asce comparative study of shear modulus in sands sabkha - fme khaled charif

8/19/2019 ASCE Comparative Study of Shear Modulus in Sands Sabkha - FME Khaled Charif

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Comparative Study of Shear Modulus in Calcareous Sand and Sabkha Soils

Khaled H. Charif 1 M. ASCE and Shadi Najjar

2, A.M. ASCE

1Engineering Manager, Fugro Middle East, P.O. Box 2863, Dubai, United Arab

Emirates, PH (971) 502509832; email: [email protected] Professor, Department of Civil and Environmental Engineering, American

University of Beirut, PO.Box 11-0236 Riad El-Solh 1107-2020; PH (961) 3108853;

email: [email protected]

ABSTRACT

The estimation of various soil moduli has always been a fundamental

component of geotechnical engineering. Since most design works involve assessment

of ground response to stress applications, an accurate estimate of the soil modulus isdeemed imperative for computational geotechnics. Due to the non linearity of the

stress-strain response of soils, the shear modulus is always a function of strain

amplitude thus making the quantification of shear modulus critical when it comes to

consideration of strain level induced by both loading scheme and soil properties. Thecomparison between the static and dynamic shear modulus as well as between various

tools used to measure the shear modulus was rarely carried out on carbonate sands

originating from marine sediments. This paper focuses on a comparison between smallstrain shear modulus (Go) measured using the down-hole seismic test (DH) and the

seismic cone penetration test (SCPT) and estimated shear modulus (Go) obtained using

available correlations with SPT and CPT. The comparison is conducted on

unconventional soils comprised of Sabkha soils and cemented calcareous sands for asite in Abu Dhabi. The paper also compares the small-strain Go to the “high” strain G

derived from cone penetration testing (CPT).

INTRODUCTION AND BACKGROUND

Many geotechnical applications require a proper evaluation or estimation of the soil“modulus” to be used as input in design or analysis. However, the “modulus” of a soil,

whether Young’s modulus, E, or shear modulus, G, is a non-unique parameter which

depends on many factors. Therefore when one reports a given value of a shear modulus,questions should be asked regarding the conditions associated with this number

(Briaud, 2001). For example, the nature of the applied load (static or dynamic) and thestrain level that is associated with the given value of the shear modulus play a role indefining the reported value of the shear modulus, which can change for the same soil if

the loading conditions or the applied strains vary. The strain level and its impact on soil

modulus have been increasingly of interest in the past few decades especially when it

comes to pavement design problems, foundation design for machines, ground responseanalyses, and soil structure interaction under dynamic and static loads.



Some geotechnical engineering problems and analyses are governed by the

small strain modulus. Examples include pavement engineering applications (correlationof resilient modulus to small strain modulus) and low-vibration machine foundation

design problems. Other engineering applications require the definition of the shear

modulus at variable levels of strains. These include the modeling of ground motion

response for seismic hazard analyses, where the proper modeling of the variation of theshear modulus with shear strain is critical for the analysis (Darendeli and Stokoe 2001).

Another example where the choice of the proper soil modulus affects the analysis and

design is the example of a pile foundation, whereby a limited percentage of load istransferred to the lower pile sections keeping the localized shear strain across the sides

at diminutive values compared to upper pile sections. Hence the modulus used for the

settlement analysis can vary from one depth interval to the other eventhough the soilaround the pile maintains homogeneity.

OBECTIVES OF THE STUDY

Several in-situ test methods have been used to interpret soil moduli under various levelsof strain. The most commonly used test methods evaluate the modulus at strain levels

analogous to those imposed by static foundation loading. In soils, the most widespreadin-situ test methods are the standard penetration test (SPT) and the cone penetration test

(CPT). Only geophysical-based field methods such us seismic CPT tests (SCPT),

seismic downhole tests (DH), and seismic crosshole tests (CH), along with fewlaboratory tests (resonant column and torsional shear), quantify the small strain

modulus. The modulus derived from SPT and CPT will be referred to as a “high” strain

Young’s modulus E which could be converted to a “high” strain shear modulus G usingPoisson’s ratio. Numerous relationships are available in the literature to derive the

Young’s/shear modulus from those tests.Geophysical-based methods for determining the small strain shear modulus G

o

coupled with laboratory tests for determining the reduction of Go with shear strain,

provide the best approach for evaluating the shear modulus at different strain levels(Darendeli and Stokoe 2001). However, geophysical field testing is rarely carried out in

conventional geotechnical site investigations for typical projects. In these projects, it is

important to have alternate means for estimating both the small strain and high strain

moduli from correlations with more conventional tests such as SPT and CPT. It isinteresting to quantify and understand the difference between the small and high strain

moduli as obtained from such correlations and to compare these estimated values with

moduli derived from SCPT and DH field test data. Such a comparison will requiresimultaneous high-quality SPT, CPT, SCPT, and DH data coming from the same zone.

The objective of this paper is to utilize high-quality SPT, CPT, SCPT, and DH

data from a site in Abu-Dhabi (UAE) to: (1) compare and contrast shear moduli that areobtained from different field test methods while benchmarking them against the results

from the downhole (DH) test results, which are expected to be the most accurate, (2)

use the results from the DH tests to evaluate the effectiveness of the correlations thatallow for estimating the small strain shear modulus from conventional CPT and SPT

data, and (3) compare the small strain (from DH) and large strain (from conventional

field tests) shear modulus with the intent of finding a relationship between the two.



The aforementioned goals have been partially addressed by several research

studies. However, what makes this study unique is the fact that the soils at the siteunder consideration have been hardly ever studied previously. These soil types consist

of calcareous cemented sands and sabkha soils. The former is a product of recent

marine deposition of carbonate sands which are cemented with calcium carbonate

whereas the latter is a loose mixture of silts and clays, occasionally with sands. Basedon the knowledge of the authors there are no studies in the literature that have tested the

effectiveness of available correlations for predicting the small strain and large strain

shear modulus in these soils.

FIELD TEST DATA AND INTERPRETATION

The site lies within the vicinity of the coast line of Abu Dhabi in the UAE. The

geology of the coastline of the United Arab Emirates and the Arabian Gulf is

represented by an area of carbonate sedimentation. Surficial deposits consist of sanddunes and evaporates together with marine sands and silts (Charif et al. 2010). In

addition, wind erosion and capillary action have led to the formation of Sabkhadeposits. The geotechnical investigation that was conducted is comprised of 8 clusters.

Each cluster is a rectangular shaped area with the spacing of the sides limited to 4m.Two boreholes and one SCPT were advanced at each cluster. Seismic Downhole tests

(DH) were conducted in 6 clusters out of the 8

Analysis of CPT Data

The variation of the CPT tip resistance and friction ratio with elevation for the testedclusters is plotted in Fig. 1. According to the borehole logs, laboratory test results, and

the CPT profile shown in Fig. 1, the soil profile can be subdivided into three mainlayers that are summarized in Table 1.

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30 35 40 45 50

Cone Tip Resistance qt (MPa)

E l e v a t i o n ( m )

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 1 2 3 4 5 6 7 8

Friction Ratio f r (%)

E l e v a t i o n ( m )

Figure 1. CPT tip resistance qt and friction ratio f r versus elevation



Table 1. Soil profile from CPT data

LayerStart

Elevation(m)

End

Elevation(m)

Layer

Thickness(m)

Soil Description

Layer 1 +4.0 +2.5 1.5 Medium dense, poorly graded, fine, Sand

Layer 2 +2.5 +0.5 2.0 Loose clayey Silt with Sand (Known as Sabkha)Layer 3 +0.5 -4.5 5.0 Loose to medium dense, poorly graded, silty Sand.

The soil profile is comprised of a 1.5m thick surfacial layer of medium dense

fine sand that is underlain by a 2.0m thick layer of Sabkha soils, which is in turn

underlain by a loose to medium dense layer of silty sand. The CPT results were plottedon a SBTn Qt1-Fr chart (see Fig. 2) developed by Robertson (1990) and further updated

by Robertson and Wride (1998) to include the cI coefficient. The normalized CPT tip

resistance tnQ was calculated according to the approach suggested by Robertson and

Wride (1998) and further updated by Zhang et al. (2002), with the stress exponent

calculated following the method suggested by Robertson (2009). As expected, results

on Fig. 2 indicate that the data corresponding to the sand and silty sand layer plotwithin zones 5 and 6 (Sands and Silty Sands) whereas points falling within zones 3 and

4 correspond to the Sabkha layer.

The CPT data presented in Figs. 1 and 2 was collected at intervals of 10cm,whereas the shear wave velocity profiles that were measured from the seismic CPT

(SCPT) and downhole data (DH) were available at an interval of 1.0m. These

measurements shall be used to derive the small strain modulus as demonstrated in the

coming interpretative section. To allow for one-to-one comparisons, the CPT readingsthat correspond to the exact depths of the SCPT and DH measurements were adopted.

1

10

100

1,000

10,000

0% 1% 10%

N o r m a l i z e d C o n e R e s i s t a n c e Q t n

Normalized Frictin Ratio Fr (%)

Poo rly-Graded Fine SandLoose Clayey Silt (Sabkha)

Poorly-Graded Silty Sand

5

1

6

7

9

8

23

Figure 2. CPT data on SBTn Qt1-Fr Chart (SBT zoning as per Robertson 1990)



Small Strain Shear Modulus from SCPT, DH, and CPT Correlations

Shear wave velocity measurements Vs collected using SCPT and DH tests were

used to calculate corresponding small strain shear modulus values Go using Equation 1:2

0 sV G ρ = (1)

where ρ is the total unit weight γ divided by gravitational acceleration. In addition, anestimate of the small strain shear modulus was calculated from the CPT tip resistance qt

using the correlation proposed by Robertson (2009) in Equation 2.

( )[ ]( )0

68.155.0

0 10 vt

I

a

qG c σ ρ

ρ −⎟⎟

⎠

⎞⎜⎜⎝

⎛ = +

(2)

where tq is the cone tip resistance, voσ is the overburden pressure, a p is the atmospheric

pressure (101kPa), and Ic is the radius of concentric circles that define the boundaries of

soil type on the Robertson (1990) SBTn chart.

The variation of the small strain shear modulus Go with elevation is presentedon Fig. 3 based on DH measurements, SCPT measurements, and CPT q t-correlation.

Three graphs are drawn to aid in the assessment of the different methods for evaluatingGo. Results on Fig. 3 lead to two major observations. The first obvious observation isthat values of Go that are deduced from SCPT field measurements are relatively larger

than those obtained from DH field measurements, especially in the cemented

calcareous sand layers. Better correspondence between DH and SCPT data is observedin the Sabkha layer, indicating that the SCPT test results may be sensitive to

cementation in the sand layers. The second observation is that values of Go that are

derived from correlation with qt exhibit a relatively good agreement with the DH data,

although they tend to slightly underestimate the DH data.

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 100 200 300 400 500 600

E l e v a t i o n ( N A D D )

Go (MPa)

Go From SCPT Meas urements

Go from DH Measurements

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 100 200 300 400 500 600


Go (MPa)

Go From SCPT Meas urements

Go from CPT Correlations

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200 250


Go (MPa)

Go From DH Meas urement

Go From CPT Correlation

Figure 3. Small strain shear modulus Go from SCPT, DH and qt-correlation



To investigate the second observation in detail, a plot showing the DH versus

the qt-correlated Go values is presented in Fig. 4a, with the different soil types labeledclearly to isolate any effect of soil type on the agreement between the two methods.

Also plotted on Fig. 4b is the ratio of Go(qt) to Go(DH) for the different soil types. An

investigation of this ratio would help in quantifying the uncertainty associated with

estimating Go with conventional CPT data in sites with calcareous cemented sands andsabkha deposits in the absence of geophysical testing. Although the number of data

points is relatively limited, results on Figs. 4a and 4b indicate clearly that estimating Go using conventional CPT data in the soils studied in this paper tends, on average, to

underestimate the value of Go, with the degree of conservatism becoming larger for

Sabkha soils and sands with relatively larger densities. The calculated ratio of Go(qt) to

Go(DH) has a mean value of 0.69 with an associated coefficient of variation of 0.68,reflecting the large scatter in the test results. The mean ratio was found to be the

smallest for Sabkha soils (mean ratio = 0.44) and the largest for the upper sand layer

(mean ratio = 0.84), with the lower sand layer having an intermediate mean of 0.68.The general under prediction of Go could be due to many reasons, one of which is the

fact that the CPT is not a “small” strain test. Also, the under prediction could be due tothe fact that Equation 2 is based on data that did not incorporate calcareous Sands andSabkha, but was rather based on siliceous, uncemented sands.

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150 200

G o

F r o m q t - C o r r e l a t i o n ( M p a )

Go From DH (MPa)

Sand (Upp er Layer)

Sabkh a (Silty Clay)

Sand (Lower Layer)

0.0

0.2

0.40.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0 50 100 150 200

R a t i o

o f G 0 ( q t ) t o G o

( D H )

Go From DH (MPa)

Sand (Upp er Layer)

Sabkh a (Silty Clay)

Sand (Lower Layer)

Figure 4. (a) Go from DH versus Go from qt, (b) Go (DH) / Go (qt) versus Go (DH)

“Small” Strain vs “Large” Strain Shear Modulus

An effort will be made in this section to estimate what is considered as a “high” strain

modulus shear modulus G from conventional CPT data using available correlations.

Among the various correlations available in the literature, a method whereby the CPTtip resistance is correlated to the large strain Young’s modulus E via the constraint

modulus M will be used to derive G, which is linked to the Young’s modulus via

Poisson’s ratio ν as follows:

( )ν +=

12

E G (3)



Lunne et al. (1997) recommended the relationships presented in Equations 4 and 5 for

correlating the CPT tip resistance to the constrained Modulus M. Two differentrelationships were provided for “sands” and “silty” soils (sabkha in this paper). It is

worth noting that these relationships were derived for silica sands, but will be used here

for calcareous sands. The relationships are formulated as:

For Sands: ( ) t MPa q M 4= MPaq t 0.10<

( ) 202 += t MPa q M MPaq MPA t 0.55.2 << (4)

For Silty Soils: ( ) t MPa q M 2= MPaqt 5.2<

( ) 54 −= t MPa q M MPaq MPA t 0.55.2 << (5)

Once, the constrained modulus is calculated, it can be used to estimate Young’s

modulus E using Equation (6). The “large” strain modulus G is then derived fromYoung’s modulus E using Equation (3):

( )( )ν

ν

−

−=

12

21 M E (6)

The “large” strain modulus G as obtained from the CPT tip resistance using the above procedure was calculated and plotted against the “small” strain modulus from the DH

tests on Fig. 5a. The results on Fig. 5a were divided based on soil type and indicate that

most of the calculated “large” strain shear moduli for the upper and lower sands rangefrom 1 MPa to 10 MPa. Interestingly, the Sabkha data points exhibited relatively small

values for the “large” strain shear modulus. The ratio of G/Go was calculated for all

soils and plotted on Fig. 5b. The data on Fig. 5b indicate that the ratio of G/G o isgenerally between 0.1 to 0.01 for the sands and between 0.01 to 0.001 for the Sabkha

soils. It is worth noting that these reductions in the shear modulus at large strains (2 to 3

orders of magnitude) are excessive and reflect the strong tendency of the cemented

calcareous sand and the Sabkhas to lose significant stiffness at large strains comparedto common soils, which generally do not lose more than an order of magnitude of

stiffness between large and small strains (Darendeli and Stokoe 2001).

0.01

0.10

1.00

10.00

100.00

0 50 100 150 200 250

G ( M P a )

G0 (MPa)

Sand (Up per Layer)Sabkha (Silty Cl ay)Sand (Lo wer Layer)

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 50 100 150 200 250

G / G o

G0 (MPa)

Sand (Upper Layer)Sabkha (Silty Cl ay)Sand (Lower Layer)

Figure 5. (a) Comparison between Go and G, (b) Ratio of G/Go for different soils



“Small” Strain Modulus from SPT Data

In addition to the CPT, DH, and SCPT tests, standard penetration tests (SPT) were

conducted at the site. The SPT data, corrected to 60% hammer efficiency (N60) wereused to derive estimates of Go to be compared to Go from DH tests. In the below

analysis, Go was calculated using Equation (7) where the shear wave velocity, Vs, wascorrelated to SPT N values as follows (Jamiolkowski et al. 1988):

21

2.017.0

601 F F z N C V s = (7)

where C1 is an empirical constant equals to 53.5 (Jamiolkowski et al 1988), z is the

depth at which the blow count N is taken, and F1 and F2 are age and soil factors

respectively. Figure 6a shows the SPT blow counts N60 versus elevation whereas Fig.

6b shows Go as measured from DH and as derived from SPT N values. As with the previous findings for CPT, the measured Go from DH is generally larger than that

derived from N. In this regard, it is very likely that destructive testing (especially thehigh energy SPT) could possibly break the cementation of calcareous sand and maycrush the actual sand particles resulting in permanent changes in the physical properties

of the soil matrix. This disturbance of the structure of the sand matrix is not possible in

the case of wave propagation in geophysical testing, resulting in relatively larger shearmoduli in comparison to those derived from SPT blow counts or tip resistance in CPT.

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200


Go (Mpa)

Go From DH

Go From SPT N-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 5 10 15 20 25 30 35 40 45 50


SPT N

Figure 6. (a) SPT N versus elevation, and (b) Go from DH and SPT



0

50

10 0

15 0

20 0

0 50 100 150 200

G o

( M p a ) M e a s u r e d U s i n g D H

Go (Mpa) Derived Using SPT N Values

Sand (Upper Layer)

Sabkha (Silty Clay)

Sand (Lower Layer)

Best Fit Line

1:1

1:2.3

4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 20 40 60 80 100

G o

( S P T , C o r r

e c t e d ) / G 0 ( D H )

Go (Mpa) from SPT N Values

Sand (Upper Layer)

Sabkha (Silty Clay)

Sand (Lower Layer)

Figure 7. (a) Go derived From SPT versus Go measured using DH, (b) Ratio of G0

derived from corrected SPT model (Equation 8) to G0 from DH.

Values of the shear modulus Go derived from SPT and those measured using DH are

plotted on Fig. 7 for comparison. As expected, results on Fig. 7 indicate that theSPT-based Go consistently underestimates the real Go for all types of soils. A simple

linear best fit line with a slope of 1:2.34 provides a reasonable improved relationship

between the SPT-based Go and the Go from DH. Analytically, this means that Equation(7) could be revised in an attempt to improve its accuracy in deriving small strain

moduli in calcareous Sand and Sabkha, based on N60 values. As a result, the following

equation is believed to provide a reasonable estimate for Go from SPT blow count N60:

( )2

21

2.017.0

60134.2 F F z N C Go ρ = (8)

The accuracy of the improved correlation is tested in Fig. 7b by plotting the ratio

between Go obtained from the improved SPT correlation and Go obtained from DH

tests. Results indicate that the improved correlation provides an acceptable model for predicting Go for Sabkha soils and calcareous cemented sands since it results in a meanvalue of 1.06 in the ratio of Go(SPT) to Go(DH) with an associated coefficient of

variation of about 0.43. These statistics indicate that the improved model is relatively

efficient at predicting Go(DH), despite the scatter that remains in the correlation.

CONCLUSION

The following conclusions could be drawn from the results of this study:

•

The derivation of the small-strain shear modulus Go from CPT qt or SPT N

based on available correlations results in underestimation of the actual values of

Go as measured by DH. The degree of conservatism in the Go estimatesincreases when SPT is used to derive Go as opposed to CPT. However, the

scatter between estimates and measured Go values is smaller for the SPT data,

making it possible to derive an improved relationship for predicting Go based onSPT data. In simple terms, it can be concluded that multiplying Go that is

obtained from existing SPT correlations by a factor of 2.34 will result in

relatively good matches with Go from DH.



•

A comparison between Go(DH) and Go(SCPT) indicated that Go using DH

showed better conformity with the variations of soil density, with the SCPTresulting in relatively high values of Go.

• The relationship between the “large” strain modulus G and the small strainmodulus Go was investigated using the CPT qt and DH data. Results indicate

that most of the calculated “large” strain shear moduli for the upper and lowersands range from 1 MPa to 10 MPa. Interestingly, the Sabkha data pointsexhibited relatively small values for the “large” strain shear modulus. The ratio

of G/G0 is generally between 0.1 to 0.01 for the sands and between 0.01 to

0.001 for the Sabkha soils. These reductions in the shear modulus at large

strains are excessive and reflect the strong tendency of the cemented calcareoussand and the Sabkhas to lose significant stiffness at large strains compared to

more conventional soils.

ACKNOWLEDGEMENTS

The writers would like to acknowledge Fugro Middle East for their contribution in providing valuable data that placed this research work on track. The help of Farhang

Model and Zenah Mattar of AUD is also recognized. The assistance of Myra Fakhoury

Charif is very much appreciated.

REFERENCES

Briaud, J. L. (2001). “Introduction to soil moduli.” Geotechnical News, June 2001,BiTech Publishers Ltd, Richmond, B.C, Canada.

Charif, K. H., Najjar, S. S., and Sadek, S. (2010). “Skin friction along drilled shafts in

weak carbonate rocks.” Geotechnical Special Publication 198 , ASCE.Darendeli, M. B. and Stokoe, K. H., II (2001). “Development of a new family of

normalized modulus reduction and material damping curves.” Geotechnical Engineering Report GD01-1, University of Texas at Austin.

Jamiolkowski, M., Ghionna, V. N., Lancellotta, R. and Pasqualini, E. (1988). “New

correlations of penetration tests for design practice”, Proceedings First Intl. Symp.

on Penetration Testing, ISOPT-1, Orlando, 20-24 March 1988, Vol. 1, A.A.Balkema, Rotterdam, 263-296.

Lunne, T., Robertson, P. K. and Powell, J. J. M. (1997). “Cone Penetration Testing in

Geotechnical Practice.” EF Spon/Blackie Academic, Rutledge Publishers, 312 p.

Robertson, P. K. (1990). “Soil classification using the CPT.” Canadian Geotechnical

Journal, 27(1), 151-158.

Robertson, P. K. and Wride, C. E. (1998). “Evaluating cyclic liquefaction potential

using the cone penetration test.” Canadian Geotechnical Journal, 35, 442-459.Robertson, P. K. (2009). “CPT interpretation - a unified approach.” Canadian

Geotechnical Journal, 46, 1-19.

Zhang, G., Robertson, P. K., and Brachman R. W. I. (2002). ‘‘Estimating liquefaction-induced ground settlements from CPT for level ground.’’ Canadian Geotechnical

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asce comparative study of shear modulus in sands sabkha - fme khaled charif

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