BARDEN, L., 1968.

Giotechnique,

18: l-24

PRIMARY AND SECONDARY CONSOLIDATION OFCLAYANDPEAT LAING BARDEN, Ph.D.,

MSc.,

A.M.T.C.E.*

SYNOPSIS The dominant viscous mechanism governing the consolidation of the majority of clays and colloidal peats is described in terms of structural viscosity and thixotropy. A simple rheological model of an element of saturated clay is developed and solved for one-dimensional consolidation. The results give encouraging agreement with a wide range of published behaviour of clay and peat. The rheological model of the clay skeleton can be applied directly without integration in the case of partly-saturated clay with continuous air voids and provides a simple theoretical basis for predicting the compression-time behaviour. A consolidation mechanism relevant to fibrous peat involves the drainage of a system of micropores into a system of coarser channels. The basic physics of this process has not yet been established and no solution is offered in this case.

Le mecanisme visqueux dominant qui regit la consolidation de la majorite des argiles et des tourbes colloidales est decrit par rapport B la viscosite de structure et a la thixotropie. Une simple maquette rheologique d’un Clement d’argile sature est developpee et la solution recherchee pour la consolidation a une dimension. Les resultats concordent d’une faGon encourageante pour une gamme etendue de modes de comportement de l’argile et de la tourbe. La maquette rheologique de l’ossature d’argile peut &tre appliquee directement sans integration dans le cas d’argile partiellement saturee avec des poches d’air continues et fournit une simple base theorique pour &dire le comnortement temnscompr&sio;l. * Un mecanisme de consolidation applicable a la tourbe visqueuse entraine le drainage d’un systeme de micropores resultant en un systeme de canaux Les principes physiques de base de plus grossiers. ce processus n’ont pas encore et6 determines et au&e solution n’est‘presentee dans ce cas.

NOTATION

coefficient of linear compressibility coefficient of non-linear structural viscosity coefficient of consolidation void ratio hydraulic gradient coefficient of permeability index in power law pressure viscous resistance to compression pressure increment ratio true time pore pressure excess mid-plane pore pressure excess

2

F H R T

TS 0’ 7

r CL *

h Yw

space variable bond resistance length of drainage path dimensionless parameter Terzaghi time factor viscosity time factor effective stress shear stress rate of shear strain effective coefficient of viscosity degree of consolidation dimensionless parameter density of water

INTKODUCTION

The mechanisms of the consolidation process and of shear failure in clay soils are interrelated topics, and knowledge of them is essential to the fundamental understanding of soil As a starting point for such a study the case of one-dimensional consolidation has behaviour. been taken, as this involves the essential physics of the process but requires the simplest mathematical and experimental treatments.

1

* Senior Lecturer in Soil Mechanics, Manchester University. 1

2

LAING

BARDEN

The consolidation process is now accepted as continuous, but is traditionally divided into primary and secondary stages. The primary stage is governed by the dissipation of pore pressure and the secondary stage is a creep under constant effective stress. While accepting its lack of fundamental significance it is still convenient to retain this simple definition ; in this Paper the necessarily arbitrary division between primary and secondary is taken in the region where the mid-plane pore pressure approaches zero. Rheological models have proved a great help in representing the stress-strain-time behaviour of clay soil under various test conditions including one-dimensional consolidation. A number of workers, Schmid et al. (1960), Saada (1962) and Wahls (1962), have investigated the rheological behaviour of soil in terms of total stresses and overall deformation of the sample, this phenomenological approach having proved successful with other materials. It is widely accepted, however, that any treatment of soil deformation that ignores the effect of pore pressure will have limited application and provide no real insight into the behaviour of the material. The rheological parameters required to provide an empirical fit to the soil behaviour in terms of total stress will change with each variation in test condition, stress system, drainage conditions, and so on. Rheological treatments in terms of effective stress recognize the essential two phase nature of saturated clay and are likely to be of a more fundamental nature. They allow a proper treatment of the two different but interlinked time effects of hydrodynamic lag and viscous creep of the skeleton. Since in a consolidating sample the pore pressure and hence effective stress varies with distance from the drainage boundary, it is clear that this requires the treatment of infinitesimal elements which must be integrated over the height of the sample. This was pointed out by Chaplin (1963) in a criticism of Wahls’ (1962) treatment in terms of total stress. In reply Wahls agreed that the treatment of an element, followed by integration, was the correct approach but that the behaviour of an element could not be obtained by direct observation. This is certainly true, but now there is sufficient indirect experimental evidence and theory available to allow the postulation of realistic behaviour of an element in the convenient form of a rheological model. After integration the predictions of the macroscopic behaviour can be checked by experiment, and the model revised as necessary until realistic predictions can be made of sample behaviour, without it being necessary to alter the rheological parameters at each change of test conditions. This approach also provides an indirect method of studying the microscopic behaviour of infinitesimal elements consisting of large numbers of clay particles, and may even clarify behaviour between adjacent particles of clay. The approach of integration of the element is the most fundamental and has been adopted by Taylor and Merchant (1940), Taylor (1942), Ishii (1951), Tan (1957), Gibson and Lo (1961), Florin (1961), Schiffman et al. (1964), Raymond (1965) and Thompson (1965). In these treatments the rheological models of the element when loaded by effective stress are those of linear visco-elasticity, with the reservation that they apply mainly at small strains. To avoid the small strain limitation Geuze (1964) proposed the use of mechanical models, Following the convention of separating a stress system into its volumetric and deviatoric components the behaviour of clay under drained isotropic volume compression (no distortion) and undrained deviatoric loading (no volume change) has been studied. The separate investigation of volumetric and deviatoric components may, however, have less fundamental significance in studies of soil deformation, when it is considered that a soil can dilate strongly under shear stress and that the basic mechanism of volume change is one of local shear. The essential non-linearity of soil behaviour also indicates that these two components cannot necessarily be superimposed as implied by linear small strain theory, and the conditions under which any super-position applies must be thoroughly investigated. Since soil deformation involves local shear failure and soil is essentially a frictional material, some form of effective stress ratio is likely to be a more fundamental parameter than either deviatoric or mean stress in governing deformation and creep. In this connexion it is worth

PRIMARY

AND

SECONDARY

CONSOLIDATION

OF

CLAY

AND

PEAT

3

noting that if a consolidation test is conducted in the triaxial cell under a stress ratio approximating the K, value, the observed secondary consolidation is often greater than in the oedometer test. This is caused by the effective stress ratio approaching a failure value, resulting in much jumping of bonds in the early undrained stages of the test, and only gradually falling to the K, value as dissipation proceeds. In the present analysis of one-dimensiona consolidation it is not proposed to separate the process into volumetric and deviatoric components, but to treat it as a single process. Generalization might be attempted in terms of the effective stress ratio. In the treatments mentioned in terms of linear rheology, the most common assumption has been what amounts to an elastic volume component (spring) and a deviatoric component represented by a Maxwell element. The combination of these gives a rheological model of onedimensional consolidation consisting of a spring in series with a Kelvin, Christie (1964). More detailed considerations of volumetric and deviatoric behaviour have led to generalized models. Thompson (1965) concluded that both components were best represented by n Kelvins in series and hence that the combined behaviour is also given by a series of Kelvins. Schiff man et al. (1964) have come to a similar conclusion when they state, ‘An infinite number of parameters (continuous distribution) would provide a secondary curve which is linear in the logarithm of time ‘. Tan (1957) has proposed multiparameter models consisting of n Maxwell elements connected in parallel with gradual decoupling to represent structural disintegration as failure is approached. It is possible that observed soil behaviour, in requiring such large numbers of linear elements to describe it, is in fact non-linear. The treatment in terms of linear elements has been necessary because exact mathematical treatment is then possible. However, the mathematics become more difficult as the number of parameters increases and it becomes impossible to fit numerical values from experimental results. For solutions to be of any practical use they must involve a minimum of parameters. It is perhaps time to investigate the possibility of introducing non-linear terms involving the minimum of parameters necessary to describe the essential physics of the problem, and to produce sufficiently accurate numerical solutions on a computer. In developing a rheological model of the stress-strain-time behaviour of an infinitesimal element of the clay it is essential to consider in detail the physical mechanisms involved in the consolidation process. Since there is a wide variety of soil structures there must be a variety of mechanisms involved. In this Paper only two basic mechanisms are considered and it is suggested that each of these embraces a range of soil structure. The first mechanism involves shear failure and jumping of bonds in a highly redundant soil skeleton followed by a gradual relaxation to a new equilibrium, the rate of relaxation being governed by the viscosity of the adsorbed water layers. This mechanism is relevant to the majority of clays and to amorphous granular (colloidal) peat. The second mechanism involves the existence of at least two levels of structure, with the drainage of a micro-pore system into a network of coarser channels. This is relevant to clays with a packet structure and to fibrous peat. The viscous mechanism is considered in detail, and the micro-pore mechanism is considered briefly, with special reference to peat. VISCOUS

MECHANISM

OF

CONSOLIDATION

To treat the viscous mechanism of consolidation in detail it is necessary to consider the physical chemistry of the clay-water system and in particular the properties of the adsorbed water. In a detailed sense general agreement has not yet been reached, Rosenqvist (1959), Michaels (1959), Low (1960), Martin (1962) and Meade (1964). However, for the qualitative considerations required in the present case there is perhaps enough agreement to warrant consideration of a simplified mechanism of the deformation of clay during consolidation.

4

LAING

BARDEN

Clay st7wture

The structure of natural and artificial clays can vary from flocculated to dispersed (Lambe, 1953). The flocculated state implies a highly redundant cardhouse structure with the majority The dispersed state implies a more parallel of particle ‘contacts’ of the edge to face variety. orientation of platelets with fewer contacts and load being transferred by double layer stresses. The ideal uniform dispersed state considered by Bolt (1956)is rare, and usually the dispersed state occurs locally in packets with an overall random effect (Olsen, 1966). The typical structure under consideration is assumed to be highly redundant with the main type of contact, whether between individual platelets or packets, of the edge to face type. This is likely to give the most important creep effects according to Tan’s concept of the jumping of bonds. The arguments, being concerned mainly with the viscous retardation effect the adsorbed water exerts on relaxation to final equilibrium, would essentially apply to an ideal dispersed system. In this case there is little jumping of bonds, and consolidation involves the retarded approach of parallel faces through a viscous double layer with equilibrium being finally reached in terms of double layer stresses. Excluded from consideration are such untypical cases as cemented material and clays exhibiting collapsing structures (Lo, 1961). The charged surfaces of the clay platelets are surrounded by adsorbed water. The degree of order (orientation) of the molecular structure of this adsorbed water is greatest at the clay surface and gradually decreases with distance from the clay until it merges into free pore water. The effective thickness of the adsorbed layer depends on the chemistry of the claywater system and also on the specific property of the water under discussion. In the present treatment the relevant property is the effective viscosity of the adsorbed water, which decreases with distance from the clay surface, and increases with time due to thixotropy as will be discussed later. During a long period of secondary compression the clay structure will creep into a stable configuration with edge to face bonds developing as the particles approach through the highly viscous water. The ‘contact’ between particles may be mineral-mineral but it is more probably via a few molecules of highly ordered, virtually solid, adsorbed water. The resistance to movement developed at each contact is usually termed the bond strength, and this will increase with time due to thixotropy. After a creep process some of these bonds will be strong and others barely stable, giving in general a wide range of strengths. Leonards and Altschaeffl (1964) suggest that the range of bond strength will be small in undisturbed clays and large in remoulded clays. Because these bonds are viscous rather than rigid, provided there is no cementing, the clay skeleton is more compressible than the pore water. Thus on the addition of a new pressure increment to a fully saturated sample with the drainage closed, the entire increment will be balanced by an equal pore water pressure.

Yielding On opening the drain free pore water will flow from the sample and volume change must begin, deformation being essentially due to shear failures at interparticle contacts. AS the structure is highly redundant there will be a wide variety of normal and shear stresses at conIt is therefore unlikely that the material will tacts, as well as a wide range of bond strengths. exhibit a clearly defined yield point and it is suggested that the continuous viscosity transition implied in Fig. l(a), is more realistic than the Bingham yield behaviour of Fig. l(b). A similar view has also been expressed by Christensen and Wu (1964). AS shear stress develops at a contact there will be various degrees of ‘failure’, since the resistance of the bonds is of a viscous rather than a cemented nature:

LAING

6

BARDEN

NON-LINEAR_ SPRING.

Fig. 2 (left). Fig. 3 (right).

Structural

Proposed

Variation of effective viscosity non-linear

rheological

model of element

viscosity

Consider a contact being formed by two particles gradually approaching through their interfering adsorbed layers, the effective viscosity increasing markedly as fhe particles approach. As in all such processes the strain rate decreases progressively with time. At first the strain rates will be at A in Fig. 2 and because of the low effective viscosity the shear resistance will be T*. As the particles approach the strain rate must become very small, but because of the high effective viscosity the shear resistance rB will still be appreciable. The continuous effective viscosity transition illustrated in Fig. 2 is well known in rheological studies. Ostwald has introduced the term structural viscosity, which usually implies that the effective viscosity decreases with rising shear stress. Ostwald also used a power law to describe this behaviour as will be discussed later. As pointed out by Scott Blair (1949) such terms as thixotropy, structural viscosity, irreversible shear breakdown, false body behaviour and rupture, which attempt to describe phenomena that are difficult to distinguish, are rather controversial, since they appear to mean different things to rheologists studying different materials. Despite this, structural viscosity and thixotropy as defined here have been used in this treatment of the rheological behaviour of clay. DEVELOPlMENT

OF A RHEOLOGICAL

MODEL

To obtain a model of the stress-strain-time behaviour of the infinitesimal element it is necessary to consider a large enough sample of particles to be statistically representative of the structure of the clay, whether cardhouse or packet. Using the Terzaghi concept of film bond and solid bond referred to, the simple model of Fig. 3 has been proposed. The outer container is filled with water and the perforated piston represents the pore-water drainage properties of the element. The effective stress-strain-time behaviour of the skeleton is given by the spring connected in parallel with the dashpot, the spring being considered to represent solid bond and the dashpot film bond. After a long period of secondary compression when static equilibrium has been obtained, all load will be transferred by the spring as solid bond, with zero pore pressure excess, and the dashpot completely relaxed to give zero film bond. On application of a new increment of total stress A$ with the drain closed, the spring and the connecting rods to the dashpot (representing the skeleton with no bonds yet broken) are more compressible than the pore water and hence Au = Op.

PRIMARY

AND

SECONDARY

CONSOLIDATION

OF

CLAY

AND

7

PEAT

The consolidation process is begun by opening the drain, allowing pore water to tlow from the element. The ensuing shearing action causes the jumping and dislocation of bonds and the increment of total stress is now shared as A$ = Ao’+$,+N where Ap

.

.

.

.

.

.

.

.

(1)

increment of total stress

AU’ increment of solid bond (spring) P” l.4

viscous film bond (dashpot) pore pressure excess

The increment of solid bond in the early stages is due to increased transfer of load through unbroken contacts and in the later stages it is due mainly to new contacts forming. When the pore pressure falls to zero at the end of the primary stage, secondary consolidation is governed by the rate of transfer of film to solid bond as the dashpot gradually transfers load to the spring. Finally after considerable time the particle contacts will cease creeping and attain stable equilibrium, with all load again transferred via solid bond in the highly adsorbed water. The consolidation process is now over except for a possible continued increase in local bond strengths due to thixotropic action. Com$onents of the model Spring element. This represents the compressibility of the element when it reaches final equilibrium, with all load transferred as solid bond. Under these conditions the overall behaviour of a sample of clay is equivalent to that of the element. The typical void ratioeffective stress plot indicates clearly that the spring in the model should be non-linear, with compressibility decreasing as effective stress increases. Dashpot element. There are two major factors to be considered: structural viscosity and thixotropy. Ostwald showed that structural viscosity can be described adequately by means of a power law. The behaviour of the infinitesimal element of clay is the resultant of the inThis requires a generalized power dividual behaviour of a wide range of individual contacts. law such as the polynomial series of the form i =

:

A,,T”

.

.

.

.

.

.

.

.

(2)

n-1

with n an odd integer to avoid sign ambiguities. viscosity the effective viscosity p is given by

By analogy with the equations of linear

1 - = i = ,i, A,,?- l cc 7 If the coefficients A,, are chosen properly, e.g. A,, > 0, it can increase in shear stress as required of structural viscosity. The effect of thixotropy is to increase the effective viscosity interesting to note that Schiffman (1959) proposed the general

.

.

.

.

.

.

.

(3)

be seen that TVdecreases with p as a function of time. viscosity law

It is

. . . (4) J = %i05Lexp (c,T)+m$09n exp (-CJ) CL The form of the relation between i, and 7 during a consolidation process can therefore be expected to be as shown in Fig. 4. St Venant element. Certain writers have considered that there is a threshold stress which Hence, in accordance with Bingham yield bemust be exceeded before yielding can start. haviour, St Venant elements have been introduced into a number of models. As discussed

LAING

8

ACTUAL PATH

BARDEN

Fig. 4.

Thixotropic

increase of effective

viscosity

earlier a continuous viscosity transition is considered the more likely physical behaviour and at present no St Venant element is thought necessary in the proposed model. This implies a void ratio-effective stress relation independent of the magnitude of the load increment. Proposed simplijed

model

Expressions such as (3) and (4) contain too many parameters to be of practical value in the present treatment and the following simplifications are introduced. It is considered that the major variation of effective viscosity during a consolidation process is caused by the highly non-linear structural viscosity, with thixotropy exerting a relatively minor effect. It is therefore essential to incorporate structural viscosity in the rheological model in a proper quantitative manner, whereas the effect of thixotropy may be introduced by intuitively modifying the predicted behaviour. In the mathematical treatment of consolidation the microscopic relationship between 7 and 9 is not of direct use at the macroscopic scale and the viscosity law must be transformed. This problem was originally considered by Taylor (1942). In one-dimensional consolidation 1; is conveniently replaced by rate of change of void ratio -se/at and 7 is replaced by an equivalent vertical stress, the viscous resistance p,. 2 A,T~ is thus most usefully expressed as -2ej2t = : B,p; and the n=1 R=l simplest of such relations is the single term -se/at = BP:. In this paper this is used as The series i, =

p, = b (-,)“’

.

.

.

.

.

.

.

.

with n an odd integer. It must be emphasized that equation (5) is purely empirical and that the viscosity parameter b has complex dimensions depending on the value of n. It is apparent that for a given clay b will increase with effective stress as the particles become more densely packed; b will also vary with time clue to thixotropy, giving the form of behaviour illustrated in Fig. 4. However, here b, k and m, will be treated as constant. The non-linear nature of the spring in Fig. 3 can easily be introduced. However, previous analyses (Barden and Berry, 1965) have indicated that this non-linearity is relatively unimportant, and hence to minimize the number of parameters involved in the mathematical treatment of the model it is assumed here that the spring is linear. Similarly the permeability of the soil is treated as constant. In summary, the model has been simplified to contain a linear spring, and a non-linear dashpot behaving according to equation (5). This non-linear Kelvin represents the behaviour of the skeleton when loaded by effective stress, and has been placed inside the Terzaghi pot which accounts for the hydrodynamic lag. The complete model, shown in Fig. 3, is considered to represent the behaviour of an element of saturated clay and must now be integrated subject to the boundary conditions of one-dimensional consolidation.

BRIMARY

AND

SECONDARY

CONSOLIDATION

INTEGRATION

OF

CLAY

AND

9

PEAT

OF ELEMENT

Barden (1965a) gives a detailed treatment of the method of solution and the following brief derivation is mainly to introduce parameters and equations used in subsequent sections. The relation between total and effective stresses is given in equation (1) Ap = Ao’+pV+u

.

.

.

.

.

.

.

.

(1)

with p,, given by equation (5). If 9 is the degree of consolidation, measured by the comPutting h = 1 -# pression of the linear spring of compressibility a, then in (1) do’ = #Ap. pore pressure zt = u/Ap gives AU’ = (I- Il)Ap and se/at = aApah/at. With a dimensionless in equation (1) givesdp = (1 - X)Ap+ and a dimensionless space variable z = ir-/H, substitution b( -aAadpah/8t)1’n+uAp. Hence

(h-u)”

.

= -g

.

.

.

.

.

.

s

which defines a dimensionless

time factor T =&‘-Q S abn

The equation

of continuity

(7)

**.*.**.*

of mass is k 3% --=-yw 822

1

ae

l+eat

.

’

’

’

’

.

*

.

.

.

.

.

.

.

-

(81

-

(9)

Making dimensionless

a% -ah g-p=ar which defines the Terzaghi

It has been found convenient

.

time factor T = 41 2 +e)t . . . . wH to define the dimensionless parameter +=

Hv

.

.

.

.

*

(10)

cb”

*..... * (11) s Equations (6) and (9) have been integrated where c = k( 1 + e)/rw is a measure of permeability. for the boundary conditions of one-dimensional consolidation using numerical methods and solutions are given in Figs 5 and 6. These solutions have been confirmed by Poskitt (1967). The basic deformation behaviour of the skeleton when subjected to an increment of effective stress is given by direct integration of equation (6) with u = 0. This gives

h = [(a-l)T,+l]l’(r-“’

.

.

.

.

.

.

.

(12)

which is also the drainage boundary equation. The process is governed It is useful to consider certain aspects of the theoretical solution. Terzaghi time factor, by two dimensionless time factors, T and T,. T, the conventional equation (lo), governs the rate of pore pressure dissipation and hence dominates the primary stage. T,, equation (7), governs the structural viscosity of the skeleton and dominates the secondary stage. It is convenient to work in terms of T and R where R = TIT,, equation (11). On The effects of parameter T are well known, but R requires preliminary consideration. the basis of fitting theory with experiment (Berry, 1965), it is found that n = 5 is a common value for many of the clays tested and it has been assumed for convenience, giving R = of cb5/H2Ap4. It is clear from Figs 5 and 6 that the greater R is the greater the importance secondary consolidation will be, and that the limiting case R = 0 corresponds to the conventional Terzaghi solution, with all consolidation as primary. If c/H2 is large, because of high permeability or a thin sample, then the primary stage is rapid and, since viscous effects are dependent on rate of strain, secondary effects will dominate.

LAING

BARDEN

----------SECONDARY

,TERZAGHl

R=O

,_ 0.1

001

TIME

Fig. 5 (above). Fig. 6 (below). Fig. 7 (below right).

Theoretical

Theoretical

.IU

I FACTOR

Theoretical

TIME

T

rates of settlement

rates of dissipation

compression

.^_

I””

of mid-plane

pore pressure

of skeleton under increment

FACTOR

T

of effective stress

PRIMARY

AND

SECONDARY

CONSOLIDATION

OF

CLAY

AND

PEAT

11

Put in another way, if the primary stage is rapid the creep is left undeveloped, whereas if it is slow there will be little undeveloped creep to follow. The viscosity parameter b is responsible for the different amounts of secondary consolidation observed with different pore fluids and also the effect of temperature. Since b can be considered to increase thixotropically, secondary effects will be greatest after a long period of rest. Also b must increase with effective stress and decreasing void ratio since the average separation of the particles is then less. Nielsen (1966) has given evidence to suggest that b may be directly proportional to p in some clays. Thus it can be seen from the term b5/Ap4 that secondary effects are particularly sensitive to pressure increment ratio A$@, and will dominate when A$/$ is small. The physical reason for the important effect of Ap is clearly the high nonlinearity of the viscosity law, Fig. 2. A large A$ in causing a high rate of strain will develop only a relatively small viscous resistance p,, which will be masked by the large increment in pore pressure Au in equation (1) leading to Terzaghi behaviour. A small Ap in causing a low rate of strain will develop a value of 9, which may be comparable with A$, and hence viscous effects rather than pore pressure will dominate in equation (1) and in the limit the process ceases to be described by the diffusion equation (9). This reasoning does not apply if the viscosity law is linear (n = l), and hence the term A$ vanishes from R as in Taylor’s Theory B. It is suggested that the major factors at present known to influence one-dimensional secondary consolidation are accounted for in the dimensionless parameter R. This will be amplified later considering detailed experimental evidence. There is, however, one possible factor that may have to be introduced. The time factor T, does not contain H and this implies that the basic creep behaviour of the skeleton as illustrated in Fig. 7 is independent of H. This implicit assumption must be seriously questioned in the light of the theoretical work by Marsal (1965) but cannot be modified at present, since there is no experimental evidence available. CRITICAL

REVIEW

OF SOME

RHEOLOGICAL

MODELS

The basic differences between the various rheological models can be seen most clearly by comparing the predicted deformation time behaviour of the skeleton loaded by a step increment of effective stress, since the Terzaghi pot representing the hydrodynamic lag is common to all models and obscures the basic behaviour of the skeleton. The behaviour of the

IIC

0.f

0.t A 0.4

0,:

0

12

LAING

BARDEN

non-linear Kelvin representing the soil skeleton in Fig. 3 is given by equation (12) andis plotted in Fig. 7 for various values of n. 1. Taylor and Merchant (1940), Ishii (1951), Tan (1957), Gibson and Lo (1961) and Florin (1961) have proposed a spring in series with a Kelvin to represent the behaviour of the skeleton. The top spring is to represent primary consolidation and the Kelvin the retarded development of secondary consolidation. This model is too simple to give an accurate representation of the consolidation process. Because of the linear viscosity of the dashpot it does not give the characteristic secondary consolidation linear with log time, and takes no account of the dominant effect of load increment ratio ApIp. An important point is the need for a top spring to provide a primary stage, and this is discussed in the next section. 2. Tan (1957), Schiffman et aZ. (1964) and Thompson (1965) have studied the volumetric and deviatoric systems separately and proposed similar multiparameter models for oneThese models are equivalent to a large number of Kelvins condimensional consolidation. nected in series, with the top Kelvin degenerated to a spring to provide a primary phase. As discussed previously, multi-parameter linear models are often attempting to describe actual non-linear behaviour. That this is not necessarily so will be seen later. However, in the present case structural viscosity is clearly the seat of strongly non-linear behaviour. This has been introduced to provide Consider the (primary) top spring in these models. the essentially instantaneous deformation of the skeleton under effective stress. Thompson (1965) introduces the top spring to provide an initial linear relation between settlement and Schiffman et al. (1964) use the top spring to define their primary phase which leads root time. to large pore pressures often occurring in their secondary phase. Consider the behaviour of the proposed non-linear Kelvin as given in Fig. 7. Certain numerical values will be assumed in order to present a numerical example. Taking the typical value of n = 5 then Ts = Ap4t/ab5. The skeleton is assumed to be initially consolidated under an effective pressure p = 10 lb/sq. in. when the product ab5 = IO2 lb/sq. in4 min. Consider the skeleton to be loaded by effective pressure increments of 1, 2, 5 and 10 lb/sq. in. giving T, = 0.01 t, T, = 0.16 t, T, = 6.25 t and Ts = 100 t for the respective values of A$/$ = 0.1, 0.2, 0.5 and 1.0. Plotted in terms of true time t min, the n = 5 curve in Fig. 7 gives for the chosen A$/$ the values plotted in Fig. 8. It can be seen that the non-linear Kelvin not only gives ‘immediate’ compressions, but that the relative proportion of immediate to final compression is dependent on the test condition APIP. The effect of Ap/p on the rate of compression of the skeleton illustrated in Fig. 8 is clearly the basic cause of the behaviour predicted in Fig. 5. 3. Taylor (Theory B, 1942) was probably the first to postulate a non-linear viscosity. This is seen in his Figs 38 and 62. Because he had no high speed computer to solve mathematically intractable non-linear equations, Taylor was forced to idealize the non-linear behaviour as linear Bingham behaviour [Fig. I), but it is clear that he did not accept the real existence of the implied yield stress. The model he treated contained a simple Kelvin and it is therefore a special case of the proposed model in Fig. 3 with n = 1. It can be seen that with n = 1 the parameter R reduces to Taylor’s parameter J and, characteristic of linear solutions, the important effect of Afi is lost. Based on the theory of rate processes Murayama and Shibata (1959, 1964) and Christensen and \Vu (1964) have arrived at models containing non-linear dashpots obeying exponential (sinh) laws. This is clearly an alternative to the power law for describing the behaviour shown in Fig. 2, but appears to be less simple to manipulate. Rosenqvist (1966), after consideration of the viscous properties of the adsorbed water, has proposed a non-linear dashpot in which the effective viscosity exhibits an exponential relation with stress. Folque (1961) has introduced a non-linear dashpot which he says corresponds to a number of linear dashpots of various viscosities connected in series, but he does not state the law. Dunn and Nielsen (1966), like the Author, have adopted the Ostwald power law to describe structural viscosity.

PRIMARY

AND

SECONDARY

CONSOLIDATION

OF

CLAY

ASD

13

PEAT

COMPRESSION

i 0.1

I

IO TIME:

Fig. 8.

Theoretical

effect of Ap/p

I

IO’

DAY

IO’

MIN

on rate of compression of skeleton

and ‘immediate’

compression

Vialov and Skibitsky (1961) and Raymond (1965) have proposed non-linear dashpots in which the viscosity is a function of time. This takes account of thixotropy but not of the more important structural viscosity discussed earlier. 4. A number of models have introduced a St Venant element to represent a bond, or a yield or threshold stress. Murayama and Shibata (1959, 1964) have assumed a constant sliding resistance, which corresponds to a low threshold stress in Fig. 2. Made1 (1957) and Folque (1961) have introduced simple St Venant elements to represent bonds. Schmid et al. (1960) have proposed a complex St Venant element which they state represents a plastic resistance which is an unspecified function of time. Rosenqvist (1966) has proposed a bond which must be exceeded before flow can begin, and subsequently exerts a resistance which depends on the rate of strain according to F = a/(1 +p). While it is now widely accepted that the dashpots in these rheological models are highly non-linear due to structural viscosity, the concept of threshold stress is much more controversial. It is suggested that much of the behaviour which in the past has been interpreted as bond (Haefeli, 1953 ; Geuze and Tan, 1954 ; and de Jong and Geuze, 1957) is in fact the result of the highly non-linear viscosity transition of Fig. 2. There is accordingly a growing body of opinion which disputes the concept of Bingham behaviour (Schiffman, 1959). Similar problems exist in applying plasticity theory, when plastic strain occurs at all levels of stress, and a certain magnitude of strain must be defined as constituting yield in studies of work hardening yield surfaces (Drucker, 1964). At present it is proposed to represent the essential behaviour in as simple a manner as possible and to discount the Bingham concept. If further study reveals the indisputable existence of important threshold stresses then the model will be generalizecl by the introduction of some form of St Venant element. It would then have to be decided whether this element should give a constant resistance independent of deformation, or a variable resistance as proposed by Schmicl et al., or by Rosenqvist.

14

LAING EXPERIMENTAL

BARDEN

ASSESSMENT

OF THEORY

Because of the obvious difficulties associated with testing an element of saturated clay, the main evidence in assessing the proposed model must be obtained from a comparison of the behaviour of saturated clay in the one-dimensional consolidation test and that predicted from integration of the model under the reIevant boundary conditions. A series of tests on undisturbed and remoulded clay and peat is being conducted at Manchester University in the new consolidation cell (Rowe and Barden, 1966), and in view of the encouraging results obtained to date (Berry, 196.5) it is hoped that these will eventually provide a quantitative assessment of the theory. However, an equally useful demonstration of the general validity of a theory is to relate it to the published experimental results of various workers. Because published results are rarely in a complete enough form to allow the fitting of numerical values to the viscosity parameters such a wide ranging comparison must be mainly qualitative. Elemental behaviour

The study of elemental behaviour requires the absence of the hydrodynamic lag. This is possible in the case of unsaturated clays, although the viscous behaviour of the skeleton may be modified to some extent by the absence of part of the free pore water. For partly saturated clays at degrees of saturation less than 90% the capillary suction prevents the pore water pressure becoming positive, and the only fluid to be expelled from the clay during compression of the soil is air. Because the air voids are interconnected to give a very high air permeability the retardation of the process due to the dissipation of air pressure will be negligible. The rate of compression is therefore controlled by the viscous creep properties of the skeleton and its adsorbed water (Yoshimi and Osterberg, 1963; and Barden 196513). Under these conditions the overall behaviour of the sample is equivalent to that of an element of the skeleton, i.e. the non-linear Kelvin in Fig. 3, and should be directly governed by equation (12). Thus from the form of the time factor 7’, (equation 7) the rate of compression should

DERWENT

1-

--

--

CLAY

PRIMARY SECONDARY

I

1

“M’O

I

\

j \ \

\\\\

.

0,

I

TIME Fig.

9.

Experimental

~

-1

-.

10

FACTOR

-. L \

I\

‘\ --._-_

100

T

effect of H and Ap/p on rates

of settlement

,000

PRIMARY

AND

SECONDARY

CONSOLIDATION

OF

CLAY

AND

PEAT

15

be independent of the thickness of the sample H but greatly influenced by Apip. Comparison of Yoshimi and Osterberg’s Figs 8 and 11 provides excellent support for the theory and explains fully their conclusion No. 3. It therefore appears that the proposed rheological behaviour of the skeleton (equation 12) provides a promising theoretical basis for predicting the rates of compression of partly saturated clays at all but high degrees of saturation (again excluding collapse behaviour). Similar elemental evidence can be obtained from the compression behaviour of freeze dried clays reported by Leonards and Altschaeffl (1964). Their .Figs 14, 15 and 16 also appear compatible with the theoretical prediction of Fig. 8 and confirm the dependence of ‘immediate ’ compression on A$/$. Nevertheless, much longer periods of creep would be necessary to assess the exact extent of this agreement. Effect of pressure

increment

ratio

Since this term raised to a power appears in R, its effects on the consolidation process can be expected to be marked. This has been confirmed in both rate of settlement and rate of mid-plane pore pressure dissipation observations by a number of workers, for example the test results of Berry (1965) plotted in Figs 9 and 10, which should be compared with the theoretical results of Figs 5 and 6 respectively. It can be seen from the theoretical results in Fig. 5 that high Ap/p gives Leonards and Girault (1961) type I settlement curves and that low A$/$ gives their type III curve. If c, values are obtained from the settlement plots by the usual curve fitting procedures low A#/$ will result in a low c, and vice versa. This is confirmed by Newland and Allely (1960) in their Fig. 1, by Taylor (1942) in his Fig. 24, by Hamilton and Crawford (1959) in their Table 1, and also in Fig. 9 of this present Paper. These c, values clearly lead to anomalous deduced permeability values. It can be seen from the theoretical results in Fig. 6 that the effect of A$/$ on mid-plane

TIME Fig.

10.

Experimental

effect

FACTOR

of H and Ap/p

5

on rate of dissipation

of U,

16

LAING

BARDEN

pore pressure is particularly strong. This has been confirmed by a number of workers, for example Hansbo (1960) in his Fig. 19. The observed experimental behaviour depends on the control at the drainage boundary. If the drain can be closed then the full build up of pore pressure Au = Ap can be obtained before beginning the consolidation process and the observed behaviour is as shown in Fig. 10. However, if the drain is always open, as in the majority of oedometer tests, then the behaviour for large values of R is as shown by Thompson (1965) in his Fig. 3 and by Northey and Thomas (1965) in their Fig. 2, and is therefore not always caused by slow response of the pore pressure measuring equipment (Whitman et al., 1961). It can be seen from the theoretical behaviour in Figs 5 and 6 and the experimental results of Figs 9 and 10 that for low values of Apip the mid-plane pore pressure dissipation is accelerated while the settlements are retarded. Hence the discrepancy between the respective fitted c, values increases as shown by Leonards and Girault (1961) in their Table 4. This also explains their conclusion Xo. 6 that the rate of dissipation of pore pressure can be reliably predicted from Terzaghi theory provided A$/$ is sufficiently large (i.e. R approaches zero). E#ect of sample thickness H

There is little experimental evidence of the effect of sample thickness on secondary consolidation. Leonards and Altschaeffl (1964) and Brinch Hansen (1961) state that the effect exists but provide no direct experimental evidence. Newland and Allely (1960) conducted some tests to investigate this point but they used a load increment ratio A$/$ = 10 and this completely masked the effect of H on R. The only clear experimental evidence appears to be curves A and B of Figs 9 and 10, which results have since been confirmed on a number of undisturbed and remoulded clays. E$ect of the viscosity parameter b

The value of b reflects the electro-chemical environment of the clay. Alteration of the pore fluid will alter b and this will govern the amount of secondary compression. Thus if a pore fluid with negligible viscosity could provide a value of b close to zero there would be only small secondary compression, as in sands. Thus while the Author agrees with Leonards and Girault (1961) that the mechanism of secondary compression is fundamentally one of jumping of bonds, it is the rate at which this adjustment proceeds which controls the relative amount of primary and secondary. Thus while there can be little secondary without jumping of bonds, similarly there can be little secondary if there is no viscous adsorbed layer. The seat of secondary lies in the combination of the two. The experiments of Leonards and Girault (1961) and of Kaul (1963) show the effect of the viscosity of the adsorbed pore fluid and of temperature on the parameter b and hence on R. The average separation of the particles as measured by the void ratio also influences the value of b, with b increasing as void ratio decreases. This is involved in the effect of dp/p. It can also be seen in the results of Thompson (1965) in his Fig. 3. He produced three types of sample classified as high, intermediate and low initial void ratio. When tested under the same conditions the low void ratio samples gave the greatest secondary effects. The effects of thixotropy can be considered to give an increase in the value of b with time, as discussed earlier. Thus long periods of rest and long increment durations result in a high value of b developing. The deformations caused in a subsequent consolidation process result in only partial remoulding, and hence much of this thixotropic increase persists throughout the subsequent consolidation process leading to increased secondary effects. This is a known experimental fact and is particularly clearly shown in the results of Northey and Thomas (1965) and Thompson (1965). It is often suggested that following an increment of short duration more secondary must develop in the next increment, but the present theory and experimental results indicate that this is not generally so.

PRIMARY

Form

of the viscosity

AND

SECONDARY

CONSOLIDATION

OF

CLAY

AND

PEAT

17

law

While there is no evidence that the power law provides the best empirical description, there is some evidence for the non-linear behaviour shown in Fig. 2. Similar curves have been deduced from experimental data, by Taylor (1942) in his Fig. 62 in tests on clay, and by Schroeder and Wilson (1962) in their Fig. 6 in tests on peat. By a method of curve fitting, Nielsen (1966) has related the power law parameters b and n to the mineralogical properties of the clay. b was shown to increase with effective stress and n was a constant for a given clay. The experimental data of the rate process workers such as Murayama and Shibata (1964) and Christensen and Wu (1964) support the general shape of the curve in Fig. 2 although they describe it in terms of a sinh curve rather than a power law. Of particular interest is the close resemblance between the postulated relation of Fig. 4 and the experimentally deduced relation between aejat and viscous resistance given by Schultze and Krause (1964) in their Fig. 10. Evidence

joy threshold

stress and quasi-preconsolidatiolz

pyessuye

Certain experimental observations such as the slow build up of pore pressure reported by Northey and Thomas (1965) suggest the existence of a bond. However, as discussed above this behaviour is compatible with the theoretical predictions of Fig. 6. Perhaps the most convincing evidence for bond development has been that of Leonards and Ramiah (1959) who showed that after long periods of rest and under a small ApIp a quasipreconsolidation pressure was evident. This has also been confirmed by Thompson (1965) and Raymond (1966). It may, however, be possible to account for this behaviour in terms of the proposed model of Fig. 3. Long periods of thixotropic increase of b in conjunction with a small A$ will result in large values of the parameter R and, according to Fig. 5, in low rates of deformation. Unless the increment duration was greatly extended then the full deformation would not be developed and an apparent preconsolidation pressure would result. Taylor (1942, p. 133) offered a similar interpretation of the tests of Langer (1936). Taylor states that possibly in natural soils of great structural strength there may be resistance that is independent of speeds of compression, but suggests that even this ‘bond’ might prove to be viscous if consideration were given to rates of deformation of a sufficiently small order of magnitude. The evidence on the effect of the magnitude of the applied load increment on the compressibility of clay is rather conflicting and at present there is no conclusive evidence to necessitate the incorporation of a St Venant element in the proposed model of Fig. 3. Further investigation of this controversial point is required. Evidence

for a top spying igz the rheological

model

It was shown on theoretical grounds and illustrated in Fig. 8 that the proposed non-linear model not only gives an ‘immediate’ compression, equivalent to the effect of the top spring in the linear models of Tan (1957), Schiffman (1959) and Thompson (1965), but that this immediate compression is also a function of the test conditions of A$/$. Experimental confirmation is given in the results of Yoshimi and Osterberg (1963) and Leonards and Altschaeffl (1964). Thompson (1965) introduced a top spring to provide an initial linear relation between settlement and root time, as is commonly observed in standard consolidation tests on saturated samples. In such tests with ApIp = 1 the behaviour of the clay generally corresponds to a low value of R and hence from the theoretical values of Fig. 5 replotted in Fig. 11 as h versus 1/T it can be seen that the settlement-root time plot is essentially linear. However, if a test is run with a small A$/$ then R will increase and according to Fig. 11 the root time plot will show a marked curvature. This is confirmed by the experimental results of Taylor (1942), Thompson

18

LAING

Fig. 11.

Theoretical

BARDEN

compression

against square root of time

(1965) and Berry (1965) and is not necessarily the result of imperfect drains as demonstrated by Newland and Allely (1960). It can therefore be seen that the use of a top spring is an artificial concept, since in the same clay it can appear or vanish according to the effect of A$/$ on T, or R. It is suggested that this concept of dividing overall compression into a ‘primary’ or essentially immediate portion, and a retarded or ‘secondary’ portion is not really fundamental. As indicated in Figs 7 and 8 the deformation is essentially continuous and so the time selected to measure the ‘immediate’ compression is arbitrary, the result also depending on such factors as A&/p and so on. From this it is suggested that the present simple definition of primary and secondary consolidation should be retained. It is not an ideal definition, but it is difficult to produce a truly fundamental alternative. Coeflcient

of secondary compression c,

This parameter is the slope of the essentially linear secondary tail of the void ratio versus log time plot, measured in the units of void ratio change per log cycle of time. It must be noted that the secondary curves in Fig. 5 are only approximately linear with log time indicating that the model, while essentially valid, is still over simplified. However, observed

PRIMARY

AND

SECONDARY

CONSOLIDATION

OF

CLAY

AND

PEAT

19

secondary compression is not always linear with log time as indicated by many published results, including Leonards and Ramiah (1959) and Lo (1961). Discussion has centred on the variation of c, with such factors as A$, 9 and e and no general agreement has been reached. A more relevant parameter would appear to be c,/Ap and this has been studied by Leonards and Girault (1961) and Madhav and Sridharan (1963). Leonards and Girault in their Fig. 2 show that c,/Ap increases for small A$/$ and small p and considered this behaviour to be a deterrent to the use of rheological models. Madhav and Sridharan in their Fig. 15 confirmed these observations, which are seen to be in general agreement with the proposed theory (Fig. 5). Discussion has also centred on whether the scaling law for secondary compression depends on Hz, H1.5 or H. Since H appears in the theoretical results of Fig. 5 in both parameters T and R the effect of H is complex, and the scaling law cannot always be stated in as simple a form as previously attempted.

MICRO-PORE

MECHANISM

OF CONSOLIDATION

One possible cause of a prolonged ‘secondary’ tail is a marked decrease of permeability during a consolidation process. A theoretical treatment including large decreases in permeability during the consolidation of partly saturated clay has been given (Barden, 1965b), and while this gives apparent secondary settlement behaviour on a semi-log plot, the pore pressure values show that it is in fact all primary consolidation. This suggests the possibility of a micro-pore structure being responsible for secondary effects ; for example a domain or packet structure containing micro-pores, interwoven by a network of macro-pores. This concept can be extended to include three or four levels of structure, extending from fissured clay down to even finer sub-microscopic structures within the individual packets. Similar mechanisms have been suggested for peat by Adams (1965) and Wilson et al. (1965) and for clays by de Jong and Verruijt (1965). The soil can be looked upon as a typical clay, but instead of the individual clay platelets being incompressible solids they are porous and compressible packets. The primary stage is the usual Terzaghi process governed by the rate of dissipation of pore pressure in the network of macro-pores, this being the pressure registered by any practical measuring device. As this pore pressure falls load is transferred to the packets, and secondary consolidation is caused by simple Terzaghi consolidation processes taking place in the micro-pores of the packets as they drain into the macro-pore network; the rate of consolidation then being independent of the overall sample dimensions. For rheological models it is necessary to represent the deformation behaviour of the packets in terms of springs and dashpots. As is already known, the Terzaghi consolidation process can be represented by a series of Kelvin elements (Wahls, 1962) ; thus if secondary consolidation is the result of simple linear Terzaghi processes taking place independently in a large number of separate micro-systems (packets) then the resultant effect, being equivalent to an infinite series of Kelvins, could be a secondary compression linear with logarithm of time. To describe the entire process the infinite series of Kelvins must be placed inside a Terzaghi pot representing primary pore pressure dissipation in the macro-pores, and this model integrated for the boundary conditions of one-dimensional consolidation. It is interesting to note that de Jong (1966) from consideration of an interconnected network of pores of various sizes also arrived at a mathematical model which is the equivalent of an infinite series of Kelvins. As stated in connexion with the similar multi-Kelvin models of Tan (1957), Schiffman et al. (1964) and Thompson (1965) it is possible that such multi-parameter linear models may in fact be an attempt to describe true non-linear behaviour. However, this cannot be presumed to be the case unless the physical basis of the non-linearity can be demonstrated clearly. For the viscous mechanism of consolidation, structural viscosity was firmly established as the cause of

20

LAING

BARDEN

a marked non-linearity (see Fig. 2). However, in the present case, if the consolidation of the micro-pore system is accepted as an essentially simple Terzaghi process then it is in fact linear. One way to distinguish between the two mechanisms would be to measure the effect on the process of the test conditions Apip and stress ratio uJu~. The viscous mechanism being based on shearing action would be accentuated by a high value of a1/u3and being highly non-linear would be influenced greatly by A$/$. On the other hand a simple micro-pore mechanism However, if the micro-pore beshould not be influenced greatly by either of these factors. haviour is complicated by a varying permeability, and hence becomes non-linear, then Ap/p will again exhibit an effect. Adams (1965) proposed that secondary consolidation of peat was controlled by the permeability of the micro-pores. He inferred from the permeability of the macro-pores that this permeability varied with sample thickness according to h/K, = (H/H,)“. He also assumed that in the expression for Darcy’s law dH1d.t = ki the hydraulic gradient i remains constant. Combining these two expressions H becomes proportional to W -c) which gives the same long term behaviour as equation (12), plotted in Fig. 7. Thus the former expression is due to a non-linear permeability relation and the latter to a non-linear viscosity relation.

EXPERIMENTAL

BEHAVIOUR

OF PEAT

MacFarlane and Radforth (1965) studied the structural arrangement of peats and the physical processes taking place during loading using a microscope and photo-micrographic techniques. They describe two extreme peat types, amorphous granular and fibrous, and state that all gradations exist between them. The amorphous granular peat has a very high colloidal fraction with the majority of the It has been shown by Schroeder and Wilson water in an adsorbed rather than a free state. (1962) to exhibit ‘pseudo plastic’ behaviour which is in effect structural viscosity. The fibrous peat has an open structure with the interstices filled with a secondary structural arrangement of non-woody fine fibrous elements. Most of the water is classed as free or capillary water, rather than viscous adsorbed water. These descriptions indicate that peat provides excellent examples of both the viscous and However, peat is a more complex material than micro-pore mechanisms of consolidation. inorganic clay and may require consideration of such factors as a moving drainage boundary caused by large strains, and a greatly decreasing permeability as the macro-pores are compressed. The present solution is therefore likely to apply only as a first approximation, but nevertheless provides a useful theoretical framework for investigating peat behaviour. Because of the general qualitative agreement between the consolidation behaviour of clay and peat as revealed in a review by MacFarlane (1965), much of the experimental behaviour discussed in previous sections is relevant to peat. However, there are some experimental results on peat that merit separate consideration. Certain peats appear to give a secondary settlement linear with log-time that appears to extend indefinitely, although it must in fact cease eventually. This behaviour will require modification of the simple model of Fig. 3. Wilson et al. (1965) have given an interesting representation of the results of consolidation tests on peat by plotting log de/& against log t as in their Fig. 3, which separates the process into two stages. The theoretical results of Fig. 5 have been replotted in Fig. 12 as log a@T against log T and the similarity is clear. The variation caused by H in their Fig. 3(a) is obtained from the effect of H in the time factor T. The variation caused by A$ in their Fig. 3(b) is obtained from the effect of Ap on R. The variation caused by initial void ratio in their Fig. 3(c) is obtained from the effect of b on R, but it is not clear in this case why the experimental curves merge at large time. While the above suggests that the theory provides a good qualitative agreement, the exact quantitative agreement has not yet been checked for peat.

PRIMARY

AND

SECONDARY

CONSOL

DATION

OF

CLAY

AND

PEAT

21

22

LAING

BARDEN

In a revealing set of tests on clay and peat, Helenelund (1951) cut up identical samples after various periods of consolidation and measured the distribution of void ratio along the vertical axis of the sample. The theoretical distributions (isochrones) plotted in Fig. 13 are confirmed, particularly by the experimental observations on undisturbed peat presented by Helenelund in his Fig. 39 which provides good evidence of the relevance of the theory to peat. CONCLUDING

REMARKS

A number of recent treatments of the rheology of clay and peat have independently arrived at a multi-parameter linear model consisting of a series of Kelvins. This raises the question of whether such models are attempting to represent complex linear behaviour or a segment of non-linear behaviour. This can be answered in a particular case only after a detailed examination of the essential physics of the process. A mechanism of consolidation of particular relevance to fibrous peat involves the drainage of a system of micro-pores into a system of coarser channels and leads to a multi-parameter model. The basic physics of this process has not yet been established properly and no solution is offered. The dominant viscous mechanism governing the consolidation of the majority of clays and colloidal amorphous granular peats has been considered in detail and described in terms of structural viscosity and thixotropy. A simple non-linear model has been arrived at and integrated for the boundary conditions of one-dimensional consolidation. The results give encouraging agreement with a wide range of published experimental behaviour of both clay and peat. The non-linear Kelvin model of the skeleton can be applied without integration to partly saturated clay where the pore air pressure dissipates rapidly, and provides a simple theoretical basis for predicting the compression-time behaviour. A critical review of a number of rheological models of clay behaviour suggests that the concept of a St Venant element representing a bond or threshold stress requires further detailed investigation. Certain experimental evidence supports the existence of a quasi-preconsolidation pressure and the dependence of the void ratio-effective stress relation on the magnitude of the pressure increment. It is possible that some of this behaviour can be explained in terms of the marked non-linearity of the structural viscosity. It remains to determine, from experiments allowing sufficient time for all creep to develop, for which materials and under which test conditions an important threshold stress exists. After a comprehensive series of tests in both a special oedometer and the triaxial apparatus Thompson (1965) concluded that his results could be explained best in terms of non-uniform deformation behaviour caused by the modification of the structure by high pore water gradients In the sense that the non-linear structural viscosity in the region of the drainage boundary. behaviour illustrated in Fig. 2 implies a low effective viscosity in the region of the drainage boundary where strain rate is high, and a higher viscosity at the impermeable mid-plane, the Author agrees with Thompson ; but does not attribute these differences to pore water gradients. ACKNOWLEDGEMENTS

The Author gratefully acknowledges the help derived from discussions with Mr P. L. Berry, Dr T. Poskitt and Mr W. B. Wilkinson. REFERENCES ADAMS, J. I. (1965). The engineering vol. 1, p. 3. Consolidation of BARDEN, L. (1965a). Consolidation of BARDEN, L. (1965b). BARDEN, L. & BERRY, P. L. (1965). Engrs 91, SM 5, 15.

behaviour

of a Canadian Muskeg.

Proc. 6th Int. Cc+

Soil Me&.,

clay with non-linear viscosity. G&technique 15, No. 4, 345. compacted and unsaturated clays. Gdotechnique 15, No. 3, 267. Consolidation of normally consolidated clay. Proc. Am. Sot. civ.

PRIMARY

BERRC;[~~‘.‘.L. (1965). BRINCH HA&EN,

AND

SECONDARY

Primary

J. (1961).

and secondary

consolidation

A model law for simultaneous

5th Inf. Conj. Soil Mech., vol. 1, p. 133.

BoLTN~G~ lX6.(1956).

CONSOLIDATION

Physico-chemical

OF

of clay.

CLAY

AND

primary and secondary

analysis of the compressibility

PEAT

M.Sc. thesis, University consolidation.

of pure clays.

23 of ManPTOC.

Ge’otechnnique 6,

CHAPLIN, T. K. (1963). Discussion of paper by Wahls (1962). Proc. Am. Sot. civ. Engrs 89, SM 3, 193. CHRISTENSEN,R. W. & Wu, T. H. (1964). Analysis of clay deformation as a rate process. Proc. Am. Sot. civ. Engrs 90, SM 6, 125. A re-appraisal of Merchant’s contribution to the theory of consolidation. CHRISTIE, I. F. (1964). Gtotecltnique 14, No. 4, 309. CRAWFORD, C. B. (1964). Interpretation of the consolidation test. Proc. Am. Sot. civ. Epzgrs 90, SM 5, 87. DE JONG, G. D. J. & GEUZE, E. C. W. A. (1957). A capacitive cell apparatus. Proc. 4th Int. Conf. Soil Mech., vol. 1, p. 52. Lecture on Secondary consolidation. DE JONG, G. D. J. (1966). King’s College, University of London. DE JONG, G. D. J. &VERRUIJT, A. (1965). Primary and secondary consolidation of a spherical clay sample. Proc. 6th Int. Conf. Soil Mach., vol. 1, p. 254. DRUCKER, D. C. (1964). Concepts of path independence and material stability for soils. Brown University, Providence R. I. DUNN, I. S. & NIELSEN, J. P. (1966). Non-linear viscosity in secondary consolidation. Bull. SM-GG-1, Eng. Expt Station, Utah State University. FLORIN, V. A. (1961). Soil Mechanics and Foundation Engineering, vol. 3. Moscow : Gosstroyizdat. Rheological properties of compacted unsaturated soils. Proc. 5th Int. Conf. Soil Mech., FOLQUE, J. (1961). vol. 1. D. 113. GEUZE, E: ‘C. W. A. (1964). Rheological and mechanical models of saturated clay particle systems. I. U. T.A.M. Symp. Rheol. Soil Mech., p. 90, Grenoble. GEUZE, E. C. W’. A. & TAN, T. K. (1954). The mechanical behaviour of clays. Proc. 2nd Int. Congr. Rheol., p. 247. GIBSON, R. E. & Lo, K. Y. (1961). A theory of consolidation for soils exhibiting secondary compression. N.G.I. Publication No. 41. HAEFELI, R. (1953). Creep problems in soil, snow and ice. Proc. 3rd Int. Conf. Soil Mech.. vol. 3, p. 239. Improved determination of preconsolidation p7essure of a HAMILTON, J. J. & CRAWFORD, C. B. (1959). sensitive clay. A.S.T.M. Spec. Tech. Pub. 254, p. 254. HANSBO, S. (1960). Consolidation of clay with special reference to influence of vertical sand drains. Swedish Geotechnical Inst. Proc., No. 18. On consolidation and settlement of loaded soil layers. Helsinki. HELENELUND, K. V. (1951). Symposium on consolidation testing of soils. A.S.T.M. Spec. Tech. General discussion. ISHII, Y. (1951). Pub. 126, p. 103. KAUL, B. K. (1963). A study of secondary time effects and consolidation of clays. Ph.D. thesis, University of Punjab, India. Proc. Am. Sot. civ. Engrs 79, Sep. No. 315. LAMBE, T. W. (1953). The structure of inorganic soils. Influence of speed of loading increment on the pressure void ratio diagram of undisLANGER, K. (1936). turbed soil samples. Proc. Int. Conf. Soil Mech., vol. 2, p. 116. Engineering properties of soils. Foundation Engi%eering, p. 66. New York: LEONARDS, G. A. (1962). McGraw-Hill. Compressibility of clay. Proc. Am. Sot. ciu. Engrs 90, LEONA;F,~~~.A. & ALTSCHAEFFL,A. G. (1964). LEONARD$, G. A. & GIRAULT, P. (1961). A study of the one-dimensional consolidation test. Proc. 5th Int. Conf. Soil Mech., vol. 1, p. 213. in the consolidation of_ claw. A.S.T.M. Soec. Tech. LEONARD?,. G. A. & RAMIAH. B. K. 11959). Time effects II . Pub. 254, p. 116. ~ ’ Secondary compression of clays. Proc. Am. Sot. civ. Engrs 87, SM 4, 61. Lo, K. Y. (1961). Clays and clay minerals, vol. 8, p. 170. Oxford: Viscosity of water in clay systems. Low, P. F. (1960). Pergamon Press. The consolidation of peat-a literature review. Tech. Paper 195, Div. of MaCFARLANE, I. C. (1965). Building Research, N.R.C., Ottawa. A study of the physical behaviour of peat derivatives MaCFARLANE, I. C. & RADFORTH, N. W. (1965). under compression. Proc. 10th Muskeg Res. Conf., p. 159. N.R.C., Ottawa. MADHAV, M. R. & SRIDHARAN,A. (1963). Discussion of paper by Wahls (1962). Proc. Am. Sot. civ. Engrs 89, SXI 4, 233. Proc. 4th Int. Conf. Soil Mech., vol. 1, p. 360. MANDEL, J. (1957). Consolidation de couches d’argiles. Stochastic processes in the grain skeleton of soils. Proc. 6th Int. Conf. Soil Mech., MARSAL, R. J. (1965). vol. 1, p. 303. Adsorbed water on clays : a review. Clays and clay minerals, vol. 9, p. 28. Oxford : MARTIN, R. T. (1962). Pergamon Press. Removal of water and rearrangement of particles during the compaction of clayey MEADE, R. H. (1964). sediments. Geological Survey Prof. Paper 497-B. Discussion of physico-chemical properties of soils. Proc. Am. Sot. civ. Engvs 85, MICH~F;, &. S. (1959). 1 , .

24

LAING

BARDEN

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