Simplified procedure to estimate ground settlement from seismic compression in compacted soils

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Simplified procedure to estimte ground settlement from seismic compression in compcted soils J.P. Stewrt & D.H. Whng University of Cliforni, Los Angeles, CA, USA.

1 Simplified procedure to estimte ground settlement from seismic compression in compcted soils J.P. Stewrt & D.H. Whng University of Cliforni, Los Angeles, CA, USA. ABSTRACT: Seismic compression is defined s the ccrul of contrctive volumetric strins in unsturted soil during strong shking from erthqukes. We describe simplified procedure for estimting ground displcements from seismic compression in compcted fill. The procedure hs three steps: () estimtion of sher strin mplitude within the fill soil mss from the pek ccelertion t the ground surfce nd other seismologicl nd site prmeters; () estimtion of volumetric strins within the fill mss bsed on compction conditions in the fill, the sher strin mplitude, nd the equivlent number of uniform strin cycles; nd () integrtion of volumetric strins cross the fill section to estimte settlement. The frmework of the present procedure is similr to tht of Tokimtsu nd Seed (987), which is strictly pplicble only to clen snds. We updte this widely used procedure to incorporte reltively recent mteril models for clen snds, nd to extend the formultion to llow nlysis of non-plstic silty snds nd low-plsticity clys. The procedure is implemented for three field cse history sites with mesured settlements, nd is found to generlly provide resonble, first-order estimtes of ground settlements given the simplifying ssumptions ssocited with this pproximte method of nlysis. INTRODUCTION Ground deformtions in compcted fill slopes from seismic compression hve been well documented in the literture (e.g. Pyke et l., 975; Stewrt et l., ), nd re recognized s representing significnt hzrd with respect to collterl loss during future erthqukes. Accordingly, the estimtion of ground settlements from seismic compression is becoming common component of geotechnicl seismic design prctice for hillside res in the mountinous res of southern Cliforni. The current stte of prctice for estimting the seismic compression of unsturted compcted fill soils consists of the methodology presented by Tokimtsu nd Seed (987), which is strictly pplicble only to clen snds. Our objective in this pper is to updte this widely used procedure to incorporte reltively recent test dt for compcted sndy soils, nd to extend the formultion to llow nlysis of recently compcted fill soils contining significnt fines. Prtil motivtion for this updte comes from lbortory testing by Stewrt et l. (), which hs shown tht clen snds cn experience up to ten times more verticl strin thn soils with fines compcted to comprble density. Consequently, current methods for estimting seismic compression my be overly conservtive, nd my not be pplicble to soils contining fines. In this pper, we present brief summry of the Tokimtsu nd Seed (987) methodology; discuss dvnces since 987 tht provide n opportunity to improve the nlysis procedure; outline new nlysis procedure similr in formt to the 987 procedure but incorporting recent dvnces; nd pply the procedure to three field cse history sites. Pper 46

2 EXISTING STATE-OF-PRACTICE FOR SEISMIC COMPRESSION ANALYSIS The originl Tokimtsu nd Seed (987) nlysis procedure is bsed on simplified representtion of the distribution of sher stress with depth in one-dimensionl soil column. If the soil column bove soil element t depth h behves s rigid body, nd the surfce pek horizontl ccelertion is PHA, then the mss of soil bove h would impose mximum sher stress of: τ PHA = g rigid, mx σ () where g = the ccelertion due to grvity nd σ o = totl overburden pressure t depth h. Soil flexibility reduces the sher stress to vlues less thn τ rigid, mx, s result of verticl incoherence of ground motion. Seed nd Idriss (97) developed simplified technique to estimte erthquke induced cycle sher stresses t depth. They multiplied τ rigid,mx by stress reduction fctor, r d (which is the rtio of the ctul sher stress t depth vs. the theoreticl rigid body sher stress). A fctor of.65 is then pplied to reduce the pek cyclic sher stress, τ mx, to the ective cyclic stress, τ, s: PHA τ =.65 σ r d () g Effective sher strin, γ, is estimted from τ using the ective sher modulus (G ), s follows: τ τ γ = = () G G G mx Gmx where G mx = smll strin sher modulus. Combining Eqs. nd leds to: G.65 PHA σ o rd γ = (4) G g G mx mx The product γ (G /G mx ) in Eq. 4 cn be redily trnslted to sher strin mplitude γ using published models for soil modulus reduction with incresing sher strin (i.e. models relting γ to G /G mx ). Tokimtsu nd Seed (987) recommended using the modulus reduction curves of Iwski et l. (978), which depend on ective stress. Hving estimted γ with the bove procedure, volumetric strins t 5 cycles of shking [(ε v ) N=5 ] re estimted using n pproprite volumetric strin mteril model (these models relte (ε v ) N=5 to γ, nd depend on the compction condition of the fill soil). Tokimtsu nd Seed (987) utilized the volumetric strin mteril model of Silver nd Seed (97), which re derived from lbortory simple sher testing of clen snds. In tht work, compction condition for snds is represented by reltive density (D r ). The vlues of (ε v ) N=5 re djusted to the volumetric strin (ε v ) for the ctul number of strin cycles (N) using the fctor C N = ε v /(ε v ) N=5. Tokimtsu nd Seed (987) recommended using C N reltions for clen snd derived from testing by Silver nd Seed (97). Prmeter N is ground motion intensity mesure (like PHA), nd Tokimtsu nd Seed (987) recommended tht it be estimted using n empiricl reltionship between mgnitude (m) nd N proposed by Seed et l. (975). The N-djusted volumetric strin ε v is multiplied by two to ccount for multi-directionl shking ects per the recommendtions of Pyke et l. (975). Hence, the finl estimte of volumetric strin t point is represented by C N (ε v ) N=5. These volumetric strins re then integrted over the depth of the soil column to clculte settlement.

ADVANCES SINCE 987 Severl fetures of the originl Tokimtsu nd Seed (987) procedure for seismic compression nlysis cn be updted. These include: () new reltions for r d developed by Seed et l.

3 ADVANCES SINCE 987 Severl fetures of the originl Tokimtsu nd Seed (987) procedure for seismic compression nlysis cn be updted. These include: () new reltions for r d developed by Seed et l. (); () new reltions for N by Liu et l. (); () new models for modulus reduction which incorporte the ects of ective stress, soil plsticity, nd other fctors, by Drendeli nd Stokoe (); nd (4) new mteril models relting sher strin to volumetric strin for sndy soils nd soils with fines by Stewrt et l. (). The following sections present the rtionle for mking these chnges nd synthesize the criticl fetures of the new model components.. Stress Reduction Fctors (r d ) The originl stress reduction fctors recommended by Tokimtsu nd Seed (987) re the fctors by Seed nd Idriss (97) tht hve been widely used for soil liquefction pplictions. These fctors, shown by the solid lines in Figure, re bsed on the results of limited number of ground response nlyses. Seed et l. () found these fctors to be bised (generlly high) bsed on reltively extensive prmetric study involving 5 combintions of site profiles nd input motions. Profiles of r d from tht study re lso shown in Figure. Using these profiles, Seed et l. () regressed r d ginst PHA, depth (z), mgnitude (m), nd verge soil sher wve velocity in the upper m (V s- ), nd recommended the following reltionship for the medin of r d : z < m: z > m: [ + ( z) ] [ ] r d = (5) + [ + ( z = ) ] [ + ] r d =.46( z ) (5b) where, =..949 PHA/ g m +. 5 Vs ( z) ( z.785 V ).4 + s = e (z=) is (z) with z set to m ( z) (.785 V ).4 s = e In ll of the bove, depth (z) is in meters nd velocity (V s- ) is in m/s. Figure. Stress reduction fctors recommended by Seed nd Idriss (97) long with ground response nlysis results of Seed et l. ()

4 . Equivlent Number of Uniform Strin Cycles (N) Using strong motion dt set for tectoniclly ctive regions, Liu et l. () developed empiricl regression equtions to evlute the equivlent number of uniform stress cycles of erthquke shking s function of mgnitude (m), site-source distnce (r), site condition (S= for rock, S= for soil), nd ner-fult rupture directivity ects. The N vlues were derived bsed on weighting fctors specific to the problem of soil liquefction triggering. However, one of the sets of weighting fctors used by Liu et l. ws found by Stewrt et l. () to be pproprite for evlution of equivlent number of uniform strin cycles (N) for the seismic compression of snd. Predictions by tht model for non nerfult conditions re shown in Figure, nd the medin model predictions re given by, exp ln( N) = ln ( b + b ( m m *)) 6.5.5m β + Sc + rc where r is in km, b =.5, b =.5, c =.75, c =.95, β =., nd m* = 5.8. This model is more consistent with dt thn the model of Seed et l. (975), which depends only on mgnitude nd is tilored to the problem of soil liquefction. Figure shows significnt differences between these models, prticulrly t lrge distnces. Soil sites Rock Sites m = 7.5 (6) Number of Cycles, N m = 6. m = 5.5 m = 6.75 m=7.5 m=6.75 m=6. Seed et l. m = Distnce, r (km) Figure. Vrition of medin vlues of N with distnce nd mgnitude from Liu et l. () long with recommendtions of Seed et l. (975).. Modulus Reduction Curves Modulus reduction curves hve criticl role in the nlysis procedure, s they re used to estimte sher strins per Eq. 4. Tokimtsu nd Seed (987) recommended the use of modulus reduction curves for clen uniform snds by Iwski et l. (978), which depend on ective stress. The model for modulus reduction by Drendeli nd Stokoe () is bsed on much lrger suite of test results, nd incorportes ects of ective stress (σ ), soil plsticity (s represented by plsticity index, PI), nd overconsolidtion rtio (OCR). Figure shows fmily of modulus reduction curves (bsed on the D&S model) for vrying PI nd σ (the ects of OCR re generlly smll, nd the plots in Figure pply for OCR =, which is generlly pproprite for fills t z >-6 m, Duncn et l., 99). Note tht the plots in Figure re formtted to directly estimte sher strin, γ from the product γ (G/G mx ). 4

5 . D&S PI= D&S PI=5 Iwski (snd). D&S PI= D&S PI=5 Iwski (snd) γ γ.. σ =. tm σ =. tm. E-5.. γ G/G mx. E-5.. γ G/G mx Figure. Modulus reduction curves from Iwski (978) nd Drendeli nd Stokoe () re-expressed in formt for estimtion of sher strin mplitude, showing ects of ective overburden stress nd soil plsticity The D&S results show tht nonlinerity decreses with incresing soil plsticity (s shown by shifting of the curves in Figure to the right s PI increses). At reltively lrge confining pressures (σ >.5 tm), the D&S curves for both PI = nd 5 re more nonliner thn those by Iwski, which cn ffect significntly the computed sher strins s shown subsequently in Section 5. Prdel (998) developed fit to the Iwski curves shown in Figure using the following eqution: b R + e γ = R (in %) (7) + where R is the product computed in Eq. 4. We use this sme regression eqution for the D&S curves, nd find nd b to be soil-type dependnt s follows: PI 5: =.94 ( p ) b 749 ( σ p ) σ = PI : =.99 ( p ).. 4 b 85 ( σ p ) σ = where p =. kp. Sher strins for PI between nd 5 cn be interpolted using Eq Mteril Models for Volumetric Strin A volumetric strin mteril model is defined s reltionship between () cyclic sher strin mplitude, γ c, nd (ε v ) N=5 nd () C N nd N. Tokimtsu nd Seed (987) recommended the use of volumetric strin mteril models tht were derived from cyclic simple sher testing of clen snds by Silver nd Seed (97). Recent simple sher testing t UCLA hs re-exmined these reltionships for clen snd nd hs developed models for severl fill soils contining fines. The UCLA test results on clen snds re synthesized in the left frme of Figure 4 t D r = 6%, nd re lso compred to the test results of Silver nd Seed (97). The recent testing ws performed on 6 snds spnning rnge of snd compositionl fctors (grdtion, grin size, grin ngulrity). No trends in (ε v ) N=5 were found reltive to these compositionl fctors, lthough the collective results provide insight into the vribility ssocited with volumetric strin mteril models for snd. The right side of Figure 4 shows medin ± two stndrd devition results for C N bsed on the testing of the 6 snds once gin, no trends with compositionl fctors ws found. Also shown is the recommended curve by Silver nd Seed (97), which predicts less settlement for erthqukes with smll number of cycles (N < 5) nd more settlement for N > 5. 5

6 .5 Verticl strin, ε v,n=5.5.5 This study, 6 snds, D r =6% Men, µ µ ± σ Silver nd Seed, 97 Crystl silic, D r = 6% C N = ε v /ε v, N= Rnge for clen snd (µ ± σ) Men, Silver & Seed (97).. Sher Strin, γ c Number of Cycles, N Figure 4. Volumetric strin mteril models bsed on simple sher testing of clen snds Testing of fill soils with fines hs been performed on four specimens from two field sites tht were investigted in detil by Stewrt et l. (). The results provide insight into the ects of essentilly non-plstic fines (PI = ) nd low-plsticity fines (PI = 5) on the seismic compression of soil with lrge fines content (pproximtely 5%). Curve fits to these test results re compred to clen snd results in Figure 5, nd show tht. For the sme Modified Proctor reltive compction (RC), soils with non-plstic fines experience less seismic compression thn clen snds for common set of bseline conditions, but these two mterils behve similrly in the sense tht RC is the principl constructionrelted fctor ffecting seismic compression (i.e. degree-of-sturtion, S, is not importnt), nd. Seismic compression in soils with low-plsticity fines decreses not only with incresing RC, but lso for moderte RCs decreses with incresing s-compcted degree-of-sturtion (S). At low S, volumetric strins from seismic compression re comprble to those for snd (t common RC), wheres t high S the strins re pproximtely one-qurter of those for snd. The C N curves for these mterils re generlly similr to the lower-bound C N curve shown in Figure 4 (i.e. the curve showing the most rpid degrdtion with N). The results shown in Figure 5 for these mterils my not be pplicble to other fill soils. Verticl Strin, ε v, N=5.5.5 Silty Snds RC=9% RC=9.5% RC=95% Rnge for snds t D r = 6% (equivlent RC 9-9%) Verticl Strin, ε v, N=5.5.5 Low-plsticity cly S = 66% S = 74% S = 88% Rnge for snd t D r = 6% (equiv. RC 9-9%) RC = 84% RC = 88% RC = 9%.. Sher Strin, γ c.. Sher Strin, γ c Figure 5. Volumetric strin mteril models bsed on simple sher testing of soils with fines 6

7 4 RECOMMENDED ANALYSIS PROCEDURE The procedure hs three generl steps: () estimtion of sher strin mplitude within the fill soil mss from the pek ccelertion t the ground surfce nd other seismologicl nd site prmeters; () estimtion of volumetric strins within the fill mss bsed on compction conditions in the fill, the sher strin mplitude, nd the equivlent number of uniform strin cycles; nd () integrtion of volumetric strins cross the fill section to estimte settlement. Detils on the first two steps follow: (). (b). Estimte PHA nd N using pproprite seismic hzrd nlyses. The PHA vlue should pply for the ground condition t the surfce of the fill. This will generlly require ccounting for ground response ects either through site-specific nlysis (preferred) or ppliction of n mplifiction fctor. Amplifiction fctor models pplicble to the shllow soil over rock configurtion of hillside fills re unvilble, but investigtions of severl specific sites by Stewrt et l. () hve generlly found PHA mplifictions of bout.5 to. for typicl design levels of shking (i.e. PHA on rock.-.7 g). Mesure or estimte sher wve velocity in fill soils, nd estimte the mximum sher modulus s G mx = V s ρ, where ρ = mss density of soil. (c). Estimte stress reduction fctors (r d ) s function of depth using the reltion in Eqs. 5. (d). Estimte the vrition of sher strin mplitude (γ ) with depth using Eq. 4 nd Figure. (). (b). Estimte (ε v ) N=5 bsed on γ nd soil compction condition using pproprite mteril models for volumetric strin (Section.4). Estimte C N nd clculte ε v = C N (ε v ) N=5. Multiply by two to ccount for multidirectionl shking ects. 5 COMPARISON TO CASE HISTORIES In this section, we compre predictions from the bove nlysis procedure to observed settlements t three sites where such settlements re relibly known from survey mesurements. One of the cse studies is fill blnket t the Jensen Filtrtion Plnt shken by the 97 Sn Fernndo, Cliforni erthquke (Pyke et l., 975), nd the other two (denoted Sites A nd B) re cnyon fills in Snt Clrit shken by the Northridge, Cliforni erthquke (Stewrt et l., ). It should be emphsized tht these cse histories do not provide sufficient dt set ginst which to clibrte the nlysis procedure. We present these comprisons merely to illustrte the generl performnce of the model for typicl design-bsis levels of shking in seismiclly ctive regions. At the Jensen site, the clyey snd fill is up to 7 m thick nd overlies.5-6 m of lluvium. The wter tble is locted in the lluvium, which liquefied during the erthquke cusing lterl spreding. Estimted pek ccelertions t the site re.5-.6 g. Observed settlements long survey bseline were.7 cm, lthough some of these settlements cn be ttributed to lterl spreding. Pyke et l. (975) estimted the settlements from seismic compression to be pproximtely 9 to cm. At Snt Clrit Site A, the sndy cly fill is up to 4 m thick nd overlies shllow lluvium nd rock. Modified Proctor reltive compctions of fill re 88%, nd the fill ws generlly compcted dry of optimum. Pek ccelertions t the site hve been estimted s.5-.7 g. Settlements s lrge s cm occurred in building t the site. Site B hs silty snd fill vrying from 5 to m thick overlying rock. Modified Proctor reltive compctions of ner-surfce fill soils were pproximtely 9%, nd pproximtely 95% t depth. Pek ccelertions t the site hve been estimted s pproximtely.8 to. g. Observed settlements of the fill rnged from bout to 6 cm. For Snt Clrit Sites A-B, the vribility of input prmeters V s nd PHA ws estimted nd integrted into the nlysis using logic tree pproch. Weighted mens nd stndrd devitions were clculted from the distributions of clculted settlements. Best estimte soil properties were used for the Jensen site. We ccount for mtric suction ects on σ in our nlysis of γ. Mtric suction does not ffect totl stress σ o, but is estimted to dd tm to σ bsed on typicl soil-wter chrcteristic 7

8 curves (Fredlund, 99). As shown in Tble, clculted settlements re resonbly consistent with observtion for Jensen nd Site A, but not for Site B. The problem t Site B ppers to be the very strong levels of shking (PHA > g), for which Figure provides unrelisticlly lrge estimtes of γ. Site-specific ground response nlysis of Site B provides unbised estimtes (Stewrt et l., ), nd pper to be needed to relibly estimte γ for very strong shking. Tble. Summry of clculted (medin one stndrd devition) nd observed settlements 6 CONCLUSIONS Site Recommended Procedure (cm) Observtion (cm) Jensen Site A 6.9 +/ Site B 4.5 +/ In this pper we present n nlysis procedure to estimte settlements from seismic compression. The procedure de-couples the clcultions of sher strin nd volumetric strin, nd utilizes recent reserch results on stress reduction fctors (r d ), soil modulus reduction curves, nd soil volumetric strin models. The results re generlly found to compre fvorbly to observtion, lthough problems in sher strin estimtion re encountered for very strong levels of shking (PHA vlues over g). REFERENCES: Drendeli M.B. nd Stokoe K.H.. Development of new fmily of normlized modulus reduction nd mteril dmping curves, University of Texs, Geotechnicl Engineering Report GD-. Duncn J.M., Willims G.W., Sehn A.L., nd Seed R.B. 99. Estimtion of erth pressures due to compction, J. Geotech. Engrg., ASCE, 7 (), Iwski T, Ttsuok F., nd Tkgi Y Sher modulus of snds under cyclic torsionl sher loding, Soils nd Foundtions, 8 (), 9-5. Fredlund, D. G. 99. Soil mechnics for unsturted soils, Wiley, New York. Liu A.H., Stewrt J.P., Abrhmson N.A. nd Moriwki, Y.. Equivlent number of uniform stress cycles for soil liquefction nlysis, J. Geotech. & Geoenv. Engrg., ASCE, 7 (), 7-6. Prdel D Procedure to evlute erthquke-induced settlements in dry sndy soils, J. Geotech. & Geoenv. Engrg., ASCE, 4 (4), Pyke R., Seed H.B., Chn C.K Settlement of snds under multidirectionl shking, J. Geotech. Engrg., ASCE, (4), Seed H.B. nd Idriss I.M. 97. Simplified procedure for evluting soil liquefction potentil, J. Soil Mech. & Foundtions Div., ASCE, 97(9), Seed H.B., Idriss I.M., Mkdisi F., nd Bnerjee N. (975). Representtion of irregulr stress time histories by equivlent uniform stress series in liquefction nlyses, Rpt. No. UCB/EERC-75-9, U.C. Berkeley. Seed, R.B., Cetin, K.O., Moss, R.E.S., Kmmerer, A.M., Wu, J., Pestn, J.M., nd Riemer, M.F.. Recent dvnces in soil liquefction engineering nd seismic site response evlution, Proc. 4 th Int. Conf. on Recent Advnces in Geotech. Eqk. Engrg. Soil Dyn., Pper No. SPL- Silver M.L. nd Seed H.B. 97. Volume chnges in snds due to cyclic loding, J. Soil Mech. & Foundtions Div., ASCE, 97(9), 7-8. Stewrt J.P., Bry J.D., McMhon D.J., Smith P.M., nd Kropp A.L.. Seismic performnce of hillside fills, J. Geotech. & Geoenv. Engrg., ASCE, 7 (), Stewrt J.P., Smith P.M., Whng D.H., nd Bry J.D. in press. Documenttion nd nlysis of field cse histories of seismic compression during the 994 Northridge, Cliforni erthquke, Report No. PEER- /9, Pcific Erthquke Engineering Reserch Center, U.C. Berkeley, October. Tokimtsu K. nd Seed H.B Evlution of settlements in snds due to erthquke shking, J. Geotech. Engrg., ASCE, (8),

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