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OEDOMETER TESTING OF VISCOUS SOILS

ESSAIS OEDOMETRIQUES DES SOLS VISQUEUX

MCnhlTAHMK Bil'JKO-n^ACTM'IHLIX TPyHTOB 13 OjJOMETP t;

DARINKA BATTELINO, Civ. Eng., M.Sc., U Diversity of Ljubljana, Yugoslavia

SYNOPSIS. In order to avoid structural disturbance, a modification of the classical oedometer - test p rocedure has been suggested. The possibility of determining the coeff icient of perm eability of viscous soils from consolidation lines observed after a slow load application has been analysed. Th e presentation of experimental data by void ratio v ersus effective stress ulofs corres ponding to different consolidation spe eds has been given support.

INTRODUCTION increases suddenly at large intervals (see e.g.Vidm ar 1956, Berrp and Iversen 1972). In this paper we shall pre sent a If the general differential equation of consolidation m odification of the classical oedometer test in ord er to get (Biot 1938) of saturated soils is applied to the on e-dim en- appropriate rheological parameters accounting tor v iscous sîonal seepage conditions, it gets the form soil properties; such test data can serve for predi cting the ôe _ 1 + e ô du . 0) consolidation of thick layers in linear strain and seepage ôt y Ôz ôz conditions. e is the void ratio, u the excess pore - pressure, z co ordinate in Hie seepage direction and k the coeffic ient of OEDOMETER TEST FOR VISCOUS SOILS permeability as defined by Darcy's law. The classic al form In linear strain conditions the deform ability of viscous soMs of equation (1) (Terzaghi 1923) has been based on the is represented by the rheological equation assumptions of linear stress - strain relationship and of constant perm eability coefficient. Substituting R ( e, é, a' , à' ) = 0 (5)

ôe _ ôe da' 5 (o - u) è is the speed of the void-ratio change, a is the effective = - (1 + e)r (2) "ôt ô7' " ôt ôt stress in the sample axis and Ô' its speed.

with a for total and vîth o' for effective pressures we get By neglecting the influence of the stress rate à' , equation Terzaghi's equation (5) gets sim plified: 1 ôu ôq ô u R ( e, è, a' ) = 0 (6) + c (3) ô t Ot The stress-rate is expected to be the more effectiv e, the (4) greater its value. Furthermore, thixotropic effects destroying or dim inishing the viscous structural resistance of the soil skeleton, can appear at larje stress rates ce occurring at The coefficient of consolidation can be obtained from the a sudden load application (Suklje 1957). In order to avoid curve of consolidation e = e(t) corresponding to a sudden such effects and to reduce the influence of the str ess-rate load increment as much as possible, a slow, continuous load increa se is to ( t = 0 — âa = a - 0o , t > 0 -+--^-=0 ), in the be recommended. At appropriate stress intervals the conti well-known way. The coefficient ot compression m is nuous total stress increase has to be stopped; afte r the defined by the strain and stress increase pore-pressures had dissipated to very small values, the so called secondary compresion must be observed during a ( m = -7-=------—^—------) and the coefficient of permeabi- 1 sufficiently long period (see example in R g .l). v ( + e o )Ja lity can then be determined from equation (4). From the secondary consolidation branches e = e(t) , 1 r 1 . . . . r 1 . r J0= COnSt the values or the void ratio e and ot the rate or However, if the structural resistance of the soil s keleton its change e can be ascertained at any time t. By u sing is important, the consolidation curve can appreciab ly é = é(t) plots, the corresponding values of e and a' decline from Terzaghi's theory, even when the load can be obtained for different chosen values of é. T he

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values usually do not overpass the rates appearing in the early phase of the secondary consolidation of o edo- meter samples of ordinary thickness (about 2 cm with bilateral drainage ).

Now, for the use in predicting consolidation develo pm ent of natural layers, the isotaches have to be given a lso for volume strain rates greater than those observed in the period of duration of the oedometer test. Conse quently, the extrapolation of secondary consolidation curves of oedometer tests is inevitable. If the void ratio decreases with the logarithm of tim e, the extrapola tion is simple, however, it is generally hazardous. In some cases it is facilitated by knowing the porosity of undisturbed samples as w ell as the stress history o f the natural layer (cf. Bjerrum 1967). If we are interes ted in knowing isotaches for greater rates appearing du ring the primary consolidation of oedometer samples, the perm eability k = k (e) should be known ond the slop e of isotaches assumed. For parabolic isochrones of degr ee n, the mean value of the excess pore-pressure u is giv en by the equation (Suklje 1969-a): y h 2 e

U = (n+ 1 ) (l+eF'T 00)

h being the length of the seepage path (half-thnick ness of the sample at bilateral drainage), e and e the respec tive mean values of the void ratio and its rate at time t (see Suklje 1957). Isochrones resulting for uniform stress fields by applying, in the consolidation equ ation (1 ) the experimentally obtained rheological relationships p') (Suklje and Kogovsek 1968, Suklje 1969-b) or the relationships corresponding to certain rheological models (Taylor 1942, Barden 1965), prove that,oh average, their F IG .). Consolidation lines ot a clay of high shape is sim ilar to parabolas of 2nc* degree (n = 2) com pressibility corresponding to a slow (in Barden's isochrone chartes n > 2 at the beginnin g load application and n < 2 at the end of the pore-pressure dissipation).

If the coefficient of perm eability as well as the p oie pressure u at the undrained boundary (in uni-latera l resulting plots e = [e(a')]f (see example in Fig.2) drainage conditions) are measured, the approximate form have been called isotaches (Suklje 1957). They can be of isochrones can be ascertained. Assuming that iso chrones expressed by analytical functions: are parabolas of degree n, we get :

e = e (o', è ) (7) Y h2 i (ID è = é ( a', e ) (8) k( 1 + ë ) u o

During the compression, perm eability coefficients k are ond then the everage effective pressure : recommended to be determined from direct perm eability tests, preferably in the last phase of each seconda ry a = c r-u = a - (12) consolidation. By inserting the equation (8 ) for e and + 1 relation (9) 0 being the total pressure at time t. The procedure can be k = k (e) (9) applied also to any stage during the continuous loa d- into the differential equation of consolidation (1 ), we con application. solve it in a numerical way taking into account the boun It depends on the speed of the 'load application an d on dary conditions of the cose treated (examples: Suklje and the susceptibility of the soil to the influence of larger Kogovsek 1968, Suklje 1969-b). The use of isotaches in stress-rates whether the resulting ( o' e ) . analysing layers of thickness of the order of magnitude e-const 1 m or 10 m, has proved that the consolidation of natural values lie on a single, continuous isotache or not. layers occurs at small consolidation speeds; their maximum

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1.10

1.00

0. 90

0. 60

0-70

6' [ kp/ cm2]

FIG .2. Isotaches of a clay of high cony.cisibility, and coefficient of perm eability versus

void ratio plot corresponding to the presented isot ache set: thin full line - first approximation, dashed thick line - final result.

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DETERMINATION OF THE COEFFICIENT OF For the isotache set presented in Fig. 2, the follo w ing analytical expression has been found to be suitable : PERMEABILITY l-KOM CONSOLIDATION LINES

The influence of the stress-rate onto the run of is otaches causes also some trouble in determining the perm eab ility frqiTi consolidation curve of viscous soils. This p rocedure, * - s. } <,4)

interesting in cases when there is no possibility o f (cf. Suklje 1969-b); values of parameters e , a', A. mecsuring k-values, cannot be but iterative. o o I and 8 . (for n = 4) are given in Fig.2. We start, e .g ., with an appropriate extrapolation o f isotaches as obtained from the secondary branches o f The isotache sets can, naturally, be conformed to a ny rheological model of the type Eq. (6). For Kelvin's body consolidation curves. According to equation (10), the with linear elastic and non-linear viscous element, used first approximations for k-values can be obtained f or various isotache points ( e, ö=a-ü ). . . The in Barden's (1965) consolidation theory, the isotac hes e = const have the equation : resulting k-values are not expected to lie on a unique e = C - a

lines obeying the logarithm ic law ot secondary comp ression, e = C - a o' (17) and dashed isotaches have been obtained in the abov e

explained way). Let us take, in the isotache. set in Fig.2, points (e^ = 0.8919, 0 = 2 kp/cm2) and In any cose we have to choose the degree n of the

parabolic isochrones for such a construction. Thus, such = 0.7691, a '= 4 kp/cm 2 ) on the isotache determination o f perm eability coefficients can give only -7 —1 e = - 10” sec 05 well as the point approximate results. Consequently, a direct observa tion of perm eability is recommended. (e_ = 0.8828, o' =2 kp/cm 2 ) on the isotache -8 -1 e = -10 sec as starting points which have been DISCUSSION ABOUT THE SIGNIFICANCE OF obtained from the directly observed secondary branc hes of ISOTACHES consolidation curves and whose reliability is beyon d doubt. In Fig. 3 we have presented the corresponding isota che Isotache sets and their analytical expression (8) represent sets tor the coefficients n = 10, 5, 1 and for b = 0. the rheological relationships for soils in one-dime nsional The comparison of these sets with the complete expe ri strain and seepage conditions as obtained in oedome ter m entally obtained isotache set (assuming the extrap olation testing. The analytical expression has to be confor med to of isotaches beyond è =-10 - ^ sec'lvalue according to the the geometrical form of isotaches and their mutual di logarithm ic law of secondary compression (Fig. 3) s hows stances. Some analytical functions corresponding to expe that the parallel lines of Barden's theory do not c orrespond rim entally obtained isotache sets have been presented by well to the observed isotaches. It can be seen also from Suklje (1969) and Battelino (1970). In several case s the the above sets that in cases of low n-values the viscous void ratios decrease, along a single isotache, with the effect practically disappears at low consolidation speeds logarithm of effective stress and, at a given effec tive occurring at the consolidation of thick layers (cf. Suklje stress o' , with the logarithm of tim e. Such isotaches 1969-a). have the equation A + B In —jjg- - e Rheological bodies connected in series are not gove rned (13 ) e„ exP by equation (6) because the stress speed appears in their C + D In -5 - stress-strain-time relationships. E.g. M erchant-Tay lor's (1940) rheological model consisting of the Hookean spring The choice of constants e o and oo is arbitrary,7 the in series with a linear Kelvin body, has the equation: parameters A ,B ,C and D can be obtained by using the - A e + B a + C o f * * (18) (e, e, o ) values of four points lying on two isotaches.

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It can be presented by several isotache sets corres ponding CONCLUSION to different stress speeds.

The m odification of the classical oedometer test by applying slow, continuous loading has been recommen ded; the loading has to be interrupted by long-term obse r vation of the secondary consolidation at certain va lues of total pressures, and accompanied by perm eability measurement during, the end phase of the observed s econ dary consolidation. Suklje's proposal ( 1957, 1969) to express the deform ability of viscous soils by isota che sets has been given support. Some isotache sets correspo nding to consolidation theories based on rheological mode ls connected in parallel have been presented and compa red with the experimentally obtained set. The possibility of determining the coefficient of perm eability from th e observed consolidation lines of viscous soils has b een analysed.

ACKNOWLEDGEMENT

The present report is a part of the research study 11 Rheological properties of soils" in progress at the Soil Mechanics Laboratory of the Faculty of Architecture , C ivil Engineering and Survey of the University of L jublja na with the financial support of the Boris Kidric F und. The author wishes to express her gratitude to Profe ssor L.Suklje For helpful discussions and advise in prep aration of this Paper.

REFERENCES

BARDEN, L. (1965), Consol idation of Clay with Non" linear Viscosity, G§otechnique, 15, 345-362.

BATTELINO, D. (1970), Contribution to the Investiga tion of rhe Consolidation of Saturated Soils Exhibiting Non linear, Anisotropic and Viscous Deform ability (in S love nian with Summary in English), University of Ljublj ana, Acta Geotechnica, 30, 1-25.

BERRE, T., and IVERSEN, K. (1972), Cedometer Tests with Different Specimen Heights on c Clay Exhibiting Large Secondary Compression, G^otechnique, 22, 53-7 0.

BJERRUM, L. (1967), Engineering Geology of Normally Consolidated Marine Clays as Related to the Settlem ents oF Buildings ( 7th Rankine Lecture), G^otechnique, 17, 83-117.

SUKLJE, L. (1957), The Analysis of the Consolidatio n Process by the Isotache Method, Proc. 4th Int.C onf. Soil Mech. Found. Eng., London, 1, 200-206; 3, 107-109.

FIG .3. Isotaches according to points 1,2,3 of Fhe observed isotaches and to Barden's rheological SUKLJE, L., and KOGOVSEK, B. (1968), Isochrones of sheme: (a) for n = 10, (b) for n “ 5, a Uniformly Loaded Layer of Viscous Soils, Ill.Sesj a (c) for n = 1 (Taylor's theory B), (d) thick Naukowa W ydzialu Budownictwa Ladovego Politechniki I ine: for b = 0 (Terzaghi); thin lines;isotaches W rocl"'vskiej 2-5 pazdziem ika 1968 r.7 W roclaw, presented ing Fig.2. Referaty ), 369-380.

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SUKLJE, L. (1969-a), Rbeologico! Aspects of Soil TAYLOR, D.W . (1942), Research on Consolidation of Mechanics, W iley-Interscience, London, 571 p. Clays, Dept, of Civil and Sanjtary Eng., Massachuse tts Inst, of Technology, Publ. Serial 82, 1-147. $UKLJE, L. (1969-b), Consolidation of Viscous Soils Subjected to Continuously Increasing Uniform Load, New TERZAGHI, K. (1923), Die Berechnung der Durchläs Advances in Soil Mechanics, Praha 1969, I, 199-235. sigkeitsziffer des Tones aus dem Verlauf der hydrod yna mischen Spannungserscheinungen, Sitzungsber. Akad. TAYLOR, D .W ., and MERCHANT, W. (1940), A Theory Wiss. W ien, m athem .-naturw. Kl., Abt. Ila, 132.Fd of Clav Consolidation Accounting for Secondary 3.U .4.H . Compression, J.Maths and Physics, 19, 167-185. VID'm AR, S. (1956), The Forms of Consolidation Curves of Oedometer tests (in Slovenian), Gradbeni vestnik , Ljubljana, Nos. 37-38, 97-102.