This research performed on the use of the DC technique for liquefaction mitigation of silty soils has provided insight and understanding regarding:
o Relating the amount of energy dissipated per unit volume of soil to post- treatment resistance to liquefaction.
o The successful use of the DC technique for densifying silty soils using supplementary wick drains.
o Developing a numerical model capable of simulating energy transfer to soil due to surface impact, pore pressure generation and dissipation, and the resulting densification.
o Predicting the post-compaction resistance to liquefaction.
o Considering the effect of specific soil conditions, and different operational parameters of the technique on the achievable densification.
o Developing design guidelines and design charts for practicing engineers to design liquefaction mitigation programs without reliance on empirical equations or expensive field trials.
Further research is needed to build on the results of this study to further advance the understanding of utilizing liquefaction mitigation techniques in silty soils, and to improve analyzing and simulation procedures. Some areas in which this effort can be continued are:
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o Analytical or numerical solution for the problem of surface impact energy portioning among the generated waves in a nonhomogenous, elasto-plastic medium.
o Direct energy-based design procedures that can relate the amount of energy dissipated per unit volume of soil due to certain densification technique to the energy dissipation from design earthquakes.
o Analyzing different available densification techniques for liquefaction mitigation such as compaction by explosives, compaction piles….
o Drainage techniques used to reduce pore pressures resulting from ground shaking are also a potential application specially if supported with large-scale testing.
o Comprehensive analytical methods are still needed to improve the prediction of the behavior of treated deposits against liquefaction particularly in dealing with energy transfer to soil in preference to using attenuation relationships.
o The effect of fines content on penetration resistance of silty soils is highly important requirement for relating soil density to the measured in-situ testing.
o Considering the effect of the existence of energy absorbing layers at shallow depths.
These areas demonstrate the many challenges that still lie ahead in developing designing and analyzing procedures for ground improvement intended for liquefaction mitigation.
APPENDIX A
PENETRATION RESISTANCE IN SANDS AND SILTY SANDS
Performance assessment of various densification techniques is usually based on in-situ tests, which can be used in clarifying various influencing parameters such as relative density, and deformation and strength characteristics of the treated soils. It has been commonly recognized that the relative density is the most important parameter.
Since the direct determination of in-situ void ratio at different depths is uncertain due to difficulty in obtaining undisturbed samples in granular deposits, relative density is often evaluated from the results of penetration tests through some available correlations. The Standard Penetration Test SPT and the Cone Penetration Test CPT are the most
frequently used tests for evaluating in-situ densification because of the more extensive database and past experience. Moreover, the available criterion for evaluating the liquefaction potential of soil deposits is based on these tests.
A major difficulty that influences in-situ penetration tests is the presence of fines.
This appendix summarizes the available relations between in-situ penetration tests results and the relative density of the soil both in clean sands and silty sands.
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A.1. Clean sands
A.1.1. SPT
The standard penetration test SPT is firmly established in the geotechnical engineering practice as a routine procedure for in-situ investigation of soil deposits. SPT- based empirical correlations for soil characterization are available. Generally, these correlations are developed through field and laboratory tests on undisturbed soils, or field performance of soil deposits with known SPT N-values.
The first attempt to correlate the blow-count of the standard penetration test N to the density of the sands is likely the work by Terzaghi and Peck (1948), and Gibbs and Holtz (1957). The correlation of Gibbs and Holtz (1957), according to the formula (A-1) by Meyerhof (1957) assumed that the penetration resistance N (SPT blow count in blows/
30 cm) increases with the square of the relative density Dr and to be in direct proportion of to the effective overburden pressure σ’v
r '
v
D = N
0.234 16σ + (A-1) Where σ’v in KPa, and Dr in percents, this correlation has been developed for normally consolidated silica sands, and it can be used in sand deposits before compaction by the densification techniques, as it is believed that its results would be satisfactory.
Peck and Bazaraa (1969) have presented another correlation in a similar form
'
r ' v
v
'
r ' v
v
D = N 75
0.773 22
D = N 75
0.193 66
for KPa
for KPa
σ σ
σ σ + <
+ ≥
(A-2)
Again, ơ’v in KPa, and Dr in percents, this correlation has been established for dense coarse sands and it can be used in sand deposits after compaction by the densification techniques. The two expressions are compared in Fig. A-1, the difference between the two correlations is obvious, and that is mainly due to the different types of sands for which they were developed.
25 50 75 100 125 150 175 200
0 20 40 60 80 10
Relative Density Dr %
Effective Vertical Stress (KPa)
0
N=5 N=15 N=25 N=5 N=15 N=25 ____ Gibbs and Holtz (1957)
--- Peck and Bazaraa (1969)
Figure A-1 Correlations of SPT blow count with relative density for sand
Marcuson and Bieganousky (1977) derived an expression based on Reid-Bedford Model sand and Ottawa sand
' 2
r v
D = 11.7 + 0.76 222 * N + 1600 - 53 * σ - 50 * Cu (A-3) Where σ’v in pounds per square inches, and Cu is the coefficient of uniformity.
Skempton (1986) expressed the relation in a general form
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r '
v
D = N
a + b 98
σ (A-4)
Where a, and b are constants that depend mainly on the grain size and Dr is in decimal. In Japan, this formula is used in the practice with values of the constants a, and b as 16, 23 respectively (Ishihara 1993), and by putting σ’v = 98 KPa i.e. 1 Kgf / cm2 the expression becomes
D = 16 Nr 1 (A-5) Where N1 is the normalized penetration resistance, and Dr is in percentage.
Tokimatsu and Seed (1984) have presented Meyerhof’s relation (Eqn. A-1) in terms of (N1)60 (Fig. A-2).
0 20 40 60 80 100
0 10 20 30 4
(N1)60 Dr %
0
Tokimatsu & Seed (1984) Cubrinovski & Ishihara (1999)
Figure A-2 Relationship between relative density and (N1)60 for clean sands
Tatsuoka et al. (1978) examined the accuracy of the original Meyerhof’s expressions by using results of SPT on normally consolidated alluvial and reclaimed
sandy deposits along with in relative densities obtained from undisturbed samples. It was found that Eqn. (A-1) tends to underestimate the relative density of fine sands and silty sands and that the parameter (a+b) tends to increase with increasing mean grain size of sands D50, and accordingly N1 / Dr2 for silty sands is smaller than that of clean sands.
Ishihara (1993) have plotted the values of the parameter (a+b) of in-situ data for clean sand deposits (Fc < 10%), and silty sand deposits (Fc > 10%) (Fig. A-3).
0 50 100
0.01 0.1 1
Mean grain size D50 (mm) N1 / Dr2 = a + b
Clean sand
Silty sand
Figure A-3 N1 / Dr
2 = a + b plotted against the mean grain size (Ishihara 1993)
The scatter of the data in Fig. A-3 is too large for a reasonably accurate evaluation of the relative density based on D50 to be made. As a result, two separate relations
between (a+b) and D50 have been defined for clean sands and silty sands. Field data values for N1/Dr2 are in the range of 40 ~ 80 for clean sands, and 10 ~ 35 for silty sands.
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Cubrinovski and Ishihara (1999) have examined the probability of the effect of samples disturbance on the relation between (a+b) and D50. Undisturbed samples for silty sands, clean sands and gravels have been recovered by means of the ground freezing technique, which is recognized as being superior in recovering sand samples of high quality as compared to the conventional technique of tube sampling. The relation
between (a+b) and D50 has been improved (Fig. A-4) but it still contains a wide range of variation to the extent that it has been concluded that reliable relation between the SPT N1-value and relative density may not be established as far as the mean grain size D50 is used as a sole measure for the grain size characteristics of sandy soils.
0 50 100 150 200
0.01 0.1 1 10 100
Mean grain size D50 (mm) N1 / Dr2 = a + b
Figure A-4 N1 / Dr
2 = a + b plotted against the mean grain size (in-situ ground freezing sampling) (Cubrinovski and Ishihara 1999)
Similar correlation to Eqn. (A-5) has been presented by Cubrinovski and Ishihara (1999)
D r
D C
N12 = (A-6)
where the parameter CD is assumed to vary depending on the grain size properties of soils. It has been indicated that the void ratio range (emax – emin) is the most appropriate index parameter for quantifying the grain size and grain size distribution in an implicit manner. Detailed examination of data for sands and silty sands indicate that the void ratio range decreases with increasing mean grain size D50, and that for an identical mean grin size, the soils with greater amount of fines tend to have wider void ratio range. Thus the void ratio range was used to reflect not only the grain size, but also the grain composition of the soil, therefore as an indication of the grading properties.
The relation between the void ratio range and the mean grain size was expressed approximately as
50 min
max
06 . 23 0 .
0 D
e
e − = + (A-7) where D50 is given in millimeters.
Typical values of the void ratio range are shown in Table A-1
Table A-1 Typical void ratio range for different soils (Cubrinovski and Ishihara 1999)
Soil Type FC (%) emax - emin
< 5 0.3 ~ 0.5
Clean sands
5 ~ 10 0.45 ~ 0.55
10 ~ 20 0.5 ~ 0.6
Silty sands
20 ~ 30 0.6 ~ 0.7
Silty soils 40 ~ 80 > 0.7
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To confirm the relation between the ratio N1 / Dr2 and emax – emin, data from natural clean sands and silty sands deposits were collected (Fig. A -5). It has been shown that the ratio is highly dependant on the void ratio range. The relation was approximated as
(emax 9emin)1.7
CD
= − (A-8)
Figure A-5 Relation between N1 / Dr
2 ratio and void ratio range (Cubrinovski and Ishihara 1999)
It should be noted here that expression (A-8) corresponds to an SPT energy rod ratio of about 78 % from the theoretical free fall energy. Results of this correlation for clean sands are shown in terms of (N1)60 in Fig. A-2.
A.1.2. CPT
Recently the CPT has become more popular test than the SPT because of the inherent difficulties and the poor repeatability associated with the SPT. The most
significant advantage of the CPT beside its simplicity, and accuracy is that it gives nearly continuous profile of penetration resistance. The CPT results are generally more
consistent and repeatable than SPT.
Similar attempts have been made to develop an empirical correlation between the relative density and CPT penetration resistance qc. The first attempt was by Schmertmann (1976) and the relation in the form
r ' 1
2 0
1 *
D = ln C
C
c v
q C
⎛ σ ⎞
⎜⎝ ⎠⎟ (A-9) Jamiolkowski et al. (1985) have established a general form for the relation (Eqn A-7).
* log c' r
v
D A B q
σ
⎛ ⎞
= − + ⎜
⎜⎝ ⎠
⎟⎟ (A-10)
In Japan, based on test results using calibration chamber, this formula is used with values of the constants A, and B as 85, 76 respectively. Eqn (A-10) with qc values corrected for overburden pressure becomes
Dr = - 85 + 76 * log (qc1) (A-11) Baldi et al. (1986) have presented another relation taking into account the
dominant influence of initial horizontal stress σ’h0 (Fig. A-6)
r ' 0.55
0
D = 1 ln 2.38 248*
c h
q σ
⎛ ⎞
⎜⎝ ⎠⎟ (A-12)
Where qc and σ’h0 are in KPa.
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Figure A-6 CPT resistance, relative density correlation (Baldi et al. 1986)
Lately, Jamiolkowski et al. (2001) have adopted the general forms of
Schmertmann (1976), and Jamiolkowski et al. (1985) (Eqns. A-6, and A-7) to fit their experimental data, and the involved parameters have been evaluated.
A.1.3. SPT – CPT correlations
There was always a need for reliable SPT-CPT correlations; so that CPT can be used in existing SPT databased design correlations.
Relating the relative density Dr to the corrected SPT blow count N1, and the corrected qc1
value in the CPT using equations (A-5), and (A-11) respectively implies that a relation is
implicitly assumed between N1 and qc1 values, qc1/ N1 takes the value of 0.6 ~ 0.8 for a small value of N1 of 5 ~ 10. Ohya et al. (1985) verified this estimation particularly for loose sand deposits with N1 < 10 based on most of the in-situ data in Japan.
Many studies have looked at the relation between SPT N-values and CPT cone penetration resistance qc, e.g. Robertson and Campanella (1985); Seed and De Alba (1986); and Andrus and Youd (1989), and a wide range of qc / N ratios over a larger range of D50 have been published (Fig. A-7).
Figure A-7 SPT – CPT relation (Stark and Olson 1995)
A direct conversion of penetration resistance to relative density is uncertain, however, because penetration resistance depends on factors other than density. The correlations are not independent on soil type. Increased lateral pressure, increased time under pressure, increased stability of structure, and prior strains can lead to increased
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penetration resistance (Seed 1979). Significant increases in penetration resistance with time after densification have been measured even though there is no accompanying increase in density (Mitchell and Solymar 1984). Fortunately, these same factors lead also to increased resistance to settlement and liquefaction. Thus, it is the penetration resistance values themselves that are important, not the actual relative density. Therefore, it has been found useful in some cases to work with an equivalent relative density (Dr)eq, which is the true relative density that sand would have to posses to exhibit the measured penetration resistance if it were freshly deposited, saturated, and normally consolidated.
Since the behavior of silty soils during dynamic compaction process is the scope of this study, the next section will focuses on the work done and recommendation for effective grain contact indices for silty soils.
A.2. Silty soils
Throughout many studies on soil liquefaction that used the penetration resistance as an index, it has been recognized that the normalized penetration resistance (N1) of silty soils is small compared to clean sands of equal relative density. This was attributed to the inclusion of fines, which may cause undrained or partially drained conditions during penetration and lead to a decrease in the measured resistance. Therefore, one reason for the continued use of the SPT has been the need to retrieve soil samples to determine the fines content of the soil. However, this has been offset by the poor repeatability of SPT data. With the increasing interest in the CPT due to its greater repeatability, it is now possible to estimate grain characteristics of the soil such as fines content and grain size.
A.2.1. Fines Content correction
Based on field performances of soil deposits with known penetration resistance from SPT or CPT, several criterions have been developed for determining the cyclic strength or residual strength of soils from case histories. For example, Fig. A-8 shows the cyclic resistance ratio CRR and the corresponding (N1)60 data from sites where
liquefaction effects were or were not observed following past earthquakes with
magnitudes of approximately 7.5. It was noted that the cyclic resistance ratio increases with increased fines content. The curves on this graph were conservatively positioned to separate regions with data indicative of liquefaction from regions with data indicative of no liquefaction. Curves were developed for granular soils with the fines contents of 5%
or less, 15%, and 35% as shown on the graph. The CRR curve for fines contents <5% is the basic penetration criterion for the procedure and is referred to as the ‘‘SPT clean sand base curve’’. It has been customary to use the relation for clean sands and to correct the measured penetration resistance of sands containing fines to fit the clean sand base curve.
Similar criterion was used for the residual strength of liquefied soils (Seed 1986).
Therefore, the correction of the measured penetration resistance to equivalent clean sand depends on the used criterion.
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Figure A-8 Data from liquefaction case histories (Summary report NCEER 1998)
A.2.1.1. SPT
Tokimatsu and Yoshimi (1983) reported a correction for standard penetration resistance determined for silty sands (N1)to an equivalent clean sand penetration
resistance (N1)cs for the effect of fines content on cyclic strength of silty sands as follows (Fig. A-9)
(N1)cs = N1 + ΔNf (A-13)
Where ΔNf is fines content correction defined as ΔNf = 0 for FC = 0~5 % ΔNf = (interpolate) for FC = 5~10 %
ΔNf = 0.1 * FC + 4 for FC > 10 % (A-14)
, and FC is fines content percentage.
Similar correction have been presented by Seed (1986) based on back analysis of a number of liquefaction failures from which values of the residual undrained strength could be calculated for soil zones in which SPT data was available. The correction factor ΔNf (Fig. A-10) takes the values
ΔNf = 1 for FC = 10 % ΔNf=2 for FC = 25 % ΔNf=4 for FC = 50 %
ΔNf=5 for FC = 75 % (A-15)
0 5 10 15
0 10 20 30 40 5
FC (%) Δ Nf
0
Seed (1986)
Tokimatsu & Yoshimi (1983) Kayen & Mitchell (1997)
Figure A-9 Different fines content correction
Kayen and Mitchell (1997) have used different correction for silty sands based on cyclic strength (Fig. A-9)
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ΔNf = 0 for FC ≤ 5 %
ΔNf = (FC -5) * 7/30 for 5 % < FC < 35 %
ΔNf = 7 for FC ≥ 35 % (A-16) Idriss and Seed (Summary report 1998) have developed the following criteria, also based on cyclic strength
(N1)60cs = A + B (N1)60 (A-17) where A and B are coefficients determined from the following equations:
A = 0 for FC ≤ 5 %
2 1.76 190
A e FC
⎡ −⎜⎛ ⎞⎟⎤
⎢ ⎝ ⎠⎥
⎣ ⎦
= for 5 % < FC < 35 %
A = 5.0 for FC ≥ 35 %
,B = 1.00 for FC ≤ 5 %
1.5
0.99 1000 B ⎡ ⎛FC ⎞⎤
=⎢ +⎜ ⎟
⎝ ⎠
⎣ ⎦⎥ for 5 % < FC < 35 %
B = 1.2 for FC ≥ 35 % (A-18) where FC is the fines content measured from laboratory gradation tests on retrieved soil samples.
Robertson and Wride (1998a) have suggested another correction using a correction factor Ks which is solely a factor of fines content
(N1)60cs = Κs (N1)60 (A-19)
Where 1 [0.75( 5 ])
s 30
K = + FC−
A.2.1.2. CPT
The same criterion was later applied to the CPT. Ishihara et al. (1993) have presented a fines content correction for the overburden corrected cone penetration resistance (qc1) to an equivalent (qc1) cs based on back analysis of residual strength as shown in Fig (A-10)
(qc1) cs = (qc1) + Δ(qc1) (A-20)
0 5 10 15 20
0 20 40
FC (%) Δ (qc1)
60
Ishihara et al. (1993)
Figure A-10 CPT correction (Ishihara et al. 1993)
Robertson and Wride (1998b) have recommended a different correction using a correction factor Kc
(qc1N) cs = Kc (qc1N) (A-21) The proposed procedure is illustrated in a flowchart (Fig. A-11). The proposed correction factor Kc is approximate since the CPT responds to many factors, such as soil plasticity, fines content, mineralogy, soil sensitivity, and stress history.
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CPT
qc fs
(tip resistance) (sleeve friction)
In-situ stresses (σv0, σ’v0) In-situ stresses (σv0, σ’v0)
Q F
Q F
= (qc - σv0) / σ’v0 = [fs / (qc- σv0)] * 100 %
= (q
c - σv0) / σ’v0 = [fs / (qc- σv0)] * 100 %
Ic = [(3.47 – log Q)2 + (log F + 1.22)2]0.5
Ic = [(3.47 – log Q)2 + (log F + 1.22)2]0.5
0.5
1 '
2 0
c a
c N
a v
q P
q P σ
⎛ ⎞⎛ ⎞
= ⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠ qc1N = Q
Pa = 100 KPa if σ’v0 is in KPa Pa2 = 0.1 MPa if qc is in MPa
Ic = [(3.47 – log qc1N)2 + (log F + 1.22)2]0.5
0.75
1 '
2 0
c a
c N
a v
q P
q P σ
⎛ ⎞⎛ ⎞
= ⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
Ic = [(3.47 – log qc1N)2 + (log F + 1.22)2]0.5
If Ic ≤ 1.64 Kc = 1.0
If Ic > 1.64 Kc = -0.403 Ic4 + 5.581 Ic3 – 21.63 Ic2 + 33.75 Ic –17.88 If Ic ≥ 2.6 Clayey silt or silty clay
If 1.64 < Ic < 2.36 and F < 0.5 % Kc = 1.0
(Qc1N)cs = Kc * qc1N
Ic>2.6 Ic<2.6
Ic>2.6 Ic<2.6
Figure A-11 Flowchart illustrating the CPT fines content correction (modified from Robertson and Wride 1998b)
It is worthy to note that, the equivalent clean sand penetration resistance (N1)60cs, and the equivalent clean sand cone resistance (qc1)cs have no physical or theoretical meaning, they do not represent the equivalent value of sand if the silt content was removed. They are only a convenience used for calculating the cyclic resistance ratio for estimating liquefaction potential or the residual undrained strength of silty sands.
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APPENDIX B
ENERGY REQUIRED TO CAUSE LIQUEFACTION
The energy dissipated per unit volume of soil can be evaluated throughout cyclic high-strain laboratory tests such as cyclic triaxial test, cyclic simple shear test, and cyclic torsional shear test (Kramer 1996). The cyclic triaxial test has been the most commonly used test for the measurement of dynamic soil properties at high strain levels.
In the cyclic triaxial test, the deviator stress, which is the difference between the axial stress and the radial stress, is applied cyclically either under stress-controlled conditions or strain-controlled conditions.
Recalling the model of two spheres in contact explained in Sec. 4.2.1, the cyclic application of the tangential force would result in a force-displacement response forming a hysteresis loop such as shown in Fig. 4-3. The area bound by the hysteresis loop
quantifies the energy dissipated in the system of particles. The corresponding stress-strain response of an assemblage of particles describes similar hysteresis loop, as shown in Fig.
B-1 from a typical stress-controlled cyclic triaxial test, which is a function of load-path.
For saturated undrained samples, the area bound by the hysteresis loop quantifies the dissipated energy, by all mechanisms, per unit volume of material.
Figure B-1 Stress-strain hysteresis loop
The cumulative dissipated energy per unit volume of soil in a cycling test is calculated from the areas of all the hysteresis loops as follows
( )(
1
1 1
1
1 2
n
i i i i
i
w − τ τ + ε+ ε )
=
=∑ + − (B-1) where τ is the deviatoric shear stress, ε is the axial strain, l is number of load increments.
During cyclic undrained shearing of soil, the soil has a tendency for volume change, and as volume change is disallowed (undrained), pore pressure generates. This process continues during cyclic loading with concurrent accumulation of energy loss, eventually leading to ending of further pore pressure changes. For loose soils subjected to undrained shear, such a state is called liquefaction.
However, because the energy dissipated by different mechanisms (as discussed in the Sec 4.2.) cannot be easily detected from the laboratory and field tests, the total energy dissipation is attributed to the frictional mechanism. The previous assumption is justified