COHESION OF COMPACTED UNSATURATED SANDY SOILS AND AN EQUATION FOR PREDICTING COHESION WITH RESPECT TO INITIAL DEGREE OF SATURATION Md. Abdul Alim 1 and Makoto Nishigaki 2 1 Assistant Pofesso, Depatment of Civil Engineeing, Rajshahi Univesity of Engineeing & Technology, Bangladesh 2 Pofesso, Gaduate School of Envionmental Science, Okayama Univesity, Okayama, Japan ABSTRACT Embankments which cay highway o ailway need fim foundations, fo that eason they ae geneally constucted with compacted sandy soils fo which shea stength plays a vey impotant ole in stability. Howeve, thee is limited available infomation in existing liteatue on shea stength behavio of unsatuated sandy soils. Geneally the satuation conditions of soils of embankment duing aining season ae neae 7%. Howeve, duing heavy ains, the soils become moe satuated theeby educing shea stength and consequently failue occus. The puposes of this study ae to obseve the shea stength vaiation of unsatuated sandy soils with degee of satuation moe than 7% and to develop a constitutive equation fo pedicting shea stength with espect to initial degee of satuation. A seies of tiaxial shea stength tests conducted on 3 types of sandy soils (taken fom Okayama and Hioshima aeas of Japan) with the same void atio but vaying degee of satuation. In all, 9 specimens of each type of soils wee consideed fo undained tiaxial tests with poe-wate pessue measuement. The specimens wee pepaed by static compaction with diffeent initial degee of satuation anging fom 7% to % but with the same void atio fo each soil type (.61,.65 and.7). The chosen void atio gives aound 9% pocto compaction. Expeimental esults show that, the shea stength deceases linealy with incease in degee of satuation. Moeove, expeimental studies to detemine the shea stength paametes of unsatuated soils ae geneally costly, time-consuming and difficult to conduct; theefoe, many equations have been poposed to pedict the shea stength of unsatuated soil with espect to matic suction in the last two decades. Howeve, the measuement of matic suction of unsatuated soil is not easy. This pape also poposes an equation to pedict cohesion of unsatuated sandy soils with espect to initial degee of satuation based on expeimental esults. 1 INTRODUCTION Many diffeent types of soils may be suitable fo use in the constuction of an embankment, anging fom ganula to moe finely sized soils; howeve, ganula soils ae highly desiable. Nomally, the coase fill mateials ae placed at o nea the bottom o base of the embankment in ode to povide a fim foundation fo the embankment and also to facilitate dainage pevent satuation. Embankments which cay highway o ailway need fim foundations, fo that eason they ae geneally constucted with compacted sandy soils fo which shea stength plays a vey impotant ole in stability. Howeve, thee is limited available infomation in existing liteatue on shea stength behavio of unsatuated sandy soils. Consideable eseach has been caied out on the behavio of unsatuated, fine-gained soils (Fedlund and Rahadjo, 1993; Fedlund et al., 1995; Mashhou et al., 1995; Miao et al., 2; Ng et al., 7; Rahadjo et al., 4; Sun et al., 7; Thu et al., 7; Vanapalli et al., 1996; Zhan and Ng, 6). On the othe hand soil with degee of satuation less than unity is called unsatuated soil. The behaviou of unsatuated soil is vey complex because it contains negative poe-wate pessue elative to the poe-ai pessue. The diffeence between poe-ai pessue ( u a ) and poe-wate pessue ( u w ) is called matic suction ( ua uw). Futhemoe, the matic suction is a function of degee of satuation which epesents the soil-wate chaacteistic cuve (SWCC). Geogaphically, unsatuated soils ae widely distibuted in semi-aid aeas of the wold (Cunningham et al., 3). The uppe suface of goundwate is called the pheatic suface o goundwate table (WT). Failue of eath stuctues may occu due to change in WT o satuation condition of soils. The WT inside the eathen embankment fluctuates all the time due to envionmental conditions, howeve, in the ainy season it fluctuates fequently because much wate infiltates into the embankment due to heavy ain and inceased ive stage. The potential slip suface may be fomed at which unsatuated soil with negative poe-wate pessues exist above goundwate table. A polonged peiod of ainfall o inceased ive stage may lead to the change in poe-wate pessues and then may esult in not only the change in the location of a potential slip suface, but also the local Austalian Geomechanics Vol 45 No 2 June 21 45
o global instability of the embankment due to shea stength eduction. Reseach into sandy soils includes Alim and Nishigaki, 9; Donald, 1956; Dumight and Nelson, 1995; Gan and Fedlund,1996; Lu and Wu, 5. Geneally in humid egion, the satuation condition of soils of embankment duing ainy season ae neae to 7%. Howeve, duing heavy ains, the soils become moe satuated theeby educing shea stength and consequently failue occus. The puposes of this study ae to obseve the shea stength vaiation of unsatuated sandy soils with degee of satuation within ange 7% to % and to develop an equation fo pedicting shea stength with espect to initial degee of satuation. A seies of tiaxial shea stength tests conducted on 3 types of sandy soils with the same void atio but vaying degee of satuation. In all, 9 specimens of each type of soils wee consideed fo undained tiaxial tests with poe-wate pessue measuement using modified tiaxial appaatus. The undained tiaxial test was chosen to keep the constant wate content in the specimens. An equation to pedict shea stength (cohesion) of unsatuated sandy soils has also been poposed. 2 SHEAR STRENGTH EQUATION OF UNSATURATED SOIL The shea stength of unsatuated soils is based on Moh Coulomb citeion. Bishop (1963) poposed shea stength equation fo unsatuated soils by extending Tezaghi s pinciple of effective stess fo satuated soils. Bishop s oiginal equation can be aanged as shown. τ = c + ( σ u ) tanφ + χ( u u ) tanφ (1) Whee, τ is shea stength of unsatuated soil; f f a a w c is effective cohesion fo satuated soil; φ is angle of fictional esistance; ( σ ua ) is net nomal stess; ( ua uw) is matic suction, and χ is a paamete dependent on the degee of satuation. The last pat of Equation (1) is the shea stength contibution due to unsatuation of soil called suction stength τ ( us Whee ). Theefoe, eaanging Equation (1), it becomes τ = c + σ ) tanφ + τ τ ( (2) f u a us us = χ( ua uw ) tanφ (3) Now fom Equation (2), the equation of total cohesion (C) of unsatuated soils can be witten as C = c + τ (4) us Then the shea stength Equation (2) becomes, τ = C + ( σ u ) tanφ (5) f a Equation (4) epesents the shea stength contibution due to unsatuation of soils. Fo stability analysis of any unsatuated slope, eseaches ae using Equations (4) and (5) to get shea stength vaiation of unsatuated soils. 3 MATERIALS The thee types of sandy soils used in this study ae called Sample-1, Sample-2 and Sample-3. The gain size distibutions of the soils ae shown in Fig. 1. The basic popeties of the 3 samples ae pesented in Table 1. Pecent fine (%) 8 6 4 2 Sample-1 Sample-2 Sample-3.1.1.1 1 1 Paticle size (mm) Figue 1: Paticles size distibution cuves of samples 46 Austalian Geomechanics Vol 45 No 2 June 21
Table 1: Basic popeties of soils Popeties Sample-1 Sample-2 Sample-3 Specific gavity, G s 2.63 2.64 2.59 Satuated pemeability, K s (cm/s) 2.2 х1-3 9.4 х1-4 1.5 х1-4 Maximum dy density, (g/cm 3 ) 1.85 1.79 1.74 Optimum wate content, (%) 14.7 15.5 18.5 Gain size analysis D 6 (mm).9.58.61 D 3 (mm).44.17.13 D 1 (mm).17.8.6 Coefficient of unifomity, C u 5.29 7.25 1.17 Coefficient of cuvatue, C c 1.26.62.46 Soil popeties used in SWCC and tiaxial tests Dy density, (g/cm 3 ) 1.63 1.6 1.53 Void atio, e.61.65.7 4 DETERMINATION OF MATRIC SUCTION Matic suctions wee detemined using a Tempe pessue cell, which opeates on the same pinciple as the conventional pessue plate appaatus. The schematic diagam of Tempe pessue cell is shown in Fig. 2. The Tempe pessue cell was placed on a suppot and the wate level maintained at the bottom of the soil specimen. When the ai pessue was set to desied matic suction, wate stated to dain fom the soil specimen though the membane filte until equilibium was attained. The outflow of wate fom the soil specimen was measued by an electonic balance. The pocedue was epeated at highe applied ai pessues until the degee of satuation less than.7 was obtained. The plot of degee of satuation against coesponding matic suctions gave the soil-wate chaacteistic cuve (SWCC) and fom the SWCC the matic suctions wee estimated as shown in Table 2. Pessue Gauge Ai compesso PC Sample Ф 3 Ф, Wie mesh Membane filte [unit : mm] Electonic Balance Figue 2: The schematic diagam of Tempe pessue cell Table 2: Estimated matic suction coesponding to degee of satuation (S ) Austalian Geomechanics Vol 45 No 2 June 21 47
Matic suction ( ua uw ) / Sample-1 Sample-2 Sample-3 Degee of satuation (S ) ( u ) a uw in kpa ( ua uw ) in kpa ( a uw ) S =.7 2.5 5 11 S =.8 1.5 3.3 8.5 S = 1 u in kpa 5 TRIAXIAL TEST PROGRAM AND PROCEDURE A seies of 27 tiaxial tests wee caied out on 3 soil samples efeeed to as Sample-1, Sample-2 and Sample-3 (9 tests fo each sample). The compacted unsatuated specimen s specifications ae pesented in Table 3. The specific amount of soil was mixed with desied quantity of wate and then compacted statically in 3 equal layes in a stainless mold of mm height and 5 mm diamete. To get satuated specimen, fist pepaed unsatuated specimen with initial degee of satuation.95 then it was satuated by flowing wate though the bottom valve of pedestal and keeping the wate head highe than the specimen height and assumed it is field satuation condition. A double-walled stain-contolled modified tiaxial appaatus, which allowed measuement of poewate pessue and volume change, was used in this study fo undained tiaxial tests. Details of the testing equipment ae shown in Fig. 3. Each test was commenced by satuating the high ai enty disc (2 bas) with deaied distilled wate. Pio to the test, the specimen was mounted on the pedestal of the tiaxial cell and ubbe membane was placed aound the specimen. O-ings wee placed ove the membane on the bottom pedestal and uppe cap. The specimen was then bought to confining pessues of kpa, 15 kpa and kpa and sheaing stated unde undained tiaxial test with poe-wate pessue measuement, while the stain-state was.1 mm/min. Duing sheaing pocess, the axial defomation, axial load, total volume change and poe-wate pessue wee measued. All the specimens have been sheaed up to 13% stain and peak deviato stesses wee obseved in this stain ange. Figue 3: Schematic diagam of double-walled modified tiaxial appaatus. 6 PRESENTATION OF TEST RESULTS AND DISCUSSION All the specimens wee sheaed unde undained tiaxial shea with poe-wate pessue measuement. The suction befoe sheaing stats is defined as initial suction and it is assumed that thee is no change in soil suction duing sheaing. Degee of satuation, confining pessue and othe specifications fo the tested specimens ae tabulated in Table 3. Deviato stess vesus axial stain elationships unde diffeent confining pessue but at the same degee of satuation ae pesented in Figs. 4, 5 and 6 of Sample-1, Sample-2, and Sample-3 espectively. All the expeimental esults show that deviato stess inceases with incease in confining pessues. Figs. 7, 8 and 9 epesent the compaison of test esults at diffeent degee of satuation but at the same confining pessue ( kpa, 15 kpa and kpa) fo Sample-1, Sample-2, and Sample-3 espectively. All figues show that at the 48 Austalian Geomechanics Vol 45 No 2 June 21
same confining pessue, deviato stess deceases as degee of satuation inceases. It means that unsatuation o matic suction is contibuting to the shea stength of unsatuated soils. Fom the expeimental esults, shea stength paametes ae calculated fo unsatuated soil using poe ai pessue while fo satuated soil using poe wate pessue in both cases using Equation (4) and Equation (5). The satuated shea stength paametes ae pesented in Table 3 Table 3: Specification of tested specimens Sample No. Specimen No. Degee of satuation ( S )* Specimen-2 Sample-1 Specimen-2 Specimen-2 Specimen-2 Sample-2 Specimen-2 Specimen-2 Specimen-2 Sample-3 Specimen-2 Specimen-2 Afte specimen pepaation Void atio* 1.61.8.61.7.61 1.65.8.65.7.65 1.7.8.7.7.7 Confining Pessue (kpa) 15 15 15 15 15 15 15 15 15 Table 4 Shea stength paametes of satuated soils Sample-1 Sample-2 Sample-3 S 1 1 1 φ (degee) 39.5 37.8 39.8 c (kpa) 8.5 9.8 11.5 Suction (kpa). 1.5 2.5. 3.3 5.. 8.5 11 Austalian Geomechanics Vol 45 No 2 June 21 49
6 5 4 3 6 5 4 3 6 5 4 3 kpa 15 kpa kpa 5 1 15 (a) kpa 15 kpa kpa 5 1 15 (b) kpa 15 kpa kpa 5 1 15 (c) Figue 4: Stess-stain elationships at diffeent confining pessue ( kpa, 15 kpa and kpa) of sample-1 (a) specimen with S =.7 (b) specimen with S =.8 (c) satuated specimen 5 Austalian Geomechanics Vol 45 No 2 June 21
6 5 4 3 (a) kpa 15 kpa kpa 5 1 15 Deviato stess, (σ 1- σ 3) (kpa) 6 5 4 3 6 5 4 3 kpa 15 kpa kpa 5 1 15 (b) kpa 15 kpa kpa 5 1 15 (c) Figue 5: Stess-stain elationships at diffeent confining pessue ( kpa, 15 kpa and kpa) of sample-2 (a) specimen with S =.7 (b) specimen with S =.8 (c) satuated specimen. Austalian Geomechanics Vol 45 No 2 June 21 51
Deviato stess, (σ 1- σ 3) (kpa) 6 5 4 3 6 5 4 3 6 5 4 3 kpa 15 kpa kpa 5 1 15 (a) kpa 15 kpa kpa 5 1 15 (b) kpa 15 kpa kpa 5 1 15 (c) Figue 6: Stess-stain elationships at diffeent confining pessue ( kpa, 15 kpa and kpa) of sample-3 (a) pecimen with S =.7 (b) specimen with S =.8 (c) satuated specimen. 52 Austalian Geomechanics Vol 45 No 2 June 21
Deviato stess, (σ1 σ3), (kpa) Deviato stess, (σ 1- σ 3) (kpa) 6 5 4 3 6 5 4 3 6 5 4 3 S=.7 S=.8 5 1 15 Axial stain, ε a, (%) (a) (a S=.7 S=.8 5 1 15 Axial stain, ε a, (%) (b) (b S=.7 S=.8 5 1 15 Axial stain, ε a, (%) Figue 7: Compaison of stess-stain elationship fo diffeent degee of satuation at the same confining pessue of kpa (a) sample-1 (b) sample-2 (c) sample-3. (c) Austalian Geomechanics Vol 45 No 2 June 21 53
Deviato stess, (σ 1- σ 3), (kpa) 6 5 4 3 S=.7 S=.8 5 1 15 Axial stain, ε a, (%) 6 5 4 3 9a S=.7 S=.8 5 1 15 Axial stain, ε a, (%) 6 5 4 3 Figue 8: Compaison of stess-stain elationship fo diffeent degee of satuation at the same confining pessue of 15 kpa (a) sample-1 (b) sample-2 (c) sample-3. (b) (c) S=.7 S=.8 5 1 15 Axial stain, ε a, (%) 54 Austalian Geomechanics Vol 45 No 2 June 21
6 5 4 3 S=.7 S=.8 5 1 15 (a) 6 5 4 3 6 5 4 3 S=.7 S=.8 5 1 15 Axial stain,ε a (%) (b) 5 1 15 Figue 9: Compaison of stess-stain elationship fo diffeent degee of satuation at the same confining pessue of kpa (a) sample-1 (b) sample-2 (c) sample-3. (c) S=.7 S=.8 Austalian Geomechanics Vol 45 No 2 June 21 55
3 Total cohesion, C (kpa) 25 2 15 1 5 C = f ( S ) Sample-1 Sample-2 Sample-3.7.8.9 1 c Degee of satuation, S Figue 1: Relationship between total cohesion and degee of satuation 5 Fictional angle, φ (degee) 45 4 35 3 Sample-1 Sample-2 Sample-3.7.8.9 1 Degee of satuation, S Figue 11: Relationship between fictional angle and degee of satuation. Calculated unsatuated cohesion called total cohesion and fictional angle ae plotted with initial degee of satuation in Fig. 1 and Fig. 11 fo Sample-1, Sample-2, and Sample-3 espectively. Fom the expeimental esults it was obseved that, the total cohesion inceases with decease in initial degee of satuation linealy. On the othe hand, vaiation of fictional angle with degee of satuation is almost the same fo Sample-1, Sampe-2 and Sample-3. It means that the fictional angle has a little ole to suction stength contibution. flow egime, which includes the spatial dimensions of the mateial boundaies, the definition of the bounday conditions, and the definition of mateial paametes. Subsuface investigation will be equied to delineate the diffeent mateial stata and the lowest bounday of the flow egime. Piezometic ecods ae used to define the bounday conditions. In situ o laboatoy pemeability tests, laboatoy evaluation of the moistue etention cuves of the unsatuated mateials, and the calculations of unsatuated pemeability functions ae also equied. Anothe impotant paamete is to estimate shea stength of unsatuated soils in the field. Selecting appopiate conditions fo analysis of slopes equies consideation of the shea stengths of soils unde dained and undained conditions, and consideation of the conditions that will contol dainage in the field. Fee daining soils ae those that ae able to dain wate completely within the constuction o loading peiod. On the othe hand, impemeable soils ae those fo which essentially no dainage can take place duing constuction o loading. 56 Austalian Geomechanics Vol 45 No 2 June 21
7 PROPOSED EQUATION The calculated total cohesion (C ) fom tiaxial test esults of the thee samples ae plotted in C plane (Fig. 1). The figue shows that the elationship betweenc and S is linea with intecept on total cohesion axis. Theefoe, the equation of total cohesion can be witten as C = a (6) ms whee, a is the intecept on the total cohesion axis and m is the slope of the line. Assumptions of this equation ae: (i) the vaiation of cohesion is linea with When the soil is satuated then, = 1 S and C = c a = c + m. Now, the Equation (6) can be witten as c m( S 1) whee, = S and (ii) S S vaies fom.7 to 1., putting these values in Equation (6) gives the intecept, C (7) C c τ us m = = 1 S 1 S Equation (8) shows that to know the slope, m of the poposed equation (Equation (7); it is needed satuated shea stength paamete c and total cohesion at any satuation condition within the ange of.7 S < 1, which can be gotten by expeiment consideing afoesaid any satuation condition. The following conclusions can be dawn fom this study: 8 CONCLUSIONS (1) It is found that the degee of satuation affects the shea stength of tested soil, and cohesion inceases with decease in degee of satuation linealy. The poposed equation epesents the cohesion component of unsatuated sandy soils as a function of initial degee of satuation. The advantages of this fomulation is that by pefoming tiaxial test of an unsatuated soil at any initial degee of satuation within the ange of.7 S < 1as well as with satuated shea stength paamete c, it is possible to estimate the cohesion component quantitatively of the unsatuated soils, which ae wetted within degee of satuation.7 to 1. Theefoe, the poposed equation could be used fo stability analysis of embankment. (2) Fiction angle has a vey little ole to suction stength contibution of unsatuated sandy soils. (3) Futhe studies ae howeve equied to examine the poposed empiical equation on diffeent soils consideing diffeent densities as well as on undistubed soil specimens. 9 REFERENCES Alim, M.A. and Nishigaki, M. (9) Shea stength behavio of unsatuated compacted sandy soils, Intenational Symposium on Pediction and Simulation Methods fo Geohazad Mitigation, Kyoto, Japan, 25-27 may, 37-312. Bishop, A.W. and Blight, G.E. (1963) Some aspects of effective stess in satuated and patly satuated soils, Geotechnique,13(3),177 197. Cunningham, M.R., Ridley, A.M, Dinnen, K. and Buland, J.B. (3) The mechanical behavio of a econstituted unsatuated silty clay, Geotechnique, 53(2), 183-194. Donald, I.B. (1956) Shea stength measuements in unsatuated non-cohesive soils with negative poe pessues. Poceedings, 2 nd Austalia and New Zealand Confeence on Soil Mechanics and Foundation Engineeing, Chistchuch, New Zealand, -25. Dumight, E.E. and Nelson, J.D. (1995) The shea stength of unsatuated tailings sand. Poceedings of the fist intenational confeence on unsatuated soils/unsat 95/Pais/Fance/6-8 Septembe, 45-5. Fedlund, D.G. and Rahadjo, H. (1993) Soil Mechanics fo Unsatuated Soils, John Wiley & Sons, Inc., New Yok. Fedlund, D.G., Xing, A., Fedlund, M.D. and Babou, S.L. (1995) The elationship of the unsatuated soil shea stength to the soil- wate chaacteistic cuve. Can. Geotech. J, 32, 44-448. Gan, J.K.M. and Fedlund, D.G. (1996) Shea stength chaacteistics of two sapolitic soils, Can. Geotech. J, 33, 595-69. Lu, N. and Wu, B. (5) Unsatuated shea stength behavio of a fine sand, Geomechanics- II, Ameican Society of Civil Engineeing, 181 Alexande Bell Dive, Reston, VA 2191 USA, 488-499. (8) Austalian Geomechanics Vol 45 No 2 June 21 57
Mashhou, M.M., Ibahim, M.I. and El-Emam, M.M. (1995) Vaiation of unsatuated soil shea stength paametes with suction, Poceedings of the fist intenational confeence on unsatuated soils/unsat 95/Pais/Fance/6-8 Septembe,1487-1493. Miao, L., Liu, S. and Lai, Y. (2) Reseach of soil-wate chaacteistics and shea stength featues on Nanyang expansive soil, Engineeing Geology, 65(4), 261-267. Ng, C.W.W., Cui, Y., Chen, R. and Delage, P. (7) The axis- tanslation and osmotic techniques in shea testing of unsatuated soils: a compaison, Soils and Foundations, 47(2), 675-684. Obeg, A. and Sallfos, G. (1997) Detemination of Shea Stength Paametes of Unsatuated Silts and Sands Based on the Wate Retention Cuve, Geotechnical Testing Jounal, 2(1), 4-48. Rahadjo, H., Heng, O.B. and Choon, L.E. (4) Shea stength of a compacted esidual soil fom consolidated dain and constant wate content tiaxial tests, Can. Geotech. J., 41, 421-436. Rohm, S.A. and Vila, O.M. (1995) Shea stength of an unsatuated sandy soil, Poceedings of the fist intenational confeence on unsatuated soils/unsat 95/Pais/Fance/6-8 Septembe,189-193. Sun, D., Sheng, D. and Xu, Y. (7) Collapse behavio of unsatuated compacted soil with diffeent initial densities, Can. Geotech. J., 44, 673-686. Thu, T.M., Rahadjo, H. and Leong, E.C. (7) Citical state behavio of a compacted silt specimen. Soils and Foundations, 47 (4), 749-755. Vanapalli, S.K., Fedlund, D.G., Pufahl, D.E. and Clifton, A.W. (1996) Model fo the pediction of shea stength with espect to soil suction, Can. Geotech. J., 33, 379-392. Zhan, T.L.T. and Ng, C.W.W. (6) Shea stength chaacteistics of unsatuated expansive clay, Can. Geotech. J., 43, 751-763. 58 Austalian Geomechanics Vol 45 No 2 June 21