CHAPTER 3 LITERATURE REVIEW ON LIQUEFACTION ANALYSIS OF GROUND REINFORCEMENT SYSTEM

Transcription

1 CHAPTER 3 LITERATURE REVIEW ON LIQUEFACTION ANALYSIS OF GROUND REINFORCEMENT SYSTEM 3.1 The Simplified Procedure for Liquefaction Evaluation The Simplified Procedure wa firt propoed by Seed and Idri (1971). The procedure ha evolved over time and till been ued worldwide to analyze liquefaction reitance of oil. The following ection dicue the Simplified Procedure a propoed by the 1996 NCEER and 1998 NCEER/NSF Workhop (Youd, et al., 2001). Seed and Idri (1971) conidered a oil column a a rigid body. A the eimic loading i excited at the bae of the oil column and the hear wave propagate to the ground urface, hear tre i generated in the oil column and can be calculated by the following equation: amax max σ r 0 * (3.1) g ( ) where: ( max ) r maximum hear tre for rigid body σ 0 total overburden preure a max peak horizontal acceleration on the ground urface g acceleration of gravity In reality, oil behave a a deformable body intead of a a rigid body. Hence, the rigid body hear tre hould be reduced with a correction factor to give the deformable body hear tre ( max ) d. Thi correction factor i called the tre reduction coefficient (r d ) and can be computed a follow: ( max ) d r d *( max ) r (3.2) 37

2 where: ( max ) d maximum hear tre for deformable body r d the tre reduction coefficient The value of the tre reduction coefficient decreae with depth a hown on Figure 3.1 with a value of unity on the ground urface. The average value of r d can be etimated with the following equation (Liao and Whitman 1986a): r d z for z 9.15 meter (3.3a) r d z for 9.15 meter < z 23 meter (3.3b) or a uggeted by Blake (1996): z z z (3.4) z r d z z z + where: z depth of interet in meter. Both equation eentially reult in imilar value a hown on Figure 3.1. Some reearcher uggeted applying the tre reduction coefficient for depth greater than 15 meter but the Simplified Procedure ha not been verified with cae hitorie for thee depth (Youd, et al, 2001). If equation (3.1) i ubtituted into equation (3.2), the maximum hear tre for deformable body ( max ) d can be calculated a: amax max d r d *σ0 * (3.5) g ( ) Figure 3.2 how an example of hear tre time hitory during earthquake. It i apparent that the time hitory how a jagged hape. For practical purpoe, a value of an 38

3 equivalent average of hear tre ( ave ) hould be ued. Seed and Idri (1971) uggeted that a value of 65% of the maximum hear tre ( max ) i reaonably accurate. They baed their prediction by appropriate weighting of laboratory tet data. Therefore, equation (3.5) can be written in term of equivalent average of hear tre ( ave ): amax ave 0.65* σ 0 * * r d (3.6) g If the equivalent average of hear tre ( ave ) i normalized with the initial effective overburden preure (σ 0 ), the term i called the eimic demand of a oil layer or CSR (Cyclic Stre Ratio). CSR σ a ave 0 max 0.65* * * rd σ0' σ0' g (3.7) The Cyclic Stre Ratio (CSR) i only one of the variable needed in the evaluation of liquefaction reitance of oil. Cyclic Reitance Ratio (CRR) i another one. CRR expree the capacity of the oil to reit liquefaction. The following paragraph explain the determination of CRR baed on Standard Penetration Tet (SPT). The dicuion i limited on SPT becaue the value of SPT blow count would be ued in numerical analye in thi reearch. Procedure are alo available baed on Cone Penetration Tet (CPT), hear wave velocity meaurement, and Becker Penetration Tet (Youd, et al., 2001). The value of CRR can be determined by uing Figure 3.3. Figure 3.3 how correlation between (N 1 ) 60 and CRR for earthquake magnitude of 7.5. (N 1 ) 60 i the SPT blow count corrected to an effective overburden preure of 100 kpa (1 tf) and to a hammer energy efficiency of 60%. Both correction factor will be dicued later in thi ection. Curve for coheionle oil with fine content of 5% or le, 15%, and 35% are hown on Figure 3.3. The curve for fine content of 5% or le i called the SPT clean and bae curve. Rauch (1998) uggeted that thi curve could be approximated by the following equation: 39

4 ( N ) ( N ) c 50 1 CRR M (3.8) c 2 [ 10 *( N ) + 45] c where: (N 1 ) 60c equivalent clean and value of (N 1 ) 60 All curve on Figure 3.3 were drawn uing equation (3.8). The curve for fine content 5% and 35% are congruent with the original curve developed by Seed and Idri (1971). The curve for fine content of 15% fall to the right of the original curve. The value of SPT blow count for oil with fine content can be adjuted to the equivalent clean and value of (N 1 ) 60 o that equation (3.8) can be ued. Thi can be done by applying contant, α and β, that are function of fine content. Hence, the effect of fine content (FC) on the value of CRR i included a ( N 1 ) 60 α + β( N 1 ) c 60 (3.9) where α and β can be determined a follow: α 0 for FC 5% (3.10a) [ 1.76 ( 190 / FC )] 2 α exp for 5% < FC < 35% (3.10b) α 5.0 for FC 35% (3.10c) β 1.0 for FC 5% (3.11a) 1.5 [ ( FC /1000)] β for 5% < FC < 35% (3.11b) β 1.2 for FC 35% (3.11c) A noted previouly, the value of SPT blow count hould be corrected a ummarized on Table 3.1. The corrected blow count (N 1 ) 60 hould be determined a follow: ( N ) N mc NCEC BC RCS 1 (3.12) 60 40

5 where: N m uncorrected SPT blow count C N correction factor for effective overburden preure C E correction factor for hammer energy ratio C B correction factor for borehole diameter C R correction factor for rod length C S correction factor for ampler with or without liner The correction factor for effective overburden preure (C N ) can be determined uing either of the following equation (Liao and Whitman, 1986a): Pa C N (3.13a) σ 0 ' or a uggeted by Kayen, et al. (1992): C N 2.2 σ ' (3.13b) P a where: σ 0 effective overburden preure P a atmopheric preure in the ame unit a σ 0 The value of C N in equation (3.13a) hould not exceed 1.7 while equation (3.13b) already limit the value of C N to 1.7. The value of effective overburden preure (σ 0 ) in both equation hould be the preure at the time SPT tet i performed. The SPT clean and bae curve can only be applied to earthquake with magnitude of 7.5. For earthquake magnitude other than 7.5, a magnitude-caling factor (MSF) hould be applied. Youd, et al. (2001) uggeted to ue the following equation to determine the value of MSF. It i alo hown on Table

6 For earthquake magnitude < 7.5: Lower bound: MSF (3.14a) M w Upper bound: 2.56 M w MSF (3.14b) 7.5 where: M w earthquake moment magnitude The value of MSF for earthquake magnitude larger than 7.5 can be een on Table 3.2. Thee value hould be ued with judgment and conideration becaue there are only few welldocumented data for liquefaction cae hitorie for earthquake magnitude larger than 8. A noted previouly (refer to Figure 3.1), the Simplified Procedure applie for level to gently lope ite and for depth le than 15 meter. Therefore, the value of CRR hould be corrected for greater depth that i for high overburden tree. The correction factor (K σ ) i hown on Figure 3.4. It i apparent that K σ i equal to unity for effective overburden preure le than 1 tf and then decreae with increaing effective overburden preure. Figure 3.4 can alo be etimated by uing the following equation: ' ( f 1) 0 σ K σ (3.15) P a where: f exponent a a function of relative denity, tre hitory, aging, and overconolidation ratio. f for relative denitie between 40% and 60% f for relative denitie between 60% and 80% There are correction factor for loping ground (high tatic hear tre) and aging but ince there i no enough data, thee correction factor hould be ued with judgment. Thee apect are till open for further reearch. 42

7 Hence, it can be concluded that the value of CRR for a particular earthquake magnitude can be determined a: CRR CRRM * MSF * (3.16) 7.5 K σ The factor of afety againt liquefaction can be written a: CRR FS L (3.17) CSR 3.2 Baez and Martin Procedure A noted in Chapter 2, effort have been developed to mitigate the damage caued by liquefaction. The effort include denification of the liquefiable oil and/or by providing drainage path for pore water preure diipation. Baez and Martin (1993, 1994) propoed a deign procedure that include both criteria above. The procedure wa developed for vibroreplacement tone column and vibro-concrete column and included denification, drainage, and tre concentration criteria. Of particular interet for thi reearch i the tre concentration criterion. Explanation for both mitigation technique can be een in Chapter 2. The baic aumption for their procedure i that the hear train in the oil and in the tone column are compatible. γ γ c (3.18) and ince γ /G, G G c c (3.19) 43

8 where: γ hear train in the oil matrix γ c hear train in the tone column matrix hear tre in the oil matrix c hear tre in the tone column matrix G hear modulu of the oil matrix G c hear modulu of the tone column Equilibrium alo require that the hear tre generated at a given depth be ditributed to the hear tre in the oil matrix and in the tone column. A + A A (3.20) c c where: the input hear tre can be etimated uing the Simplified Procedure (Seed and Idri, 1971) uing equation (3.6) A total plan area A +A c A plan area of the oil matrix A c plan area of the tone column The ratio between the area of tone column and the total plan area can be written a: A A c r A (3.21) and the ratio between the hear modulu of the tone column and the hear modulu of the oil can be written a: G c G r (3.22) G 44

9 Therefore, uing equation (3.22), equation (3.19) can be written a c (3.23) Gr By uing equation (3.19), (3.20), (3.21), (3.22), and (3.23), the hear tre in the oil can be determined a follow: a 0.65σ 0 g max r d 1 1+ A r ( G 1) r (3.24) Baez and Martin (1993, 1994) defined the ratio expreed in equation (3.24) a the hear tre reduction factor (K G ). Thi factor hould be introduced becaue the Simplified Procedure doe not take into account incluion of any reinforcing element. It i obviou that if there are no reinforcing element intalled in the ground (G r 1), the value of K G will be equal to unity and the hear tre in the oil will be equal to that uggeted by equation (3.6). Equation (3.24) can be applied to develop a chart howing K G a a function of area replacement ratio (A r ) and the hear modulu ratio (G r ) a hown on Figure Goughnour and Petana Procedure Goughnour and Petana (1998) modified the procedure propoed by Baez and Martin (1993, 1994) by including the effect of lenderne ratio of the tone column and the vertical tre ratio. The lenderne ratio i defined a the ratio of the height to the width of the tone column and the vertical tre ratio i the ratio of overburden preure within the tone column to the overburden preure within the oil matrix. They argued that the column might experience bending which i likely caued by the large lenderne ratio of the column. They derived equation by taking into account the effect of the lenderne ratio of the tone column and uggeted that the equivalent hear modulu of 45

10 the tone column with taking into account the effect of the lenderne ratio can be determined uing: G cm πd c 2λ 2 E c (3.25) where: d c the diameter of the tone column λ the wave length E the elatic modulu of the tone column The elatic modulu of tone column can be etimated uing the value of the hear modulu of the tone column: where: ν Poion ratio E c ( ν ) Gc 2 1+ (3.26) By ubtituting equation (3.26) into equation (3.25), the following equation hould be obtained: 1 πd c G cm Gc ( 1+ ν ) (3.27) 2 λ 2 where all term have been explained previouly. It can be een that the value of G cm i equal to or larger than the value of G c for a value of d c /λ equal to or larger than 0.4. In practice, thee value of d c /λ are unlikely to be found. Therefore, the value of G cm might be maller than the value of G c and G. It mean the tone column i more flexible than the oil. Goughnour and Petana (1998) argued that the hear 46

11 tre in the oil would actually increae becaue the tone column will move together with the oil. Thi may ound contradictory but it can be explained ince the hear tre on the interface between the oil matrix and the tone column i aumed to be negligible. It can be concluded that the preence of tone column fail to reduce the hear tre perceived by the oil matrix. Thi i the cae for typical lenderne ratio ued in practice. Goughnour and Petana (1998) alo uggeted the ue of the vertical tre ratio (n) that i the ratio of the effective overburden preure within the tone column to the effective overburden preure within the oil matrix. n σ ' 0 c (3.28) σ ' 0 (1989): The value of σ 0 can be etimated uing equation propoed by Goughnour and Jone ( σ 0 ' ) ave + ( n 1) σ 0 ' (3.29) 1 A r where: (σ 0 ) ave the average overburden preure in the oil matrix. The typical value of n vary between 4 and 10 baed on model tet and 2 to >10 baed on field meaurement. Barkdale and Bachu (1989) uggeted a different approach to calculate the vertical tre ratio (n). σ 0 ' n σ ' 0 c G r 1 ν 1 2ν 1 ν 1 2ν c (3.30) where G r i from equation (3.22). 47

12 A a concluion of their tudy, Goughnour and Petana (1998) uggeted the ue of the following value of hear tre reduction factor (K G ) intead of the one uggeted by Baez and Martin (1993, 1994) in equation (3.24): K G 1+ A 1+ A r r ( n 1) ( G 1) r (3.31) Note that the only new term introduced here i the nominator, 1+A r (n-1), intead of unity a uggeted by Baez and Martin (1993, 1994). 3.4 Calculation Example An example i given in thi ection to decribe the ue of the three procedure explained in the previou ection. Suppoe there i a oil profile with clean and at a depth of 5 feet a hown on Figure 3.6. Later on, a tone column i intalled for thi ite. The parameter for the oil, the earthquake, and the tone column are a follow: Soil parameter: Saturated unit weight (γ at ) 120 pcf Corrected SPT blow count [(N 1 ) 60 ] 10 blow/feet Shear modulu (G ) 100 MPa 2,100,000 pf Poion ratio 0.3 Earthquake parameter: Earthquake magnitude 7.5 Peak horizontal acceleration on the ground urface (a max ) 0.45g 48

13 Stone column parameter: Diameter (d c ) 3 feet Length 14.5 feet (intalled to depth of the rock urface) Shear modulu (G c ) 220 MPa 4,620,000 pf Poion ratio Simplified Procedure (Seed and Idri, 1971) 1. Determination of the tre reduction coefficient uing equation (3.3) or (3.4) or Figure 3.1. By uing equation (3.3) for depth le than 9.15 m, the value of r d for depth of 5 feet (1.524 meter): r d ( *1.524) Calculation of the Cyclic Stre Ratio (CSR) uing equation (3.7). Firt, the total and the effective overburden preure have to be determined: σ 120*5 600 pf 0. 3 tf 0 ( ) *5 288 pf tf σ 0 ' Uing equation (3.7), the value of CSR can be determined: ave CSR σ ' * g * * g 3. Calculation of the Cyclic Reitance Ratio (CRR) uing equation (3.8) or Figure 3.3. Since, the oil i clean and, no correction for fine content i needed and ince the SPT blow count i already a corrected one, there i no need for correcting the SPT blow count. Therefore, uing equation (3.8) the CRR value become: 49

14 CRR ( 34 10) 135 [( 10*10) + 45] M Calculation of the Magnitude Scaling Factor (MSF) uing equation (3.14). The earthquake magnitude i 7.5. Hence, the earthquake magnitude i not neceary to be corrected uing MSF. 5. Calculation of the correction for high overburden preure (K σ ) uing equation (3.15) or Figure 3.4. From tep 2, it wa obtained that the effective overburden preure (σ 0 ) i le than 1 tf. Therefore, the correction for high overburden preure (K σ ) i equal to unity (refer to Figure 3.4). 6. Calculation of the corrected CRR uing equation (3.16). Since the value of MSF and K σ are equal to unity, CRR CRR M Calculation of factor of afety againt liquefaction (FS L ) uing equation (3.17). The factor of afety againt liquefaction can be calculated a FS L Since the factor of afety againt liquefaction i le than unity, thi ite i uceptible to liquefaction Baez and Martin Procedure (1993, 1994) 1. Determination of the hear modulu ratio (G r ) uing equation (3.22). The ratio between the hear modulu of the tone column and the hear modulu of the oil can be computed a: 50

15 G r 4,620,000 2,100, Calculation of the area replacement ratio (A r ) uing equation (3.21). Suppoedly, it i required to have an area replacement ratio (A r ) 10%, that i the area of tone column cover 10% of the total plan area. 3. Calculation of the hear tre reduction factor (K G ) uing equation (3.24) or Figure (3.5). K G 1 1+ [0.1* ( 2.2 ) ] 4. Calculation of the hear tre induced by the earthquake ( ave ) uing equation (3.6). The hear tre induced by the earthquake ( ave ) or the input hear tre can be etimated uing the Simplified Procedure (Seed and Idri, 1971). 0.45g 0.65* 600* * g pf 5. Calculation of the hear tre in the oil ( ) uing equation (3.24). Therefore, the hear tre in the oil matrix ( ) can be determined a K G * 0.89* pf Goughnour and Petana Procedure (1998) 1. Determination of the vertical tre ratio (n) uing equation (3.30). The only difference of thi procedure to that of Baez and Martin (1993, 1994) i in the calculation of the hear tre reduction factor (K G ). For thi procedure, the value of K G can be etimated uing equation (3.31). Firt, the vertical tre ratio (n) ha to be determined: 51

16 (1 0.2) 1 (2*0.2) 2.2 n 1.68 (1 0.3) 1 (2 *0.3) 2. Calculation of the hear tre reduction factor (K G ) uing equation (3.31). After the value of n i obtained, the value of the hear tre reduction factor (K G ) can be computed a follow: K G ( 1) ( 1) Calculation of the hear tre in the oil ( ) uing equation (3.31). The hear tre induced by the earthquake ( ave ) ha been etimated uing the Simplified Procedure (refer to Section tep 4). Therefore, the hear tre in the oil matrix ( ) can be determined a K G * 0.95* pf It can be concluded that for thi example the Goughnour and Petana procedure give lightly higher hear tre in the oil matrix ( 165 pf) compared to that of the Baez and Martin procedure ( 154 pf). 52

17 Table 3.1 Correction to SPT (after Youd, et al., 2001) Factor Equipment variable Term Correction Overburden preure - C N (P a /σ 0 ) Donut hammer C E Safety hammer C E Energy ratio Automatic-trip C Donut-type hammer E mm C B 1.0 Borehole 150 mm C B 1.05 diameter 200 mm C B 1.15 < 3m C R m C R 0.8 Rod length 4 6 m C R m C R m C R 1.0 Sampling method Standard ampler C S 1.0 Sampler without liner C S

18 Table 3.2 Magnitude caling factor (after Youd, et al., 2001) Earthquake magnitude, M w Lower bound [equation (3.14a)] Upper bound [equation (3.14b)]

19 0 Stre reduction coefficient, r d Depth (m) 10 Range for different oil profile by Seed & Idri (1971) Approx. average value from eq. (3.4) Approx. average value from eq. (3.3) Figure 3.1 Value of tre reduction coefficient veru depth 55

20 Shear Stre (kf) Time (ec.) Figure 3.2 Example of hear tre time hitory during earthquake 56

21 FC35% 15% >5% 0.4 CRR SPT clean and bae curve 0.1 All curve were drawn uing eq. (3.8) Corrected blow count, (N 1 ) 60 Figure 3.3 SPT clean-and bae curve for magnitude 7.5 earthquake 57

22 K σ Dr < 40% (f0.8) Dr 60% (f0.7) Dr > 80% (f0.6) Effective overburden preure, σ 0 ' (atm unit, e.g. tf) Figure 3.4 K σ correction factor (after Youd, et al., 2001) 58

23 Shear tre reduction factor, KG G r 2 G r 3 G r 4 G r 5 G r Area replacement ratio, A r (%) Figure 3.5 The hear tre reduction factor, K G (after Baez and Martin, 1993, 1994) 59

24 Ground water table 5 feet 14.5 feet Clean and Rock Figure 3.6 Soil profile for calculation example 60