An Experimental and Theoretical Study on the Dilatancy of Sand and Clays

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1 An Exerimental and Theoretical Study on the Dilatancy of Sand and Clay Author Chu, J., Kim, S., h, Erwin, Balaubramaniam, Bala, Bergado, D. Publihed 004 Conference Title To the enz of the Earth Coyright Statement 004 New Zealand Geotechnical Society Inc.. Ue hyertext link to acce the conference' webage. The attached file i oted here with ermiion of the coyright owner[] for your eronal ue only. No further ditribution ermitted. Downloaded from htt://hdl.handle.net/1007/05 Link to ublihed erion htt:// Griffith Reearch nline htt://reearch-reoitory.griffith.edu.au

2 An Exerimental and Theoretical Study on the Dilatancy of Sand and Clay J. Chu PhD Aociate Profeor, School of Ciil and Enironmental Engineering, Nanyang Technological Unierity, Singaore S. R. Kim PhD Preident, ESC Engineering & Conultant Co. Ltd., Seoul, Korea Y. N. h MEng PhD Candidate, School of Engineering, Griffith Unierity, Autralia A. S. Balaubramaniam PhD, FIEAut, FACSE Profeor, School of Engineering, Griffith Unierity, Autralia. D. T. Bergado PhD Profeor, School of Ciil Engineering, Aian Intitute of Technology, Thailand. Summary: Rowe (196) tre dilatancy relationhi for and, and Schofield and Wroth (1968) (Rocoe et al., 1963), and Rocoe and Burland (1968) energy equation for oft clay are claical work in decribing the tredilatancy behaiour of and and clay. Howeer, the tre-dilatancy behaiour of oil i affected by the tre and train ath followed by the oil and it i difficult to ue a ingle equation to model the tre-dilatancy behaiour of all oil. In thi aer, the hitorical deeloment of the tre-dilatancy theorie i briefly reiewed. The generalied tre-dilatancy behaiour of clay and and i reented. Comarion between the exerimental oberation and the theoretical rediction are made. The uitability of different tre-dilatancy theorie to different oil under different teting condition i examined. The data reented can alo be ued to examine other tre-dilatancy theorie rooed by other reearcher. INTRDUCTIN Dilatancy of oil i an imortant henomenon that differentiate the latic behaiour of oil from that of metal. It i alo one of the deformation characteritic of oil that cannot be modelled roerly by the claical laticity that wa deeloed eentially for metal. Whether the dilatancy behaiour of oil can be modelled roerly ha been an imortant criterion in examining the uefulne of any latic model for oil. Since the ioneer work of born Reynold, more exerimental tudie on the tre-dilatancy behaiour of oil hae been made. It i generally undertood now that the normally and lightly oerconolidated clay a well a looe and deelo oitie ore reure during undrained hear or tend to reduce in olume under drained condition. n the other hand, heaily oer conolidated clay and dene to ery dene and deelo negatie ore reure during hear and tend to increae in olume under drained condition. Baed on the exerimental oberation, eeral tredilatancy theorie hae been deeloed. The critical tate concet of the work of Rocoe, Schofield, Wroth, Poorohab, Thurairajah and Burland in the deeloment of a ucceful tre-train theory foe oil obtained the latic dilatancy ratio in term of an energy diiatie function, which ued the critical tate arameter, M deendent on the angle of friction of the oil. Such an exreion ha it origin in the work of Taylor at MIT on the interlocking behaiour of and and the boundary energy correction for hear in the direct hear aaratu. Rowe (1957) at the Unierity of Mancheter worked in arallel with the Rocoe Grou at Cambridge deeloed the mot ucceful tre-dilatancy relation. Exerimental behaiour of oil in the laboratory and in the field indicated that the Cambridge dilatancy relation modelled the behaiour of normally conolidated clay and looe and and the Rowe (196) tre- dilatancy relation i more aroriate in the cae of dene and. The work of Drucker, Pooroohab and Caladine aed the way to relate the latic dilatancy ratio to yield locu and latic otential and thi in turn heled to derie an undrained tre ath, which indicated the magnitude of the deeloment of ore reure in clayey oil. Extenie exerimental tudie erformed by Balaubramaniam (1969), faoured a non-aociated flow rule of the tye originally formulated by Rocoe and Poorohab (1963), and heled to exlain the latic hear train of oerconolidated clay within the tate boundary urface. Baed on the work of Loudon (1967), Rocoe and Burland rooed a econd et of contant deiator tre yield loci within the tate boundary urface, to obtain the undrained comonent of the latic hear train which need to be added to the train from the olumetric yield loci obtained from an aociated flow rule to fully decribe the hear train for tre ath of the non radial tye in which the tre ratio increae or decreae monotonically during drained and undrained hear. Pender (1978) wa the firt to deelo a latic dilatancy relation for oerconolidated clay which can cature the deeloment of oitie ore reure in normally and lightly oerconolidated clay and negatie ore reure in heaily oerconolidated 1

3 clay. The extenie exerimental work carried out by Balaubramaniam and hi co-worker at AIT on the tre-train behaiour of oft Bangkok clay below the tate boundary urface eem to uort in mot intance the work of Pender (1978), while ariou tye of refinement eem better in modelling the detailed behaiour. Thee data are reented here on clay in the hoe that thi work would be helful in deeloing better tre train model in line with the work of Puzrin and Houlby (001), Collin and Kelly (00) and other. The tre-dilatancy reone of Sydney and to ariou tre and train ath are reented. A general tredilatancy relationhi i alo rooed baed on the exerimental oberation. STRESS-DILATANCY BEHAVIUR F CLAY ne of the mot oular tre-dilatancy relationhi for clay i the one adoted in the Cam-clay model (Schofield and Wroth 1968). Baed on the work hyothei: dw = ' + q = M' (1a) We hae: q = M ' (1b) where M = 6inφ c /(3 inφ c ). Under three dimenional condition, the latic work can be written a 1 : dw = ' + βq (a) where (3 + μν ) β = (b) (3 + μ )(3 + ( ν ) ) and μ and ν are Lode tre arameter and Lode latic train arameter reectiely. Then q β = M ' Under axiymmetric condition, β = 1 and Eq. (c) degenerate to Eq. (1b). It hould be noted that a modified relationhi to Eq. (1) ha alo been rooed by Rocoe and Burland (1968). (c) Figure 1. Tyical tre ath of the behaiour of lightly oerconolidated clay (Kim, 1991) Figure. ( /, / e ) relationhi for a contant tre ratio line from the K 0 conolidation tet. Kim (1991) made a comrehenie tudy on the behaiour of oft Bangkok clay below the tate boundary urface. He conducted triaxial conolidation and welling tet (both iotroic and K 0 conolidation and welling) a well a four erie of undrained triaxial tet (three of them are in comreion and one in extenion) 1 Under three dimenional condition, = (σ 1 + σ + σ 3 )/3, q =[ (σ 1 σ ) + (σ 1 σ 3 ) + (σ σ 3 ) ] 0.5 /, ε = ε 1 + ε + ε 3, and ε = [(ε 1 ε ) + [(ε ε 3 ) + [(ε 1 ε 3 ) ] 0.5 /3.

4 and ten erie of drained tet (a hown in Figure 1). Subequent tudent erformed contant tet and alo tre robing tye of tet. The ariation in the latic dilatancy ratio, / with / e i hown in Figure, for a tre ratio η = q/ = 0.6 a obtained from CID tet on lightly oerconolidated clay. Similar relationhi were alo etablihed for the entire tre ratio from iotroic conolidation to the critical tate both on the comreion and extenion ide. From thee data, the ariation of d d with η for comreion and extenion e tet are hown in Figure 3. Thi figure illutrate how the latic train increment ector rotate within the tate boundary urface with reect to tre ratio, η and the reduction of / e. The general exreion for the latic dilatancy ratio on the comreion ide can be exreed a: M η M 3 M = η + η η M + η e (3) Figure 3. Variation of the ( /, / e ) lot with the tre ratio within the tate boundary urface. Thi equation will gie the ame latic dilatancy ratio a the Rocoe and Burland (1968) theory for normally conolidated clay and for the oerconolidated tate will hae the ratio at any articular tre ratio rogreiely reduce with decreaing alue of /. The tre ath within the SBS for the tre robing e exeriment i hown in Figure 4 in the (q/ e, / e ) lot. Contant alue of Δ q + Δ were obtained on each tre ath a hown in Figure 5a and the train ath in ( ε, ε ) lot are hown in Figure 5b. The train ath were initially circular and then ditorted in hae to omewhat like ellie. The dilatancy ratio of graded rockfill, lime treated clay and cement treated clay are hown in Figure 6. Thee relationhi are imilar in hae to the rediction of Rocoe and Burland (1968) but different in magnitude. 3

5 5 Figure 4. Stre robe ath in (q/ e, / e ) lot (after Khan, 1999) q (ka) 70 r=10 ka r=0 ka r=30 ka r=40 ka r=60 ka r=80 ka SBS (ka) Figure 5a. Stre increment circle (after Pornong, 001) Figure 5b. ( ε, ε ) lot for Δ + Δq = 10 kpa with fitting (after Pornong, 001). 4

6 1 Lime treated clay Cement treated clay Rrockfill Predicted (Rocoe & Burland, 1968) Dilatancy, (d/)η STERSS-DILATANCY BEHAVIUR F SAND Stre Ratio, η Figure 6. Variation of dilatancy with tre ratio ne inherent limitation of the Cam-clay tre-dilatancy relationhi i the condition that when η = M, = 0, een though it i not at the critical tate. Thi aarently doe not aly to dene and. For and, Rowe tredilatancy equation (Rowe, 196; 1966) i more frequently ued. Rowe tre-dilatancy equation i written a: σ ' 1 = K 1 (4) σ ' 3 1 where K i related to an angle of oil friction. Eq. (4) inherently aume that the oil i rigid latic o the tre-dilatancy behaiour i not affected by the tre leel. To oercome thi limitation, a modified Rowe tre dilatancy equation ha been rooed by Wan and Guo (1988), which retain the format of Eq. (3), with K being calculated a: * 1+ in φ K = and in φ * = ( e / e * cr ) α in φc (5) 1 in φ where φ * i the friction angle mobilized along a certain macrocoic lane which eole during deformation hitory, φ cr and e cr are the friction angle and oid ratio at the critical tate. Rowe tre-dilatancy equation ha been examined uing exerimental data by eeral reearcher. Lee (1966) and Lo and Lee (1990) concluded that Eq. (3) could decribe the behaiour of dene and in conolidated drained (CD) triaxial tet well. Howeer, Lee (1966) and Lee and Ingle (1968) alo howed that the equation i not alicable to unloading and reloading and the tre-dilatancy relationhi for the ot-eak region i different from that for the re-eak region. Thi i further roen by Chu et al. (199) and a ot-eak tre-train relationhi ha been etablihed by Chu et al. (199). Uing data obtained from contant tre ratio (σ 1 /σ 3 ) and contant tre increment ratio (dσ 1 /dσ 3 ) ath tet, Lo and Lee (1990) further obered that in general, Eq. (3) i not alicable to decribing the comlete tre-dilatancy behaiour of and along σ 1 /σ 3 and dσ 1 /dσ 3 ath. It hould alo be ointed out that Rowe tre-dilatancy relationhi calibrated uing triaxial CD tet may not be alicable to drained tet under three-dimenional condition. The tre dilatancy reone of dene Sydney and to a erie of contant b (b = (σ σ 3 )/(σ σ 3 )) true-triaxial tet are reented in Figure 7. It can be een that the tre-dilatancy relationhi i affected by the b alue. In general, the larger the b, the higher the tre ratio for a gien dilatancy ratio. For drained tet, the tre ratio σ 1 /σ 3 and q/ i conertible. The Rowe tre-dilatancy Equation fit the tet for b = 0 cloely, but i unable to model the other tet with other b alue (Chu 1991). For and heared along a σ 1 /σ 3 ath, it i obered (Lo and Lee 1990; Chu 1991) that the train increment ratio reult in / 1 being contant. n the other hand, when and i heared along a train ath with contant train increment ratio / 1, the tre ath will aroach a contant tre ratio σ 1 /σ 3 or q/ (Chu 1991). Some examle for dene Sydney and are hown in Figure 8. It i obered from all the tre ath and train ath 5

7 tet that there i a relationhi between the tre ratio and the train incremental ratio and the higher the dilatancy ratio, / 1, the higher the tre ratio, q/. It ha been etablihed by Chu (1991, 1994) and Chu and Lo (1994) that thi relationhi i unique, irreectie of whether tre ath or train ath control i ued. Thi relationhi can be written a: q = α β for ' 1 d 1 ε 1 f (6) where α and β are two material contant. For dene Sydney and, α = 1.4 and β = When / 1 ( / 1 ) f, q/ will reach the failure tre ratio (q/ ) f and will not change. For oil at different denitie, ( / 1 ) f and (q/ ) f alue will be different, but α and β are not enitie to the ariation of denity. Chu and Lo (1994) hae further roed that the aboe tre-dilatancy relationhi i alo alicable to three dimenional condition when generalied tre and train arameter are ued. Figure 7. Stre-dilatancy behaiour obtained from contant b tet Figure 8. Stre ratio eru train behaiour of dene and obtained from contant train increment ratio ath 5 4 Rowe Cam-clay Chu&Lo σ' 1 /σ' / 1 Figure 9. Comarion of different tre-dilatancy relationhi The tre-dilatancy relationhi exreed in Eq. (4) i comared with the Rowe tre-dilatancy equation, Eq. () and the tre-dilatancy equation deried in the Cam-clay model, Eq. (1b) in Figure 9 under axiymmetric condition. For the conenience of comarion, q/ ha been conerted into σ 1 /σ 3. The critical tate friction angle for Sydney and i and the correonding M = 1.3. K =.9 i ued for Eq. () (Chu 1994). It can be een from Figure 9 that the three tre-dilatancy relationhi are all different. Rowe tre-dilatancy equation rereent the CD behaiour of dilatie and, wherea the Cam-clay equation deict the behaiour of 6

8 NC or moderately C clay. The tre-dilatancy equation of Chu and Lo (1993) i only alicable to the aymtotic tate obtained along contant σ 1 /σ 3 or contant / 1 ath, which include undrained and drained ath. Deite of the difference, the 3 cure aear to merge at the failure oint, indicating that failure tate i indeendent of the tre or train ath leading to failure. The horizontal line in Figure 9 indicate that although in general, the tre ratio increae with the dilatancy ratio, the alue i caed at the failure tre ratio. CNCLUSINS Some claical tre-dilatancy theorie are reiewed and examined uing exerimental data obtained for clay and and. A the tre-train behaiour of oil i greatly affected by the tre ath and train ath adoted, no ingle theory can decribe the tre-dilatancy behaiour of all oil. Along contant tre ratio σ 1 /σ 3, tre incremental ratio dσ 1 /dσ 3, or train increment ratio / 1 ath, the tre-dilatancy behaiour of oft Bangkok clay i different from that of Sydney and. Neerthele, tre-dilatancy relationhi between the tre ratio and dilatancy ratio can be etablihed for both clay (Figure 6) and and (Figure 9). Although the theorie of Rocoe and Burland (1968) and Rowe (196) are able to redict ome of thoe relationhi for certain tre ath, each theory ha it limitation and further exerimental and theoretical tudie on the tre-dilatancy behaiour of oil are till required. REFERENCES Balaubramaniam, A. S. (1969). Some factor influencing the tre-train behaiour of clay, PhD. Thei, Cambridge Unierity, UK. Collin, I. F. and Kelly, P. A. (00). A thermomechanical analyi of a family of oil model. Geotechnique, 5(7), Chu, J. (1991). Strain oftening behaiour of granular oil under train ath teting. PhD. thei, Unierity of New South Wale. Chu, J. (1994). Study on the tre-dilatancy behaiour of and by train ath teting. Prefailure Deformation of Geomaterial. Ed. Shibuya, S., Mitachi, T., and Miura, S., Chu, J. and Lo, S-C. R. (1994). Aymtotic behaiour of a granular oil in train ath teting. Geotechnique, 44(1), Chu, J., Lo, S-C. R., and Lee, I. K. (199). Strain oftening behaiour of a granular oil in train ath teting. J. Geotech. Engng., ASCE, 118, No., Khan, M. R. A. (1999). Stre-Strain Behaiour of Soft Bangkok Clay below the State Boundary Surface under Aniotroic Condition, M. Eng. Thei, Aian Intitute of Technology Bangkok. Kim, S.R., (1991). Stre-Strain Behaiour and Strength Characteritic of Lightly erconolidated Clay, PhD Thei, Aian Intitute of Technology, Bangkok. Lee, I. K. (1966). Stre-dilatancy erformance of feldar. J. Soil and Found., ASCE, 9(3), Lee, I. K. and Ingle,. G. (1968). Strength and deformation of oil and rock. Chater 4 in Soil Mechanic Selected Toic, Ed. I. K. Lee, Lo, S-C. R. and Lee, I. K. (1990). Reone of a granular oil along contant tre increment ratio ath. J. Geot. Engng, ASCE, 116(3), Loudon, P. A. (1967). Some deformation characteritic of Kaolin, PhD Thei, Cambridge Unierity, UK. Pender, M.J. (1978). A Model for the Behaiour of erconolidated Soil, Geotechnique, 8(1) Pornong, A. (001). Modelling the behaiour of oerconolidated clay, M. Eng. Thei, Aian Intitute of Technology, Bangkok. Puzrin, A. M. and Houlby, G. T. (001). A thermomechanical framework for rate-indeendent diiatie material with internal function, Int. J. Platicity, 17, Rocoe, K. H. and Burland, J. B. (1968). n the Generalized Stre-Strain Behaiour of Wet Clay, In: Engineering Platicity, Cambridge, Rocoe, K. H. and Pooroohab, H. B. (1963). A theoretical and exerimental tudy of train in triaxial tet on normally conolidated clay, Geotechnique, 13(1) Rocoe, K. H., Schofield, A. N. and Thurairajah, A. (1963). Yielding of Clay in State Wetter than Critical, Geotechnique, 13(3), Rowe, P. (1957). C e =0 hyothei for normally loaded clay at equilibrium, Proc. of 4 th ICSMFE, London, Vol. 1, Rowe, P. W. (196). The tre-dilatancy relation for tatic equilibrium of an aembly of article in contact, Proc. Roy. Soc., London, A69, Schofield, A. N. and Wroth, C. P. (1968). Critical State Soil Mechanic, McGraw-Hill, London. Wan, R.G. and Guo, P. J. (1988). A imle contitutie model for granular oil: modified tre-dilatancy aroach. Comuter and Geotechnic,,