Evaluation of triggering acceleration required for commencement of liquefaction.

Earthquake induced liquefaction is one of the most severe seismic hazards that can damage structures founded on both shallow and deep foundations. Significant amounts of damages have been directly or indirectly attributed to the liquefaction phenomenon in several earthquakes. Assessment of liquefaction potential of sandy soils has attracted considerable attention over the past few decades. Number of techniques have been developed to estimate the likelihood that liquefaction may or may not occur at a given site under specified conditions. Richards et. al. (1999) have proposed a new concept of triggering acceleration for commencement of liquefaction. Authors of this paper have carried out the work to investigate a method for evaluating the triggering acceleration for the initiation of liquefaction in fully saturated sands. Once the initial fluidization occurs, the liquefaction is inevitable which ultimately results into considerable damages. The present work deals with the evaluation of triggering acceleration indicating initiation of liquefaction. Authors have developed a method to compute this acceleration based on model already established by them (1999); which has been used to demarcate "yes" and "no" zones of liquefaction in terms of earthquake magnitude, standard penetration values, initial overburden stress on level ground and epicentral distance.

INTRODUCTION

Liquefaction is one of the most severe seismic hazards that can damage structures founded on both shallow and deep foundations and disrupt buried lifelines with potentially catastrophic consequences for water supply and fire following earthquakes. Assessment of liquefaction potential for sandy soils has attracted considerable attention over the past 30 years. A number of techniques have been developed to estimate the liklihood that liquefaction may or may not occur at a given site under specified conditions. Number of mathematical/numerical models are developed by Davis and Berill(1982), Trifunac (1995), Zhang (1998) and Phatak and Pathak(1999), using the field data for prediction of liquefaction.

Phatak and Pathak (1999) have developed a model for the determination of sites prone to liquefaction based on the seismic energy methodology using Gutenberg-Richter (1956) relation for energy released from an earthquake attenuated for geometric spreading (Kayen and Mitchell, 1999). According to this methodology, for an earthquake of magnitude, M, the total radiated energy E is, E = [10.sup.1.5M + 1.8]

Only a fraction of this energy will be contained in seismic waves reaching the site. Some energy will be dissipated by an elastic attenuation along ray paths, and further attenuation occurs due to geometric spreading. The most simple energy attenuation model for spherically expanding waves is an inverse relationship based on the square of the epicentral distance. Pore pressure increase [DELTA] u, will be determined from the dissipated energy density within the soil. The factors responsible to cause liquefaction can be considered to be earthquake magnitude, M, source to site distance, R, effective overburden stress, [??] and standard penetration values, N.

Richards proposed a concept of triggering acceleration for commencement of liquefaction. The equation proposed indicates that, acceleration required for initial fluidisation is a sole function of the friction angle of the soil. However, authors of this paper have shown that this need not necessarily be true. Triggering acceleration which initiates liquefaction will be a function of the parameters responsible to cause liquefaction as stated above. The purpose of this work is to investigate a method for evaluating the triggering acceleration required for the commencement of liquefaction in fully saturated sands, in terms of these parameters.

METHOD

The model "A" separating the "yes" and "no" zones of liquefaction developed by the authors has been used for estimating triggering acceleration. For this purpose, 57 case histories of liquefaction and no liquefaction were collected from the data of Davis and Berrill (1982).

The following steps are carried out:

1. The relation between Liquefaction Potential ([10.sup.1.5M]/[??]x[r.sup.2]) and corrected SPT blow count ([bar.N]) as obtained in model "A" is given by the equation of the straight line separating the 'yes' and 'no' zones of liquefaction as,

[log.sub.10] [10.sup.1.5M]/[??]x[r.sup.2] = 7.3825 [log.sub.10] [bar.N]-9.6375 (1)

where,

M = earthquake magnitude in Richter scale 

r = epicentral distance (km)

[??] = effective overburden stress (kPa)

[bar.N] = corrected SPT blow count = [C.sub.N] x N

where,

N = raw SPT blow count

[C.sub.N] = overburden correction factor given by Seed et al

[C.sub.N] = 1-1.25 [log.sub.10] {[??] (kPa)/107.6}

2. Rearranging the terms of equation (1) and obtaining the expression for M on left hand side,

1.5 M = 7.3825 [log.sub.10] [bar.N] + 1.5 [log.sub.10] [??] + 2 [log.sub.10] r - 9.6375 (2)

3. The values of M calculated from equation (2) for validated cases from 57 case histories are compared with actual M in the database (Fig. 1).

[FIGURE 1 OMITTED]

4. Similarly, corrected SPT blow count N can be obtained by substituting the values of M calculated from equation (2) and [??] and R from the database as,

7.3825 [log.sub.10] [bar.N] = 1.5 M - 1.5 [log.sub.10] [??] - 2 [log.sub.10] r + 9.6375 (3)

5. From these corrected SPT blow count (.N), the raw SPT blow count (N) values are calculated using the relationship given by Seed et al (1979).

6. The raw SPT blow count (N) values thus calculated are observed to be the same as those in the database (Fig. 2) thus satisfying the equation (1).

[FIGURE 2 OMITTED]

7. A plot of Log ([10.sup.1.5M]/[??]x[r.sup.2]) and Log N (Fig 3) for the 57 case histories not only separates the "yes"and "no"zones of liquefaction but the points on the line indicate triggering acceleration.

[FIGURE 3 OMITTED]

8. Thus the boundary separating the liquefaction and no liquefaction is defined by the equation,

[log.sub.10] [10.sup.1.5M]/[??]x[r.sup.2] = 7.3825 [log.sub.10] [bar.N] - 9.6375 (4)

where,

M = Earthquake magnitude calculated from equation (3)

[??] = Effective overburden stress (kPa)

r = Epicentral distance in km

[bar.N] = Corrected SPT blow count

9. The values of PGA are obtained using the Gutenberg-Richter (1956) peak ground acceleration (PGA) attenuation relation with actual M values as,

log a (g) = log [F.sub.a] - 2.1 + 0.81 M - 0.027 [M.sup.2] (5)

where, [F.sub.a] is given by following relations

log [F.sub.a] = - 1.029 - 1.725 log R; R [less than or equal to] 75 km

= - 3.115 - 0.634 log R; R > 75 km

where, M = Earthquake Magnitude in Richter scale

R = Epicentral distance (Km)

10. Thus, substituting the M calculated from equation (4) which is required for initiation of liquefaction, equation (5) will give the acceleration which will trigger liquefaction. It has been observed that the values of this acceleration are less than the PGA values as expected and for the cases where liquefaction has not occurred, the triggering acceleration value is more than the PGA value thus validating the method developed.

PROOF CHECKING OF THE METHOD

The method developed was checked on totally new data.collected from Niigata-1964, Tokachi-Ken Oki-1968, and Loma-Prieta-1989 earthquakes for the sites where liquefaction has occurred. The data contains earthquake magnitude, M, epicentral distance, r, effective overburden stress, [??], and corrected standard penetration values,[bar.N].

For processing of data, following steps are carried out :

1. The liquefaction potential values (L.P) are obtained using model 'A' with actual M in the database.

2. The corrected SPT blow count values ([bar.N]) are obtained using overburden correction factor given by Seed 1979.

3. Based on the method developed herein, values of M are calculated.

4. The values of PGA are obtained using the Gutenberg-Richter relation with actual M values.

5. Substituting the M calculated in the Gutenberg-Richter PGA attenuation relation, triggering acceleration is obtained which is required for initiation of liquefaction.

Table 1 shows the processed data. From the table it can be seen that for 'yes' liquefaction cases the triggering acceleration value is less than the PGA value, thus proves reliability of the method.

CONCLUSION

In order to assess the possibility of liquefaction hazards, it is necessary to determine triggering acceleration which is a function of earthquake magnitude, M, epicentral distance, r, initial effective overburden stress, [??], and corrected Standard Penetration values, [bar.N]. Authors have developed a method to predict this acceleration which could trigger the liquefaction. Thus to minimize the liquefaction hazard, this acceleration should be obtained for the sites prone to liquefaction, in addition to PGA.

REFERENCES

Davis, R.O. and Berrill, J.B. (1982). "Energy Dissipation and Seismic Liquefaction in Sands", J. Earthquake Engg. and Structural Dynamics, 10, 59-68.

Phatak, D.R. and Pathak, S.R. (1999). "Assessment of Liquefaction Potential During Earthquakes by Arias Intensity : Discussion, J. Geotech. Engg., ASCE, 125(7),626-627.

Phatak, D.R. and Pathak, S.R. (2000). "Seismic Earth Pressure on Retaining Structures", Discussion, J. Geotechnical Engineering, ASCE, 126(12), 1216-1217.

Richard, Rowland Jr., Huang, C. and Fishman, K. L. (1999). "Seismic Earth Pressure on Retaining Structures", J. Geotechnical Engineering, ASCE, 125(9), 771-778.

Seed, H. B.(1979). "Soil Liquefaction and Cyclic Mobility Evaluation for level ground during earthquakes", J. Geotech. Engg., ASCE ,105 (2), 201-255.

Trifunac, M. D. (1995). "Empirical Criteria for Liquefaction in Sands Via Standard Penetration Tests and Seismic Wave Energy", J. Soil Dynamics and Earthquake Engineering, 14(6), 419-426.

Zhang, Liayang (1998). "Assessment of Liquefaction Potential Using Optimum Seeking Method", J. Geotechnical Engineering, ASCE, 124(8), 739-748.

SNEHAL R. PATHAK

Department of Civil Engineering, Govt. College of Engineering Pune, 411005, Maharashtra State, INDIA

DHANANJAY R. PHATAK (Retd.)

Department of Civil Engineering, Govt. College of Engineering Pune, 411005, Maharashtra State, INDIA

Table 1. Earthquake cases with 'Yes' liquefaction

Sr.   Earthquake              Site             M    [a.sub.max]
No.

 1.   Niigata (1964)          kwagashicho     7.5     0.0170
 2.   Niigata (1964)          kwagashicho     7.5     0.0170
 3.   Niigata (1964)          kwagashicho     7.5     0.0170
 4.   Niigata (1964)          kwagashicho     7.5     0.0170
 5.   Tokachiken-Oki (1968)   Hachinoe        7.8     0.0581
 6.   Loma-Prieta (1989)      San Francisco   7.5     0.0690
                               Oka - Bay

Sr.   Earthquake                Trigging       N     Liquefaction
No.                           acceleration
                                model A

 1.   Niigata (1964)             0.0029       7.24       Yes
 2.   Niigata (1964)             0.0059       9.0        Yes
 3.   Niigata (1964)             0.0079       9.3        Yes
 4.   Niigata (1964)             0.0085      10.17       Yes
 5.   Tokachiken-Oki (1968)      0.0058       9.5        Yes
 6.   Loma-Prieta (1989)         0.0059      10.0        Yes