Liquefaction and dynamic properties of gravelly soils M.D. Evans Civil Engineering Department, Northeastern University, ^20 Snell Engineering Center, CASL4 ABSTRACT Liquefaction of gravelly soil has received much attention in recent years as several case histories have been reported where gravel and gravelly soil has liquefied. As a result, much research has been focused on assessing the liquefaction potential of gravelly soils both in situ and in the laboratory. Laboratory liquefaction assessment typically includes performing undrained, cyclic triaxial tests to determine liquefaction resistance and dynamic material properties. However, the potentially adverse effects of membrane penetration and compliance must be considered. Membrane compliance may result in pore fluid redistribution, soil densification, and increased liquefaction resistance in the undrained triaxial test, making it difficult to properly evaluate the performance of the prototype material in situ. This paper presents results of undrained, cyclic triaxial tests performed on gravel specimens and sluiced gravel specimens. This paper will show the corrected cyclic strength of gravel specimens to be as low as 60% to 70% of the uncorrected strength. Increases in gravel specimen density of up to 20 percentage points or more due to membrane compliance are also documented. The bases for these determinations are presented in this paper. INTRODUCTION The phenomenon of liquefaction of sandy soil is fairly well understood by the geotechnical profession. Many researchers have investigated the phenomenon over the last 30 years (Seed and Lee*, Castro^, Seed^, and many others), and it is generally well accepted that loose, clean sands may develop excess pore pressures during earthquake loading, and may undergo extreme strength loss and large deformations. Liquefaction of gravelly soils, however, may not be so well established in the geotechnical community. For years, gravels were considered to be completely free draining and no consideration was given to assessing liquefaction
318 Soil Dynamics and Earthquake Engineering potential. Gravelly soils may be free-draining under ideal conditions, but drainage is often impeded. A gravelly soil may be bounded by a low-permeability cap, for example, temporarily restricting drainage. Such formations may occur in an alluvial fan containing gravelly soil interlayered with finer material, or in a gravel embankment where drainage is impeded by silt deposition on the upstream face (Evans et al.4). Evans and Harder^ summarized several case histories where gravelly soil has liquefied in situ, including gravelly soil in two embankment dams. Grain size distributions for some of these soils are shown in Figure 1. Since gravelly soil liquefaction has been documented, more attention has been devoted to assessing the liquefaction potential of such soils. Indeed, many researchers have investigated various aspects of gravel liquefaction in the triaxiai test (Wong&, Banerjee et al7, Evans and Seed*, Hynes^, Seed et al.^, and Evans^). However, gravel-sized particles present unique complications to conventional sampling and laboratory testing techniques. Gravel particles create membrane compliance problems in triaxiai tests, artificially reducing the laboratory liquefaction potential,.resulting in an unconservative assessment of in situ liquefaction potential. Thus, assessing the liquefaction potential of a gravelly soil presents unique challenges to the design engineer. This paper will address how some of the challenges associated with laboratory assessment of liquefaction potential may be overcome. Sand Gravel Rockfdl (1) Shimen Dam (Wang, 1984) " (2) Pence Ranch (Harder, 1988) (3) Whiskey Springs (Harder, 1988; Andrus et al., 1986) (4) _1_ Baihe Dam (Tamura and Lin, 1983) I 10 Grain Size (mm) Figure 1: Grain size curves for gravelly soils that have liquefied. 100 1000
Soil Dynamics and Earthquake Engineering 319 CYCLIC TRIAXIAL TESTING IN LIQUEFACTION ANALYSIS Introduction It is always preferable to sample and test high quality, undisturbed samples from the soil layer of interest. Sampling gravelly soil can be extremely difficult, however, due to lack of cohesion and large particle sizes. Therefore, specimens are typically reconstituted in the laboratory to accurately model in situ conditions, especially density, structure, and stress history (Mulilis et al.^). The specimens are installed in the triaxial cell, subjected to lateral and axial stresses representative of the in situ effective stress, allowed to consolidate, and then subjected to a cyclic deviator stress, a^c, under undrained conditions until the sample liquefies. Several test specimens are subjected to various cyclic stress levels to define a relationship between cyclic stress ratio, Gfo/2G-$c, and number of cycles required to cause liquefaction, N/. Test Program In this paper, a comparative study was made between the results of sluiced and unsluiced gravel specimens. Approximately half the specimens were tested in a conventional, compliant system; and the other half were tested in a specially prepared, low-compliance system prepared by sluicing, or washing sand into the voids of the gravel specimens. This procedure filled the peripheral specimen voids with sand, significantly reducing the amount of membrane penetration that occurred during consolidation, also minimizing membrane compliance effects during undrained loading. Grain size distributions of the gravels and sluicing sands used in this study may be found in Figure 2. Specimens were constructed by dry pluviation following generally accepted procedures. A detailed description of the sluicing procedure and control is presented by Evans and Seed&. The membranes used to confine the 71-mm diameter specimens were manufactured of latex rubber by 3-D Polymers of Gardena, California. They were 69 mm in diameter, 230 mm tall, 0.30 mm thick, with an elastic modulus of about 1330 kpa. Drained hydrostatic compression and rebound tests and undrained cyclic triaxial loading tests were performed on sluiced and unsluiced 71-mm and 3 05-mm diameter specimens composed of uniformly-graded gravel at various relative densities. The results of some of these tests are presented below. Membrane Penetration and Compliance Before any effective confining pressure is applied to the triaxial specimen, the confining membrane is stretched flat over the surface of the specimen, bridging the peripheral sample voids. The membrane will penetrate into the peripheral voids, continuing to penetrate further with each effective pressure increase until no more penetration is possible. Figure 3 shows a photograph of a 71-mm diameter gravel specimen (9.5-mm by 4.75-mm particles) confined with a single membrane. The severe degree of membrane penetration is apparent in this figure.
320 Soil Dynamics and Earthquake Engineering 100 80 60.= Sand, Gravel Rockfill, / San Francisco TT- Dune Sand /Aswan High Dam 9.5-mm by 4.75-mm / 50-mm Maximum Gravel I / Parallel Gradation 40 20 0.1 1 10, 'Aswan High Dam - / 50-mm Maximum /Modified Gradation ^wan High Dam - Rockfill Field Gradation Grain Size (mm) Figure 2: Field and laboratory material gradations. 100 1000 Figure 3: 71-mm diameter gravel triaxial specimen
Soil Dynamics and Earthquake Engineering 321 Unit membrane penetration curves for 71-mm diameter triaxial sand specimens and unsluiced 9.5-mm by 4.75-mm gravel specimens are plotted in Figure 4. Unit membrane penetration in the gravel specimens is significantly greater than values for sand. It may also be seen that about 20% of the unit membrane penetration in two membrane systems is not recovered during unloading. Thus, unit membrane penetration could be overestimated by up to 20% by using the load portion of the curve rather than the unload portion. Lin and Selig^ found no significant difference between load and unload unit membrane penetration for specimens of medium to coarse sand. The sluiced gravel specimens tested in this study exhibited unit membrane penetration values in the range shown for sand in Figure 4 and showed no appreciable difference in behavior during loading versus unloading. The use of load versus unload curves should, therefore, be determined on a case by case basis. When the investigator is in doubt, unit membrane penetration should preferably be determined from unload curves. 20 1.4 1.2 Effective Confining Pressure (kpa) 50 100 150 9.5-mm x 4.75-mm Gravel 71-mm Diameter Specimens 200 I Sand aana (by toy others) otnersj 0.0 Figure 4: Unit membrane penetration curves for gravel (after Evans**).
322 Soil Dynamics and Earthquake Engineering DENSITY CHANGES DUE TO MEMBRANE COMPLIANCE Introduction During undrained cyclic loading, the effective confining pressure is reduced as pore pressure develops and the membrane rebounds from the penetration sites. Water drains from interior voids and migrates to the peripheral voids previously occupied by the membrane as the membrane rebounds. No volume change can occur within the membrane, thus the outward flow of pore water from the interior sample voids to the peripheral voids must be balanced by consolidation of the grain structure (Evans etal.4). Measured Volume Changes Height and total volume changes were measured in hydrostatic compression and rebound tests performed on sluiced and unsluiced specimens. The specimens were assumed to behave isotropically, thus, the skeletal volumetric strain was computed to be equal to three times the axial strain. Volumetric strain due to membrane penetration may be determined by subtracting the skeletal volumetric-vstrain from the total measured volumetric strain. Compression and rebound curves for total and skeletal volumetric strains measured in sluiced and unsluiced gravel specimens are shown in Figure 5. It may be seen that the skeletal volumetric strain measured in the unsluiced specimens is a very small percentage of the total volumetric strain. Axial strains measured during consolidation were essentially identical for both sluiced and unsluiced specimens. Therefore, the sluicing sand does not appear to influence compression of the gravel structure during hydrostatic consolidation. It may also be noted in Figure 5 that only about 0.5% volumetric strain due to membrane penetration occurred in the sluiced specimens over the range of confining pressures shown. 'For unsluiced specimens confined with two membranes, however, about 3.6% volumetric strain occurred due to membrane penetration over the same range of confining pressures. Thus, about 85% of the membrane penetration volume change was eliminated by sluicing the gravel specimen with sand. This reduction in membrane penetration resulted in a corresponding reduction in membrane compliance effects, as will be shown subsequently. Density Changes Density changes in undrained tests caused by membrane compliance may be computed from membrane penetration volume changes measured during drained hydrostatic rebound. Data like that shown in Figure 4 and 5 may be used to compute the total volumetric rebound that would result from a specific change in effective pressure during undrained loading. Volumetric strain values may then be converted to corresponding increases in relative density. Figure 6 shows the increase in relative density of gravel specimens versus residual pore pressure ratios developed in the test. Once residual pore pressure ratios are determined at the end of a test, one can determine the increase in relative density caused by membrane
Soil Dynamics and Earthquake Engineering 323 compliance. Note that Figure 6 is specific to the material and membrane properties tested and is not universally applicable. These data may be determined quickly and easily at the start of each new testing program. However, for the purposes of this paper, it may be seen that the relative density of gravel specimens may increase by up to 20 percentage points or more for some test conditions. For example, if a 25% relative density gravel specimen developed 80% residual pore pressure at failure, the relative density would have increased during the test by about 20 percentage points to 45% as may be seen in Figure 6. Thus, although the intent was to test a specimen with a relative density of about 25%, the relative density gradually increased to 45% due to membrane compliance. The resulting value of cyclic loading resistance is, therefore, erroneously high and unconservative and does not represent actual in situ material properties. Confining Pressure (kpa) 50 100 200 9.5-mm by 4.75-mm Gravel 71-mm Diameter * 50% (1) Skeletal Strain (2) Sluiced, 2 Membranes (3) Unsluiced, 4 Membranes (4) Unsluiced, 2 Membranes (5) Unsluiced, 1 Membrane Note: Skeletal Strain Estimated as Three Times Axial Strain Figure 5: Volumetric strains measured in gravel specimens.
324 Soil Dynamics and Earthquake Engineering Cyclic Loading Resistance Artificial increases in specimen density serve to increase the cyclic loading resistance of the soil. Comparison of the cyclic loading resistance of sluiced and unsluiced 9.5-mm by 4.75-mm gravel at a relative density of 58% is shown in Figure 7 It may be seen that the cyclic loading resistance of the sluiced gravel is considerably lower than that for the unsluiced gravel. In fact, the sluiced specimens only had about 70% of the cyclic loading resistance of the unsluiced specimens. Thus, to account for the effects of membrane compliance in such specimens, only 70% of the cyclic loading resistance determined by laboratory testing should be used as a basis for evaluating prototype performance. Additional comments on the use of sluicing to mitigate compliance effects are provided in the following section. 30.S a. 25 9.5-mm x 4.75-mm Gravel 71-mm Diameter Specimens 2 Membranes E ^ j I II 20 15 3, 10 40 50 60 70 80 90 100 Residual Pore Pressure Ratio Developed in Undrained Triaxial Tests (percent) Figure 6: Increase in relative density caused by residual pore pressure development and membrane compliance in undrained tests (after Evans and Harder^).
Soil Dynamics and Earthquake Engineering 325 0.2* q 9.5-mm x 4.75-mm Watsonville Gravel 71-mm Diameter Specimens 2 Membranes, (^=200 kpa Dr * 58% 1 10 100 Number of Stress Cycles, NC, Causing 5% Double Amplitude Strain Figure 7: Cyclic loading resistance of 71-mm diameter gravel specimens (after Evans et al/) CYCLIC TRIAXIAL TESTING APPLICATION Aswan High Dam The Aswan High Dam is one of the largest rockfill dams in the world impounding one of the largest reservoirs (164 billion cubic meters). The dam was completed in 1970 and is located on the Nile River approximately 700 kilometers upstream of Cairo. It has a total volume of approximately 42 million cubic meters and a maximum height of 111 meters. This dam is one of the few major rockfill dams to have had major portions of its dumped rockfill mass sluiced with a fine dune sand during construction (see Wilson and Marsa!**). Rockfill sluicing was proposed for this project to avoid the need to construct afilterblanket over the alluvial foundation sand deposits. Byfillingthe rockfill voids with sand, it was judged that foundation sands would not be washed upward into the voids of the completed rockfill dam, thus eliminating the need for afilterblanket (Abu-Wafa and Hanna Labib^* 20)
326 Soil Dynamics and Earthquake Engineering A seismic stability investigation was performed for the Aswan High Dam in the mid-1980's by Woodward Clyde Consultants in San Francisco and the late Professor H. Bolton Seed (Cluff and Clufipl). The dam was found to be safe for the maximum probable earthquake. A portion of the project involved assessing the cyclic strength of portions of the zoned rockfill dam. During the seismic stability evaluation, the sluiced rockfill zones were determined to be the most critical in terms of stability. A laboratory testing program was initiated to determine the cyclic loading resistance of the sluiced rockfill (Evans and Seed**). During this testing program, it was noted that gravel triaxial specimens that were sluiced with sand had a smoother specimen-to-membrane contact surface, and thus experienced reduced membrane penetration volume changes during consolidation. If membrane compliance effects could be minimized, then a much more accurate determination of the rockfill's cyclic loading resistance could be made. Aswan High Dam Triaxial Test Results Grain size curves for the Aswan High Dam screened rockfill and the Egyptian dune sand used for sluicing are shown in Figure 2. Particles up to 1000-mm diameter are present in the rockfill. A slightly modified Aswan High Dam gradation was prepared for laboratory testing that was nearly parallel to the field gradation and had a maximum particle size of 50 mm. Undrained, cyclic tests were performed on 305-mm diameter sluiced and unsluiced triaxial specimens of this material. Both Aswan granite gravel sluiced with Egyptian dune sand and Watsonville gravel sluiced with San Francisco dune sand were tested. The results of these tests are shown in Figure 8 where it may be seen that the cyclic loading resistance of the sluiced gravel specimens is considerably lower than the cyclic loading resistance of the unsluiced gravel specimens. Only about 65% of the cyclic stress ratio that resulted in 5% double amplitude strain in 10 stress cycles in the unsluiced gravel specimens was required to cause a corresponding failure in the sluiced gravel specimens. In these tests, the sluiced specimens developed nearly 100% pore pressure ratio at stress levels causing only about 12 % pore pressure ratio in the unsluiced specimens. Thus, compliance effects are.reduced considerably in the sluiced specimens. It is believed that the difference in these cyclic loading resistance values is primarily due to reduced membrane compliance effects in the sluiced specimens. Sluiced gravel specimens were completely constructed of gravel to create the desired particle structure, and then the voids were sluiced with sand. Therefore, the individual gravel particles formed a continuous, stable load carrying structure and the voids between these particles arefilledwith sand. Sand in the gravel voids may contribute slightly to the cyclic loading resistance of the sluiced gravel specimens by preventing rearrangement of the gravel particles. The sand that is sluiced into the gravel specimen voids is in a very loose condition, however, even the very loose sand has greater shearing resistance than the water in the voids of the
Soil Dynamics and Earthquake Engineering 327 unsluiced specimens. Therefore, the sand in the gravel voids may contribute slightly to the cyclic loading resistance of the sluiced gravel specimen if it has any direct effect on loading resistance at all. For the purpose of this analysis, the contribution of the sand to the cyclic loading resistance of the sluiced gravel specimens was considered to be negligible (as described by Evans and Seed^); and the net effect of the sluicing sand was to reduce membrane compliance effects. 0.5 0.4 Aswan High Dam - 50-mm Maximum Modified Gradation 305-mm Diameter Specimens Dr % 42%, (T3c=200kPa 0.3 0.2 0.1 0.0 O - Watsonville Gravel - Unsluiced # - Watsonville Gravel Sluiced with San Francisco Dune Sand A- Aswan High Dam Gravel Sluiced with Egyptian Dune Sand 1 10 100 Number of Stress Cycles, NC, Causing 5% Double Amplitude Strain Figure 8: Effect of sluicing on the cyclic loading resistance of Aswan gravel (after Evans and Harder^). Dam
328 Soil Dynamics and Earthquake Engineering MEMBRANE COMPLIANCE CORRECTION The results of these tests and approximately 100 additional tests on other gravels were used to develop a correction for membrane compliance, shown in Figure 9. This figure was developed for uniformly graded gravels, isotropically consolidated to about 200 kpa in 71-mm and 305-mm triaxial tests, and failing in approximately 10 to 30 stress cycles. The correction shown in the figure for 71-mm diameter specimens represents an average value developed from data presented by Evans and Seed* and Martin et al.22. The noncompliant cyclic loading resistance may be determined by multiplying the compliant, laboratory determined cyclic loading resistance by the proposed correction factor. It should be noted that uniformly graded gravelly soils will experience significant membrane compliance effects while very well-graded gravelly soils will experience lesser membrane compliance effects. Therefore, the results of liquefaction tests performed on very well-graded gravelly soils tested in the triaxial test will require smaller corrections for membrane compliance than those shown in Figure 9. I i a u 1-5 a i s o" II = V, 1.00 0.75 0.50 305-mm Diameter T 71-mm Diameter k c.2 I 0.25 Uniformly Graded Gravel. Triaxial Specimens Q3c=200 kpa N» 10 to 30 cycles 1.0 3.0 10 30 Mean Grain Diameter, Dgo (mm) 100 Figure 9: Correction for membrane compliance effects (after Evans and Harder*).
SUMMARY AND CONCLUSIONS Soil Dynamics and Earthquake Engineering 329 It appears that sluicing may significantly reduce the effects of membrane compliance in undrained, cyclic triaxial tests performed on uniformly-graded gravel specimens. The membrane compliance corrections developed using these materials may represent upper-bound membrane compliance effects for materials tested under similar conditions. Either finer-grained or more wellgraded gravels would be less severely affected by membrane compliance. The results of this investigation suggest that a reasonably accurate assessment of the noncompliant cyclic loading resistance of uniformly-graded gravels may be determined by any of the following methods: Testing sluiced specimens; Testing unsluiced specimens and using only 60% to 70% of the value of cyclic loading resistance determined for isotropically consolidated specimens; or Testing unsluiced specimens and using the correction factor shown in Figure 9. Membrane compliance may cause excessive pore water redistribution during undrained testing, leading to significantly changed density at the end of the test. Volume changes measured during drained hydrostatic rebound may be used to compute changes in specimen density that are expected to occur during undrained cyclic loading. Relative densities of uniformly-graded gravels may increase by 20 percentage points or more during undrained cyclic loading due to membrane compliance. Unit membrane penetration for gravel specimens sluiced with sand was reduced to the range other investigators found for sand specimens. The reader should be reminded that this paper presented membrane compliance effects and corrections for uniformly-graded gravelly soils. These soils undergo the most severe membrane compliance effects and probably represent upper bound membrane compliance effects. More well-graded soils, or soils having smaller maximum particle sizes are anticipated to be less severely affected by membrane compliance. ACKNOWLEDGMENTS Portions of the work described herein were funded by Grant No. MSS-9110153 from the National'Science Foundation. The support of the Foundation is greatly appreciated. The author also acknowledges the support of the late Prof. H. Bolton Seed who inspired, motivated, and reviewed much of this work.
330 Soil Dynamics and Earthquake Engineering APPENDIX I. - REFERENCES 1. Seed, H.B., Lee, K.L. (1966), "Liquefaction of Saturated Sand During Cyclic Loading," JSMFD, ASCE, 92(6), Proceedings Paper 4972. 2. Castro, G. (1975), "Liquefaction and Cyclic Mobility of Saturated Sands," J. of the Geotech. Engrg. Div. (JGED), ASCE, 101(6). 3. Seed, H. B. (1979), "Soil Liquefaction and Cyclic Mobility Evaluation for Level Ground During Earthquakes," Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT2, February, 1979. 4. Evans, M.D., Seed, H.B., and Seed, R.B. (1992), "Membrane Compliance and Liquefaction of Sluiced Gravel Specimens", J. of Geotech. Engrg., ASCE, 118(6). 5. Evans, M.D. and Harder, L.F.(1993), "Liquefaction Potential of Gravelly Soils in Dams", Geotech. Practice in Dam Rehabilitation, Geotech. Engrg. Div./ ASCE Specialty Conf., Raleigh, NC, (1993). 6. Wong, R., Seed, H.B., and Chan, C.K. (1975) "Cyclic Loading Liquefaction of Gravelly Soils," J. of Geotech. Engrg., ASCE, 101(6). 7. Banerjee, N.G., Seed, H.B., Chan, C.K. (1979). "Cyclic Behavior of Dense Coarse-Grained Materials in Relation to the Seismic Stability of Dams," EERC Report No. UCB/EERC-79/J3, Univ. of Calif, Berkeley. 8. Evans, M. D. and Seed H. B. (1987), " Undrained Cyclic Triaxial Testing of Gravels - The Effect of Membrane Compliance", EERC Report No. UCB/EERC-87/08, Univ. of Calif, Berkeley. 9. Hynes, M. E. (1988), "Pore Pressure Generation Characteristics of Gravel Under Undrained Cyclic Loading", Dissertation in Partial Fulfillment of the Degree of Doctor of Philosophy, Univ. of Calif, Berkeley. 10. Seed, R. B., Anwar, H. A. and Nicholson, P. G. (1989) "Elimination of Membrane Compliance Effects-in Undrained Testing of Gravelly Soils", Proc. of the Twelfth Int. Conf. on Soil Mech. and Found. Engrg., Rio de Janeiro, Brazil, August, pp 111-114. 11. Evans, Mark D.(1992), "Density Changes During Undrained Loading - Membrane Compliance", J. of Geotech. Engrg., ASCE, 118(12). 12. Harder, L. F. (1988), "Use of Penetration Tests to Determine the Cyclic Loading Resistance of Gravelly Soil During Earthquake Shaking," Ph.D. Theses, Department of Civil Engineering, University of California, Berkeley. 13. Andrus, R.D., Youd, T.L., and Carter, R.R. (1986), "Geotechnical Evaluation of a Liquefaction Induced Lateral Spread, Thousand Springs Valley Idaho," Proc. of the Twenty-Second Annual Symposium on Engineering Geology and Soils Engineering, Boise, ID, February, 1986. 14. Tamura, C. and Lin, G. (1983), "Damage to Dams During Earthquakes in China and Japan," Report of Japan-China Cooperative Research on Engineering Lessons from Recent Chinese Earthquakes Including the 1976 Tangshan Earthquake (Part I), Edited by Tamura, C., Katayama, T., and Tatsuoka, F., University of Tokyo, November, 1983.
Soil Dynamics and Earthquake Engineering 331 15. Wang, W. (1984), "Earthquake Damages to Earth Dams and Levees in Relation to Soil Liquefaction," Proc. of the International Conference on Case Histories on Geotechnical Engineering, 1984. 16.Mulilis, IP., Seed, H.B., Chan, C.K., Mitchell, IK., and Arulanandan, K. (1977) "Effects of Sample Preparation on Sand Liquefaction," J. of Geotech. Engrg., ASCE, 103(2). 17. Lin, H. and Selig, E. T. (1987), "An Alternative Method for Determining the Membrane Penetration Correction Curve", Geotechnical Testing Journal GTJODJ, Vol. 10, No. 3, Sept., 1987. 19. Abu-Wafa, T., Hanna Labib, A. (1970), "New Techniques Applied To The Design "And Construction of The High Aswan Dam," Proc. of the Tenth Congress on Large Dams; Montreal, Canada, June, 1970. 20. Abu-Wafa, T.; Hanna Labib, A. (1971), "Aswan High Dam: Rockfill built under water," Civil Engineering Magazine, ASCE; August, 1971. 21. Cluff, L.S. and Cluff, IL. (1990), "Seismic Safety of the Aswan High Dam, Egypt", H. Bolton Seed Memorial Symposium Proc., Vol. 2, May 1990, Editor: I M. Duncan, pp 17-42. 18. Wilson, S. D. and Marsal, R. I (1979), "Current Trends in Design and Construction of Embankment Dams," Published by the American Society of Civil Engineers, New York, NY. 22. Martin, G.R., Finn, W.O.L., and Seed, H.B. (1978) "Effects of System Compliance on Liquefaction Tests," J.of Geotech. Engrg., ASCE, 104(4). APPENDIX n. - NOTATION Dj. = relative density 050 = particle diameter for 50% finer by weight NC = number of stress cycles N/ = number of cycles required to cause liquefaction TU = residual pore pressure ratio minor principal stress at consolidation cyclic deviator stress cyclic stress ratio in the triaxial test