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LABOMTORY CONSOLIDATION OF SOME
GERALD PATRICK R.4YMONDD
A theory of consolidation is developed assu~nine: e = I -ulog,,(k/k,) = --C * log, (gig,). Solutions are given for the case o! a thin bed of clay sknbjected to an instantaneous load increment. I t is shown how the soil parameters may be obtained from standard laboratory consolidation tests. I t is intended to discuss the application of the theory to field cases in a later a p r .
One-dimensional gainage tests per- formed in both the oedometer and triaxlal cell are presented. The tests in the tri- axial cell were pesfomed using hydro- static loading. The laborator work was B conducted on some remoulde New South Wales soils, some artificially de sited North American soils, and some unEturbed On- tario mils using hstantanmus loading and large load ratios. Discussion is mainly illustrated with the tests performed on the artificially deposited soils.
The propounded theory was found to be in reasonable but not complete agreement with the test results.
B'Arcy's law was found to be valid for the soils tested.
Bans le prksent article, 19sw a ddvelogp6 une thkorie de consoIidation bast% sur l'kcguation: e 4 I logIo(k/k,) = -C logIo(s/sa). Des ssHutions ssnt donn6es Dour Be cas d'une
P
couche mince d'argile soumise A un accrois- sement instantank de la charge. I1 est mon- tr& comment les parametres de csnsolidation des sols peuvent btre sbtenus au moyen d'essais standard de cansolidatisn en labora- toke. Lkpplicaticsn de cette thkorie alpx cas gratiques sur le terrain sera disctat6e dans un article subs6quent.
Bes essais comportant un drainage uni- dimensionnel ont Qtk exkutds dans l'mdo- m&tre et dans la cellule triaxiaHe oh une charge hydrsstatique a kt6 employ6e. E9&tude en laboratoire a 6t6 exhcut6e sur des sols remmis de New South Wales, des sols typiques de l'Am6rique du Nord qui ont 6t4 d&posks artificiellement, et des sols nonrernaasi6s en provenance de 1'8ntario ; durant les essais, des chargements instm- tanks et des rapports de chargement 6levks ont 6th empIoy4s. La discussion porte prin- ci alement sur les essais ex6cut6s sur les s o t dbposh artiiiciellement.
I1 a 6th csnstatk qu9uwe concordance rai- sonnable mais non complhte existait eaatre la thkorie propos6e et les n6sultats des essais et que la loi de Darcy est valide pour les sols employ& dans ces essais.
a = C / l c = the Terzaghi coefficient of consolidation
co = a constant C = the negative slope of the e ur. loglo o curve, assumed constant D = the depth at which the projected linear decrease in ~u becomes zero
measured from the surface of the soil deposit e = the void ratio h = the length of the drainage path
H = the thickness of the soil deposit I = the slope of the e vs. loglo k curve, assumed constant k = the coefficient of permeability
m = the modulus of volume change
*Associate Professor of Civil Engineering, Queen9s University, Kingston, Ont.
217
Canadian Ceotechnical Journal, vol. 111, no. 4. Nov., 1966. Printed in Canada.
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218 CANADIAN GEBTECHNICAL JOURNAL
M = ( r r / Z ) ( 2 N + 1 ) h7 = an integer p = the total stress S = the settlement t = the time T = the time factor
u, U = the excess pore pressure a, = the velocity of flow V = the volume change w = loge ( cr/a, ) z = the depth Z = x /H a - a constant A = an increment of
y, = the bulk density of water y, = the effective density of the soil
E = the base of natural logarithm a = the effective stress 6 = (a/crs) l - - ~ = (O-/U~)~--~ for thin deposits
p = ye - @p,/D) )/a8
f = the final value i = the initial vdue
9% = the value at zero void ratio o = a value defined where used s = the initial vi~lue at the surface of the compressible soil deposit t = the value at time t z = the value at a depth z
Many overpasses built in Canada have long approach embankments of con- siderable height. For example, overpasses over railroads usually require cmbankments which are built to a height of about thirty feet. If these embank- ments are built of soil weighing about twice the weight of water and are constructed on a saturated compressible soil of a similar weight in which the water table is atnor near the surface, the load ratio (ratio of the final effective overl~urden to initial effective overburden) would be greater than two, to a depth of approximately twice the height of the embankment. The same argu- ment applies also to soft deposits beneath large earth dams, ore piles, and the Bike.
Apart from the obvious question of how little and how fast will the embankment settle, it is often desirable to accelerate the settlement Boy overloading the embankment (termed preloading). The overload is generally allowed to remain until the maximum excess porewater pressure is equal to the overload. For such a method to be economical, a reasonably accurate
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RAYMOND : LABORATORY CONSOLlDA'F6ON OF CLAYS 219
prediction of the rates of dissipation of the porewater pressures must be made rather than a prediction of the rates of settlement, although the tww are usually milsidered interdependent.
When the soil is not strong enough to maintain the full height of an embank- ment two main alternates are commonly used. Either berms are built on either side of the embanhen t or the embankment is built in stages.
The method of stage construction consists of building the first stage to such a height that the partly built embankment is just on the point of failure. The second stage is then built when the excess porewater pressures induced by the first stage have dissipated to such an extent that the gain in strength of the soil is sufficient to withstand the rotational forces of the first and second stages of the embankment. As many stages as desired may be used, although for low embankments two stages are more usual. Here again the main criterion is the prediction of the rates of dissipation of porewater pressures and thus the rates of gain in strength rather than the rates of settlement.
It is generally believed that the rates of primary settlement are related in sane manner to the rates of dissipation of the porewater pressures. For this reason, the work reported here will be mainly concerned with the rate of primary consolidation rather than the effects of secondary consolidation. Nevertheless, it is believed that secondary consolidation occurs during primary consolidation and therefore should not be completely ignored. This is, however, believed to be more important when studying the rate of consolidation of soils subjected to small load increments ratller than large load increments.
The purpose of this paper is to examine the effects of large load ratios on the rate of consolidation of laboratory test specimens of fine grained soil. A discussion of the application of the theory to thick deposits will be left to a later paper.
Introduction Attention has recently been focused on the variable behaviour of the con-
solidation coefficients of soils during consolidation. McNabb ( 1960) has derived the one-dimensional consolidation equation in a very general form. Lo (1960) has attempted to take into account the variability of the coefficient of consolidation. Richart (1957) has solved, by means of finite differences, the problem considering a variable void ratio, and Schiffman ( 1958) has considered the case of a non-constant relationship for the vaIue of the coefficient of permeability. Ransbo (1960) has considered the case of a variable coefficient of permeability for the solution to the problem of the consolidation of clays by sand drains. Barden and Berry (1965) have developed a theory based on equation 1 of this paper. Unfortunately, all the above theories are diEcult to apply in practice because the authors fail to outline the method of obtaining the soil parameters OH the method is very involved.
Gray (1936) and Davis and Raymond (1965) have considered the case of a constant coefficient of consolidation and a linear relationship between the void ratio to an arithmetic scale newus the effective pressure to a logarithmic scale. Schiffman and Gibson (1965) have considered the effect of the variation
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2.20 CANADIAN CEBTECHNICAB, JOURNAL
with depth d the coefficients of permeability, compressibility, and con- solidation.
This paper considers the case of a linear relationship between the void ratio to a natural scale and the coefficient of permeability to a logarithmic scale combined with a linear relationship between the void ratio to a natural scale and the effective pressure to a logarithmic scale. It will also be assumed that the increase in porewater pressure is equal to the increase in total load on the soil and varies linearly with depth, and that the strains are small. It should be clearly understood that a linear stress-strain relationship is only approximated when both the stress increase and the strains tend to zero. If only one of these is small then the relationship does not necessarily approximate a linear relationship.
Assumptions and derivation of theory In n mass of real soil, the coefficients of compressibility, permeability, and
consolidation vary during the consolidation process. In order to establish a theory of consolidation which takes into account this variable behaviour of the soil, it seems reasonable to examine more closely the variation of the roefficients of compressibility, permeability, and consolidation.
Taylor (1948) discusses the permeability of clays and states that, for fine- grained soils, it has been found experimentally that a plot of the void ratio to an arithmetic scale against the coefficient of permeability to a logarithmic scale approximates a straight line for many soils. It has also been found experimentally that, for a normally consolidated or overconsolidated fine- grained soil, a plot of the void ratio to an arithmetic scale against the effective pressure to a logarithmic scale approximates a straight line for many soils. Expressing these relationships mathematically:
where
e = the void ratio, I = a constant, k = the coefficient of permeability, k, = the apparent value of k at zero void ratio, C -- a constant, a = the effective stress, vn = the apparent value of a at zero void ratio.
It must be realized that these relationsllips are only valid over a limited range. For example, at zero void ratio the coefficient of permeability would be zero.
Assuming that Darcyb law of flow through porous media is valid for soils, then :
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RAYMOND : LABORATORY CONSOLIDATION OF CLAYS
a = C/% zr = the excess pressure in the pore-fluid,
yw = the density of water, z = the depth, u = the velocity of flow.
Differentiating equation 2 with respect to depth, then:
It will be assumed that the degree of saturation of the soil is 100 per cent and the pore fluid and the soil particles are incompressible in relation to the soil skeleton. Equating the rate of water lost due to the change of flow with respect to depth per unit area to the rate of volume decrease per unit area, both within a small element of soil of thickness dz (this is possible since the pore fluid and soil particles are assumed incompressible in reIation to the soil skeleton ) , then :
or:
where t = the time. Equation 5 is the general solution for one-dimensional strain and drainage since no assumptions as to type of loading, rate of change of loading, etcetera, have been made.
Dwing the consolidation process ( 1 + e ) varies far less than the effective pressure so that it may be considered constant and equal to ( I f e01.I
Equation for field application In most problems requiring an estimate of the rate of collsolidation of thick
sail deposits the effect of lateraI drainage is important. In some eases, however, the loid spreads with depth and covers a sufficiently large area so that the problem may be considered a one-dimensional problem. Thus the change in porewater pressure is approximately equal to the change in vertical sbesiO2
In many compressible soil deposits the change in bulk density with respect to depth is sufficiently small that it may be assumed constant. In addition, the increase in water pressure with respect to depth is approximately constant although not always hydrostatic. In such a deposit where the load decreases linearly with depth the effective stress at any depth may be approximately expressed as:
lThis is equivalent to assuming that the strains are very small. Z-CVhile this may not be an exactly correct assumption it is very commonly made.
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222 CANADIAN GEOTECWICAL JOURNAL
w, = the initial effective stress at the surface of the compressible soil deposit, y, = the effective density of the soil,
~p = the change in total pressure (subscript s refers to the value at the surface of the compressible soil deposit ),
au = the change in water pressure which initially has been assumed equal
to Ap, D = the depth at ~711ich the projected linear decrease in AU becomes zero
rraeasarred from the surface of the soil deposit ( D > H ) , : = the depth measured from the surface of the soil deposit.
Differeiltiating equation 6 and using the substitutions:
the general solution for field application may be obtained from equation 5 as:
dw $ 2 ~ aw -- - * p.e -m *---
ar - az az (for a = 11)
where H = the depth of the layer,3
Since the main concern sf this work is the consolidation behaviour sf laboratory test specimens a detailed discussion of these equations will not be presented here.
Solution for labomtory tests (p = 0) For the standard laboratory test the self weight of the specimen is sinall
and the load is assumed constant with depth. Under such coilditions p = O and equation 9 reduces to the equation solved by Davis and Raymond ( 1965). Equation 10 was solved by finite differences. With instantaneous loading and
3WInen p = 0 it is more convenient to use M as the length o f the drainage path as in Tenraghi's theory.
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RAYMOND : LABOUTORY CONSOLIDATION OF CLAYS 223
p = 0 tlae rate of settlement in terms of the dimensionless time factor is dependent only of the boundary value of 8. The degree of settlement or volume change is given by:
The solutions are given in Figure 1 and some dissipation of mid-plane pore- water pressure-settlement characteristics are given in Figure 2.
Figure 1 indicates that as a first approximation the rate of settlement may be fitted to Terzaghi's theory using the time to reach 50 per cent settlement. Figure 2 indicates that the Davis and Raymond solution may be used to fit the ratcs of dissipation of porewater pressures to the rates of settlement.
FIGURE 1. Rate of settlement for different boundary values of 6, instantaneous loading, and p CL 0
Examining the equation for the dimensionless time factor the rate of settle- ment for a constant load ratio may be seen to depend on Representing the rate of settlement by the time to reach 50 per cent settlement, then for a constant load ratio :
where cr, = the initial eifective stress = c8 when p = 0. Taking logarithms and substituting in equation 1:
ei = the initial void ratio, t, = the apparent value of t 5 0 when ei = 0.
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CANADIAN GEOTECHNPCAL JOUBNAL
SETTLEMENT
FIGVRE 2. Mid-plane p.w.p,-settlement characteristics when u = 0, P, and 2 for instan- ta~~eotls loading and = 0
Thus for a constant load ratio the time to reach 50 per cent consolidation will increase with an increase in initial load only if (assuming an increase in load causes n settlement) :
Assuming that the standard method of testing (or that the load ratio is kept constant) is used and that the idealized relationships are approximated, the resulting values of the time to reach 50 per cent consolidation (assuming the same curve fitting method was used each time) plotted to a logarithmic scale against initial void ratio4 to a natural scale should result in a straight line relationship of slope a/ ( l - a). This relationship is, of course, valid for any value of load ratio as long as the load ratio is constant.
The normal plot of e - log a- will result in the value of C and thus having obtained both C and a the value of I may be calculated. Having obtained C and I the boundary value of t9 may be calculated and thus from Figure 1 the theoretical time factor at 50 per cent consolidation. The third parameter co may now be calculated from the test results of any load increment and the definition of time factor. It is suggested that the test results may be idealized by using a value of the t50 obtained from the e - log tSo line.
In order to simplify the obtaining of co and enable analysis of tests where different load ratios have been used the average void ratio for each load increment should be used in the e - log tho plot. Very approximately for the ear - log tSo plot (the error is small for a load ratio of two and decreases as the load ratio decreases ) :
$Since, for a consta~lt load ratio, the amount sf settlement is constant, the average or final void ratio anay also be used to obtain a/ ( l - a $ .
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RAYMOND: LABORATORY CONSOLIDATION OF CE.4Y8
where:
h = the length of the drainage path oo = the effective stress fromthe e - log cr plot obtained for the same void
ratio as tS0 from the e,, - log t 5 0 plot = Exponential [!;(log of + log ail = v'E, ui
Alternatively Terzaghi's theory may be used to obtain the inferred value of the coeEcient of permeability. The value of I is then obtained from an e - log k plot. Again if the average void ratio is used for each increment then very approximately the e., - log k plot should be the true e - log k plot for the soil. From equation 1:
thus facilitating the calculation of coo For undisturbed soils where C changes as the soil goes from an overcon-
solidated to a normally consolidated state the e - log k plot will often be found to give a straighter line than the e - log t plot.
Tests were conducted on four remoulded New South n7ales (Australia) sdls, five North American artificially deposited soils, and three undisturbed soils. The results of these tests are reported in detail elsewhere Raymond (1965), (1966a), and Bacon (1966). Some of the results obtained with the semsulded soils have been published by Davis and Raymond ( 1965) in support of the case of a = 1. Discussion in this paper will, therefore, be restricted mainly to the points made in the previous section and to the interpretation of laboratory tests.
The tests on the remoulded soils were designed to establish two points. First, the measurement of porewater pressures at the base of an oedometer using different load ratios. These results are presented by Davis and Raymond (1965) and approximate the theoretical predictions. Second, to investigate the effect of the length of the drainage path and the value of the initial load. The ratios of the maximum to minimum values of length of drainage path, initial effective stress, and the coefficient of consolidation (assuming Terzaghi9s theory to be valid and using the semi-logarithmic curve fitting method outlined by Casagrande and Fadum, 1940) are given in Table I.
Ratis max: min of
Drainage Initial Terzaghi path effective coeEcient sf
length stress consolidation
Blackman's point soil Hurswille soil Mascot soil Port Kembla soil
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These results were obtained from tests on different specimens. Each specimen was, in general, subjected to different load ratios, etc. Despite the large differ- ences in initial stress and length of drainage path the coefficient of consolida- tion was found to be approximately constant. This would tend to confirm the fact that for these soils a is approximately equal to one and furthermore the assumed validity of Darcy's law is not in serious error for these results.
Tests on artificially deposited soils The primary purpose of the tests on the artificially deposited soils (which
were prepared in a similar manner to that described by To~7nsend and Gay, 1964) was, first to obtain two unlike soils for an investigation of the sinaultaneotas consolidation of two unlike soils, and second, to determine the properties of the two soils used in the simultaneous consolidation tests.This investigation was supplemented by additional tests to illustrate some of the points presented in the previous seetion.
All tests were performed in either a 1 in. high by B in. diameter plastic oedometer pot using a Bishop type of loading press, or a triaxial cell suitable lor 1?6 in. diameter specimens. The triaxial tests were performed using hydro- static pressure and allowing, in general, one-way drainage. The porewater pressure was measured at the base of the cell (impermeable boundary). The effective stress was increased by decreasing the back pressure, the cell pressure remaining constant at all times. The equipment used was similar to that described by Bishop and Henkel (1957) except for the porewater pressure gauge which was similar to that described by Raymond ( 1963).
The engineering classification properties of the soils were determined from air-dried artificially deposited soil which remained after the test specimens had been obtained. The results are given in Table 11.
TABLE II
Engineering Classification Properties of the Artificially Deposited Soils
Soil Type Bentonite Don Valley Leda New Liskeard
Soil properties Liquid limit 118.4 Plastic litnit 46.2 Plasticity index 72.2 Average initial moisture corltent 88.8
Grain size analysis % finer than by weight 200 Mesh 97.5 0.06 nana 97 0.02 ~nrrr 94 0.006 mrn 77 0.002 rlnm 55
The test results were plotted on several graphs. Figure 3 illustrates a typical plot of the void ratio at the end of primary consolidation against the effective
SThe results of the investigation of the shtdtanesus consolidation of two tanlike soils is reported elsewhere by Raymond and Ghana ( 1966).
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RAYMOND: LABQBA'fe)RP CONSOLIDATION OF CLAYS
0 I 10
EFFECTIVE STRESS MG./CM.
DON VALLEY 0 0.26
L A
FIGURE 3. Typical void ratio-logarithm 0% effective stress characteristics
stress. In all cases the results approximate straight lines. Figure 4 illustrates a typical e - log k plot. From incremental tests the void ratio change has been indicated in the direction of the void ratio axis and is plotted against the eoeBcient of permeability calculated assuming Terzaghi's theory to be valid. In addition some direct permeability tests were run on one specimen of each soil and the results plotted with the results obtained in the same test apparatus (oedometer of triaxial cell) and on the same soil. Figure 4 shows results obtained from the permeability tests and from the incremental tests using a load ratio of 2.
From Figure 4 it may be seen that the e - log k plots are slightly curved. Nevertheless it is apparent that to assume a straight line relationship is more realistic of the true behaviour of the soil than to assume the slope is equal to infinity (k = a constant results in I = infinity). In actual practice the value of I (and also C if the e - log o plot is curved) is best determined over the stress range likely to occur in the field. Table I11 gives the values of C , I and
TABLE 111
Bedometer Test Results
Incremental tests Permeability tests
(C-I)/ (C.I)/ (C.I!/ Soil type C I (C-I)" (C-I)t co" cot 1 (C-1) cO*
Beratorlite 0.64 0.3:3 0.68 0.68 0.068 0.092 0.33 0.68 0.076 Dora Valley 0.26 0.46 -0.60 -0.60 0.827 0.014 0.41 -43.71 0.036 Kingston 0.30 0.72 -8.85 -1.00 0.012 8.041 Leda 0.29 -0.29 -0.50 0.064 0.4389 0.59 -0.57 0.131 ?Jew Liskeard 0.41 0.65 -1.11 -1.00 0.011 0.012 0.55 -1.61 0.020
"Calculated from e - log K plot. tFrsm e - log c plot.
KG-CM-Min. KG-CM-&/%in. ~rnits units
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228 CANADIAN GEOTECmICAL JOURNAL
F P G ~ 4. Typical void ratio-lspri&mn of coefficient of permeability characteristic
( C . I ) / ( C - I) (the slope of the e - log c plot where c is the Terzaghi co- eBcient sf consolidation) and CQ based on all the test results for the sedsmeter tests and Table IV gives the values for the hydrostatic consolidation tests.
TABLE IV
Hydrostatic Consalidatian Test Results
Incremental tests Permeability tests
(C-I>/ (C-I>/ (C.I)/ Soil type C I (6-I)* (C-I>? co* 60t I (C-I)" co*
Bentonite 0.56 0.29 0.60 0.50 0.030 0.040 0.29 0.60 0.845 Don Valley 0.21 8.37 -0.49 -0.55 0.039 0.036 0.37 -0.49 0.043 Ixda 0.27 8.49 -0.60 -0.52 0.066 0.066 n'ew Liskeard 8.39 0.46 -2.56 -2.00 0.019 0.015 8.46 -2.56 0.018
*Calculated from e - log k plot. tFrorn e - log c plot.
KG-CNI-Min. KG-CM-Min. units units
In Figure 4 results are given for a test on remoulded Leda clay. These results were obtained on a specimen of artificially deposited soil remoulded at constant water content and obtained from the same deposited sample as the other Leda soil results shown in Figure 4. Fhile the values of C and I are only slightly different for these two specimens of Leda soil the value of co of the remoulded specimen is less than 50 per cent of the value for the
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RAYMOND: LABORATORY GONSBLIBA'PION OF CLAYS 229
"undisturbed specimen. Thus it is not unreasonable to expect a certain amount of scatter in the results.
The incremental test results and the direct n~easurement results shown in Figure 4 ( e - log k plot) were unfortunately obtained from different speci- mens. A similar e - log k plot obtained from the hydrostatic consolidation test results is shown in Figure 5. In this case a load ratio of 2 was used for the
8-01 0.1 B 18 CQEFFlClENT OF PERMEABILITY CM./Mlbl
FIGURE 5. Compa~is~m of hfened and directly measured vdue of the coegcierat of pmeabiIity obtained from the same test
incremental tests and the direct permeability tests performed at the end of each load increment. The results for each soil shown in Figure 5 were obtained from the same specimen and clearly show that the inferred coefficient of permeability and thus co (calculated form an e - log k plot) tends to be less than that obtained from direct tests. This believed to be due to the effects of secondary consolidation causing a quasi-preconsolidation pressurn. The phenomenon is in agreement with the arguments presented by Raymond ( 1966b ) regarding the eff eds of a quasi-preconsolidation pressure on the inferred value of the coefficient of permeability. Raymond (1966b) further- more suggests that a quasi-preconsolidation pressure will have little effect on the rate of settlement or volume change. Figure 6 demonshates this latter point and is a typical dimensionless plot of a set of hydrostatic consolidation test results fitted to Terzaghi's theory. In addition the porewater pressures at the impermeable boundary tended, initially, to drop rapidly after which they followed the predicted characteristics as might be expected from a soil exhibiting a small quasi-preconsolidation pressure ( Raymond, 1966b). Some typical results of percentage dissipation of porewater pressure against Terzaghi time factor calculated from the time to reach 50 per cent primary volume change are shown in Figure 7. Thus the results obtained from the hydrostatic
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FITTED TEWZAGHl TIME FACTOR
FIGURE 6. Typical volume change-time factor characteristics obtained from hydrostatic: consolidation tests
F I G ~ E 7. Typical dissipation of porewater pressure-time factor c%aaracteristics
consolidation tests were found to be in reasonable agreement with the pro- pounded theory ( f or large load ratios ).
'The resuIts of oedometer and hydrostatic eonsoHidation test results are summarized in Tables III and IV. These results, while not in complete agree- ment are close enough to suggest that, for practical purposes, either test may be used to obtain the soil parameters.
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RAYMOND: LABORATORY CONSOLIDATION OF CLAYS 23 1
Permeability tests Because of the effects of secondary consolidation care had to be taken
when performing the permeability tests. For the hydrostatically consolidated samples a constant head and large hydraulic gradient were used (the pressure difference across the sample was about one tenth on the consolidation pres- sure). The coefficient of permeability was calculated by assuming Darcy's Iaw to be valid.
FIGUHE 8. Apparatus used for the falling head permeability tests
For the oedometer tests a falling head test was performed in a Casagrande- type oedometer cell made from plastic. In order to reduce the effects of secon- dary consolidation, the oedometer press was modified ( a lever being added) so that a constant specimen height could be maintained during the permea- bility testo The ecpipment used is shown in Figure 8. The effect of maintaining the height of the specimen constant during the permeability test probably caused the stresses initially acting upon the specimen to change (probably decreasing). It is also probable that there is a change in void ratio within the specimen although the average void ratio must remain constant.
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232 CANADIAN GEOTECHNICAL JOURNAL
If Darcy2s law of flow through porous media is valid the falling head permeability test results should lie on a straight line when plotted with the excess head on a logaritlunic scale against time on a natural scale. Due to the low permeability of the soil, small precision-bore capillary tubes6 were used for the standpipes of the permeability equipment. The excess head would therefore be the difference in water levels minus the correction for capillary rise. A set of typical results are shown in Figure 9 and plot, with the exception of the points at very small hydraulic gradients, as a straight line. The deviation in the results at low hyc8raulic heads is probably due to uncontrollable test errors such as small temperature changes. Alternatively, it may be caused by Darcy's law not being valid at very small gradients, as was suggested by Hansbo (1960). In view of the smallness of the difference, it is difficult to come to any definite conclusion based on these particular test results.
FIGURE 9. Typical resa~lts from the falling head permeability tests
From the slopes of the plots of the excess head on a logarithmic scale against time on a natural scale, it is possible to calculate the coeEcient of permeability of the soils provided Darcyk law is assumed valid.
It is worth noting that a 20 ft. thick bed of clay draining in two directions and loaded with seven feet of fill will have an initial porewater pressure of approximately 14 ft. of water. When approximately 50 per cent settlement has occurred the mid-plane porewater pressure according to Terzaghis theory wiBI be about 10 ft. sf water. Dividing the mid-plane porewater pressure by the drainage length gives an apparent hydraulic gradient of 1. The actrlal hydraulic gradient is theoretically zero at the mid-plane and, according to
GSeveral sizes were used hitially but the value of the coefficient sf permeability was foa~nd to be independent of the size of the capihry tube.
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RAYMOND: LABBRATBRY GONS6)EIDATION OF CLAYS 233
Terzaghi's theory, approximately 2. at the permeable boundary at a time represented by the time factor T.
Test on undisturbed soils An insufficient number of tests have been performed on undisturbed soils
to undertake a full discussion at this time. Once the preconsolidation pressure has been exceeded, however, there is little difference between the results obtained and the results from the artificially deposited soils. Onby insensitive undisturbed soils have been tested.
1. A theory of consolidation based on linear relationships between the void ratio to a natural scale and both the effective stress and the coefficient sf permeability to a logarithmic scale has been developed and solved for thin beds of clay. It has been shown how the parameters defining the theory may be obtained f ron~ standard laboratow tests.
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2. The theory is in reasonable, although not complete, agreement with the test results obtained using large load ratios on four remoulded New South Wales soils and four artificially deposited Ontario soils and an artificially deposited Bentonite soil.
3. Once the preconsolidation presswe of an undisturbed soil has been exceeded it was found to behave in a similar manner to an artificially deposited soil.
4. The measured rates of dissipation of mid-plane porewater pressure in relation to the measured rates of settlement (volume change) were found to be in better agreement with the propounded theory than with Terzaghi's theory of consolidation for the larger load ratios used. For the smaller load ratios used the rates of dissipation of porewater pressure in relatiw to the rates of settlement (volume change) were observed to be much faster than predicted by either Terzaghi's theory or the propounded theory, particularly for the initial dissipation of the porewater pressure.
5. The void ratio-logarithm of effective stress relationship was found to b approximately linear for the normally consolidated range of the soils used.
6. The void ratio-logarithm of the coefficient of permeability, while not a perfect straight line relationship, was found to be a good approximation to a straight line.
7. The results sugest that Darcy's law is valid even for hydraulic gradients less than 1 and certainly for hydraulic gradients greater than 1, provided the soil is fully saturated.
The work reported is a combination sf work conducted under Project 4-33 sf the Ontario Joint Highway Research Programme, work supported by a Canadian National Research Grant, and work cond~icted at the University of Sydney, Australia. The majority of the tests on artificially deposited soils were performed by Mr. H . T. Charm and Mr. A. 8. Bacon while post-graduate students at Queen's U~liversity.
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R Z F E ~ C E S
BACON, A. R., 1966. The permeability of clay as measured with a faIling head oedometes apparatus. hfSc thesis, Queen's University.
BARDEN, L., and BERRY, P. L., 1965. Coilsolidation of normally consolidated clay. Prsc. ASCE 91, SM 5 : 15-35.
BISHOP, A. W., and HENKEL, B . J., 1957. The Ibfemlrement of Soil Properties in the Triaxhl Test ( London : Arnold ) .
CASAGRANDE, A., and FADUM, R., 1940. ATotes on Soil Testing for Engineering Purposes. Harvard University Graduate School of Engineering, Publication 268.
DAVIS, E. H., and RAYMOND, G. P., 1965. A non-Iinear theory consolidation. Gkotech- nique 15: 161-73.
GRAY, H., 1936. Progress re ort on research on the consolidation of fine-grained soils. Proc. 1st. Int. Conf. So i l Biech. and Found. Eng. 2: 138-41.
HANSBB, S., 1960. Consolidation of clays with special reference to influence of vertical sand drains. Proc. Royal Swedish Geotehnkak Inst., no. 18.
L E O N A ~ S , G. A,, and ALSCHAEFFL, A. G., 1964. Compressibility of clay. Proc. ASCE 90, Shl 5: 133-55.
L E O N A ~ S , G. A., and C I ~ U L T , P., 1961. A study of the one-dimensional consolidation test. PTOC. 5th Iazt. Canf. So41 Mech. and Found. Eng. ( Paris 1: 213-18.
LO, K. k'., 1960. Discussion of Measurement of the coeEcient of consolidation of lacus- trine clay, by 19. FV. Rowe. Gkotechnique 10, no. 1: 36-9.
MclV~sw, A., 1980. A mathematical treatment of one-dimensional soil consolidation. Quarterly of Applied Math . 17, no. 4: 337-47.
RAYMOND, G. P., 1963. A simple pore water pressure gauge. Symposiunt of L ~ ~ o T ~ P ~ o T ~ Shear Testing sf Soils, ASTM, STP 361: 3724 .
RAYMOND, G. P., 1965. Rate of settlement and dissipation of porewater pressure during consolidation of days subjected to simple loading and one-dimensional drainage. PhB thesis, University of London.
RAYMOND, G. P., 1966a. The Comolidutwm of Some Normally Consolidated Fine Grained Soils Subjected to Large Load Watbs and Bne-Dimensional Drainage, DHQ Report no. 103, Toronto.
RAYMOND, C. P., 1966b. Gonsoliclation of slightly overconsolidated soils. Proc. ASCE 92, SXI 5: 1-28.
RAYMOND, C. P., and CHAN, H. T., 1966. The Consolidation of Multi-Eaycred Soib Subejcted to Large Load Ratios and Om-Dimensism1 Elruinage. DHQ Report no. 104, Toronto.
RICHART, F. E., 1957. Review of the theories for sand drains. Proe. ASCE 83, paper 1301. SCHIFFMAN, R. L., 1958. Consolidation of soil under time dependent loading and varying
permeability. Roc. HRB 37: 584-617. SCHIFFMAN, R. L., and GIBSON, R. E., 1964. The consolidation of non-homogeneous clay
layers. Paoc. ASCE 90, SM 5: 1-30. TAYLQR, B. W., 1948. Fundnm72entals of Soil Mechualics (New k'ork: ?Viley). TOWNSEND, D. L., and GAY, G. C. W., 1964. Triaxid shear tests on artificial varved clays.
0 JHRP Report 27, Queen's University.
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