For Review Purposes Only/Aux fins d'examen seulementbartlett/pubs/Journal and...For Review Purposes Only/Aux fins d'examen seulement 4 Average Effective Stress and Coefficient of Consolidation

For Review Purposes Only/Aux fins d'examen seulement

1Current Affiliation: Assistant Professor, Ph.D., P.E., Okan University, Department of Civil Engineering, Akfirat Campus, 34959, Tuzla/Istanbul/Turkey. [email protected]

NEW METHOD TO DETERMINE PROPER STRAIN RATE FOR CONSTANT RATE OF STRAIN CONSOLIDATION TESTS

A. Tolga Ozer, Evert C. Lawton, Steven F. Bartlett

A. T. Ozer1. Formerly Research Assistant, University of Utah, Department of Civil and Environmental Engineering, 122 South Central Campus Drive, Suite 104, Salt Lake City, Utah 84112-0561.

E. C. Lawton. Professor, Ph.D., P.E., University of Utah, Department of Civil and Environmental Engineering, 122 South Central Campus Drive, Suite 104, Salt Lake City, Utah 84112-0561. [email protected]

S. F. Bartlett. Associate Professor, Ph.D., P.E., University of Utah, Department of Civil and Environmental Engineering, 122 South Central Campus Drive, Suite 104, Salt Lake City, Utah 84112-0561. [email protected]

Corresponding Author: A. T. Ozer, Assistant Professor, Ph.D., P.E., Okan University, Department of Civil Engineering, Akfirat Campus, 34959, Tuzla/Istanbul/[email protected]: +90-216-677-1630 Ext. 1978Fax: +90-216-677-1486


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Abstract:

The development of a new semi-empirical method to predict the proper strain rate for constant

rate of strain (CRS) consolidation tests is described herein. The validity of the proposed method

is analyzed using experimental results from CRS and incremental loading tests on four types of

soil - Lake Bonneville Clay, Massena Clay, kaolinite and montmorillonite. It is found that the

maximum allowable strain rate depends on the initial void ratio of the soil and thus is related to

the compressibility of the soil. The effect of the strain rate on the distribution of the pore

pressure within the sample is investigated by comparing values of effective vertical stress

calculated using the linear equation from Wissa et al. (1971) with values of effective stress at the

base of the specimen determined from measured values of pore pressure. Overall the proposed

method predicts the maximum allowable strain rate very well for three of the four soils and

moderately well for the other soil.

Keywords: CRS consolidation test, strain rate, Lake Bonneville clays


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INTRODUCTION

Since its development by Smith and Wahls (1969), the constant rate of strain (CRS)

consolidation test has been plagued by two problems: (1) An unknown distribution of pore water

pressures across the height of the specimen, ranging from zero at the top to a known (measured)

value at the bottom, which makes it difficult to determine average pore pressure and hence

average effective axial stress in the specimen; and (2) difficulty in determining the proper

deformation rate at which to perform the test for the type of soil being tested unless the tester

have significant experience with similar types of soils. The tradeoff is that a fast rate is desired

to complete the test as quickly as possible, but the rate should not be so high as to induce

excessive excess pore pressures in the specimen.

In this paper a new semi-empirical method to calculate the proper strain rate for CRS

testing of soils is described. An inherent advantage of this method is that the uncertainty relating

to the distribution of pore pressures within the specimen is minimized. The method is based

primarily on extensive testing of Lake Bonneville clay from the Salt Lake Valley in Utah. In

addition, the applicability of this method to three other types of soil (Massena clay, kaolinite, and

montmorillonite) is analyzed using data from CRS tests found in the open literature.

BACKGROUND

Although ASTM has standardized the CRS test since 1982 as D4186, many different

methods and theories have been developed to determine the proper rate at which to conduct the

test; and to calculate the average effective vertical stress v and coefficient of consolidation

vc at any point during the test. The ASTM standard as well as alternative methods and

theories will be reviewed in the subsections below.


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Average Effective Stress and Coefficient of Consolidation

ASTM D4186 has always recommended using one of the theories developed by Wissa et

al. (1971) to estimate v and vc . From 1982 through 2005, the nonlinear theory was

recommended; since 2006 the linear theory has been recommended with the equations for the

nonlinear theory given in an appendix. The nonlinear theory is based on assumptions that the

virgin compression index cC is constant and the distribution of excess pore water pressure is

parabolic. The linear theory is based on assumptions that the coefficient of volume

compressibility vm is constant and the distribution of excess pore pressure is linear.

Smith and Wahls (1969) developed a mathematical model for the CRS test that first

established a relationship for v and vc . They assumed that the permeability of the soil is

constant over the depth of the sample at any time, the void ratio of the soil varies linearly with

depth, and the distribution of pore water pressure is parabolic.

Rate of Strain

ASTM D4186-82 provided suggested rates of strain as a function of liquid limit of the

soil as shown in Table 1. In 1989 the recommendation was changed to keep the absolute value

of the ratio of base excess pore pressure to vertical total stress vbu ratio,pressurepore

between 3 and 30% at any time during the test. This criterion was reaffirmed in 1998. In 2006

the recommendation was changed to produce a value of vbu between 3% and 15% at the end

of the loading phase.

Smith and Wahls (1969) proposed an equation for strain rate based on their theoretical

model, which expresses strain rate as a function of coefficient of consolidation vc , virgin

compression index ( CC ), a proportionality constant m that falls within the range of 0.6 to 0.8,


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initial void ratio oe , initial height of the specimen oH , and maximum pore pressure

maxvbu . However, unless vc and cC are determined using another method prior to

performing the CRS test, at least one trial consolidation test must first be conducted to use their

equations. In addition, they indicated that their theory appears to be valid only for tests in which

vbu does not exceed approximately 50 %.

Gorman et al. (1978) conducted CRS consolidation tests on undisturbed specimens of

three common Kentucky region clays. They proposed that a strain rate should be selected such

that bu is at least 7 kPa but vbu does not exceed 30 to 50 % at any time during the test. If the

liquid limit of the soil to be tested is less than 60 percent, they recommended using a strain rate

of 0.01 %/min, and if it is greater than 60 %, then a rate of 0.005 %/min should be used.

Lee (1981) stated that in contrast to small strain theories, large strain theory indicates that

CRS consolidation depends on the applied strain rate. It was shown that the consolidation

process is determined by a dimensionless strain rate parameter which is a function of strain

rate, 0H , and vc . Lee found that when the strain rate is very small, the solution is not very

sensitive to the various strain rates used. Comparison between small and large strain solutions

showed that the small strain solution can be used as a reasonable approximation when

0.1< <0.2.

Armour and Drnevich (1985) developed a strain-rate equation that depends on

permeability, liquidity index, and the desirable maximum pore pressure ratio based on the work

of Wissa at al. (1971). In contrast to the findings of Armour and Drnevich, Crawford (1988)

indicated that strain rate effects do not depend on the liquid limit. Larson and Sallfors (1986)

stated that the results from incremental loading (IL) consolidation tests agree with the results


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from CRS tests conducted on Swedish clay if vbu is limited to 10 %. Sandbaekken et al.

(1986) reported that for Norwegian clays, the strain rate for a CRS test should be chosen so that

vbu never exceeds 10 %. Znidarcic et al. (1986) proposed an analysis for CRS consolidation

that is based on one-dimensional theory of nonlinear finite strain consolidation (Gibson at al.,

1967).

Nash et al. (1992) conducted CRS tests on specimens of soft clay from Bothkennar to

examine the effects of strain rate on preconsolidation stress. They found that higher strain rates

produced higher predicted values of preconsolidation pressure. Leroueil et al. (1983 and 1985)

observed similar strain rate dependency for preconsolidation pressure and overconsolidation ratio

for a variety of Champlain Sea clays and for clays at a Gloucester test site. Similar conclusions

were reached for Eastern Canada clays by Silvestri et al. (1986) and for heavily overconsolidated

naturally cemented clay (Leda Clays) by Vaid et al. (1979). Silvestri et al. (1986) also stated that

values of vc increased with increasing strain rate.

Lee et al. (1993) reported on the application Lee’s (1981) data reduction procedure to the

results of three series of CRS consolidation tests on Singapore marine clay. The study confirmed

that the upper limit of dimensionless strain rate parameter is 0.1. In practice, vc can be

determined from charts by Carrier III (1985) for normally consolidated clays. Lee et al. (1993)

also confirmed that the fastest rate can be calculated using the maximum threshold value of of

0.1 for their proposed data reduction method, but the lowest feasible rate depends on the

accuracy of the pore pressure transducer and further research was needed.

Sheahan and Watters (1997) applied the non-linear theory of Wissa et al. (1971) to the

results of CRS tests on resedimented specimens of Boston blue clay. Results from the CRS tests


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for three different strain rates compared well with IL test results despite the fact that vbu in

the fastest test exceeded 70 % at any time during the test.

DEVELOPMENT OF NEW METHOD FOR PROPER STRAIN RATE

Void Ratio-Time Relationship

Since the area of the specimen and the volume of solids remain constant during a one-

dimensional consolidation test, the relationship between change in strain () and change in void

ratio (e) is simplified compared to the general case of three-dimensional strain, and the

following well-known equation expressing this relationship can be derived using phase relations:

[1] 1001

%0e

e

The rate of strain during a CRS test, usually expressed in percent strain, can be written as

follows:

[2] t

R

%

Substituting [1] into [2], replacing t with t, and solving for e results in the following equation:

[3] RtAeee o

where;

[4] 100

1 0eA

A is a constant that depends on the initial void ratio of the specimen. R is positive for

compression and negative for decompression.

Experimental Values of vbu for Lake Bonneville Clay

A total of forty four CRS consolidation tests were performed on specimens of Lake

Bonneville Clays from two research sites (South Temple and North Temple) at a strain rate of


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0.00229 mm/min (0.009%/min) (Ozer 2005). The maximum value of vbu in the normally

consolidated range during the loading phase of these tests varied from 3 to 7% for specimens

from the North Temple site and from 2 to 14% for the South Temple site. These results

essentially meet the requirements for vbu according to D4186-06, indicating that this is a

proper strain rate for these Lake Bonneville specimens. It was also found that values of v

calculated using the linear theory of Wissa et al. (1971) (D4186-06) are nearly identical to the

values of effective stress at the base of the specimen vb for all tests on Lake Bonneville clay

at this strain rate. A representative comparison of v and vb for one test conducted at the rate

of 0.00229 mm/min is shown in Fig. 1.

Six CRS tests were performed at higher strain rates (0.0356, 0.0180, 0.00889, 0.00762,

0.00356 and 0.00305 mm/min) to provide additional insight into the effect of strain rate on

excess pore pressure. The maximum value of vbu ratio within the normally consolidated

range during the loading phase of the test conducted at a strain rate of 0.0356 mm/min was 31%,

which is considerably higher than recommended maximum value of 15 % by 4186-06. Similar

behavior was observed in the other tests conducted at higher strain rates (0.018 mm/min, 0.00889

mm/min, and 0.00762 mm/min). The maximum value of vbu in the normally consolidated

range during the loading phase was 6% for the tests conducted using strain rate of 0.00356

mm/min.

At these six higher strain rates, values of v and vb were significantly different when

a maximum value of vbu of more than 15 % occurred during the normally consolidated range

of the loading phase. Values of v and vb for CRS tests conducted at two of the higher strain


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rates - 0.0356 (0.14 %/min, which is the fastest rate used to test Lake Bonneville Clays) and

0.00356 mm/min (0.014 %/min) - are compared in Figure 1.

PROPOSED MODEL

The unique relationship between void ratio and time, which depends on the strain rate

( R ) and the initial void ratio ( oe ), is given in eq. [3] To apply the proposed semi-empirical

model to determine a proper strain rate for the CRS consolidation test, an incremental loading

(IL) consolidation test must first be performed and the e - v relationship established from the

results. After determination of oe from the IL test, an e - v curve can be constructed for any

strain rate using eq. [3]. According to the proposed model, the proper strain rate is the one that

produces an e - v curve that best matches the curve from the IL consolidation test. This strain

rate is assumed to be the maximum allowable strain rate for that soil.

e also depends on elapsed time, as can be seen in eq. [3]. If v is less than the

preconsolidation stress ( p ), the specimen is overconsolidated (OC) and reaches pore pressure

equilibrium very rapidly in an IL test. If v is greater than p , the specimen is normally

consolidated (NC) and pore pressures are dissipated much slower. The development of effective

stress in a CRS test is assumed to occur as shown in Figure 2, which is similar in concept to the

e-log v relationship. From this figure it can be seen that the constant for the OC ( OCC ) is

defined as follows:

[5] vOC

tC

log


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The constant for the NC region ( NCC ) has the same definition but a different value. Solving eq.

[5] for the time required to produce a given change in v for recompression within the OC

region produces the following result:

[6] vOCCt log

The corresponding equation for virgin compression within the NC region is as follows:

[7] vNCCt log

For a loading increment that spans p (partly recompression and partly virgin compression), the

corresponding equation is as follows:

[8] p

vNC

v

pOC CCt

2

1

loglog

The proposed method to find the proper strain rate for a CRS test consists of the

following steps:

1. Conduct an IL consolidation test on an undisturbed specimen of the soil. From the results

of this test, develop the e- v log relationship.

2. Determine appropriate values of the coefficients OCC and NCC .

3. Find the strain rate that produces a theoretical e - v log curve from eq. [3] that most

closely approximates the curve from the IL test. This value of strain rate is the

recommended value to conduct the CRS tests.

EXAMPLE ILLUSTRATING APPLICATION OF THE MODEL

In this section, an example will be provided to illustrate the proposal model. The

e- v log relationship given as the dashed line in Figure 3 was obtained from an IL test conducted

on an undisturbed specimen from the North Temple research site at an elevation of 1278.298 m


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with 0e = 1.920 and p ≈ 149 kPa. In this IL test, the load was doubled each time and eqs. [6]

and [7] can be written as:

[9] OCOC TCt 2log

[10] NCNC TCt 2log

Best-fit values of OCT = 60 and NCT = 500 were found for Lake Bonneville clays using the

results of the CRS tests conducted by Ozer (2005). The procedure used to determine these

values will be discussed later. eqs. [9] and [10] can be rearranged to solve for the corresponding

values of OCC and NCC as follows:

[11] 1992log

60OCC

[12] 16602log

500NCC

Next a series of e - v log curves are generated using eq. [3], the coefficients OCT , NCT ,

OCC and NCC , and varying R . The curve generated from this procedure that most closely

matches the results of the IL test is recommended as the proper strain rate at which the CRS tests

should be conducted.

As shown in Figure 1 for a strain rate of 0.00356 mm/min (0.014 %/min), the maximum

value of vbu in the normally consolidated range during the loading phase of the test is less

than recommended 15 %. In addition, the values of vb and v are nearly the same. In contrast,

as also shown in Figure 1, for the test conducted at a strain rate of 0.0356 mm/min and the other

CRS tests conducted at high strain rates (0.018 mm/min, 0.00889 mm/min, 0.00762 mm/min),

there were noticeable differences between the measured values of vb and the calculated values


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of v . Therefore, the maximum appropriate strain rate for the Lake Bonneville clay is 0.00356

mm/min using this method.

Sample calculations are given here to illustrate how the ve log curve is generated

using eq. [3] and a strain rate of 0.00432 mm/min (0.017 %/min). The applied stresses in the IL

test were 26.4, 52.7, 106, 211, 428, 844, and 1690 kPa. For each loading increment within the

OC region ( pv ), the time to the end of primary consolidation, 100t , is equal to OCT

according to eq. [9]. So, for the first loading increment of 0 to 26.4 kPa, 100t is 60 min and the

total elapsed time from the beginning of the test, totalt , is also 60 min. The void ratio at the end

of the first loading increment is found from Eq. [9] as follows:

[13] 890.1100

920.1160017.0920.1)4.26(

kPae

Similar calculations are performed for the other loading increments within the OC region to

produce predicted values of void ratio of 1.860 and 1.831 at stresses of 52.7 and 106 kPa,

respectively.

For the loading increment that spans p (106 to 211 kPa), a portion of the load is within

the OC region and a portion within the NC region. The calculation of 100t for this loading

increment is as follows:

[14] min280149211log1660

106149log199loglog 2

1100

p

vOC

v

pOC CCt

The total elapsed time to a stress of 211 kPa is 460 min and the corresponding void ratio is

calculated as follows:

[15] 692.1100

920.11460017.0920.1)211(

kPae


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Similar calculations are used for the loading increments within the normally consolidated region

using NCT in place of OCT . The results for this loading rate are summarized in Table 2 along

with the results from the IL test and the results for two other strain rates (0.00406 and 0.00381

mm/min = 0.016 and 0.015 %/min) calculated using eq. [3]. These results are compared

graphically in Figure 3.

The coefficient of determination ( 2R ) between the values of void ratio determined from

the results of the IL test and the corresponding values calculated using eq. [3] are found from the

following equation:

[16] 23.

22

ILEq

ILIL

eeeeR

where ILe is void ratio from the IL test, ILe is the average void ratio from IL test, and 3.Eqe is the

void ratio calculated using Eq. [3]. The calculated values of 2R using Eq. [16] for strain rates of

0.00432, 0.00406, and 0.00381 are 71.8, 81.3, and 91.9 %, respectively. Hence, for this soil

(Upper Bonneville Clay, North Temple Site, Elevation 1278.298 m), the predicted maximum

strain rate at which the CRS tests should be conducted is 0.00381 mm/min (0.015 %/min) using

this proposed method. This rate is very close to the rate of 0.00356 mm/min (0.014%/min)

determined to be the appropriate rate by comparing values of vb and v at the same void ratios.

In Figure 4, experimental results from an IL consolidation test and predicted results from

eq. [3] at three different strain rates for Lower Bonneville Clay (South Temple, Elevation

1273.236 m) are compared. Using eq. [16], values of R2 are found to be 99.6, 86.0 and 70.2 %

for 00305.0R , 00279.0R and 00356.0R mm/min, respectively. Hence, for this soil, the

predicted maximum strain rate at which the CRS tests should be conducted is about 0.00305

mm/min.


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The predicted maximum strain rate for Lake Bonneville Clay at various elevations using

the proposed model is given in Table 3. As seen in Table 3, the calculated maximum strain rate

for the CRS consolidation test is 0.00381 mm/min (0.015 %/min) for Bonneville Clay. As

shown in Figure 1, values of vb and v for a CRS test conducted at a strain rate of 0.00356

mm/min (0.014 %/min) are nearly identical and the maximum value of vbu was 6 % within

the NC range of the loading phase.

Strain rates approximately 10, 5 and 2.5 times faster (0.0356 mm/min, 0.018 mm/min,

and 0.00762 mm/min, respectively) than the recommended maximum strain rate for the Upper

Bonneville Clay (0.00381 mm/min) were applied. As shown in Figure 1, values of vb and v

were substantially different for these rates. In addition, using a rate approximately10 times faster

(0.0356 mm/min) produced a maximum value of vbu ratio within the NC range of the loading

phase was 31 %, which is significantly more than the recommended value of 15 %. The same

behavior was observed for the rates 5 and 2.5 times faster, which produced maximum values of

vbu of 20 and 18 %, respectively, also exceeding 15 %.

As can be seen in Table 3, the calculated maximum strain rate for the Lower Bonneville

Clay using the developed method is 0.00330 mm/min (0.013 %/min). For the test that was

conducted at the strain rate of 0.00305 mm/min (0.012 %/min), there was little difference in

values of vb and v a maximum value of vbu of 4 % was produced within the NC range of

the loading phase. Therefore, the developed model has also provided reliable prediction of the

appropriate maximum strain rate for the Lower Bonneville Clay.


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APPLICATION OF THE PROPOSED MODEL TO OTHER CLAYS

In the previous section, the proposed model was used to determine maximum strain rate

for Lake Bonneville clay using the criteria for vbu from D4186-06. In this section, a similar

procedure will be used to determine the applicability of the proposed model to other clays based

on data found in the literature. Smith (1967) conducted CRS consolidation tests for three

different soils and compared these results with results from IL tests conducted on the same

materials. Two of the soils used in Smith’s research were commercially prepared - calcium

montmorillonite and kaolinite. The third soil tested was a natural soil (Messana Clay) from New

York. The predicted maximum strain rates for these three soils were found using the proposed

model, with the results shown in Figures 5 through 7.

As can be seen in Figure 5, the best-fit strain rate for montmorillonite using the proposed

model is 0.00381 mm/min. Smith (1967) conducted five CRS consolidation tests using four

different strain rates (0.0152, 0.00610, 0.00244 and 0.000610 mm/min) and the maximum values

of vbu within the NC range during of the loading phases for these tests are summarized in

Table 4. The tests conducted at strain rates of 0.0152 and 0.00610 mm/min produced values of

vbu greater than the recommended maximum value of 15 % within the NC ranges of the tests.

In contrast, the tests at rates of 0.00244 and 0.000610 mm/min produced maximum values of

10% and 3%, respectively, both within the recommended range of 3% to 15%. The

recommended maximum strain rate according to the proposed model of 0.00381 mm/min falls

within the range of strain rates for Smith’s tests that would be expected to produce the maximum

permissible value of 15% (0.00244 to 0.00610 mm.min). Furthermore, Smith (1967) indicated

that the compressibility of montmorillonite increased with decreasing strain rate, and CRS tests


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conducted at strain rates of 0.00244 and 0.000610 mm/min produced similar values of

compression index (0.88 and 0.86, respectively) with the value obtained from the IL test (0.88).

Smith (1967) performed tests on remolded specimens of kaolinite at six different strain

rates (Table 4). In all these tests there was no pronounced value of p since the specimens were

NC remolded. All the CRS tests conducted produced maximum values of vbu more than 15

% during the loading phase of the tests. The recommended maximum strain rate for kaolinite

using the proposed model is 0.00035 mm/min (Figure 6), which is less than the minimum rate

use for the kaolinite specimens, indicating that the proposed model gives a reasonable result for

kaolinite.

For the Mesanna Clay, use of the proposed model produces a recommended maximum

rate of 0.00533 mm/min (Figure 7). Smith conducted only one CRS test - at a rate of 0.00610

mm/min - which is 14 % faster than the recommended maximum rate. A maximum value of

vbu of 4% was generated within the NC range of the loading phase of this test, which is less

than the recommended 15 %. Therefore, the proposed model appears to underpredict somewhat

the maximum strain rate for this clay, which is conservative.

When the calculated e - v log curves for Lake Bonneville clays (upper and lower),

montmorillonite, and Mesanna clay are compared with the corresponding curves from IL tests

(Figures 3, 4, 5, and, 7, respectively), the calculated curves match well with test curves. In each

case, values of OCT = 60 min and NCT = 500 min were used. These factors were developed for

LakeBonneville Clay and doubling the load for each increment in the IL test, which is the same

loading procedure Smith used in his IL tests. However, when a value of OCT = 60 (since samples

is used for kaolinite (Figure 6), the correlations are reasonable but not as good, probably because

the specimens were remolded and behaved as NC clay). In Figure 8, the effects of using other


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values for OCT factor are shown for kaolinite at the recommended maximum deformation rate of

0.00035 mm/min. As seen in this figure, using OCT = 275 min produced a predicted curve that

correlates best with the curve obtained from the IL test. Therefore, it appears that further

research is needed with respect to the OCT factor for remolded clays.

APPLICATION OF OTHER METHODS TO LAKE BONNEVILLE CLAY

Maximum recommended strain rates were also calculated for Lake Bonneville Clays

using Smith’s method, Lee’s Method, and Armour and Drnevich’s Method. The calculated

maximum strain rates using those methods were 1.67, 0.428, and 0.109 mm/min respectively.

These maximum strain rates are considerably higher than the recommended value of 0.00381

mm/min obtained using the proposed method and validated by experimental evidence. Thus,

these other techniques do not appear to predict reasonable values of maximum strain rate for

Lake Bonneville Clay. Smith and Wahls (1969) and Lee (1981) related the recommended strain

rate to vc , and Armour and Drnevich (1985) proposed a strain rate equation based on liquidity

index (LI ). This study has found that e is a better predictor of maximum strain rate than either

vc or LI.

CONCLUSIONS

The proposed semi-empirical model to determine an appropriate strain rate for CRS tests

to be performed on a given soil, an IL test must first be performed on a specimen of the soil and

the corresponding e -log v curve established from the results. Using eq. [3] and empirical time

factors for the OC and NC regions, a series of predicted e -log v curves can be developed by

varying the strain rate. The rate that produces the e -log v curve that is closest to the curve

from the IL test curve is chosen as the maximum allowable strain rate for that soil. This


18

proposed method was applied to data from CRS and IL tests performed on Lake Bonneville

Clays conducted by Ozer (2005), and for similar data on three types of soils reported in Smith

(1967). Values of the empirical time factors determined from results of CRS tests on Lake

Bonneville Clays were used in all analyses. The proposed method was able to predict maximum

strain rates that agreed well with results from CRS tests for three (Lake Bonneville Clay,

Messena Clay and montmorillonite) of the four soil types, and moderately well for the fourth soil

type (kaolinite). Additional research is needed on other soil types to determine if the method and

empirical time factors are generally applicable to all types of soils.

An extensive evaluation of base excess pore pressures generated during CRS tests as a

function of strain rate was undertaken. Values of vbu were compared with ve log curves

calculated using the linear theory of Wissa et al. (1971) and with vbe log curves calculated

using measured values of bu . From these comparisons, it was found that ve log and

vbe log curves were nearly the same when the values of vbu within the NC portion of the

loading phase were within the range of 3% to 15 % recommended by ASTM D4186-06. Based

on these results, it appears that the criterion established for vbu in ASTM D4186-06 give

reasonable guidance for selection of the proper strain rate.


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REFERENCES

Armour, D. W., and Drnevich, V. P. 1985. Improved techniques for the Constant-Rate-of-Strain

Consolidation test. In Consolidation of Soils: Testing and Evaluation, Orlando, Fla., 24

January 1985, ASTM Committee D-18 Symposium on Soil and Rock, pp. 170-183.

ASTM D 4186-82. 1982. Standard test method for one-dimensional consolidation properties of

soils using controlled-strain loading. American Society of Testing Materials, Vol. 04.08., pp.

534-538.



565-569.

ASTM D 4186-89 (Reapproved 1998). 2001. Standard test method for one-dimensional

consolidation properties of soils using controlled-strain loading. American Society of Testing

Materials, Vol. 04.08., pp. 512-517.



520-533.

Carrier, M. D. III. 1985. Consolidation parameters derived from index tests. Geotechnique,

35(2): 211-213.

Crawford, C. B. 1988. On the importance of rate of strain in the consolidation test. Geotechnical

Testing Journal, GTJODJ, 11(1): 60-62.

Gibson, R. E., England, G. L., and Hussey, M. J. L. 1967. The theory of one-dimensional

consolidation of saturated clays: I, finite non-linear consolidation of thin homogeneous layers.

Geotechnique, 17(3): 261-273.


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Gorman C. T., Hopkins, T. C., and Drnevich V. P. 1978. Constant-rate-of-strain and controlled-

gradient consolidation testing. Geotechnical Testing Journal, GTJODJ, Vol. 1(4): 3-15.

Larsson, R. and Sallfors G. 1985. Automatic continuous consolidation testing in Sweden. In

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Lee, K. 1981. Consolidation with constant rate of deformation. Geotechnique, 31(2): 215-229.

Lee, K., Choa, V., Lee, S. H., and Quek, S. H. 1993. Constant rate of strain consolidation of

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22

Figure Captions:

Figure 1. Comparisons between Effective Vertical Stress at the Base of the Specimen and the

ones Calculated from ASTM D4186-06

Figure 2. Assumed Relationship between Effective Vertical Stress and Elapsed Time in a CRS

Consolidation Test

Figure 3. Comparison of Results from IL Consolidation Test with Results from Equation [3]

Using Three Values of Strain Rate (North Temple, Elevation 1278.298 m)

Figure 4. Comparison of Results from IL Consolidation Test with Results from Equation [3]

Using Three Values of Strain Rate (South Temple, Elevation 1273.236 m)

Figure 5. Comparison of ve log Curves for Montmorillonite from Results of IL Test and

Predicted Using Equation [3]

Figure 6. Comparison of ve log Curves for Kaolinite from Results of IL Test and Predicted

Using Equation [3]

Figure 7. Comparison of ve log Curves for Mesanna Clay from Results of IL Test and

Predicted Using Equation [3]

Figure 8. Comparison of IL Consolidation Test Result with Equation [9] for R = 0.00035

mm/min and Different Time Values


Effective Stress, 'v(kPa)

0 50 100 150 200 250 300 350 400 450 500

Stra

in, (

%)

0

2

4

6

8

10

12

14

16

18

20

Avg. Effective Stress, R=0.0356 mm/minBase Effective Stress, R=0.0356 mm/minAvg. Effective Stress, R=0.00356 mm/minBase Effective Stress, R=0.00356 mm/minAvg. Effective Stress, R=0.00229 mm/minBase Effective Stress, R=0.00229 mm/min

FIGURE 1


FIGURE 2

Elap

sed

Tim

e, t

Effective Stress, v (log Scale)

1

1

OCC

NCC

p


Effective Stress, 'v (kPa)

10 100 1000 10000

Voi

d R

atio

, e

0.8

1.0

1.2

1.4

1.6

1.8

2.0

IL TestFrom Eq.3 when R=0.00432 mm/min = 0.017 %/minFrom Eq.3 when R=0.00406 mm/min = 0.016 %/minFrom Eq.3 when R=0.00381 mm/min = 0.015 %/min

FIGURE 3

N. Temple B3Sample Elevation: 1278.298 m



10 100 1000 10000

Voi

d R

atio

, e

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

IL TestFrom Eq.3 when R = 0.00279 mm/min = 0.011 %/minFrom Eq.3 when R = 0.00305 mm/min = 0.012 %/minFrom Eq.3 when R = 0.00356 mm/min = 0.014 %/min

FIGURE 4

S. TempleSample Elevation: 1273.236 m



10 100 1000

Cha

nge

in V

oid

Rat

io,

e

0.0

0.2

0.4

0.6

0.8

1.0

1.2

IL TestFrom Eq.3 when R=0.00381 mm/min = 0.015 %/minFrom Eq.3 when R=0.00356 mm/min = 0.014 %/min

FIGURE 5


Effective Stress,'v (kPa)

10 100 1000 10000

Cha

nge

in V

oid

Rat

io,

e

0.0

0.1

0.2

0.3

0.4

0.5

IL Test #301From Eq.3 when R=0.00035 mm/min = 0.0014 %/minFrom Eq.3 when R=0.0003 mm/min = 0.0012 %/min

FIGURE 6



10 100 1000 10000

Cha

nge

in V

oid

Rat

io,

e

0.0

0.2

0.4

0.6

0.8

1.0

IL Test #301IL Test #302From Eq.3 when R=0.00406 mm/min = 0.016 %/minFrom Eq.3 when R=0.00533 mm/min = 0.021 %/min

FIGURE 7


Effective Stress, 'v(kPa)

10 100 1000 10000

Cha

nge

in V

oid

Rat

io,

e

0.0

0.1

0.2

0.3

0.4

0.5

0.6

IL Test #301100150275350

FIGURE 8

Kaolinite R=0.00035 mm/min = 0.0014 %/min


Table 1. Suggested Rates of Strain for CRS Consolidation Test by ASTM D4186-82

Liquid Limit(%)

Rate of Strain(% per min.)

< 40 0.0440 - 60 0.0160 - 80 0.004

80 - 100 0.001100 - 120 0.0004120 - 140 0.0001

Table 2. Comparison of Results from IL Consolidation Test with Results from eq. [3] Using Three Values of Strain Rate (North Temple, Elevation 1278.298 m)

Void Ratio, ev Equation [3] for R (mm/min) =

(kPa) 100t totalt IL Test 0.00432 0.00406 0.003810 --- --- 1.92 --- --- ---

26.4 60 60 1.876 1.890 1.892 1.894

52.7 60 120 1.851 1.860 1.864 1.867

106 60 180 1.816 1.831 1.836 1.841

211 280 460 1.662 1.692 1.705 1.719

428 500 960 1.448 1.443 1.471 1.500

844 500 1460 1.256 1.195 1.238 1.281

1690 500 1960 1.091 0.947 1.004 1.062


2

Table 3. Calculation of the Maximum Upper Limit of the Strain Rate for Bonneville Clay at Different Elevations Using the Proposed Model

IL Consolidation Test

Elevation(m) Location

Predicted Maximum Upper Limit of R

(mm/min)

1279.790 North Temple(Upper Bonneville) 0.00381

1278.640 South Temple(Upper Bonneville) 0.00356

1278.298North Temple

(Upper Bonneville) 0.00381

1273.596North Temple

(Lower Bonneville) 0.00330

1273.236 South Temple(Lower Bonneville) 0.00305


3

Table 4. CRS Test Results from Smith (1967)

Strain Rate, R

Maximum value

of vbu a

Material (mm/min) (%)Montmorillonite 0.01520 54

0.00610 30

0.00244 10

0.000610 3

Mesanna Clay 0.00610 4

Kaolinite 0.06010 94

0.03050 89

0.01520 83

0.00610 67

0.00244 27

0.000609 18

a In the Normally Consolidated Range During Loading Phase of the Test

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