield urface. According to the propoed model, the tructure of the oil at σ 3 = 3500 kpa i effectively completely detroyed, ince the oil ha a very high detructuring index, i.e., b = 30. Thu,

17 Liu and Carter 1329 Fig. 17. Behaviour of natural Corinth marl (tet data after Anagnotopoulo et al. 1991). (a) Deviatoric tre and train relationhip. (b) Volumetric and deviatoric train relationhip. the oil behaved eentially a a recontituted material throughout thi tet. Detructuring of thi ample wa confirmed by Lagioia and Nova (1995). Conidering the wide range of initial tree, it i een that the propoed model provide ucceful prediction of the behaviour of thi natural and highly tructured calcarenite. Simulation of the behaviour of thi calcarenite have alo been made, where a part of the tet data wa firt employed to determine the model parameter. The value of the model parameter ued for the imulation (a oppoed to prediction ) are lited in Table 5. Comparion between the theoretical imulation and the experimental data for four tet are alo hown in Fig The imulation are repreented by broken line. It can be een that the behaviour of the natural calcarenite ha been imulated atifactorily with the et of revied model parameter. It i noted that the difference in parameter value adopted for the prediction (Table 4) and imulation (Table 5) are generally relatively minor, with one important exception. It i noted in particular that for the imulation the value of κ wa permitted to vary from tet to tet while the value of E*, Young modulu for fully drained condition, wa held contant for all tet. Behaviour of Corinth marl Reult of the experimental work performed by Anagnotopoulo et al. (1991) on a natural Corinth marl have been compared with the model imulation. Two et of tet were reported: a et of three iotropic compreion tet on both natural and recontituted Corinth marl, and a et of five hearing tet on the intact and partially detructured oil. From the firt et of tet, the oil parameter e IC *, λ, κ, b, and p y,i have been identified, and their value are lited in Table 6. The meaured and imulated behaviour of

18 1330 Can. Geotech. J. Vol. 39, 2002 Fig. 18. Shearing behaviour of clayhale (tet data after Wong 1998). (a) Deviatoric tre and train relationhip. (b) Volumetric train and deviatoric train relationhip. the oil in iotropic compreion i hown in Fig. 16. Two iotropic compreion tet on recontituted Corinth marl are reported, and ome mall dicrepancie on the iotropic compreion line are oberved between the two tet ample, which were aumed to be identical. For mot natural oil, i.e., not artificially manufactured ample, ome dicrepancy in the tre and train behaviour i expected due to material variance. The iotropic tet that gave the better imulation of the hearing behaviour of the Corinth marl wa elected for identifying the model parameter. The initial value of the additional void ratio, i.e., e i, wa found to be The value of parameter ω wa etimated by auming 1 ω e i = 0.5, baed on eq. [19]. The value of Poion ratio wa aumed a The critical tate trength M* wa determined baed on the econd et of tet, i.e., the final trength of the oil reached under monotonic hearing. The value of M* i the only parameter determined from the data from the hearing tet. Both the imulation and the experimental data are hown in Fig. 17. For all five compreion tet, the confining preure were kept contant at 98, 294, 903, 1500, and 4000 kpa, repectively, and the axial loading wa increaed until the pecimen failed. For the firt four tet, the initial tre tate of the oil wa within the initial tructural yield urface, defined by p y,i = 3800 kpa, and therefore the oil ample for thee tet are aumed to be intact. For the fifth tet, the initial tre tate of the oil exceed the initial tructural yield urface and the oil ample ha experienced partial detructuring. It i een that the propoed model give a reaonable repreentation of the behaviour of the highly tructured, tiff Corinth marl.

19 Liu and Carter 1331 Behaviour of La Biche clayhale The reult of the experimental work performed by Wong (1998) on a natural clayhale, a Canadian La Biche hale, have been compared with the model imulation. Table 7 how the value of the model parameter ued. A comparion between the imulation and the experimental data i hown in Fig. 18. It i een that the propoed model ha the capability of modelling the behaviour of thi tructured clayhale. For the clayhale in the tet with σ 3 = 500 kpa, the volumetric deformation remain compreive even though the hear trength of the oil often from a peak of 2600 to 1800 kpa. Thi type of behaviour ha been widely oberved in tructured clay and clayhale (e.g., Bihop et al. 1965; Lo 1972; Georgiannou et al. 1993; Robinet et al. 1999; Carter et al. 2000). A explained elewhere by Liu and Carter (2002), adopting a contant value of E* overall implie a value of κ that varie between tet. The following value were ued here: κ = for the tet with σ 3 =50kPa,κ = for the tet with σ 3 = 250 kpa, and κ = 0.02 for the tet with σ 3 = 500 kpa. Concluion The Modified Cam Clay model ha been generalized o that the iotropic variation of the mechanical propertie reulting from the preence of oil tructure can be decribed. A new hierarchal model, referred to a the Structured Cam Clay model, wa propoed. Beide the original five parameter introduced in the Modified Cam Clay model, three new parameter have been introduced. They are: b, the detructuring index, p y,i, the ize of the initial tructural yield urface, and ω, a parameter decribing the effect of oil tructure on the platic flow rule. Value of the firt two parameter can be determined from an iotropic compreion tet or an oedometer tet. The third parameter can be determined from the volumetric train and deviatoric train curve obtained from a hearing tet. Overall, the propoed model ha been ued to predict both the compreion and hearing behaviour of five tructured oil. The computation cover wide range of tre, initial void ratio, and oil tructure. It ha been demontrated that the propoed model uccefully decribe many important feature of the behaviour of tructured oil and ha ignificantly improved the performance of the Modified Cam Clay model by quantifying the important influence of oil tructure. In particular, the fact that the new model i able to predict imultaneou material oftening and compreive volumetric train i conidered to be a ditinct advantage over the Modified Cam Clay model. Becaue the Modified Cam Clay model form the bai of the new model, obviouly the new model i uitable only for thoe oil for which the behaviour of the recontituted material can be decribed adequately uing the Modified Cam Clay model. Aniotropic feature of oil behaviour, either due to the recontituted parent oil or due to the preence of oil tructure, were not tudied in thi paper but will be the topic of future reearch. Thi paper ha concentrated on introducing the new model and it baic feature and therefore only the behaviour of oil under fully drained condition ha been conidered. The author alo plan a future invetigation of the performance of the model for undrained condition and a ytematic tudy on the identification of model parameter from tet commonly carried out by engineer in geotechnical practice. Acknowledgement Some of the work decribed here form part of the reearch program of the Special Reearch Centre for Offhore Foundation Sytem, etablihed and upported under the Autralian Reearch Council Reearch Centre Program. In addition, a Large Grant from the Autralian Reearch Council in partial upport of thi work i alo gratefully acknowledged. 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