A simple procedure for estimating preconsolidation pressure from soil compression curves

SOIL TECHNOLOGY ELSEVIER

Soil Technology 8 (1995) 139-151

A simple procedure for estimating preconsolidation pressure from soil compression curves M.S. Dias Junior, F.J. Pierce * Department

of Crop and

Soil Sciences, Michigan

State University,

East Lansing,

MI 48824,

USA

Received 29 December 1994; accepted 31 May 1995

Abstract Classical graphics and regression procedures have been used to estimate preconsolidation pressure (or) from soil compression curves, but none of these procedures is easy to use and they often involve subjective judgement. This paper presents a simple procedure for estimating up from uniaxial compression tests for either saturated or unsaturated soil conditions. We evaluated five methods for estimating crp from standard soil compression curves for an applied stress sequence of 25, 50, 100, 200, 400, 800, and 1600 kPa. Four methods estimated or, as the intersection of two lines: (a) the regression line obtained for the first two, three, four or five points of the applied stress sequence in the secondary compression portion of the compression curve and (b) the extension of the virgin compression line determined from the points associated with applied stress of 800 and 1600 kPa. Method 5 consisted of the Schmertmann method. The up determined for each method was compared to or estimated using the graphical procedure of Casagrande for 288 soil compression curves from three soils in Michigan and from values reported in the literature. Methods 1 and 5 fit our data best at low tr,, (high soil water content) while methods 2 and 3 fit the data better at high crr,( low soil water content). Based on a low RMSE ( 18), a high RZ (0.92). and closeness of fit to the 1:l line, a combination of methods 1 and 3 was selected as the best estimation procedure. For data from the literature, methods 1 and 2 provided the best estimate based on lowest RMSE of 5 to 9, R2 of 0.98 to 0.99, and the closest fit to the 1: 1 line. The combined methods were not tested for published data since matric potentials for measured values were unknown. The final procedure, combined methods 1 and 3, was programmed into a computer spreadsheet provided in an Appendix. This procedure provides a fast and reliable estimation of or, for saturated and unsaturated soil conditions and eliminates subjective judgment associated with classical graphical procedures. Kqvwords:

Soil compressibility; Preconsolidation pressure; Spreadsheet

* Corresponding author. Tel. ( + I-517) 3559285; Fax ( + 1-517) 353-5174. 0933-3630/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO933-3630(95)00015-l

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1. Introduction The compressive behavior of a soil is expressed graphically in the relationship between the logarithm of applied stress and some parameter related to the packing state of soil, most often void ratio or bulk density (Casagrande, 1936; Leonards, 1962; Holtz and Kovacs, 198 1) . When no previous stress has been applied, this relationship is theoretically linear and any applied stress results in an unrecoverable deformation (Larson and Gupta, 1980; Larson et al., 1980; Culley and Larson, 1987; Gupta and Allmaras, 1987; Lebert and Horn, 1991). However, when a soil has experienced a previous stress, an applied stress less than the maximum previously applied stress will result in deformation that is relatively small and recoverable (Stone and Larson, 1980; Gupta et al., 1989; Lebert and Horn, 1991). Applied stresses greater than the maximum previously applied stress will result in deformation that is unrecoverable, i.e. soil compaction. The preconsolidation pressure (a,) corresponds to the stress that divides the soil compression curve into a region of small, elastic and recoverable deformation (secondary compression curve) and a region of plastic and unrecoverable deformation (virgin compression curve) (Holtz and Kovacs, 1981; Jamiolkowski et al., 1985). In saturated soils, err, is used in settlement theory to estimate the load support capacity of soil (Leonards, 1962; Holtz and Kovacs, 1981). According to Holtz and Kovacs ( 1981)) the preconsolidation pressure is an indication of the maximum previously applied stress sustained by a soil and defines the limit of elastic deformation in the soil compression curve. Thus, in agriculture, application of stress greater than the highest previously applied stress should be avoided (Gupta et al., 1989; Lebert and Horn, 1991) in order to avoid unrecoverable soil deformations since the preconsolidation pressure should be the maximum stress applied to soil to prevent further soil compaction. In agricultural soils, loads are applied to unsaturated soils and up has been shown to increase with decreasing soil water content (Lebert et al., 1989; Lebert and Horn, 1991). Stress history is important to the compressive behavior of unsaturated soils since additional soil compaction occurs only when the applied stress exceeds oP (Gupta et al., 1989; Lebert and Horn, 1991). The importance of stress history is recognized, particularly as it relates to conservation tillage systems (Culley and Larson, 1987; Larson et al., 1988) and root growth and penetration in soils (Romkens and Miller, 197 1) . Romkens and Miller ( 197 1) reported that the preconsolidation pressure is a predictor of the critical strength at which root elongation ceases, indicating that soils with considerable preconsolidation pressure are more likely to reduce root growth. Methods used for determination of up are summarized graphically in Fig. 1. The Casagrande (1936; Fig. la), Burmister (1951; Fig. lb), and Schmertmann (1955; Fig. lc) procedures are graphical methods developed for saturated soils but have been applied to unsaturated soils. The Casagrande method remains a standard for comparison to other methods (Jose et al., 1989). Additional methods have been used to estimate LT~in unsaturated soils, primarily involving regression (SPllfors, 1975; Fig. Id; Culley and Larson, 1987; Jose et al., 1989; Fig. le; Lebert and Horn, 1991; Fig. lf) and prediction from undrained shear strength and effective vertical overburden pressure (Anderson and Lukas, 1981). None of these estimation techniques is considered a standard technique and, in general, they are not always easy to use and often involve subjective judgement.

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141

a Zasagrande Log

Applied

!Schmertmann Log

Applied

(1936) Stress

(kPa)

Log Applied

(kPa)

Applied

Stress

(kPa)

(1955) Stress

Stress

(kPa)

e Jose Log

et al., (1989) Applied

Stress

(kPa)

Log

Applied

Fig. 1. Illustration of several methods used to estimate preconsolidation curves: (a) Casagrande, 1936, (b) Burmister, 1951, (c) Schmertmann, 1989, and (f) Lebert and Horn, 1991.

Stress

(kPa)

pressure (a,) from soil compression 1955, (d) Skillfors, 1975, (e) Jose et al.,

The graphical construction suggested by Casagrande ( 1936) is based on the choice of the point in the consolidation curve with minimum radius of curvature. It has been shown that as soil sample disturbance increases, the selection of this point is increasingly more difficult and up will be lower than those obtained for undisturbed soil samples (Schmertmann, 1955; Brumund et al., 1976; Holtz and Kovacs, 1981). Also, when using undisturbed soil samples, the selection of the point of minimum radius can be difficult to determine at high soil water content (w) because the compression curve is nearly linear (Dias Junior, 1994). This paper evaluates a number of procedures for estimating up from uniaxial compression tests for either saturated or unsaturated soil conditions. The procedures were evaluated against the Casagrande graphical estimation procedure and published values of up. The procedure that best met the performance criteria for prediction of uTpwas programmed into standard computer spreadsheet software. The proposed procedure provides a consistent,

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repeatable, and easy to use procedure for the estimation of up that eliminates subjective judgment associated with classical graphical procedures.

2. Material

and methods

2. I, Procedure for estimating up Our goal was to develop a single, best procedure for estimating up from soil compression curves obtained for an applied stress sequence of 25,50,100,200,400,800, and 1600 kPa (standard sequence according to Bowles, 1986). Dias Junior (1994) reported that as o decreases, the curvature of the compression curve, and thus the number of points in the secondary compression curve, increases. Therefore, a procedure to estimate crP should consider changing the number of points that belong to the secondary compression curve in the fitting of the appropriate regression line (Fig. 2). In addition, as the soil dries, the virgin compression curve is shifted up and to the right in a such a way that for the lower w, only two points remain in the virgin compression curve for applied stress of 800 and 1600 kPa. We evaluated five different methods for estimating gr, as follows: the first four methods estimate or, as the intersection of two lines: (a) the regression line obtained for the first two, three, four or five points of the applied stress sequence in the secondary compression portion of the compression curve and (b) the extension of the virgin compression line determined from the points associated with applied stress of 800 and 1600 kPa (Fig. 2). Method 5 consisted of the Schmertmann ( 1955) method, in which up is determined as the intersection of a horizontal line at the initial bulk density to the extension of the virgin compression line (Fig. lc). Each method was programmed as a different spreadsheet pro-

Fig. 2. Illustration curves.

of methods

1 through

Applied

Stress

-

4 used to estimate preconsolidation

pressure (a,)

from soil compression

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cedure. In each procedure, values of bulk density corresponding to the standard applied stress sequence were entered for each soil compression curve and or, determined as described above. The crp determined for each method was compared to (or estimated using the graphical procedure of Casagrande ( 1936) for our data (Dias Junior, 1994) or from or reported in selected references. Our data included 288 compression curves determined as part of a study to evaluate the effects of tillage and wheel traffic on the compressive behavior of three soils in Michigan (Dias Junior, 1994) managed under long-term no-tillage and plowed tillage systems. The soils included the Kalamazoo loam (fine loamy, mixed, mesic, Typic Hapludalfs) located at Kalamazoo, MI, the Capac loam (fine loamy, mixed, mesic, Aeric Ochraqualfs) located at East Lansing, MI, and the Misteguay silty clay (fine, mixed (calcareous), mesic, Aeric Haplaquepts) located at Saginaw, MI. These soils had been cropped in notillage management for the last 13, 14, and 9 years, respectively. Measurements from the literature were taken from studies by Burmister ( 1951), Crawford ( 1964), Jose et al. ( 1989)) Reinert ( 1990)) and Kassa ( 1992). The relationships between applied stress and deformation were obtained by carefully extracting data from figures in those references. The accuracy of the estimation procedure was determined using three criteria: the degree of coincidence between predicted and observed values using the root mean square error (RMSE) of Loague and Green ( 199 1) RMSE

=

[ t

(P;-O;)%I]~~~*~OO/G

i=l

(1)

where Pi is the predicted value, Oi are the observed values, n is the number of samples, and 0 is the mean of the observed data; the R2 of the regression of observed on predicted up; and the nearness of the regression line to the 1:l line. These criteria formed the basis for selection of the best procedure for estimating op.

3. Results and discussion The regressions of predicted versus Casagrande method determined up for the 288 soil samples from the Michigan tillage studies are given in Fig. 3. Method 1 had the lowest RMSE (22) and highest R* (0.87), but tended to underpredict relative to the 1:l line at up > 200 kPa (corresponding to soil matric potentials < - 100 kPa) . Method 5 (Schmertmann, 1955) had a similar R2 (0.85) to method 1 but higher RMSE (33) and appeared to predict well at low up. All points, however, were above the 1:l line. Methods 2, 3, and 4 had higher RMSE (28, 34, 36, respectively), had lower R2 (0.80,0.7 1,0.66 respectively), and tended to overpredict at low op (high w) but better predict at higher or, (lower w) . Since the performance of the methods appeared to vary depending on the range of up (and, therefore, o), methods 1 and 5 (for up < 200 kPa) were combined with methods 2 and 3 (for up > 200 kPa) and the regression of observed on predicted up recalculated. The or of 200 kPa was chosen by inspection of Fig. 3 because it was at this or, that the consistency of the methods varied and this up corresponded to a matric potential of - 100 kPa for the soils measured by Dias Junior ( 1994).

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800 * .

Capac Misteguay Kalamazoo

Method 1

.Methoa 2

0

400

600

800

cpH &Pa) Fig. 3. Regressions of preconsolidation pressure ( upc) determined by the Casagrande preconsolidation pressure ( npM) estimated by methods 1 through 5 for 288 compression series in Michigan.

( 1936) procedure on curves from three soil

All four combination methods predicted up well, as all had RMSE of 18 or 19 and R2 of 0.90 to 0.92. By inspection of Fig. 4, the combination of methods 1 and 3 corresponded bestto the 1: 1line having lowest FUSE ( 18) andhighestR* (0.92). Therefore, we selected the combination of methods1 and 3 asthe bestestimationprocedurefor or, for unsaturated soil conditions and usedthis combination in the final spreadsheet(Appendix A). 3.1. Comparison

to published

values of cr,,

Table 1 gives or obtained from selectedreferencesand thoseestimatedusingmethods1 through 5. Linear regressionswere performed for or, determined for both saturated and

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145

800 600 400 200 8000 600 400

2i5 b'

200 Method 1 & 3

8000 600

1

cPC

= 64.46

+ 1.06 op,

R2 = 0.91

400 200 Mehtod 5 & 2

8000 600

I 0

100

200

300

400

500

600

700

800

900

oPrnWW Fig. 4. Regression of preconsolidation pressure (upc) determined by the Casagrande ( 1936) procedure on preconsolidation pressure ( uPM) estimated by combinations of methods 1 and 5 (for up < 200 kPa) in combination with methods 2 and 3 (for v,, > 200 kPa) for 288 compression curves from three soil series in Michigan.

unsaturated soil conditions, and for saturated and unsaturated combined (Table 2). Prediction of up was good for all methods but methods 1 and 2 predicted best for all wetness conditions, with RMSE values of 5 to 9, R* values of 0.98 to 0.99, and close correspondence to the 1: 1 line (intercepts near 0 and slopes near 1). Because the compression tests in published studies were done at relatively high o and the matric potentials were not given, it was not possible to apply the combined methods as performed for the Dias Junior ( 1994) data. However, the combination of methods 1 and 3 would have performed well for published data since method 1 is used for high w and method 3 is used for low o.

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MS. Dim Junior,

Table I Comparison of preconsolidation 5 for saturated and unsaturated

pressures (up) soil conditions

F.J. Pierce/Soil

obtained

Technology

from selected

Preconsolidation

references

pressure Estimation

Reference

Butister,

195 I

Crawford.

1964

Jose et al., 1989

Reinert,

Kassa,

Lit.

Method

1990

1992

BWtIliste1 BWtllister Casagrande Casagrande log-log log-log log-log log-log Casagrande Casagrande Casagrande Casagrande statistical statistical statistical statistical statistical statistical statistical statistical

Saturated 15 350 300 62 105 114 120 102 Unsaturated 174 134 61 17 94 82 63 32 70 40 25 20

8 (1995)

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with estimates

obtained

using method

1 through

(kPa) method

1

2

3

4

5

81 372 218 238 95 103 126 98

89 351 291 256 95 99 126 101

109 360 311 289 102 99 126 111

155 441 358 343 111 105 128 120

71 270 271 224 90 92 120 92

172 139 68 14 95 73 60 29 63 37 23 18

168 117 59 13 94 92 63 31 67 45 25 21

163 138 81 11 104 126 69 34

183 178 116 I 138 156 79 35 118 71 43 38

loo 89 31 11 29 18 31 9 44 34 16 10

79 51 29 26

Table 2 Coefficients of linear regressions of preconsolidation pressure (up) obtained from selected references on estimates of up obtained using methods 1 through 5 for saturated and unsaturated soil conditions (up li,C,.uYrr = a + bo, me,,,od) and RMSE of the predicted values Method

a

b

1 2 3 4 5 Unsatwated 1 2 3 4 5 Saturated and Unsaturated I 2 3 4 5

7.92

R2

RMSE

- 1.99 10.01 - 11.13

0.98 1.01 0.96 0.77 1.23

0.98 0.99 0.98 0.95 0.98

9 5 10 31 19

3.50 - 1.81 -4.16 -4.00 15.66

0.97 I .05 0.95 0.74 1.46

0.99 0.98 0.92 0.85 0.82

7 9 23 55 59

3.41

1.00 1.02 0.97 0.80 1.10

0.99 0.99

9

0.66

0.12 -4.78 -5.13 21.05

0.98 0.95 0.94

7 15 41 34

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This spreadsheetprocedureprovides a fast and reliable estimationof up, which is important since the determination of cT,hasbeen somewhatimprecise,largely due to the nature of the standardgraphic estimation procedures,such as Casagrande( 1936) and Schmertmann (1955). While other methods have been used to estimate gr, in unsaturatedsoils, primarily involving regression(Lebert et al., 1989; Lebert and Horn, 1991), none is considered to be a standardtechnique. Since the importance of preconsolidationpressurein understandingcompaction of unsaturated soils is increasingly recognized (Culley and Larson, 1987; Lebert et al., 1989; Lebert and Horn, 1991), this techniqueoffers a simple yet reliable method of estimating up. In the future, this procedure may be most useful as researchbeginsto assessthe impact of (or on root penetration,particularly asthe soil dries, the importance of which was demonstratedmore than two decadesago by Rijmkens and Miller (1971).

4. Summary For saturated and unsaturated soil conditions, crp can be estimatedby using a simple spreadsheetprocedure which usesa combination of methods depending on w. The up estimatedwith this procedurecorrespondedwell to standardgraphicalmethodsandliterature values. This procedure provides a fast and reliable estimation of or, for saturated and unsaturatedsoil conditions and eliminates subjective judgment associatedwith classical graphical procedures.

Acknowledgements The authorsacknowledgethe financial supportof the Brazilian governmentin sponsorship of Mr. Dias Junior, through the MEC-CAPES agency and the support of the Michigan Agricultural Experiment Station.

Appendix A. A spreadsheetprocedure for estimation of preconsolidation pressure (up) for a standard applied stresssequenceusing a combination of methods 1 and 3. The first step is to load the spreadsheetcell commandsinto the spreadsheetprogram in the order presented.The code was developed in Quattro Pro Version 4.0/5.0 (Borland International, Inc. Scotts Valley, CA, 950666, USA). This procedure works on Excel Version 5.0 (Microsoft Corp., One Microsoft Way, Redmond, WA 98052, USA), by changingthecell D$12 toB$41 (Yintercept) andcellC$18 toB$42 (slopeorXcoefficient). These changesadjust the range of output for Excel. Once loaded, the spreadsheetwill calculate all the necessaryparametersfor op. First, replace the samplebulk densitieswith your values that correspondto the standardapplied stress.For Quattro Pro, enter “Tools”, then “Advanced Math”, then “Regression”, and enter “Go”. For Excel, enter “Tools”, then “Data Analysis”, then “Regression”, and enter “OK”. This updatesthe spreadsheet for the regressionoutput, up, and the correspondingbulk densities.At the sametime, a

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graphic plot similar to Fig. 2 is redrawn and can be viewed by the user in Quattro Pro in the Graphics subdirectory ( “View”) and in Excel in the “Current” subdirectory. The spreadsheet can be altered, for example, to accommodate different applied stress sequence. cell#:input Al: “STRESS Bl: “LOG STRESS Cl: [Wll] “BULKDENS Dl: [ W9] “B.D retav El: [ W9] “B.D reg Fl: [W16] ‘* * METHOD 1 [W16] “CSC = F2: G2: (F4) (C4-C3)/(B4-B3) A3: 25 B3: (F4) @LOG(A3) c3: (F4) [Wll] 1.5531 D3: (F4) [W9] (G$lO* (B3-B$8) +C$8) E3: (F4) [W9] (D$12+C$18*B3) F3: [Wl6] “x = G3: (F4) (G2* (-B4) +C4-C9-GlO* (-B9))/(GlO-G2) A4: 50 B4: (F4) @LOG(A4) c4: (F4) [Wll] 1.5624 D4: (F4) [W9] (G$lO* (B4-B$8) +C$8) E4: (F4) [WP] (D$12+C$18*B4) AS: 100 B5: (F4) @LOG(AS) c5: (F4) [Wll] 1.5809 DS: (F4) [W9] (G$lO* (B5-B$8) +C$8) E5: (F4) [W9] (D$12+C$18*B5) F5: [W16] ‘Prec press reta= G.5: (FO) lO”G$3 A6: 200 B6: (F4) @LOG(A6) C6: (F4) [Wll] 1.6199 D6: (F4) [W9] (G$lO* (B6-B$8) +C$8) E6: (F4) [W9] (D$12+C$18*B6) F6: [W16] ‘Bulk Dens reta= G6: (F2) (G2* (@LOG(G$5) -B4) +C4) Al: 400 B7: (F4) @LOG( A7) c7: (F4) [Wll] 1.6779 D7: (F4) [W9] (G$lO* (B7-B$8) +C$8) E7: (F4) [W9] (D$12+C$18*B7) A8 800 B8: (F4) @LOG(A8)

M.S. Dias Junior,

a: D8: E8: A9: B9: c9: D9: F9: FIO: GlO: Bll: Ell: Fll: Gil: A12: D12: F12: G12: A13: D13: E13: A14: D14: E14: F14: G14: A15: D15: E15: F15: G15: A16: D16: E16: E17: A18: C18: E18:

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(F4) [Wll] 1.7587 (F4) [W9] (G$lO* (B8-B$8) +C$8) (F4) [W9] (D$12+C$18*B8) 1600 (F4) @LOG( A9) (F4) [Wll] 1.8578 (F4) [W9] (G$lO*(B9-B$8) +C$8) [WI61 ‘* * METHOD 3 [W16] “Cvcc = (F4) (C9-C8)!(B9-B8) ‘Regression Output: [W9] ‘B.Dscc [WI61 “X = (F4) (D$12+G$lO*B$9-C$9)/(G$lO-C$18) ‘Constant (F4) [ W9] 1.4445859880058 [ W 161 “Log Pre pressu = (F4) @LOG(G$14) ‘Std Err of Y Est (F4) [ W9] 0.01065 1455299629 (F4) [W9] (G$2* (B3-B$4) +C$4) ‘R Squared (F4) [ W9] 0.9 1348565970866E14: (F4) [W9] (G$2* (B4-B$4) +C$4) [ W 161 ‘Prec. Pressure = (FO) lO”G$ll ‘No. of Observations LW914 (F4) [W9] (G$2* (B5-B$4) +C$4) [W 161 ‘Bulk Density = (F2) (D$12+C$18*G$12) ‘Degrees of Freedom [W912 (F4) [W9] (G$2* (B6-B$4) +C$4) (F4) [W9] (G$2* (B7-B$4) +C$4) ‘X Coefficient(s) (F4) [WI11 0.072717005997085 (F4) [W9] (G$2* (BS-B$4) +C$4)

References Anderson, T.C. and Lukas, G.R., 1981. Preconsolidation pressure predicted using Su/p’ ratio. In: R.N. Yong and F.C. Townsend (editors), Laboratory Shear Strength of Soil. Symposium ASTM. Special Technical Publication 740. Chicago, IL. 25 June 1980. Philadelphia, PA, pp. 502-515.

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Schmertmann, J.H., 1955. The undisturbed consolidation behavior of clay. Trans. AXE, 120: 1201-1233. Stone, J.A. and Larson, W.E., 1980. Rebound of five one-dimensionally compressed unsaturated granular soils. Soil Sci. Sot. Am. J., 44: 819-822.