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Frost heave prediction for clayey soils
Cold Regions Science and Technology, 15 ( 1988 ) 233-238
233
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
FROST HEAVE P R E D I C T I O N FOR CLAYEY SOILS Chen Xiaobai and W a n g Yaqing Lanzhou Institute of Glaciology and Geocryology, Academia Sinica, Lanzhou (China)
ABSTRACT Frost heave prediction for clayey soils was and is one of the most important problems in the field of frozen ground mechanics. Based on the results of frost susceptibility test of clayey soils with unidirectional freezing in the laboratory, a statistical model offrost heave prediction is proposed in this paper. The main factors influencing frost heave are considered, such as initial water content W, initial dry unit weight 7d, groundwater level Hw, frost penetration rate Vf and plasticity index Ip. As a function of above factors, the frost heave ratio r1 couM be expressed by: ~1= BoWl~'~oA2HwB~Vfnqp m, in where Bo to B5 are characteristic constants of soils. The calculated frost heave ratio is very close to the observational one with a probability P=71% while absolute error ~< + 1% and with P= 85% while ~< + 2%.
INTRODUCTION Frost heave prediction for clayey soils has been developing for about half a century, but more work still needs to be done. From the review of frost susceptibility tests (Chamberlin, 1981 ), we know that the size grading of soil is usually used as a criterion of frost susceptibility, and sometimes considering moisture or groundwater level. Recently, the numerical simulation of coupled heat and mass transfer of soils during freezing is developing under the advance of computer, but it is still difficult to be applied in engineering practice because of difficulty in determining the hydraulic-physical properties of soils during the processes of freezing and thawing. The author's earlier work described the influence of critical frost penetration rate causing ice segre-
0165-232X/88/$03.50
gation, surcharge stress and groundwater level on frost heave (Chen et al., 1983), and about ice segregation and frost susceptibility of sandy gravel in an open system (Chen et al., 1987 ). In recent years, they have conducted a series of unidirectional frost susceptibility tests indoors for understanding the influence of initial water content, initial dry unit weight, groundwater level, frost penetration rate and plasticity index on frost heave ratio. After analysing 69 group results including clayey loam and sandy loam, a statistical model of frost heave prediction of clayey soils without overburden stress was proposed and discussed in this paper.
SAMPLES AND EXPERIMENTAL APPARATUS The size grading, limit water content and total ion content of three kinds of soil are listed in Table 1. Samples 11 cm in diameter and 130 to 150 cm in length were put in the plexiglass cylinder cells with unidirectional freezing and water supply reservoir (see Fig. 1 ). The tests were conducted under given one step boundary temperature condition, initial dry unit weight and water content, groundwater level.
A STATISTICAL MODEL OF FROST HEAVE PREDICTION Experimental results Experimental results are listed in Table 2, containing three kinds of soil with total 69 frost susceptibility tests under given initial water content, dry
© 1988 Elsevier Science Publishers B.V.
234 TABLE 1 The physico-chemical properties of samples NO.
I II 111
Percentage of less than following size (mm)
Limit water content (%)
Ion content me/100 g soil
.25
.10
.05
.01
.005
W]
Wo
Io
Wm*
100 100 100
98 97 66
81 80 36
57 42 15
43 29.7 11
33.6 27.0 23.7
23.0 19.5 19.0
10.6 7.5 4.7
15.7 11.9 12.2
11.99 2.54 6.52
* 14~: Maximum molecular water capacity under 65 kg/cm: for 10 minutes.
,,ermo,o,oo
and B5 = characteristic constants of soils. Based on the results listed in Table 2, the characteristic constants of soils can be calculated and the type ofeqn. 1 is as follows: 17= 2.7023
.'-
_o
X 1 0 - 5 W3°2°3~d 538384Vf- l2t81Hw -0"221910 1.0892
Plexiglass cell
(2) with a correlation coefficient r=0.9197 and a deviation s = 0.6964. The distribution of the probable error is shown in Fig. 2. The calculated frost heave ratio is very close to the observational one with a probability P = 71% while its absolute error e < + 1%, and with P = 85.5% while e < + 2%. Therefore, eqn. 1 is satisfactory for predicting frost heave of clayey soils considering main factors.
Q9 e,,
GWL
Insulation
Fig. 1. Frost susceptibility test apparatus.
unit weight, groundwater level and frost penetration rate.
Statistical model of frost heave prediction After analysing the results listed in Table 2, the authors recommended that the comprehensive effect of main factors on frost heave be equal to the product of that caused by each factor and got a statistical model of frost heave prediction as follows: rl=Bo wB'~)d B2vfB3Hw B4Ip Bs
( 1)
where, q = frost heave ratio, %; W=initial water content in the freezing part, %; Yd= initial dry density in the freezing part, g/cm3; Vr=frost penetration rate, cm/day; Hw=groundwater level, cm; Ip = plasticity index of samples, %; Bo, B~, B2, B3, B4
Effect of each factor on frost heave As discussing the effect of each factor on frost heave, frost penetration rate should be considered which provided in the author's earlier work (Chen et al., 1983 and 1987). ( 1 ) Initial water content W: As a frost susceptibility index, frost heave ratio is directly affected by initial water content in frozen part of samples. For example, the frost heave ratio of No. 1, with Ip= 10.6, ya = 1.50 g/era 3 and H,~= 50 em, vs. both of initial water content and frost penetration rate is shown in Fig. 3. It is obvious that under high frost penetration rate, the frost heave ratio is slowly increased with water content. However, underlow penetration rate, heave
235 TABLE 2 Frost susceptibility test results under various freezing conditions No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
W (%) 29.75 38.02 30.07 33.18 41.35 46.02 32.03 45.45 30.47 34.48 30.04 30.40 31.92 34.46 32.63 33.57 25.77 27.09 27.85 29.77 36.73 43.55 16.29 17.10 16.29 16.66 19.74 19.74 19.18 19.18 20.83 20.83 19.38 20.53 20.26 19.65 19.05 18.00 17.10 10.40 17.90 29.21 37.04 14.30 14.80 18.80 19.70 18.52 18.99 17.89 18.61 12.17 12.17 16.24 20.32 15.53 19.45 15.68 16.24 14.90 14.90 16.05 16.83 26.04 28,60 25.00 27.00 29.50 31.86
Ya (g/c m3)
1.34 1..i9 1.37 1.20 1.39 1.19 1.37 1.18 1.38 1.19 1.40 1.19 1.37 1.18 1.37 1.20 1.37 1.20 1.37 1.20 1.35 1.20 1.53 1.52 1.53 .25 .44 .24 .45 .25 .46 .26 1.45 1.45 1.48 1.44 1.25 1.55 1.50 1.52 1.50 1.44 1.24 1.59 1.63 1.55 1.55 1.55 1.56 1.56 1.56 1.45 1.36 1.45 1.38 1.44 1.36 1.45 1.36 1.47 1.38 1.44 1.35 1.43 1.36 1.46 1.37 1.44 1.36
Vr (cm/day) 3.34 4.39 1.92 1.80 5.58 5.43 1.62 2.09 5.45 7.43 4.09 4.42 5.37 4.96 6.48 8.62 4.20 4.41 2.76 3.78 1.78 1.45 4.57 2.31 5.13 3.03 3.51 6.42 3.20 3.35 2.80 2.53 3.78 5.91 5.07 1.65 1.44 6.13 5.35 7.17 6.57 2.33 2.30 4.56 3.35 3.13 3.25 8.39 8.73 2.99 2.95 4.37 4.88 5.50 5.38 6.96 5.61 3.13 3.25 5.42 4.89 6.17 4.48 5.98 5.00 9.68 8.71 1.83 1.55
H,,, (cm)
I o (%)
r/(%)
44.00 44.00 44.00 44.00 44.00 44.00 44.00 44.00 74.50 74.50 74.50 74.50 74.50 74.50 90.00 90.00 90.00 90.00 90.00 90.00 0.10 0.10 90.00 90.00 77.00 107.50 106.50 107.50 106.50 107.50 72.00 72.00 72.00 72.00 34.50 34.50 34.20 49.00 60.00 49.00 60.00 0.10 0.10 87.00 70.00 87.00 70.00 87.00 70.00 87.00 70.00 71.00 70.60 71.00 70.60 71.00 70.60 95.00 95.00 95.00 95.00 95.00 95.00 43.50 43.00 43.50 43.00 0.10 0.10
10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70
6.71 5.61 10.29 9.23 5.64 4.13 17.30 10.05 3.19 2.94 2.57 2.28 4.15 1.35 2.05 0.92 1.87 1.31 1.18 0.54 37.60 39.70 0.42 1.09 1.05 0.13 0.93 0.14 2.32 0.67 6.61 4.92 1.17 0.46 3.15 8.17 5.58 1.12 0.55 1.44 1.53 47.78 40.54 0.08 0.14 1.39 1.57 0.34 0.52 1.03 1.18 0.09 0.16 0.09 0.84 0.03 0.57 0.32 0.32 0.11 0.18 0,10 0.10 1.33 1.37 0.55 0.73 20.80 22.30
236 No. 21. 30 18' 26
15. 21 12. 17 9 13 6 8.6 3 4.3 0i
j [-[-] !
!
,
I
Absolute error (%) Fig. 2. The distribution of probable error for the statistical model of frost heave prediction. 50 ly 40
of samples listed in Table 2 is limited in 1.18 to 1.61 g / c m 3, so any extent of the results should be proven yet. As an example, the frost heave ratio of No. 1, with an initial water content W = 30%, groundwater level Hw = 50 cm, vs. both initial dry density of sample and penetration rate is shown in Fig. 4. It is obvious that under the condition mentioned above the frost heave ratio will increase with the unit weight as a power function. Its increase speed will be much more under low frost penetration rate. The reason is that the porosity of soil will decay while the density rises for unsaturated soil, consequently, the saturation degree increases if the initial water content keeps constant. In addition, our experimental resuits show that the hydraulic conductivity coefficient of soil will increase intensively with the saturation degree as a logarithmic function (Shen and Wang, 1984). And on the other hand, the capillary height will raise while soil becomes consolidated which promotes water migrated towards frost front. However, after the dry unit weight is more than that of the critical one, the hydraulic conductivity coefficient will decrease because of decay of poros-
30 50
20
40
10 30
10
20
30
40
20
W(%) Fig. 3. Frost heave ratio of No. 1 vs. both of initial water content and frost penetration rate. ratio will increase in a l a r g e s c a l e w i t h w a t e r content. In addition, the lower the penetration rate, the l e s s the critical water content for beginning frost heave is. In other words, there is not a constant w a t e r content for beginning frost h e a v e . (2) Initial dry unit weight Yd: The dry unit weight
10
1.0
1.2
1.4
1.6 Y d ( g / c m ~)
Fig. 4. Frost heave ratio of No. 1 vs. initial dry unit weight and frost penetration rate.
237 ity which limits water migrated towards the frost front, as a result, the frost heave will be restrained after soil density is big enough. (3) Groundwater level Hw: Groundwater level will influence on water supply during freezing which affects on frost susceptibility of soils. As an example, the frost heave ratio of No. 1, with a unit weight of 1.50 g/cm 3, initial water content of 30%, vs. both the groundwater level and frost penetration rate is shown in Fig. 5. It is known that the frost heave ratio will intensively decrease with the increase of groundwater level, especially under lower penetration rate. But, if the frost penetration rate is so quick that the soil water is hardly migrated towards the frost front, then the groundwater level is not important for influencing on the frost susceptibility of soil. Conversely, under lower frost penetration rate, a large amount of soil water will migrate towards the frost front and be accumulated below ice lens in the frozen fringe, so the frost susceptibility will be much stronger even though the groundwater level is relatively deeper. (4) Plasticity index Ip: It is well known that the higher the plasticity index, the more the bound water
in soil is. So, the plasticity index of soil directly affects on the water migration in soils. Besides above, the mineral constituents and ion compositions and content will influence on the thickness of water film in soils. The plasticity index of the samples is limited from 4.7 to 10.6, so, the extent of the results proposed in this paper should be proven again. As an example, under the condition of initial water content W= 30%, groundwater level Hw= 50 cm, initial dry unit weight ~d= 1.50 g/cm 3, the frost heave ratio vs. both of the plasticity index and frost penetration rate is shown in Fig. 6. Our experimental results show that while the plasticity index is limited from 4.7 to 10.6, the frost heave ratio is almost increased with the plasticity index linearly under different frost penetration rate. However, clay with high plasticity index, because the interaction between particle surface and water is very strong, so its hydraulic conductivity coefficient is very small which prevents water migrating towards the frost front. Therefore, the frost susceptibility will decrease also. As a result, it is difficult to find a functional
50
50
40
40
30
3~
1.2 1.5
20
20 2 3
10
5 0
20
40
60
80
100
Hw(cm) Fig. 5. Frost heave ratio of No. 1 vs. groundwater level and frost penetration rate.
2
4
6
8
10 [p(~)
12
Fig. 6. Frost heave ratio of No. 1 vs. both plasticity index and frost penetration rate.
238 expression of frost heave ratio containing a single factor. And the frost susceptibility of soil could be described only under considering the comprehensive effect of all main factors on the frost heave. Besides above, the frost susceptibility test will be much simplified with the help of the statistical model of frost heave prediction.
tion coefficient of 0.92 which might be useful to the frost heave prediction for clayey soils. ( 3 ) With the help of the statistical model of frost heave prediction, the frost susceptibility tests will be much simplified.
ACKNOWLEDGMENT CONCLUSIONS ( 1 ) It is difficult to have a functional expression of frost heave ratio considering a single factor. The frost susceptibility of soil can be described as long as considering the comprehensive effect of all main factors influencing on it. (2) The statistical model of frost heave prediction: r/=Bo W ~'7o B2Vff~Hw B4Ip B5 could be fitted by three kind samples with total 69 frost susceptibility tests satisfactory with a correla-
The authors are grateful to the Chinese Academy of Sciences for their support.
REFERENCES Chamberlin, E.J., ( 1981 ). Frost susceptibility of soil: Review of index tests. CRREL Monograph 81-2. Chen, X.B., Wang, Y.Q. and Jiang, P., (1983). Proceedings of4th ICOP, pp. 131-135. Chen, X.B., Wang, Y.Q. and He, P., (1987). Bulletin of Sciences, 32(23): 1812-1815. Shen, Y.L,, Wang, Y.Q., ( 1984). J. of Glaciol. and Geocryol., 6(4): 61-68.
233
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
FROST HEAVE P R E D I C T I O N FOR CLAYEY SOILS Chen Xiaobai and W a n g Yaqing Lanzhou Institute of Glaciology and Geocryology, Academia Sinica, Lanzhou (China)
ABSTRACT Frost heave prediction for clayey soils was and is one of the most important problems in the field of frozen ground mechanics. Based on the results of frost susceptibility test of clayey soils with unidirectional freezing in the laboratory, a statistical model offrost heave prediction is proposed in this paper. The main factors influencing frost heave are considered, such as initial water content W, initial dry unit weight 7d, groundwater level Hw, frost penetration rate Vf and plasticity index Ip. As a function of above factors, the frost heave ratio r1 couM be expressed by: ~1= BoWl~'~oA2HwB~Vfnqp m, in where Bo to B5 are characteristic constants of soils. The calculated frost heave ratio is very close to the observational one with a probability P=71% while absolute error ~< + 1% and with P= 85% while ~< + 2%.
INTRODUCTION Frost heave prediction for clayey soils has been developing for about half a century, but more work still needs to be done. From the review of frost susceptibility tests (Chamberlin, 1981 ), we know that the size grading of soil is usually used as a criterion of frost susceptibility, and sometimes considering moisture or groundwater level. Recently, the numerical simulation of coupled heat and mass transfer of soils during freezing is developing under the advance of computer, but it is still difficult to be applied in engineering practice because of difficulty in determining the hydraulic-physical properties of soils during the processes of freezing and thawing. The author's earlier work described the influence of critical frost penetration rate causing ice segre-
0165-232X/88/$03.50
gation, surcharge stress and groundwater level on frost heave (Chen et al., 1983), and about ice segregation and frost susceptibility of sandy gravel in an open system (Chen et al., 1987 ). In recent years, they have conducted a series of unidirectional frost susceptibility tests indoors for understanding the influence of initial water content, initial dry unit weight, groundwater level, frost penetration rate and plasticity index on frost heave ratio. After analysing 69 group results including clayey loam and sandy loam, a statistical model of frost heave prediction of clayey soils without overburden stress was proposed and discussed in this paper.
SAMPLES AND EXPERIMENTAL APPARATUS The size grading, limit water content and total ion content of three kinds of soil are listed in Table 1. Samples 11 cm in diameter and 130 to 150 cm in length were put in the plexiglass cylinder cells with unidirectional freezing and water supply reservoir (see Fig. 1 ). The tests were conducted under given one step boundary temperature condition, initial dry unit weight and water content, groundwater level.
A STATISTICAL MODEL OF FROST HEAVE PREDICTION Experimental results Experimental results are listed in Table 2, containing three kinds of soil with total 69 frost susceptibility tests under given initial water content, dry
© 1988 Elsevier Science Publishers B.V.
234 TABLE 1 The physico-chemical properties of samples NO.
I II 111
Percentage of less than following size (mm)
Limit water content (%)
Ion content me/100 g soil
.25
.10
.05
.01
.005
W]
Wo
Io
Wm*
100 100 100
98 97 66
81 80 36
57 42 15
43 29.7 11
33.6 27.0 23.7
23.0 19.5 19.0
10.6 7.5 4.7
15.7 11.9 12.2
11.99 2.54 6.52
* 14~: Maximum molecular water capacity under 65 kg/cm: for 10 minutes.
,,ermo,o,oo
and B5 = characteristic constants of soils. Based on the results listed in Table 2, the characteristic constants of soils can be calculated and the type ofeqn. 1 is as follows: 17= 2.7023
.'-
_o
X 1 0 - 5 W3°2°3~d 538384Vf- l2t81Hw -0"221910 1.0892
Plexiglass cell
(2) with a correlation coefficient r=0.9197 and a deviation s = 0.6964. The distribution of the probable error is shown in Fig. 2. The calculated frost heave ratio is very close to the observational one with a probability P = 71% while its absolute error e < + 1%, and with P = 85.5% while e < + 2%. Therefore, eqn. 1 is satisfactory for predicting frost heave of clayey soils considering main factors.
Q9 e,,
GWL
Insulation
Fig. 1. Frost susceptibility test apparatus.
unit weight, groundwater level and frost penetration rate.
Statistical model of frost heave prediction After analysing the results listed in Table 2, the authors recommended that the comprehensive effect of main factors on frost heave be equal to the product of that caused by each factor and got a statistical model of frost heave prediction as follows: rl=Bo wB'~)d B2vfB3Hw B4Ip Bs
( 1)
where, q = frost heave ratio, %; W=initial water content in the freezing part, %; Yd= initial dry density in the freezing part, g/cm3; Vr=frost penetration rate, cm/day; Hw=groundwater level, cm; Ip = plasticity index of samples, %; Bo, B~, B2, B3, B4
Effect of each factor on frost heave As discussing the effect of each factor on frost heave, frost penetration rate should be considered which provided in the author's earlier work (Chen et al., 1983 and 1987). ( 1 ) Initial water content W: As a frost susceptibility index, frost heave ratio is directly affected by initial water content in frozen part of samples. For example, the frost heave ratio of No. 1, with Ip= 10.6, ya = 1.50 g/era 3 and H,~= 50 em, vs. both of initial water content and frost penetration rate is shown in Fig. 3. It is obvious that under high frost penetration rate, the frost heave ratio is slowly increased with water content. However, underlow penetration rate, heave
235 TABLE 2 Frost susceptibility test results under various freezing conditions No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
W (%) 29.75 38.02 30.07 33.18 41.35 46.02 32.03 45.45 30.47 34.48 30.04 30.40 31.92 34.46 32.63 33.57 25.77 27.09 27.85 29.77 36.73 43.55 16.29 17.10 16.29 16.66 19.74 19.74 19.18 19.18 20.83 20.83 19.38 20.53 20.26 19.65 19.05 18.00 17.10 10.40 17.90 29.21 37.04 14.30 14.80 18.80 19.70 18.52 18.99 17.89 18.61 12.17 12.17 16.24 20.32 15.53 19.45 15.68 16.24 14.90 14.90 16.05 16.83 26.04 28,60 25.00 27.00 29.50 31.86
Ya (g/c m3)
1.34 1..i9 1.37 1.20 1.39 1.19 1.37 1.18 1.38 1.19 1.40 1.19 1.37 1.18 1.37 1.20 1.37 1.20 1.37 1.20 1.35 1.20 1.53 1.52 1.53 .25 .44 .24 .45 .25 .46 .26 1.45 1.45 1.48 1.44 1.25 1.55 1.50 1.52 1.50 1.44 1.24 1.59 1.63 1.55 1.55 1.55 1.56 1.56 1.56 1.45 1.36 1.45 1.38 1.44 1.36 1.45 1.36 1.47 1.38 1.44 1.35 1.43 1.36 1.46 1.37 1.44 1.36
Vr (cm/day) 3.34 4.39 1.92 1.80 5.58 5.43 1.62 2.09 5.45 7.43 4.09 4.42 5.37 4.96 6.48 8.62 4.20 4.41 2.76 3.78 1.78 1.45 4.57 2.31 5.13 3.03 3.51 6.42 3.20 3.35 2.80 2.53 3.78 5.91 5.07 1.65 1.44 6.13 5.35 7.17 6.57 2.33 2.30 4.56 3.35 3.13 3.25 8.39 8.73 2.99 2.95 4.37 4.88 5.50 5.38 6.96 5.61 3.13 3.25 5.42 4.89 6.17 4.48 5.98 5.00 9.68 8.71 1.83 1.55
H,,, (cm)
I o (%)
r/(%)
44.00 44.00 44.00 44.00 44.00 44.00 44.00 44.00 74.50 74.50 74.50 74.50 74.50 74.50 90.00 90.00 90.00 90.00 90.00 90.00 0.10 0.10 90.00 90.00 77.00 107.50 106.50 107.50 106.50 107.50 72.00 72.00 72.00 72.00 34.50 34.50 34.20 49.00 60.00 49.00 60.00 0.10 0.10 87.00 70.00 87.00 70.00 87.00 70.00 87.00 70.00 71.00 70.60 71.00 70.60 71.00 70.60 95.00 95.00 95.00 95.00 95.00 95.00 43.50 43.00 43.50 43.00 0.10 0.10
10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 10.60 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70
6.71 5.61 10.29 9.23 5.64 4.13 17.30 10.05 3.19 2.94 2.57 2.28 4.15 1.35 2.05 0.92 1.87 1.31 1.18 0.54 37.60 39.70 0.42 1.09 1.05 0.13 0.93 0.14 2.32 0.67 6.61 4.92 1.17 0.46 3.15 8.17 5.58 1.12 0.55 1.44 1.53 47.78 40.54 0.08 0.14 1.39 1.57 0.34 0.52 1.03 1.18 0.09 0.16 0.09 0.84 0.03 0.57 0.32 0.32 0.11 0.18 0,10 0.10 1.33 1.37 0.55 0.73 20.80 22.30
236 No. 21. 30 18' 26
15. 21 12. 17 9 13 6 8.6 3 4.3 0i
j [-[-] !
!
,
I
Absolute error (%) Fig. 2. The distribution of probable error for the statistical model of frost heave prediction. 50 ly 40
of samples listed in Table 2 is limited in 1.18 to 1.61 g / c m 3, so any extent of the results should be proven yet. As an example, the frost heave ratio of No. 1, with an initial water content W = 30%, groundwater level Hw = 50 cm, vs. both initial dry density of sample and penetration rate is shown in Fig. 4. It is obvious that under the condition mentioned above the frost heave ratio will increase with the unit weight as a power function. Its increase speed will be much more under low frost penetration rate. The reason is that the porosity of soil will decay while the density rises for unsaturated soil, consequently, the saturation degree increases if the initial water content keeps constant. In addition, our experimental resuits show that the hydraulic conductivity coefficient of soil will increase intensively with the saturation degree as a logarithmic function (Shen and Wang, 1984). And on the other hand, the capillary height will raise while soil becomes consolidated which promotes water migrated towards frost front. However, after the dry unit weight is more than that of the critical one, the hydraulic conductivity coefficient will decrease because of decay of poros-
30 50
20
40
10 30
10
20
30
40
20
W(%) Fig. 3. Frost heave ratio of No. 1 vs. both of initial water content and frost penetration rate. ratio will increase in a l a r g e s c a l e w i t h w a t e r content. In addition, the lower the penetration rate, the l e s s the critical water content for beginning frost heave is. In other words, there is not a constant w a t e r content for beginning frost h e a v e . (2) Initial dry unit weight Yd: The dry unit weight
10
1.0
1.2
1.4
1.6 Y d ( g / c m ~)
Fig. 4. Frost heave ratio of No. 1 vs. initial dry unit weight and frost penetration rate.
237 ity which limits water migrated towards the frost front, as a result, the frost heave will be restrained after soil density is big enough. (3) Groundwater level Hw: Groundwater level will influence on water supply during freezing which affects on frost susceptibility of soils. As an example, the frost heave ratio of No. 1, with a unit weight of 1.50 g/cm 3, initial water content of 30%, vs. both the groundwater level and frost penetration rate is shown in Fig. 5. It is known that the frost heave ratio will intensively decrease with the increase of groundwater level, especially under lower penetration rate. But, if the frost penetration rate is so quick that the soil water is hardly migrated towards the frost front, then the groundwater level is not important for influencing on the frost susceptibility of soil. Conversely, under lower frost penetration rate, a large amount of soil water will migrate towards the frost front and be accumulated below ice lens in the frozen fringe, so the frost susceptibility will be much stronger even though the groundwater level is relatively deeper. (4) Plasticity index Ip: It is well known that the higher the plasticity index, the more the bound water
in soil is. So, the plasticity index of soil directly affects on the water migration in soils. Besides above, the mineral constituents and ion compositions and content will influence on the thickness of water film in soils. The plasticity index of the samples is limited from 4.7 to 10.6, so, the extent of the results proposed in this paper should be proven again. As an example, under the condition of initial water content W= 30%, groundwater level Hw= 50 cm, initial dry unit weight ~d= 1.50 g/cm 3, the frost heave ratio vs. both of the plasticity index and frost penetration rate is shown in Fig. 6. Our experimental results show that while the plasticity index is limited from 4.7 to 10.6, the frost heave ratio is almost increased with the plasticity index linearly under different frost penetration rate. However, clay with high plasticity index, because the interaction between particle surface and water is very strong, so its hydraulic conductivity coefficient is very small which prevents water migrating towards the frost front. Therefore, the frost susceptibility will decrease also. As a result, it is difficult to find a functional
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Hw(cm) Fig. 5. Frost heave ratio of No. 1 vs. groundwater level and frost penetration rate.
2
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Fig. 6. Frost heave ratio of No. 1 vs. both plasticity index and frost penetration rate.
238 expression of frost heave ratio containing a single factor. And the frost susceptibility of soil could be described only under considering the comprehensive effect of all main factors on the frost heave. Besides above, the frost susceptibility test will be much simplified with the help of the statistical model of frost heave prediction.
tion coefficient of 0.92 which might be useful to the frost heave prediction for clayey soils. ( 3 ) With the help of the statistical model of frost heave prediction, the frost susceptibility tests will be much simplified.
ACKNOWLEDGMENT CONCLUSIONS ( 1 ) It is difficult to have a functional expression of frost heave ratio considering a single factor. The frost susceptibility of soil can be described as long as considering the comprehensive effect of all main factors influencing on it. (2) The statistical model of frost heave prediction: r/=Bo W ~'7o B2Vff~Hw B4Ip B5 could be fitted by three kind samples with total 69 frost susceptibility tests satisfactory with a correla-
The authors are grateful to the Chinese Academy of Sciences for their support.
REFERENCES Chamberlin, E.J., ( 1981 ). Frost susceptibility of soil: Review of index tests. CRREL Monograph 81-2. Chen, X.B., Wang, Y.Q. and Jiang, P., (1983). Proceedings of4th ICOP, pp. 131-135. Chen, X.B., Wang, Y.Q. and He, P., (1987). Bulletin of Sciences, 32(23): 1812-1815. Shen, Y.L,, Wang, Y.Q., ( 1984). J. of Glaciol. and Geocryol., 6(4): 61-68.