Determining the Coefficient of Consolidation and Horizontal Permeability by Radial Drainage

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/4 Determining the Coefficient of Consolidation and Horizontal Permeability by Radial Drainage Mesure du coefficient de consolidation et de la perméabilité horizontale par drainage radial by V.

1 /4 Determining the Coefficient of Consolidation and Horizontal Permeability by Radial Drainage Mesure du coefficient de consolidation et de la perméabilité horizontale par drainage radial by V. E sc a r io, Ing. C.C.P., M.S., H ead o f the Soil M echanics D ep artm en t at the L ab o rato rio del tran sp o rte y M ecanica del Suelo, A lfonso X II, 3. M adrid and S. U r ie l, Ing. C.C.P., o f said C enter Summary The anisotropy of natural clay deposits is due to the presence of some thin layers having a higher permeability which increases the coefficient of horizontal permeability as compared with the vertical one. The authors describe radial permeability tests and their standardisation undertaken by the Soil Mechanics Laboratory of Madrid, using undisturbed samples having a maximum diameter of 4 inches of various heights from Huelva blue clay. These tests were carried out in a triaxial equipment with drainage only towards the cylindrical surface. Drainage was ensured by providing a layer of micaceous sand around the sample. Seepage towards the porous baseplates was avoided by inserting waterproof plates between them and the soil sample. The consolidation curve was obtained by measuring the quantity of water expelled from the sample and by its vertical strain. The coefficient of consolidation is derived from independent adjustment of prim ary and secondary consolidations. This type of test can be carried out more rapidly than alternative ones, owing to the large area of the draining surfaces : it is therefore possible to use large test samples. These give an improved statistical picture of the peculiarities of the natural deposits. The smearing effect caused by trimming is also reduced. Since a triaxial equipment is used, it is possible to take full advantage of saturation by pressure in the pore water, etc. In those problem s w here drainage in tw o or three dim ensions is involved, as w ith vertical sand drains for exam ple, the determ ination o f the coefficient o f horizontal perm eability and consolidation is very im portant. In earth dam s, the higher perm eability horizontally raises the satu r ation line considerably, w hich reaches the dow nstream slope at points higher than if the em bankm ent were hom ogeneous, unless adequate drainage is provided. The determ ination o f both coefficients o f perm eability is generally carried out either by consolidation tests, w ith samples cut in the tw o required directions, or in the triaxial equipm ent, in w hich drainage is tow ards the porous baseplates. A n cedom eter has the disadvantage o f using a thin sample, in w hich the sm earing effect created by trim m ing will reduce the coefficient o f consolidation. If the soil is not very hom ogeneous, the sam ples m ay n o t be truly representative o f the deposits. The height o f the sam ples for the triaxial test, w ith drainage tow ards the baseplates, w ould also be lim ited to a fraction of the boring diam eter if they have to be trim m ed for m easuring the coefficient o f horizontal perm eability. This problem has been overcom e by testing w ith drainage tow ards the cylindrical surface o f the sam ple, so that we can use sam ples of Sommaire L anisotropie des dépôts naturels d argile, due à l existence de quelques couches minces d une perméabilité plus grande, produit une augmentation du coefficient de perméabilité horizontale, par rapport à celui de perméabilité verticale. On y décrit les essais de perméabilité radiale et leur systématisation effectués au Laboratorio del Transporte y Mecánica del Suelo, avec des éprouvettes cylindriques mesurant jusqu à 06 cm (4") de diamètre et de hauteur variable, sur des échantillons non remaniés d argiles bleues de H uelva. On réalise ces essais dans l appareil triaxial avec drainage par la surface cylindrique exclusivement. Ce type de drainage reste assuré par une couche de sable micacé entourant l échantillon. La filtration vers les plaques poreuses des bases reste interdite en plaçant entre celles-là et l éprouvette des plaques imperméables. On obtient la courbe de consolidation en partant de l eau expulsée par l éprouvette et de sa déformation verticale. On détermine le coefficient de consolidation au moyen d un ajustement indépendant des consolidations prim aire et secondaire. L avantage le plus im portant de ce type d essai est sa grande rapidité par rapport aux autres méthodes, due à l ampleur de la surface drainante, étant ainsi possible d utiliser des éprouvettes de dimensions plus grandes qui reflètent statistiquement, d une manière plus approchée, les particularités des dépôts naturels. Les perturbations causées par la mise en place de l éprouvette, sont aussi diminuées. Lorsqu'on utilise l appareil triaxial, on peut, en même temps, profiter des avantages bien connus de la saturation par pression de l'eau interstitielle, etc. the m axim um height taken by the cell. T he m axim um distance follow ed by the w ater is the radius o f the sam ple, prim ary consolidation being achieved in a com paratively short tim e. V arious m ethods have been applied to ensure lateral drainage, the m ost efficient being to surround the sam ple w ith a thin layer o f sand ; alternative m ethods, such as filter strips, have not given satisfactory results (R ow e, 959). Perm eability tests w ith radial drainage have been carried out in the M adrid L aboratory, where they have been standardised by using a layer of m icaceous sand having a com pressibility sim ilar to th at o f the soil being tested. The authors give the theoretical basis for the consolidation equation, the adjustm ent o f the curve necessary to obtain the coefficient of consolidation, an d the results o f their tests. Theoretical basis for the consolidation equation The follow ing assum ptions are m ade :. The soil is n o t hom ogeneous so far as its com pressibility is concerned, À being the ratio between horizontal and vertical strain upon a sam ple subjected to triaxial pressure. 2. There is no friction between the sam ple and baseplates. 83

3. Perm eability o f the drainage layer is infinite when com pared w ith th at o f the soil. The existing pressure on the surface o f the sam ple is therefore equal to the atm osphere pressure. 4.

By isolating an elem ent o f the sam ple to a distance r from the axis (Fig.

2 3. Perm eability o f the drainage layer is infinite when com pared w ith th at o f the soil. The existing pressure on the surface o f the sam ple is therefore equal to the atm osphere pressure. 4. The soil is saturated. 5. T he displacem ents o f the points o f a horizontal plane are th e sam e in the direction o f the longitudinal axis o f the sam ple (case o f equal strain). By isolating an elem ent o f the sam ple to a distance r from the axis (Fig. (b), if we call it = u(r,t), the pore pressure at a tim e t, then the difference between the volum e o f w ater flowing into and out o f the elem ent will be.. k /ò u ò 2 //.. A V = ( - b -r- 5 r I dr dz dd Y u\ or d r ( ) If we take k T C v l y ht rt 2 Ya inv R 2 equation (5) m ay be thus expressed : u = 2 u0e +2X ( - ^ 2... (6) This equation represents a distribution o f pore pressures in the form o f a p araboloid (Fig. 2) w ith a m axim um in the axis o f the sam ple of _ 8r» «max = 2 u0e l+*r (7) <t SAMPLE7 -SURFACE OF SAMPLE i ^medb g ^nwx Fig. (a) Scheme of arrangem ent of the consolidation test in the triaxial apparatus, with drainage towards the cylindrical surface ; (b) Cylindrical element of the sample. (a) Dispositif pour l'essai de consolidation dans l appareil triaxial, avec drainage vers la surface cylindrique ; (b) Elément cylindrique de l'échantillon. If is the strain per u n it length along the z axis, the change in volum e m ay also be expressed by A V = s(l + 2 X )rdrdzdq E quating both values, we get k ( + 2X) I Ò2 «ÓÍ/ òr2 + r ö r j Since the value of the vertical strain is independent o f r an d only a function of tim e (equal strain), we have -u öiti _ ( + 2X) y<o I òr2 r* 7 ~òr] f ( t ) F rom the integration o f equation (4) we obtain u = 2_ ^ ( R 2 _ r2} ^ R 2 >e (I + 2X)ya R 2mv w ith the follow ing conditions : òu. F o r r = R u = 0 and for r = 0 = 0 b r 2. F o r t = 0, beginning o f the consolidation, the total p o re pressure in the surface o f the sam ple m ust be equal to tcr2u0; being the applied lateral pressure. 84 (2) (3) (4) (5) Fig. 2 The average value Distribution of pore pressures within the sample during consolidation. Distribution des pressions interstitielles dans l échantillon pendant la consolidation. value is equal to one h alf o f the m axim um Hmed 'V ' STju l + 2y E quation (5) shows th at for t = 0 the distribution o f pore pressure is a paraboloid, w hich appears to conflict w ith the uniform distribution taking place w hen the sam ple is subjected to triaxial pressure before drainage begins. T here m ust be an interm ediate stage betw een these tw o extrem e distributions, w ith radial consolidation only, w ith o u t vertical one. A readjustm ent o f pore pressures takes place until distribution is parabolic, at wich stage the vertical consolidation will start. A lthough this phase is o f purely theoretical interest, since it has only a slight influence on the test, the authors have tried to m easure the pore pressure along the axis o f the sam ple during initial consolidation. They have n o t reached any final conclusion how ever, because the tim e lag o f the m esuring instrum ents is probably m uch greater th an th at specified for producing the required readjustm ent. It is n o t possible to confirm this hypothesis by observing the onset o f vertical consolidation, because this phase is obscured by the initial consolidation o f the sam ple, together w ith the adjustm ent betw een the sam ple and the baseplates. T he authors nevertheless consider th at this subject should be investigated. E quation (8) m ay be expressed as follows : it being at A Wmed 8C log + Ik ( + 2A) R 2 = U n itary vertical strain in a tim e t = T otal u n it strain related to 00 per cent o f the prim ary consolidation. (8) (?)

Vt = V olum e drained by the sam ple in a tim e t. V = V olum e drained referred to 00 per cent o f the prim ary consolidation.

3) is a straight line, whose slope is T he above shows th at the slope is independent o f the initial errors and depends only upon those included in the estim ated 00 per cent prim ary consolidation.

equation (). If s s is greater th an zero, it can readily be show n by equation ( 2) th at the slope gradually decreases until it becomes zero w hen A at = z s.

3 Vt = V olum e drained by the sam ple in a tim e t. V = V olum e drained referred to 00 per cent o f the prim ary consolidation. It can easily be dem onstrated th at log tfmed Wn = logl - ^ = log ( - (0) M ) The theoretical representation o f the consolidation in a diagram med t - lo g «0 (Fig. 3) is a straight line, whose slope is T he above shows th at the slope is independent o f the initial errors and depends only upon those included in the estim ated 00 per cent prim ary consolidation. If s s = 0, the diagram corresponding to the end of prim ary and the beginning o f secondary consolidation is a straight line, its slope having the correct value from which cv m ay be derived through equation (). If s s is greater th an zero, it can readily be show n by equation ( 2) th at the slope gradually decreases until it becomes zero w hen A at = z s. C o n v ersely, if es is less than zero, the slope o f the curve will tend to be infinite after reaching a m inim um value. The three types o f curves are show n in Fig. 4. t tg a = - ( + 2 X)R2 > = ;r < I EB Fig. 3 Theoretical diagrams of consolidation. Diagram me théorique de consolidation. Fig. 4 Adjustment of the actual diagram of consolidation. Ajustement des diagrammes de consolidation réels. A ssum ing th at n o disturbances exist, w ith wich the authors deal later, equation () determ ines the value Cv as a function o f the three values tg a, X and R. This linear relationship is m odified a t the outset by initial consolidation, by readjusttm ent betw een baseplates and sam ple, by reduction o f the volum e o f air w hich m ay have been trapped and by the w ater expelled from the layer o f m icaceous sand. The influence o f these initial errors lasts for only a com paratively short tim e which, for sam ples 6 inches high and 4 inches in diam eter, for the soils tested m ay be from 0 to 5 m inutes. T he secondary consolidation also influences the diagram t - log Wmed It can be show n th at (Fig. 4) tg a ' = tga or tg a ' = tg a - + A a, e + y - k - cs In this form ula, the follow ing nom enclature is used : tg a ' = slope o f the curve at any p o in t for a given value of A o r V. tg a = slope o f the curve a t any p o in t for the correct value o f A or V. s, = E rro r in the estim ate o f A or V. Fig. 5 Sample surrounded by a layer of micaceous sand, ready for test. Echantillon entouré par une couche de sable micacé, préparé pour l'essai. 85

Fig. 6 COMPRESSIBILITY CURVE OF MICACEOUS SI NO 50V. BEACH SAND. -------- 50% MICA.

micaceous sand. Compressibilité des échantillons destinés à l'essai, et des couches de sable micacé.

4 Fig. 6 COMPRESSIBILITY CURVE OF MICACEOUS SI NO 50V. BEACH SAND % MICA. 0,42 < d <,9 MM AVERAGE CHARACTERISTICS OF THE HUELVA BLU E CLA Y S ZONE OCCUPIED BY THE COMPRESSIBILITY CURVES OF HUELVA BLU E CLAYS Compressibility of samples to be tested and of the layers of micaceous sand. Compressibilité des échantillons destinés à l'essai, et des couches de sable micacé. In order to get w ith accuracy the value o f Cv it will be necessary to try several values o f the 00 per cent o f prim ary consolidation until we obtain a straight line from the end of initial pertu rb atio n on. Tests carried out Tests on radial perm eability o f undisturbed sam ples of blue clays, from sites near the proposed H uelva harbour, w ere carried out at the M adrid L ab oratory (Fig. (a)). V ertical flow was avoided by placing a thin plastic sheet betw een the sam ple and the porous baseplates. The 5 mm layer o f m icaceous sand surrounding the sam ple consists o f a m ixture o f 50 per cent m ica retained between N o. 6 and 40 sieves o f the A m erican Society for Testing M aterials, and 50 per cent fine beach sand. The com pressibility o f this m ixture (Fig. 6) is slightly greater than th at o f the clay, in order to ensure th at the consolidation pressure will be fully exerted. The layer o f m icaceous sand was placed w ith the aid o f a cylinder divided into three 20 degree sections, the diam eter of w hich was cm greater th an th at o f the sam ple, to the inner portion o f wich a m em brane is adjusted w ith slight suction. T he sand was m ixed w ith w ater and the solution was poured in to ensure th at the drainage layer was com pletely saturated. In order to keep this sand in place until the test was undertaken, a suction ranging from 0-05 to 0T kg per sq. cm was applied, as soon as the upper baseplate was in position. Sam ples o f 4 inches diam eter, their height varying from 4 to 8 cm, have been used w ith increasing consolidation pressures o f to 8 kg per sq. cm. R eadings have been taken of the vertical strain at each loading stage, o f the volum e of w ater expelled from the sam ple, and o f the volum e o f w ater introduced into the cell. (Fig. 7.) R eadings were taken every 5 m inutes for a period of seven hours, the last one 24 hours after the test had been started. I5 30' (TIME ICM.= 30M=.800 SEC SCALES CONSOLIDATION I CM.: 0, / R2tge*x.800 R : 4.72 CM (jj O 2 o oc CVISTRAIN)= 2,48 xlo-4cm.^sec Cv IW.EX P ) =2.77x IO-4CM2/SEO. CL z o < Q o</) 2 O o Fig " x 6" sample during radial permeability test. Echantillon 4" x 6" pendant l essai de perméabilité radiale. Fig. 8 Standard consolidation diagrams, adjusted : upper curve = sample strains, lower curve = water volume expelled by sample. Diagrammes types de consolidation : ccurbe supérieure = déformations de l échantillon, courbe inférieure = volume d eau expulsé par l échantillon.

T he value A, the ratio betw een horizontal and vertical com pressibility, has been determ ined by m easuring the height and diam eter o f the sam ple for each consolidation pressure.

5 W ith very plastic clays, m ore then 80 per cent o f the prim ary consolidation occurs within the first seven hours on samples o f 4 inches diam eter. F u rth er observation from 7 to 24 hours are n o t necessary, because the form er tim e is adequate for obtaining the curve. T he value A, the ratio betw een horizontal and vertical com pressibility, has been determ ined by m easuring the height and diam eter o f the sam ple for each consolidation pressure. M easurem ents o f diam eter were obtained by the optical system proposed by the a u th o rs; in this particular case o f H uelva clays, A is practically equal to unity. Two typical diagram s obtained after adjustm ent and correction are show n in Fig. 8. T he m ain slope is n o t affected by the initial period from 5 to 30 m inutes. The upper curve corresponds to the percentage consolidation derived from m easuring the strain o f the sa m p le ; the low er one refers to the volum e o f w ater expelled under a pressure o f 8 kg per sq. cm. O nly sm all differences are obtained w hen using either procedure, except for a few isolated cases. A sum m ary o f results obtained w ith various clay sam ples c c 0 0 M M M DC 0 VERTICAL DEFORMATION A EXPELLED WATER x WATER INTRODUCEDINTOTHE CELL is show n in Fig. 9. F o r a lateral pressure o f only kg per sq. cm, the coefficient o f consolidation is about four times higher th an th at corresponding to higher pressures. This large difference m ay be due to the fact th at this pressure is approxim ately equal to th at in the n atural ground a t the level from w hich sam ples were extracted. F rom this it appears that for pressures low er than th at o f consolidation, the perm eability is m uch higher according to the direction o f the planes o f sedim entation. This fact is particularly im portant where a clay stratum is relieved from pressure, as in the case o f H uelva clays, where dredging will be undertaken and where vertical drains will be installed. Conclusions. A perm eability test in which drainage is tow ards the surface o f a cylindrical sam ple, surrounded by a layer o f m icaceous sand, has the tw in advantages o f rapidity and o f the ability to use a sam ple o f the m axim um height adm itted by a triaxial cell. The accuracy attained appears to be greater than w hen using alternative m ethods. 2. The coefficient o f consolidation or o f perm eability can be determ ined by adjustm ent which is independent o f initial disturbance and o f secondary consolidation. 3. The use o f a layer o f m icaceous sand, having a com pressibility sim ilar to th a t o f the soil being tested, has proved to be satisfactory. Fig. 9 M c C IP g G. 0 M M 9 CO JtM M MM M Cm2/SEC. Values of the coefficient of consolidation of the blue clays from Huelva, obtained by radial permeability tests. Valeurs du coefficient de consolidation des argiles bleues de Huelva, obtenues par des essais de perméabilité radiale. O References [] B a r r o n R. A. (947). Consolidation of Fine-Grained Soils by Drain Wells. Proceed. A.S.C.E., Jun. 947, Vol. 73, p. 8. [2] I s h ii, Y. (957). "Estim ation of C and mv Values for the Design of Sand D rains. Proceed. IV Int. Conf. Soils Mech., Vol. I, p. 32. [3] R ic h a r t, F. E. (957). A Review of the Theories for Sand Drains. Proceed. A.S.C.E., Jul. 957, Vol. 83, SM-3, p [4] R o w e, P. W. (959). Measurement of the Coefficient of Consolidation of Lacustrine Clay. Geoth. Vol. IX. Sep. 959, p. 07. [5] E s c a r i o, V., U r i e l, S. (960). Optical Methods of Measuring the Cross Section of samples in the Triaxial Test. 87

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