initiation of soil liquefaction under static loading conditions
TRANSCRIPT
INITIATION OF SOIL LIQUEFACTION UNDER STATIC
LOADING CONDITIONS
By Steven L. Kramer,1 Member, ASCE, and H. Bolton Seed,2 Honorary Member, ASCE
ABSTRACT: Liquefaction of loose, saturated sands may be caused by cyclic or static (monotonically increasing) undrained loading. Most previous studies of static liquefaction behavior have emphasized liquefaction susceptibility and the behavior of liquefied soils. An experimental investigation is undertaken to evaluate the stress conditions required to initiate liquefaction and the influence of various parameters on those stress conditions. The static liquefaction resistance, denned as the shear stress increase under undrained conditions required to initiate liquefaction, is observed to increase with increasing relative density and confining pressure, and to decrease dramatically with increasing initial shear stress level. At high initial shear stress levels, initiation of liquefaction is observed to result from increases in shear stress under undrained conditions of only a few percent of the initial shear stress. The distinction between the initiation and the effects of liquefaction is discussed, and an expression for a factor of safety against the initiation of liquefaction is proposed.
INTRODUCTION
Liquefaction of loose, saturated sands may be caused by cyclic or static (monotonically increasing) undrained loading. The behavior of such materials under cyclic loading has received a great deal of attention from researchers since the dramatic effects of liquefaction were observed in Niigata, Japan (Japan National Committee 1965; Ohsaki 1966) and Alaska (Grantz et al. 1964; Seed and Wilson 1967) during earthquakes in 1964. Stimulated by the need for evaluation of the potential for liquefaction affecting critical structures such as nuclear power plants, the liquefaction behavior of sands under cyclic loading conditions has become relatively well understood. The liquefaction behavior of sands under static loading conditions, however, has received considerably less attention, though extremely important laboratory studies of this phenomenon have been made in the past 20 years by Castro and Poulos (Castro 1969; Castro and Poulos 1977; Geotechnical Engineers, Inc. 1982; Poulos et al. 1985). These and most other (Begemann et al. 1977; Bjerrum et al. 1971; Dierichs and Forster 1985; Durham and Townsend 1973; Highter and Tobin 1980; Highter and Vallee 1980; Johnson 1982; Lindenberg and Koning 1981; Torrey 1981) available studies of static liquefaction have emphasized and interpreted results in terms of the properties of soils after liquefaction has occurred. The research described in this paper is concerned with the conditions surrounding the initiation of liquefaction.
'Asst. Prof., Dept. of Civ. Engrg., Univ. of Washington, Seattle, WA 98195. 2Prof. of Civ. Engrg., Univ. of California, Berkeley, CA 94720. Note. Discussion open until September 1, 1988. To extend the closing date one
month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on April 15, 1987. This paper is part of the Journal of Geotechnical Engineering, Vol. 114, No. 4, April, 1988. ©ASCE, ISSN 0733-9410/88/0004-0412/$1.00 + $.15 per page. Paper No. 22334.
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LIQUEFACTION FAILURE
Liquefaction failure often leads to the development of instabilities in large masses of soil, commonly referred to as flow slides. Occurrences of many flow slides have been reported, however, for which no significant source of cyclic loading has ever been identified. In this paper, liquefaction resulting from the application of noncyclic shear stresses will be referred to as static liquefaction.
Flow slides have been observed in both man-made and natural soil deposits. Since Hazen (1920) first used the term liquefaction to describe the 1918 failure of Calaveras Dam in California, flow slides resulting from static liquefaction have been observed in a number of hydraulically filled earth dams (Hazen 1920; Middlebrooks 1942) and in several similarly constructed tailings dams (Jennings 1979; Kleiner 1976; Lucia 1981). Many of the flow slides in natural deposits resulting from static liquefaction have been observed in coastal and/or offshore areas (Andresen and Bjerrum 1968; Bjerrum 1971; Koppejan et al. 1948; Senour and Turnbull 1948; Terzaghi 1956). The descriptions of the circumstances surrounding the great majority of the slides in natural deposits indicates that some relatively sudden lowering of the water level outboard of the slope was observed almost immediately prior to the initiation of the flow slide (Andresen and Bjerrum 1968; Bjerrum 1971; Koppejan et al. 1948; Senour and Turnbull 1948; Terzaghi 1956).
PREVIOUS WORK
According to Bjerrum et al. (1961), liquefaction was first achieved in laboratory tests by researchers at the U.S. Waterways Experiment Station in the early 1950's. In the late 1950's, Bjerrum et al. achieved liquefaction in stress-controlled triaxial compression tests on loose fine sands typical of those known to have been involved in flow slides in Norwegian fjords. Based on an unspecified number of tests on anisotropically consolidated samples, Bjerrum et al. remarked that "it was surprising to see, however, the small increase in deviator stress required to cause failure in the undrained tests. . ."
More recently, research regarding liquefaction under static loading has focused primarily on the susceptibility of soils to liquefaction and on the large-strain behavior of liquefied soil. The determination of liquefaction susceptibility has usually been related to the large-strain stress-strain-volume change behavior of the sand. Castro and Poulos (1977) called the state in which a soil sample is flowing under constant shear stress at constant effective minor principal stress and at constant volume [later modified by Poulos (1981) to include the requirement of constant velocity], the "steady-state of deformation," and the relationship between the steady-state effective stress and the void ratio the "steady-state" line). Experimental evidence presented by Castro and Poulos indicates that the position of the steady-state line is a unique soil property, but also that the position and inclination of steady-state lines vary widely even for apparently similar soils. The inclination of the steady-state line for many soils is such that small variations in void ratio can lead to rather large variations in steady-state effective stress. Evaluation of the position and inclination of the steady-state line therefore requires very careful sampling and testing
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(Poulos et al. 1985). Castro and Poulos suggest that the steady-state line marks the boundary between conditions in which a sand is, or is not, susceptible to liquefaction.
Steady-state concepts have been incorporated into proposed procedures for evaluation of liquefaction hazards. Casagrande (1976) proposed that the liquefaction potential of a sand be expressed as
Lp = % ^ (1)
in which <r'3i = the initial effective minor principal stress; and a'3f = the effective minor principal stress during steady-state flow. Castro and Poulos (1977), based on Mohr-Coulomb strength criteria, rewrote the above equation in terms of the angle of friction of the sand and the pore pressure parameter A during steady state flow in the form:
2 sin <b LP=A -1 r-^- (2)
p 1 - sin <|> These expressions imply that the liquefaction potential of a given sand is a function of the relationship between the initial and steady-state confining pressures for sand of a given density, and that liquefaction potential increases with increasing confining pressure. According to these expressions, other factors such as initial shear stress level have no influence on liquefaction potential.
Poulos et al. (1985) recently presented procedures for liquefaction evaluation that included a definition of a factor of safety against liquefaction as the ratio of the undrained steady-state shear strength to the driving shear stress (which is required to maintain static equilibrium). According to this definition, the factor of safety against liquefaction of an element in drained equilibrium under some shear stress greater than the steady-state shear strength is less than unity, regardless of the magnitude of the peak shear strength, which must be exceeded to reach steady-state conditions. This definition may be interpreted as a factor of safety against flow sliding for a sand that has reached the steady state of deformation.
Other investigators (Begemann et al. 1977; Bjerrum et al. 1971; Dierichs and Forster 1985; Durham and Townsend 1973; Geotechnical Engineers, Inc. 1982; Highter and Tobin 1980; Highter and Vallee 1980; Johnson 1982; Lindenberg and Koning 1981; Torrey 1981) have tested loose sands and have observed behavior similar to that observed by Castro. Each of these subsequent investigations was also primarily concerned with evaluation of the influence of various factors on the position of the steady-state line for the primary purpose of evaluating the liquefaction susceptibility of a particular sand.
More recently, investigators (Hanzawa 1980; Ishihara et al. 1975; Sladen et al. 1985; Vaid and Chern 1985) have begun to explicitly study the stress conditions surrounding the initiation of liquefaction. Vaid and Chern (1985) [41] described the monotonic loading response of two fine sands and developed a three-dimensional effective stress state representation of undrained response. Sladen et al. (1985) developed, on the basis of isotropically consolidated triaxial tests on loose, fine sand, the concept of
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a "collapse surface" state describing the effective stress conditions at which liquefaction would occur.
INITIATION OF LIQUEFACTION
Previous studies have identified the conditions of stress and density under which sands are and are not susceptible to liquefaction. However, both in the field and in the laboratory, liquefaction of an element of soil can only occur if shear stresses applied under undrained conditions are greater than or equal to those required to initiate liquefaction. Consequently, a full evaluation of the liquefaction potential or factor of safety against liquefaction at a given site would appear to require knowledge of the increases in shear stress under undrained conditions required to initiate liquefaction. The increase in shear stress under undrained conditions required to initiate liquefaction will be referred to hereafter as the static liquefaction resistance of the soil. Since the majority of the previous studies have been primarily concerned with evaluation of liquefaction susceptibility, a laboratory investigation was undertaken for the purpose of determining static liquefaction resistance.
LABORATORY TESTING PROGRAM
A laboratory testing program was undertaken to evaluate the static liquefaction resistance of two sands under various conditions of relative density, confining pressure, and initial stress conditions. Other factors known to influence cyclic liquefaction resistance include grain angularity, overconsolidation ratio, previous strain history, length of time under sustained pressure, and grain structure or fabric. The influence of these parameters on cyclic liquefaction resistance was summarized by Seed (1976). It seems reasonable to believe that these parameters will also affect the static liquefaction resistance of a sand to some degree.
One of the sands, hereafter referred to as Sacramento River fine sand (SRFS), was a clean, uniform, fine sand. SRFS is the portion of the Sacramento River sand widely used in previous investigations (Lee and Seed 1967; Seed and Lee 1967) which passes through a No. 50 sieve. The sand was sieved in this manner in order to achieve a grain size distribution similar to those of fine sands known to have been involved in static liquefaction failures. The other sand, referred to as silty sand (SS), was a fine, uniform sand containing approximately 12% fines which was obtained from the site of an actual static liquefaction flow slide failure. Grain-size distribution curves for each sand are shown in Fig. 1. Other pertinent characteristics of each sand are listed in Table 1.
The samples were prepared by tamping six portions of nearly equal dry weight bulked at water contents of 6-8% into layers of equal height inside a forming mold. The dry weights of each portion were varied in such a way as to maximize the uniformity of density throughout the sample after tamping. Interior layer surfaces were lightly scarified to improve sample homogeneity at the layer boundaries. The samples were evacuated by application of a high vacuum applied through a reservoir of deaired water and then saturated by slow removal of the vacuum. Cell and back pressures were simultaneously increased until an acceptable B-value was obtained. B-values of 0.97-0.99 were routinely obtained at back pressures
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100
i I 80 a
S 6 0
J -
10 5 2 I 0.5 0.2 0.1 0.05 0.02 0.01 Grain Diameter, D-mm.
FIG. 1. Grain-Size Distribution of Sacramento River Fine Sand and Silty Sand
of about 3 kg/cm2 (ksc). The cell pressure was then increased slowly under drained conditions to provide the desired effective confining pressure. Anisotropic consolidation was achieved by increasing the deviator stress to the desired level under drained conditions. All samples were then allowed to reach a state of drained equilibrium under the imposed initial stress conditions before testing under undrained conditions. The sample volume was carefully measured immediately after sample preparation, and all volume changes during saturation and consolidation were recorded for subsequent computation of relative density at the end of consolidation.
The samples were loaded manually by a CKC electro-pneumatic (load-controlled) loader. The samples were subjected to an approximately constant rate of loading, in which the deviator stress was increased in small, equal increments at 30-sec intervals. All samples were loaded at the same rate. Initiation of liquefaction was typically observed at very low axial strains as a rapid increase in strain rate with concurrent pore pressure increase to a constant residual value.
TABLE 1. Grain-Size Characteristics of Sacramento River Fine Sand and Silty Sand
Sand (1)
SRFS
ss
Mean grain size, D50
(mm) (2)
0.205 0.120
Effective grain size,
A o (mm)
(3)
0.150 0.070
Coefficient of
uniformity (4)
1.41 2.00
Coefficient of
curvature (5)
0.98 1.02
Maximum dry
density (Mg/m3)
(6)
1.703 1.629
Minimum dry
density (Mg/m3)
(7)
1.354 1.161
\
Sacramento River Fine Sand *•
\*-Silty Sand
y I
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LABORATORY TEST RESULTS
The laboratory investigation described in this paper studied the effects of relative density, confining pressure, and initial shear stress on static liquefaction resistance. The investigation included over 100 tests on both of the previously described sands at various relative densities, confining pressures, and initial shear stress levels. The observed influence of each of these parameters on static liquefaction resistance is described and illustrated by typical test results in the following sections.
Effect of Relative Density The influence of soil density on static liquefaction resistance was
investigated by a number of tests. The density of the test specimens will be expressed in terms of relative densities. While many others have expressed density in terms of void ratio, the wide variation in void ratio (particularly at the steady state of deformation) for different soils makes comparison of their relative behaviors very difficult. While relative density may not be an ideal state parameter, it is considered suitable for the purposes of this paper.
The stress-strain and pore-pressure behavior of four isotropically consolidated, undrained (ICU) tests on SRFS at different relative densities is
5
4
u
I » 3 VI ®
o o 2
'> «
I
0 0 5 10 15 20 25
Axial Strain - percent
2 a o 0 » i f 01 '
o £ a- = 0
m </> w S £
UJ
-2 0 5 10 15 20 25
Axial Strain - percent
FIG. 2. Effect of Relative Density on Stress-Strain and Pore-Water Pressure Response
417
Sacramento River Fine Sand For all tests ' o \ • 2 .00 ksc
44%
• 37 %
- 3 2 %
^zz.—I 1 ••
"----, 47 %
• i i
—1 id% 37%
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1 1 1 r
For oil tests ' a , = 2.00 ksc
Kc= 1.00 e - Sacrameto River Fine
Sand
B - Silty Sand
B e ee e
J I I I " " 2 0 25 30 35 40 15
Relative Dens i ty - percent
FIG. 3. Effect of Relative Density on Deviator Stress at Failure
shown in Fig. 2. Each of the samples was consolidated to a minor principal effective stress of 2.0 ksc. The sample consolidated to and tested at a relative density of 47% exhibited dilative behavior with decreasing excess porewater pressure and increasing deviator stress at high strains. The sample tested at 44% relative density initially appeared to liquefy, straining rapidly to about 10% axial strain after the maximum deviator stress was reached, but then began to dilate at higher strains. This type of behavior was first observed and described as "limited liquefaction" by Castro (1969). In view of the potential damages that could be associated with strains of this order of magnitude, liquefaction was considered to have been initiated in samples exhibiting this type of behavior. The samples tested at relative densities of 37 and 32% both liquefied. After the peak deviator stress was reached, both the excess porewater pressure and the rate of straining increased rapidly as the sample strained at a residual deviator stress less than the peak deviator stress. The increase in deviator stress under undrained conditions required to initiate liquefaction in samples tested at 32, 37, and 44% relative density was successively larger. These results indicate that the static liquefaction resistance increases with increasing relative density. This behavior was observed consistently for both SRFS and SS, as shown in Fig. 3. Since the laboratory testing program shows that static liquefaction resistance increases with increasing relative density, the potential for initiation of liquefaction can be considered to decrease with increasing relative density. It should be noted that, at relative densities greater than those corresponding to the steady-state line (which for this series of tests appears to be slightly greater than 44%), the soil will exhibit dilative behavior, and there will be no potential for liquefaction.
Effect of Confining Pressure In order to study the influence of confining pressure on static liquefac
tion resistance, a series of tests were performed on samples consolidated
2.0
r\ r\
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a l
Sacramento River Fine Sand For all tests' D , * 3 I %
-Confining Pressure - ksc
5 10 15 20 Axial Strain - percent
o l ' 0
J. • 1 1 5<—Confining Pressure - ksc
0 5 10 15 20 25 Axial Strain - percent
FIG. 4. Effect of Confining Pressure on Stress-Strain and Pore-Water Pressure Response
to different confining pressures. The stress-strain and pore pressure behavior of four ICU tests on SRFS samples consolidated to relative densities of approximately 35% at confining pressures ranging from 1.0-5.0 ksc is shown in Fig. 4. The increase in deviator stress under undrained
» 2.0 -
1
Sacramento R For all tests:
-
-
9 9 9
§ 1
1 1 1
ver Fine Sand Dr= 3 2 % - 3 8 %
Kc= 1.00
i i i i
i
9 9
9
1
-
-
-
0.0 2.0 . 3.0 4.0 Confining Pressure - ksc
FIG. 5. Effect of Confining Pressure on Deviator Stress at Failure
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conditions required to initiate liquefaction can be seen to increase as the confining pressure is increased. The results of these tests thus indicate that static liquefaction resistance increases with increasing confining pressure. This type of behavior was observed consistently throughout the testing program as shown in Fig. 5. It should be noted that no results are presented for SS in Fig. 5 because all tests on SS samples were performed at the same confining pressure (2.00 ksc). The undrained deviator stress required to initiate liquefaction can be seen to increase nearly in proportion to the confining pressure. These results indicate that static liquefaction resistance increases with increasing confining pressure. Consequently, the potential for initiation of liquefaction can be considered to decrease with increasing effective confining pressure.
Effect of Initial Shear Stress A series of tests were performed on samples consolidated to different
initial shear stress levels in order to study the influence of initial shear stress level on static liquefaction resistance. The results of three aniso-tropically consolidated, undrained (ACU) tests and one ICU test on samples of SRFS at relative densities ranging between 32-38% are shown in Fig. 6. The samples were subjected to various levels of initial shear stress by consolidation to principal effective stress ratios of 1.0, 1.5, 2.0, and 2.25. Liquefaction was initiated in the isotropically consolidated sample, which was in equilibrium under zero shear stress at the beginning
1 1 1
Sacramento River Fine Sand For all tests • Dr = 3 2 %
V
AV \ \ ^ \ v^ ^ — - ,
- 3 8 %
i
- 1
Ke /-1.50 /V2.00
-/^2.25
-
-
5 10 15 20 Axial Strain - percent
5 10 15 20 Axial Strain - percent
FIG. 6. Effect of Initial Shear Stress on Stress-Strain and Pore-Water Pressure Response
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&
1.0
o.s
0.6
0.4
1 1 1 1 Sacramento River Fine Sand For all tests: <r, = 2 .00 ksc
3c Dr ^ 3 5 %
%/ 9 /
% / i /
0.2
1 J
/
•
"
-
' 0.0 0.2 0.1 0.6 0.8 1.0 1.2
FIG. 7. Influence of Initial Shear Stress on Static Liquefaction Resistance of Sacramento River Fine Sand
1.0
o.e
0.6
0.4
i
0.2
Silty S For oil
and tests
9
1 ' 1
a. • 2.00 ksc
Dr = 30 % - 4 0 %
% / • /
9 /
1 1 1
i -7
-
-
i
0.0 0 .2 0 .4 0 .6 O.B 1.0 1.2
FIG. 8. Influence of Initial Shear Stress on Static Liquefaction Resistance of Silty Sand
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of the test, by an undrained increase in deviator stress of approximately 0.9 ksc. In the samples consolidated to principal effective stress ratios of 1.5, 2.0, and 2.25, the increases in deviator stress under undrained conditions required to initiate liquefaction were approximately 0.6, 0.25, and 0.13 ksc, respectively. It can clearly be seen that the static liquefaction resistance in these samples decreases significantly as the initial shear stress level increases. This aspect of soil behavior has been observed by others (Bjerrum et al. 1961; Castro 1969; Castro and Poulos 1977; Geotechnical Engineers, Inc. 1982) in a limited number of tests on very loose samples but has not been investigated in detail.
Tests were performed on a number of samples at varying levels of initial shear stress. It is convenient and instructive to express the results of the tests in terms of the maximum shear stresses, which act on a plane inclined at 45° from the minor principal stress axis. Figs. 7 and 8 show (for SRFS and SS, respectively) the variation of maximum shear stress at failure, arfy/2, as a function of the maximum shear stress at the end of consolidation, crdc/2, both normalized by the effective confining pressure at the end of consolidation. The line inclined at 45° represents the stress conditions at the end of consolidation. The static liquefaction resistance is thus proportional to the vertical distance between each data point and the 45° line. The data clearly show a strong influence of initial shear stress level on the additional shear stress required to initiate liquefaction. Fig. 7 shows that at a principal effective stress ratio of 1.5, an increase in shear stress under undrained conditions of 53% would be required to initiate liquefaction, while at a principal effective stress ratio of 2.25, a shear stress increase of only 6% is required. At higher levels of initial shear stress, even smaller undrained shear stresses are required to initiate liquefaction.
Castro (1969) reported the results of three anisotropically consolidated tests performed to evaluate the influence of initial shear stress level on the position of the steady-state line. Interpreted in the same manner as the tests performed in this investigation, the behavior is generally similar, as shown in Fig. 9. Geotechnical Engineers, Inc. (1982) also performed several ACU tests on very loose samples (£),. = 16-19%). Careful interpretation of the results of these tests also indicates similar behavior as shown in Fig. 10.
The laboratory data clearly indicate that liquefaction may be initiated by very small changes in shear stress under undrained conditions in sand deposits that have been subjected to high shear stress levels under drained conditions. This behavior may very likely be responsible for many reported cases of "spontaneous liquefaction" where no source of loading of any kind was observed. Clearly, the static liquefaction resistance of a sand decreases as the level of initial shear stress increases. Consequently, potential for initiation of liquefaction can be seen to increase with increasing initial shear stress level and may be very high at high levels of initial stress.
Strain at Failure Since liquefaction of a soil deposit may also be initiated by rapidly
imposed boundary deformations, e.g., creep rupture of a clay shale underlying a hydraulic fill embankment, the strain at which liquefaction is initiated is of interest. Initiation of liquefaction was observed to occur at
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"f
2°",.
1
Bonding Sand B 0
D. = 33 %
FIG. 9. Influence of Initial Shear Stress on Static Liquefaction Resistance on Banding Sand B (Castro 1969)
Banding Sand No. 6 For oil tests ' o \ = 4 , 0 k6c
D. = 16 % - 19 %
2° i .
20",
FIG. 10. Influence of Initial Shear Stress on Static Liquefaction Resistance of Banding Sand No. 6 (Geotechnlcal Engineers, Inc. 1982)
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2°V
Sacramento River Fine Sand For oil tests' er, ' 2.00 ksc
Relative Densityi 4 0 %
2o\
FIG. 11. Influence of Relative Density and Initial Shear Stress on Static Liquefaction Resistance of Sacramento River Fine Sand
%
1 1 I I
Sacromento River Fine Sond For oil tests' Dr<-35%
/%/
Confining / / / / Pressure -ksc SS/s
'3^^^/ """5 /
/ I I I i
1 J
W
-
-
0.0 0.2 0.4 0.6 o.e i.o
FIG. 12. Influence of Confining Pressure and Initial Shear Stress on Static Liquefaction Resistance of Sacramento River Fine Sand
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very low axial strains in the two sands tested in this investigation—typically on the order of 1-2%. The axial strain at failure was observed to increase slightly with increasing relative density and confining pressure and to decrease slightly with increasing initial stress level. These low strains at failure indicate that many types of conventional slope instrumentation, based on periodic measurements of inclination or displacement, may not provide adequate warning of impending instability for sands of this type. Larger strains may be required in other materials such as the thickened tailings described by Poulos et al. (1985).
Summary of Laboratory Investigation The laboratory investigation described herein has clearly shown the
influence of relative density, confining pressure, and initial shear stress level on the static liquefaction resistance of two fine sands. The results represent the behavior of over 60 tests. Fig. 11 shows increasing static liquefaction resistance with increasing relative density. Fig. 12 shows increasing static liquefaction resistance with increasing confining pressure, though the shear stress normalization procedure may at first glance make it appear otherwise.
It has long been known that the susceptibility of sand to liquefaction depends on the relationship between the void ratio and confining pressure. This investigation has demonstrated the influence of void ratio (or relative density) and confining pressure on the static liquefaction resistance of fine sand. The static liquefaction resistance was observed to increase with increasing relative density. As the relative density increased to the point where the void ratio approached the critical void ratio, the samples began to display dilative behavior, and liquefaction was not observed. However, the static liquefaction resistance of samples consolidated to high confining pressures was observed to be significantly greater than that of those consolidated under lower confining pressures.
The static liquefaction resistance was found to be particularly sensitive to the initial shear stress level. The static liquefaction resistance decreased with increasing level of initial shear stress. At high levels of initial shear stress, liquefaction was initiated by an increase in shear stress, under undrained conditions, of only a few percent of the initial shear stress.
The initiation of liquefaction was observed at very low strains for the sand tested. The relatively small displacements that would be expected to result from such small strains in most field situations may also help to explain the occurrence of flow slides historically attributed to "spontaneous liquefaction."
CHARACTERIZATION OF LIQUEFACTION BEHAVIOR
The possible behavior of a soil mass in the field with respect to liquefaction is currently expressed in two ways—in terms of liquefaction potential or in terms of a factor of safety against liquefaction. In discussing liquefaction potential or the factor of safety against liquefaction, it is desirable that a distinction be made between the triggering of liquefaction and the potential effects of liquefaction. The triggering of liquefaction results in some reduction in the shear strength of the soil after the peak shear strength has been reached. The potential effects of liquefaction are related to the magnitude of this strength reduction. Evaluation of the
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potential behavior of sands at a given site should include separate evaluation of both the potential for triggering or occurrence and the potential consequences of triggering liquefaction (i.e., the loss in shearing resistance).
Initiation of Liquefaction It has been demonstrated that static liquefaction can only occur if the
shear stress acting on the soil is increased by a sufficient amount under undrained conditions. The magnitude of the increase in shear stress under undrained conditions required to initiate liquefaction has been referred to as the static liquefaction resistance. If an element of soil is subjected to an increase in shear stress under undrained conditions of magnitude less than the static liquefaction resistance, the soil will not liquefy. If the soil is subjected to an increase in shear stress under drained conditions, it will not liquefy. It thus appears that evaluation of the potential for occurrence of liquefaction in a soil deposit subjected to some change in stress conditions should be based on the stresses required to initiate liquefaction, or the static liquefaction resistance. Such potential may be expressed in terms of a factor of safety against the initiation of liquefaction.
The results of an undrained test causing failure of a loose sand sample and the comparative effect of a stress application less than that causing failure are shown schematically in Figs. 13(a and b). Factors of safety are usually defined as the ratio of the shear strength of the soil to the shear stress induced in the soil. Because of this convention, a factor of safety of unity denotes a condition of incipient failure, i.e., applied or induced shear
Jv I
I s
'1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 .
> * -
\ Stable
\ 1 1
'.Unstable
\
Time
1 1 1 1
j Unstable
/ / / / / / Stable
— Tj
'f
\ ~Xi
F.S.
V
• V r d r, -T r
TV
- - - T r
Time
(a)
Strain
(b)
FIG. 13. (a) Schematic Illustration of Effects of Undrained Loading of Loose Sand Sample; (b) Typical Stress-Strain in Diagram with Illustration of Terms
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stresses equal to those required to initiate failure. To be consistent with this approach, the factor of safety against the initiation of static liquefaction may be expressed as:
Shear stress required to initiate liquefaction F S = (3)
Shear stress developed by loading in soil mass For the stress-strain curves shown in Figs. 13(a and b), the factor of safety against liquefaction for an undrained increase in shear stress from some initial shear stress T,- to a developed shear stress jd would be given by
F.S. = 7-1 (4)
It should be noted that the numerator of the expression for factor of safety is the sum of the static liquefaction resistance and any initial shear stress. In this manner, the effects of all parameters affecting static liquefaction resistance are properly considered.
The influence of the initial shear stress level on the liquefaction resistance of sands is particularly important. The liquefaction resistance has been observed to be strongly dependent on the initial stress conditions; thus, a liquefaction stability analysis must be capable of accurately evaluating the stress conditions throughout any liquefaction-susceptible material. Localized zones of high initial stress, which may occur in the vicinity of surface or subsurface geometric or material discontinuities, must be carefully evaluated. The potential for future increases in shear stress under drained conditions, such as those that may be caused by creep or settlement deformations at adjacent boundaries, must also be considered. These requirements, along with those associated with the strain-softening nature of liquefiable sands, limit the effectiveness of limit equilibrium methods for stability analyses in such cases.
Effect of Liquefaction The occurrence of liquefaction results in a reduction in soil shear
strength that may be large or small. The magnitude of the strength loss after initiation of liquefaction does not directly affect the factor of safety against initiation of liquefaction, but it has a large effect on the consequences of liquefaction. After liquefaction has been initiated in an element of soil, that element deforms until it reaches the steady state of deformation. In the process, the shearing resistance drops from the peak undrained shear strength to the steady-state shear strength. The amount of deformation required to reach equilibrium conditions depends on the difference between the peak and the residual shear strengths. If the reduction in shearing resistance is large, flow sliding may develop. If the previously discussed factor of safety proposed by Poulos et al. (1985) is greater than one, flow sliding will not develop.
Bishop (1967) expressed the reduction in undrained strength of a strain-softening material in terms of a "brittleness index" defined as:
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where ly = peak undrained shear strength; and jr = residual undrained shear strength, as shown in Figure \3(b).
The residual shear strength has been described by others as the steady-state shear strength. The peak shear strength is the sum of the liquefaction resistance and any initial shear stress. A large brittleness index, therefore, indicates a large reduction in shear strength that could lead to the progressive development of large deformations after the initiation of liquefaction. On the other hand, the initiation of liquefaction in a material with a low brittleness index may not lead to significant deformations.
SUMMARY
The static liquefaction resistance of loose, saturated sand is affected by a number of parameters. A comprehensive laboratory testing investigation was undertaken to determine the influence of relative density, confining pressure, and initial shear stress level on the static liquefaction resistance of two fine sands. The static liquefaction resistance, defined as the shear stress increase under undrained conditions required to initiate liquefaction, was consistently observed to increase with increasing relative density and confining pressure, and to decrease with increasing initial shear stress level.
A distinction should be made between the initiation of liquefaction and the potential effects of liquefaction. Evaluation of the liquefaction hazard for a particular site should include evaluations of both the potential for the initiation of liquefaction and the potential effects of liquefaction. Since static liquefaction can only occur if the static liquefaction resistance has been exceeded, an expression for a factor of safety against the occurrence of liquefaction has been proposed.
The occurrence of liquefaction leads to some reduction in the shear strength of the soil. The shear strength reduction may be large or small and its magnitude, which may be described by Bishop's "brittleness index," will strongly influence the effects of liquefaction.
ACKNOWLEDGMENTS
The studies described herein were supported by a grant from the National Science Foundation. The support of the National Science Foundation is gratefully acknowledged. The assistance of R. B. Seed and F. Szerdy is also acknowledged.
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