The Shear Strength of a Fine Sand

Transcription

1 1/5 The Shear Strength of a Fine Sand La résistance au cisaillement du sable fin b y L. Bje r r u m, S. K r in g s t a d, O. K u m m en eje, N o rw e g ia n G e o te c h n ic a l In s titu te Summary The author gives the results of a series of triaxial tests on a fine sand. Tests were carried out on drained and undrained samples, and the sand was tested in both dense and loose condition, but maximum attention was devoted to tests on very loose sand. Whereas the tests on dense and medium dense sand gave norm a l results, the tests on loose sand showed several unexpected results. The angle of internal friction was found to decrease rapidly as the porosity increased above 44 per cent. In the undrained tests with pore-pressure measurements, values as low as 11 were found in the very loose sand. Another characteristic property of the loose sand is the high pore pressures developed in undrained tests. The pore pressure parameter, A, was found to be as high as 2-7 in the very loose sand with initial porosity per cent. Introduction The bottom s o f the m ajority of fjords on the west coast o f N orw ay are occupied by enorm ous deposits o f loosely com pacted fine sand, carried into the fjords by glacier w ater and by postglacial rivers. In these subaqueous sand deposits, flow slides occur at intervals. These slides are characterized by a tem porary liquefaction o f large sand masses (T erzagh i, 1957). D uring last six years, the N orw egian G eotechnical Institute had the opportunity o f investigating one flow slide shortly after it had occured and to study in detail a num ber o f older slides in the T rondheim F jord. In this connection, samples were taken from the fjord bottom and a num ber o f undrained triaxial tests carried out in an attem pt to reproduce in the laboratory the phenom ena observed in nature. All tests were, how ever, unsuccessful. The structure o f the loose sand was so unstable th at the sam ples collapsed during setting up of the testing m achine, and consolidation was m uch greater than in the n atural deposits. D uring a visit in 1956 to the flow slide w asted banks o f the Mississippi R iver in the U.S.A., one au th o r discussed the problem s o f flow slides w ith the engineers at the W aterw ays E xperim ent S tation in Vicksburg. They were able to show him the results o f a series o f undrained triaxial tests on fine sand, in which they had succeeded in reproducing liquefaction of the sand sam ples in the laboratory. In the certain belief that w hat was possible in Vicksburg m ight also be done in N orw ay, it was subsequently decided to m ake a few m ore tests w ith the sand sam ples from the N orw egian flow slides. It m ust be adm itted how ever, th at com plete liquefaction was never observed in the N orw egian tests. The interpretation of the shear strength data o f these tests proved nevertheless to be m ost interesting and surprising, as friction angles as low as 11 were observed. It was thus decided Sommaire Les auteurs présentent une série d'essais triaxiaux sur sable fin. Dans cette série, il y avait des essais de cisaillement drainés ainsi que des essais de cisaillement non drainés, et ils furent effectués sur du sable ferme comme sur du sable meuble. On a étudié avant tout les essais effectués sur du sable très meuble. Tandis que les essais sur sable ferme et moyennement ferme ont donné des résultats norm aux, ceux obtenus avec du sable meuble ont été à plusieurs points de vue étonnants. C est ainsi qu'on a trouvé que l angle de frottement interne diminuait rapidement quand la porosité augmentait pour dépasser 44 pour cent. Lors des essais non drainés, et com portant des mesures de la pression interstitielle, on a trouvé, dans le sable très meuble, des valeurs aussi basses que 11. Les pressions interstitielles, élevées qui se développent dans les essais non drainés, sont une autre propriété caractéristique du sable meuble. On a trouvé que le paramètre A de la pression interstitielle atteignait même 2-7 dans le sable très meuble dont la porosité initiale était de 47 à 48 pour cent. to continue the tests to obtain a com prehensive picture of the shear strength properties o f a fine sand for the full range o f possible porosities. The results o f these tests are described below. Sand used for testing T he sand used in the tests is a fine sand obtained from a deposit at V algrinda, south o f Trondheim. The grain size Fig. 1 P a r tic le s iz e in mm Particle size distribution of fine sand. Granulométrie du sable fin. 29

2 distribution o f the sand is given in Fig. 1. The specific gravity o f the sand is 2-74 t/m 3. The standard m axim um and m inim um porosities o f the sand were found to be 46-2 per cent and 39-2 per cent respectively, the m axim um value being determ ined by dry deposition (K olbu szew ski, 1948) and the m inim um value by vibrating a dry sand sam ple. D r. I. Th. R osenqvist investigated the m ineralogical com position o f the sand and found it to be com posed m ainly of quartz w ith som e feldspar and hornblende. A few ore m inerals and biotite grains were observed. T he m ajority o f the quartz grains and especially those ranging in size between 0-03 mm and 0-1 m m were vell-rounded and polished, indicating th at the sand had been subjected to long transport. Testing procedure T he triaxial equipm ent used for the tests is the standard apparatus developed at the N orw egian G eotechnical Institute. A com plete description o f this equipm ent has been published in the N.G.I. publication series N os. 21 and 35. The lay-out o f the apparatus as used in the sand tests is show n diagram - m atically in Fig. 2. L oading p r e s s Proving ring Triaxial cell R eduction g e a rs and motor B urette C apillary tube P o re-p ressu re m easuring devise Bourdon g a g e 0-12 kg/crr)2 Screw control M ercury w ater m anom eter Test tube C onstant p ressu re cell Table top E xtra coupling for undrained te sts G land cock P iston valve Fig. 2 Layout of triaxial apparatus. Présentation des appareils triaxiaux. All tests were carried out on cylindrical sam ples w ith a diam eter o f 3-57 centim etres and a height o f 8-0 centim etres. T he sam ple is contained in a 0-05 m illim itre thick rubber m em brane w hich is sealed to the base o f the cell and to a top cap. D uring the placing o f the sam ple a split m ould is used for supporting and surrounding the rubber m em brane and the sam ple. In order to cover the full range o f possible porosities of the sand, three different m ethods o f building up the sam ple were adopted, resulting in a dense, a m edium dense and a loose deposit. T he lowest range o f porosities was obtained by tam ping single layers o f wet sand w ith a rod (diam eter 7 m illim etres). The sand has a m oisture content of ab o u t 15 per cent during the process, and the porosities obtained in this w ay varied from 35 per cent to 39 per cent. M edium dense packing o f 'the sand was also obtained by light tam ping, b u t at a placem ent m oisture content o f 8 per cent. The tam ping rod had a diam eter o f 2-9 centim etres. The porosites w hich resulted from this procedure varied from 40 per cent to 43 per cent. F o r obtaining m axim um porosity, sand w ith 11 per cent m oisture content was placed very carefully in the m ould. A t this w ater content capillary forces create an adhesion betw een the grains resulting in a honeycom b structure. The porosity o f sam ples places in this way was ab o u t 75 per cent. A very slow upw ards flow o f w ater through the sam ple was then applied, during which the structure collapsed and 30

3 the sam ple consolidated. If the process o f saturation was slow enough, a very hom ogeneous sam ple w ith a final porosity o f ab o u t 46 per cent was obtained. A fter the sam ple had been deposited and saturated, the top cap was placed and sealed to the rubber m em brane. The sam ple was then subjected to a very light vacum (50 centimetres of w ater) by a low ering o f the burette which is connected to the porous filter plate a t the bottom o f the sam ple. T he strength o f the sam ple, consolidated for this pressure, was then sufficient to perm it the rem oval o f the split m ould. T he dim ensions o f the sam ple were m easured and w hen the upper section o f the triaxial cell had been m ounted, the cell pressure was slowly increased, and the burette was sim ultaneously raised. M ost sam ples were consolidated under an all-round pressure, but som e undrained tests were also perform ed on samples consolidated anisotropically. The anisotropical consolidation was done by increasing the cell pressure in steps, as well as the additional vertical load on the sam ple. The ratio between the vertical and lateral stresses was controlled so th at the cross-section o f the sam ple rem ained constant during consolidation. W hen consolidation was com plete, the shear tests were carried out by subjecting the sam ple to a constant rate of strain. T he types o f test perform ed were as follows : volum e test is th at it will give correct pore pressure m easurem ents even if the sam ple is n o t com pletely saturated. Test results T he results o f the final series o f tests, consisting o f 24 drained tests, 19 consolidated constant-volum e tests and 12 consolidated undrained tests are presented below. As there is no difference betw een the results o f the undrained and the constant-volum e tests, they will be discussed below under the sam e designation, undrained tests. In the discussion o f the results m axim um em phasis will be given to the results o f the tests with loose sand. Stress-Strain curves In Fig. 3 are plotted a typical set o f stress-strain and volum e change-strain curves as observed in the drained tests. The three curves represent the results o f tests on a dense, a m edium Drained tests. T he m ajority o f the drained tests were carried out as conventional drained triaxial tests by increasing the axial strain until failure. The rate o f strain selected was 0-2 per cent strain per m inute. In order to investigate the effect o f the considerable consolidation which inevitably takes place in conventional drained tests on loosely deposited sand, a series o f tests was perform ed on loose sand in which failure was produced by decreasing lateral pressures. T he tests were carried out as for a norm al drained test w ith the sam e rate o f strain, but during the tests the cell pressure was reduced at such a rate th at a constant axial stress was m aintained. Consolidated undrained tests. A fter consolidation o f the sam ple, steps were taken to ensure com plete saturation. This was done b y increasing the cell pressure at the same tim e as a back pressure was applied to the pore w ater. D uring this operation the effective stresses in the sam ple rem ained unchanged and under the increased pressure the air bubbles in the pore w ater were com pressed and dissolved (see B j e r r u m and H u d e r, 1957). A n excess pressure o f 8 kg/cm 2 was used in all tests. In order to increase the accuracy o f m aintaining and m easuring the effective stresses during the test, a special connection betw een the cell pressure and the pore pressure units was established (see Fig. 2). The shear test was m ade by bringing the sam ple to failure a t a constant rate o f deform ation, 0-2 per cent strain per m inute. D uring the test, pore pressures were m easured by balancing the m ercury U in the special plastic pore pressure device (see Fig. 2). Consolidated constant volume tests. A fter com pletion of consolidation, the drainage system from the bottom filter plate was connected to a capillary tube (see Fig. 2). The sam ple was subjected to an axial strain in the sam e w ay and at the sam e rate as in the conventional undrained test. D uring the test, the cell pressure was regulated in such a w ay th at there was no w ater squeezed out o f o r sucked into the sam ple, as indicated by a constant level in the capillary tube. The pressure in the p ore w ater was thus kept unchanged during the test and equal to the atm ospheric pressure. As there is no change in the volum e o f the sam ple, the test is identical to a conventional undrained test and the change in cell pressure can be assum ed equal to the pore pressure set up in the corresponding undrained test on a com pletely saturated sam ple ( B je r ru m, 1954). The advantage o f the constant Fig. 3 S tr a in in p e r c e n t Drained tests. Typical stress-strain and volume change curves for dense, medium and loose sand. Samples consolidated at 1 kg/cm2. Essais drainés. Courbes typiques de tension-déformation et de variation de volume, relatives aux sables ferme, moyen et meuble. Echantillons consolidés à 1 kg/cm'2. and a loose sam ple which were all consolidated at the same pressure, 1-0 kg/cm 2. As seen from the curves the dense sand shows a heavily dilatant structure, resulting in a net volum e increase during the shear. It fails at a low strain, ab o u t 4 per cent. The loose sand shows, on the contrary, a considerable volum e reduction during the test and the strain at failure is ab o u t 13 per cent. Fig. 4 shows in a sim ilar w ay the stress-strain curves observed in the undrained tests. M oreover, the diagram shows the directly m easured pore pressure. The strain at failure, derived from the stress-strain curves, is o f special interest. W hereas the strain at failure for the densest sand sam ples varies from 6 per cent to 10 per cent, the failure strain increases rapidly for increasing porosity. A m edium dense sam ple w ith a porosity o f 40 per cent thus shows a strain at failure o f 24 per cent. F o r still higher porosities, the strain a t failure decreases again and for the very loose sam ples w ith porosities from 44 per cent to 46 per cent the failure strain is, on the average, as low as 0-5 per cent. 31

4 Fig. 4 S tr a i n n p e r c e n t Undrained tests. Typical stress-strain and pore pressure curves for dense, medium and loose sand. Samples consolidated at 1 kg/cm2. Essais à teneur en eau courante. Courbes typiques de tension-déformation et de pression interstitielle, pour sables ferme, moyen et meuble. Echantillons consolidés à 1 kg/cm2. Fig. 5 In itia l p o r o s ity in p e r s e n t Undrained tests. Pore pressure param eter A at failure plotted against initial porosity. Essais à teneur en eau constante. Le param ètre A de la pression insterstitielle à rupture, en fonction de la porosité initiale. Pore pressure param eter, A In the stress-strain diagram s in Fig. 4 are also show n som e typical pore pressure curves as observed in undrained tests. Three curves are given in Fig. 4, representing tests w ith a dense, a m edium and a loose sam ple consolidated at 1 kg/cm 2. C orresponding to the volum e increase observed in the drained tests, Fig. 3, a large negative pore pressure is set up in u n d rained tests on dense sand. D uring the undrained tests on very loose sand, surprisingly high pore pressures are observed, which result in extrem ely low shear strengths. This finding is illustrated in Fig. 4, but it is m ore clearly observed by a calculation o f the pore pressure param eter A. ( S k e m p t o n, 1954). The pore pressure p aram eter, A, is defined by the follow ing equation A u = A o n i + A(A oi A s m ) in which A n is the pore pressure set up by the change in m ajor and m inor principal stresses, A a i and A o m. Fig. 5 shows the A values observed at failu re defined as occurring at the m axim um values o f (a/ a m ) plotted against the initial porosities o f the samples. In Fig. 5 it is of interest to see th at for porosities below 44 per cent negative pore pressures are observed a t failure. F o r sam ples w ith porosities from 44 per cent to 47 per cent, the A values vary from zero to one, while for porosities above 44 per cent, the pore pressure param eter, A, increases rapidly. The loosest sam ple which has been tested in this series, having an initial porosity o f 48 per cent, had thus the A value of 2-7. In order to illustrate the significance o f this high value of A, it can be m entioned th at it is the m axim um value which has hitherto been observed at the Institute and is approxim a tely twice the values observed in norm ally consolidated clays. The unstable structure o f the loose sand is not only illustrated by the A values at failure, but also by an observed additional increase in pore pressure after failure. All tests 32 were carried out under a constant rate o f strain. A t the point o f failure the applied deviator stress, therefore, reaches a m axim um value and rem ains constant for a certain range o f strain before it decreases. A t failure therefore, there is no change in total stresses on the sam ple. A t the point o f failure the pore pressures in the dense and m edium sand show ed a tendency to decrease o r to rem ain unchanged. In the loose Fig. 6 S tr a in in p e r c e n t Undrained tests. Variation in pore pressure param eter A during typical undrained tests on dense, medium, loose and very loose samples. Essai à teneur en eau constante. Variation du paramètre A de pression interstitielle au cours d essais typiques non drainés sur échantillons fermes, moyens, meubles et très meubles.

5 Fig. 7 In itial p o ro s ity in p e r c e n t P o ro s ity a t f a ilu r e in p e r c e n t D rained tests. Angle of internal friction plotted against initial porosity (left) and porosity at failure (right). Essais drainés. Angle de frottem ent interne en fonction de la porosité initiale (à gauche), et de la porosité à rupture (à droite). sand, how ever, a very pronounced increase in pore pressure was observed at failure. This is clearly illustrated in Fig. 6, which shows the A values observed during typical undrained tests. T he p o in t o f failure is indicated on each curve so th at the change in pore pressure a t failure can be seen directly from the diagram. The angle of internal friction T he angle o f internal friction found by the drained tests are plotted in Fig. 7 as a function o f the porosity. Two diagram s are show n in w hich the friction angle is plotted against the initial p o rosity and against the porosity a t failure respectively. 45 E ach point in Fig. 7 represents one test only, the friction angle being com puted from the value o f the principal stress ratio at failure, assum ing th at the cohesion is zero. T he diagram s in Fig. 7 shows the w ell-known decrease in angle of internal friction for increasing porosity. H ow ever, the tests on very loose sam ples indicate th at in the loose range the friction angle decreases rapidly for increasing porosity, resulting in a sharp bend o f the curves. The very loose sam ples thus show ed friction angles as low as about 20. As the pore w ater pressures were m easured in the undrained tests, the effective stresses at failure are know n. F ro m these values the angle o f internal friction can be com puted in the sam e w ay as done for the drained tests. In Fig. 8 the friction a; 35 O o o < 15 o c o n s o li d a te d u n d r a in e d te s t 4- c o n s o li d a te d c o n s t a n t v olum e t e s t 0 % \ +- O + \ +.+ o < 15 3 \ 1 1 > In itia l p o r o s i t y in p e r c e n t P o r o s i ty a t f a ilu r e in p e r c e n t \ Fig. 8 Undrained tests. Angle of internal friction plotted against initial porosity (left) and porosity at failure (right). Essais à teneur en eau constante. Angle de frottem ent interne en fonction de la porosité initiale (à gauche), et de la porosité à rupture (à droite). 33

6 angles are show n in two diagram s, plotted in the one against initial porosity and in the other against the porosity at failure. T he curves in Fig. 8 show clearly that the friction angle o f the dense and m edium dense sam ples varies w ithin the norm al range o f values, 41 to 34. F o r sam ples with higher porosities than 44 per cent, how ever, a m ost surprising and unexpected drop in friction angle w ith increasing porosity is observed. F rom the 34 which is m easured in the m edium dense sam ples, the friction angle decreases to ab o u t 10 in the very loose sam ples w ith initial porosities o f per cent. In order to com pare the results o f the drained tests with those o f the undrained tests, it is necessary to plot the friction angles against the porosity at failure. Such a plot of the friction angle observed in drained and undrained tests is show n in Fig. 9. As seen from the diagram, the cp values observed in the undrained tests are sm aller than the values com puted from the drained tests. T he difference is sm allest in the m edium dense range of porosities. T he greatest difference is found in the very loose sand where it am ounts to as m uch as 10. This m eans th at the friction angle observed at failure in the undrained test is about half the value found in the drained tests. Fig. 9 Porosity at failu re percent Comparison of the angle of internal friction observed in drained and undrained tests. Comparaison des angles de frottement interne observés aux essais drainés à ceux à teneur en eau constante. The effective principal stress ratio The friction angles plotted in Fig. 7 and Fig. 8 are com puted for the failure values o f the effective stresses observed in the tests. Failure is here defined as the p o in t w here the deviator stress (<7/ c h i') shows a m axim um on the stress-strain diagram. F o r the drained tests the p o in t o f failure defined in this w ay is identical w ith the point a t w hich the principal stress ratio reaches a m axim um. In the undrained tests this is generally n o t the case. This fact is clearly illustrated in Fig. 10, w hich shows the principal stress ratio plotted against the strain for typical tests on dense, m edium an d loose sand. Two diagram s are show n in Fig. 10, giving curves for the drained tests and the undrained tests. O n each curve is indicated the poin t of failure w here a i a n i has a m axim um. Fig. 10 shows th at the failure points do n o t coincide w ith the points o f m axim um principal stress ratio in the undrained tests. In the dense and m edium dense sand g i g i u continues to increase after the p eak value o f the principal stress ratio Fig S tr a i n Drained tests 15 p e rc e n t 5 1Q S t r a i n Undrained 15 in p e r c e n t Typical curves of principal stress ratio plotted against strain for drained tests (left) and undrained tests (right), with dense, medium and loose sand. Courbes typiques du rapport des tensions principales, en fonction de la déformation aux essais drainés (à gauche) et aux essais non drainés (à droite). tests 34

7 has been reached, the m axim um value being first observed at a higher strain than th at at which cn /o m is a m axim um. A t this higher strain a reduction in ailaui has occurred so th at the m easured friction angle corresponding to m ax. g a m is som ew hat sm aller th an th at at m ax. g i / g h i. The m axim um principal stress ratio represents o f course the point of m axim um obliquity of the resultant force on the failure plane which m eans th at at this point friction is fully mobilized. The reason w hy g i g h i can still be increased is that the dilatant structure o f the dense and m edium dense sand will cause a steady reduction in pore pressures over the range o f strains before and after the friction has been fully mobilized and the effective stress on the failure plane will therefore continue to increase. This m eans further th at the shear resistance o f the sam ple will continue to increase and the deviator stress can consequently be raised above the value corresponding to the m axim um principal stress ratio. In loose sand the conditions are ju st the opposite. As seen from Fig. 10, an increase in principal stress ratio is observed before and after failure. The m axim um value o f this ratio is, thus, first reached at a strain which is times the strain a t the peak value o f the deviator stress. T his finding is a result o f the steady and rapid increase in pore pressure which occurs during the tests w ith loose sand. This increase in pore pressure w ith increasing strain causes a reduction in effective stress on the failure plane w hich m ore than com pensates the corresponding increase in friction, w ith the result th at g i g h i decreases. The friction a n g l: a t m ax. g i a m is thus considerably sm aller than the m axim um value observed at m ax. G l/g lll. Fig. 11 shows a diagram in which a com parison is m ade betw een the cp values corresponding to the m axim um principal stress ratio as observed in drained and undrained tests. The com parison shows th at there is a general agreem ent betw een the cp values found in the drained and undrained tests on the loose and m edium dense sand. The friction angles observed in the undrained tests on dense sand, how e ver, are som ew hat sm aller than the values from the drained tests. As discussed by T a y l e r (1948) and B i s h o p (1950), a p art o f the drained shear strength o f a dense sand can be attrib u ted to the force required to cause dilatancy against the confining pressure. This force can be com puted from the observed rate o f volum e change at failure. Such a com putation has been m ade for all drained tests and the dilatancy com ponent substracted from the total strength. The values o f the internal friction angle corrected for the dilatancy com ponent are also plotted in Fig. 11 which shows that there is alm ost com plete agreem ent between the friction angle com puted from the drained and the undrained tests over the whole range of porosities. The present test results thus confirm a recent finding from a review o f available triaxial tests on undisturbed norm ally consolidated clay ( B j e r r u m, S i m o n s, 1960), th at there is general agreem ent between the friction angles observed in drained and undrained tests if the undrained values are com puted for the m axim um principal stress ratio. This result indicates th at in cases where a long-term stability problem has to be analysed on the basis of a series o f undrained tests with pore pressure m easurem ent, failure shculd be selected at th at point where the principal stress ratio reaches a m axim um ( H o l t z, 1947). O n the other hand, practical problem s where excess pore pressures are set up by a change in stress should, in principle, be analysed in term s o f effective stresses on the basis of undrained tests w ith pore pressure m easurem ents, the failure point corresponding to the m axim um value o f gi am being used. This point o f view is strongly supported by the results o f the undrained tests on the very loose sand, where the use o f the m axim um principal stress ratio as failure criterion w ould lead to an overestim ate o f the friction angle o f 5 to 8. Earth pressure at rest T he m ajority o f the tests were carried out on sam ples initially consolidated under an all-round cell pressure. Several tests in which the sam ples were consolidated anisotropically were perform ed, how ever, using a principal stress ratio such th at there was no change in diam eter of the sam ple during consolidation. The ratio o f the m inor and m ajor principal stresses observed during consolidation is the coefficient of earth pressure at rest, K 0. The observed values o f K0 are Porosity at failure in percent Fig. 11 The friction angle determined at maximum principal stress ratio as observed in drained and undrained tests. L angle de frottement déterminé au rapport maximal des tensions principales, observé aux essais drainés et aux essais non drainés. Fig In itia l p o r o s ity in p e r c e n t Coefficient of earth pressure at rest plotted against initial porosity. Coefficient de pression du sol en repos, en fonction de la porosité initiale.

8 plotted against the initial porosity in Fig. 12. The values vary from 0-25 in dense sand to 0-65 in very loose sand. The high values observed in loose sand are considerably higher than found in previous tests on sand, and they are approxim ately o f the sam e order as m easured in norm ally consolidated clay. T here were no essential differences in the results o f the shear tests on isotropically and anisotropically consolidated sam ples. It was surprising to see, how ever, the sm all increase in deviator stress required to cause failure in the undrained tests on loose sand. This finding is illustrated in Fig. 13 which, in the case o f m arine deposits, seems to be a function of the plasticity index o f the clay. ( S k e m p t o n, 1948). In n a tu rally occurring strata o f soils w ith low plasticity, the value o f the ratio o f undrained strength and effective overburden pressure is o f the order ( B j e r r u m, 1954). It is obviously o f interest to com pare the results o f the undrained tests on the loose sand w ith these values. In order to do this, the undrained triaxial tests were interpreted in a sim ilar w ay to th at used for clay. T he undrained shear strength was taken equal to half o f the deviator stress at failure, and this value was divided by the pressure for which the sam ple was initially consolidated. W here the sam ples consolidated under an anisotropical stress condition, the m axim um principal stress was used. Test results indicate clearly th at the shear strength ratio decreases w ith increasing porosity. T he value observed in dense sand show som e scattering, but they are o f less interest in this connection. The values com puted from the tests w ith loose sand are plotted against the initial porosity in Fig. 14. to - 1«In itia l p o r o s ity in p e rc e n t Fig. 14 Ratio of undrained shear strength and consolidation pressure observed on loose sand. R apport entre la résistance au cisaillement (échantillon non drainé) et la pression de consolidation, rapport calculé à la base d essais effectués sur du sable meuble. Fig. 13 Stra in in p e rc e n t D eviator stress, principal stress ratio and pore pressure plotted against strain as observed in an undrained test on a loose anisotropically consolidated sand sample. Difference entre tensions principales, rapport de tensions principales, et pression d eau interstitielle, en fonction de la déformation observée dans un essai non drainé sur un échantillon de sable meuble consolidé de façon anisotrope. w hich gives typical stress-strain and pore pressure readings from an undrained test on an anisotropically consolidated loose sam ple. Ratio of undrained shear strength and consolidation pressure In norm ally consolidated clays, the ratio o f the undrained shear strength to the pressure under w hich the clay was consolidated, is constant. This constant is a characteristic param eter 36 T he shear strength ratio m easured in the loosest condition o f the sand (see Fig. 14), is believed to be com parable w ith the corresponding values in norm ally consolidated m arine clays, as the loose sand and the m arine clay b o th represent the loosest possible deposition o f a m a te ria l1. As seen from Fig. 14, the ratio o f the undrained shear strength to the consolidation pressure o f the loosest sand, initial porosity per cent, is o f the order 0-11 to These values are very sim ilar to the values observed for norm ally consolidated clay w ith low plasticity. A further discussion o f the sim ilarities betw een loose sand and norm ally consolidated clays is given in a separate paper prepared for the C onference. Conclusions F rom the above triaxial tests on fine sand the follow ing m ain conclusions can be draw n : 1. It has been proved th at shear tests on a fine sand are useful in a general study o f som e o f the factors w hich control the shear strength o f soils. By varying the porosity o f the sand, its shear strength properties can be changed over a very wide range from the m ost heavily overconsolidated to the loosest and m ost sensitive soils. 1. Concerning the effect of initial deposition on the shear strength, see Bjerrum, 1954, and Bjerrum and Rosenqvist, 1956.

9 2. The tests have show n th at the friction angle varies w ith the porosity over a m uch w ider range than hitherto supposed. It is o f special interest to observe th at the friction angle decreases very rapidly w hen the porosity exceeds a certain value. In the drained tests the friction angle was found to vary from 19 to 42, w hereas the undrained tests on the very loose sand showed values as low as In the consolidated undrained tests on loose sand it was observed th at the m axim um value o f the deviator stress was reached before the friction was fully mobilized, which is explained as resulting from the rapid increase in pore pressure w ith strain. In the tests on dense sand, on the other hand, the undrained shear strength continued to increase som ew hat after the friction was fully mobilized, as a result of a steady decrease in pore pressure. The friction angle observed at m axim um deviator stress was for all porosities sm aller than found a t the m axim um principal stress ratio and the difference is greatest for the densest and the loosest samples. 4. The friction angle observed in the drained tests agrees very well w ith the values from the consolidated undrained tests provided th at the m axim um principal stress ratio is used as failure criterion and th at the drained values are corrected for the dilatancy com ponent. 5. T he ratio o f the undrained shear strength to the effective pressure under w hich the sam ple was consolidated is in the loosest sand of the order o f T8. These values are surprisingly sim ilar to the ratios observed from vane tests in n o r m ally consolidated clay w ith low plasticity. T he test results thus indicate a general validity o f the w ell-known correlation o f decreasing undrained shear strength ratio w ith decreasing plasticity index observed in norm ally consolidated m arine clays. References [1] A n d r e s e n, A., B j e r r u m, L., D i B i a g i o, E., and K j a e r n s l i, B. (1957). Triaxial equipment developed at the Norwegian Geotechnical Institute. Oslo, 52 p. (Norwegian Geotechnical Institute, Publ., 21). [2] B i s h o p, A. W. (1954). Discussion on : Penman A. D. M. Shear characteristics of a saturated silt, measured in triaxial compression.geotechnique, vol. 4, No. 1, pp [3] (1950. Discussion on : Skempton, A. W., and Bishop, A. W. The measurement of the shear strength of soils. Geotechnique, vol. 2, No. 2, pp [4] and E l d i n, A. K. G. (1953). The effect of stress history on the relation between cp and porosity in sand. International Conference on Soil Mechanics and Foundation Engineering, 3. Zürich. Proceedings, vol. I, pp [5] (1950). Undrained triaxial tests on saturated sands and their significance in the general theory of shear strength. Geotechnique, vol. 2, No. 1, pp [6] B je r r u m, L. (1954). Geotechnical properties of Norwegian marine clays. Geotechnique, vol. 4, No. 2, p (Norwegian Geotechnical Institute. Publ., 4). [7] (1954). Theoretical and experimental investigations on the shear strength of soils. Thesis. (The Swiss Federal Institute of Technology). Oslo, 113 p. (Norwegian Geotechnical Institute. Publ., 5). [8] and B is h o p, A. W. (1960). The relevance of the triaxial test to the solution of stability problems. Oslo, 56 p. (Norwegian Geotechnical Institute, Publ., 34). [9] and H u d e r, J. (1957). Measurement of the permeability of compacted clays. International Conference on Soil Mechanics and Foundation Engineering, 4. London. Proceedings, vol. 1, pp (Norwegian Geotechnical Institute, Publ., 26). [10] and R o s e n q v is t, I. T. (1956). Some experiments with, artificially sedimented clays. Geotechnique, vol. 6, No. 3, pp (Norwegian Geotechnical Institute. Publ., 25). [11] and S im ons, N. E. (1960). Comparison of shear strength characteristics of normally consolidated clays. (Norwegian Geotechnical Institute. Publ., 35), pp [12] C a s a g r a n d e, A. (1936). Characteristics of cohesionless soils affecting the stability of slopes and earth fills. Boston Society of Civil Engineers. Journal, vol. 23, No. 1, pp (H arvard University. Graduate School of Engineering. Publ., 173, Soil mechanics series, 2). [13] C h e n, L.-S. (1948). An investigation of stress-strain and strength characteristics of cohesionless soils by triaxial compression tests. International Conference on Soil Mechanics and Foundation Engineering, 2. Rotterdam. Proceedings, vol. 5, pp [14] G e u z e, E.C.W.A. (1948). Critical density of some Dutch sands. International Conference on Soil Mechanics and Foundation Engineering, 2. Rotterdam. Proceedings, vol. 3, pp [15] H o l t z, W. G. (1947). The use of the maximum principal stress ratio as the failure criterion in evaluating triaxial shear tests on earth materials. American Society for Testing Materials. Proceedings, vol. 47, pp [16] K o l b u s z e w s k i, J. J. (1948). General investigation of the fundamental factors controlling loose packing of sands. International Conference on Soil Mechanics and Foundation Engineering, 2. Rotterdam. Proceedings, vol. 7, pp [17] Komiteen for grunnundersôkelser i Trondheim havneomrade (The Committee on Field Investigations in T rondheim Harbour), (1953). Innstilling. Trondheim, 45 p. [18] L a n g e r, C. (1938). [Caractéristique du sable boulant] ; compte rendu des recherches effectuées durant l année Institut technique du bâtiment et des travaux publics Annales, vol. 3, No. 6, pp [19] N a s h, K. L. (1953). The shearing resistance of a fine closely graded sand. International Conference on Soil Mechanics and Foundation Engineering, 3. Zurich. Proceedings, vol. 1, pp [20] P e n m a n, A.D.M., (1953). Shear characteristics of a saturated silt, measured in triaxial compression. Geotechnique, vol. 3, No. 8, pp [21] R u t l e d g e, R. C. and T a y l o r, D. W. (1947). Cooperative triaxial shear research program of the Corps of Engineers and pressure distribution theories, earth pressure cell investigation and pressure distribution data. Vicksb., Miss. 332 p. (Publ. by Waterways Experiment Station, Vicksb., Miss.) [22] S k e m p to n, A. W. (1954). The pore pressure coefficients A and B. Geotech nique, vol. 4, No. 4, pp [23] T a y l o r, D. W. (1948), Fundamentals of soil mechanics. N.Y., Wiley, p [24] T e r z a g h i, K. (1947). Shear characteristics of quicksand and soft clay. Texas Conference on Soil Mechanics and Foundation Engineering, 7. Austin. Proceedings 10 p. [25] (1956). Varieties of submarine slope failures. Texas Conference on Soil Mechanics and Foundation Engineering, 8. Austin. Proceedings, 41 p. (H arvard soil mechanics series, 52). Teknisk ukeblad, vol. 104, nr. 43, 44, 1957, pp , (Norwegian Geotechnical Institute. Publ., 25). [26] Waterways Experiment Station, Vicksb., Miss. (1950). Potamology investigations. Triaxial tests on sands, Reid Bedford Bend, Mississippi river. Vicksb., Miss. 54 p. (Report, 5-3). 37