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Cohron sheargraph data: interpretation using critical state soil mechanics
Soil & Tillage Research, 26 ( 1993 ) 211-225
211
Elsevier Science Publishers B.V., Amsterdam
Cohron sheargraph data: interpretation using critical state soil mechanics J.M. K i r b y a a n d P.D. Ayers b aCSIRO Division of Soils, GPO Box 639, Canberra, A.C.T. 2601, Australia bAgricultural and Chemical Engineering Department, Colorado State University. Fort Collins, CO 80523, USA (Accepted 14 January 1993)
ABSTRACT Critical state soil mechanics was used to explain the differences in stress paths recorded in sheargraph tests in weak, strong and medium-strong soils. It was projected that the cohesion of both peak and ultimate strength lines would be near zero for weak and medium-strong soils, but the peak cohesion would be high for strong soil. The friction angle of the peak strength line was projected to be lower than that of the ultimate line for strong soils and less than or equal to that of the ultimate line for weak and medium-strong soils. The projections about the type of stress path and the relationship between cohesion and friction for peak and ultimate strength lines were tested by performing field sheargraph tests in a Vertisol. It was found that the friction angle of the ultimate line was higher than that of the peak line, which suggests that in loose to medium dense soils it may be more appropriate to use the ultimate line for tine design procedures that employ the friction angle in calculations. The different forms of stress path recorded in field sheargraph tests were associated with different regimes of soil behaviour in laboratory shear, in which the height change during shear was measured. Tests with strong soil resulted in sheargraph tests that showed brittle stress paths with well defined shear stress peaks, and in laboratory shear tests that showed shear accompanied by expansion. Tests with weaker soil resulted in sheargraph stress paths without well defined peaks, and in laboratory shear accompanied by compression. Shear accompanied by expansion is desirable in tillage for seedbed preparation and therefore the sheargraph may be useful in identifying the right soil conditions for tillage.
INTRODUCTION
The Cohron sheargraph is one of a number of torsional shear devices used to assess soil strength in situ (Cohron, 1963; Freitag, 1971; McKyes, 1989). In common with other similar instruments, it offers the advantages over laboratory tests of speedy results and minimal disturbance of the soil. All field torsional shear devices suffer from the disadvantage that the stress distribution on the shear surface and the geometry of the shear plane cannot Correspondence to. J.M. Kirby, C S I R O Division of Soils, G P O Box 639, Canberra, A.C.T. 2601, Australia.
© 1993 Elsevier Science Publishers B.V. All rights reserved 0167-1987/93/$06.00
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J.M. KIRBY AND P.D. AYERS
be known exactly (Freitag, 1971 ). The various devices have been found to give different values for cohesion and friction, and these may differ again from laboratory measurements (Payne and Fountaine, 1952; Bailey and Weber, 1965; Dunlap et al., 1966). The differences may arise from difficulties in interpreting the stress system and failure geometry. Differences between field and laboratory measurements may be due to soil disturbance induced during sampling and transport to the laboratory (Payne and Fountaine, 1952 ). Ayers ( 1987 ) showed that the failure points measured by a Cohron sheargraph may not be linear which further complicates the estimation of cohesion and friction. On the other hand, Schafer et al. (1963) considered that the cohesion and friction were reliably measured by a torsional test. Wills ( 1963 ) and Kuipers and Kroesbergen (1966) also considered that differences between shear devices were small. The problems of interpretation not-withstanding, the advantages of field torsional shear devices are sufficient to ensure their continued use (Olsen, 1984; Ayers, 1987). Ayers ( 1987 ) reported a large number of measurements with a sheargraph to examine the relationships between cohesion, friction, moisture content and density. The results were found to be very reproducible. Sheargraph data are usually analysed to estimate the soil strength parameters of cohesion and friction angle. This paper reports an interpretation of results from the Cohron sheargraph in terms of the critical state concept. A comprehensive review of soil strength and deformation as offered by the critical state concept has been described by Hettiaratchi ( 1987 ) and Kirby ( 1989, 1991 ) for agricultural soils. This concept divides soil deformation into two regimes, in one of which the soil compresses during shear and in the second of which it expands during shear. The former regime occurs, for example, in rice puddling or the formation of ploughpans, while the latter regime occurs (desirably) during conventional tillage for seed-bed preparation. Several predictions of sheargraph results arising from the critical state concept are outlined and the degree to which they describe results from in situ tests is examined. The results from in situ sheargraph tests are also compared with the results from laboratory direct shear box tests. EXPLANATION OF SHEARGRAPH RESULTS BASED ON THE CRITICAL S T A T E CONCEPT
The design and operation of the Cohron sheargraph was fully described by Cohron (1963). As shown in Fig. l, it consists of a shear head (which is a grousered plate of radius 20.3 m m ) that grips the soil. This is attached to a spring which, when pushed down, causes the plate to exert a normal stress on the soil. When twisted, the spring exerts a torsional force on the plate, which causes a shear stress to be exerted on the soil. Compression or torsion of the spring is controlled by hand via the handle at the top of the sheargraph and is
COHRON SHEARGRAPH DATA
213
Handle
- -
Bearings
- -
Recording drum
Recording
Spring
H==~--Shear
head
Fig. I. Schematicdiagram of the Cohron sheargraph. recorded by a pen on graph paper attached to the recording dram (Fig. 1 ). The graph paper is supplied with the sheargraph and is calibrated for normal and shear stress in units of psi. The m a x i m u m normal stress that can be recorded is 20 psi (about 140 kPa). The Cohron sheargraph is operated in such a way that the normal stress is increased from zero to a predetermined value while the shear stress is zero (Stage I in Fig. 2). The normal stress is then held constant while the shear stress is increased (Stage II in Fig. 2). This requires considerable practice. Usually, the operator cannot hold the normal stress truly constant during this stage of the test and a certain a m o u n t of 'wobble' is recorded on the graph paper. Once the shear stress reaches a maximum, the shear and normal stresses are released together (Stage III in Fig. 2). This stage is easier to control and the recorded trace is usually much smoother during this phase of the test. The stress path (sequence of shear and normal stresses) is recorded on a chart. The exact shape of the stress path will depend on the properties of the soil, in particular whether it is normally or over-consolidated. In traditional interpretations of sheargraph results only the m a x i m u m shear stress is used in the analysis for cohesion and friction. The friction angle is
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J.M. KIRBY AND P.D. AYERS
III e-
II
l
~>
Normal stress, Fig. 2. General form of the stress path in a sheargraph test. Stage I, normal stress increased at start of test. Stage II, shear stresses increased until excessive rotation of the sheargraph occurs. Stage III, shear and normal stresses reduced.
the slope of the straight line fitted to a number of points of maximum shear stress at several normal stresses. The cohesion is the intercept of the straight line. In this paper the whole stress path will be examined. Typically, pore water pressures are not measured and effective stresses are not determined. The analysis is therefore based on the total applied stresses.
Critical state diagram and yield behaviour The critical state concept considers that a continuously deformed particulate material will come to a critical state in which further deformation proceeds without change in stress or volume. The critical state is defined by a unique line in stress-void ratio space (Fig. 3). The critical state concept is usually defined in terms of stress invariants, but will be discussed here in terms of normal and shear stress to be consistent with the use of a sheargraph in which these are the recorded variables. This approach is less general than the use of invariants because the influence of horizontal stress is not accounted for (see Kirby, 1989, 1991 ). The critical state concept can be broadened to incorporate state boundary or yield surfaces. Yield~urfaces define the onset of permanent, or irrecoverable, deformation. With reference to Fig. 3, the soil can exist in a stress state on or within a yield surface in shear stress/ normal stress/void ratio space. Within the yield surface behaviour is elastic and can be described by elastic walls. For instance a sample at A (Fig. 3) would, on removal of stress to B, experience an increase in volume owing to elastic rebound. The elastic wall is, therefore, not parallel to the normal stress
COHRON SHEARGRAPHDATA
21 5
lShear /stress
Normal stress ,~
Criticalstate
Normally / I ] /.,"~ consolidated I / ~ / / surface / / [ " / / / ~'Over consolidatedsurface Void ratio Fig. 3. Critical state diagram. See text for explanation of A - D .
axis. The elastic wall increases in size with decreasing void ratio, i.e. the soil is becoming stronger with increasing density. Projecting an elastic wall onto the shear stress/normal stress plane gives Fig. 4 (see Kirby, 1989, 1991 ). The critical state line defines shear and normal stress conditions at which shear takes place with no volume change. To the left of the critical state line, on the over consolidated yield surface, shear is strain softening and accompanied by a volume increase, as shown by the stress path beginning at point C on Fig. 4. On the normally consolidated part of the yield surface, shear is strain hardening and accompanied by a volume decrease (stress path beginning at D, Fig. 4 ). Shear at constant normal stress on the yield surfaces causes the surfaces to change as shown in Fig. 4. The overall paths followed are shown in Fig. 3. It can be seen from Fig. 4 that the peak shear stress experienced by an over consolidated sample is given by the point of intersection of the stress path with the yield surface, whereas for a normally consolidated sample the peak shear stress is given by the critical state line (which strictly is reached only after infinite deformation ). In a sheargraph test, the stress path could start at any normal stress, a, between the origin and the point at which the yield surface meets the axis (shown as trm on Fig. 4). o m is the m a x i m u m compressive stress experienced by the soil. This stress could be a stress experienced prior to the sheargraph test in which case the test will be performed with tr< o m. Alternatively, the maxim u m stress could be that imposed by the sheargraph in the first stage of the
216
J.M. KIRBY AND P.D. AYERS
Yielding with volume increase
I r-
• • Changing size
Yielding with volume decrease
I
r
I -..1~ I I I
'',
, of yieldsurface~ ',
~.,.,~,~ ,,,l-/
.......
~xx xx
B
C
Normalstress, o
A (~m
Fig. 4. Yield surface and critical state line projected onto a normal stress-shear stress plane. Lines C and D show stress paths followed by over-consolidated soil and normally consolidated soil respectively. The dashed lines indicate the change in the size of the yield surfaces that accompanies shear at constant normal stress.
test, in which case tr= o"m. The shear stresses should increase until the amount of deformation is excessive. This should happen either when the yield surface is reached on the over consolidated yield surface where volume increase occurs (Fig. 4), or as the critical state line is approached on the normally consolidated yield surface where volume decrease occurs. After the onset of yielding, the stress path should move towards the critical state line (see Kirby, 1989). The critical state line is, by definition, the line defining the ratio of shear to normal stress when the soil is sheared to a very large deformation. Therefore, once the critical state line is reached, the stress path should remain on the line as the stresses are reduced at the end of the test. When deformation takes place on the normally consolidated surface, the size of the yield surface increases as the soil becomes denser and stronger (Fig. 4 ). The stresses in a sheargraph test should approach the critical state line in the later stages, but the actual critical state is unlikely to be observed in a shear test (see Kirby, 1991 ). The critical state is reached after very large (strictly infinite) deformations whereas deformations in the sheargraph are limited. Furthermore, shear in the expansive regime is restricted to local zones (Kirby, 1991; Kirby and Blunden, 1991 ), whereas the critical state is usually taken to imply general deformation. Therefore, the path followed by the sheargraph test back to the origin in the final stages is unlikely to define the critical state line. In this paper, this path will be referred to as the ultimate line to denote the ultimate condition reached in a sheargraph test.
217
COHRON SHEARGRAPH DATA
Behaviour of weak soil Weak soil is here defined as being soil which is sheared on the normally consolidated surface (Figs. 3 and 4 ). The m a x i m u m stress, am, is imposed by the sheargraph at the time of normal stress application. Thus the stress paths start from the points labelled o"m (Fig. 5 ) and, at first, show increasing shear stresses at constant normal stress. However, as the shear stresses increase, the soil should compress and become denser and stronger and the yield surface should increase in size such that the stress path remains on the surface (e.g. Kirby, 1989), as shown by Path III in Fig. 5. As the ultimate line is approached with increasing shear stress, the soil begins to fail causing the grousered plate in contact with the soil to rotate. The test is discontinued by reducing the normal stress. Reduction of the normal stress at this stage should result in the shear stress remaining approximately constant, following the yield surface until the ultimate line is reached. The stress path should then travel down the ultimate line. The stress path is therefore projected to rise vertically, curve to the left and then follow a line to the origin, as shown in Fig. 5. Three such stress paths for tests at different a m (i.e. ami , O'mII and O'miii ) would all show the same shape, but increase in size with increasing o"m (Fig. 5 ). Since they all show the same shape, it is projected that lines fitted to the peak shear stresses and the ultimate lines would both show no (or, taking experimental variation into account, small ) cohesion intercepts (Fig. 5 ). The friction angle of the peak line is projected to be equal to or less than that of the ultimate line. Based on the critical state soil mechanics relationships between shear and volume change, Ultimate strength l i n e ~ Peaks t r e n g t h ~ ~ l i ~ Increased sizeof yield surface l l I ~
.........J~
..,~.~..
~
d IIl ,s~ S
%%
,%
'\ > °ml
°ml]
(~mIII
Normal stress, o Fig. 5. Stress paths predicted for weak samples. Stress paths I, H and []I each starts at a different maximum stress O'mi, O'mlI and 0"mlilimposed by the sheargraph. The increased size of the yield surface resulting from the soil becoming denser and stronger is shown by the dotted lines.
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J.M. KIRBY AND P.D. AYERS
it is also projected that shear would be accompanied by a decrease in the volume of the soil. In weak soils, shear stress and deformation tend to increase gradually, without any clear discontinuity, until the critical state condition is achieved at infinite shear strain. Once the critical state is achieved, the soil may be deformed with little or no change in shear or normal stress. In practice, a sheargraph test will be discontinued before the critical state is achieved as the operator can impose only a finite deformation. The actual amount of deformation at which the operator chooses to discontinue the test, and therefore the peak shear stress recorded, is somewhat arbitrary. However, it is projected from the critical state concept that the friction angle of the peak strength line can never be greater than, and would generally be less than that of the ultimate line. The difference between the two would depend on the choice of when to discontinue the test.
Behaviour of strong soil Strong soil is defined as being soil which is sheared on the over consolidated surface (Figs. 3 and 4). Thus the yield surface (the surface of stress states describing the onset of permanent deformation) is large. Yielding would begin once the yield surface is reached and the shear stresses should reduce (abruptly in the case of very brittle soil) until the ultimate line is reached. Thus, the stress path is projected to rise vertically, then fall vertically and then turn and follow a line towards the origin (Fig. 6). The ultimate line is projected to show a zero (or, taking experimental variation into account, small) cohesion intercept, but the peak line is projected to show a large cohesion intercept. The slope (friction angle) of the peak line is projected to be lower than that of the ultimate line (Fig. 6 ). Shear is projected to be accompanied
Peastkrengtline. h ~ 1 ? ~o
~,~--~ ~UItimatsterengtlhine III
,t I !
Normstalress,c Fig. 6. Stress paths predicted for strong samples.
219
C O H R O N SHEARGRAPH DATA
by volume increases. It is also projected that the difference in shear stress between the peak and ultimate lines ('peakedness' of the stress path) and the volume increase would both be larger for tests at smaller normal stresses (see stress paths I, II and III in Fig. 6 ). This 'peakedness' is associated with brittle failure.
Behaviour of medium strong soil Medium-strong soil is soil which is sheared partly on the over consolidated surface and partly on the normally consolidated surface (Figs. 3 and 4). It is projected that both types of stress path would be present (Fig. 7 ). Stress paths that meet the yield surface at about its intersection with the ultimate line would rise vertically and then sharply turn and follow a line towards the origin, as shown by stress path II in Fig. 7. The ultimate line is projected to have a zero (or, taking experimental variation into account, small) cohesion intercept. The peak line is projected to have a moderate cohesion intercept and a friction angle a little less than the ultimate line. The difference in cohesion and friction between the two lines would depend on the actual stress levels in relation to O'm and on the shape of the yield surface. Thus, in Fig. 7, if stress paths I, II and III were located at different values of normal stress, then they would meet the yield surface at different points and different peak shear stress values would be recorded. Hence, a different peak line with different cohesion and friction would be interpreted from the data. Shear is projected to be accompanied by only small volume changes, with the soil expanding in some tests and compressing in other, higher stress, tests. The predictions made above were tested experimentally by performing sheargraph tests on soil in different states (of density and moisture content),
Peak strength line ~
~Ultimate ~ . . .strength . ~ ~ jline.
s"
i/
Normalstress,~ Fig.7. Stresspathspredictedformedium-strongsamples.
II>
220
J.M. KIRBY AND P.D. AYERS
such that it had different strengths. Samples were also taken to the laboratory to perform shear box tests and examine the predictions of volume change. MATERIALS AND METHODS
The soil used for this study was a Vertisol at the University of Queensland, Gatton College, Qld. Wheeltracks and permanent beds and different depths at this site had quite different strengths. Several areas were chosen such that a range of strengths could be investigated. Tests were performed at the surface or at depths of up to 150 ram. The Cohron sheargraph tests were performed in situ at this site. At each location, nine tests were performed--three each at normal stresses of 35, 69 and 103 kPa ( 5, 10 and 15 psi). In the strongest soil the sheargraph could not be pushed in manually. Therefore, a short column of soil that fitted the inside of the grousered plate was carved with a pocket knife. Soil samples were also taken at locations adjacent to the sheargraph tests. The samples were taken in thin-walled, square-sectioned metal containers which were 2 cm high and 6 cm on each side. The samples were transported to the laboratory, where they were transferred from these containers into a shear box having the same dimensions. The procedure in the shear box tests followed that described by Sallberg ( 1965 ). Shear tests were performed at the same normal stresses as the sheargraph tests. The change in height was measured during each test. After each test the soil was weighed, dried in an oven at 105 °C and weighed again to determine the moisture content. Statistical analysis of the data was performed using GENSTAT 5, PC version (GENSTAT, 1987). RESULTS AND DISCUSSION
The soil was classified as being weak, weak to m e d i u m or strong according to the shape of the sheargraph chart. Examples of sheargraph charts from tests in weak and strong soil are shown in Figs. 8 and 9. The stress paths followed shapes similar to those of Figs. 5 and 6. Figure 10 shows a sheargraph chart that has some features of a medium-strong soil, i.e. the stress paths rise vertically and then turn sharply left to follow the ultimate line (see stress path II in Fig. 7 ). The soil of this sheargraph chart was classified as weak to medium. No chart showed all the features predicted for a medium-strong soil. The cohesion and friction angles of both peak and ultimate lines from nine test series are given in Table 1. The soil conditions in the table are identified on the basis of the shape of the stress paths on the sheargraph charts. The table shows that the ultimate cohesion was small for all the soil conditions tested, as predicted. The peak cohesion was large in strong soil, but small in weak and weak to m e d i u m soil. The ultimate friction angle was always higher than
221
C O H R O N S H E A R G R A P H DATA
100
Or)
5O
0
50
1O0
Normal stress, kPa
Fig. 8. Stress paths recorded in field sheargraph tests on weak soil. Note: for clarity, only one straight line is shown in the earlypart of the test at each level of normal stress; in practicethree lines wererecordedand each showedsome 'noise' (see text for explanation). the peak angle of friction, but the difference between the two was small in the case of the weak to medium soil. In the strong soil, the ultimate angle of friction was much higher than the peak angle of friction, again following the predicted behaviour. Table 2 shows summary data for the height changes and density that accompanied shear in the laboratory shear box tests. As shown in the table, both the density and height changes were significantly different among the weak, medium and strong soil. The density was regarded as an estimate only, because sinkage of the ridged shear box plates into the soil made it difficult to estimate the volumes of samples accurately. The volume was estimated from height measurements taken with the ridged plates in place and thus the strong soil, into which there was little or no sinkage, was likely to be overestimated. Therefore the density of the strong soil was likely to be underestimated and the difference in density between the strong and weak soil was, if anything, greater than that shown in the table. The samples of strong soil increased in height, and therefore volume, during shear, whereas the samples of weak soil decreased in height and therefore volume (Table 2 ). This behaviour agreed with the predictions. The mediumstrong soil also decreased in height (though not as much as the weak soil) in contrast to the prediction that there would be little or no volume change. A
222
J.M. KIRBY AND P.D. AYERS
100 0,_
50
I 50 Normal stress, kPa
0
I 100
Z>
Fig. 9. Stress paths recorded in field sheargraph tests on strong soil. Note: for clarity, only one straight line is shown in the early part of the test at each level of normal stress; in practice three lines were recorded and each showed some 'noise' (see text for explanation).
100 ¢x3 O.-
e-
~
50
m
I> 50 100 Normal stress, kPa Fig. 10. Stress paths recorded in field sheargraph tests on weak to medium-strong soil. Note: for clarity, only one straight line is shown in the early part of the test at each level of normal stress; in practice three lines were recorded and each showed some 'noise' (see text for explanation).
COHRON SHEARGRAPHDATA
223
TABLEI
Cohesionand ~ictionofpeakandultimatelines~om thefieldsheargraphtests Soil condition
Weak Weak Weak Weak-medium Weak-medium
Strong Strong Strong Strong
Cohesion (kPa)
Friction angle
peak
ultimate
peak
ultimate
R 2 (peak)
12.4 11.8 6.0 0.3 3.9 94.2 61.5 56.2 31.7
3.5 2.1 4.9 0.7 2.1 0? 0 6.3 4.9
34 21 30 43 38 48 27 27 44
44 31 33 45 38 56? 45 46 46
0.912 0.664 0.821 0.982 0.837 0.321 0.575 0.774 0.821
~This soil exhibited very brittle behaviour, with abrupt release of shear stress after failure. This made identification of the ultimate line difficult and the values of cohesion and friction angle are uncertain; this is indicated by the question marks. TABLE 2 Summary data for height change and estimated density in shear box tests
Weak Medium strong
Strong Probability leveP
Height change (mm)
Density ( m g m -3 )
- 1.05 - 0.53 0.39 < 0.001
1. I 1.5 1.7 < 0.001
~The probability level is the probability that the means of the different soils come from the same population.
number of reasons could explain the failure to meet this criterion. Firstly, the shear box had limited travel and samples were still changing volume at the end of tests. All samples decreased in height initially, but the strong samples and most of the medium-strong samples then increased in height at a later stage of the test. It is probable that, had the shear box been capable of further shear displacement, the medium-strong samples would have shown less decrease in height. It is also known that height change is affected by the stress conditions (Kirby, 1986) and speed (Blunden et al., 1992) in shear tests. Other reasons could include disturbance of the soil during sampling, and errors in height change measurements owing to the ridged plates sinking in as the tests progressed. The prediction that the 'peakedness' of the stress paths would be related to the volume change could not be tested with the data available.
224
J.M. KIRBYANDP.D.AYERS
CONCLUSIONS
In summary, the volume change of the weak, medium and strong soil partially followed the conceptual model. To the extent that the predictions failed, the failure can be attributed to a number of factors in the sampling and testing procedure. The stress paths and cohesion and friction of both the peak and ultimate lines followed the predictions. Several considerations follow from these findings. Firstly, in loose and medium dense soil the friction angle of the ultimate line was always higher than that of the peak line. If these data were used for predicting forces on tines, higher forces would be predicted using the friction angle of the ultimate line. The friction angle of the peak line thus might result in an inadequate design. It is questionable which friction angle is appropriate in tine design. These considerations apply also to other design procedures that use the friction angle. Wroth ( 1984, 1987 ) pointed out that some forms of direct shear box test may also underestimate friction angles and therefore be inappropriate for civil engineering soil mechanics design. Secondly, Kirby ( 1991 ) showed that soil failure in the expansive regime is appropriate for conventional tillage, while the compressive regime is appropriate for preparation of rice soils. Since the stress paths recorded by the sheargraph were successfully identified with these regimes of failure, it appears that the sheargraph could be used as a simple field tool for assessing whether soil is in the right condition for various forms of tillage. Thirdly, the ultimate line measured in the various sheargraph tests seems to separate the two forms of shearing behaviour. As such it might be identified with the critical state line. However, as was noted in the Introduction, friction angles measured with a sheargraph may not correspond to those measured by other forms of shear test. The slope of the ultimate line may well differ from the slope of the critical state line measured in other tests. Furthermore, as noted previously, the critical state is unlikely to be observed in sheargraph tests. Thus the ultimate line, while being somewhat analogous to the critical state line, should not be identified as being exactly equivalent to it.
REFERENCES Ayers, P.D., 1987. Utilizing the torsional shear test to determine soil strength-properties relationships. Soil Tillage Res., 10: 373-380. Bailey, A.C. and Weber, I.A., 1965. Comparison of methods of measuring soil shear strength using artificial soils. Trans. Am. Soc. Agric. Eng., 8:153-160. Blunden, B.G., Kirby, J.M., Humphries, E. and Muirhead, W.A., 1992. Mechanical properties of a cracking grey clay used for rice production in Australia. Soil Tillage Res., 26:55-67. Cohron, G.T., 1963. Soil sheargraph. Agric. Eng., 44: 554-556. Dunlap, W.H., Vandenberg, G.E. and Hendrick, J.G., 1966. Comparison of soil shear values
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obtained with devices of different geometrical shapes. Trans. Am. Soc, Agric. Eng., 9: 896900. Freitag, D.R., 1971. Methods of measuring soil compaction. In: K.K. Barnes, W.M. Carleton, H.M. Taylor, R.I. Throckmorton and G.E. VandenBerg (Editors), Compaction of Agricultural Soils. Am. Soc. Agric. Eng., St. Joseph, MI, pp. 47-105. GENSTAT 5 COMMITTEE, 1987. GENSTAT 5 reference manual. Clarendon Press, Oxford, 749 pp. Hettiaratchi, D.R.P., 1987. A critical state soil mechanics model for agricultural soil. Soil Use Manage., 3: 94-105. Kirby, J.M., 1986. The critical state concept and the behaviour of powders in the ring shear cell test. Powder Technol., 47 (2): 71-78. Kirby, J.M., 1989. Measurements of the critical state and yield surfaces of some unsaturated agricultural soils. J. Soil Sci., 40 ( 1 ): 167-182. Kirby, J.M., 199 I. Strength and deformation of an agricultural soil--measurement and practical significance. Soil Use Manage., 7 (4): 223-229. Kirby, J.M. and Blunden, B.G., 199 I. Interactions of soil deformations, structure and permeability. Austr. J. Soil Res., 29:391-404. Kuipers, H. and Kroesbergen, B., 1966. The significance of moisture content, pore space, method of sampling and type of shear annulus used in laboratory shear testing of soils. J. Terramechanics, 3:17-28. McKyes, E., 1989. Agricultural Engineering Soil Mechanics. Elsevier, Amsterdam, 292 pp. Olsen, H.I., 1984. A torsional shearing device for field tests. Soil Tillage Res., 4:599-61 I. Payne, P.J.C. and Fountaine, E.R., 1952. A field method of measuring the shear strength of soils. J. Soil Sci., 3( 1 ): 136-144. Sallberg, J.R., 1965. Shear strength. In: C.A. Black, D.D. Evans, J.L. White, L.E. Ensminger and F.E. White (Editors), Methods of Soil Analysis--Physical and Mineralogical Properties, Including Statistics of Measurement and Sampling, Agronomy No. 9. Am. Soc. Agron., Madison, WI. Schafer, R.L., Bockhop, C.W. and Lovely, W.G., 1963. Vane and torsion techniques for measuring soil shear. Trans. Am. Soc. Agric. Eng., 6: 57-60. Wills, B.M.D., 1963. The measurement of soil shear strength and deformation moduli and a comparison of actual and theoretical performance of a family of rigid tracks. J. Agric. Eng. Res.,8:ll5-131. Wroth, C.P., 1984. The interpretation of in situ soil tests. G6otechnique, 34 (4): 449-489. Wroth, C.P., 1987. The behaviour of normally consolidated clay as observed in undrained direct shear tests. G6otechnique, 37 ( 1 ): 37-43.
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Elsevier Science Publishers B.V., Amsterdam
Cohron sheargraph data: interpretation using critical state soil mechanics J.M. K i r b y a a n d P.D. Ayers b aCSIRO Division of Soils, GPO Box 639, Canberra, A.C.T. 2601, Australia bAgricultural and Chemical Engineering Department, Colorado State University. Fort Collins, CO 80523, USA (Accepted 14 January 1993)
ABSTRACT Critical state soil mechanics was used to explain the differences in stress paths recorded in sheargraph tests in weak, strong and medium-strong soils. It was projected that the cohesion of both peak and ultimate strength lines would be near zero for weak and medium-strong soils, but the peak cohesion would be high for strong soil. The friction angle of the peak strength line was projected to be lower than that of the ultimate line for strong soils and less than or equal to that of the ultimate line for weak and medium-strong soils. The projections about the type of stress path and the relationship between cohesion and friction for peak and ultimate strength lines were tested by performing field sheargraph tests in a Vertisol. It was found that the friction angle of the ultimate line was higher than that of the peak line, which suggests that in loose to medium dense soils it may be more appropriate to use the ultimate line for tine design procedures that employ the friction angle in calculations. The different forms of stress path recorded in field sheargraph tests were associated with different regimes of soil behaviour in laboratory shear, in which the height change during shear was measured. Tests with strong soil resulted in sheargraph tests that showed brittle stress paths with well defined shear stress peaks, and in laboratory shear tests that showed shear accompanied by expansion. Tests with weaker soil resulted in sheargraph stress paths without well defined peaks, and in laboratory shear accompanied by compression. Shear accompanied by expansion is desirable in tillage for seedbed preparation and therefore the sheargraph may be useful in identifying the right soil conditions for tillage.
INTRODUCTION
The Cohron sheargraph is one of a number of torsional shear devices used to assess soil strength in situ (Cohron, 1963; Freitag, 1971; McKyes, 1989). In common with other similar instruments, it offers the advantages over laboratory tests of speedy results and minimal disturbance of the soil. All field torsional shear devices suffer from the disadvantage that the stress distribution on the shear surface and the geometry of the shear plane cannot Correspondence to. J.M. Kirby, C S I R O Division of Soils, G P O Box 639, Canberra, A.C.T. 2601, Australia.
© 1993 Elsevier Science Publishers B.V. All rights reserved 0167-1987/93/$06.00
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J.M. KIRBY AND P.D. AYERS
be known exactly (Freitag, 1971 ). The various devices have been found to give different values for cohesion and friction, and these may differ again from laboratory measurements (Payne and Fountaine, 1952; Bailey and Weber, 1965; Dunlap et al., 1966). The differences may arise from difficulties in interpreting the stress system and failure geometry. Differences between field and laboratory measurements may be due to soil disturbance induced during sampling and transport to the laboratory (Payne and Fountaine, 1952 ). Ayers ( 1987 ) showed that the failure points measured by a Cohron sheargraph may not be linear which further complicates the estimation of cohesion and friction. On the other hand, Schafer et al. (1963) considered that the cohesion and friction were reliably measured by a torsional test. Wills ( 1963 ) and Kuipers and Kroesbergen (1966) also considered that differences between shear devices were small. The problems of interpretation not-withstanding, the advantages of field torsional shear devices are sufficient to ensure their continued use (Olsen, 1984; Ayers, 1987). Ayers ( 1987 ) reported a large number of measurements with a sheargraph to examine the relationships between cohesion, friction, moisture content and density. The results were found to be very reproducible. Sheargraph data are usually analysed to estimate the soil strength parameters of cohesion and friction angle. This paper reports an interpretation of results from the Cohron sheargraph in terms of the critical state concept. A comprehensive review of soil strength and deformation as offered by the critical state concept has been described by Hettiaratchi ( 1987 ) and Kirby ( 1989, 1991 ) for agricultural soils. This concept divides soil deformation into two regimes, in one of which the soil compresses during shear and in the second of which it expands during shear. The former regime occurs, for example, in rice puddling or the formation of ploughpans, while the latter regime occurs (desirably) during conventional tillage for seed-bed preparation. Several predictions of sheargraph results arising from the critical state concept are outlined and the degree to which they describe results from in situ tests is examined. The results from in situ sheargraph tests are also compared with the results from laboratory direct shear box tests. EXPLANATION OF SHEARGRAPH RESULTS BASED ON THE CRITICAL S T A T E CONCEPT
The design and operation of the Cohron sheargraph was fully described by Cohron (1963). As shown in Fig. l, it consists of a shear head (which is a grousered plate of radius 20.3 m m ) that grips the soil. This is attached to a spring which, when pushed down, causes the plate to exert a normal stress on the soil. When twisted, the spring exerts a torsional force on the plate, which causes a shear stress to be exerted on the soil. Compression or torsion of the spring is controlled by hand via the handle at the top of the sheargraph and is
COHRON SHEARGRAPH DATA
213
Handle
- -
Bearings
- -
Recording drum
Recording
Spring
H==~--Shear
head
Fig. I. Schematicdiagram of the Cohron sheargraph. recorded by a pen on graph paper attached to the recording dram (Fig. 1 ). The graph paper is supplied with the sheargraph and is calibrated for normal and shear stress in units of psi. The m a x i m u m normal stress that can be recorded is 20 psi (about 140 kPa). The Cohron sheargraph is operated in such a way that the normal stress is increased from zero to a predetermined value while the shear stress is zero (Stage I in Fig. 2). The normal stress is then held constant while the shear stress is increased (Stage II in Fig. 2). This requires considerable practice. Usually, the operator cannot hold the normal stress truly constant during this stage of the test and a certain a m o u n t of 'wobble' is recorded on the graph paper. Once the shear stress reaches a maximum, the shear and normal stresses are released together (Stage III in Fig. 2). This stage is easier to control and the recorded trace is usually much smoother during this phase of the test. The stress path (sequence of shear and normal stresses) is recorded on a chart. The exact shape of the stress path will depend on the properties of the soil, in particular whether it is normally or over-consolidated. In traditional interpretations of sheargraph results only the m a x i m u m shear stress is used in the analysis for cohesion and friction. The friction angle is
214
J.M. KIRBY AND P.D. AYERS
III e-
II
l
~>
Normal stress, Fig. 2. General form of the stress path in a sheargraph test. Stage I, normal stress increased at start of test. Stage II, shear stresses increased until excessive rotation of the sheargraph occurs. Stage III, shear and normal stresses reduced.
the slope of the straight line fitted to a number of points of maximum shear stress at several normal stresses. The cohesion is the intercept of the straight line. In this paper the whole stress path will be examined. Typically, pore water pressures are not measured and effective stresses are not determined. The analysis is therefore based on the total applied stresses.
Critical state diagram and yield behaviour The critical state concept considers that a continuously deformed particulate material will come to a critical state in which further deformation proceeds without change in stress or volume. The critical state is defined by a unique line in stress-void ratio space (Fig. 3). The critical state concept is usually defined in terms of stress invariants, but will be discussed here in terms of normal and shear stress to be consistent with the use of a sheargraph in which these are the recorded variables. This approach is less general than the use of invariants because the influence of horizontal stress is not accounted for (see Kirby, 1989, 1991 ). The critical state concept can be broadened to incorporate state boundary or yield surfaces. Yield~urfaces define the onset of permanent, or irrecoverable, deformation. With reference to Fig. 3, the soil can exist in a stress state on or within a yield surface in shear stress/ normal stress/void ratio space. Within the yield surface behaviour is elastic and can be described by elastic walls. For instance a sample at A (Fig. 3) would, on removal of stress to B, experience an increase in volume owing to elastic rebound. The elastic wall is, therefore, not parallel to the normal stress
COHRON SHEARGRAPHDATA
21 5
lShear /stress
Normal stress ,~
Criticalstate
Normally / I ] /.,"~ consolidated I / ~ / / surface / / [ " / / / ~'Over consolidatedsurface Void ratio Fig. 3. Critical state diagram. See text for explanation of A - D .
axis. The elastic wall increases in size with decreasing void ratio, i.e. the soil is becoming stronger with increasing density. Projecting an elastic wall onto the shear stress/normal stress plane gives Fig. 4 (see Kirby, 1989, 1991 ). The critical state line defines shear and normal stress conditions at which shear takes place with no volume change. To the left of the critical state line, on the over consolidated yield surface, shear is strain softening and accompanied by a volume increase, as shown by the stress path beginning at point C on Fig. 4. On the normally consolidated part of the yield surface, shear is strain hardening and accompanied by a volume decrease (stress path beginning at D, Fig. 4 ). Shear at constant normal stress on the yield surfaces causes the surfaces to change as shown in Fig. 4. The overall paths followed are shown in Fig. 3. It can be seen from Fig. 4 that the peak shear stress experienced by an over consolidated sample is given by the point of intersection of the stress path with the yield surface, whereas for a normally consolidated sample the peak shear stress is given by the critical state line (which strictly is reached only after infinite deformation ). In a sheargraph test, the stress path could start at any normal stress, a, between the origin and the point at which the yield surface meets the axis (shown as trm on Fig. 4). o m is the m a x i m u m compressive stress experienced by the soil. This stress could be a stress experienced prior to the sheargraph test in which case the test will be performed with tr< o m. Alternatively, the maxim u m stress could be that imposed by the sheargraph in the first stage of the
216
J.M. KIRBY AND P.D. AYERS
Yielding with volume increase
I r-
• • Changing size
Yielding with volume decrease
I
r
I -..1~ I I I
'',
, of yieldsurface~ ',
~.,.,~,~ ,,,l-/
.......
~xx xx
B
C
Normalstress, o
A (~m
Fig. 4. Yield surface and critical state line projected onto a normal stress-shear stress plane. Lines C and D show stress paths followed by over-consolidated soil and normally consolidated soil respectively. The dashed lines indicate the change in the size of the yield surfaces that accompanies shear at constant normal stress.
test, in which case tr= o"m. The shear stresses should increase until the amount of deformation is excessive. This should happen either when the yield surface is reached on the over consolidated yield surface where volume increase occurs (Fig. 4), or as the critical state line is approached on the normally consolidated yield surface where volume decrease occurs. After the onset of yielding, the stress path should move towards the critical state line (see Kirby, 1989). The critical state line is, by definition, the line defining the ratio of shear to normal stress when the soil is sheared to a very large deformation. Therefore, once the critical state line is reached, the stress path should remain on the line as the stresses are reduced at the end of the test. When deformation takes place on the normally consolidated surface, the size of the yield surface increases as the soil becomes denser and stronger (Fig. 4 ). The stresses in a sheargraph test should approach the critical state line in the later stages, but the actual critical state is unlikely to be observed in a shear test (see Kirby, 1991 ). The critical state is reached after very large (strictly infinite) deformations whereas deformations in the sheargraph are limited. Furthermore, shear in the expansive regime is restricted to local zones (Kirby, 1991; Kirby and Blunden, 1991 ), whereas the critical state is usually taken to imply general deformation. Therefore, the path followed by the sheargraph test back to the origin in the final stages is unlikely to define the critical state line. In this paper, this path will be referred to as the ultimate line to denote the ultimate condition reached in a sheargraph test.
217
COHRON SHEARGRAPH DATA
Behaviour of weak soil Weak soil is here defined as being soil which is sheared on the normally consolidated surface (Figs. 3 and 4 ). The m a x i m u m stress, am, is imposed by the sheargraph at the time of normal stress application. Thus the stress paths start from the points labelled o"m (Fig. 5 ) and, at first, show increasing shear stresses at constant normal stress. However, as the shear stresses increase, the soil should compress and become denser and stronger and the yield surface should increase in size such that the stress path remains on the surface (e.g. Kirby, 1989), as shown by Path III in Fig. 5. As the ultimate line is approached with increasing shear stress, the soil begins to fail causing the grousered plate in contact with the soil to rotate. The test is discontinued by reducing the normal stress. Reduction of the normal stress at this stage should result in the shear stress remaining approximately constant, following the yield surface until the ultimate line is reached. The stress path should then travel down the ultimate line. The stress path is therefore projected to rise vertically, curve to the left and then follow a line to the origin, as shown in Fig. 5. Three such stress paths for tests at different a m (i.e. ami , O'mII and O'miii ) would all show the same shape, but increase in size with increasing o"m (Fig. 5 ). Since they all show the same shape, it is projected that lines fitted to the peak shear stresses and the ultimate lines would both show no (or, taking experimental variation into account, small ) cohesion intercepts (Fig. 5 ). The friction angle of the peak line is projected to be equal to or less than that of the ultimate line. Based on the critical state soil mechanics relationships between shear and volume change, Ultimate strength l i n e ~ Peaks t r e n g t h ~ ~ l i ~ Increased sizeof yield surface l l I ~
.........J~
..,~.~..
~
d IIl ,s~ S
%%
,%
'\ > °ml
°ml]
(~mIII
Normal stress, o Fig. 5. Stress paths predicted for weak samples. Stress paths I, H and []I each starts at a different maximum stress O'mi, O'mlI and 0"mlilimposed by the sheargraph. The increased size of the yield surface resulting from the soil becoming denser and stronger is shown by the dotted lines.
218
J.M. KIRBY AND P.D. AYERS
it is also projected that shear would be accompanied by a decrease in the volume of the soil. In weak soils, shear stress and deformation tend to increase gradually, without any clear discontinuity, until the critical state condition is achieved at infinite shear strain. Once the critical state is achieved, the soil may be deformed with little or no change in shear or normal stress. In practice, a sheargraph test will be discontinued before the critical state is achieved as the operator can impose only a finite deformation. The actual amount of deformation at which the operator chooses to discontinue the test, and therefore the peak shear stress recorded, is somewhat arbitrary. However, it is projected from the critical state concept that the friction angle of the peak strength line can never be greater than, and would generally be less than that of the ultimate line. The difference between the two would depend on the choice of when to discontinue the test.
Behaviour of strong soil Strong soil is defined as being soil which is sheared on the over consolidated surface (Figs. 3 and 4). Thus the yield surface (the surface of stress states describing the onset of permanent deformation) is large. Yielding would begin once the yield surface is reached and the shear stresses should reduce (abruptly in the case of very brittle soil) until the ultimate line is reached. Thus, the stress path is projected to rise vertically, then fall vertically and then turn and follow a line towards the origin (Fig. 6). The ultimate line is projected to show a zero (or, taking experimental variation into account, small) cohesion intercept, but the peak line is projected to show a large cohesion intercept. The slope (friction angle) of the peak line is projected to be lower than that of the ultimate line (Fig. 6 ). Shear is projected to be accompanied
Peastkrengtline. h ~ 1 ? ~o
~,~--~ ~UItimatsterengtlhine III
,t I !
Normstalress,c Fig. 6. Stress paths predicted for strong samples.
219
C O H R O N SHEARGRAPH DATA
by volume increases. It is also projected that the difference in shear stress between the peak and ultimate lines ('peakedness' of the stress path) and the volume increase would both be larger for tests at smaller normal stresses (see stress paths I, II and III in Fig. 6 ). This 'peakedness' is associated with brittle failure.
Behaviour of medium strong soil Medium-strong soil is soil which is sheared partly on the over consolidated surface and partly on the normally consolidated surface (Figs. 3 and 4). It is projected that both types of stress path would be present (Fig. 7 ). Stress paths that meet the yield surface at about its intersection with the ultimate line would rise vertically and then sharply turn and follow a line towards the origin, as shown by stress path II in Fig. 7. The ultimate line is projected to have a zero (or, taking experimental variation into account, small) cohesion intercept. The peak line is projected to have a moderate cohesion intercept and a friction angle a little less than the ultimate line. The difference in cohesion and friction between the two lines would depend on the actual stress levels in relation to O'm and on the shape of the yield surface. Thus, in Fig. 7, if stress paths I, II and III were located at different values of normal stress, then they would meet the yield surface at different points and different peak shear stress values would be recorded. Hence, a different peak line with different cohesion and friction would be interpreted from the data. Shear is projected to be accompanied by only small volume changes, with the soil expanding in some tests and compressing in other, higher stress, tests. The predictions made above were tested experimentally by performing sheargraph tests on soil in different states (of density and moisture content),
Peak strength line ~
~Ultimate ~ . . .strength . ~ ~ jline.
s"
i/
Normalstress,~ Fig.7. Stresspathspredictedformedium-strongsamples.
II>
220
J.M. KIRBY AND P.D. AYERS
such that it had different strengths. Samples were also taken to the laboratory to perform shear box tests and examine the predictions of volume change. MATERIALS AND METHODS
The soil used for this study was a Vertisol at the University of Queensland, Gatton College, Qld. Wheeltracks and permanent beds and different depths at this site had quite different strengths. Several areas were chosen such that a range of strengths could be investigated. Tests were performed at the surface or at depths of up to 150 ram. The Cohron sheargraph tests were performed in situ at this site. At each location, nine tests were performed--three each at normal stresses of 35, 69 and 103 kPa ( 5, 10 and 15 psi). In the strongest soil the sheargraph could not be pushed in manually. Therefore, a short column of soil that fitted the inside of the grousered plate was carved with a pocket knife. Soil samples were also taken at locations adjacent to the sheargraph tests. The samples were taken in thin-walled, square-sectioned metal containers which were 2 cm high and 6 cm on each side. The samples were transported to the laboratory, where they were transferred from these containers into a shear box having the same dimensions. The procedure in the shear box tests followed that described by Sallberg ( 1965 ). Shear tests were performed at the same normal stresses as the sheargraph tests. The change in height was measured during each test. After each test the soil was weighed, dried in an oven at 105 °C and weighed again to determine the moisture content. Statistical analysis of the data was performed using GENSTAT 5, PC version (GENSTAT, 1987). RESULTS AND DISCUSSION
The soil was classified as being weak, weak to m e d i u m or strong according to the shape of the sheargraph chart. Examples of sheargraph charts from tests in weak and strong soil are shown in Figs. 8 and 9. The stress paths followed shapes similar to those of Figs. 5 and 6. Figure 10 shows a sheargraph chart that has some features of a medium-strong soil, i.e. the stress paths rise vertically and then turn sharply left to follow the ultimate line (see stress path II in Fig. 7 ). The soil of this sheargraph chart was classified as weak to medium. No chart showed all the features predicted for a medium-strong soil. The cohesion and friction angles of both peak and ultimate lines from nine test series are given in Table 1. The soil conditions in the table are identified on the basis of the shape of the stress paths on the sheargraph charts. The table shows that the ultimate cohesion was small for all the soil conditions tested, as predicted. The peak cohesion was large in strong soil, but small in weak and weak to m e d i u m soil. The ultimate friction angle was always higher than
221
C O H R O N S H E A R G R A P H DATA
100
Or)
5O
0
50
1O0
Normal stress, kPa
Fig. 8. Stress paths recorded in field sheargraph tests on weak soil. Note: for clarity, only one straight line is shown in the earlypart of the test at each level of normal stress; in practicethree lines wererecordedand each showedsome 'noise' (see text for explanation). the peak angle of friction, but the difference between the two was small in the case of the weak to medium soil. In the strong soil, the ultimate angle of friction was much higher than the peak angle of friction, again following the predicted behaviour. Table 2 shows summary data for the height changes and density that accompanied shear in the laboratory shear box tests. As shown in the table, both the density and height changes were significantly different among the weak, medium and strong soil. The density was regarded as an estimate only, because sinkage of the ridged shear box plates into the soil made it difficult to estimate the volumes of samples accurately. The volume was estimated from height measurements taken with the ridged plates in place and thus the strong soil, into which there was little or no sinkage, was likely to be overestimated. Therefore the density of the strong soil was likely to be underestimated and the difference in density between the strong and weak soil was, if anything, greater than that shown in the table. The samples of strong soil increased in height, and therefore volume, during shear, whereas the samples of weak soil decreased in height and therefore volume (Table 2 ). This behaviour agreed with the predictions. The mediumstrong soil also decreased in height (though not as much as the weak soil) in contrast to the prediction that there would be little or no volume change. A
222
J.M. KIRBY AND P.D. AYERS
100 0,_
50
I 50 Normal stress, kPa
0
I 100
Z>
Fig. 9. Stress paths recorded in field sheargraph tests on strong soil. Note: for clarity, only one straight line is shown in the early part of the test at each level of normal stress; in practice three lines were recorded and each showed some 'noise' (see text for explanation).
100 ¢x3 O.-
e-
~
50
m
I> 50 100 Normal stress, kPa Fig. 10. Stress paths recorded in field sheargraph tests on weak to medium-strong soil. Note: for clarity, only one straight line is shown in the early part of the test at each level of normal stress; in practice three lines were recorded and each showed some 'noise' (see text for explanation).
COHRON SHEARGRAPHDATA
223
TABLEI
Cohesionand ~ictionofpeakandultimatelines~om thefieldsheargraphtests Soil condition
Weak Weak Weak Weak-medium Weak-medium
Strong Strong Strong Strong
Cohesion (kPa)
Friction angle
peak
ultimate
peak
ultimate
R 2 (peak)
12.4 11.8 6.0 0.3 3.9 94.2 61.5 56.2 31.7
3.5 2.1 4.9 0.7 2.1 0? 0 6.3 4.9
34 21 30 43 38 48 27 27 44
44 31 33 45 38 56? 45 46 46
0.912 0.664 0.821 0.982 0.837 0.321 0.575 0.774 0.821
~This soil exhibited very brittle behaviour, with abrupt release of shear stress after failure. This made identification of the ultimate line difficult and the values of cohesion and friction angle are uncertain; this is indicated by the question marks. TABLE 2 Summary data for height change and estimated density in shear box tests
Weak Medium strong
Strong Probability leveP
Height change (mm)
Density ( m g m -3 )
- 1.05 - 0.53 0.39 < 0.001
1. I 1.5 1.7 < 0.001
~The probability level is the probability that the means of the different soils come from the same population.
number of reasons could explain the failure to meet this criterion. Firstly, the shear box had limited travel and samples were still changing volume at the end of tests. All samples decreased in height initially, but the strong samples and most of the medium-strong samples then increased in height at a later stage of the test. It is probable that, had the shear box been capable of further shear displacement, the medium-strong samples would have shown less decrease in height. It is also known that height change is affected by the stress conditions (Kirby, 1986) and speed (Blunden et al., 1992) in shear tests. Other reasons could include disturbance of the soil during sampling, and errors in height change measurements owing to the ridged plates sinking in as the tests progressed. The prediction that the 'peakedness' of the stress paths would be related to the volume change could not be tested with the data available.
224
J.M. KIRBYANDP.D.AYERS
CONCLUSIONS
In summary, the volume change of the weak, medium and strong soil partially followed the conceptual model. To the extent that the predictions failed, the failure can be attributed to a number of factors in the sampling and testing procedure. The stress paths and cohesion and friction of both the peak and ultimate lines followed the predictions. Several considerations follow from these findings. Firstly, in loose and medium dense soil the friction angle of the ultimate line was always higher than that of the peak line. If these data were used for predicting forces on tines, higher forces would be predicted using the friction angle of the ultimate line. The friction angle of the peak line thus might result in an inadequate design. It is questionable which friction angle is appropriate in tine design. These considerations apply also to other design procedures that use the friction angle. Wroth ( 1984, 1987 ) pointed out that some forms of direct shear box test may also underestimate friction angles and therefore be inappropriate for civil engineering soil mechanics design. Secondly, Kirby ( 1991 ) showed that soil failure in the expansive regime is appropriate for conventional tillage, while the compressive regime is appropriate for preparation of rice soils. Since the stress paths recorded by the sheargraph were successfully identified with these regimes of failure, it appears that the sheargraph could be used as a simple field tool for assessing whether soil is in the right condition for various forms of tillage. Thirdly, the ultimate line measured in the various sheargraph tests seems to separate the two forms of shearing behaviour. As such it might be identified with the critical state line. However, as was noted in the Introduction, friction angles measured with a sheargraph may not correspond to those measured by other forms of shear test. The slope of the ultimate line may well differ from the slope of the critical state line measured in other tests. Furthermore, as noted previously, the critical state is unlikely to be observed in sheargraph tests. Thus the ultimate line, while being somewhat analogous to the critical state line, should not be identified as being exactly equivalent to it.
REFERENCES Ayers, P.D., 1987. Utilizing the torsional shear test to determine soil strength-properties relationships. Soil Tillage Res., 10: 373-380. Bailey, A.C. and Weber, I.A., 1965. Comparison of methods of measuring soil shear strength using artificial soils. Trans. Am. Soc. Agric. Eng., 8:153-160. Blunden, B.G., Kirby, J.M., Humphries, E. and Muirhead, W.A., 1992. Mechanical properties of a cracking grey clay used for rice production in Australia. Soil Tillage Res., 26:55-67. Cohron, G.T., 1963. Soil sheargraph. Agric. Eng., 44: 554-556. Dunlap, W.H., Vandenberg, G.E. and Hendrick, J.G., 1966. Comparison of soil shear values
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obtained with devices of different geometrical shapes. Trans. Am. Soc, Agric. Eng., 9: 896900. Freitag, D.R., 1971. Methods of measuring soil compaction. In: K.K. Barnes, W.M. Carleton, H.M. Taylor, R.I. Throckmorton and G.E. VandenBerg (Editors), Compaction of Agricultural Soils. Am. Soc. Agric. Eng., St. Joseph, MI, pp. 47-105. GENSTAT 5 COMMITTEE, 1987. GENSTAT 5 reference manual. Clarendon Press, Oxford, 749 pp. Hettiaratchi, D.R.P., 1987. A critical state soil mechanics model for agricultural soil. Soil Use Manage., 3: 94-105. Kirby, J.M., 1986. The critical state concept and the behaviour of powders in the ring shear cell test. Powder Technol., 47 (2): 71-78. Kirby, J.M., 1989. Measurements of the critical state and yield surfaces of some unsaturated agricultural soils. J. Soil Sci., 40 ( 1 ): 167-182. Kirby, J.M., 199 I. Strength and deformation of an agricultural soil--measurement and practical significance. Soil Use Manage., 7 (4): 223-229. Kirby, J.M. and Blunden, B.G., 199 I. Interactions of soil deformations, structure and permeability. Austr. J. Soil Res., 29:391-404. Kuipers, H. and Kroesbergen, B., 1966. The significance of moisture content, pore space, method of sampling and type of shear annulus used in laboratory shear testing of soils. J. Terramechanics, 3:17-28. McKyes, E., 1989. Agricultural Engineering Soil Mechanics. Elsevier, Amsterdam, 292 pp. Olsen, H.I., 1984. A torsional shearing device for field tests. Soil Tillage Res., 4:599-61 I. Payne, P.J.C. and Fountaine, E.R., 1952. A field method of measuring the shear strength of soils. J. Soil Sci., 3( 1 ): 136-144. Sallberg, J.R., 1965. Shear strength. In: C.A. Black, D.D. Evans, J.L. White, L.E. Ensminger and F.E. White (Editors), Methods of Soil Analysis--Physical and Mineralogical Properties, Including Statistics of Measurement and Sampling, Agronomy No. 9. Am. Soc. Agron., Madison, WI. Schafer, R.L., Bockhop, C.W. and Lovely, W.G., 1963. Vane and torsion techniques for measuring soil shear. Trans. Am. Soc. Agric. Eng., 6: 57-60. Wills, B.M.D., 1963. The measurement of soil shear strength and deformation moduli and a comparison of actual and theoretical performance of a family of rigid tracks. J. Agric. Eng. Res.,8:ll5-131. Wroth, C.P., 1984. The interpretation of in situ soil tests. G6otechnique, 34 (4): 449-489. Wroth, C.P., 1987. The behaviour of normally consolidated clay as observed in undrained direct shear tests. G6otechnique, 37 ( 1 ): 37-43.