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Research of soil–water characteristics and shear strength features of Nanyang expansive soil
Engineering Geology 65 (2002) 261 – 267 www.elsevier.com/locate/enggeo
Research of soil–water characteristics and shear strength features of Nanyang expansive soil Linchang Miao*, Songyu Liu, Yuanming Lai College of Traffic Engineering, Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, China Received 8 December 2000; accepted 31 October 2001
Abstract Nanyang expansive soil is investigated in its unsaturated state in this paper. The wetting – drying cycle tests of soil – water characteristics of Nanyang expansive soil have been performed in the laboratory. The test results show that the soil – water characteristic curve of the pre-load specimen can well reflect the soil property function of expansive soil. The strength features of the different suction states of the unsaturated expansive soil are also investigated. The hyperbolic model of the suction strength is presented and the parameters of this model are easily determined by tri-axial tests of unsaturated soils. The hyperbolic model is conveniently applied to predict suction strength of an unsaturated soil. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Expansive soil; Soil – water characteristic curve; Suction; Suction strength; Hyperbolic model
1. Introduction The expansive soil is a particular clay that is of special characteristics (i.e., swell – shrinking, crack and over-consolidation characteristics). The characteristics of the expansive soil are strongly related to the change in suction. The behavior of an unsaturated soil is strongly related to the pore size and pore geometrical distribution. As a result, the soil –water characteristic curve defines the degree of saturation corresponding to a particular suction in the soil and becomes a dominant relationship for understanding unsaturated soil behavior, but parameters of the equation of the soil –water characteristic *
Corresponding author. E-mail addresses: [email protected] (L. Miao), [email protected] (S. Liu), [email protected] (Y. Lai).
curve are difficult to determine. A number of equations have been proposed to best-fit the soil – water characteristic curve empirically. The following equation is the one proposed by Fredlund and Xing (1994) to best-fit the soil – water characteristic curve empirically: hðua uw ,as ,ns ,ms Þ ¼ Cðua uw Þ
hs fln½eððua uw Þ=as Þns gms
ð1Þ
where: h = volumetric water content, hs = volumetric water content at saturated, e = 2.718, ua = pore air pressure, uw = pore water pressure, (ua uw) = matric suction, af = soil parameter related to the air entry of the soil and equal to the inflection point on the curve, nf = soil parameter related to the rate of desaturation, mf = soil parameter related to residual water content, and C(ua uw) = correction factor to ensure that the function goes through 1,000,000 kPa of suction at zero
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water content. However, the conventional soil –water characteristic curve does not consider the actual stress state of soil mass in the field, and some parameters are determined with difficulty. The shear strength equation for an unsaturated soil is presented by Fredlund et al. (1978) as: sf ¼ cVþ ðr ua Þtan/Vþ ðua uw Þtan/b
field is usually subjected to certain stress. Thus, there are some unestimated errors using Eq. (3) to compute soil property function for unsaturated soils. For this reason, the soil – water characteristic curve and shear strength features of Nanyang expansive soils have been studied in the paper.
ð2Þ
where: sf = shear strength of an unsaturated soil, c V= effective cohesion of the soil, /V= effective angle of shearing resistance for a saturated soil, (r ua) = net normal stress, (ua uw) = soil suction, and /b = angle of shearing resistance relative to an increase in suction, but /b is difficult to determine. Fredlund et al. (1994) and Vanapalli et al. (1996) suggested several models for predicting the shear strength of an unsaturated soil using the soil –water characteristic curve and the saturated shear strength parameters. Eq. (3) given below can be used for predicting the shear strength of unsaturated soil: sf ¼ cVþ ðr ua Þtan/Vþ ðua uw Þtan/V h hr
hs hr
ð3Þ
where: hs = saturated volumetric water content, hr = volumetric water content at residual condition. The second term of Eq. (3) is the shear strength contribution due to suction. It can be expressed as h hr sus ¼ ðua uw Þtan/V ð4Þ hs hr where sus is suction strength. It indicates that the soil – water characteristic curve can be used to compute soil property functions for unsaturated soils approximately. However, soil – water characteristic curve is conveniently measured in the laboratory, whereas the soil in the
2. Physical mechanical parameters of Nanyang expansive soils Nanyang is located in Henan Province, China. It is a semi-arid region, and there is a lot of expansive soil in Nanyang area. The canal of China Middle Route South-to-North Water Transfer will cross through the area. The canal is a typical cut and fill high slope in expansive soils. In order to ensure the engineering safety of this canal, the mechanical parameters, deformation, soil –water characteristic curve, shear strength feature and slope stability must be investigated. The physical mechanical parameters of Nanyang expansive soils are measured in the laboratory and given in Table 1. The mineral components of Nanyang expansive soils are given in Table 2. These parameters show that Nanyang expansive soil is the middle grade expansive soil and the content of illite and montmorillonite is higher.
3. The soil –water characteristic curve The swell – shrinking deformation of expansive soil is strongly related to the variation of water content. It will be swelling as water content increases and shrinkage as water content decreases. The soil – water characteristic curve defines the relationship between the soil suction and volumetric or gravimetric water content, so the suction of the expansive soil should be related to water content.
Table 1 The physical mechanics parameters of Nanyang expansive soils Specific gravity
Dry density (g/cm3)
NMC W0 (%)
WP (%)
2.7
1.63
21.4
26.5
WL (%)
58.3
IP
31.8
Free sweling (%)
c V(kPa)
74.0
32.0
/ (j)
21.3
Granularity (%) > 0.05 mm
0.05 – 0.005 mm
< 0.005 mm
< 0.002 mm
6.7
48.6
44.7
24.8
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Table 2 The mineral components of Nanyang expansive soils (%) Montmorillonite Illite Kaolinite Felspar Hydromic Chlorite Others 23.1
38.5 8.3
10.1
5.5
6.4
8.1
The soil – water characteristic curve of a soil is conventionally measured by means of a pressure plate extractor in which any vertical or confining stress cannot be applied and volume change of the soil specimen is assumed to be zero. The soil in the field is usually subjected to certain stress. Although it is theoretically recognized that the stress state of a soil has some influence on the soil –water characteristic curve (Fredlund and Raharjo, 1993), Vanapalli et al. (1996, 1998) examined the influence of the total stress state on the soil –water characteristic curve of a compacted finegrained soil indirectly. In this paper, the influence of the stress state and wetting –drying cycles is studied for the soil – water characteristic curve of Nanyang expansive soil. For Nanyang expansive soil, two group tests of the soil –water characteristic curve are made using 15 bar of the pressure plate. One group specimen is saturated allowing volumetric change (i.e., no pre-load exerting on the specimen). The other group specimen is saturated maintaining constant volume (i.e., exerting a pre-load on the specimen). The two group expansive soil specimen are remolded specimen with a dry density of 1.5 g/cm3. Three wetting– drying cycles are measured for each group specimen in this test. Fig. 1 is the soil –water characteristic curve of no pre-load exerted on the specimen. Measured results show that the wetting –drying cycles of the expansive soil specimen are of obvious effect for the soil – water characteristic curve of the no pre-load specimen. There is a marked hysteresis between the drying and wetting curve for all no pre-load expansive soil specimen. The hysteresis potential is reduced as the number of wetting –drying cycles increases, and will tend to be stable. The soil – water characteristic curve of the exerting pre-load expansive soil specimen is shown in Fig. 2. From Fig. 2, it can be seen that the hysteresis between the drying and wetting curve is more stable as the number of wetting –drying cycles increases, and the influence of the wetting– drying cycles of the preload specimen is smaller than that of the no pre-load specimen. So the soil – water characteristic curve of
Fig. 1. Soil – water characteristic curve of no pre-load exerted on the specimen.
the pre-load specimen can well reflect the soil property function of expansive soil. Comparing Fig. 1 with Fig. 2, the two soil –water characteristic curves have obvious differences. This phenomena is mainly caused by the arrangement in different initial stress state. Further, the size of the hysteresis loops of between the drying and wetting curve seems to be dependent on the initial stress state of soil specimen. Parameters hs, hr determined would be stable and identical for one soil using the soil – water characteristic curve of the pre-load specimen. Fig. 3 is the soil – water characteristic curve of the pre-
Fig. 2. Soil – water characteristic curve of pre-load exerted on the specimen.
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load Nanyang expansive soil specimen in total suction range. The air entry value and the residual value of Nanyang expansive soil are approximately 25 and 1500 kPa, and parameters hs = 33.7% and hr = 9.2% according to Fig. 3, respectively.
4. Shear strength test 4.1. Shear strength test of saturated expansive soil The shear strength test of the saturated expansive soil is measured by using conventional tri-axial. The specimens are the remolded expansive soil specimen and dry density is 1.5 g/cm3. The tri-axial test results are shown in Fig. 4. The measured parameters of remolded expansive soil specimen is cV= 32 kPa, /V= 21.3j. 4.2. Shear strength test of the unsaturated expansive soils The specimens have been prepared to predetermine water content and density condition by static compaction. The specimens are the remolded Nanyang expan-
sive soil. The dry density is 1.5 g/cm3, and the initial water content is 17%. The tests of unsaturated soils are performed by controlling suction in us = ua uw = 50, 80, 120 and 200 kPa with unsaturated tri-axial. The tests are made under the condition of draining water, and the shear rate is 0.009 mm/min. Figs. 5– 8 show the stress –strain curve of the unsaturated soil tests in us = 50, 80, 120 and 200 kPa, respectively. Tri-axial test data are given in Table 3. In Table 3, ctotal = cV+ sus, cV is effective cohesive, sus is suction strength and (/b = tan 1(sus/us)) is the angle of shearing resistance relative to an increase in suction. /b decreases with suction increase. It is a nonlinear relationship between /b and suction. 4.3. Hyperbola model of suction strength The tri-axial tests of the unsaturated expansive soils demonstrate that cVand /Vare invariable, i.e., c V( = 32 kPa) and /V( = 21.3j) are independent from suction. Fig. 9 shows the relationship between us(us = ua uw) and sus, which is nonlinear. If sus and us are transformed to 1/us and 1/sus, it becomes an approximate linear relationship between 1/us and 1/sus. But when
Fig. 3. Soil – water characteristic curve of pre-load exerted on the specimen of Nanyang expansive soil.
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Fig. 6. Tri-axial test results of unsaturated expansive soil (us = 80 kPa).
Fig. 4. Tri-axial test results of saturated expansive soils.
us = 0, 1/us will be singularity, so 1/us and 1/sus may be transformed to 1/(us + pat) and 1/(sus + pat), where pat is atmospheric pressure. Fig. 10 shows the relationship between 1/(us + pat) and 1/(sus + pat). We can use a linear equation to describe that:
soils, so that sus = 0. If us = 0 and sus = 0 in Eq. (5), Eq. (5) will become: b¼
1a pat
ð6Þ
Inserting Eq. (6) to Eq. (5), we can obtain: 1 a ¼ þb sus þ pat us þ pat
ð5Þ
sus ¼
aus 1 þ 1a pat us
ð7Þ
where a and b are the test parameters and are determined by regressive analysis of test data of unsaturated soil. For Nanyang expansive soil, a = 0.54 and b = 0.0046 kPa 1. When us = 0, the soils are saturated
Eq. (7) is a hyperbola equation. This is the hyperbola model of the suction strength of unsaturated soils. When us = 0 in Eq. (7), sus = 0; and us ! l in Eq. (7), sus ! (a/(1/ a))pat. It indicates that the limit of
Fig. 5. Tri-axial test results of unsaturated expansive soils (us = 50 kPa).
Fig. 7. Tri-axial test results of unsaturated expansive soil (us = 120 kPa).
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Fig. 8. Tri-axial test results of unsaturated expansive soil (us = 200 kPa).
sus is (a/(1 a))pat. This illustrates that the suction strength is finite. Thus, equation of unsaturated soil strength can be re-written as: aus ð8Þ sf ¼ cVþ ðr ua Þtan/Vþ 1 þ 1a pat us When soil is saturated, i.e., us = 0, Eq. (8) will be reduced as follows: sf ¼ cVþ ðr ua Þtan/V We can apply the hyperbola model of suction strength to the practical engineering and predict and calculate the shear strength of unsaturated soils based on suction data of unsaturated soils. However, parameter a in Eq. (7) is constant for a certain range suction of unsaturated soil tri-axial, i.e., it is relative to the range suction of the test.
Fig. 9. The relationship curve between us and sus.
model of the suction strength, Eq. (4) (Vanapalli’s (1996) model) and Eq. (7) (the hyperbola model of this paper) could be used to calculate suction strength of Nanyang expansive soils, respectively. The calculating suction strength are shown in Table 4. The calculating results show that the calculating suction strength of Vanapalli’s model is increased as us > 1000 kPa (i.e., water content of the soil specimen is higher) and decreased as us > 1000 kPa (i.e., water content of the soil specimen is lower). This phenomenon illustrates that Vanapalli’s model might be used to describe the strength feature of an unsaturated soil in low suction. But the suction strength of the hyperbola model is increased as soil suction increases and there is a limit suction strength, which accords with prac-
4.4. Suction strength analysis Considering the soil – water characteristic curve of pre-load expansive soil specimen and the hyperbolic Table 3 Shear strength data of Nanyang expansive soil us (kPa) Ctotal (kPa) sus (kPa) c V(kPa) / V(j) /b (j)
50 51.2 19.2 32.0 21.3 21.0
80 59 30.6 31.8 21.4 20.9
120 71 39 32.1 21.2 18.0
200 89.3 57.3 31.9 21.3 16.0
Fig. 10. The means of parameters a and b.
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Table 4 Calculating suction strength of Nanyang expansive soils us (kPa) h (%) sus (kPa) in Eq. (4) sus (kPa) in Eq. (7)
10 32.9 3.8 5.2
50 31.6 17.8 21.9
100 29.6 32.5 37.0
150 28.1 45.1 47.9
tical condition. The hyperbola model of the suction strength could be used to reflect the strength behavior of an unsaturated soil. In Table 4, the calculating suction strength of both Vanapalli’s model and the hyperbola model are of basic agreement when soil suction is smaller than 300 kPa, which illustrates that the hyperbola model of suction strength is of reliability to describe the strength feature of an unsaturated soil.
5. Discussion What we just discussed is the essential problem that the engineering stability of the expansive soil slope will be assured in the canal of Middle Route South-to-North Water Transfer in China. The strength of the expansive soil is a problem too. This is related to the suction strength of expansive soil. Thus, the following work must be done. (1) Suction measure of the expansive soil. One method is to directly measure soil suction with sensors in the field. Another method will be to indirectly get the soil suction from the soil – water characteristic curve, but the method may produce some error. Our research results illustrate that the soil –water characteristic curve of pre-load specimen is better than that without pre-load specimen. (2) Stability research of expansive soil. If soil suction has been obtained, we can use the hyperbola model of suction strength presented in this paper to calculate suction strength and total cohesion of expansive soil and to predict the stability of expansive soil slope.
6. Conclusions (1) The soil –water characteristic curve and the size of the hysteresis loops are influenced by the initial
200 27.4 57.9 56.3
250 26.6 69.2 62.8
300 25.3 76.9 68.1
400 23.8 92.9 76.1
500 22.1 102.6 81.8
750 20.2 131.3 91.0
1000 16.0 108.2 96.4
stress state of the soil specimen. The hysteresis potential is reduced as the number of wetting– drying cycles increases and will tend to stabilize at last for without pre-load expansive soil specimen. (2) The hysteresis loops between the drying and wetting curve for pre-load expansive soil specimen are more stable, and the influence of the number of wetting –drying cycles is smaller, too. The soil –water characteristic curve of the pre-load specimen could well reflect the soil property function of expansive soil. Using the soil – water characteristic curve of the pre-load specimen, parameters hs, hr determined would be stable and identical for an unsaturated soil, and could predict the shear strength of unsaturated soils with Eq. (3). (3) The hyperbola model of suction strength presented by this paper could be used to reflect the strength behavior of an unsaturated soil and is of reliability to describe the strength feature of an unsaturated soil. The hyperbola model has an advantage in that the model parameter might be easily determined and has obvious meaning. The hyperbola model could conveniently be applied to predict suction strength. References Fredlund, D.G., Raharjo, H., 1993. Soil Mechanics for Unsaturated Soils. Wiley Interscience, New York. Fredlund, D.G., Xing, A., 1994. Equations for the soil – water characteristic curve. Can. Geotech. J. 31, 521 – 532. Fredlund, D.G., Morgenstern, N.R., Widger, R.A., 1978. The shear strength of unsaturated soil. Can. Geotech. J. 15, 313 – 321. Fredlund, D.G., Xing, A., Huang, S., 1994. Predicting the permeability functions for unsaturated soils using the soil – water characteristic curve. Can. Geotech. J. 31, 533 – 546. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E., Clifton, A.W., 1996. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33, 379 – 392. Vanapalli, S.K., Pufahl, D.E., Fredlund, D.G., 1998. The effect of stress on the soil – water characteristic behavior of a compacted sandy-clay till. 51st Canadian Geotechnical Conference, Edmonton, 81 – 86.
Research of soil–water characteristics and shear strength features of Nanyang expansive soil Linchang Miao*, Songyu Liu, Yuanming Lai College of Traffic Engineering, Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, China Received 8 December 2000; accepted 31 October 2001
Abstract Nanyang expansive soil is investigated in its unsaturated state in this paper. The wetting – drying cycle tests of soil – water characteristics of Nanyang expansive soil have been performed in the laboratory. The test results show that the soil – water characteristic curve of the pre-load specimen can well reflect the soil property function of expansive soil. The strength features of the different suction states of the unsaturated expansive soil are also investigated. The hyperbolic model of the suction strength is presented and the parameters of this model are easily determined by tri-axial tests of unsaturated soils. The hyperbolic model is conveniently applied to predict suction strength of an unsaturated soil. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Expansive soil; Soil – water characteristic curve; Suction; Suction strength; Hyperbolic model
1. Introduction The expansive soil is a particular clay that is of special characteristics (i.e., swell – shrinking, crack and over-consolidation characteristics). The characteristics of the expansive soil are strongly related to the change in suction. The behavior of an unsaturated soil is strongly related to the pore size and pore geometrical distribution. As a result, the soil –water characteristic curve defines the degree of saturation corresponding to a particular suction in the soil and becomes a dominant relationship for understanding unsaturated soil behavior, but parameters of the equation of the soil –water characteristic *
Corresponding author. E-mail addresses: [email protected] (L. Miao), [email protected] (S. Liu), [email protected] (Y. Lai).
curve are difficult to determine. A number of equations have been proposed to best-fit the soil – water characteristic curve empirically. The following equation is the one proposed by Fredlund and Xing (1994) to best-fit the soil – water characteristic curve empirically: hðua uw ,as ,ns ,ms Þ ¼ Cðua uw Þ
hs fln½eððua uw Þ=as Þns gms
ð1Þ
where: h = volumetric water content, hs = volumetric water content at saturated, e = 2.718, ua = pore air pressure, uw = pore water pressure, (ua uw) = matric suction, af = soil parameter related to the air entry of the soil and equal to the inflection point on the curve, nf = soil parameter related to the rate of desaturation, mf = soil parameter related to residual water content, and C(ua uw) = correction factor to ensure that the function goes through 1,000,000 kPa of suction at zero
0013-7952/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 3 - 7 9 5 2 ( 0 1 ) 0 0 1 3 6 - 3
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L. Miao et al. / Engineering Geology 65 (2002) 261–267
water content. However, the conventional soil –water characteristic curve does not consider the actual stress state of soil mass in the field, and some parameters are determined with difficulty. The shear strength equation for an unsaturated soil is presented by Fredlund et al. (1978) as: sf ¼ cVþ ðr ua Þtan/Vþ ðua uw Þtan/b
field is usually subjected to certain stress. Thus, there are some unestimated errors using Eq. (3) to compute soil property function for unsaturated soils. For this reason, the soil – water characteristic curve and shear strength features of Nanyang expansive soils have been studied in the paper.
ð2Þ
where: sf = shear strength of an unsaturated soil, c V= effective cohesion of the soil, /V= effective angle of shearing resistance for a saturated soil, (r ua) = net normal stress, (ua uw) = soil suction, and /b = angle of shearing resistance relative to an increase in suction, but /b is difficult to determine. Fredlund et al. (1994) and Vanapalli et al. (1996) suggested several models for predicting the shear strength of an unsaturated soil using the soil –water characteristic curve and the saturated shear strength parameters. Eq. (3) given below can be used for predicting the shear strength of unsaturated soil: sf ¼ cVþ ðr ua Þtan/Vþ ðua uw Þtan/V h hr
hs hr
ð3Þ
where: hs = saturated volumetric water content, hr = volumetric water content at residual condition. The second term of Eq. (3) is the shear strength contribution due to suction. It can be expressed as h hr sus ¼ ðua uw Þtan/V ð4Þ hs hr where sus is suction strength. It indicates that the soil – water characteristic curve can be used to compute soil property functions for unsaturated soils approximately. However, soil – water characteristic curve is conveniently measured in the laboratory, whereas the soil in the
2. Physical mechanical parameters of Nanyang expansive soils Nanyang is located in Henan Province, China. It is a semi-arid region, and there is a lot of expansive soil in Nanyang area. The canal of China Middle Route South-to-North Water Transfer will cross through the area. The canal is a typical cut and fill high slope in expansive soils. In order to ensure the engineering safety of this canal, the mechanical parameters, deformation, soil –water characteristic curve, shear strength feature and slope stability must be investigated. The physical mechanical parameters of Nanyang expansive soils are measured in the laboratory and given in Table 1. The mineral components of Nanyang expansive soils are given in Table 2. These parameters show that Nanyang expansive soil is the middle grade expansive soil and the content of illite and montmorillonite is higher.
3. The soil –water characteristic curve The swell – shrinking deformation of expansive soil is strongly related to the variation of water content. It will be swelling as water content increases and shrinkage as water content decreases. The soil – water characteristic curve defines the relationship between the soil suction and volumetric or gravimetric water content, so the suction of the expansive soil should be related to water content.
Table 1 The physical mechanics parameters of Nanyang expansive soils Specific gravity
Dry density (g/cm3)
NMC W0 (%)
WP (%)
2.7
1.63
21.4
26.5
WL (%)
58.3
IP
31.8
Free sweling (%)
c V(kPa)
74.0
32.0
/ (j)
21.3
Granularity (%) > 0.05 mm
0.05 – 0.005 mm
< 0.005 mm
< 0.002 mm
6.7
48.6
44.7
24.8
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263
Table 2 The mineral components of Nanyang expansive soils (%) Montmorillonite Illite Kaolinite Felspar Hydromic Chlorite Others 23.1
38.5 8.3
10.1
5.5
6.4
8.1
The soil – water characteristic curve of a soil is conventionally measured by means of a pressure plate extractor in which any vertical or confining stress cannot be applied and volume change of the soil specimen is assumed to be zero. The soil in the field is usually subjected to certain stress. Although it is theoretically recognized that the stress state of a soil has some influence on the soil –water characteristic curve (Fredlund and Raharjo, 1993), Vanapalli et al. (1996, 1998) examined the influence of the total stress state on the soil –water characteristic curve of a compacted finegrained soil indirectly. In this paper, the influence of the stress state and wetting –drying cycles is studied for the soil – water characteristic curve of Nanyang expansive soil. For Nanyang expansive soil, two group tests of the soil –water characteristic curve are made using 15 bar of the pressure plate. One group specimen is saturated allowing volumetric change (i.e., no pre-load exerting on the specimen). The other group specimen is saturated maintaining constant volume (i.e., exerting a pre-load on the specimen). The two group expansive soil specimen are remolded specimen with a dry density of 1.5 g/cm3. Three wetting– drying cycles are measured for each group specimen in this test. Fig. 1 is the soil –water characteristic curve of no pre-load exerted on the specimen. Measured results show that the wetting –drying cycles of the expansive soil specimen are of obvious effect for the soil – water characteristic curve of the no pre-load specimen. There is a marked hysteresis between the drying and wetting curve for all no pre-load expansive soil specimen. The hysteresis potential is reduced as the number of wetting –drying cycles increases, and will tend to be stable. The soil – water characteristic curve of the exerting pre-load expansive soil specimen is shown in Fig. 2. From Fig. 2, it can be seen that the hysteresis between the drying and wetting curve is more stable as the number of wetting –drying cycles increases, and the influence of the wetting– drying cycles of the preload specimen is smaller than that of the no pre-load specimen. So the soil – water characteristic curve of
Fig. 1. Soil – water characteristic curve of no pre-load exerted on the specimen.
the pre-load specimen can well reflect the soil property function of expansive soil. Comparing Fig. 1 with Fig. 2, the two soil –water characteristic curves have obvious differences. This phenomena is mainly caused by the arrangement in different initial stress state. Further, the size of the hysteresis loops of between the drying and wetting curve seems to be dependent on the initial stress state of soil specimen. Parameters hs, hr determined would be stable and identical for one soil using the soil – water characteristic curve of the pre-load specimen. Fig. 3 is the soil – water characteristic curve of the pre-
Fig. 2. Soil – water characteristic curve of pre-load exerted on the specimen.
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L. Miao et al. / Engineering Geology 65 (2002) 261–267
load Nanyang expansive soil specimen in total suction range. The air entry value and the residual value of Nanyang expansive soil are approximately 25 and 1500 kPa, and parameters hs = 33.7% and hr = 9.2% according to Fig. 3, respectively.
4. Shear strength test 4.1. Shear strength test of saturated expansive soil The shear strength test of the saturated expansive soil is measured by using conventional tri-axial. The specimens are the remolded expansive soil specimen and dry density is 1.5 g/cm3. The tri-axial test results are shown in Fig. 4. The measured parameters of remolded expansive soil specimen is cV= 32 kPa, /V= 21.3j. 4.2. Shear strength test of the unsaturated expansive soils The specimens have been prepared to predetermine water content and density condition by static compaction. The specimens are the remolded Nanyang expan-
sive soil. The dry density is 1.5 g/cm3, and the initial water content is 17%. The tests of unsaturated soils are performed by controlling suction in us = ua uw = 50, 80, 120 and 200 kPa with unsaturated tri-axial. The tests are made under the condition of draining water, and the shear rate is 0.009 mm/min. Figs. 5– 8 show the stress –strain curve of the unsaturated soil tests in us = 50, 80, 120 and 200 kPa, respectively. Tri-axial test data are given in Table 3. In Table 3, ctotal = cV+ sus, cV is effective cohesive, sus is suction strength and (/b = tan 1(sus/us)) is the angle of shearing resistance relative to an increase in suction. /b decreases with suction increase. It is a nonlinear relationship between /b and suction. 4.3. Hyperbola model of suction strength The tri-axial tests of the unsaturated expansive soils demonstrate that cVand /Vare invariable, i.e., c V( = 32 kPa) and /V( = 21.3j) are independent from suction. Fig. 9 shows the relationship between us(us = ua uw) and sus, which is nonlinear. If sus and us are transformed to 1/us and 1/sus, it becomes an approximate linear relationship between 1/us and 1/sus. But when
Fig. 3. Soil – water characteristic curve of pre-load exerted on the specimen of Nanyang expansive soil.
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265
Fig. 6. Tri-axial test results of unsaturated expansive soil (us = 80 kPa).
Fig. 4. Tri-axial test results of saturated expansive soils.
us = 0, 1/us will be singularity, so 1/us and 1/sus may be transformed to 1/(us + pat) and 1/(sus + pat), where pat is atmospheric pressure. Fig. 10 shows the relationship between 1/(us + pat) and 1/(sus + pat). We can use a linear equation to describe that:
soils, so that sus = 0. If us = 0 and sus = 0 in Eq. (5), Eq. (5) will become: b¼
1a pat
ð6Þ
Inserting Eq. (6) to Eq. (5), we can obtain: 1 a ¼ þb sus þ pat us þ pat
ð5Þ
sus ¼
aus 1 þ 1a pat us
ð7Þ
where a and b are the test parameters and are determined by regressive analysis of test data of unsaturated soil. For Nanyang expansive soil, a = 0.54 and b = 0.0046 kPa 1. When us = 0, the soils are saturated
Eq. (7) is a hyperbola equation. This is the hyperbola model of the suction strength of unsaturated soils. When us = 0 in Eq. (7), sus = 0; and us ! l in Eq. (7), sus ! (a/(1/ a))pat. It indicates that the limit of
Fig. 5. Tri-axial test results of unsaturated expansive soils (us = 50 kPa).
Fig. 7. Tri-axial test results of unsaturated expansive soil (us = 120 kPa).
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L. Miao et al. / Engineering Geology 65 (2002) 261–267
Fig. 8. Tri-axial test results of unsaturated expansive soil (us = 200 kPa).
sus is (a/(1 a))pat. This illustrates that the suction strength is finite. Thus, equation of unsaturated soil strength can be re-written as: aus ð8Þ sf ¼ cVþ ðr ua Þtan/Vþ 1 þ 1a pat us When soil is saturated, i.e., us = 0, Eq. (8) will be reduced as follows: sf ¼ cVþ ðr ua Þtan/V We can apply the hyperbola model of suction strength to the practical engineering and predict and calculate the shear strength of unsaturated soils based on suction data of unsaturated soils. However, parameter a in Eq. (7) is constant for a certain range suction of unsaturated soil tri-axial, i.e., it is relative to the range suction of the test.
Fig. 9. The relationship curve between us and sus.
model of the suction strength, Eq. (4) (Vanapalli’s (1996) model) and Eq. (7) (the hyperbola model of this paper) could be used to calculate suction strength of Nanyang expansive soils, respectively. The calculating suction strength are shown in Table 4. The calculating results show that the calculating suction strength of Vanapalli’s model is increased as us > 1000 kPa (i.e., water content of the soil specimen is higher) and decreased as us > 1000 kPa (i.e., water content of the soil specimen is lower). This phenomenon illustrates that Vanapalli’s model might be used to describe the strength feature of an unsaturated soil in low suction. But the suction strength of the hyperbola model is increased as soil suction increases and there is a limit suction strength, which accords with prac-
4.4. Suction strength analysis Considering the soil – water characteristic curve of pre-load expansive soil specimen and the hyperbolic Table 3 Shear strength data of Nanyang expansive soil us (kPa) Ctotal (kPa) sus (kPa) c V(kPa) / V(j) /b (j)
50 51.2 19.2 32.0 21.3 21.0
80 59 30.6 31.8 21.4 20.9
120 71 39 32.1 21.2 18.0
200 89.3 57.3 31.9 21.3 16.0
Fig. 10. The means of parameters a and b.
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Table 4 Calculating suction strength of Nanyang expansive soils us (kPa) h (%) sus (kPa) in Eq. (4) sus (kPa) in Eq. (7)
10 32.9 3.8 5.2
50 31.6 17.8 21.9
100 29.6 32.5 37.0
150 28.1 45.1 47.9
tical condition. The hyperbola model of the suction strength could be used to reflect the strength behavior of an unsaturated soil. In Table 4, the calculating suction strength of both Vanapalli’s model and the hyperbola model are of basic agreement when soil suction is smaller than 300 kPa, which illustrates that the hyperbola model of suction strength is of reliability to describe the strength feature of an unsaturated soil.
5. Discussion What we just discussed is the essential problem that the engineering stability of the expansive soil slope will be assured in the canal of Middle Route South-to-North Water Transfer in China. The strength of the expansive soil is a problem too. This is related to the suction strength of expansive soil. Thus, the following work must be done. (1) Suction measure of the expansive soil. One method is to directly measure soil suction with sensors in the field. Another method will be to indirectly get the soil suction from the soil – water characteristic curve, but the method may produce some error. Our research results illustrate that the soil –water characteristic curve of pre-load specimen is better than that without pre-load specimen. (2) Stability research of expansive soil. If soil suction has been obtained, we can use the hyperbola model of suction strength presented in this paper to calculate suction strength and total cohesion of expansive soil and to predict the stability of expansive soil slope.
6. Conclusions (1) The soil –water characteristic curve and the size of the hysteresis loops are influenced by the initial
200 27.4 57.9 56.3
250 26.6 69.2 62.8
300 25.3 76.9 68.1
400 23.8 92.9 76.1
500 22.1 102.6 81.8
750 20.2 131.3 91.0
1000 16.0 108.2 96.4
stress state of the soil specimen. The hysteresis potential is reduced as the number of wetting– drying cycles increases and will tend to stabilize at last for without pre-load expansive soil specimen. (2) The hysteresis loops between the drying and wetting curve for pre-load expansive soil specimen are more stable, and the influence of the number of wetting –drying cycles is smaller, too. The soil –water characteristic curve of the pre-load specimen could well reflect the soil property function of expansive soil. Using the soil – water characteristic curve of the pre-load specimen, parameters hs, hr determined would be stable and identical for an unsaturated soil, and could predict the shear strength of unsaturated soils with Eq. (3). (3) The hyperbola model of suction strength presented by this paper could be used to reflect the strength behavior of an unsaturated soil and is of reliability to describe the strength feature of an unsaturated soil. The hyperbola model has an advantage in that the model parameter might be easily determined and has obvious meaning. The hyperbola model could conveniently be applied to predict suction strength. References Fredlund, D.G., Raharjo, H., 1993. Soil Mechanics for Unsaturated Soils. Wiley Interscience, New York. Fredlund, D.G., Xing, A., 1994. Equations for the soil – water characteristic curve. Can. Geotech. J. 31, 521 – 532. Fredlund, D.G., Morgenstern, N.R., Widger, R.A., 1978. The shear strength of unsaturated soil. Can. Geotech. J. 15, 313 – 321. Fredlund, D.G., Xing, A., Huang, S., 1994. Predicting the permeability functions for unsaturated soils using the soil – water characteristic curve. Can. Geotech. J. 31, 533 – 546. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E., Clifton, A.W., 1996. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33, 379 – 392. Vanapalli, S.K., Pufahl, D.E., Fredlund, D.G., 1998. The effect of stress on the soil – water characteristic behavior of a compacted sandy-clay till. 51st Canadian Geotechnical Conference, Edmonton, 81 – 86.