Geotechnical Testing Journal

Geotechnical Testing Journal Mohammed Shukri Al-Zoubi1

DOI: 10.1520/GTJ20130097

Consolidation Analysis by the Modified Slope Method VOL. 37 / NO. 3 / MAY 2014

Geotechnical Testing Journal

doi:10.1520/GTJ20130097

/

Vol. 37

/

No. 3

/

May 2014

/

available online at www.astm.org

TECHNICAL NOTE Mohammed Shukri Al-Zoubi1

Consolidation Analysis by the Modified Slope Method Reference Shukri Al-Zoubi, Mohammed, “Consolidation Analysis by the Modified Slope Method,” Geotechnical Testing Journal, Vol. 37, No. 3, 2014, pp. 540–547, doi:10.1520/GTJ20130097. ISSN 0149-6115

ABSTRACT Manuscript received May 20, 2013; accepted for publication January 6, 2014; published online March 21, 2014. 1

Civil and Environmental Engineering Dept., Faculty of Engineering, Mutah Univ., Jordan, e-mail: [email protected]

The slope method (Al-Zoubi, 2008, Geotech. Test. J., Vol. 31, No. 6, pp. 526–530) in which the coefficient of consolidation cv was expressed as function of the EOP settlement dp and pffiffi slope m of the initial linear portion of the observed dt t curve is modified for improving the procedure used for estimating the EOP dp. The slope method EOP dp values were pffiffi estimated using the point at which dt t curve starts to deviate from the initial linear portion. In this note, the EOP dp is determined based on a unique relationship between the pffiffi ratio of the secant slope of dt t curve at 50 % consolidation to the secant slope at any pffiffi time arbitrarily selected beyond the initial linear portion of the dt t curve (theoretically, at U 52:6 %) and average degree of consolidation U. The modified slope method requires a minimum of four compression-time data points for better cv estimates. Two types of EOP settlement are identified; local EOP settlement dpi is obtained at a specific Ui value as is the case in the Taylor method and global EOP settlement dp is determined independently of any U value. The modified slope method yields dp and cv values quite similar to those of the Casagrande method. Keywords coefficient of consolidation, Taylor, Casagrande, slope method, and end of primary consolidation

Introduction The computation of settlement of structures built on compressible soil deposits due to the consolidation of these deposits is usually performed by the use of the Terzaghi theory that requires the determination of the end-of-primary (EOP) settlement dp and coefficient of consolidation cv . The observed soil compression exhibits initial compression, primary consolidation, and secondary

C 2014 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. Copyright V

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SHUKRI AL-ZOUBI ON MODIFIED SLOPE METHOD

compression. Hence, the recognition of the range of primary consolidation of the observed compression of soils is an important step for a realistic application of the Terzaghi theory to settlement analysis because the Terzaghi theory was developed only for the primary consolidation. This recognition is commonly accomplished by matching or fitting the Terzaghi theoretical U–T relationship to the observed compression-time curve at a specified U value or over a range of U based on similarity between the observed and theoretical compression-time curves that can be presented and interpreted in different ways where U is the average degree of consolidation and T is the time factor. The log t method (Casagrande and Fadum 1940) uses the theoretical U log T relationship to estimate the time at 50 % consolidation for computing cv and to estimate EOP dp as well. The log t method uses a procedure to interpolate the EOP settlement between primary consolidation and secondary compression utilizing the similarity between theoretical pffiffi U log T relationship and observed dt log t curve. The t method devised by Taylor (1948) utilizes characteristic features pffiffiffiffi of the theoretical U T relationship for estimating the time at 90 % consolidation to computecv . Sridharan and Rao (1981) and Sridharan et al. (1987) used the linear T=U–T relationship (rectangular hyperbola fitting method) observed in the range 60 % U 90 % to estimate cv . Cour (1971), Robinson (1997), and Mesri et al. (1999) endorsed the inflection point method for estimating the time at 70 % consolidation to compute cv . Lovisa and Sivakugan (2013) conducted a study on the importance of selecting an appropriate dp value and on how well the experimental U–T curves obtained using dp and cv values fitted with the theoretical U–T curve. It should be pointed out that numerous other methods were developed to estimate the coefficient of consolidation cv and/or end of primary settlement dp (e.g., Scott 1961; Sivaram and Swamee 1977; Asaoka 1978; Parkin 1978; Robinson and Allam 1996; Robinson and Allam 1998; Robinson 1999; Mesri et al. 1999a; Feng and Lee 2001; Singh 2007; Al-Zoubi 2008a, 2008b, 2010). The EOP dp can be determined either explicitly as is the case in the log t method (Casagrande and Fadum 1940) or pffiffi implicitly as is the case in the t method (Taylor 1948). Al-Zoubi (2008b) presented the slope method in which the coefficient of consolidation cv was expressed as a function of the pffiffi slope m of the initial linear portion of the observed dt t curve and EOP dp . The slope method determines cv independently of any specific value of U (theoretically, in the range 0 U 52:6 %). Based on the approach furnished by the slope method (Al-Zoubi 2008b), the difference in cv values obtained by the various existing methods for a particular pressure increment (where the slope m is the same for all methods) can be explained by differences in EOP dp values obtained either explicitly or implicitly by these methods. In other words, the various existing methods differ in estimating cv for a particular pressure increment by the way in which the EOP dp is

estimated. The EOP dp values of the slope method were estipffiffi mated using the settlement de at which dt t curve starts to deviate from the initial linear portion; the identification of the settlement de may be subjected to judgment because careful identification may not always be possible by using the discrete data points commonly recorded in oedometer tests. In this note, the slope method is modified by proposing a new procedure for estimating the EOP dp such that this estimation is based on a more rigorous approach using the later stages of consolidation (U 52:6 %). Two types of EOP settlement are distinguished—local and global EOP settlements. Experimental results of oedometer tests on clayey soils (Table 1) show that the local EOP settlements vary depending on the method being used (i.e., depending on the U value at which the method is applied) and global EOP settlement for a given pressure increment is a unique value and is independent of any specific U value.

Slope Method of Al-Zoubi (2008b) According to Al-Zoubi (2008b), the coefficient of consolidation may be given by the following expression (1)

cv ¼

p m Hm 2 4 dp

where: m ¼ the slope of the initial linear portion of the observed pffiffi dt t curve, and dp ¼ the EOP settlement (where dp ¼ Rp R0 ; R0 and Rp are the initial and final compressions, respectively). Two compression-time data points (t1 , R1 ) and (t2 , R2 ) are required to compute the slope m and the initial compression R0 (where R1 and R2 are the dial readings at t1 and t2 , respectively). These two points must be selected such that R1 and R2 are on pffiffi the initial linear portion of the observed dt t curve as shown in Fig. 1. The initial compression Ro may thus be obtained from the following expression (2)

Ro ¼

pffiffiffiffiffiffiffiffiffiffi R2 R1 t2 =t1 pffiffiffiffiffiffiffiffiffiffi 1 t2 =t1

The Casagrande and Taylor methods utilized the same basis used to obtain Eq 2; however, in the Casagrande method, t2 is selected to be 4t1 , and thus Ro becomes equal to 2R1 R2 (i.e., D ¼ R0 R1 ¼ R1 R2 ). In the Taylor method, Ro is obtained graphically as the intercept of initial linear portion of the pffiffi dt t curve. Hence, the slope, Taylor, and Casagrande methods are similarly affected by the factors that influence the initial portion. However, these methods differ in the way by which the EOP dp is estimated (Al-Zoubi 2008a). pffiffi The slope m of the initial linear portion of the dt t curve can be expressed as follows

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TABLE 1 Basic properties of the clayey soils utilized in the present study. Particle size Soil

Sand %

Silt %

Clay %

Liquid limit %

Plastic limit %

Specific Gravity G

8

23

69

108

42

2.76

Mutah clay (Mutah-0) Chicago Blue Clay (CBC - 3)

15 4

60 64

25 32

44 29

26 17

2.73 2.73

Madaba clay (Madaba-6; Mad-t1)

14

41

45

55

25

2.78

Azraq Green Clay (AGC-5, AGC-6, AGC-8)

(3)

R2 R1 m ¼ pffiffiffiffi pffiffiffiffi t2 t1

while both R0 and m can be obtained from the initial linear pffiffi portion of the dt t curve, the final compression Rp value must be determined from the later stages of consolidation (theoretically, at U 52:6 %) such that at least one additional data point (ti , Rti ) must be selected from the consolidation data for estimating the EOP settlement dp . pffiffi The settlement de at which the observed dt t curve starts to deviate from the linear portion, as shown in Fig. 1, was considered by Al-Zoubi (2008b) for estimating EOP dp (theoretically, at U ¼ 52:6 %). The settlement de was observed to range from 40 to 60 % of the EOP settlement of the Casagrande method averaging at 50 % such that dp ¼ 2de (Al-Zoubi 2008b). Results of oedometer tests showed that the cv and dp values of the slope method were quite similar to those of the Casagrande method that gave almost identical dp values to those defined by pore water pressure measurements (Mesri et al. 1994; Robinson 1999). However, the estimation of the EOP dp requires a careful pffiffi identification of the settlement de at which the observed dt t curve starts to deviate from the linear portion that may not

always be possible by using the discrete data points commonly recorded in oedometer tests as stated earlier. In this note, the EOP dp is determined based on a unique relationship established between the ratio of the secant slope pffiffi m50 % of the observed dt t curve at 50 % consolidation to the secant slope mti at any time arbitrarily selected beyond the pffiffi initial linear portion of the dt t curve and the average degree of consolidation U as shown in the following section.

Modified Slope Method (Current Study) The Terzaghi theoretical one-dimensional consolidation relationship between average degree of consolidation U and the time factor T may be given for U 52:6 % by the following expression (Terzaghi 1943; Olson 1986) (4)

Selection of compression-time data points for the modified slope method.

8 p2 T 4 p2

In the Terzaghi theory, the consolidation time t is defined in terms of time factor T, longest drainage path Hm , and coefficient of consolidation cv as follows (5)

FIG. 1

lnð1 U Þ ¼ ln

t¼

THm2 cv

On the other hand, the settlement dt may be expressed in terms of average degree of consolidation U and EOP settlement dp by the following expression (6)

dt ¼ U dp

where dp ¼ Rp Ro ; Rp is the dial reading at the end of primary consolidation. EOP SETTLEMENT dpi ESTIMATED BASED ON THE RATIO pffiffiffi OF SECANT SLOPES OF dt t CURVE

The time factor can be expressed, based on Eqs 1 and 5, in terms of the slope m and the EOP settlement dpi as follows:

(7)

T¼

p m 2 ti 4 dpi


Combining Eqs 4 and 7 yields the following expression: (8)

8 p2 p m 2 lnð1 Ui Þ ¼ ln 2 ti 4 4 dpi p

FIG. 2

A unique relationship between the ratio of the secant slope at Ui ¼ 50 % to that at any Ui value (U > 52.6 %) and the average degree of consolidation, Ui.

Knowing that the EOP settlement dpi ¼ dti =Ui (Eq 6), Eq 8 may be rewritten after rearranging terms as follows: (9)

lnð1 Ui Þ ¼ ln

2 8 p3 m ffiffiffi p Ui p2 16 dti = ti

Equation 9 can thus be expressed in terms of the ratio of secant slopes (ROSSi ¼ m50 % =mti ) in the following form: (10)

lnð1 Ui Þ ¼ ln

8 p3 m2 Ui p2 16 m2ti

dti mti ¼ pffiffiffi ti

(11)

where: pffiffi mti ¼ the secant slope of the observed dt t curve at any arbitrarily selected time, and m ¼ m50 % as long as the initial portion of the observed pffiffi dt t curve is linear. Iterative technique is required for the solution of Eq 10 for Ui using three dial readings selected such that the first two readings [(t1 , R1 ) and (t2 , R2 )] are selected from the initial linear pffiffi portion of the observed dt t curve for computing the slope mand the initial compression Ro whereas the third reading (ti , Rti ) is arbitrarily selected at any time (or Ui ) beyond this linear portion as demonstrated in Fig. 1 for computingmti ; different third reading (ti , Rti ) may be selected. In order to avoid the use of the iterative technique for the solution of Eq 10 for Ui , Fig. 2 is prepared such that a unique relationship is obtained between the ratio of the secant slope of pffiffi the dt t curve at 50 % consolidation to the secant slope at any time arbitrarily selected beyond the initial linear portion of pffiffi the dt t curve and average degree of consolidation Ui . In other words, the EOP settlement dpi can be estimated either by Eq 10 or by Fig. 2 based on the ratio of the secant slopes m=mti pffiffi (m ¼ m50 % as long as the initial portion of the dt t curve is linear). The EOP dpi value estimated by using a single Ui value is referred herein to as local EOP settlement. The ratio of secant slopes (m=mti ) can also be expressed in terms of (Ti ; Ui ) as follows: (12)

ROSSi ¼

pffiffiffiffiffi m50 % 112:65 Ti ¼ Ui ; % mti

Values of the ratio of secant slopes ROSSi at particular Ui values are listed in Fig. 2. The Taylor method determines the coefficient of consolidation at U ¼ 90 %; the ratio of secant slopes ROSSi used in the Taylor method is 1.153 as demonstrated in Fig. 2 by the dashed line. Hence, the Taylor method

can be considered as a special case of the modified slope method where the third point is selected at 90 % consolidation. Figure 2 can be used for estimating the EOP dpi by considering three compression-time data points without using iterative technique required to solve Eq. 10 for dpi ; the first two points [(t1 ,R1 ) and (t2 ,R2 )] are selected as in Fig. 1 for computing the slope mand the initial compression Ro from the early stage of consolidation such that these two points are on the initial linear pffiffi portion of the dt t curve as shown in Fig. 1 whereas the third reading (ti ,Rti ) can be arbitrarily selected at any time (or at any Ui ) beyond this initial linear portion for computing mti as shown in Fig. 1; (t3 ,R3 ) or (t4 ,R4 ) can be selected for the analysis. The EOP dpi obtained by the modified slope method (Eq 10 or Fig. 2) is shown to vary depending on the arbitrarily selected settlement dti at which the observed compression curve is matched or fitted with the theoretical compression relationship (Table 2); the subscript i was added to dp because of the dependence of dp on the arbitrarily selected dti value. Figures 3 and 4, however, show that the EOP dpi estimates vary linearly with the arbitrarily selected dti values for two specimens of Chicago blue clay (CBC) and treated Madaba clay (Mat-t1). Similar trend was also observed by Al-Zoubi (2008a). The linear relationship between dpi and dti in the primary consolidation range can be expressed as follows:

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544


TABLE 2 Results of the modified slope method using compression–time data obtained from Taylor (1948), p. 248. Early stages of consolidation Time (min) Dial Reading (25.4 104 mm)

0

0.25

1

2.25

4

6.25

9

12.25

16

1500

1451

1408

1354

1304

1248

1197

1143

1093

m (mm /min1/2)

0.274

R0 (25.4 104 mm)

1517

Later stages of consolidation Time (min)

20.25

25

30.25

36

42.25

60

100

200

400

1440

Dial Reading (25.4 104 mm)

1043

999

956

922

892

830

765

722

693

642

settlement dti mm

1.204

1.316

1.425

1.511

1.587

1.745

1.910

2.019

2.093

2.220

MSM (Eq 10 or Fig. 2) MSM

1.674

1.717

1.780

1.791

1.806

1.864

1.911

2.018

2.092

2.220

MSM cv =Hm2 (103 min1)

21.1

20.1

18.7

18.4

18.1

17.0

16.2

—

—

—

Local Ui , %

71.8

76.6

80.1

84.3

87.8

93.5

99.8

—

—

—

Global U, %

62.7

68.5

74.2

78.7

82.6

90.8

99.4

—

—

—

EOP dpi , mm

(13)

dpi ¼ a þ bdti

(14)

dpi ¼ dti

where a and b are the intercept and slope of this linear relationship, respectively. Figure 3 and Table 2 show that as the compression-time curve approaches the EOP consolidation the estimated dpi value approaches the arbitrarily selected dti value; therefore, the following expression can be suggested at the EOP consolidation:

It should, however, be pointed that although Eq 10 is only applicable for primary consolidation, it was found that if the compression-time data points were selected from the secondary compression range, the estimated dpi values were observed to be practically equal to the assumed dti values (Fig. 3 and Table 2).

FIG. 3 Dependence of the estimated EOP dpi value on the arbitrarily selected

FIG. 4 Dependence of the estimated EOP dpi value on the arbitrarily

dti value as obtained by Eq 10 or Fig. 2 (data for Chicago blue clay; Taylor 1948).

selected dti value as obtained by Eq 10 or Fig. 2 (data for treated Madaba Clay: Mad-t1).


Hence, a global EOP settlement dp for a given pressure increment may be obtained, based on Eqs 13 and 14, by the following formula: (15)

dp ¼

a 1b

Equation 15 shows that the global EOP settlement dp can be obtained from the linear relationship between the EOP settlement dpi and the arbitrarily selected settlement dti in the primary consolidation range by extrapolation without the need to continue the test into the secondary compression range as illustrated in Fig. 3 because EOP dp is only a function of a and b that can be obtained from the primary consolidation range. This extrapolation requires at least two compression-time data points in the range U 52.6 % as demonstrated in Fig. 1 to obtain the global EOP settlement dp . Hence, the modified slope method requires at least four compression-time data points to be selected from the compression-time curve; at least two data points (e.g., (t1 ,R1 ) and (t2 ,R2 ) shown in Fig. 1) must be selected from the early stages of consolidation (theoretically, U 52.6 %) such that these two points are on the initial linear portion of the observed pffiffi dt t curve for computing the initial compression R0 and slope m and at least two data points such as (t3 ,R3 ) and (t4 ,R4 ) shown in Fig. 1 must be selected from the later stages of consolidation (U >52.6 %) for estimating the global EOP settlement dp (as demonstrated in Fig. 3 or 4) and thus for calculating the coefficient of consolidation cv by Eq 1. The EOP settlement values obtained by the Taylor and Casagrande methods are also shown in Figs. 3 and 4. The EOP settlement of the Taylor method is on the linear relationship in the primary consolidation, while the EOP settlement dp of the Casagrande method is quite close to the global EOP settlement of the modified slope method. The Taylor method EOP settlement dpi values are about 84.8 and 86.5 % of the global EOP settlement dp values of the modified slope method for the specimens of the Chicago blue clay and treated Madaba clay as shown in Figs. 3 and 4, respectively. These results show that the Taylor method yields local type of EOP settlement whereas the Casagrande method yields global EOP settlement. The existing methods that use fitting procedures at a single Ui value (e.g., Taylor’s method) inherently includes limitations due to the fitting procedure of the observed compression-time curve in which the actual time to EOP consolidation exhibits a definite value (i.e., tp ) to the Terzaghi theory in which the theoretical time to EOP consolidation is infinity, resulting in different cv and dp values as obtained by these methods. This limitation is overcome in this study by modifying the slope method by using forward extrapolation to obtain the global EOP settlement dp , which is independent of any specific Ui value.

GRAPHICAL PROCEDURE FOR THE MODIFIED SLOPE METHOD

can be used for estimating the EOP dpi by considering four compression-time data points to estimate two local EOP dpi values and the global EOP dp value. The procedure can be summarized as follows: Figure 2

(a) Select two compression-time data points [(t1 ,R1 ), (t2 ,R2 )] as shown in Fig. 1 such that the two points are pffiffi on the initial linear portion of the observed dt t curve. (b) Compute R0 from Eq 2 and m from Eq 3. (c) Arbitrarily select a third data point (t3 ,R3 ) from the later stage of consolidation beyond the initial linear portion pffiffiffiffi (Fig. 1). Compute dt3 ¼ R3 R0 and mt3 ¼ d3 = t3 . (d) Calculate ROSSi ¼ m=mt3 and obtain U3 from Fig. 2. (e) Compute local EOP settlement dp3 ¼ dt3 =U3 . (f) Repeat C to E at least once; using; for example, (t4 ,R4 ) as shown in Fig. 1. (g) Compute another local EOP settlement dp4 ¼ d4 =U4 . (h) Calculate a and b where (16)

(17)

b¼

dp4 dp3 dt4 dt3

a ¼ dp3 bdt3

(i) Calculate global EOP settlement dp ¼ a=ð1 bÞ. (j) Calculate cv by Eq 1.

Comparison of the Modified Slope Method with the Taylor and Casagrande Methods Experimental results of oedometer tests on 7 specimens of four clayey soils (Table 1) are used to assess the modified slope method and to compare it with the slope, Casagrande, and Taylor methods. Figure 5(a) shows that the modified slope method yields quite similar cv values to those of the Casagrande method. On the other hand, Figs. 5(a) and 5(b) show that the modified slope and Casagrande methods generally yield lower cv values than those of the Taylor method. The experimental results presented for the Taylor and Casagrande methods are consistent with those reported by Sridharan and Prakash (1995), Hossain (1995), Robinson (1999), and Al-Zoubi (2008b, 2010). Figure 5(c) shows that cv values of the modified slope method are quite similar to those of the original slope method; however, the modified slope method provides more robust identification of EOP settlement. The validity of the modified slope method is also verified by comparing the experimental results with the Terzaghi theory throughout the entire primary consolidation stage. Excellent agreement exists between the experimental and theoretical U–T

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546


FIG. 5 Comparison of cv values of the slope, modified slope, Casagrande, and Taylor methods.

FIG. 6

Comparison of experimental U–T curves obtained using the modified slope method for two soils with the Terzaghi theoretical relationship.

curves in the primary consolidation stage as shown in Fig. 6 for two specimens of Chicago blue and treated Madaba clays; the experimental curves were obtained by normalizing the compression–time data using dp and cv values evaluated by the modified slope method.

Summary and Conclusions The slope method of Al-Zoubi (2008b) in which the coefficient of consolidation cv was expressed as a function of the slope m of pffiffi the initial linear portion of the dt t curve and EOP settlement dp is modified in this note to improve the procedure used for estimating dp . The slope method uses the point at which the pffiffi dt t curve starts to deviate from the initial linear portion for estimating the EOP dp . In this note, the EOP dpi is determined based on a unique relationship established between the ratio of pffiffi the secant slope of the dt t curve at 50 % consolidation to the secant slope at any time arbitrarily selected beyond the pffiffi initial linear portion of the dt t curve (at U 52:6 %) and average degree of consolidation Ui . The MSM requires a minimum of four compression–time data points for better estimates of the coefficient of consolidation; two data points are required from the early stages of consolidation (U 52:6 %) for computing the slope m and for back-calculating the initial compression R0 (by using backward extrapolation) and two data points from the later stages of consolidation (U 52:6 %) for computing the EOP settlement (by using forward extrapolation). Based on the analysis presented in this note, two types of EOP settlement were realized; the local EOP settlement dpi is obtained by matching the theoretical and observed compression-time curves at a specific Ui value as is the case in the Taylor method that is shown to be a special case of the modified slope method such that three compression-time


data points are used. On the other hand, the global EOP settlement dp is determined independently of any specific U value by forward extrapolation using four or more compression–time data points. Experimental results of oedometer tests presented in this note show that the modified slope method yields quite similar dp and cv values to those of the slope and Casagrande methods. These results also show that the Taylor method yields lower dp values but higher cv values than those of the modified slope and Casagrande methods.

References Al-Zoubi, M. S., 2008a, “Consolidation Characteristics Based on a Direct Analytical Solution of the Terzaghi Theory,” Jordan J. Civ. Eng., Vol. 2, No. 2, pp. 91–99. Al-Zoubi, M. S., 2008b, “Coefficient of Consolidation by the Slope Method,” ASTM Geotech. Test. J., Vol. 31, No. 6, pp. 526–530. Al-Zoubi, M. S., 2010, “Consolidation Analysis Using the Settlement Rate-Settlement (SRS) Method,” Appl. Clay Sci., Vol. 50, No. 1, pp. 34–40. Asaoka, A., 1978, “Observation Procedure of Settlement Prediction,” Soils Found., Vol. 18, No. 4, pp. 87–101. Casagrande, A. and Fadum, R. F., 1940, Notes on Soil Testing for Engineering Purposes, Harvard Soil Mechanics, Series No. 8, HSM, Cambridge, MA. Cour, F. F., 1971, “Inflection Point Method for Computing cv,” ASCE J. Soil Mech. Found. Eng. Div., Vol. 97, No. 5, pp. 827–831. Feng, T.-W. and Lee, Y.-J., 2001, “Coefficient of Consolidation From the Linear Segment of the t1/2 Curve,” Can. Geotech. J., Vol. 38, pp. 901–909. Hossain, D., 1995, “Discussion on ‘Limitations of Conventional Analysis of Consolidation Settlement,” ASCE J. Geotech. Eng., Vol. 121, No. 6, pp. 514–515. Lovisa, J. and Sivakugan, S., 2013, “An In-Depth Comparison of CV Values Determined Using Common CurveFitting Techniques,” Geotech. Test. J., Vol. 36, No. 1, pp. 1–10. Mesri, G., Feng, T. W., Ali, S. and Hayat, T. M., 1994, “Permeability Characteristics of Soft Clays,” Proceedings of the XIII ICSMFE, New Delhi, India, Jan 5–10.

Mesri, G., Feng, T. W., and Shahien, M., 1999a, “Coefficient of Consolidation by the Inflection Point Method,” ASCE J. Geotech. Geoenviron. Eng., Vol. 125, No. 3, pp. 716–718. Mesri, G., Stark, T. D., Ajlouni, M. A., and Chen, C. S., 1999b, “Closure on Secondary Compression of Peat With and Without Surcharging,” ASCE J. Soil Mech. Found. Eng. Div., Vol. 103, No. 3, pp. 417–430. Olson, R. E., 1986, “State of the Art: Consolidation Testing. In Consolidation of Soils: Testing and Evaluation,” ASTM Spec. Tech. Publ., 892, ASTM International, West Conshohocken, PA, pp. 7–70. Parkin, A. K., 1978, “Coefficient of Consolidation by the Velocity Method,” Geotechnique, Vol. 28, No. 4, pp. 472–474. Robinson, R. G., 1997, “Consolidation Analysis by Inflection Point Method,” Geotechnique, Vol. 47, No. 1, pp. 199–200. Robinson, R. G., 1999, “Consolidation Analysis with Pore Water Pressure Measurements,” Geotechnique, Vol. 49, No. 1, pp. 127–132. Robinson, R. G. and Allam, M. M., 1996, “Determination of Coefficient of Consolidation From Early Stage of Log t Plot,” Geotech. J., Vol. 19, No. 3, pp. 316–320. Robinson, R. G. and Allam, M. M., 1998, “Effect of Clay Mineralogy on Coefficient of Consolidation,” Clays Clay Miner., Vol. 46, No. 5, pp. 596–600. Scott, R. F., 1961, “New Method of consolidation-coefficient evaluation,” ASCE J. Soil Mech. Found. Eng. Div., Vol. 87, No. SM 1, pp. 29–39. Singh, S. K., 2007, “Diagnostic Curve Methods for Consolidation Coefficient,” ASCE Int. J. Geomech., Vol. 7, No. 1, pp. 75–79. Sivaram, B. and Swamee, P. K., 1977, “A Computational Method for Consolidation Coefficient,” Soils Found., Vol. 17, No. 2, pp. 48–52. Sridharan, A., Murthy, N. S., and Prakash, K., 1987, “Rectangular Hyperbola Method of Consolidation Analysis,” Geotechnique, Vol. 37, No. 3, pp. 355–368. Sridharan, A. and Rao, A. S., 1981, “Rectangular Hyperbola Method for One-Dimensional Consolidation,” ASTM Geotech. Test. J., Vol. 4, No. 4, pp. 161–168. Sridharan, A. and Prakash, K., 1995, “Discussion on ‘Limitations of Conventional Analysis of Consolidation Settlement,” ASCE J. Geotech. Eng., Vol. 121, No. 6, pp. 517–518. Taylor, D. W., 1948, Fundamentals of Soil Mechanics, Wiley, New York. Terzaghi, K., 1943, Theoretical Soil Mechanics, Wiley, New York.

Copyright by ASTM Int’l (all rights reserved); Tue Apr 15 11:20:32 EDT 2014 Downloaded/printed by Mohammed Shukri Al-Zoubi (Mutah University, Civil and Environmental Engineering Department, Mutah University, Mutah, Karak, Jordan, 61710) Pursuant to License Agreement. No further reproduction authorized.

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