ANALYSIS and DESIGN of EARTH STRUCTURES to RESIST SEISMIC SOIL LIQUEFACTION Peter M

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ANALYSIS AND DESIGN OF EARTH STRUCTURES TO RESIST SEISMIC SOIL LIQUEFACTION Peter M. Byrne, Civil Engineering Department, The University of British Columbia, Vancouver, British Columbia, Canada Ernest Naesgaard, Civil Engineering Department, The University of British Columbia, Vancouver, British Columbia, Canada Mahmood Seid-Karbasi, Civil Engineering Department, The University of British Columbia, Vancouver, British Columbia, Canada

ABSTRACT The National Building Code of Canada, 2005 has increased the seismic loading from a 10% chance of exceedance to a 2% chance of exceedance in 50 years event. This has increased the design accelerations by a factor of about 2 in Greater Vancouver as well as many other areas of Canada. For the design earthquakes scenario the risk of soil liquefaction and resulting damage to existing building and lifeline structures has greatly increased. This paper examines liquefaction induced damage to civil engineering structures in past earthquakes as well as the characteristic liquefaction response observed in laboratory tests. State-of-Practice as well as State-of-Art procedures for analysis and design of building and structures supported on potentially liquefiable soils are examined. Reliable prediction of seismic displacements of foundations, and design to limit displacements to prevent collapse of the supported structure is the challenge. State-of-practice analysis is based on a total stress approach in which it is assumed that the liquefiable soil will remain undrained at the in situ void ratio. It is further assumed that this is a conservative assumption as drainage during and after shaking will lead to lower void ratios and stiffer and stronger material. State-of-art coupled stress-flow effective stress analyses together with field experience and laboratory model tests show that this is an unconservative assumption in layered materials, and has led to a number of failures. Liquefaction generates excess pore pressures that drain upwards. If the liquefiable stratum contains silt or clay sub-layers that block the flow, this can result in a temporary expansion of the sand directly beneath the silt, and lead to a greatly reduced strength resulting in large displacements or flow slides. These concepts are discussed in relation to developing better analysis and design procedures for remediation of liquefaction effects.

RÉSUMÉ Le Code National de Bâtiment de Canada, 2005 a augmenté le chargement sismique d'un événement avec 10% de chance d’être excédé à un 2% de chances en 50 ans. Ceci a augmenté les accélérations de conception par un facteur d'environ 2 dans le Grand Vancouver de même que dans beaucoup de secteurs au Canada, et a fortement augmenté le risque de liquéfaction de sol et les dommages résultants au bâtiment existants et les structures de ligne de sauvetage en cas du plus haut tremblement de terre de conception. Cet article examine les dommages induits par liquéfaction aux structures d'ingénierie civile dans les tremblements de terre passés de même que la réponse caractéristique de liquéfaction observée dans les tests de laboratoire. L’Etat de Pratique de même que des procédures d’Etat d'Art pour l'analyse et la conception de bâtiment et des structures soutenues sur les sols potentiellement liquéfiables sont examinées. La prédiction fiable de déplacements sismiques de fondations, et la conception pour limiter des déplacements pour empêcher l'effondrement de la structure soutenue est le défi. L’analyse d’Etat de Pratique est basée sur une approche de tension totale dans laquelle il est supposé que le sol liquéfiable restera non drainé au rapport de vides in situ. On suppose encore que ceci est une prétention conservatrice car drainage pendant et après la secousse mènera à des rapports de vides plus bas et le matériel sera plus raide et plus fort. Analyses d’Etat d’Art de tension effectives à écoulement d’effort couplé ensemble avec l'expérience de champ et les tests de modèle de laboratoire montrent que ceci est une supposition non conservatrice dans des matériaux à couches, et a mené à un nombre de ruptures. La liquéfaction produit des pressions de pore excessives qui drainent vers l'haut. Si la couche liquéfiable contient des sous-couches de silts ou argile qui bloquent le flux, ceci peut avoir pour résultat une expansion temporaire du sable directement en dessous du silt, et mener à une forte réduction de la résistance ayant pour résultat de grands déplacements ou écoulements de pentes. Ces concepts sont discutés par rapport à mieux développer les procédures d'analyse et conception pour le redressement des effets de liquéfaction.

1. INTRODUCTION generation of high pore water pressures and large reductions in soil shear stiffness and strength that has led Earthquakes have caused severe damage to civil to very large shear deformations. In addition, the bulk engineering structures, particularly where soil liquefaction stiffness of the soil skeleton greatly reduces upon was observed. Liquefaction can occur in granular soils liquefaction and can result in large post-liquefaction whose pore spaces are filled with water, and involves settlements as pore water pressures dissipate; resulting in further damage.

The detrimental effects of liquefaction on urban infrastructures came into prominence during the 1964 Magnitude 7.5 PGA  0.2 g, Niigata earthquake. At Niigata, liquefaction caused apartment buildings to overturn, manholes and wood pilings to float out of the ground, bridge decks to fall off their supports and roadways and embankments to crack and spread (Figures 1 and 2). Liquefaction induced damage was also very severe during the Kobe earthquake of 1995, M7.1 with PGA  0.5 g. Damage to port facilities was Figure 1. Collapse of building in Niigata earthquake, particularly severe due to very large lateral displacements Japan, 1964, M=7.5 of the order of 3 m from soil liquefaction (Figures 3 to 7).

Soil liquefaction resulted in major damage in Turkey during the M7.5 earthquake event with PGA  0.5 g in 1999. Here liquefaction of silty soils (which previously had been deemed to be resistant to liquefaction) gave rise to large movements (Figures 8 and 9). Figure 10 shows an attempt to numerically simulate the overturned building of Figure 9.

Probably the best documented case histories of liquefaction effects on earth structures are the San Fernando dams in California, during the earthquake of 1971. The crest of the upper dam moved 1.5 m downstream, while the lower dam had a flow slide on its Figure 2. Collapse of Showa Bridge in Niigata upstream side which removed the crest of the dam. The earthquake, Japan, 1964, M=7.5 slide occurred shortly after severe shaking had ceased. The earthquake was a magnitude, M6.6 event with Peak Ground Acceleration, PGA = 0.5 g. A plan view of the San Fernando dams is shown in Figure 11. A view of the upper dam is shown in Figure 12. The failed section of the lower dam is shown in Figures 13 and the failure mode is depicted in Figure 14.

The flow failure of the upstream slope of the Lower San Fernando dam was not expected at the time and resulted in a detailed study of the dam and the possible causes of the failure. The sands present at the site had relative densities of about 55%, and laboratory testing carried out on undisturbed samples after the failure showed high shear strengths, more than sufficient to prevent a flow Figure 3. Large lateral spreads damaged many port slide. It was argued at the time that minor disturbance structures in Kobe 1995 earthquake caused compaction of the samples and led to the high measured strength. Recent research suggests that localized expansion of the sand layers occurred after shaking due to redistribution of water associated with generated excess pore pressures. The expansion of the sand in turn caused its strength to drop and accounts for the failure. This hypothesis is supported by the observations that the slide occurred some time after the end of strong shaking; allowing time for redistribution of water and related expansion to take place. The expanded zones are very localized and difficult to detect. In addition, upon dissipation of excess pore pressure the expanded zones will compact. During the failure process the fine and coarse layers of the hydraulically placed dam also mixed. This mixing further reduces the strength of Figure 4. Bridge collapse due to foundation lateral the liquefied soils (Byrne, 1989; Baziar and Dobry, 1995; spreading in Kobe 1995 earthquake and Naesgaard and Byrne, 2005). Figure 5. Bridge span collapse due to foundation Figure 8. Subsidence and lateral spreads in 1999 Turkey spreading in 1995 Kobe earthquake. earthquake.

Figure 6. Damaged port facilities due to foundation failure Figure 9. Building over-turning collapse due to foundation in 1995 Kobe earthquake. failure, Turkey 1999 earthquake.

Figure 7. Soil movements at bridge foundation, 1995 Figure 10. Model of building over-turning collapse, Turkey Kobe earthquake. (Photos in Fig. 1 to 7 from 1999 earthquake. http://cee.uiuc.edu/sstl/education/liquefaction) Upper San Fernando Dam

Lower San Fernando Dam

Figure 11. Aerial view of San Fernando dams. Figure 13. Failure of Lower San Fernando dam due to liquefaction in 1971 earthquake.

Figure 12. Upper San Fernando dam after 1971 earthquake. Figure 14. Rebuilt model of Lower San Fernando dam Failure mode (Seed et al., 1973).

Damage to earth structures from seismic liquefaction The seismic loading that buildings and structures are arises from soil movements and can be categorized as required to withstand in Canada are prescribed by the follows: National Building Code of Canada, NBCC. Over the past 30 years, the seismic loading has increased dramatically a) Flow slides and bearing failures with very large from a 100 year event, to a 475 year event (10% chance movements that occur during or after shaking when of exceedance in 50 years), to a 2475 year event (2% the post-liquefaction strength drops below the static chance of exceedance in 50 years) in NBCC 2005. In driving shear stress. Greater Vancouver, the design peak ground acceleration, PGA has gone from about 0.10 g to 0.46 g in that 30 year b) Lateral Spreads & shear Induced foundation period, a factor in excess of 4. Many older buildings had displacements that occur intermittently (and built-in structural “over-strength”, so that if located on firm progressively increase) during earthquake shaking ground the buildings may still be adequate under the when the combined static and inertial driving forces increased seismic loading of the new building code. exceed the soil strength. However the strength is However, older buildings located on liquefiable soils are greater than the static driving shear stress and not likely to meet the new code requirements as movements stop when shaking ceases. liquefaction potential is directly related to acceleration level, and if the new code earthquake were to occur c) Post-liquefaction settlements due to could be severely damaged. Foundations for new consolidation arise from dissipation of excess pore buildings will require a higher level of treatment to prevent water pressures associated with liquefaction. High liquefaction occurrence, and/or curtail resulting excess pore pressure and liquefaction disrupt the soil displacements under NBCC, 2005. The increased fabric making it much more compressible. This has seismic design levels in the building code make it two effects: 1) it reduces the coefficient of important that we fully understand the liquefaction consolidation and thus slows down the rate of phenomenon and develop new and improved analysis dissipation of excess porewater pressure after procedures for predicting liquefaction response. Such liquefaction, and 2) it greatly increases the amount of analyses if verified against case histories will allow a settlement arising from dissipation of excess reliable assessment of liquefaction response. porewater pressure. This settlement is in addition to shear induced settlements. This presentation will focus on understanding the In practice, for testing purposes, the random oscillating liquefaction response, and discuss analysis procedures seismic stresses, τxy, are replaced with an equivalent that allow rational design of foundation treatment to uniform cyclic stress cyc. In addition, it has been found reduce displacements to tolerable levels. that liquefaction depends largely on Cyclic Stress Ratio, CSR = cyc/'vo, where 'vo is the initial vertical effective stress prior to the earthquake, and cyc is an equivalent 2. SOIL RESPONSE TO SEISMIC LOADING uniform cyclic stress often set equal to 0.65 x max where max is the peak horizontal dynamic shear stress from the An earthquake applies time histories of acceleration at earthquake. the base of a soil structure as shown in Figure 15. The horizontal accelerations induce oscillating horizontal Cyclic simple shear loading is depicted in Figure 16a. dynamic shear stresses, xy as shown in Figure 15b. The Typical shear stress-strain results for loose Fraser River effects of such cyclic shear stresses on soil behaviour sand tested in undrained (constant volume) conditions can be assessed by applying them to elements of the soil are shown Figure 16b, and stress path response in terms under simple shear conditions and observing the of shear stress vs. normal effective stress is shown in response. Figure 16c. From Figure 16b, it may be seen that the shear stress-strain response is stiff for a number of cycles Such tests show that cyclic loading causes a granular soil in the pre-liquefaction stage, with shear strain less than to contract. If contraction is prevented or curtailed by the 0.2%, followed by an abrupt change to a post liquefaction presence of a low compressibility fluid such as water in stage with very much softer response and strains of 10%. the pores that cannot escape, it induces excess pore The stress path followed is shown in Figure 16c where it pressure and a consequent reduction in stiffness and may be seen that starting from an initial vertical effective strength. If the excess pore pressure rises to reduce the stress of 100 kPa, the effective normal stress drops with effective stress to zero, the soil has essentially zero each cycle until the phase transformational line, or stiffness and strength and is said to have liquefied. constant volume friction angle cv  33 is reached after 6 However, unless it is very loose, the soil dilates as it is cycles. Once this has occurred, loading and unloading loaded causing the pore pressure to drop, and the soil takes place close to the cv line, with loading involving an regains strength and stiffness. Since seismic loading increase in effective stress and unloading involving a occurs rapidly there is generally little time for drainage to decrease in effective stress. This is illustrated in more occur, and testing to simulate field conditions is generally detail in Figure 17 where it may be seen that prior to carried out under undrained or constant volume liquefaction the stress path is below the  line and conditions. cv

xy Time (b)

´0 xy

(a) Earthquake motion

Acc. Time

Figure 15. Cyclic shear stress induced by base acceleration in an earth fill Embankment. ´0

cyc

(a)

cyc 30 30 Point of =3.75% Point of =3.75% ' =100kPa; D =40% 'vc=100kPa; Drc=40% vc rc (i.e. Assumed triggering point (i.e. Assumed triggering  /' =0.10;  /' =0.0 cyc/'vc=0.10; st/'vc =0.0 20 of liquefaction) cyc vc st vc point of liquefaction for 20

comparison purposes) ) ) a a P P 10 k k

10 ( (

t t

, s s s s

e 0 e 0 r t r t

S 0 25 50 75 100 125

-15 -10 -5 0 5 10 15 r r a a e -10 e -10 h h S S

-20 -20 (b) (c) Vertical Effective Stress, 'v (kPa) -30 -30 Shear Strain,  (%) Figure 16. (a) cyclic simple shear loading, (b) shear stress-strain response, and (c) effective stress path (tests data from Sriskandakumar, 2004).

 f

pt = cv

´

pt = cv

Figure 17. Effective stress path following liquefaction. contraction occurs upon cyclic loading. Once the cv line number 15 derives from a magnitude, M7.5 earthquakes is reached, further loading causes dilation as the stress which causes about 15 equivalent cycles. If the design point moves up just above the cv line. Upon unloading, earthquake is different than M7.5 then corrections for the the stress point drops slightly below the cv line and the appropriate number of cycles are made. soil contracts, driving the stress point back to the origin or zero effective stress (liquefied) state. Upon reloading the In practice, elements in the soil structure will likely have a static bias that will cause shear strain to accumulate in soil dilates, moving up just above the cv line gaining strength (de-liquefies). In subsequent unloading and the direction of the bias as shown in Figure 19. In this reloading cycles, the pattern repeats itself. Note that case the bias was sufficient to prevent a change in sign of although the soil liquefies during cyclic loading, it the shear stress (no crossover), large strains can maintains its critical state strength at large strain. The accumulate once the stress point reaches the cv line and post-liquefaction strength and stiffness depends very the stress point essentially moves up and down the  line much on its density. Higher densities will have much as loading and unloading occurs. higher post liquefaction stiffness and critical state strengths. The cyclic stress-strain response of dense sand, Dr = 80% is shown in Figure 20. it may be seen that there is a The test results shown above are for an applied CSR = gradual accumulation of shear strain with number of 0.1, and triggered liquefaction in 6 cycles. If a higher CSR cycles leading to a gradual decay in stiffness with no loss is applied the test element liquefies in less cycles, and if a in strength. The strain increase is less than 0.02% on the lower CSR is applied it takes more cycles to liquefy as first cycles, and 10% after about 20 cycles. shown in Figure 18 in terms of CSR versus number of cycles to liquefaction. The CSR, that causes liquefaction The cyclic response of a soft low plasticity silt is shown in in 15 cycles, is commonly taken as a reference and is Figure 21. It may be seen that the shear strain increases referred to as the cyclic resistance ratio, CRR. For the gradually with strain and there is no abrupt change in (dry pluviated) loose Fraser sand tested CRR= 0.09. The shear strain. The soft silt behaviour is similar to that of

0.2 60

'vc=100kPa; Drc=80%  /' =0.30;  /' =0.0 cyc vc st vc 40 0.15 ) a

P 20 k (

R ,

S 0.1 s s C

e 0 r t

S -15 -10 -5 0 5 10 15

r a

0.05 e -20 h S Point of =3.75% (i.e. Assumed -40 triggering point of liquefaction) 0 0 5 10 15 20 No of Cycles -60 Shear Strain, (%) Figure 18. CSR vs. No. of cycles for Fraser river Figure 20. Stress-strain response for dense Fraser River sand, DR =40% and ’c = 100 kPa (tests data sand, Dr= 80% (Sriskandakumar, 2004). from Sriskandakumar, 2004).

OCR = 1.0 20 30 CSR = 0.20  'vc=100kPa; Drc=40% )

a ec = 0.884 cyc/'vc=0.065; st/'vc =0.1 20 P 10 k W = 36.2% (

) t a

, P 10 s k ( s

e 0

, r t s s

0 S e

r -15 -10 -5 0 5 10 15 r t

S -15 -10 -5 0 5 10 15 a

r e a -10 e -10 h h

Point of =3.75% S S

(i.e. Assumed triggering -20 point of liquefaction) -20

-30 Shear Strain, (%) Shear Strain,  (%) Figure 19. Stress-strain response for Fraser River sand with shear stress bias (Sriskandakumar, Figure 21. Stress-strain response of low plasticity Fraser 2004). River silt (Wijewickreme and Sanin, 2005). dense sand in that it has a gradual increase in strain with earthquakes. Cone, Standard penetration, or Becker each cycle of stress rather than an abrupt increase as for penetration tests are commonly used with corrections for a loose sand. the magnitude of the design earthquake, stress level, and, static shear stress or bias. The CRR at any location A great deal of high quality cyclic loading data for sandy can be expressed as: soils is available and indicate the characteristic behaviour shown above. The CRR and post-liquefaction stiffness and strength increase with density, and the post- CRR = CRR1 * Km * Kσ * Kα [1] liquefaction strength conforms with critical state concepts.

Back analysis of field data gives post-liquefaction where CRR1 is obtained from the NCEER, 1997 workshop strengths that are significantly lower than the critical state chart (Youd et al., 2001) shown in Figure 22, and Km, Kσ, strength determined from laboratory tests on undisturbed Kα, are corrections for earthquake magnitude, effective samples tested at the in situ state. The reason for this overburden pressure, and static bias respectively. These apparent difference is related to expansion of the soil are addressed in Youd et al., 2001. skeleton associated with redistribution of water during and after shaking ,and will be discussed in detail in a 3.2 Flow Slide Assessment later section of this paper. The factor of safety against a flow slide, Fflow is computed from standard limit equilibrium analysis procedures using 3. STANDARD PRACTICE FOR LIQUEFACTION a post-liquefaction strength in those zones predicted to ASSESSMENT liquefy from the triggering analysis. Post-liquefaction strengths are based on field experience during past In dealing with liquefaction, three aspects arise: earthquakes and are significantly lower than values obtained from direct testing of undisturbed samples at in a) Will the design earthquake trigger liquefaction in situ void ratios. Post liquefaction strength may be significant zones of the foundation or earth structure, expressed directly in terms of penetration resistance, Su and if so, as suggested by Seed and Harder (1990) and shown in b) Will the post-liquefaction strength be adequate to Figure 23, or as a strength ratio Su/ /'vo as shown in preserve stability and prevent a flow slide in the Figure 24 (Olson and Stark, 2002). It may be seen that absence of inertia forces, and if so, the values of strength ratio are low, in the range 0.03 to c) Will the displacements be tolerable? 0.13. Computed factors of safety, Fflow > 1.2 to 1.25 are generally considered satisfactory (Byrne et. al., 1994). The standard practice approach uses three separate analyses to respond to the three aspects; a triggering analysis, a flow slide analysis, and a displacement analysis.

3.1 Triggering Analysis

A triggering analysis involves comparing the cyclic stress ratio (CSR) caused by the design earthquake with the cyclic resistance ratio (CRR) that the soil has because of its density. The result is expressed in terms of a factor of safety against triggering liquefaction, Ftrig = CRR/CSR. Ftrig in the range 1 to 1.4 are generally considered acceptable and assure that seismic displacements will be small and tolerable (Byrne and Anderson, 1991, Youd et al., 2001).

The CSR is normally computed from an equivalent elastic dynamic analysis such as SHAKE using strain compatible moduli and damping , where CSR = 0.65 x max/'vo , and max is the maximum computed dynamic stress at a specific location during the design earthquake. CSR may also be computed from a simplified formula based on SHAKE analyses, but this approach is not recommended as the values are very sensitive to the specific site characteristics and the frequency content of the design earthquake. Figure 22. MCEER Recommended chart for CRR CRR is generally computed indirectly from penetration evaluation based on (N1)60 (Youd et al., 2001). resistance values and field experience during past (a) 

Time (s) (b) Figure 23. Residual strength for liquefied sand vs. (N1)60 (Seed and Harder, 1990).

Time (s)

(c)

Time (s) (d)

Figure 24. Normalized residual strength for liquefied sand Figure 25. Newmark-rigid block model of seismic slope vs. (N1)60 (Olson and Stark, 2002). motion (Modified from Day, 2002).

3.3 Seismic Displacements base and displacement down the plane is instigated each time the base acceleration exceeds the yield acceleration Seismic displacements that arise during shaking are and causes the block to move in discontinuous steps commonly based on Newmark (1965) who modelled a during the period of strong shaking as shown in Figure potential sliding block of soil as a rigid mass resting on an 25. Note that even the peak acceleration may only induce inclined plane as shown in Figure 25. The acceleration a small displacement as it lasts for only a fraction of a that would just cause yielding and movement down the second. Peak accelerations greater than the yield plane is called the yield acceleration (ay) in gravity units , acceleration imply an instantaneous factor of safety less and corresponds to the seismic coefficient, k, that would than unity. This does not imply failure, but some limited reduce the factor of safety to unity. This is readily displacement that can be calculated from the equation of obtained from limit equilibrium analyses described in motion and the prescribed earthquake motion. The Section 3.2 and can take the reduced strength associated standard practice approach of the past evaluated with liquefaction into account. dynamic stability based on factor of safety and a seismic coefficient. This past procedure is generally not Newmark modelled the mass on the inclined plane as a appropriate and should be replaced by a displacement single-degree-of-freedom rigid plastic system, applied the approach such as the simple one proposed by Newmark. design time history of acceleration at the base and solved the equation of motion to obtain the displacement of the Seismic displacements associated with liquefaction can mass caused by the shaking. Basically yielding at the also be estimated from empirical equations such as Youd et al. (2002). These equations are based on field observations during many past earthquakes and can be a closely simulates conditions in the field. The earth useful guide for existing conditions, but are of limited use structure of concern is modelled as a collection of for design of remedial measures. discrete zones or elements. In the early stages of the analyses stiff moduli representing pre-triggering Seismic displacements also occur due to dissipation of conditions are specified. The stress pulses in each zone excess pore pressure. Since the earthquake loading is are computed with time as they occur and are weighted rapid, occurring in a matter of 10 to 100 seconds, it is depending on the size of the pulse as compared to the generally assumed that these occur after earthquake reference pulse that would cause liquefaction in 15 shaking has ceased and are essentially vertical. A chart cycles. So a small pulse may account for a half cycle or for estimating vertical strains associated with post less, whereas a large pulse may count for 2 or 3 cycles or liquefaction consolidation is shown in Figure 26 and more. When or if the cycle count reaches 15 in any indicates that strains could vary between about 0.5% and element, it is deemed to have liquefied and given much 5% depending on pre-earthquake relative density. reduced strength and stiffness properties consistent with post liquefaction response. In this way, the most severely loaded or looser zones will liquefy first and the extent of liquefaction will expand with further shaking as observed in centrifuge model tests. If sufficient elements liquefy and their residual strength is not adequate for stability, then a flow slide is predicted.

The procedure makes use of both state-of-practice triggering and residual strength charts and, thus is a logical extension of the current state-of-practice approach discussed in Section 3. The method is described in detail in Beaty and Byrne (1999), and Beaty (2001). An example of predicted displacement from such a liquefaction analysis is shown in Figure 27. Note that excess pore pressures are not computed in this approach. They are indirectly accounted for by prescribing much softer post- liquefaction stress-strain relations and residual strength Figure 26. Relationships for volumetric reconsolidation values after liquefaction has been triggered. strain as a function of equivalent uniform cyclic stress ratio, (N1)60-CS for Mw = 7.5 (Wu 2002). 5. STATE-OF-ART EFFECTIVE STRESS ANALYSES, FINN LOOSE COUPLED MODEL The state-of-practice liquefaction procedures have a number of shortcomings: The three aspects of The strength and stiffness of soil is governed by effective liquefaction; triggering, flow slide, and displacements are stress, and so it is desirable to evaluate seismic response addressed in three separate analyses. In fact they are of soil in terms of effective stresses. Pore pressure rise part of a single liquefaction response in which pore and liquefaction are caused by the tendency of soil to pressure rise and liquefaction occur at different rates and contract when subjected to cyclic shear loading. Martin et times in various zones of the earth structure causing the al. (1975) presented a 4 parameter shear-volume response of the structure to change as it softens. coupling model for predicting the increment of volumetric Redistribution of excess pore pressure may create more p compaction per load cycle, dε v. Their data showed that severe conditions, and finally dissipation and p dε v depended on both the level of shear strain in the reconsolidation occurs as the soil regains its strength. No current cycle as well as the accumulated volumetric strain direct account of these aspects is considered in state-of from prior cycles, but was independent of effective stress practice procedures, and in particular no direct account of level. The associated rise in pore pressure for saturated pore pressure rise and redistribution effects on response p undrained conditions is du = dε v * Ke, where Ke is the is considered. These shortcomings can lead to predicted elastic bulk modulus of the soil. Based on this concept response that is not realistic, and remedial designs that Martin et al. developed the first dynamic effective stress can be overly conservative, or unsafe depending on site model in which shear strains were evaluated in each conditions. element allowing the pore pressure rise at the end of each shear cycle to be computed. The total rise in pore These aspects will be examined in state-of-art pressure for undrained conditions is simply the sum of the liquefaction analyses. pore pressure increments. The strength and moduli are reduced in each element in accordance with the drop in effective stress as pore pressure rise occurs. Dissipation 4. STATE-OF-ART TOTAL STRESS DYNAMIC of excess pore pressure can also be accounted for by ANALYSIS allowing flow between elements. This approach is commonly referred to as the Finn model and was used in This procedure addresses the liquefaction response the TARA program (Finn et al., 1986). taking pre-triggering, triggering, and post-triggering aspects into account in a single analysis that more Figure 27. (a) finite difference mesh of the Lower San Fernando Dam, (b) Predicted distorted mesh and displacement vectors of 1971 liquefaction-induced upstream slope failure (Beaty and Byrne, 1999).

Later versions of the TARA program (TARA 3F, Finn et al., 1995) and the FLAC Finn model are based on a  Failure (Plastic)

simpler two parameter shear volume coupling model by

p p

Byrne (1991), dε = γ * C * Exp(-C *ε /γ) where γ is the

v 1 2 v p shear strain in the current cycle , ε v is the accumulated volumetric strain from prior cycles, and C1 and C2 are soil parameters that depend on relative density. This procedure is referred to as a loose coupled approach because the pore pressure is updated at the end of each Elastic zone cycle or half cycle of shear strain rather than at every time step.

The Finn model can adequately capture the pore ’ pressure rise up to the point of triggering of liquefaction for level ground conditions, but cannot simulate the post- Figure 28. Elastic and plastic zones in Mohr-Coulomb liquefaction response where dilation and pore pressure model. drop occurs during each load cycle as depicted in Section 2. TARA 3F handles post-liquefaction conditions by switching to a total stress approach and specifying a residual strength as discussed in Section 3 and a nominal soil models. However, because the cyclic response of shear stiffness. granular soil is complex, most soil models are either too complex and have too many parameters, or are too simple and do not allow predictions that are in reasonable 6. STATE-OF-ART EFFECTIVE STRESS ANALYSES, agreement with laboratory tests. FULLY COUPLED UBCSAND is a modified form of the built-in Mohr model in A number of fully coupled effective stress models exist for FLAC. The Mohr model has basically 2 elastic predicting seismic response and liquefaction including parameters that specify shear and bulk moduli, and 3 DYNAFLOW (Prevost, 1985) and UBCSAND (Byrne et al. plastic parameters, that specify friction, cohesion, and 1995, Puebla et al., 1997; Beaty & Byrne, 1999, Byrne et dilation angle. The model is elastic when the stress state al., 2004). Such models are based on plasticity concepts, is below the strength envelope, and plastic when the and shear-volume coupling effects are computed at each stress point is on the failure envelope as shown in Figure time step rather than at the completion of each half cycle 28. The plasticity model used assures that the stress of strain. Computer programs such as FLAC (Itasca, point does not exceed the strength envelope. 2005) have dynamic and flow capabilities and a range of The UBCSAND modification to the Mohr model involves

allowing plastic yielding below the strength envelope. In p 

d Фd > Фcv shear stress versus normal stress space, the yield loci Plastic strain vector , are radial lines from the origin of stress space, and the  directions of the plastic strains are as shown on Figure 29 when shear and normal strains are superposed upon the Yield locus Фd = Фcv stress space.

It may be seen from Figure 29 that for a stress point Фd < Фcv below the constant volume friction angle (phase transformation), the plastic vector is directed to the right indicating contraction, while at phase transformation state the vector is vertical indicating no plastic volume change, above the phase transformation line the vector is directed Figure 29. Moving yield loci and plastic strain increment to the left indicating expansion. This plastic shear-volume vectors. effect is taking place at all loading stages, and is given by the simple expression:

p Dense dε v = dγ * (Sin(cv) – Sin(d)) [2] 

, s s e where d is the friction angle developed at any stage of r t S loading and varies between 0 and f, the peak friction r

angle. a e

h Loose For Fraser River sand the constant volume friction angle, S cv is 33 degrees and all other parameters are related to relative density or Standard Penetration value, (N1)60.

Characteristic monotonic stress strain undrained Shear Strain,  response is shown in Figure 30 for very loose and dense sand. The UBCSAND model will capture this response. Dense Note that the very loose sand strain softens and the u

, model, predicts this behaviour with no need for any e r external load shedding device. u s s e r P

The results of cyclic simple shear constant volume tests e Shear Strain, are shown in Figure 31 together with predictions from r  o P

UBCSAND. It may be seen that the predictions are in s reasonable agreement with the measurements. Additional s e c tests having a range of applied CSR values were also x Loose predicted, and a comparison of predicted and measured E liquefaction resistance is shown in Figure 31c. Note that the model captures the stiff pre-liquefaction stage, the onset of liquefaction at the appropriate number of cycles, and the very much softer post-liquefaction response. Note also that the post-liquefaction resistance at large strain is 

 , cv high and there is no indication of a low strength ratio s Dense s corresponding to the back calculated values from field e r case histories. t S

r a e h S

6.1 Analysis of Level and Sloping Ground Conditions

An effective stress analysis of a 10m high sand column Loose resting on a rigid base with and without a non-liquefiable silt layer located at a depth of 4m was examined (Figure 32). The column represents an infinite slope with a one Normal Stress, ’ degree ground slope. An idealized harmonic acceleration Figure 30. Characteristic response of sand to undrained motion was applied at the base (Figure 33) and time loading in terms of (a) stress-strain, (b) excess pore pressure, and (c) effective stress path. 20 TEST DATA )

a 10 P k ( 0 s s e r

t -10

S PREDICTION -20 -15 -10 -5 0 5 10 15 Strain (%) 1 RU = 0.95 0.8 TEST DATA 0.6 u R 0.4

0.2 PREDICTION 0 0 2 4 6 8 No. of Cycles 0.2 TEST DATA 0.15 R

S 0.1 C 0.05 PREDICTION 0 0 5 10 15 20 No. of Cycles Figure 31. Comparison of predicted and measured response for Fraser River Sand, a) stress-strain, b) & c) Ru & CSR vs. No. of cycles ( tests data from Sriskandakumar, 2004).

(a) case I (b) case II

Groundwater table 10

9 Sand 8

7 Barrier 6

5 Element: (1,13) 4 (1,10) (1,5) 3 (1,3)

-1 Firm impervious ground -1 0 1 2 3 4

Figure 32. Ground conditions used in the study, (a) case I, uniform profile without low permeability sub-layer, (b) case II, profile with low permeability sub-layer (Seid-Karbasi and Byrne, 2006). histories of excess pore pressure ratio (R ) at various u 3 Harmonic Motion depths were predicted (Figure 34).

) 2 2

It may be seen that for conditions; (a) without, and (b) ^ s / with the silt layer the peak excess pore pressure Ru is 1 m ( close to unity (zero effective stress state) during most of n

o 0 i

the shaking and then drops with time as excess pore t a r

pressures dissipate. However, at the upper location just e

l -1 e

below the silt layer (location (1,13) in Figure 32) the Ru c c -2 values are higher for (b), with the silt layer, and remain A significantly higher for some time after shaking has stopped. This effect is caused by the presence of the silt -3 0 1 2 3 4 5 6 7 8 layer. The excess pore pressure generated by the motion Time (s) must drain upward. The silt layer acts as a barrier and curtails the upward flow causing expansion and Figure 33. Acceleration time history for base input motion. accumulation of water beneath the silt.

In Figure 35 it may be seen that very high shear Further analyses predict that in layered deposits the deformations are predicted directly beneath the silt layer pattern of contraction at the base of sand layers and where the Ru values were highest. The predicted expansion at the top occurs regardless of the thickness of maximum surface displacements are significantly higher the individual sand layers. This means that sand with the presence of the silt layer (Figure 36). Note that elements just below the barrier are being subjected to displacements continue for some time after the shaking inflow causing them to expand regardless of the thickness has ceased when the silt layer is present. of individual sand layers. Such expansion can greatly soften their response (Seid-Karbasi, 2006). The predicted change in volumetric strains as a function of depth after 30 s are presented in Figure 37. It shows The results of monotonically loaded triaxial tests in which that the bottom 2/3 of the sand layer beneath the barrier water is injected into the sample (inflow tests) are contracts, while the top 1/3 expands, and that most of the compared with results of conventional undrained tests in expansion occurs directly beneath the barrier leading to a Figure 39a, b and c (Eliadorani, 2000). The principal thin localized zone of high shear strain or a shear band. stress difference versus axial strain is shown in (a) and indicates that a small amount of inflow causes a dramatic The coupled stress-flow effective stress analysis indicates reduction in stress difference. The amount of inflow with that layered sand deposits likely do not remain undrained axial strain is shown in (b) and indicates that a 1 or 2 % during seismic loading and that expansion during and inflow or expansion strain can reduce the resistance to after shaking can occur leading to significantly lower essentially zero. The stress paths are compared in (c) stiffness and strength in thin zones directly beneath silt or and indicate that 1 to 2% inflow can drive the sample to clay layers of low permeability (Seid-Karbasi and Byrne, the zero effective stress state with zero shear resistance. 2004; Naesgaard et al., 2005; and Seid-Karbasi, 2006). Without a silt layer, no significant expansion and no strain The predicted responses for both undrained and inflow localization occurred. conditions from the UBCSAND model are also shown on Figure 39 as the continuous lines, and are in remarkably Shaking tests conducted by Kokusho (1999) & (2003), good agreement with the measured data. The inflow tests show that the presence of a silt layer results in expansion were predicted using the same soil parameters as for the and the formation of a water film at the base of the silt undrained case but with specified volumetric expansion layer, and a flow failure some time after shaking has conforming to the laboratory test as per Figure 39b. This ceased, while uniform sand (without a silt layer) is stable indicates that the model can account for the effect of during and after simulated seismic loading. This is inflow. The numerical model simulations together with demonstrated in cartoon form in Figure 38. Centrifuge physical model tests in which a water film is observed to tests conducted at The University of California, Davis with form at the base of barrier layers during or after shaking a thin silt layer within a sand model also show localization indicates that flow of water and expansion at the base of directly beneath the silt layer and the formation of a barrier sub layers within sand deposits is real and should water-rich zone under simulated seismic loading, be considered in liquefaction assessment. (Kulasingam, 2003; Malvick, 2005; and Malvick et al., 2005). Centrifuge tests at C-CORE in Newfoundland with The concept that the appropriate liquefaction response of simulated seismic loading also showed little slope sand can be determined from recovery and testing of movement for sand slope models without a silt barrier undisturbed samples at the in situ void ratio is flawed for layer, however the presence of a silt barrier layer in a layered material in which a large contrast in permeability similar model resulted in a post-shaking flow failure exists. The triggering resistance most likely can be (Phillips et al., 2004; Phillips and Coulter, 2005; and obtained from such tests as there may be little time for Naesgaard et al., 2005). drainage effects during the short period of strong shaking. However, the post-liquefaction response in field (a) (b) 1 1

0.8 0.8

0.6 0.6 u u R R 0.4 0.4 (1,13) (1,13) 0.2 0.2

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Time (s) Time (s) 1 1

0.8 0.8

0.6 0.6 u u R R 0.4 0.4 (1,10) (1,10) 0.2 0.2

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Time (s) Time (s) 1 1

0.8 0.8

0.6 0.6 u u R R 0.4 0.4 (1,3) (1,3) 0.2 0.2

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Time (s) Time (s)

Figure 34. Excess pore pressure ratio Ru vs. time at selected points with increasing depth, (a) case I, (b) case II (Seid-Karbasi and Byrne, 2006). (m) (m) 10 10 (a) (b) 9 9

8 8

7 7

6 6

5 5

4 4

3 3

2 2

1 1

0 0

-1 -1 -1 0 1 2 3 4 (m) -1 0 1 2 3 4 (m)

Figure 35. Deformation pattern of soil profile (a) without barrier, case I (with max. lateral displacement of 0.95 m after 14 s), (b) with barrier, case II, with max. lateral displacement of 1.75 m after 30 s (Seid-Karbasi and Byrne, 2006).

Barrier Base

2 5 With Barrier 1.5 No Barrier )

m 6 ( s i 1 Contraction Expansion d - ) X m (

0.5 t 7

End of shaking p e D 0 0 5 10 15 20 25 8 Time (s) Figure 36. Surface lateral displacement vs. time for profiles with and without barrier (Seid-Karbasi and 9 Byrne, 2006).

10 -0.5 0 0.5 1 Volumetric strain (%) Figure 37. Profile of volumetric strain beneath the barrier layer, after 30s (Seid-Karbasi and Byrne, 2006). Figure 38. Post shaking slope failure due to pore pressure redistribution (adapted from Kokusho, 1998).

Figure 39. Predictions of element undrained and partially drained triaxial test on Fraser River sand, (a) stress–strain, (b) volumetric strains, and (c) stress paths (from Atigh and Byrne 2004). conditions will not be at constant volume, as flow of water into thin zones beneath low permeability silt or clay layers k (m/s) cause expansion and perhaps a water film to occur and 8.81 e-7 result in a marked reduction in strength and stiffness. 8.81 e-4 This explains why back calculated strengths from field 8.81 e-2 case histories are significantly lower than undrained strengths from undisturbed samples. Strengths obtained from undisturbed samples of sand at the Lower San Fernando dam required a reduction factor of 20 (Castro et al., 1989) to bring them into agreement with back calculated values from the flow failure that occurred on Vertical drain the upstream face of dam. In addition, time for redistribution of generated excess pore water pressure and expansion to occur can explains why a number of field case histories, including the Lower San Fernando dam, failed some time after severe shaking (Seid-Karbasi and Byrne, 2004).

The lower than expected back calculated strengths from case histories do not imply that critical state principles do not apply to liquefaction induced flow slides. In fact it explains why greatly reduced strengths can occur. The (a) sand element has expanded to a higher void ratio and hence a lower critical state strength. In the limit, the sand skeleton can only expand to its maximum void ratio at critical state. Further inflow cannot be absorbed by the element and will appear as a water film.

6.2 Drainage Effects Ru(max) 0.65 The effect of drains on liquefaction response is examined 0.70 in Figure 40 for a sand stratum containing a silt barrier 0.75 layer and an infinite slope having a gently sloping ground 0.80 condition of 1 degree. The drain is represented by a 0.85 single column of loose material with a coefficient of 0.90 permeability 100 times that of the sand (see Figure 40a). 0.95 The same ground motion was applied at the base as 1.00 before. Contours of Ru values as well as flow vectors after 3.5 s of shaking are shown in Figure 40b. The results show that water flows horizontally into the drain and then up and out, and predicted Ru values are much lower than without the drain. The highest predicted Ru values occur beneath the left edge of the barrier as expected. Predicted Ru values with time are compared with and without the drain for the three cases in Figure 41. Predicted displacements with the drains were small.

A field experiment in which seismic shaking was simulated for conditions with and without drains is shown in Figure 42 and confirms that drains can be effective in (b) reducing excess pore pressures. Centrifuge tests at C- CORE also confirmed the beneficial effects of drains in preventing flow failure (Phillips et al., 2004; Phillips, R., and Coulter, 2005; and Naesgaard et al., 2005). A post- Figure 40. Treated ground condition, (a) model with shaking flow failure was generated in a model with a silt drain curtain (b) Ru (max) and flow vectors at 3.5s (Seid- barrier; however flow failure did not occur in a subsequent Karbasi and Byrne, 2006). similar model in which the barrier was perforated with drains (Figure 43). 120 1 Uniform 100 0.8 80 0.6 Test without drain u ) 60 Test with drain R % (

0.4 u 40 R

0.2 20

(a) 0 0 0 5 10 15 20 -20 Time (s) 0 1 2 3 4 1 Time (sec)

0.8 Figure 42. Measured Ru in field liquefaction test for case (a) without drain and, (b) with drain (data from 0.6 Chang et al. 2004). u R 0.4 w ith Barrier 0.2 (b) 0 0 5 10 15 20 Time (s) 1 With Drain 0.8

u 0.6 R 0.4

0.2 (c) 0 0 5 10 15 20 Time (s)

Figure 41. Predicted time history of Ru at mid depth of loose sand for soil profile (a) without barrier layer, (b) with barrier layer and, (c) with barrier layer treated with drain curtain (Seid-Karbasi, 2006).

Figure 43 (a) Initial and displaced profile of centrifuge test CT5 with three drainage slots (b) numerical analysis of same, and (c) comparison of vertical displacement near crest with (CT5) and without (COSTA-C) drainage slots. Post-shaking flow initiated in the COSTA-C test at approximately 70s. 6.3 Back-Analysis of Lower San Fernando Dam failing block and in achieving ongoing failure after end-of- Failure earthquake shaking (Naesgaard et. al., 2006).

In 1971 the Lower San Fernando Dam was shaken by a The liquefiable portions of hydraulic fill soils were large earthquake with a peak velocity pulse of around assumed to have (N1)60 values varying from 12 to 17 0.6m/s and peak ground acceleration of approximately while the clayey core of the dam was given undrained 0.5 g (Seed, 1973; Seed et al., 1989; Castro et al., 1989, shear strength of 20% of the vertical overburden Castro, 1995). Approximately 20 to 30 s after the end of pressure. The UBCSAND constitutive model was used for earthquake shaking the upstream face of the dam the potentially liquefiable portions of the dam while the catastrophically failed leaving only 1.5m of free-board and Mohr Coulomb model was used for the clayey core and putting a large population at risk (Figures 11, 12, 13). portions of the dam above the water table. Figure 44 Extensive investigation and analyses of the dam were shows the model grid, locations of low permeability conducted following the event. From the studies it was barriers, and the final displaced shape at 119s when the concluded that the hydraulic fill soil within lower and analysis ended due to excessive distortion of the central portions of the dam had liquefied and overlying elements (the failing mass still had a velocity of 0.2 m/s). portions of the dam had flowed out riding on the liquefied The identical analysis was also repeated (i) with ‘flow-off’ soil (Figure 14). so as to emulate undrained behaviour and (ii) with ‘flow- on’ but without the low permeability barriers. In both Numerous back-analyses of the dam have been cases deformations stopped at end-of-shaking with conducted (Seed et al., 1973, Seed and Harder, 1990, deformations much less (6 to 8m) than that when the Beaty, 2001) using both total stress and effective stress barriers were present (>36m) (Figure 45). This clearly models, but none have emulated the post-shaking failure demonstrates the importance of considering the effects of mechanism that was actually observed. By including low pore-water redistribution. The analyses indicate that permeability barrier layers and underlying layers of higher impermeable barriers and vertical and lateral migration of permeability the post-shaking failure mechanism has pore water play a key role in the failure mechanism. been emulated, both in approximate geometry of the

Figure 44. Lower San Fernando Dam analysis (a) FLAC grid, (b) assumed (N1)60 and cohesion in core, (c) location of low permeability barriers with vertical permeability in cm/s, and (d) 5m lateral displacement contours at 120s (Naesgaard et al., 2006). e

D Expansion from inflow ecs

e0 C e0

B A

Undrained cyclic loading CS Line

Figure 45. Lower San Fernando Dam numerical analysis: A = acceleration time history input at model base; B, C, & D = horizontal displacement of upstream face (point 'x' in figure 44) from (B) undrained silty barriers as illustrated analysis with flow-off, (C) analysis with flow-on but no barriers to vertical flow, and (D) analysis with flow-on and low permeability barriers as illustrated in figure 44c. (Pcs)exp P0 (Pcs) P Figure 46. Critical state conditions for undrained and inflow conditions

calculated from field case histories for given density 6.4 Effective Stress Summary conditions indicates that factors other than in situ density play an important role in post-liquefaction shear strength The results of coupled stress-flow effective stress and should be considered as noted by Malvick et al. 2005 analyses show that redistribution of void ratio can be very and Seid-Karbasi and Byrne, 2006). important in sand and gravel deposits containing low permeability silt or clay layers. Such layers can act as barriers to upward flow and dissipation of excess pore 7. SUMMARY AND CONCLUSIONS pressures generated by seismic loading. The effect is to cause an expansion of the soil in a thin zone directly Seismic loading has caused severe damage to civil beneath the barrier layer. The expansion concept is engineering structures in past earthquakes. The design illustrated in Figure 46 in terms of critical state concepts. and retrofit of these structures in Canada is largely The initial state (eo-P'o) is assumed to lie below the critical governed or guided by the National Building Code of state line at point A as shown on the figure. If Ru rises to Canada. NBCC 2005 has increased the seismic loading unity during shaking then the stress point moves to point from an event having 10 % chance of exceedance in 50 B if the element remains undrained and has zero effective years, to a 2475 year event having a 2% chance of stress. However, if it is sheared at constant void ratio it exceedance in 50 years. This has lead to a doubling of will dilate and fail at point C on the critical state line and the peak ground acceleration in Greater Vancouver, and will have a shear strength greater than the drained large increases in other areas of Canada. strength. If however, inflow takes place and the element expands, it can remain at the zero effective stress state Liquefaction is caused by the tendency of granular soils and continue to expand until it finally reaches the critical to compact under cyclic shear loading. If compaction is state at zero effective stress, point D, and has zero shear prevented or curtailed by the presence of water that strength. Any further inflow to the element will result in the cannot escape, it causes pore pressure rise and formation of free water, or a water film at the sand-silt softening of soil response. If pore pressure rise causes interface. the effective stress to drop to zero, the stiffness and strength also drop to zero and the soil liquefies. However, The strength actually mobilized in any zone will depend unless the soil is very loose, it will dilate and recover on the in situ void ratio prior to shaking and the amount of strength and stiffness. In general shear strains are small inflow. The inflow in turn depends on the site stratigraphy and soil stiffness and strength remains high prior to as it reflects the presence and degree of permeability liquefaction. Once liquefaction is triggered in significant contrast, as well as the magnitude and duration of zones of a foundation, strains and displacements become shaking. The wide variation in residual strength back large and a possible flow side is a concern. This is the characteristic liquefaction response, and analyses by Ryan Phillips at C-CORE and the insight into the flow procedures should take this into account. liquefaction problem provided by the work of T. Kokusho.

The current state-of-practice approach for analysis and design for liquefaction is based on a three stage total REFERENCES stress approach in which; 1) triggering of liquefaction , 2) possibility of a flow slide, and 3) seismic displacements Atigh, E. and Byrne, P.M. (2004) Liquefaction Flow of are examined in three separate analyses. Because Submarine Slopes Under Partially Undrained earthquake loading is applied rapidly it is assumed that Conditions: An Effective Stress Approach, Canadian the process occurs undrained. This is generally a Geotech. Journal, 41: 154-165. conservative assumption for assessing the triggering of Baziar, M.H., and Dobry, R. (1995) Residual Strength liquefaction. However, for post-liquefaction conditions it and Large Deformation Potential of Loose Silty Sands, may be highly unconservative as observed from field J. Geotech. Engineering Div., ASCE, 121(12): 896-906. experience, physical model tests, as well as effective Beaty, M. H. (2001) A Synthesized Approach for stress numerical modelling procedures. Estimating Liquefaction-Induced Displacements of Geotechnical Structures, Ph.D. Thesis, University of State-of-art effective stress coupled stress-flow dynamic British Columbia, Vancouver, Canada. analyses show that for a uniform sand deposit, excess Beaty M., H. and Byrne, P. M. (1999) A Synthesized pore pressures generated by seismic shaking drain Approach for Modeling Liquefaction and upward to the surface, and soil elements at all depths Displacements, FLAC and Numerical Modeling in contract as water escapes to the surface, and liquefaction Geomechanics, 339-347. flow failures do not occur even for loose sand deposits. Byrne, P.M. (1989) Liquefaction Review Report, Mufulira This is in accord with dynamic centrifuge modelling tests. Mine, Zambia, Report to Mines Safety Department, However, if low permeability silt or clay layers are Republic of Zambia and Zambia Consolidated Copper present, they impede the upward flow of water causing Mines Ltd. inflow and expansion in the sand directly beneath the low Byrne, P. M., and Beaty, M. H. (1997) Post-Liquefaction permeability barrier layer. This in turn can involve a very Shear Strength of Granular Soils: large reduction in residual strength during and after Theoritical/Conceptual Issues, Workshop on Post- shaking and could result in flow failures even in medium Liquefaction Shear Strength of Granular Soils, Urbana- dense sands. The amount of expansion depends on the Champion, Illinois, 16-45. density of the soil and the level and duration of shaking. Byrne, P. M. (1991) A Cyclic Shear-Volume Coupling and Analyses indicate that the actual thickness of the sand Pore Pressure Model for Sand. Second Int. Conf., layer itself is not a significant factor. Recent Advances in Geotechnical Earthquake Engg., and Soil Dynamics, St. Louis, Missouri, 2: 47-55. The results indicate that it is very important to identify the Byrne, P.M., and Anderson, D.L. (co-chairs) (1991) stratified nature of the soils present at a specific site, and Earthquake Design in the Fraser Delta, Task Force take permeability contrasts and mesh size into account in Report, City of Richmond, B.C. publication and Soil modelling and analysis. The results also indicate that Mech. Series No. 150, Dept. of Civil Engineering, drains can be very effective in preventing the barrier layer University of British Columbia, Vancouver, B.C. effect. They may not prevent the triggering of liquefaction Byrne, P.M., Imrie, A.S. and Morgenstern, N.R. 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