European Journal of Soil Science, December 1997, 48, 739-748

Variation of the critical-state boundaries of an agricultural soil

B . A . A D A M S & D . W U L F S O H N Department of Agricultural and Bioresource Engineering University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, S7N 5A9, Canada

Summary The critical-state theory can be applied profitably to analyse the mechanical behaviour of agricultural soil. Critical-state parameters and other soil properties are affected by the microstructure and unsaturated nature of agricultural soils. We determined the critical-state boundaries of an agricultural soil in both saturated and unsaturated triaxial tests and examined the effects of matric suction and initial structure on critical-state boundaries. On the compression plane, the presence of air and matric suction in the pores of unsaturated soil significantly affected critical-state boundaries by increasing compressibility, A. On the deviatoric stress-mean net stress plane, the strength increased with matric suction. On this plane, the critical-state lines for the unsaturated tests had non-zero intercepts. For a given soil structure, the frictional parameter M remained fairly constant with matric suction change. However, a change in the initial microstructure resulted in a change in M, causing the position of the critical-state line to ‘pivot’ in state space.

Introduction

The critical-state theory of soil mechanics unifies strength and volume change behaviour of granular materials in a single framework. A knowledge of the critical-state boundaries of a soil reveals much about its behaviour. Hettiaratchi & O’Callaghan (1980) illustrated the applicability of the theory to agricultural soils by qualitative analyses of compaction and cultivation.

Changing environmental conditions can result in variation of the water content of soil. The quantity of pore water and the presence of pore water pressure during loading significantly influences the strength and volume change behaviour of a soil. Water content directly influences the structure of the soil. Negative pore water pressures at the air-water interfaces in unsaturated soils produce an internal stress (i.e. the matric suction) within the pores. The relation between water content and soil suction (i.e. the soil-water characteristic curve) becomes a fundamental constitutive relation that governs many aspects of unsaturated soil behaviour. The primary feature of unsaturated soil mechanics is the incorporation of suction as an independent stress variable in constitutive (stress-strain) relations. The critical-state theory as originally formulated applies to saturated soils. An unsaturated critical-state theory

Correspondence: B. A. Adams, Eastern Cereal and Oilseed Research Centre, Agriculture and Agri-Food Canada, 960 Carling Avenue, Ottawa. Ontario, KIA OC6, Canada. E-mail: adamsb@em.agr.ca Received 19 November 1996; revised version accepted 25 June 1997

is more relevant to agricultural soils which undergo both strength and volume (structural) changes during compaction and tillage. Alonso et al. (1990), Toll (1990) and Wheeler & Sivakumar (1995) studied the mechanical behaviour of unsaturated soils using a critical-state framework with suction as an independent variable.

When adapting the critical-state theory to agricultural soils, attention must be drawn to certain issues. It is generally accepted that it is necessary to investigate the variation of critical-state parameters (i.e. the state boundaries) with water content (or matric suction) and to consider the influence of microstructure. But the effect of method of specimen prepara- tion, the interactive roles of water content, matric suction and stress history, and the existence of a ‘cohesion-like’ non-zero intercept of the critical-state line on the q-p’ plane need further research.

We applied a simple critical-state model within a framework of unsaturated soil mechanics to the study of the behaviour of an agricultural soil. We examined the effect of initial soil structure and matric suction on the critical-state boundaries of the soil and simulated the behaviour upon wetting such as that caused by rain or melting snow.

Literature Review

Critical-state theory and unsaturated soils

Schofield & Wroth (1968) presented the fundamentals of the critical-state theory for saturated soils. The basis of ‘unsaturated

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740 B. A. Adams & D. Wulfsohn

soil mechanics’ is the inclusion of soil matric suction as an independent stress variable, without attempting to define a single-valued stress function (or ‘effective stress’).

There is a growing body of evidence that the critical-state theory can be extended to agricultural soils. Hettiaratchi & O’Callaghan (1980) presented a simplified version of the theory and qualitatively analysed compaction and cultivation problems as a result of slipping wheels and cutting blades or tines. Other workers, including Leeson & Campbell (1983), Kirby (1991), Petersen (1993) and O’Sullivan et al. (1994), have since provided more experimental evidence supporting application of the theory to agricultural soils. Research has shown, however, that there are some significant departures from the original theory because of the unsaturated nature of agricultural soils. Towner (1983) cautioned that appropriate stresses must be used in describing the stresses in the soil for critical-state assumptions to apply.

Variation of soil properties with water content and soil structure

The importance of soil structure, water content and degree of saturation for agricultural activities cannot be overemphasized. Soil properties such as air permeability, strength characteristics, infiltration capacity, pore size distribution and erodibility depend on the structure of the soil (O’Sullivan & Simota, 1995). Water content, matric suction and degree of saturation are closeJy tied to the soil structure. The degree to which water content and degree of saturation affect soil structure depends on the texture. Dawidowski & Koolen (1987) showed that the matric suction of soil of any particular pore size distribution changed upon loading with no change in degree of saturation.

Water content plays a significant role in the soil physical condition and its mechanical behaviour. Greacen (1960) showed reductions in soil strength with increases in water content, whilst Mullins et al. (1990) observed that some soils (i.e. ‘hardsetting’ soils) become sticky and actually increase in strength when wet. Ley et al. (1989) observed pronounced increases in shear strength over a narrow range of gravimetric water contents (i.e. 2%) with matric suctions between 100 and 1000 kPa for a tropical soil.

Studies have shown that the critical-state boundaries of agricultural soils are related to water content and soil micro- structure (Leeson & Campbell, 1983; Hettiaratchi & O’CaI- laghan, 1985; Hettiaratchi, 1987; Kirby, 1991; Petersen, 1993; O’Sullivan et al., 1994). Critical-state parameters are also influenced by the method of specimen preparation. Specimens of similar structure are formed by preparing specimens at the same water content and density. Soils compacted at different water contents and bulk densities must be considered as ‘different’ soils when determining unique strength parameters (Fredlund & Rahardjo, 1993). Different microstructures are produced in remoulded and cemented specimens. Hettiaratchi (1987) showed that the variation of critical-state parameters

with water content differed in remoulded and cemented spe- cimens.

Effect of matric suction on soil behaviour

An important variable, related to water content, that affects unsaturated critical-state boundaries is the matric suction (Toll, 1990; Wheeler & Sivakumar, 1995). Whereas water content can be considered a deformation state variable, matric suction is a stress-state variable. Since soil problems involve stress changes and deformation, both these variables are important.

The total suction in a soil consists of matric suction (a result of surface tension at air-water interfaces) and osmotic suction (a result of the dissolved salts in the pore water). The effects of osmotic suction changes on soil behaviour is relevant to both saturated and unsaturated soils; however, matric suction changes are specific to unsaturated soil behaviour. Matric suction is closely related to the pore size distribution and the water content of the soil. The relation between water content (or degree of saturation) and matric suction is referred to as the soil-water characteristic, water potential or water retention curve. It has been suggested that the water characteristic is an important constitutive relation for unsaturated soils (Fredlund & Rahardjo, 1993). Matric suction has been shown to affect both volume change and strength of unsaturated soils. Numer- ous studies have shown that the shear and tensile strength of soils generally increase with matric suction. Cui & Delage (1993) observed stiffening for a silt at larger matric suctions from a series of triaxial tests. Transition from ductile to brittle failure as a result of increase in matric suction was also observed in these tests; postpeak softening was shown for suctions of 400 kPa or larger. Compressibility of soil decreases with increases in suction, whereas the preconsolidation pressure increases (Cui & Delage, 1993; Wheeler & Sivakumar, 1995; Makouk et al., 1995).

Applied stresses and the resulting structural changes also affect matric suction. Larson & Gupta (1980) showed that as applied stress increased, pore water pressure became more negative down to a minimum value, after which it increased. Horn et al. (1994) related the water content and matric suction to soil structure in single aggregates and bulk soil. They noted that the precompression stress is exceeded at about the same time the value of the negative pore water pressure is exceeded. Adams (1996) and Wulfsohn et al. (1994, 1996) observed significant changes in matric suction when the applied load exceeded some transition stress related to the specimen matric suction.

Consideration of matric suction as an independent stress variable permits the isolation of its effect on soil physical behaviour. Combined with its role in soil-water relations, matric suction becomes a vital link in the analysis of soil- plant and soil-implement relations.

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Critical-state boundaries of an agricultural soil 741

A critical-state model for unsaturated soils

Alonso et al. (1990) proposed a theoretical framework for the critical-state behaviour of unsaturated soils based on unsaturated soil mechanics principles. Toll (1990) and Wheeler & Sivakumar (1995) presented further experimental data to support such an approach. MaPtouk et al. (1995) applied the framework in describing the preyield and postyield behaviour of a collapsible unsaturated silty soil.

Alonso et al. (1990) presented a simple critical-state model that reduced to the Modified Cam Clay model when matric suction is zero. The following are the modified forms of the equations describing the critical-state boundaries. The parameters in these equations are readily determined from triaxial tests. The normal compression line is given by

v = N (s) - 4 s ) In -, P ’ Pr

q = 0. ( 2 )

The critical-state line is given by P’ v = r ( s ) - A&) In -, Pr

(3)

The unloading-reloading line is given by P’ v = v&) - K@) In - .

(5 ) Pr

In these equations v = specific volume = 1 + e; e = void ratio; p ’ = mean net stress = (0, + 02 + 03)/3 - u,; q = deviatoric stress = o1 - 03;

s = matric suction = (u, - u,);

(6) (7) (8)

N (s), r ( s ) or vK(s) are specific volumes at p’ = pr; pr = reference pressure at which N (s), r (s) or vK (s) are determined; il = slope of the normal compression line on the v-p’ plane; &, = slope of the critical-state line on the v-p’ plane; K = slope of the unloading-reloading line on the v-p’ plane; M = slope of the critical-state line on the q-p‘ plane; qo = intercept of the critical-state line with the q axis; 01, 0 2 , 0 3 are principal normal stresses; u, = pore air pressure; u, = pore water pressure.

Materials and experimental methods

A sandy clay loam soil (48.1% sand, 23.6% silt and 28.3% clay) was used in this study. It has a liquid limit of 32.9%, a plastic limit of 18.8%, a specific gravity of solids of 2.65, a maximum dry density of 1.65 g cm-3 and an optimum compac- tion water content of 18%. Batch soil samples were prepared by spraying fine droplets of a predetermined amount of water

Table 1 Initial (as compacted) state of unsaturated triaxial specimens

Test type D W

Initial wet bulk density /g cm-3 1.2 1.2 Initial specific volume 2.56 2.61 Compaction water content I% 16.1 20.2 Degree of saturation I% 21.2 32.5

D = dry of optimum W = wet of optimum

with air dried soil that passed through sieve size 10 (2-mm opening).

Soil specimens (length to diameter ratios of 0.4 for soil- water characteristic specimens and 2 for uniaxial compression and triaxial tests) were formed by compacting soil samples using a teflon-capped graduated piston in a cylindrical mould (Adams, 1996). A typical triaxial specimen (140-mm length by 70-mm diameter) was formed by sequential compaction of five 28-mm layers of predetermined amounts of soil. Two uniform soil structures (referred to as types D and W) with initial states as shown in Table 1, were formed by the compaction process. Type D represents specimens compacted at a water content drier than the optimum water content, whilst type W are specimens prepared at a water content wetter than the optimum.

Uniaxial compression tests were conducted using a triaxial apparatus to determine the precompression stress. A cylinder compacted with soil to a wet bulk density of 1.2 g cm-3 was placed between the base pedestal and the load platen of the triaxial apparatus. Uniaxial pressure was applied at a controlled rate of 10 kPa min-’.

Triaxial tests were conducted in a modified cell. Special low and high air discs were integrated into the triaxial cell. The modifications (Adams, 1996; Wulfsohn et al., 1994) permit measurement and control of matric suction and the measure- ment of both pore air and pore water volume changes. Each test specimen was enclosed within a composite membrane made of a slotted aluminium foil sandwiched between two rubber membranes to reduce diffusion of air between the specimen and cell water. The specimen was sealed at the base onto a saturated high air entry disc to ensure continuity between pore water in the specimen and the water in the pore water (pressure and volume) measuring systems. The saturated disc allows water to flow across as long as its air entry value is not exceeded. A coarse corundum disc sealed to the top of the specimen allowed free flow of air between the specimen and a digital controller, which served to control the air pressure and measure the volume change (Adams et al., 1996). After setting up and equilibrating the system to the desired matric suction, the net confining stress on the unsaturated specimen was (03 - u,) = 0. The matric suction (u, - u,), at this stage was 50 kPa for type W and 300 kPa for type D specimens. Saturated type W specimens (u, - u, = 0 kPa) were produced

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742 B. A. Adams & D. Wulfsohn

. . . . ._y

0.1 1 10 100 1000 10000 Matric suction I kPa

Figure 1 Soil-water characteristics for a sandy clay loam soil formed to two different soil structures.

by wetting after setting them up in the cell. Saturated and unsaturated type W specimens allow the comparison of the behaviour of a soil with matric suction with that of similar soil (i.e. same structure) when the matric suction is reduced to zero by wetting.

At the first stage of testing the specimens were isotropically compressed in the cell over a range of net confining pressures from 2 to 250 kPa. During isotropic compression the principal normal stresses are equal, 0 1 = ~2 = 03, so that the net confinin’g stresses on the unsaturated and saturated specimens are given by

and p t = 0 3 - u,

p” = (01 + 0 2 + 03)/3 - u, = 0 3 - u,

using the equations for the mean net stress and for the effective stress respectively.

The second stage involved applying a deviatoric stress to fail the specimens. For consolidated drained (CD) and constant gravimetric water content (CW) tests specimens were loaded at quasi-static rates of 2 mm h-’ and 10 mm h-’ respectively. Consolidated undrained (CU) tests for saturated specimens were controlled at 2 mm h-l. A constant pore-air pressure (i.e. Au, = 0) was maintained during unsaturated CD and CW tests. In CD tests, both pore air and pore water were allowed to drain from the specimen (i.e. Auw = Au, = 0), so that matric suction remained constant. For the CW tests, only pore air was allowed to drain (i.e. Au, = 0), while pore water remained undrained. Thus, pore water pressure (and hence, matric suction) may vary during CW tests.

Results

Soil-water characteristic curves for type D and W structures determined using pressure cells are shown in Figure 1. Qpe W structure retained slightly more water than type D, probably

2.6 1

2.6 -

- f 2.4 - 0

0 L .-

g 2.2 - rn

2.0 -

Water content -0- 20% -C- 16%

1 10 100 1000

Axial stress I kPa

Figure 2 Uniaxial compression of specimens of types D and W soil structures.

a result of the larger initial specific volume. In both cases, the soil-water characteristic relation indicated that gravimetric water content changed from 60% to 20% over a matric suction change of about 150 kPa and from 20% to 12% over a matric suction range of 1350 kPa (i.e. from 150 kPa to 1500 Wa). This suggests that the water content dominates the mode of soil-water behaviour for wetter states, whereas the matric suction governs soil-water behaviour for drier states.

Figure 2 shows the behaviour of the two structures under uniaxial compression. Since both types had the same initial wet bulk density, the drier soil (type D) had more particles per unit volume and a smaller initial specific volume (Table 1). Figure 2 shows the precompression pressures of types D and W to be 48 kPa and 28 kPa respectively.

Critical-state is defined for saturated soils undergoing loading as the state when no significant changes in mean stress, deviatoric stress, pore water pressure and volume with strain occur. It is presumed that for unsaturated soils, a matric suction criterion (i.e. no changes in suction with axial strain) would apply at ‘critical-state’ (Wheeler & Sivakumar, 1995). In laboratory tests, this condition may be achieved only under very slow (static) test rates and fairly large initial suctions. In agricultural applications rapid loading and constant water content situations are usual, so that the assumption of ‘no change in suction’ condition and the definition of an unsaturated critical-state needs further investigation.

At the ends of all our tests, changes in mean stress, deviatoric stress and specific volume with axial strain were insignificant. However, during the constant water content (CW) tests, matric suction changes measured at the ends of the specimens varied between - 14% and + 4%. Under the quasi-static loading rates we used, pore water pressure is expected to increase at the end platens before dissipating through the specimen. In this situation, matric suction measured at the end of the specimen is somewhat less than at the middle (Bishop et al., 1960).

Typical stress-strain relations obtained from triaxial tests

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Critical-state boundaries of an agricultural soil 143

250

Unsaturated CD 200

m

0 'E 8 100

'2 0

50

0 0 10 20 30 40 50 60

Axial strain I 'YO

Figure 3 Stress-strain relationships for type W soil structure for three test regimes under a net confinement pressure of 50 kPa.

for the type W structure are shown in Figure 3. Little or no changes in the deviatoric stress are evident at large axial strains. Under an initial confining pressure of 50 Wa the saturated specimen reached critical-state at about 8% axial strain, with a corresponding deviatoric stress of about 48 P a . For the unsaturated tests critical-state was attained at axial strains of about 43%. The specimens deformed uniformly by 'barrelling' symetrically. Large axial strains up to about 50% were also reported Dawidowski & Koolen (1987). Dawidowski et.al. (1990) showed that specimens deformed by 5 0 4 5 % of the original lengths remained homogeneous after such large deformations. Note that homogeneous laboratory specimens were used in our experiments and in the studies reported above.

The unsaturated CD (constant suction) specimens reached critical-state at a slightly larger deviatoric stress in comparison with the CW specimens. This is because the undrained water phase in CW tests produced increased pore water pressures (i.e. smaller matric suction), resulting in a slight loss of strength.

Figure 4 and 5 show the variation of matric suction with axial strain during constant water content tests on types D and W specimens. Matric suction in the drier, type D specimens deviated less than ? 2% from the initial value of 300 P a , whereas it varied from - 14% to + 4% of the initial value of 50 kPa for the wetter, type W specimens. Slight increases in matric suction with axial strain were observed at small axial strains and under small net confining stresses (less than 30 P a ) . The general trend observed, however, is a continuous but slight decrease in matric suction with increasing axial strain. Reduction of matric suction with increasing axial strain was more pronounced in type W specimens at net confining pressures exceeding 30 kPa. A possible reason for this is that type W specimens contained more water and were more nearly saturated, Continuous loading of the reduced pore space increased pore water pressures, resulting in smaller matric suction. It appears that there is a threshold stress beyond which matric suction changes with axial strain become significant.

4 I

B Net confining stress IkPa

-f 29 u 39 - -T- 51

r" -v- 60

. g 300 .- c a 0 .-

1 O l I 0 10 20 30 40 50 60

Axial strain / %

Figure 4 Variation of matric suction with axial strain in CW tests for type D structure.

55 , I

Net confining stress lkPa B 50 .

.- I s -0-2

r" 45

a u 9 0 --t 19

-0- 30 - 38 -o- 48

'i -

0 10 20 30 40 50 60

Axial strain / %

Figure 5 Variation of matric suction with axial strain in CW tests for type W structure.

Equations (1) to (4) were fitted to the experimental data in Figures 6 to 10 by linear regression. The regression lines in Figures 8 and 10 were extended (dashed lines) to determine the intercepts (90) on the q axis.

The normal compression line and unloading line for saturated and unsaturated type W specimens are shown in Figure 6. The normal compression line for the saturated specimens lies well below that of the unsaturated series and had a smaller compression index. During the consolidation stage of the tests, large volumes of water drained from the saturated specimens, resulting in significant volume changes from the initial state. The slope of the normal compression line for the unsaturated series (A = 0.25) was almost three times that of the saturated series (A = 0.092). This implies that along their normal compression lines the unsaturated specimens were more com- pressible than the saturated specimens. This arises because of the large amount of air in the voids of the unsaturated specimens. Both series of saturated and unsaturated tests

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744 B. A. Adams & D. Wulfsohn

2.6

2.4

2.2 - P

i v) 2.0

1.8

1.6

10

%rated url

100 Net confining stress / kPa

1000

Figure 6 Normal compression lines (ncl) and unloading-rebound lines (url) for saturated and unsaturated tests for type W structure on the specific volume-net confining stress plane.

1 . _ _ _ _ ~

2'6 T -T---

O ' C ' ' , , ' "4 10 100 lo00

Mean net stress / kPa

Figure 7 Normal compression lines (ncl) and projection of critical- state lines (csl) for saturated and unsaturated tests for type W structure. V, CW tests; A, CD tests.

showed little recovery of deformation (i.e. small svalues) on unloading. This was not surprising as the specimens had undergone large plastic deformations. Small ri-values for agri- cultural soils have also been reported by Kirby (1991).

Figure 7 shows that the slopes of the normal compression line and the critical-state line on the v-p' plane were sensibly identical within each series of tests, but again, the lines for the saturated soil lie well below those of the unsaturated case. The percentage difference in &s (slope of critical-state line) between the saturated and unsaturated series is similar to that observed for d (slope of the normal compression line). The relative positions of the critical-state lines for the saturated and unsaturated series on the q-p' plane are shown in Figure 8. The difference in the location of the critical-state lines is a result of matric suction. A constant suction of 50 kPa was

300 @

200

?? r ; -

//

/ /

,A' /' I v //

0 40 80 120 160

Mean net stress / kPa

Figure 8 Critical-state lines for saturated and unsaturated tests for type W structure on the deviatoric stress-mean net stress plane. CW tests; A, CD tests; ., CU tests.

2.6

1.6 1 O L - ' , ' ' " ' I

V,

10 100 Mean net stress / kPa

1000

Figure 9 Normal compression lines (ncl) and critical-state lines (csl) for types D (open points) and W (closed points) structures.

maintained in the CD specimens, whereas matric suction between 43 and 50 kPa was measured in the CW specimens at critical-state. The independence of critical-state on stress path is shown by the same line defining critical-state for the CW and CD tests in Figure 8.

Figure 9 shows that the normal compression boundary for type D specimens lay below that for type W specimens because of the initially denser structure. The slopes, or compressibility, during isotropic normal compression were similar. Critical- state points of all types D and W specimens appear to lie on the same critical-state line. Best-fit lines drawn through data points, however, show that the slopes of the critical-state lines for type W specimens (& = 0.26) was 1.6 times larger than that of type D specimens (& = 0.16). The critical-state lines intersect at a mean net stress of about 120 kPa (Figure 9).

The projections of the critical-state lines on the deviatoric stress plane for types D and W unsaturated specimens are

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Critical-state boundaries of an agricultural soil 745

400

300 B . I p!

200 0 ‘C 0

m - ‘8 a

100

0 I----

0 50 100 150 200

Mean net stress / kPa

Figure 10 Critical-state lines for (open points) type D and (closed points) type W structures on the q-p‘ plane. *, type W specimen at zero net confining stress.

shown in Figure 10. The regression line through type W specimens excludes the specimen tested under zero net confin- ing stress. Non-zero intercepts of the critical-state lines were observed for both type W and type D specimens on the q-p’ plane. The slope of the critical-state line (frictional parameter M) for type D specimens was about 1.3 times more than that of type W specimens. This could be attributed to the different states of the specimens at the end of isotropic compression prior to shearing. For example, under a net confining stress of 60 kPa a typical type W test specimen attained a wet bulk density of 1.48 g cm-3 and degree of saturation of 46.3%, after isotropic compression. A type D specimen under similar stress attained a wet bulk density of 1.52 g cm-3 and degree of saturation of 41.6% after compression. Type W specimens were generally looser and wetter than type D specimens. The particles in type D specimens were more closely packed and thus had more frictional contact and less water in the pores. These conditions are favourable for the development of greater strength.

Variation in the critical-state line will be due partly to different values of matric suction in the specimens. The initial matric suctions in types D and W specimens after isotropic compression were 300 kPa and 50 kPa respectively. Tests of type D specimens at a 50 kPa suction would be needed to determine to what extent the difference in the slopes in Figure 10 is a result of matric suction as opposed to structural differences.

The orientation of the critical-state lines in Figure 10 is further indication of the ‘cross-over’ of critical-state lines observed in Figure 9. The existence of some overlap indicates that the structures produced in types D and W specimens will have similar behaviours over a range of applied stress. An intersection was also observed in the uniaxial compression tests (Figure 2). From Figures 2, 3, 9 and 10, differences in

behaviour for types D and W specimens become apparent and are reflected in variation of the critical-state boundaries for the two structures.

Discussion

Our experimenta1 data apply to the behaviour of an agricultural soil within the subcritical zone of the critical-state space in which the soil under loading approaches the critical-state whilst shrinking. The subcritical zone thus provides the basis for the analysis of compaction problems. This zone is bounded by the critical-state wall (a vertical wall joining the critical-state line and the v-p’ plane), the normal compression line, and the Roscoe surface (Hettiaratchi, 1987). We discuss the variation in the boundaries associated with the subcritical zone for the sandy clay loam soil below.

Variation of critical-state boundary with matric suction

Figures 4 and 5 show the variation of matric suction with axial strain up to the critical-state. Some value of matric suction at the critical-state is associated with each test (CD or CW). The lines through the test points reaching this critical-state at the same matric suction (‘isomatric’ lines) define the critical-state boundaries at that matric suction. Figures 7 to 10 show the isomatric critical-state boundaries at matric suctions of 0, 50 and 300 kPa. Linear regression through the data points indicates that the tests belong to different boundaries identified for each matric suction.

A property of the critical-state line is that its location in state space is unique and independent of stress path. This uniqueness for unsaturated type W specimens is shown here in that the CW tests ended on the same critical-state line defined for the constant suction CD tests (Figures 7 and 8). The fact that the critical-state lines defined for unsaturated type W specimens in Figures 7 and 8 are isomatric boundaries (i.e. at a matric suction of 50 kPa) suggested that the matric suction changes (within 2 7 kPa) measured over the CW tests were not significant (Figure 5). This means that under certain conditions the matric suction remains constant during constant water content loading. It should be noted that our constant water content specimens were initially loose (wet bulk density of 1.2 g ~ m - ~ ) , had an initial water content of 20%, and were subjected to fairly small stresses. Hence, the pore water pressure changes were small (i.e. ? 7 kPa).

For unsaturated type W specimens, the decrease in matric suction (from 50 kPa to 0 kPa) as the soil became saturated resulted in boundary shifts on the v-p‘ plane such that compressibility of pore space decreased (Figure 6). On the same plane and scale the unsaturated series had a wider subcritical domain than the saturated series (Figure 7). Thus, for the same type of stress path and the same initial net stress, the stress state of the saturated soil traverses the Roscoe surface over a shorter path than the unsaturated

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746 B. A. Adams & D. Wulfsohn

soil. Figure 7 also shows that the yield surface grows in size as the soil gets drier.

Although matric suction generally increases strength and reduces deformability, the specific volume of the unsaturated specimens in Figure 7 decreased by about 20% before reaching critical-state: evidence of large deformations. The mean net stress had increased 2 to 3 times on reaching this state. Thus, a combination of stress and volume changes and the resulting compaction could cause soil structural damage even with the existence of matric suction in the soil.

On the q-p’ plane, an increase in suction resulted in an increase in strength (Figure 8). The shift in the position of the critical-state line indicates the formation of a new state bound- ary surface as a result of an increase in matric suction. The critical-state line for the unsaturated series had a non-zero intercept with the q axis. The evidence of ‘strength’ at zero mean net stress is attributed to the internal matric suction (Wheeler & Sivakumar, 1995). Wheeler & Sivakumar (1995) found that the intercept of the critical-state line on the q axis (i.e. qo) varied with matric suction in a non-linear manner. Figure 8 shows that the critical-state frictional parameter, M, for this soil was not sensitive to a 50 kPa matric suction change. Insensitivity of M to matric suction change was also observed by Wheeler & Sivakumar (1995) for an unsaturated clay soil over a matric suction range of 300 kPa. Data presented by Delage et al. (1987) and Maitouk et al. (1995) suggest that M is a strong function of suction for some highly frictional soils, but that as net stress increases the effect of suction on strength decreases. Petersen (1993) and Kirby (1991) showed a systematic variation of M over a wide range of moisture contents. In these latter studies, stresses were expressed in terms of total (applied) stresses.

Variation of critical-state boundary with soil structure

Figure 9 shows an overlap in the subcritical domains for type D and W specimens. The Roscoe surface for type D specimens appears to have emerged from below that of type W specimens. Though the projections of the critical-state lines from both series appear to lie along the same line, the critical-state line (limiting the Roscoe surface) for type D specimens increased slightly above that of type W specimens. This slight rise is seen in the slope of the critical-state line in the q-p’ plane (Figure 10). Hence, these two series of tests produced inter- secting state boundaries, with the boundaries for type D rising slightly over the boundaries for the type W series at the line of intersection. The closeness in the critical-state lines in Figures 9 and 10 could be because the shear deformation of the types D and W initial structures produced similar structures at critical-state.

This observation indicates that hardening occurred in the drier soil with the larger matric suction. Even when soil is worked when it is drier, there is still the possibility of the soil becoming harder if it is compacted. It is also possible that soils

of initially different structures may deform under continuous shearing to similar structures.

Pivot point and critical-state boundaries

Hettiaratchi & O’Callaghan (1985) proposed that on the v- In p’ plane, the normal compression and critical-state lines each pivot about some point in state as water content varies. They also suggested that the pivot point for the critical-state line is the origin on the q-p’ plane. O’Sullivan et al. (1994) applied the pivot point concept to their experimental data. They showed that the slopes of the critical-state lines were generally about 12% higher than those of the normal compres- sion lines and that these two lines tended to pivot about a point as water content changed. On the q-p‘ plane, the critical- state line passed through the origin and increased in slope with decreasing water content.

The concept of a pivot point at the origin on the q-p’ plane is not supported, however, by the experimental data of Wheeler & Sivakumar (1995) and some of the data in our study. Our experimental data for specimens with similar structure but different matric suction agree with the results of Wheeler & Sivakumar (1995) and Petersen (1993) who observed that the critical-state line formed an intercept with the q axis of the q- p ’ plane. On the v-p’ plane, the slopes of the normal compres- sion and critical-state lines had similar values. A common feature in this series of triaxial tests, and those of Wheeler & Sivakumar (1995) and Petersen (1993), is that soil specimens having similar structures but different water contents or matric suction were used. O’Sullivan et al. (1994), however, used remoulded specimens of different structures.

Our two unsaturated tests series for different structures (types D and W) agree qualitatively with the observations of O’Sullivan et al. (1994) and the pivot point concept. Figure 9 shows that the critical-state lines of the two soils on the v- In p’ plane pivot about a point at p‘ = 120 kPa with the drier soil having a smaller compressibility, As. A pivot point (not at the origin) is also shown in Figure 10 for the critical-state lines on the q - p’ plane.

It is evident that the variation of critical-state boundaries with water content is affected by the manner of specimen preparation. The use of specimens with cemented structures results in a different variation of the critical-state boundaries with water content from that obtained using remoulded specimens.

Conclusions

The critical-state theory is a powerful tool for qualitatively interpreting agricultural soil behaviour and ultimately for formulating unified constitutive models for predictive studies. For successful application and interpretation of the theory, factors which affect the structure of the soil such as soil type, water content, degree of saturation and matric suction, must

0 1997 Blackwell Science Ltd, European Journal of Soil Science, 48,739-748

be taken into account. Studies have shown that the critical- state boundaries of unsaturated soils vary with soil structure, water content and suction. Consideration of matric suction as an independent stress variable permits the isolation of its effect on soil physical behaviour.

For the sandy clay loam soil we tested, changes in matric suction changed the slopes of the normal compression lines and the critical-state lines on the v-p’ plane. A matric suction change also affected the intercept parameter, qo, on the q-p’ plane but had negligible effect on the slope of the critical-state line on this plane (i.e. M remained constant). For a constant matric suction and soil structure, a unique critical-state line was established independent of stress path. A change in structure produced a rotation of the critical-state line about a point on the v-p’ plane with a slight difference in the slope of the critical-state line, whilst the slopes of the normal compres- sion lines were unaffected.

In conclusion, we demonstrated the manner in which matric suction and structural changes affect critical-state parameters for a sandy clay loam soil. The consideration of matric suction as an independent stress variable permitted us to determine its effect on soil behaviour. The presence of matric suction in unsaturated specimens resulted in an intercept of the critical- state line (qo) on the q-p’ plane. Matric suction also caused significant differences in A and As for the unsaturated speci- mens in comparison to the saturated specimens. A structural change influenced the parameters M, qo and &.

A proper understanding of the variability of the critical-state boundaries of an unsaturated soil requires knowledge of both water content and suction and their interactions with soil structure. It is important to note the variation in soil structure resulting from reconstituted specimen preparation or the in situ variation when critical-state boundaries are to be determined. Specimens of identical stress history and structure must be used to determine unique state boundaries of the soil.

Acknowledgements

We thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support and Professor D. G. Fredlund, University of Saskatchewan, for valuable advice.

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