16532_04b

Threeposition torque arm

Driving mechanism, 720 ratio

0 Hand crank

- Ball bearing, guide coupling

& Ball bearing, guide coupling

6 &Drive shoe

Figure 4.18 Vane shear test arrangement (Acker Sampling Catalogue and Design Manual NAVFAC DM 7.1, 1982).

145

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Copyright © 1990 John Wiley & Sons Retrieved from: www.knovel.com

146 SOIL PARAMETERS FOR PILE ANALYSIS A N D DESIGN

equipment description are also provided in ASTM D 2573 ( A S T M A N N U A L Book 1989).

The main features of this test procedure are to push a four-bladed vane attached to the end of a rod into the undisturbed clay below the bottom of a boring. The vane is then turned by applying a torque at the top by turning the crank at a uniform rate. According to the ASTM D 2573 procedure, the torque applied to the vane should not exceed O.l"/s. The failure mode around a vane is complex. However, test interpretation based on simplified assumptions of a cylindrical failure surface corresponding to the periphery of the blade and of a uniform strength mobilization on that surface can be made (Aas, 1965). Based on these assumptions, the undrained shear strength, c, = S,, of a clay for a measured torque T can be obtained from the following relationship:

T c, = - k

where

c, = undrained shear strength of clay, lb/ft2 (kN/m2) T = torque 1 b-ft (N-m) k = constant, depending on dimensions and shape of vane, ft' (m')

I 1 I 1 I I 0 20 40 60 80 100 120

Plasticity index, Zp

0.4 I

Figure 4.19 Vane correction factor as a function of plasticity index (Bjerrum, 1973).


SOIL PARAMETERS FOR STATIC DESIGN 147

For a length-to-width ratio of vane of 2 : 1,

k = 0.0021D3 in in.-lb units and k = 0.00000366D3 in metric units (ASTM D 2573, 1988). D = measured diameter of vane in inches (or centimeters).

Since the undrained shear strength of clays is known to be time dependent, the vane test results must be corrected for time effect factor, p, as shown on Figure 4.19 (Bjerrum, 1973).

As for cone penetration tests, vane shear tests should also be combined with borings so that soil samples can be recovered for laboratory testing and

Control

unit

Figure 4.20 Schematic representation of the Menard-type prebored pressuremeter (Robertson, 1986).



correlations. This test is very useful for soft sensitive soils that cannot be sampled for laboratory testing.

Pressuremeter Tests As indicated in Table 4.4, the pressuremeter test method is a highly rated test. This device essentially consists of an expandable cylindrical tube placed at the bottom of a borehole. This cylinder is then expanded under controlled conditions against the surrounding soil. Existing pressuremeters can be divided into three main groups: prebored, self-bored, and full displacement. The prebored pressuremeter test is performed in a predrilled hole, the self-bored pressuremeter is self-bored into the soil to minimize soil disturbance, and the full displacement pressuremeter is pushed into the soil with a solid tip (Robertson, 1985).

The most widely used pressuremeter was developed by Menard (1956). This is a prebored type pressuremeter as shown in Figure4.20. This instrument is expanded by applying air pressure to a liquid filling the lines and the instrument. The volume expansion is measured by measuring the amount of liquid forced into the expanding central section, which is protected by two guard cells, one above and one below it. A typical pressure-volume increase curve is shown in Figure 4.21 in which A refers to the initial volume of the pressuremeter V,. B

Volume increase, cm

Figure 4.21 meter test (Robertson, 1986).

Idealized pressure-expansion curve from Menard-type prebored pressure-



defines the upper limit of the linear diagram. V, is the mean of volumes Vo and V,. The corresponding pressures are Po, P,, and P, respectively.

The undrained shear strength, S,, of clays can be estimated from the following semiempirical relationship (Robertson 1986).

PL. - Po S" =- 5.5 (4.7)

P , defines the maximum pressure and the corresponding volume is V, (Figure 4.21). The pressuremeter modulus, E,,,, is obtained from the slope of the linear portion of the pressure-volume increase curve (Figure 4.21) as follows:

E , = 2.66 ( Vo + V,)( P/u) (4.8)

where

V, = initial volume of the measuring cell, Po = Pressure corresponding to initial volume V,. V,,, = volume change read on the volumeter at a pressure corresponding to

the mean pressure in the pseudoelastic range P/u = slope of the pressure volume curve (AB).

In the absence of experimental data, the values of E, for preliminary design may be estimated with the help of Table 4.5 for different soils.

Based on French experience on the Menard type pressuremeter, empirical design procedures have been developed for both the shallow and deep foundation (Baguelin et al., 1978; Mair and Wood, 1987). The pressuremeter is a useful tool for investigation and design of foundations when dealing with soils that are hard

TABLE 4.5 Typical Menard Pressuremeter Values (Canadian Foundarion Engineering Manual, 1985)

Type of Soil

Soft clay Firm clay Stiff clay Loose silty sand Silt Sand and gravel Till Old fill Recent fill

P L Limit Pressure

(kPa) 50-300

300-800 600-2500 100-500 200- 1500

1200-5000 1000-5000 400-1000

50-300

&IP, 10 10 15 5 8 I 8

12 12


150 SOIL PARAMETERS FOR PILE ANALYSIS AND DESIGN

to investigate by conventional methods (e.g., granular soils, till, soft rock, and frozen soil).

Laboratory Testing Laboratory testing is carried out to classify the soils and to provide soil parameters for design. The type and number of soil tests will depend on a number of factors such as:

1. Degree of variation of soils at the site 2. Soils information available from previous explorations in the area on

3. Character of soils 4. Requirements of structure such as importance of differential settlements

similar soils

Following is a brief description of these tests. For details, consult testing manuals and other relevent publications such as Lambe (1951), Terzaghi and Peck (1967), Prakash et al. (1979), and Annual Book of Standards, ASTM (1989).

A tterberg Limits Determination of Atterberg limits for engineering purposes according to ASTM Designation D 4318-83 requires obtaining the liquid limit, plastic limit and plasticity index of soils.

0.01 2 3 4 5 6 8 0 . 1 2 3 4 5 6 8 1 . 0 2 3 4 5 6 8 1 0 20 406080100

Preconsolidation pressure (TSF)

Figure 4.22 Preconsolidation pressure vs. liquidity index (Design Manual NAVFAC DM 7.1, 1982).



The liquid limit (LL) of a soil is the limiting water content of a saturated soil beyond which the soil will attain a liquid state. The soil has infinitesimal strength at liquid limit.

The plastic limit (PL) is the percent water content of a wet soil below which it does not exhibit any plasticity. Thus, plastic limit defines a boundary between the plastic and nonplastic states.

The plasticity index (PI) is the difference between the liquid limit and plastic limit (PI = LL - PL) and signifies the range of water content over which the soil remains plastic.

As we present in the following paragraphs, these soil characteristics (e.g., LL, PL, and PI) can be empirically related with certain engineering soil properties.

Unconfined Compressive Strength The unconfined compression test is carried out on clay samples (undisturbed or remolded) to determine shear strength, S,, under undrained conditions. ASTM D 2166-66 (1989) describes its detailed test procedure. The undrained strength, S,, is then obtained by dividing the unconfined compressive value, q,, by 2.

Approximate values of the unconfined compressive strength, q., can also be obtained from the following relationship (Design Manual NAVFAC DM 7.1, (1 982).

qu = 2S, = 2pc(0.1 1 + 0.0037 PI) (4.9)

where

p, = preconsolidation pressure (i.e., the maximum past effective normal stress at which the soil deposit has been consolidated), This can be obtained from consolidation test or can be approximated 'from Figure 4.22.

PI = plasticity index as discussed above

Consolidation Parameters One-dimensional consolidation tests as per ASTM D 2435-80 are conducted to determine compression (or settlement) characteristics of fine-grained cohesive soils under applied loads. The soil parameters determined by this test are compression index, C,, coefficient of consolidation, C,, and the preconsolidation pressure, a,.

The typical void ratio (e ) versus log a: plot, obtained from consolidation test ASTM D 2435, is shown schematically in Figure 4.23. In this figure e, is the initial void ratio, j jc is the preconsolidation pressure, C, is the recompression index, and C, is the virgin compression index. For further details, standard textbooks on soil mechanics, such as Terzaghi and Peck (1967) should be referred to.

The preconsolidation pressure P, is the maximum normal effective stress to which the material in situ has been consolidated by a previous loading. If the existing effective overburden pressure, &, is larger than pC then the soil is called under consolidated, if a:,, = j , then the soil is called normally consolidated, and if



Recompression zone

Effective normal 0;

pressure (log scale) Figure 4.23 Typical void ratio vs. logo: curve from consolidation test.

abo is less than jjc then the soil is called ouerconsolidated. The ratio @&,,) is called the ouer consolidation ratio (OCR). If OCR is between 1 to 4, then the soils are called lightly overconsolidated while if this ratio is greater than 4, they are called heavily overconsolidated. These concepts and terms are later used in settlement calculations in Chapter 5 (Section 5.1.10).

Approximate values of compression index, C, can also be obtained from following relationships (Design Manual NAVFAC DM 7.1 1982). Similar other relationships have been proposed by Nishida (1956), Hough (1969) and Sowers ( 1979).

1 . C, = 0.009 (LL - 10 percent)

2. C, = 0.01 15 w, for organic soil 3. C, = 1.15 (e, - 0.35) for all clays 4. C, = (1 + e,)(0.1 + (w, - 25p.006) for varved clays where LL is the liquid

for inorganic soils with sensitivity less than 4

limit, w, is the natural moisture content and, e, is the initial void ratio.

Shear Parameters The direct shear tests are carried out as per ASTM test procedure D 3080-72 (1979) on cohesionless soils to determine the angle of internal friction, &. The triaxial test is generally not used to determine shear



400

350

c 5 $ 300 a 5: b n

5 250 v1

c .- < g 200 .- 4 v1 e!

8 5 150

4 3 100 .- E 3

50

parameters for design of piles. The shear parameter c = c, = S, for 4 = 0 for cohesive soils determined from unconfined compressive strength test has previously been discussed.

- / -

Kahl, et al. (1968)

A Muhs and Weiss (1971)

Y - g- 0 Kerisel(1961) e V O J .

-$- X Melzer(1968) ?c% -+ /

I

I I 1/ 2

s E

-g

- .. + x' :: e

- 5

7 ~~

" /A 0 [Very loose A

/IX LJ 0

4.1.3 Design Parameters

This section presents the info.mation on strength parameters, soil-pile adhesion, and elastic soil parameters both for the cohesionless and cohesive soils that are required for static pile design.

Strength Parameters The two commonly used strength parameters in pile design are the angle of internal friction (6') for cohesionless soils and the undrained shear strength (S,) for cohesive soils.

friction



The angle of internal friction can either be obtained from laboratory testing (Section 4.1.2) or from the correlations established with field penetrometer test values (e.g., N or qc). Figure 4.24 presents a relationship between the static cone penetration test (CPT) values, qc and the angle of internal friction, @, values. Meyerhof (1976) recommends the use of this relationship for pile design. If only standard penetration test values, N are available at a site, then Figure 4.15 should be used to first obtain the equivalent qc values. Figure 4.24 can then be used to obtain Cp' values.

Another method of obtaining the angle of internal friction, as recommended in Design Manual NAVFAC, DM 7.1 (1982), consists of the following:

1. Obtain the relative density, D,, for the field measured, N, values from Figure 4.25.

2. Then from Figure 4.26, for the known soil or dry density (or void ratio or porosity) and D, from (1) above, obtain the angle of internal friction, 4',

Example 4.1 explains the use of both the foregoing methods to estimate the 4' value from field test data for cohesionless material. The first method using the qc /N relationship and then the use of qc versus 4 relationship yields Cp' = 36" while the use of the N, D,, and 4' relationship yields 4' = 35".

Standard penetration resistance, N blows/ft

Figure 4.25 Correlations between relative density and standard penetration resistance in accordance with Gibbs and Holtz (1957) (NAVFAC Design Manual DM 7.1, 1982).


45 Angle of internal friction

vs dens0 (for coarse-grained sods)

40 - ln Q)

M aJ 2!

3 -e 35

effective stress failure envelopes

Approximate correlation is for cohesionless materials without plastic fines

c 0 .& 0 .- L - - m E 5 30 - 0 0) - 3

25

2075 80 90 100 110 120 130 140 150



Example 4.1 During a site investigation work, borehole logs indicated the SPT value of 20 at a depth of 25 ft in sand. Laboratory grain size analysis indicated that the sand had mean grain size, D,, = 0.004 in. (0.1 mm). The density of the overburden soil was estimated to be 125 Ib/ft3 and dry density of this sand was estimated at 1 101b/ft3. No groundwater table was observed in the borehole. Estimate the angle of internal friction for the sand.

SOLUTION

Method 1 qc = 3.8 x 20 = 76bar for N = 20

From Figure 4.24, for qc = 79 tons/ft2, 6' = 36"

From Figure 4.15, q , /N = 3.8 for Ds0 = 0.1 mm

= 7 6 0 kPa = 79 tons per square foot

Method 2 Vertical effective stress = a: = 125 x 25 = 3125 lb/ft2 = 3.125 kips/ft2 From Figure 4.25 for N = 20, a: = 3.125 kips/ft2, D, = 64 percent From Figure 4.26 for Yd = 110 psf, D, = 64%, 6' = 35"

The undrained shear strength, S,, of a cohesive soil can either be obtained from laboratory testing of undisturbed soil sample or by field vane shear tests, equation (4.6), on soft cohesive soils and pressuremeter tests, equation (4.7), on stiff soils.

TABLE 4.6 Guide for Consistency of Fine-grained Soils (Terraphi and Peck, 1967, Design Manual NAVFAC, DM 7.1, 1982, Canadan Foundation Engineering Manual, 1985)

Estimated Range of S, = c, SPT Penetration

N Values* Estimated Consistency k Pa kips/ft2

< 2 Very soft (extruded < 12 < 0.25 between fingers when squeezed)

finger pressure)

strong finger pressure)

by thumb but penetrated only with great effort)

indented by thumbnail)

difficulty by thumbnail)

2-4 Soft (molded by light 12-25 0.25-0.50

4-8 Firm or medium (molded by 25-50 0.50- 1 .OO

8-15 Stiff (readily indented 50-100 1.00-2.00

15-30 Very stiff (readily 100-200 2.00-4.00

> 30 Hard (indented with > 200 > 4.00

'The Canadian Foundation Engineering Manual does not recommend the relationship with N.



0.7

0.6

< 0.5 0.4

?

0.3

0.2

0.1

0

For normally consolidated natural deposits, S, can also be estimated by the following relationship (Skempton, 1948; Bjerrum and Simons 1960).

- -

- - -

-

-

I 1 I I , I -

S, = C, = aL(O.1 + 0.004PI) (4.10)

where a i is the effective vertical overburden pressure and PI is the plasticity index. This equation is similar to equation (4.9) except that j c has been replaced with a: for normally consolidated soils Le., u: = jc. Equation (4.9) is applicable for both the normally and overconsolidated soils and therefore is generalized form of equation (4.10). However, both equations would yield similar results for normally consolidated soils.

Consistency of cohesive soils and the approximate relationships with N and S, can be obtained from Table 4.6. Since these relationships are approximate, they

0.9 l’O i

Very Soft Firm Stiff Very stiff Hard soft

Figure4.27 Variation of cdS, with c, for different pile materials for driven piles (developed from data in Tomlinson, 1963).



should only be used in the preliminary design. For final design, field and/or laboratory determined S, values should be used.

Soil-Pile Adhesion (c,) Estimation of soil-pile adhesion (c,) is complex. It depends on factors such as (1) soil consistency, (2) method of pile installation, (3) pile material, and (4) time. Reliable values of c, can only be obtained by performing full-scale pile load tests in the field. Figure 4.27 can be used as a guide for estimating c, values for driven piles in clay with different consistency (Tomlinson, 1963). These values have also been recommended by Tenaghi and Peck (1967). The soil-pile adhesion value c, is also termed as side friction. For drilled piles or piers, c, can be estimated from Table 4.7.

TABLE 4.7 Design Parameters for Side Friction for Drilled Piers in Cohesive Soils (NAVFAC Design Manual, DM 7.2, 1982)

Limit on Side Side Resistance Design Category ca/cu Shear-tsf Remarks

A. Straight-sided shafts in either homogeneous or layered soil with no soil of exceptional stiffness below the base 1. Shafts installed dry or by 0.6 2.0

the slurry displacement method

drilling mud along some portion of the hole with possible mud entrapment drilled dry

B. Belled shafts in either homogeneous or layered clays with no soil of exceptional stiffness below the base

2. Shafts installed with 0.3(a) O.S(a) (a) CJC, may be increased to 0.6 and shear increased to 2.0 tons per sq. ft. for segments

1. Shafts installed dry or by 0.3 0.5

2. Shafts installed with 0.1 5( b) 0.3( b) (b) CJC, may be increased to

the slurry displacement methods

drilling mud along some portion of the hole with possible mud entrapment drilled dry

0.3 and side shear increased to 0.5 tons per sq. ft. for segments

C. Straight-sided shafts with base 0 0

D. Belled shafts with base resting 0 0

resting on soil significantly stiffer than soil around stem

on soil significantly stiffer than soil around stem


SOIL PARAMETERS FOR DYNAMIC DESIGN 159

Elastic Soil Parameter The most common elastic soil parameter required in pile design is the modulus of elasticity, E,. In cohesionless soils, the static elastic modulus, E, may be estimated from empirical methods using relations of E, with SPT N values or with static cone penetration qc values. Many studies relating N values with E, indicate that such relationships are of little use because the relationships vary significantly and the ratio of predicted to observed settlements based on these E, values may range between 0.12 to 20 (Talbot, 1981; Robertson, 1986). This is due to the fact that E, depends on a large number of variables as explained in Section 4.2. Therefore, these relationships should not be used unless local experience supports them. A value of E, can, however, be estimated from results of the static cone penetration test, qc, as follows (Schmertmann, 1970).

E, = c,qc (4.1 1)

where C, is a constant and depends on the soil compactness as follows (Canadian Foundation Engineering Manual, 1985):

Silt and sand C1 = 1.5 Compact sand C, = 2.0

Sand and gravel C1 = 4.0 Dense sand Ci = 3.0

For cohesive soils, the values of E,, as recommended by the Canadian Foundation Engineering Manual (1985) can be estimated from the following relationship.

E, = CZDC (4.12)

where pc is the preconsolidation pressure and C2 is a constant such that C , = 80 for stiff clays, C, -60 for firm clays, and C, =40 for soft clays. These relationships are approximate at best and may be used only in preliminary design.

4.2 SOIL PARAMETERS FOR DYNAMIC DESIGN

Several problems in engineering practice require a knowledge of dynamic soil properties. In general, problems involving the dynamic loading of soils are divided into small- and,large-strain amplitude responses. In a pile foundation, the amplitudes of dynamic motion and, consequently, the strains in the soil are usually small for machine foundations whereas during an earthquake or blast loading, large strains may occur. A large number of field and laboratory methods have been developed for determination of the dynamic soil properties. The principal properties that are used in dynamic soil-pile analysis include dynamic moduli, such as Young’s modulus E and shear modulus G, with corresponding spring constants; damping; and Poisson’s ratio. The first two are dependent on


160 SO

IL PAR

AM

ETERS FO

R PILE A

NA

LYSIS A

ND

DESIG

N

Figure 4.28 Dynamic shear modulus vs. shear strain y (after Prakash and Pun, 1980; Prakash, 198 1).



Dynamic shear strain yo

Figure 4.29 Normalized shear modulus (G/G,,,,J vs. shear strain, ye.

strain amplitude ( y e ) since behavior of the soil is nonlinear (Figure 4.28). In Figure 4.29, the plot of G vs. ye (in Figure 4.28) has been normalized by dividing the ordinate with G,,,, the value of G at small strain

In this section, a brief discussion of the laboratory and field methods used to determine dynamic soil moduli is presented along with typical values of dynamic soil moduli and damping.

or smaller).

4.2.1 Elastic Constants of Soils

The behavior of a soil is nonlinear from the beginning of stress application. For practical purposes, the actual nonlinear stress-strain curves of soils are linearized. Therefore, a modulus and a Poisson's ratio are not constants for a soil but depend on several parameters as will be explained further. Two moduli used in dynamic loading are Young's modulus and shear modulus.

If a uniaxial stress 6, is applied to an elastic cylinder that causes axial strain E,,

then Young's modulus E is defined as

" 2 E = - &,

The lateral strains E, and E,, are

(4.13)

E, = Ey = - VE,

where v is Poisson's ratio.

(4.14)



Tangent modulus

0 Y) Y)

E! ;j

Strain t

Figure 430 Definitions of secant and tangent modulus.

If shear stress, 5, is applied to an elastic cube, there will be a shear distortion, ye, and shear modulus G is defined as

5 7 G=- or ye =- Y O G

(4.15a)

Of the three constants (E, G, and v), only two are needed, because they are related as follows:

E = 2G(1+ V ) (4.15b)

The Young’s modulus E and shear modulus G may be measured in terms of either tangent modulus or secant modulus. Tangent modulus is the slope of the tangent to a stress-strain curve at a particular point on the curve and is strain dependent (Figure 4.30). Secant modulus is the slope of a straight line connecting two separate points of a stress-strain curve. Based on a linear stress-strain relationship, the above elastic constants have been defined.

4.2.2 Factors Affecting Dynamic Modulus

Based on the study of dynamic elastic constants, the factors on which these depend are (Hardin and Black 1968):

1. Type of soil and its properties (e.g., water content and yd) and state of

2. Initial (sustained) static stress level or confining stress disturbance.



3. Strain level 4. Time effects 5. Degree of saturation 6. Frequency and number of cycles of dynamic load 7. Magnitude of dynamic stress 8. Dynamic prestrain

Type of Soil, its Properties and Initial Static Stress Level Since the soil modulus is strain dependent (Figure 4.30), more than one method is needed to determine the variation of modulus with strain.

The large amount of data on the values of soil constants that had been collected was analyzed by Hardin (1978), who developed a mathematical formulation of soil elasticity and soil plasticity in terms of effective stresses. On this basis, the maximum value of the shear modulus, G,,,, (at low shear strain of

is expressed by equation (4.16a) (Hardin and Black 1969):

(2.973 - e)2

(1 + e ) G,,, = 12300CR' (50)0.5 (4.16a)

in which OCR is the overconsolidation ratio, e the void ratio, and k a factor that depends on the plasticity index of clays, Table 4.8, and do the mean effective confining stress in psi, equals

or 50 = (51 + 5 2 + 53)/3

do = (6, + 5), + 5,)/3.

(4.16b)

(4.16~)

If the shear modulus is determined at a mean effective confining pressure of can be ( ~ 7 ~ ) ~ , its value at any other mean effective confining pressure

determined from equation (4.17)

(4.17)

Effective overburden pressure (3, may be used in place of bo in equation (4.17).

TABLE 4.8 Values of k after Hardin and Drnevich, 1972

Plasticity Index PI k

0 20 40 60 80

100

0 0.18 0.30 0.4 1 0.48 0.50



Magnitude 01 strain

Phenomena

10-6 1 0 - ~ 104 1 0 4 10" lo-' I I I 1

Slide, Cradu, differenw compaction, liquifacation romement Wave propagatbn, vibration

I Mechanical &aracleristics Elastic I Elastic plastic I Failure

I I I

I Angle of Constants Shear modulus, Poisson's ratio. damplng ratio Internal friction

I I cohesbn I Seismk wave

method

3 vibration test

8 Repealed loading test -

~~~~ ~~

Wave propagatlor

Resonant column test

Repeated loading test I

Figure 4.31 Ishihara, 1971).

Strain level associated with different in-situ and laboratory tests (after

Struin Level Figure 4.3 1 shows strain levels associated with different pheno- menon in the field and in corresponding field and laboratory tests. Typical variations of G versus shear strain amplitude for different types of in-situ tests are shown in Figure4.28. The soil modulus values may vary by a factor of 10, depending on the strain level.

It is customary to plot a graph between normalized modulus (defined as G value at a particular strain, divided by G,,, at a strain of and shear strain (Figure 4.29).

The shear strains induced in soil may not be precisely known (Prakash and Puri, 1981). In the case of wave propagation tests, the shear strain amplitudes are low and are assumed to be of the order of The shear strain induced in soil essentially depends on the amplitude of vibration or settlement, which in turn depends on superimposed loads, the foundation contact area, and soil characteristics. The measured values of amplitude or settlement take care of the factors affecting them. In vertical vibrations, the shear strain amplitudes, Y e , is equal to the ratio of the amplitude or settlement to width of the oscillating footing for all practical purposes, both at low and high strains (Prakash, 1975; Prakash and Puri, 1977; Prakash and Puri, 1988). For values of and v, in the range of interest, it is reasonable to assume, therefore, that Y e 2 E,.



Time EHects The effect of duration of confinement at a constant pressure on the magnitude of shear moduli is well established both in natural and prepared soils (Anderson and Stokoe, 1977; Prakash and Puri, 1987; Richart 1961).

In Figure 4.32, the time-dependent behavior at low strain levels can be characterized by an initial phase when modulus changes rapidly with time, followed by a second phase when the modulus increases almost linearly with the logarithm of the time. For the most part, the initial phase results from the void ratio changes and increase in effective confinement during primary consolidation. The second phase-in which the modulus increases almost linearly with the logarithm of time-is probably due largely to the decrease in void ratio and changes in the soil structure due to a strengthening of the physicochemical bonds in the case of cohesive soils and to an increase in particle contact for cohesionless soils. This increase in modulus proceeds at a constant confining stress and is referred to as the long-term time eflects and represents the increase in the modulus with time that occurs, after primary consolidation is completed.

The long-term time effects may be described as:

1. Coefficient of shear modulus increase with time, IC.

in which t , and t , are the times after primary consolidation, and AG is the change in low-amplitude shear modulus from t , to t , (Figure 4.32).

Duration of confinement (log scale)

Figure 1977).

432 Phases of modulus-time response in soils (after Anderson and Stokoe,


TABLE 4.9 Typical valws of 1, and NG Confining Low-Amplitude Typical Typical Pressure Shear Modulus I., N:

Soil Type Specimen Type (kN/m2)’ G,o0o(kN/m2)’ (kN/m2)’ E) Reference

EPK kaolinite Ottawa sand Quartz sand Quartz silt Dry clay Kaolinite Bentonite

Agsco sand Ottawa sand Airdried EPK Kaolinite

Saturated EPK Kaolinite

Silty sand Sandy silt Clayey silt Shale

Vacuum extruded 200-300 14O,OOO-l90,OOO 24,000-35,000 Compacted by 70-280 50,OOO- 180,OOO 1,400-5,500

raining and tamping

Vacuum extruded 70-550 4,000-170,OOO 1,ooO-8,500

Compacted by 70-280 so,o0o-11o,OOO 2,000-10.000 raining and tamping

Vacuum extruded

Undisturbedd 70-220 80,OOO-2,6W,OOO 2,000-22,9M

17-18 1-1 1

5-25

1-17

1-14

Hardin and Black (1968) Afifi and Woods (1971)

Marcuson and Wahls (1972)

Afifi and Richart (1973)

Stokoe and Richart (1973a, b)


Boston blue clay Undisturbedd 9 Clays Undisturbedd 1 Silt Clay fills Undisturbedd

Decomposed marine Undisturbedd

San Francisco Undisturbedd

Dense silty sand Undisturbedd Stiff OC' clay Undisturbedd

limestone

Bay mud

70-700 32,500-54.000 5 7,000 15-18 Trudeau et al. (1974) 35-415 13,000-235.000 26,000-23,500 2-40 Anderson and Woods

35-70 SO,Ooe200,000 4,200- 15,000 7- 14 Stokoe and Abdel-razzak

325-830 365,000- 1,300,MMl28,000-102,000 3-4 Yang and Hatheway (1976)

(1975,1976)

(1972)

17-550 7,600-150,000 725-32,000 8-22 Lodde (1977)

220-620 45,000-180.000 5,000-17,000 4-10 Fugro, Inc. (1977) 1,280- 1,300 300,000-320,000 14,000-26,ooO 4-8 Fugro, Inc. (1977)

~~~ ~ ~

Source: Anderson and Stokoe, 1977, copyright ASTM. Reprinted with permission. ' I , defined by equation. 4.18a. bN, defined by equation. 4.18b. E 1 kN/m2 = 0.145 psi. dNorninally undisturbed. 'Overconsolidated.



Numerically, I, equals the value of G for one logarithmic cycle of time. 2. Normalized shear modulus increase with time, N,.

in which Glooo is the shear modulus measured after lo00 minutes of constant confining pressure (after completion of the primary consolidation).

The duration of primary consolidation and the magnitude of the long-term time effect vary with such factors as soil type, initial void ratio, undrained shearing strength, confining pressure, and stress history. Typical values of IG and N G are given in Table 4.9

The results of a number of tests show that long-term modulus increases occur at low to intermediate strain levels (0.001 to 0.1 percent) for stiffer clays (Lodde, 1977). Preliminary results from a long-term modulus increases occur in clean, dry sands at strain amplitudes up to 0.1 percent as well.

Because of the general similarity between the increase in moduli with time at low- and high-shearing strain amplitudes, it seems reasonable to conclude that many of the factors that affect the low-amplitude modulus-time response also affect the high-amplitude modulus-time response (at the start of high-amplitude cycling) (Anderson and Stokoe, 1977). Anderson and Stokoe also proposed a method that can be used to predict the in-situ shear moduli from laboratory tests after allowing for time effects.

Degree of Saturation Biot (1956) showed that the presence of fluid exerts an important influence on the longitudinal wave velocity. However, shear wave velocity change was very small. The fluid affects the shear wave velocity only by adding to the mass of the particles in motion. Therefore, for an evaluation of V, or G in cohesionless soils, the in-situ unit weight and the effective pressure are considered.

Frequency and Number of C y c h of Dynamic Load Hardin and Black (1969), found that for number ofcycles between 1 and 100, the dynamic shear modulus of dry sands increased slightly with number of cycles whereas for cohesive soils the modulus decreased. Low strain shear modulus was found to be practically unaffected by the frequency of loading.

Magnitude of Dynamic Stress The magnitude of dynamic stress controls the shear strain levels induced in the soil, and hence the dynamic shear modulus should be expected to decrease with increase in the dynamic stress.

Dynamic Prestrdn The test data of Drnevich, Hall, and Richart (1967) from torsional vibration type resonant column equipment show that the value of the


50

45

40

35

- 30 E 25

2

J .-

3 3 8 20

15

10


lo, 104 105 106 107

Cycles of high-amplitudc torsional vibration

Figure 433 Effect of number ofcycles of high-amplitude vibration on the shear modulus at low amplitude (C-190 Ottawa sand, eo = 0.46, hollow cylindrical specimens) (after Drnevich, Hall, and Richart, 1967).

dynamic shear modulus generally increased with the number of prestrain cycles, as shown in Figure 4.33. The soil samples were first subjected to high-amplitude vibrations (dynamic prestrain) for a predetermined number of cycles and then the low-amplitude vibration modulus was determined. No data are available on the effect of dynamic prestrain on the dynamic shear modulus of clays and silts.

There are several laboratory and field methods for determination of dynamic soil properties that are described briefly as follows.

4.23 Laboratory Methods

The following laboratory methods are used to determine the dynamic elastic constants and damping values of soils:

1. ,Resonant column 2. Cyclic simple shear 3. Cyclic torsional simple shear 4. Cyclic triaxial compression

The resonant column test for determining the modulus and damping characteristics of soils is based on the theory of wave propagation in prismatic rods (Richart et al., 1970). Either compression waves or shear waves can be



propagated through the soil specimen so that either the Young’s modulus or shear modulus is determined.

In such a test, more often a soil sample is subjected to vibrations at the first- mode resonance at which the material in a cross section at every elevation vibrates in phase with the top of the specimen. The shear wave velocity and shear modulus are then determined on the basis of system constants and the size, shape, and weight of the soil specimen (Drnevich et al., 1977). In a resonant column test, different end conditions can be used to constrain the specimen (Figure 4.34). Each configuration requires a slightly different type of driving equipment and methods of data interpretation. In the fixed-free apparatus (Figure 4.34a) the distribution of angular rotation, 8, along the specimen is 4 sine wave, but by adding a mass

X

Rigid mass ($I1;;

Weightless spring

Driving fone

(C)

Driving force- ,

e a t )

0.5

Specimen, nonrigid distributed mass

(d)

Figure 4.34 Schematic of resonant column end conditions (after Hardin, 1965, 1970; Drnevich, 1967). (a) J / J o = 03, (b) J / J o = 0.5, (c) free-free (d) fixed base-spring top.



with polar mass moments J,. at the top of the specimen (Figure 4.34b) the variation of ye along the sample becomes nearly linear. Later models of the fixed- free device (Drnevich, 1967) take advantage of end-mass effects to obtain uniform strain distribution throughout the length of the specimen. In Figure 4.34d, the sample has a fixed base and a top cap partially restrained by a spring, which in turn reacts against an inertial mass. If the spring in Figure 4 .34~ is weak compared to the specimen, this configuration could be calledfree-free. In such a case, a node will occur at midheight of the specimen, and the rotation distribution would be a sine wave. By adding end masses, the rotation distribution can also be made nearly linear. For K O = 1.0 tests, the inertial mass is balanced by a counterweight, but if one changes the counterweight, an axial load can be applied to the specimen.

In Figure 4.35, a hollow cylinder is used for test so that the shearing strain is

Taring spring - Rot. LVDT

Vert. accelerometer

Membranes

Drive

/ coils

O-ring k /

Pnuun

Figure 435 Hollow specimen resonant column and torsional shear apparatus Drnevich, 1972).

(after


-z A

Figure 436 Idealized stress conditions for element of soil below ground surface during an earthquake.

Shearing chamber Plan view

Soil sample

Soil deformation

Elevation

Figure 4.37 Schematic diagram illustrating rotation of hinged end plates and soil deformation in oscillatory simple shear (after Peacock and Seed, 1968).



more or less uniform along the height of the specimen. Unlike the strain distribution in a solid sample with zero strain in the center and maximum at the periphery (Drnevich, 1967,1972), the torque capacity of this device was increased to produce large shearing strain amplitudes. Anderson (1974) used a modified Drnevich apparatus to test clays at shearing strain amplitudes up to 1 percent. Woods (1978) tested dense sands on the same device at shearing strain amplitudes up to 0.5 percent at 40 psi (276 kN/m2) confining pressure. Drnevich et al. (1977) described a calibration procedure and aids for reducing data of compression or shear wave propagation along a cylindrical sample.

A soil element at xx, as indicated in Figure 4.36, may be considered to be subjected to a series of cyclic shear stresses, which may reverse many times during dynamic loading. In the case of a horizontal ground surface, there is no initial shear stress on the horizontal plane.

In practice, initial static shear stresses are present in the soil (k,-initial condition). Oscillatory shears may be introduced due to ground motion or a machine load at the surface of the ground. A simple shear device simulates all these loadings and consists of a sample box, an arrangement for applying a cyclic load to the soil, and an electronic recording system (Figure 4.37), Peacock and Seed (1968). Kjellman (1951), Hvorslev and Kaufman (1952), Bjerrum and Landra (1966), and Prakash et al. (1973) have described this type of apparatus.

Typical shear-stress, shear-strain relationships obtained during cyclic simple shear tests are shown in Figure 4.38a. A soil exhibits nonlinear stress-strain behavior. For purposes of high-stress, high-strain loading as in an earthquake, this behavior can be represented by a bilinear model (Figure 4.38b) defined by three parameters: (1) modulus G, until a limiting strain, yy, is reached, (2) modulus G, beyond strain yr and (3) strain y y (Thiers and Seed, 1968).

Typical simple shear stress-strain plots of San Francisco Bay mud for different cycles of loading are shown in Figure 4.39 for cycles 1,50, and 200, with about 4 percent shearing strain. The decrease in peak load as the number of cycles increase is reflected by the progressive flattening of the stress-strain curves. However, corrections for confining pressure and other factors need to be applied, as described in section 4.2.2.

A major drawback of most of the cyclic simple shear apparatus is that they do not permit measurement or control of lateral confining pressures during cyclic loading. Therefore, the value of ko is not known and hence the effect of the KO condition on the behavior of soils cannot be studied.

Cyclic torsional simple shear is used to provide the capability of measuring confining pressure and controlling KO conditions. Ishihara and Li (1972) modified a triaxial apparatus to provide torsional straining capabilities. As in resonant column sample, the shear strain distribution in a hollow sample is more uniform.

The apparatus configuration (Figure 4.35) has an advantage in that both resonant column and cyclic torsional shear tests can be performed in the same device. For details refer to Woods (1978), Iwasaki et al., (1977) and Prakash and Puri (1988).



Shear stress I Shear ,

b) 0)

Figure 4.38 (a) Stress-strain curve of a soil, (b) bilinear model (after Thiers and Seed, 1968).

Shear

b) Cycle 1

Shear stress

&g/crn2) r Shear

ocg/crn2)

stmsr r o.20 t o.20 t

-0.20

a31 Cyck 50

Figure 4.39 (a) Stress-strain curves and bilinear models in San Francisco Bay mud (a) Cycle No. 1, (b) cycle No. 50, (c) cycle No. 200 (after Thiers and Seed, 1968).

Cyclic triaxial tests have been extensively used to study the stress-deformation behavior of saturated sands and silts (Puri, 1984), and Seed (1979). Also, Young’s modulus, E, and the damping ratio, r, have often been measured in cyclic triaxial tests (Figure 4.40) when strain-controlled tests have been conducted. These tests are performed in essentially the same manner as the stresscontrolled tests for liquefaction studies.

As in all laboratory attempts to duplicate dynamic field conditions, cyclic triaxial tests have the following limitations:



Vertical stress

I /

1 Area of Hysteresis Loop 2T Area of Triangle OAB & OA'B' D - -

Figure 4.40 Equivalent hysteretic stress-strain properties from cyclic triaxial test.

1. Shearing strain measurements below 1 percent are generally difficult. 2. The extension and compression phases of each cycle produce different

results (Annaki and Lee, 1977); therefore, the hysteresis loops are not symmetric in strain-controlled tests. In stress-controlled tests, the samples tend to neck.

3. Void ratio redistribution occurs within the specimen during cyclic testing

4. Stress concentrations occur at the cap and base of the specimen being

5. The principal stress changes direction by 90" during each cycle.

(Castro and Poulos, 1977).

tested.

Void ratio redistribution is common to all cyclic shear tests, whereas the other limitations are related mostly to the cyclic thaxial test.

For details on laboratory methods, the reader is referred to Woods (1978), Silver (1981), Puri (1984), and Prakash and Puri (1988).

There are several available field methods with which the dynamic soil properties and damping of soils can be determined. Salient features of these methods will now be described.



4.2.4 Field Methods

The following methods for determining dynamic properties of soil are in use:

1. Cross-borehole wave propagation test 2. Up-hole or down-hole wave propagation test 3. Surface wave propagation test 4. Standard penetration test 5. Footing resonance test 6. Cyclic plate load test

Brief descriptions of these tests are presented here. For details, the reader is referred to Prakash and Puri (1988).

In the cross-borehole method, the velocity of shear wave propagation (Vh is measured from one borehole to another (Stokoe and Woods, 1972). A minimum of two boreholes are required, one for generating an impulse and the other for the sensors. In Figure 4.41, the impulse rod is struck on top, causing an impulse to travel down the rod to the soil at the bottom of the hole. The shearing between the rod and the soil creates shear waves that travel through the soil to the vertical motion sensor in the second hole; and the time required for a shear wave to

Capacitive

Figure 4.41 wave propagation.

Sketch showing cross-bore hole technique for measurement of velocity of



///I////

(a) Up hole S = Source R = Receiver

Figure 4.42 (a) Up-hole and (b) down-hole techniques for measurement of velocity of wave propagation.

traverse the known distance is monitored. Alternatively, shear wave may be generated at any depth in a borehole with a special tool. The arrival of the shear wave is monitored at the same elevation in the second borehole (ASTM D 4428, 1989).

Up-hole and down-hole tests are performed by using only one borehole. In the up-hole method, the sensor is placed at the surface, and shear waves are generated at different depths within the borehole, while in the down-hole method, the excitation is applied at the surface, and one or more sensors are placed at different depths within the hole (Figure 4.42). Both the up-hole and the down-hole methods give average values of wave velocities for the soil between the excitation and the sensor (Prakash and Puri, 1988).

The shear modulus G is then determined as

or v,=m G = p V s

(4.19a)

(4.19b)

where p is mass density of the soil. The Rayleigh wave (R wave) travels in a zone one-half to one-third its

wavelength below the ground surface (Ballard, 1964). An impact or other harmonic vibration at the surface is used to sample soil for dynamic moduli.

The velocity of the Rayleigh waves, V,, is then given by

in which f is the frequency of vibration at which the wavelength (A,) has been measured.

It is important to note that the Rayleigh wavelength (A,) will vary with the frequency of excitation (f). For smaller f, the A R is larger and the soil will be sampled to a larger depth (Prakash and Puri, 1988; Stokoe and Nazarian, 1985).



TABLE 4.10 Representative Values of Poisson’s Ratio

Type of Soil V

Clay Sand Rock

0.5 0.3-0.35 0.15-0.25

The Rayleigh wave velocity V, and shear wave velocity V, are generally approximately equal, therefore:

and G== V i p

E==2pVi(l+ v)

(4.21)

(4.22)

in which p is the mass density and v the Poisson*s ratio of the soil. Values of v from Table 4.10 may be used.

More recently, the interpratication of surface wave by a method called the spectral analysis of surface waves (SASW) has been developed (Stokoe and Nazarian, 1985). In the field, two vertical velocity transducers are used as receivers. The receivers are placed securely on the ground surface symmetrically about an imaginary centerline. A transient impulse is transmitted to the soil by means of an appropriate hammer. The range of frequencies over which the receivers should function depends on the site being tested. To sample deep materials, 50 to lOOft, the receiver should have a low natural frequency, in range of 1 to 2 Hz. In contrast, for sampling shallow layers, the receivers should be able to respond to high frequencies in the range of 1OOOHz or more.

Several tests with different receiver spacing are performed. The distance between the receivers after every test is generally doubled. The geophones are always placed symmetrically about the selected, imaginary centerline. The raw data obtained from the impact test is reduced with the help of a Dynamic Signal Analyzer (DSA) and the inversion curve is obtained.

A typical shear wave profile for a site in which the velocity profiles have been determined both by the crosshole method and SASW method show a good tally between the values measured by the two methods. The SASW method is very economical and less time consuming than the cross-borehole method and has the advantage of complete automation. The detailed description of this technique is given by Nazarian and Stokoe (1984). However, the inversion techniques applicable to soils are still not perfected (1990).

In the Standard Penetration Test (SPT), a standard split spoon sampler is driven with a 140-lb hammer that falls freely through a distance of 30 in. The number of blows for 12 in. of penetration of the split spoon sampler is designated as the N value. This is N~ersurcd. In a design problem using N values, a correction for effective overburden pressure is applied (Peck et al., 1974). Although the test is designated as a standard test, there are several personal errors as well as errors



that are equipment based. Therefore, the use of SPT to measure any soil property has been questioned by many engineers (Woods, 1978). Recent careful studies by Kovacs (1975), Kovacs et ai. (1977a. 1977b), Palacios (1977), and Schmertmann (1975, 1977) have described the potential of SPT for obtaining consistent and useful soil properties. Seed (1979) and Seed and Idriss (1982) presented correlations between SPT and observed liquefaction.

Imai (1977) developed a correlation between (uncorrected) N and shear wave velocity, V,(m/sec), in 943 recordings at four urban locations in Japan and established the following relationship:

Then, (4.23)

(4.19b)

In the above relationship, he converted the M values over 50 or under 1 for the penetrating length at the time of 50 or 1 blows into the number of blows for 30-cm penetration. Prakash and Puri (1981, 1984) successfully applied the above relationship in predicting dynamic soil properties at different depths.

In footing resonance tests and free vibration test, a test footing 1.5 x 0.75 x 0.70m high is cast either at the surface or in a pit 4.5 x 2.75 m at a suitable depth and is excited in vertical or horizontal vibrations.

From the natural frequency determined either in the forced or free footing vibration tests, the soil modulus is determined (Prakash, 1981a; Prakash and Puri, 1988).

The cyclic plate load test is a static test. There is ample evidence to show that in non-cohesive soils, the values of soil modulus from this test match with those from dynamic tests at appropriate strains and confining pressures (Prakash, 1981a; Prakash and Puri, 1988).

4.25 Selection of Design Parameters

The modulus of a given soil varies with strain and the confining pressure. It is therefore necessary to make a plot of G vs. shear strain. G values are determined at a mean effective confining pressure corresponding to the depth of soil and at a shear strain that may be induced in the soil when the pile is subjected to dynamic load. Prakash (1981a) and Prakash and Puri (1981) used a mean confining pressure CO1, of 1 kg/cm2 or (1000KN/m*) to reduce the data from different tests to a common confining pressure for comparison purpose only using Equations (4.17) and (4.164

(4.17)

- 6,+8,+6, 3

uo = (4.16~)



VOID RATIO

Figure 4.43 Variation of shear wave velocity and shear modulus with void ratio and confining pressure for dry round and angular sands (After Hardin and Richart, 1963).



where

The variation of modulus with strain is determined from different tests and a plot similar to that in Figure 4.28 is obtained. This plot is then used to select the design value at a predetermined strain and confining pressure. In the absence of experimental data, values of shear modulus at low strain for preliminary design may be selected from Figure 4.43 and Equation (4.16a). The following numerical examples explain the selection method of dynamic design parameters.

Example 4.2 In a deposit of dry sand with G = 2.70 and dry density of 1 12 1 b/ft ', estimate the shear wave velocity at 10, 20, and 30ft below ground level. Also determine G,,,.

SOLUTION

2.7 x 62.4 112

- 1 = 0.504 1 = G Y W e=---- G Y W Y d = -

1 + e Yd

3.46 slugs 112 32.4

v * = m p = - =

SHEAR MODULUS Equation (4.16a) will be used to compute G,,

(2.973 - elZ (60)'/2 G,,, = 1230 OCR' l + e

where do is effective all-around stress in psi.

Let

then Also,

At 10' Depth

(4.16~)

6,= 10 x 112= 11201b/ft2

= 0.55 kg/cm2



6 h = 6, X 0.5 = 5601b/ft2

= 0.273 kg/cm2

60 = 7461b/ft2 = 5.1851 1b/h2

= 0.364 kg/cm2

1230(2.973 - 0.504)2 (5.185)l,2 1 + O S 0 4 G,., =

= 4985(5.1 85)”2

= 11,352 lb/in.2 = 5.543 kg/cm2

= 78,271 kN/m2

V, = /T = 687.7 ft/sec = 209.6 m/sec

At 2 0 Depth

6, = 20 x 112 = 2240 lb/ft2 = 1.094 kg/cm2

dh = 11201b/ft2 = 0.545 kg/cm2

= 0.73 kg/cm2 6, = 1493 lb/ft2 = 10.37 lb/in.2

G,,,= 4985(10.37)’” = 16054 Ib/in.2 = 7.84 kg/cm2 = 110,690 kN/m2

V, = /F = 8 17.78 ft/sec = 249.3 m/sec.

At 3 0 Depth

6, = 30 x 112 = 33601b/ft2 = 1.64 kg/m2

6h = 16801b/ft2

Bo = 22401b/ft2 = 15.551b/i11.~

= 0.82 kg/cm2

= 1.094 kg/cm2

=: 9.6 kg/cm2 = 135,569 kN/m2 G,,, = 4985(15.55)”2 = 19,6621b/i11.~

v, = JF = 905 ft/sec = 275.8 m/sec



Example 4.3 A sand layer in the field is 20m thick. The groundwater table is located at a depth 5 m below the ground surface. Estimate the shear modulus G,,, up to a depth of 20 m below the ground surface. The sand has a void ratio of 0.6, a specific gravity of soil solids of 2.7, and Poisson's ratio of 0.3.

SOLUTION

Gy, 2.7 1 + e 1 +0.6

)Id=-- -- x l

yd = 1.6875 g/Cm3 = 0.0016875 kg/cm3 = 105.31b/ft3

e=0.6 G=2.7 v = O . 3

2.7 + 0.6 x l G + S e

Y t = ( -)Yw l + e =

= 2.0625 g/cm3 = 0.0020625 kg/cm3 = 128.7 Ib/ft3

8, = 7 . Z

Depth z = 5 m

bu=- - 1'6875 (5) 100 = 0.84375 kg/cm2 '

lo00

= 1728 lb/ft2 5, = 0.361 1 kg/cm2 = 739 Ib/ft2

e,, = 0.522 kg/cm2 = 1069 Ib/ft2 Depth z = 10m

au = (2*0625 - ') (5) 100 + 0.84375 = 1.37475 kg/cm2 lo00

=28151b/ft2 '

61, = 0.5884 kg/cm2 = 1205 lb/ft2

do = 0.8505 kg/cm2 = 1742 Ib/ft2

Depthz=lSm

5, =(2*0625 - "(10) 100 + 0.84375 = 1.90625 kg/cm2 lo00

= 3904 Ib/ft2

6 h = 0.81587 kg/cm2 = 1671 Ib/ft2

6, = 1.1793 kg/cm2 = 2415 Ib/ft2



Depth z = 20m

- (2.0625 - 1) 6, = (15) 100 + 0.84375 = 2.4375 kg/m2 lo00

= 4992 lb/ft2 6, = 1.04325 kg/cm2 = 21361b/ft2

Bo = 1.508 kg/cm2 = 3088 lb/ft2

FOR CLEAN SANDS

(2.17 - e)2 l + e

G,,, = 700 (do)1’2

where C0 is expressed in kg/cm2

= 1,636,480 lb/ft2 = 78,355 kN/m2

G,,,at(lO)m = 1078.39(0.8505)’/2 = 994.6kg/cm2 = 2,037,1001b/ft2 = 97,537 kN/m2

Gm,,at(15)m = 1078.39(1.1793)1’2 = 1171.05 kg /m2 = 2,398,498 lb/ft2 = 114,840kN/m2

G,,, at (20)m = 1078.39(1.508)’/2 = 1324.2 kg/cm2 = 2,712,174 lb/ft = 129,859 kN/m2

Example 4.4 A uniformly graded dry-sand specimen was tested in a resonant column device with confining pressure of 3Opsi. The shear wave velocity V, determined by torsional vibration of the specimen was 776 ft/sec. The longitudinal wave velocity determined on a similar specimen in longitudinal vibrations was 1275 ft/sec. Determine:

(a) Low-amplitude Young’s modulus (E) and shear modulus (G). The specific

(b) Poisson’s ratio (c) Estimation of G,,, at a confining pressure of 15 psi.

gravity of soil solids is 2.7


SOIL PARAMETERS FOR PERMAFROST 185

SOLUTION

V, = 750 ft/sec

V, = 1275 ft/sec

Assuming y,, = 112 lb/ft3

Yd l12 lb x sec’ g 32.2 ft4 Mass density, p = - = - = 3.478

(a) E = p V: = (1275)’ x 3.478 = 5,654,348 Ib/ft’ = 2760 kg/cm2

G = pV; = (776)2 x 3.478 = 2,094,525 lb/ft2 = 1022 kg/cm2

(b) E = 2G(1 + V )

:. v = - - 2G

- 1 ~0.35 5,654,348 2(2,094,525)

- -

2,094,525 = (30)0.5

G2

G, = 1,481,053 Ib/ft’ = 723 kg/cm’ = 70,213 kN/mz

4 3 SOIL PARAMETERS FOR PERMAFROST

With the development of resources in cold regions of the world, the need for geotechnical information on seasonal and permanently frozen ground has been growing. A great deal ofresearch, design, and construction activity in the past two decades has provided a lot of geotechnical information in this area. Andersland and Anderson (1978), Johnston (1981) and Morgenstern (1983) provide updated and excellent documentation on geotechnical related design and construction data for permafrost areas. This section briefly outlines the geotechnical information from these sources that are relevant for pile design in permafrost area.

4.3.1 Northern Engineering Basic Consideration

Permafrost is the thermal condition in soil and rock when the ground stays colder than the freezing temperature of water over at least two consecutive years. Continuous permafrost areas are those areas where permafrost occurs every- where beneath the exposed land surface with the exception of widely scattered

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