soil dilation and shear deformations during liquefaction · soil dilation and shear deformations...

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1238 Proceedings: Fourth International Conference on Case Histories in Geotechnical Engineering, St. Louis, Missouri, March 9-12, 1998. SOIL DILATION AND SHEAR DEFORMATIONS DURING LIQUEFACTION Ahmed· W. Elgamal Univ. of California, San Diego La Jolla. CA-USA 92093 Ricardo Dobry Rensselaer Polytech. Instit. Troy. NY-USA 12180 Ender Parra INTEVEP. SA Venezuela Zhaohui Yang Columbia University NY. NY-USA 10027 ABSTRACT Paper No. 3.24 Recent records of seismic site response have documented a salient liquefaction-induced cyclic shear-deformation mechanism. During liquefaction, these ground accclcralion records have suggested a possible strong innuem:e of soil-skeleton dilation at large cyclic shear strain excursions. Such phases of dilation can result in significant regain in shear stiffness and strength, leading to: i) associated instances of pore-pressure reduction. ii) appearance of spikes in lateral acceleration records (as a direct consequence of the increased shear resistance), and iii) a strong restraining effect on the magnitude of cyclic and accumulated permanent shear strains. As presented in this study, these response effects are also thoroughly documented by a large body of experimental research (mainly employing clean sands and dean non-plastic silts), including centrifuge experiments, shake-table tests, and cyclic laboratory sample tests. A number of efforts to computationally simulate this aspect of soil behavior are presented. In addition, the framework for a newly developed computational model is discussed. KEYWORDS Liquefaction, cyclic-mobility. sand. dynamics, constitutive modeling, earthquake, dilation, soil, plasticity INTRODUCTION Recent records of seismic site response have documented a salient liquefaction-induced shear-deformation mechanism. In particular, these ground acceleration records suggest a possible strong influence of soil dilation at large cyclic shear strain excursions. Such phases of dilation can result in significant regain in shear stiffness and strength, leading to: i) associated instances of reduction, ii) appearance of spikes in lateral acceleration records (as a direct consequence of the increased shear resistance), and most importantly, iii) a strong restraining effect on the magnitude of cyclic and accumulated permanent shear strains. This restraint on shear strain has been noted and referred to as a form of cyclic-mobility in a large number of pioneering liquefaction studies (e.g .. Seed and Lee 1966, Casagrande 1975, Castro 1975, Castro and Poulos 1977. Seed 1979). For the important situations of hiascd strain accumulation due to an initial locked-in shear stress, this pattern of behavior may play a dominant role in dictating the extent of such deformations. Tn addition to the evidence provided by recorded seismic response (which is still scarce), the above mentioned effects are also thoroughly documented by a large body or experimental research (employing clean sands and clean non- plastic silts), including centrifuge experiments, shake-table tests, and cyclic laboratory sample tests. In this paper. a summary is provided of the relevant: i) seismic response case histories, ii) recorded experimental response, and iii) constitutive models developed to address this phenomenon. In addition, the framework of a newly developed computational model is presented and discussed. DILATION In general, at low confinement levels, dense granular soils exhibit a dilative response when subjected to shear loading conditions (Lamhe and Whitman 1969). Under cyclic shear excitation, a sand mass will undergo this coupled shear- dilation process in a manner analogous to that shown in Fig. I (Youd 1977). In a saturated state, the dilation-induced increase in volume is accommodated mainly due to the migration of tluid into the created additional pore-space. The relatively low soil permeability (and/or the relatively fast rate of loading) will hinder this water migration process resulting in: i) an immediate reduction in pore-water pressures and associated increase in effective confinement, and ii) a resulting possible sharp slow-down of the deformation process. This slow-down occurs due to: i) the slow-down in dilation (and consequently in the coupled shear straining process), which is directly proportional to the rate of inward tluid flow, and ii) the instantaneous increase in soil stiffness resulting from the increase in effective confinement (due to pore-pressure Fourth International Conference on Case Histories in Geotechnical Engineering Missouri University of Science and Technology http://ICCHGE1984-2013.mst.edu

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1238

Proceedings: Fourth International Conference on Case Histories in Geotechnical Engineering, St. Louis, Missouri, March 9-12, 1998.

SOIL DILATION AND SHEAR DEFORMATIONS DURING LIQUEFACTION

Ahmed· W. Elgamal Univ. of California, San Diego La Jolla. CA-USA 92093

Ricardo Dobry Rensselaer Polytech. Instit. Troy. NY-USA 12180

Ender Parra INTEVEP. SA Venezuela

Zhaohui Yang Columbia University NY. NY-USA 10027

ABSTRACT Paper No. 3.24

Recent records of seismic site response have documented a salient liquefaction-induced cyclic shear-deformation mechanism. During liquefaction, these ground accclcralion records have suggested a possible strong innuem:e of soil-skeleton dilation at large cyclic shear strain excursions. Such phases of dilation can result in significant regain in shear stiffness and strength, leading to: i) associated instances of pore-pressure reduction. ii) appearance of spikes in lateral acceleration records (as a direct consequence of the increased shear resistance), and iii) a strong restraining effect on the magnitude of cyclic and accumulated permanent shear strains. As presented in this study, these response effects are also thoroughly documented by a large body of experimental research (mainly employing clean sands and dean non-plastic silts), including centrifuge experiments, shake-table tests, and cyclic laboratory sample tests. A number of efforts to computationally simulate this aspect of soil behavior are presented. In addition, the framework for a newly developed computational model is discussed.

KEYWORDS

Liquefaction, cyclic-mobility. sand. dynamics, constitutive modeling, earthquake, dilation, soil, plasticity

INTRODUCTION

Recent records of seismic site response have documented a salient liquefaction-induced shear-deformation mechanism. In particular, these ground acceleration records suggest a possible strong influence of soil dilation at large cyclic shear strain excursions. Such phases of dilation can result in significant regain in shear stiffness and strength, leading to: i) associated instances of pore-pre~sure reduction, ii) appearance of spikes in lateral acceleration records (as a direct consequence of the increased shear resistance), and most importantly, iii) a strong restraining effect on the magnitude of cyclic and accumulated permanent shear strains. This restraint on shear strain has been noted and referred to as a form of cyclic-mobility in a large number of pioneering liquefaction studies (e.g .. Seed and Lee 1966, Casagrande 1975, Castro 1975, Castro and Poulos 1977. Seed 1979). For the important situations of hiascd strain accumulation due to an initial locked-in shear stress, this pattern of behavior may play a dominant role in dictating the extent of such deformations.

Tn addition to the evidence provided by recorded seismic response (which is still scarce), the above mentioned effects are also thoroughly documented by a large body or experimental research (employing clean sands and clean non­plastic silts), including centrifuge experiments, shake-table tests, and cyclic laboratory sample tests. In this paper. a

summary is provided of the relevant: i) seismic response case histories, ii) recorded experimental response, and iii) constitutive models developed to address this phenomenon. In addition, the framework of a newly developed computational model is presented and discussed.

DILATION

In general, at low confinement levels, dense granular soils exhibit a dilative response when subjected to shear loading conditions (Lamhe and Whitman 1969). Under cyclic shear excitation, a sand mass will undergo this coupled shear­dilation process in a manner analogous to that shown in Fig. I (Youd 1977). In a saturated state, the dilation-induced increase in volume is accommodated mainly due to the migration of tluid into the created additional pore-space. The relatively low soil permeability (and/or the relatively fast rate of loading) will hinder this water migration process resulting in: i) an immediate reduction in pore-water pressures and associated increase in effective confinement, and ii) a resulting possible sharp slow-down of the deformation process. This slow-down occurs due to: i) the slow-down in dilation (and consequently in the coupled shear straining process), which is directly proportional to the rate of inward tluid flow, and ii) the instantaneous increase in soil stiffness resulting from the increase in effective confinement (due to pore-pressure Fourth International Conference on Case Histories in Geotechnical Engineering

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reduction). In the following sections, a scl of rccorJcJ responses is shown, in which dilative effects appear to have played a major role.

UNDRAINED CYCLIC LABORATORY TESTS

The mechanism of interest may be illustrated by the response shown in Figures 2 and 3 (Arulmoli eta/. 1992. Taboada and Dobry 1992). This response is representative of a large number of undrained laboratory experiments conducted to study the cyclic behavior of Nevada Sand (with relative densities in the range of about 40%-f,Oo/t, ).

The simple shear test (Fig. 2) shows: i) mcrcasc m shear stiffness and strength at large shear strain excursions, along with an associated increase in effective confinement (reduction in excess pore-pressure.) and ii) a cycle-by-cycle degradation in !-;trcngth as manifeslcJ by Lhe occurrence of increasingly larger strain excursions, for the same level of applied shear stress. It may be observed that as the shear strain increases, the sand skeleton is forced into dilation (soil behavior changes from contractive to dilative along the phase transformation envelope of shear strength).

The triaxial test (Fig. 3) shows the situation when an existing driving shear stress is present (Dobry et a!. 1995). This existing stress forces the strain to occur in a biased preferred direction, on a cycle by cycle basis (Fig. 3). In these cycles, the dilation-induced increase 111 strength (shear stress) during liquefaction is seen to evolve such that a net finite increment of permanent (down-slope) shear strain occurs. The magnitude of such increments determines the total accumulated permanent deformation.

In summary, during liquefaction it may be noted that: i) the regain in shear strength (appearance of stress spike) follows a phase of softer soil response that results in yielding at very low shear strength, ii) this regain may virtually arrest further straining during a given cycle, and iii) in the presence of a driving shear .'itress, cyclic loading may result in a pattern of cycle-by-cycle accumulation of permanent strain increments, each ending with a stress spike.

Under conditions of dynamic excitation, a shear stress spike may be also manifested in the appearance or a corresponding spike in a recorded acceleration history. This was clearly manifested (Fig. 4) in the data of Yoshimi and Oh-oka (1975), who employed a dynamic shear testing technique (tests on fine sand from Bandaijima, Niigata at a relative density of about 37%).

Therefore, during liquefaction of a level ground subjected to cycles of uniform base excitation, a recorded acceleration history may display (Fig. 4a): i) a few acceleration spikes around the onset of liquefaction (ru ::: 1.0), anJ ii) a possible disappearance of spikes thereafter. The spikes may disappear due to: i) further softening of the soil, thus allowing for larger cyclic deformations Lo occur without reaching a high enough

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strain to cause dilation (and a corresponding stress or acceleration spike), and/or ii) reduction in cyclic shear strains due to a base isolation mechanism created by subsequent liquefaction of underlying soil layers. In the level ground case, the spikes will be equally visible on both sides of the recorded acceleration response (with uniform cycles of excitation). When a driving shear stress is present (e.g., near the free face of a slope, behind a yielding retaining wall, or along a mildly inclined ground surface), the biased (down-slope) cyclic strains will generally he associated with larger dominant spikes (compared to the up-slope direction). This will lead to an asymmetric pattern of acceleration, which might persist during the low shaking tail end of an earthquake, denoting the continued accumulation of large cyclic deformations (lateral spreading). In this regard, the low shaking phase may allow for reversal of loading direction, and re-accumulation of an additional strain increment during a subsequent cycle.

The response depiclcd by Figure 2 has been documented in laboratory tests for numerous sands. Figure 5 (Seed and Lee 1966) shows two typical stress-strain loops for samples of loose and dense sand during liquefaction. where the influence of dilatancy is clearly manifested. Lee and Schofield (1988) showed a cycle of sand response (Fig. 6) as documented by Tatsooka (1972) in triaxial test investigations. Ishihara (1985) presented stress controlled cyclic torsion shear test results that constitute nne of the prime examples of dilative soil response during liquefaction (Fig. 7). Additional tests have been also reported hy (Figs. 8-12) Tatsuoka eta/. (1986), Yamashita et a/. (1989), Hyodo eta/. (1991), Kawakami eta/. (1994), Shamoto eta/. (1997) and Zhang eta/. (1997) using Toyoura sand at a relative density in the range of about 50% to 100%. Response of the Masado soil (high quality relatively undisturbed samples) that liquefied at Port Island during the Hyogo-kcn Nambu earthquake (Soils and Foundations 1996) is also seen (Fig. 13) to demonstrate a similar mechanism (Hatanaka et al. 1997). This mechanism or increase in soil stiffness at large strains, might partially account for the observation (Scott 1997) that most dock movement at Port Island resulled from the first earthquake acceleration peaks, not liquefaction.

SHAKE TABLE STUDIES

Dilative soil behavior has been frequently observed in shake table studies. Most of these studies were conducted in Japan. Using Toyoura sand with relative densities in the range of 68%-79t;;:_,, a series of such lcsts was conducted by Koga and Matsuo ( 1990). A sample or the recorded accelerations and pore pressures is shown in Fig. 14.

Using a shear beam approach, Koga and Matsuo (1990) developed an extremely effective 1-dirncnsional simple procedure to calculate shear stress and shear strain histories, directly from the recorded accelerations (Fig. 14b). The calculated slrcss-strain histories are shown in Fig. 15. It is noted here that the observed acceleration spikes (Fig. 14) correspond to instanls of reduction in excess pore pressure,

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and are manifested as an increase in shear stress at large shear strain amplitudes (Fig. 15). The calculated stress-strain histories are quite similar in character to those observed in cyclic laboratory tests (e.g., Fig. 2).

Acceleration spikes similar to those observed hy Koga and Matsuo (1990) are often observed in shake table tests (Fig. 16) such as those conducted by Okumura Co. (Ishihara et al. 1991). In these tests, loose Sengenyama sand was used at a relative density of 40%. Sasaki et a/. ( !991. 1992) report a series of tests (Figs. 17-19) in which the liquefiable layer was a loose mountain sand (Mt. Sengen-yama sand) built by an underwater drop method. In these tests, the characteristics of dilative soil response are evident from the recorded acceleration spikes and the corresponding ace-lateral displacement response (Fig. 19b). Towhata and Toyota (1994) studied the response of a pipe in liquefied Toyoura sand and reported a similar response mechanism (Fig. l9c). Additional shake table tests were also conducted (Shamoto eta!. 1996) using Toyoura sand at a relative density of 53% (Fig. 20). The reported results also demonstrate the above-described aspect of dilatant soil response (in the form of response acceleration spikes).

IN-SITU SEISMIC RESPONSE

The Wildlife Refuge (California, USA): This site is located on the West Side of the Alamo River in Imperial County, southern California. Evidence of liquefaction was observed at or near the site following the 1930, 1950, 1957, 1979, and 1981 Imperial Valley earthquakes (Youd and Wieczorek 1984 ), These observations triggered an interest in the site, which was instrumented in 1982, in an insightful effort (Yuud and Wieczorek 19t<4) by the United States Geological Survey (USGS). In 1987, the site was shaken hy two main earthquakes (Holzer et al. 19S9), including the Superstition Hills earthquake (Mw :::: 6.6), whil:h caused a sharp increase in recorded pore-water pressure. In addition, subsequent field investigations showed evidence of site liquefaction and ground fissures. The surface records displayed peculiar acceleration spikes (Holzer et al. 1989) associated with simultaneous instants of excess pore-pressure drop (Fig. 21 ).

Using the simple approach of Koga and Matsuo (1990), the site lateral seismic response during liquefaction was inferred from the stress-strain and effective-path histories (Pigs. 22 and 23) of the Superstition Hills earthquake (Zeghal and Elgamal 1994). At low effective confining pressures (high excess pore pressures), the effective stress-path clearly exhibited a reversal of behavior from contractive to dilative (Pig. 22). as the line of phase transformation was approa(.'hcd (National Research Council 1985). Such a mechanism is a consequence of soil dilation at large strain excursions, resulting in associated instantaneous pore-pressure drops as documented by the laboratory tests (Fig. 22b) ofVucetic and Dobry (1988).

Aomori Harbor (Japan): Towhata et a/. (1996) presented (Fig. 24) a ground surface lateral acceleration history recorded

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at Aomori Harbor during the 1968 Tokatchi-Oki earthquake. This history was recorded at a location where liquefaction of subsoil was observed. In fact, the Wildlife site acceleration record (Pig. 21) shows a pattern of spikes, which is quite similar to that of this Aomori Harbor record (Fig. 24). Thus, a shear stress-strain response of similar characteristics to that at Wildlife might have occurred at Aomori Harbor during this earthquake.

Port Island (Kobe, Japan): Port Island is an artificial (reclaimed) island located on the west-south side of Kobe, Japan. In the phase completed by 1981, 436 ha were reclaimed by bottom dumping from barges (Nakakita and Watanabe 19~1). Soil (Fig. 13) in the artificial reclaimed layer (ORourke 1995, Sitar 1995, Soils and Foundations 1996) consisted of decomposed weathered granite fill (Masado soil mined from the nearby Rokko mountains) with grain sizes ranging from gravel and cobble-sized particles, to fine sand (2 mm mean particle size, wirh silt-sized particles or smaller of less than 10% hy weight).

A downhole accelerometer array was installed at the Northwest corner of Port Island in August 1991(1wasaki 1995). The array consisted of triaxial accelerometers located at the surface, 16 m, 32 m, and 83 m depths. This array documented the observed widespread liquefaction of reclaimed ground during the 1995 Hyogoken-Nambu earthquake. Using the recorded downhole accelerations, the corresponding one-dimensional shear stress-strain response was evaluated (Elgamal et a/. 1995, 1996a). At shallow depths, the stress-strain histories indicated (Fig. 25): (I) a noticeable reduction in stiffness with slight but visible signs of shear strain hardening at elevation 24m, and (2) an abrupt sharp loss of stillness and reduction of yield strength ncar the surface at Sm depth. It is noted here that no clear signs of permanent lateral deformations were observed at the array site.

Kushiro Port (Japan): lai et a/. ( 1995) presented downhole accelerations recorded during the 1993 Kushiro-oki earthquake. The downhole array is located in Kushiro port. Upper layers at this site included saturated sand with shear wave velocities of 250 m/scc. The recorded accelerations showed clear spikes at ground surface and at 2 m depth (Fig. 26). These spikes were attributed to sand dilation, and were successfully ~imulated by a noteworthy computational model (Fig. 27) as will be discussed below. In this case, acceleration spikes do not necessarily denote ru values approaching or equal to 1.0, but may nevertheless be associated with significant increas-e in excess pore-water pressure.

CENTRlHIGE EXPERIMENTS

Lee and Schofield ( 198S) reported the occurrence of spiky acceleration response ncar the slopes of saturated model sand embankments (Figs. 28) The soil was Leighton Buzzard sand, which was in a dense state during this observed spiky response. The spikes were appropriately attributed to an underlying dilative mechanism as suggested qualitatively -for

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instance· by the triaxial testing results (Fig. 6) of Tatsuoka (1972).

A large body of centrifuge experiments using Nevada Sand (Arulmoli et a/. 1992. Taboada and Dobry 1992) has also shown clear evidence of cyclic dilative soil response effects. Many of these experiments are described in (Arulanandan and Scott 1993. 1994) as part of the YELACS project (Taboada and Dobry 1993. Scott eta/. 1993. Wilson eta/. 1993. Dobry and Taboada 1994. Whitman and Ting 1994). Relative density of the Nevada sand varied within the range of about 40% to 75% in these tests. A representative set of recorded accelerations is shown in Figs. 29-31. In addition to YELACS. a number of RPI Ph.D_ theses contain extensive evidence of this response (e.g .. Liu 1992. Taboada 1995. Adalier 1996, Abdoun 1997). A large number of studies (mostly using Nevada Sand) conducted at the University of California, Davis (e.g .• Divis et al. 1996. Arulanandan eta/. 1977. Balakrishnan et aL 1997, Wilson et aL 1997) also show a similar response (e.g., Fig. 32).

The basic nature of associated shear stress-strain response is clearly manifested by bat:k-calculated shear stress-strain lateral-deformation histories as reported hy Dohry et al. (1995) and Elgamal et al. (1996b). These histories (Fig. 33) are based on the recorded acceleration and displacement responses of infinite mild-slope dynamic simulations in a set of pioneering tests conducted by Taboada (1995), and duplicated by Scott et al. ( 1993).

COMPUTATIONAL MODELS

A number of t:omputaLional models have become available recently to simulate the processes associated with sand dilation Juring liquefaction (Prevost 1985. Pastor and Zienkicwicz 1986, Matsuoka and Sakakibara ( 1987), Nishi and Kanatani 1990, Iai 1991, Anandaraph 1993, Aubry eta/. I 993, Bardet et a/. 1993, Byrne and Mcintyre 1994, Proubet 1991. Li 1990, 1993, Kimura eta/. 1993, Tobita and Yoshida 1995 ). The general response characteristics of these models may be inferred from Figures 34-39. Many of the essential features of cyclic mobility have been successfully modeled by (lai 1991 ), under undrained loading conditions as shown by the computed acceleration during the 1993 Kushiro-oki earthquake (Fig. 27).

At this point, few results have been published to show the performance of these constitutive models for the important case of an acting driving shear stress (e.g., lateral spreading situation, near and below slopes, the retaining wall prohlcm). Such situations demand a high degree of control over accumulated cycle by cycle deformations (Fig. 3) as depicted in Fig. 40 (Tateishi ct al. 1995).

Recently, a simple displacement-controlled sliding-block approach was proposed to simulate the dilatant stick-slip process shown in J-ligs. 3 and 40b. This new simplified

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approach (Fig. 41) is described in Abdoun (1994), Abdoun and Elgamal (1995), and Taboada eta/. ( 1996).

NEW CONSTITUTIVE MODEL

A new soil con~titutive model was developed (Parra 1996), based on the original framework of plasticity theory for frictional cohesionlcss soils presented by Prevost (1985). The main purpose of this model is to simulate the characteristics of soil response described ahove, including the biased accumulation of cyclic shear strains due to the presence of a locked-in driving shear stress. A Biot-type theory for solid­fluid coupled analyses after the works of Chan (1988) and Zienkiewicz et a!. (1990) was also numerically implemented for that purpose (Ragheb 1994, Parra 1996). This coupled formulation and the developed constitutive model were implemented in a general purpose 2-D (plane strain and axisymmetric) finite element program (see Appendix 1). A typical response of this constitutive model is shown in Figs. 22a and 42. The model was developed and thoroughly calibrated by laboratory and centrifuge tests on Nevada Sand (Parra 1996). It was also calibrated and employed to simulate (Fig. 43) the recorded Port Island downhole array response during the 1995 Hyogo-kcn Nambu, Kobe earthquake (Elgamal eta/. 1996b).

SUMMARY AND CONCLUSIONS

During liquefaction (r11 approaching 1.0) of clean sands, the phenomenon or regain in shear strength at large shear-strain excursions (also known as a form of cyclic-mobility) may be of paramount importance in restricting the extent of shear lateral deformation due to seismic excitation. Consequently, constitutive models that capture this phenomenon are essential in analyse:-. of such an important soil response mechanism. These models must reliably model the cycle-by-cycle biased accumulation of permanent deformations, especially in the presence of an imposed locked-in driving shear stress. Currently, further quantification of the underlying response mechanisms is underway through laboratory, shake-table, and centrifuge experiments (e.g., effects of extent of load reversal, number of load cycles. level of driving shear strength, and relative density of soil on magnitude of accumulated shear strain).

In this paper, a review of reported cyclic-mobility response was presented, as documented by experiments and case histories. Efforts towards computational simulation of this response were also surveyed.

Under conditions of an imposed driving shear stress, the tendency for soil dilation during liquefaction appears to have a dominant impact on the magnitude of seismically-induced accumulated shear deformations in clean sands (and possibly clean non-plastic silts). This applies to most situations of relative density encountered in practice (e.g .. relative density Dr > 3Ylr> ). In this regard, residual strength during

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liquefaction (before the onsel of dilation and associated regain in shear strength) may only play a relatively minor role. This residual strength on the other hand, might play a more significant role for sandy/silty soils with or vvithout stratification (e.g., sands mixed with sills and days). Research in this area is needed to clarify and quantify the associated deformation mechanisms in such commonly em;ountered natural and constructed soil formations.

ACKNOWLEDGMENTS

The research reported herein was supported by the United States Geological Survey (grant No. 1434-HQ-97-GR-03070), INTEVEP, SA, Venezuela, and the National Science Foundation (grant No. MSS-9057388). This support is gratefully acknowledged. The employed Port Island downhole acceleration data were provided by the Committee of Earthquake Observation and Research in the Kansai Area (CEORKA), Japan, with the help of Dr. Y. Iwasaki.

APPENDIX I

Description of New Computational Model

Soil was modeled as a two-phase material using the Biot ( 1962) formulation for porous media. This formulation was incorporated in a general purpose 2-D finite clement program (Raghcb 1994, Parra 1996) using the u-p formulation (in which displacement of the soil skeleton, u, and pore pressures, p, arc the unknowns) suggested by ZicnkicwicL et al. (1990). The computational scheme follows the methodology of Chan (1988), which is based on the following assumptions: small deformations and rotations, density of the solid and t1uid is constant in both time and space, porosity is locally homogeneous and constant with time, incompressibility of the soil grains, and equal accelerations for the solid and fluid phases.

Therefore, the general coupled formulation after the spatial discreti~:ation and Galerkin approximation ts expressed as follows:

Mii+ fBr ~r'dl:l-Qp -f' = 0 (Ia) n

Gii+Qrti+Hp+Sp-f" =O ................... (lbJ

Where M is the mass matrix, 8 is the strain-displacement

matrix, a' is the effective stress vector, Q is the di.s~.:rete gradient operator coupling the solid and fluid phases, u is the displacement vector, p is the pore pressure ve(;tor, G is the dynamic seepage force matrix, H is the permeability matrix, S

is the compressibility matrix, and r-'' and f f' are the prescribed boundary conditions for solid and fluid phase respectively. A superposed dot denotes time derivative. Viscous damping is added for the solid phase in the form of Rayleigh damping ( C =aM+ jJK ), where K is the initial

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stiffness matrix). Pur earthquake loading problems, G IS

usually neglected so that symmetry of the global matrix is attained.

Equation l is integrated in time using a simple single step predictor multi-corrector scheme of the Newmark type (Katona and Zicnkicwicz 1985 ), with an automatic time stepping split algorithm, incorporated to improve the rate of convergence. The prcdir..:tor is calculated using the initial stiffness matrix method, as the high degree of non­associativity shown in the behavior of the solid phase for granular materials, produces a non-symmetric tangent stiffness matrix that requires a non-symmetric matrix solver. Experience hased on analyses of non-associative plasticity shows that the initial stiffness method performs reasonably well (Chan 1988).

The second term in Eq. la is defined by the soil constitutive model. In this study, a new model is developed and used, based on the original work on plasticity theory for frictional cohesionless soils (Prevost 1985). The new model (Parra 1996) provides nexihility in modeling the cyclic mobility phenomenon. Special attention is given to the way the deviatoric-volumetric strain coupling occurs under cyclic loading, especially for loading-unloading-reloading situations above the phase transformation line, and ncar the liquefaction condition ( p' = 0 condition).

The constitutive equation is written in incremental form as follows (Prevost 1985):

a=E:(>J-i:"J (2)

Where if is the rate of effective stress tensor, E is the rate of

deformation tensor, f:P is the plastic rate of deformation tensor, and E is the isotropic elastic coefficient fourth order tensor. In this equation the superposed dot denotes a material derivative. The plastic rate of deformation tensor is defined

by: t 11 ~ P ( L}, where P is a symmetric second-order tensor

which defines the direction of plastic deformation in stress, L

is the plastic loading function; and the symbol ( } denotes the

McCauley's brackets (viz., L~O if L<O). Otherwise, L is defined as: L = Q: 0' I 1/' where H' is the plastic modulus, and Q is a symmetric second-order tensor which defines, in stress space, the direction of the outer normal to the yield

surface (Q~ VJ /IIVJII ).

The yield function, f, representing the states of stress for which plastic tlow occurs, is selected as a family of nested cone surfaces connected at the apex as follows (Lacy 1986):

3 ' ' 1=-(s-pa):(s-pa)-m"p- =0 2

where s ~a- pb is the dcvialOric.: stress tensor, p ~ p -a with p and a representing the effective mean normal stress and the attraction at the apex (given by the amount of residual shear strength) respectively, a is the kinematic deviatoric tensor Fourth International Conference on Case Histories in Geotechnical Engineering

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defining the coordinates of the yield surface, and m 1s a material parameter to dcscrihe the friction angle ¢ .

The flow rule is chosen so that the deviatoric component of flow P' = Q' (associative flow rule in the deviatoric plane), and the volumetric component P"' gives the desired amount of dilation or contraction in accordance with laboratory or t1eld observations. Consequently, P"' defines the degree of non-associativity of the flow rule and is given as follows (Parra 1996 ):

3P' (1]/f[)' -II" (;: ) (1]11]) 2 +I d ~-~

Where T7 = ((3/2)s : s) I 12 lp is effective stress ratio, rr is a

material parameter defining the stress ratio at the phase

transformation (PT) line, If' d is a dilation function scaling the

amount of dilation confining pressure

;J = f(t:j -e;')

or contraction depending on the level of and cumulative plastic deformation, and

is an effective dilation function triggered

at the point when the cumulative plastic deformation in the

dilative zone£j. reaches a predefined yielding level E;1

• The

sign of (ry/f[)2 -I dictates dilation or contraction. If

negative, the stress point lies below the PT line and contraction takes place. On the other hand, when the sign is positive the stress point lies above the PT line and dilation occurs. However, contrary to the original Prevost ( 1985) formulation, contraction above the PT line is performed towards the point where dilation started, which acts as a memory for the dilation-contraction condition. At the point of initial liquefaction or p' = 0 only dilation i.s allowed and

upon contraction P"' is set equal to zero.

A purely deviatoric kinematic rule is chosen according to: pU = bJ.l, Where J.l is a deviatoric tensor defining the direction

of translation (Lacy 1986) and b is the amount of translation dictated by the consistency condition.

The integration of the constitutive equations is performed using a stress point algorithm based upon the radial return method in the deviatoric plane (Lacy 1986), with an automatic strain stepping split algorithm, which guarantees convcrgcm:e and accuracy at all levels of strain (Parra 1996).

REFERENCES

Abdoun, T. [19941. "Prediction of Soil Deformation Due to Seismically Induced Liquefaction," MS Thesis, Dept. of Civil Engineering, Rensselaer Polytechnic Institute, Troy, NY.

Abdoun, T. and Elgamal, A. -W. 119951. "Predtction of Seismically-Induced Lateral Deformation During Soil Liquefaction," Eleventh African Regional Conference on Soil Mechanics and Foundation Engineering, International Society

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for Soil Mechanics and Foundation Engineering, Cairo, Egypt, Dec. 11-15, 1995.

Abdoun, T. [1997j. "Modeling of Seismically Induced Lateral Spreading of Multi-Layered Soil and Its Effect on Pile Foundations," Ph.D. Thesis, Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy, NY.

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1246

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Fourth International Conference on Case Histories in Geotechnical Engineering Missouri University of Science and Technology http://ICCHGE1984-2013.mst.edu

A. PARTICULATE GROUP CONTAINING A HOLE

£. l.ARG£, CLOCKWISC: STRAIN CREATES NEW. SWALL. HOLES

B. SWALL. COUNTER· CUX:KWIS[ STI<AIN COLLAPS~ HOLE

,(1

r. AITl:H TI:HMINATION OF .STH.AINING MANY SWAl.L HOLES REMAIN

C. LAHG£ STRAIN CREA Tf.S Nf.W, SWAl.L HOLES I)U£ TO OILATt:NCY

,(1

G. JtENEW[U CUlCKWI5£ STRAIN CAUSES RtNI:WEO OILATENCY

'\,

1247

Figure I. Diagrammatic cross section of particulate group showing packing changes that occur during cyclic loading (Youd 1977).

a) Stress-Strain curve

-25 -20 -15 -10 -5 0 5

-10 0

Shear Strain (%)

20 30 40 50 60 Mean Effective Stress (kPa)

10 15

b) Stress Path

70 80

Figure 2. Stress-strain curve and stress-path for Nevada Sand with Dr=60% obtained from undrained cyclic simple shear (CSS) test (Arulmoli eta/. 1992).

20

90 1Ditial ~ _. ofJ~•21.5kh

~·,c---------+,--------~,~-------,~,---------'., AD!.ni:D {~)

Figure 3a. Stress-strain and excess-pore-pressure histories during an undrained stress-controlled cyclic triaxial test of Nevada Sand (D.=40%) with an imposed static (initial) dcviatoric stress (Arulmoli eta/. 1992). Fourth International Conference on Case Histories in Geotechnical Engineering

Missouri University of Science and Technology http://ICCHGE1984-2013.mst.edu

.. • •o .. JO • ~

Neve.da Sand (Dr- 40.6 7.}

"' 20 :! 10 • .. 0 -• •o • !!. •O

• • 20 . 0 ~

• -20 • 100 0 eo 7 • 00

"' •o • 20 • w 0 0 2 4 6 a 10 12

Time (sec) ~ • 60 0. 50 "' -~ 40 ~ • 30 • ~ 0 20 -~ • 10 0 ~

• 0 > ~-10

lnit.ial devi.at.oric •treu oHsel • 16.\) KPa -20

0 10 20 30 40 Axial strain (7.)

Figure 3b. Sttess, strain and excess pore pressure histories during an undrained stress-controlled cyclic triaxial test of Nevada sand (Dr= 39. I%) with an imposed stalic (initial) deviatoric stress (Taboada and Dobry, 1992).

2>

-) 1

Shea.r St:-a.ln (pcrcwt.)

7 100

~ • 80 .. • • 00 El e; 40 .. I 20 -J

0

.:. -2Q

Sbe.a.r St.rain (puce..nL)

Figure 3c. Stress, strain and excess pore pressure histories during an undrained stress-controlled cyclic triaxial test of Bonnie silt with an imposed static (initial) deviatoric stress (Arulmoli eta!. I 992).

0

ot bottom

Aece\erotion (;ot)

cf top

Sheer mcin , .. , Shear stre-ss

a1 bottom (kljl/'"'2 )

EJ:cess por-e pressure

(1-lg/c;m')

•oo 0

200

I248

o;". 0..9!1 k;/m\11

h•t.4,1g/cm1

Dr•o42%

Figure 4a. Typical oscillograph records for the completely reversed shear tests (Yoshimi and Oh-oka I 975).

R•41% dz'o•0.97kgkm2

Shear stress 02

(kij!/cm2l 01 0

0.

1.0 Excess

pore pressure ( kg/r;;m2) 0

0

Sheor stroin 10 ( %)

20

1·~- r~ u VC1*--... , b -1 . -· . -.:~r-~~· ·n · i · 1 ~ - :. ~~_!,o-:·'!: I 811 Jj· f-h t::;: ; :: .. ~h~ r! l r ID~- 'I ; :rr:~r I"!Tp_;

C - • • - Np • ~ '(i ~v· • i j ' . - . -W:~ -1-;.T-· _} 11 I ..J... I . ' : ! ' I t

. _j_ . till I 1 li 'J ! :t : ·rl:! . ~L ... ~J. ' . .· ~lJILII ;·-·r - ~+ . ·- "-- --lJ--

. -. ... -. . "f- - . f-:'+ -; .. + =-r ·--.. . .. . ;:·.··:+··.";!'' ... .,

- ' - . .. .. . ' ... " -~ . I .. '"' I sec

Figure 4b. Typical oscillograph records for the partially reversed shear tests (Yoshimi and Oh-oka I975).

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I. !

I I

';;.. ._ .. ---;---,---__...;.--,--"1 l J, -.. -l :~ j·;_-i_- t' . '--.:. _, -I' I I I . ' . ·-1 :-~ t -;--+ r-11H----1

, I I I.

I I

i t--'---<---:---;--7--f ----­I

Figure 5. Hysteresis curves for cyclic loading test on Sacramento River Sand (Seed and Lee 1966).

30

20

, ·5

~

E 1 c J,'

C> -": <> ~

05 ~

~ ~

" " " 0·0 "' "'

-0 5

-1·0

- 2·0 L.:...J:---'::-7-~---''--..J -~ -2 0 2 4 6

A.;Jt:ial slrain ,-.. : %

Figure 6. Variation in shear stress with axial strain reported by Tatsuoka 1972 (after Lee and Schofi1ed 1988).

1249

• ~ ..-..:.- \nt

T..y'cr • on1 0.•75., • cr,.,.uv,a fyJ ,.._ loG"CC

"' "'

.,.

T_iol'ool_. ,...,

't.oi/~•0.7H , o.o75'1o.Ko•'LO a;;• •• 0!/""' ,,,. ... _ ICI"d

b)

5t,...,. perth

a)

---

Figure 7. Stress-strain curve and stress path in cyclic torsional test on dense sand (Ishihara 1985).

--·-~

• r ;, ~ ! •

'

' ..

- - I - -

"'c"' • " • ~'.!..,.-.l~ rl . ~· ,. .. ,. , .... ,,,

en ",. ..

"-~ / __ uu ....-?.

· .··Wf -~ .. . l .

~ . '1, ... ;

__,.. .. ,_I--· t:"""l-C",'•t.c:'l•fll•..., - Cl :

C', ·•l.!l(l.f"ll .... l

, C.O C.J t.O .. ., • ' ~ .. ·• • •. _t•PIC'II\I~ ~"':_~'"':- ll~!~l.p'l• .. :••"ll ~;

·;... ..,.,

.

- ...

---

'

Figure 8a. Stress path and stress-strain hysteresis loop in tests by H. Kato (Tatsuoka et al. 1986).

.

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·, ·~ 0.2 ... "' • 0.0

p' '"g1'~~) . c~ f.,)

Figure 8b. Stress path and stress-strain hysteresis loop in tests by M. Okamoto, T. Torii andY Yamada (Tatsuoka et a/. 1986).

( . )

.l.olal IVllft Ia {:)

(.,

. :, uo

""

(., Figure 9. Relationship between deviatoric stress and axial strain, a) reversal, b) Intermediate, c) no reversal (Hyodo et a/. 1991).

1250

tl

""' E l/1 " "" tl "' ..!!. .., .. ., , ., ., ~ ... , ti ~ ... , .. .,

.c; -a II U)

-tl ·II ·II ... -II ·II , II II " II II

Shear strain y (%)

Figure 10. Relationship between shear stress and shear strain (Dr=53%, tlcr;=0.2, cr,'= l.Okgf/cm2

, f=O.IHz (Kawakami et a/. 1994).

.. 20 (a) Cy::licJ~di,..~_.fl.,-5ith

0. ioili.ll ~taclk:lll

"'-.. 10

.,; M 0 ~ Dr • 75" M ~ 1=0.01Hz m ·10 m a',•JOOkPa "' ' "' -- sial~ at zero •"-ctivt

·20 CQilrinit'JQ 5tress

-· -6 -· ·2 0 2 4 6 8

Shear strain, y ('Yo)

20 (b) .. 0. "'- 10 .. .,; M

~

" - UncJrainet! COndiliOn m ·1 0 Cyclic /or.sion lttst m r. Toyo~.o~ta und

"' ·20

0 10 20 30 40 50

Mean effectWe stress, U:, (I<Pa)

Figure II. Post liquefaction shear stress-strain response (Shamoto et al. 1997).

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~ "-1 ... :i ~

!

~ 20

10

0

-2 0

0 10 20 >O 40 50

Mean etfeetlve stre:ss, a: (kPa)

' I ' ' (b) -- BefG-r• inil,.l

Jiq..oel•ct'otl -- All~ irtJiial .J· f,quef•cl;on

--f} II V· Dr= 75%

II II II 1/ d'.=lOOt-.Pa

Cyclic rorsion resl Undrai!led condition

' 0 2 • 6 8

Shear strait\, y (%)

Figure 12a. Effective stress-path and stress-strain hysteresis observed in a cyclic undrained torsion test on saturated sand (Zhang eta!. 1997).

30

-;;- {a} Pattem-1

"-20

r:t.=lOOkh

"' .. 10 Dr ... 75%

ti 0 ~ ~ -1 0 ---- Befor~ initial • • liqUflfBction t5 -20 --Afler inflial

lique/Bction

-30 -6 -4 -2 0 2 4 6

Shear strain, y (%)

40

-;;- (b) Panem-2 "~

"- 20 u.-.:lOOl.Pa

"' .. Dr• 75%

,; w 0 ~ ~ -- Before initial • jjquefllCtiOf'l • ·20 .c

U) -- Ah~r initi•l liqueflJction

·40 ·6 -4 ·2 0 2 4 6

ShEar strain, y (%)

Figure I2b. Shear stress~strain relationship observed in undrained torsion tests for two patterns of irregular cyclic loading (Zhang eta!. 1997).

1251

100 (a)

--. !U a. ~ ~

II) \1) <ll .... - 0 II)

.... 0 -rcr ·-> Ill 0

-1 00 l__---'---L___---'----'

-10 0 10 Axial strain (%)

100~---.----.-----.----.

(b)

\1) 1,/) <ll

~ O~Ud~----r-~----------------1 .... 0 -rcr ·-> <ll 0

-1 00 l__---'---L___---'-----'

0 100 200 Effective mean principal stress (kPa)

Figure 13. Stress-strain relationship and stress path for undrained cyclic triaxial test on gravely fill soil (Hatanaka et al. 1997).

7'1

I

,1.:5• .,. .,. • ~J .

}'&'

•• • ,r.ctf'lt'I'CJIT'If"if"f • P,v.,P. tr.a.1'50..1tlff'

,. Si"ot"' lolrAin 0"'-'9" f t'S~Attrnff'it ,...., ...

(trit in c.m)

Figure 14a. Model configuration and Lransducer location (Koga and Matsuo 1990).

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• ~ .. • • • ~ .. ..

s TJDc (~cc.:)

Figure 14b. Recorded time histories for base excitation of 220 gal (Koga and Matsuo 1990).

10

.,'r.,~.~~~ •• ~.~ •••••• ,, ... ~.~.,~.h~ .• ~.~ .• ~~~-~.>r.~~~"'~~~~l 1:1 location ~ P12 ~

."). -- -- ~--- ----------- ..... •• I

• ~ ~ • " • 0 • • " ~ . .-1 • ~ -:5 0 5

She•r th·•in : "r /U

0 ~

~ . : 0 1----""':1:~ . • " ~ . " . • ~ •

Shear strain : "'1\)

Figure 15. Calculated shear stress-strain histories (Koga and Matsuo 1990).

1252

r_ .. ·-

Figure 16. Time histories of acceleration and lateral deformations (Ishihara et al. 1991 ) .

, c- •CFtCP'\21 ··c ;() f., ...... ""." " ilr·" ;;;;

::l 5~ ••

<l OLI --~~~~----------------' ' tr -~L I I I I I I I I I I t I I 1 I I I I I I I I It I I I 1 It I ~~~P'o .. s ~ ! 1 ~ : s ~~ 2! •.

eco!~

CJ •ooL '' u o! ...... :1llllq 11111111 , ... . , ..

< -•oo~ "'"111]]1"' -aoo:.. ,

I 1 t 1 I I I 1 I I I I I 1 I I t I I I I I I I I I If I I I 'IS((J - s ~ ~ 1 c 1 s 20 ~~

Figure 17. Time history of Behavior of ground (Sasaki et al. 1991).

0·1

35

~I------~·--~~·,--.~·~~~~~~~~ X 0 1-B 208 3·8 4.8 6.0 (m)

X==1.8m

300 Accel. A-17 go l

0~~~~~~~~--~ -300

4 Excess pore pn?ss. P-17, kPa qv'o 0

-4 6 Lateral disp. 0-5, em

0o 10 Second

Figure 18. Time histories of recorded response (Sasaki eta!. 1992).

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400

0

5

~u~~~ 1~;1

18

/J~~IlliJ IIIJlliJJJAIJJ

~Yj" "

.

0 w-10 0 0

...

Excess >!!"• mlt'r Rrt'$Urt' P-18, kPa

laiNCI di~bcement D-6, on -. ..

5 10 15 Elcpsed lime, sec.

'

20

Figure 19a. Time histories of recorded response (Sasaki et al. 1992).

_400 0

~2 '§ G:) 200 .!:! 7 e "" .)J.

'0 c

e 0

C) 200

£ill!. [ 1- .. --~::¥1- :·jj l 1st cycv ~~ 7 h -=

rc: -- ----[ PWR1 Model 5, Stage 4 )

0 5 10 15 t.oterct disp!ocement. 0-6 1 (em)

Figure 19b. Approximate idea of stress-strain relationship in liquefied layer (PWRI model 5, stage 4) (Sasaki et al. 1992).

-·~ ~+--+.::...J..-!1-+-+--+-+-+--l

·ZD ·15 ·1D ·5 I 5 10 15 ZO 25

Figure 19c. Response of model pipe in liquefied ground (Towhata and Toyota 1994).

50-

0 ~Mlt.l•.Mi•• o·A>-'...,..1''' ' " I' •' ' ~ll'IIJJ1'Trr .-''f rr~ ..... JI"'r""" r n

-50~---------L----------~--------~ 0 5 !0 15

fnput: ~ax=250 gn.

10

Time (s)

Figure 20. Time histories of input and ground surface response (Shamoto et al. 1996).

15

1253

Figure 21. Recorded response at the Wildlife refuge site, Superstition Hills earthquake (Holzer et al. 1989).

L fi l • " ~ _,

~1Wialtl7~

_,,, c-;,---:---:-;---;-;;-;---;---;-~----;.,--;;--;;-----.o" '-:.1.!1 -1 ~.J D 11.3 1.) D ID 20 )0 40

NSS-..u .... C•) 'YCIIk:oi~IICclittc-lkh)

Figure 22a. Wildlife-refuge NS shear stress-strain and effective-stress histories during the Superstition Hills 1987 earthquake (evaluated from acceleration histories and computed by new constitutive model).

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SANO B TEST 11 e:,,.-0.68%

OEVIATOFI VEFHICAL LOA.O

Figure 22b. ReCord of deviator vertical load versus pore pressure for Jest II (Vucetic and Dobry, I 988).

• NS, 13~~1<1.~ Sec NS, 1.4.3!--l~.=.!i Sec:

' p • ' " " NS.JS.<I~J:.oo Sec NS, ll.6."-20..3S Sci:

' rt c • ., .. .. NS.l'H~!l.JOSec I EW, ~-!5-2!.-C(l Sec

' . r D

~ _, ..

-I • I -I D I

Figure 23. Selected Stress-strain loops of Wildlife-refuge response during Superstition Hills earthquake.

~ v

200

0

<-2ooo~--~--~,~o--~--_~2~0--_~--~,~o--~--~.o Tim~ in Sf'cond

Figure 24. Aomori Harbor NS, 1968 Tokachi-oki earthquake (Towhata et al. 1996).

100

0

-100

0

8.0m

U/ ~ 4.15-6.05 s 6.30-8.30 s

24.0m

I ~ 4.05-5.~3 s 5.63-7.20 s

·I 0 I ·I 0 Shear str>in (%)

1254

~ o--...

8 70-10 90s 19.90-Q!O s

~ 0 8 20-9.56 s IQ.90-I,.JO s

·I 0 ·I 0

Figure 25. Selected stress-strain loops, Port Island, Hyogo­ken Nambu earthquake (Elgamal et al. 1995) .

5 r.~n~.~,.~(-7~7~m~)--------------------,N~~

.: ·~~~~~\l(lo!j<:·1~ ¥••· 2.0~

Figure 26. Recorded acceleration, Kushiro-oki earthquake 1993 (lai et al. 1995) .

~ ., 5 - Ground Surface Computed a

~ 0 0: Max. 3.5 0 -5 ·--5

"' Ground Surface Recorded .... "' 0 -"' u

Max. -4.6 u < -5

50 60 10 20 30 40

Time (s)

Figure 27. Recorded and computed accelerations at the ground surface (lai et al. 1995).

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12·7 .... -10!

~~: -37·1

11·8

••• -H ...

31·1

••• -27·4

41·1 % _.,,

116-(1

• -$7-~

"' • -61·4

"' ' -13Hl 3~·6

• -le-ti

.... • .,. '" • -lS 2

..l.,ll~_A_I\ . . . v.MMMMMMM"'-"

.f\ .J':""~'f-,,f\J\,f-..f\ A

' I

'""~ "~"~"'~'A •' . '.. .. .. ' A~--"J:;

v y • •

..i, .1.1..! J. -.1 -.1 A • ,

.1'1./l.J/1 M.J<l...!l..tl!..LI .A ··~rr•~··

"" v I I

AA A • v v v .

0 " '"' '"

• Time mt

""'

'"

PPTWI ,. . kPa·dN

;~t"' kP.x!"' PPT2lJ~ ,. .

kPa'droo

PPlO"lJ3

''" ~Pa"dN

llCC•2-'~

"'" .,...,,.. ... ccns >000 . ...

... ccn.~ 100·0 .,.,,,..,.

A.CC968 2000 %1d ...

A.CC•22~

""" ""'

A.CCllU 1011 &O""!Crt'l<! bll~}

... cc ;x)..]..1

>000 ·-Figure 28. Recorded response in c..-:ntrifuge test (Lee and Schofield 1988 ).

""' 0 _,

r: ~-200

r: ; <·""'

""' 0 _,.,

AMI (ln tl

• .. 10 u loa. h.:) Tunc(-)

Figure 29. RPJ and Ca!Tech Model 2 acceleration histories at free surface (AH3(. 2.5m depth (AH4), and 5m depth (AH5), and input acceleration (AHl) at !Om depth (Taboada and Dobry 1993, Scott eta!. 1993).

" .

1255

t _: r--~~~~:/!W~~W~ j~i~Vi~Jt~~~N'~"'''V{/N.._ 0 10 20 " .}0 .}5 <0

Figure 30. Recorded horizontal acceleration in UCD Model 7 (Wilson eta!. 1993)

'"r-----~~~~-------------------------,

'"' t so .! 0

j.;: 1 ..... i -:100

.:! -~!(!

·""' .,, L---'--------------------------------~

" " " ,.

Tlt.A l joul

Figure 31. Pore-pressure and acceleration near surface of backfill, test 2e (Whitman and Ting 1994).

5.0 10.0 12.5 15.0 lime {s)

Figure 32a. Recorded lateral accelerations at UCD (Divis et al.1996).

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g ,,

i " " I <5

-1.0

u g ,. .5 0.5 .. .. .I

i •• _,. .u

Figure 32b. Recorded acceleration response at UCD (Wilson et al. 1997).

l.lJ Ill I

0 ~,..._----------------·---------------------·--------------I ' " lUI-

2 . .).., to,. ...-T'l'\rf""'i'\_~A o -tV1JJffffT)()I)~--------------------··---·-··

·I I 1011-

" ' ,_

: "'-~---·---·---- .. ·-'-~---1 ,._

' - " ' ,_

·I ~---.. ·--------·----·-'

tc012"fll012-

0 . , 10 " "

1256

Figure 32c. Recorded acceleration response at UCD (Balakrishnan et al. 1997).

"' 10

"'-0 ...... -------I r.- l • ~~

,_ t.:u. , "' ""' .. :~, .... ___ I r- l ' ' • " -~ • • 10 IJ- >Ja

" "' ~~~:::~ I r- j • • ' io t'z-.... • ).H•

" " ~:~~~ -· I

,._ ' ' ' ; .'o t't-lll .... 1 4 ' ••

~"'~---I r-. ' • ~~' • 110\J- U•

" 0 10 " •

Figure 33. RPI and Ca!Tech Model 2 shear stress-strain histories (Elgamal et al. 1996).

TorsiOI\OI •hf'OI" t..st To,/(·.,.-')•0.1\7 O.•n.%, _,_ •• ~1!1 kPa

F"~l rt .... r •OI'Id

[b) O:..pohlll

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Figure 34b. Iai model performance and measured data (lai 1991, Ishihara 1985).

r., d' ,!'•.no ''':l v :n

j_ I -1.0 ~ 1.0.

v.~ r., (%)

II -~.>

Figure 35. Computed results: effective stress path and shear stress-strain (Nishi and Kanatani 1990).

1257

" " Jt 0~~~-----f~---1----f,--~--~-i ~ ...

. ,.

p (l<pa) .

Figure 36. Undrained simple shear response (Li 1993 ).

50 100 a 'v (kPa)

-2~Y,UJ~LU~o~LU~~,

y (%)

Figure 37.Effective stress path and shear stress-strain response (Kimura et al. 1993).

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····-------.----, Eipcnmcnt Calculation

.. ..a. 5

.... o.. -4 -a -l -1 z 7,, (X)

1258

0 "-~ -c 0 ·o 0 > .< . . ~ . ~ _., c 0 u • •

meon ptessure (io:Po)

Figure 38. Simulation of shear slrcss-strain response (Tobita and Yoshida 1995).

Figure 39. Predicted effective stress path (Bardet eta!. 1993).

(a) Experimental results 0·~-r--r.,~~~~~ .. -.

;~1 .. -r T r·-· I I --·r·.

' ' ... t·· ·---~-----

·-····-----!

··-----------------. . ------1-----

(b) Simulated results 0>.--r-~=---=~~r-•

i ; -·r-· . . ' -- -:- ---~ --- ----i f· -- ···-·-T·-· i I .;. .. -- ---· + ··--J ... I j - ----··-·-··

~ i .

"-~··· le-1.1 i -------1·--··· __ .. _____ _ I i ,;wj>lili'::Z --.,-··;; t

' ------~---

.Ci.1 ILl 0.~ 0.1 0.1 1.1 1.2 .C.~ .. ,--;.~.,;--;,~~;--;0~ ... :--.~.>0 .ela o.z 0.4 u u u u .e_L,.,--;.~.,:--:,~,.:--:,~,.:--:,~ • Ll.t¥1 trllai'w't StrUI ta!IO $I'd' ,_rift Mtil'l .rlte11V1 IWU.I rali:l Slw.a' al3il

:Sr.• jQ.IJ i ------- ... -·--· --······-----.. ------. : 1

·-······;.,,,, ______ ; _______________ _

;s--·--·' --·--r~-!···~!-----~-----,J.·-···--

'

··--i--1

' ; I ----··-·····-··•·"--··--!---! . ~ ;,~-:;:';--:;:';--;::';--;::';--;';;--;'. .~ .. ,...---,;.~_ ..... ~ ..... ~ ... ...,.~ .. ··J\c---,;';---,;';--.';--;,~.-7 .. ~.--!,.a.ll ... ICIO 1• •• ,.. ..... ll'fiiC.'IYI snn tJ!Iio S.. .,..

. ............... __ .. ' '

(c) Experimental results (Series C-2) (d) Simulated results (Series C-2) '·''r;=-;r---r-..---r-..---, r---r-~-~-, 0.1 , ,-,:--,,--,--,

t--riio 11.1. j ; har•.,_,.. t11 ; ShMt._rllfiD II. I) ! j 11 -taN~ _,..-,~•ifG.:IG''f-""'1"'"'" Ni.ri)iiji tniiN¥ ·e:» .... T........ 0- ~-..... -.--~"li.l6T"--T'---!e ~~~--- .. --!-- --+-.. --+---·-+-·--- )(A.UI .. !.--------!-----·---~----·--- -!o ~'-'----·J·---·--1·----r-----·j-----

~:· :::::t:.::.tf:t.:t~: ::::::.J~~--J~~::: !:, ::::l:::::.l:~t:t.t:: ~G ·---! ........ i. 1·-----~---...l...... . ::::::~·J· • ~-\Y-·-··l ~'-' ....... ! ....... .L ..... l ........ t ........ l....... ---------y---------1-------- ' ..... jo -+·-·--. t· --:·-·-·+--·-·

~~~- , l ! l l ::~::::~::r.:~~:: .. :r::::::::J ... ..... ~~-; :~~::r~_:::~~r:::::J,:=::::r .. ::::~J,::::::: : ...... , ......... ; ........ ; ....... : ....... T...... ! ! ! l ... , .(1 t';----;!:;----;!-;---,;!;;----,;';--;';--7

11.1 0.2 U 11.1 U 1.0 1.2 -e.10 .0~ I.CIO o• IIID 0:0 D.2 0.C 01 0.1 1.0 1.2 Ut¥1 tlletliYt strtn raiio Stu Slrain M•an trllldHt Pen ralio

Figure 40b. Comparison between experimental and computer simulated response, Series C (Tateishi eta!. 1995).

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Shear Stress

Oiluioa slope m

Inflcctioa. poim

"Yt

Shear Strain

500

0

-500 'il ~ 500 ~ ~

0 .g E -" -500 § <

Figure 41. Simplified shear stress-strain relation (Abdoun 1994 ). 500

IJ~IIIII. ~ 10 15 N

Tllllll..c)

' '1 ("W'i"' ;---.---;;:,---,.----!20 ~~_,.--,,--,,:-, -";';,,---!.~

z" •• L • l• ! ' '-• _,

r-(...:J A.....:st-mr'l-l

l/

51DUJO AJ.ii Snit (I}

Figure 42. Simulation of cyclic triaxial undrained test with stress bias (Parra 1996).

0

1

5

0

1259

Stage l1Staatj Stqc3

i ' i

~ ' tvV'""·L ·~'" ,.

' ' ' ' (Surface, N44W)

' ' '

w.~~~~~~ (16m, N44W) ' ;

~

' '

·~ ~· • ~~"" • cA . .. ' '

! ~ : I I

I I (32m, N44W) .. . ! ,)--·---------- c - ------I

I ,. -I ' • ' ·-· ' ' . I

' ' ' ' ' -Recorded '' ' ' --- · Comp'uted (8 m) __ -I '

5 10 15 20 25 30 35 40 Tune(sec)

Figure 43. Port Island recorded and computed accelerations (Eigamal et al. 1996a).

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