Liquefaction Occurrence Risk Analysis Considering Site Effect: Tehran South-East Case Study   Akram Bajelan M.Sc. Student of Mazandaran University, Babol, Iran e-mail: Ak_Bajelan@yahoo.com Asskar Janalizadeh Choobbasti Ph.D., Associate Professor, Mazandaran University, Babol, Iran e-mail: sskar@nit.ac.ir Amir Hamidi Assistant Professor, Tarbiat Moallem (Kharazmi) University, Tehran, Iran e-mail: hamidi@tmu.ac.ir

ABSTRACT

In liquefaction potential studies, Seed "simplified" method is widely used to estimate CSR. The site conditions and earthquake specifications are ignored in this method. So it is necessary to evaluate the earthquake induced stresses using soil response analysis or the new relations developed to calculate the stress reduction coefficient (r_d) must be used.

In this study we investigate Tehran South-East that is prone to liquefaction according to the basic surveys. The shear stresses resulted from earthquake are estimated through soil response analysis, using EERA software. EERA evaluates the soil dynamic response by resolving the differential equation of wave motion in alluvium with horizontal layers through equivalent linear method. Soil strength stress is calculated using SPT results through various methods. With comparison of these two stresses, the liquefaction reliable coefficient in soil different layers is evaluated and high-risk regions of liquefaction are identified.

The results show the regions prone to liquefaction occurrence. In these specified boreholes the liquefaction risk is analyzed and seismic risk curve is estimated for different seismograph, return cycles and epicentral distance. Finally, with eliminating the acceleration between the seismic risk curve and the liquefaction occurrence on surface curve, the probability of increase of any amount of liquefaction is identified. A high probability of liquefaction occurrence on surface is obtained for many cases.

Keywords: Liquefaction, Soil Response Analysis, Equal Linear Method, Risk Analysis, Tehran South-East.

Introduction

Safeguarding against earthquake hazards has two aspects. The first is resistant making the building against destroying effects of dynamic forces, and the second is safeguarding the place against geotechnical events. One of the most effectiveness ways for mitigation of earthquake hazard is identifying the occurrence probability of incidences such as liquefaction. Quantitative assessment of the likelihood of “triggering” or initiation of liquefaction is the necessary first step for most projects involving potential seismically induced liquefaction. There are two general types of approaches available for this: (1) use of laboratory testing of “undisturbed” samples, and (2) use of empirical relationships based on correlation of observed field behavior with various in-situ “index” tests. The use of laboratory testing is complicated by difficulties associated with sample disturbance during sampling and the high cost. The prominent approach in engineering processes is in-situ “index” test.

ASSESSMENT of Liquefaction Resistance

The value of cyclic stress ratio that leads to liquefaction is called cyclic resistance (CRR). In most of countries SPT is the most usual field test for liquefaction resistance assessment. The widely used SPT-based correlation is the “deterministic” relationship proposed by Seed, et al. (1984, 1985). This relationship is based on comparison between SPT N-values, corrected for both effective overburden stress and energy, equipment and procedural factors affecting SPT testing (to N1,60-values) vs. intensity of cyclic loading, expressed as magnitude-weighted equivalent uniform cyclic stress ratio (CSReq). Although widely used in practice, this relationship is dated, and does not make use of an increasing body of field case history data from seismic events that have occurred since 1984. It is particularly lacking in data from cases wherein peak ground shaking levels were high (CSR > 0.25)  an increasingly common design range in regions of high seismicity. This correlation also has no formal probabilistic basis, and so provides no insight regarding either uncertainty or probability of liquefaction.

The other widely used deterministic relationship in liquefaction resistance assessment is of the Iwasaki et al. (1982):

(1)

where N is the standard penetration number according to Japan Standard Code, D₅₀ is the mean diameter of particles (in mm) and FC is the percent of the passed fine particles through sieve No.200.

Efforts at development of similar, but formally probabilistically-based, correlations have been published by a number of researchers, shown in Figure 1, with the deterministic relationship of Seed et al. superimposed (dashed lines) for reference.

In this study the relations proposed by Seed et al. (2003) are used. The new correlations for assessment of liquefaction probability and resistance are:

(2)

where P is the probability of liquefaction in decimals, and F is the standard cumulative normal distribution.

(3)

Where F^-1 is the inverse of standard cumulative normal distribution.

Assessment of Earthquake Loading

The excess pore pressure level required for triggering liquefaction depends on the magnitude and duration of cyclic loading resulted from earthquake. The studies show an essential relation of the excess pore pressure to the cyclic shear stress, so earthquake loading is represented through cyclic shear stresses. There are two ways of predicting the loading: a full analysis of ground response or using the simplified methods.

Figure 1. Comparison of Best Available Probabilistic Correlation for Evaluation of Liquefaction Potential (All Plotted for M_w=7.5, s'_v = 0.65 atm, and Fines Contents

Seed and Idriss (1971) simplified method is the most widely used correlation:

(4)

in the above relationship the site conditions and earthquake specifications are not included. Cetin and Seed (2000, 2003) propose a new, empirical basis for estimation of rd as a function of; (1) depth, (2) earthquake magnitude, (3) intensity of shaking, and (4) site stiffness:

(5)

It is noted, however, that in-situ CSR (and rd) can “jump” or transition irregularly within a specific soil profile, especially near sharp transitions between “soft” and “stiff” strata, and that CSR (and rd) are also a function of the interaction between a site and each specific excitation motion. Accordingly, the best means of estimation of in-situ CSR within any given stratum is to directly calculate CSR by means of appropriate site-specific, and event-specific, seismic site response analyses, when this is feasible.

Here, shear stress resulted from earthquake is calculated through ground response analysis using EERA software, that evaluates the soil dynamic response by solving the differential equation (by equal linear method) of wave motion in the alluviums with horizontal layers.

Evaluation of Liquefaction Effects

In Geotechnical engineering it isn’t important inherently to estimate the liquefaction occurrence, but its hazard and destructive effects on near regions and buildings are concerned. Indeed it is possible for a horizontal layer to be liquefied without any destruction or significant effect on the surface.

Iwasaki (1989) introduced the liquefaction potential index (P_L) as a representative of liquefaction occurrence strength:

(6)

where Z is the depth (in meter)  F(Z) is a function of liquefaction safety factor (F.S) as follows

Equation 4 gives values of P_L from 0 to 100.

Iwasaki evaluated the index for 63 samples of liquefied and 22 samples of unliquefied soil and concluded that P_L>15 represents a very high-risk liquefaction, and P_L>5 indicates a liquefaction with restricted destructive effects.

Case Study

According to the past studies on Tehran, site specifications of Tehran South-East are prone to liquefaction occurrence. So the probability of liquefaction occurrence is evaluated for a district of Tehran South-East considering site effect. IIEES^[1]data resulted from boreholes of 20m depth are used to sub-zonate the Tehran South-East

Seismographs Used

The seismographs used in this study are those whose frequency contents and tectonically regimes are similar to the bedrock actual seismograph. The seismograph, whose predominant period is a portion of 0.5 to 2.0 of bedrock actual predominant period, is the appropriate one. Since the epicentral distance of 50-60 km between Tehran and the main neighbor faults (Mesha, North Tehran, Rey, Kahrizak, 2003) the predominant period of the rock motion for the expected earthquakes in Tehran is taken to be 0.3sec, considering Seed’s attenuation relationship (Seed et al. 1969).

The time steps of selected seismographs are changed for adaptation of the seismograph predominant period with the actual predominant period of bedrock. This new time step is:

(7)

where T₀, t₀ are the predominant period and time step of the selected seismographs, respectively, and T is the actual predominant period of bedrock. Finally respecting the above mentioned factors, 3 seismographs of Loma Prieta, Tabas and Ghazvin (Manjil earthquake) are selected and their maximum acceleration is normalized to 0.35g suggested for Tehran in 2800 code.

Site Seismic Response Analysis in Tehran South East

Equivalent linear dynamical analysis is performed by EERA, which is software capable of finding the soil dynamical response by solving the differential equation of the wave movement in horizontal sedimentary layers by Equivalent-Linear model of soil stress-strain relatioship under cyclic loading.

The peak acceleration and the ground acceleration response spectra are calculated for boreholes. Then each spectrum is normalized to the related peak ground acceleration. Figures 2 to 6 show the normalized response spectra selected from 27 studied boreholes, and Iran standard code 2800 (3rd edition) response spectra. The acceleration response spectrum in each borehole is the average of normalized acceleration response spectra of various movements.

Figure 2. Normalized response spectra in borehole No.1, and Iran standard code 2800 response spectra.

Figure 3. Normalized response spectra in borehole No.2, and Iran standard code 2800 response spectra.

Figure 4. Normalized response spectra in borehole No.3, and Iran standard code 2800 response spectra.

Figure 5. Normalized response spectra in borehole No.4, and Iran standard code 2800 response spectra.

Figure 6. Normalized response spectra in borehole No.5, and Iran standard code 2800 response spectra.

Inserting the soil layers data as EERA[2] software inputs, equal linear dynamical analysis is performed to evaluate the site response in each borehole. The cyclic shear stress is calculated and the mean cyclic shear stress (of different input motions) is estimated in each layer. The Cyclic Resistance Ratio (CRR) is evaluated using Seed and Iwasaki (past) methods, as well as Seed (2003) later method, and the liquefaction safety factor in identified layers is calculated. Finally the liquefaction occurrence potential is evaluated in each borehole. (See Table.1 and Fig.7)

Earthquake Risk

Evaluation and analysis of Iran seismic risk has been performed by many researchers such as Vilson (1930)  Niazi and Basford (1968)  Norouzi (1971, 1972, 1976) , Banisadr (1971)  Berberrian (1973)  Roshandel, Nemat-nasser and Addel, (1978)  Ahmadi and Norouzi (1980)  Ahmadi, Mostaghel and Norouzi (1981, 1989).

Ahmadi, Mostaghel and Norouzi found the distribution of Iran earthquakes and their risks using Poisson’s distribution model.

According to Poisson’s model, occurrence probability of N earthquakes with a magnitude of M (or larger) in a time interval of t, is:

(8)

where N is the annual rate of earthquake occurrence;

(9)

where a and b are regional seismicity constants.

Table 1. Values of Probability of Liquefaction Occurrence on the Surface in Case Region

Borehole Number	PL (Seed)	PL (Iwasaki)	PL (Cetin & Seed)
			P=5%	P=20%	P=35%	P=50%	P=95%
1	3.76	4.18	3.72	2.91	2.40	2.03	0.56
2	0.14	0.18	0.18	0.17	0.16	0.15	0.11
3	2.28	5.06	5.75	2.72	1.70	1.11	0.15
4	1.69	0.99	3.29	1.78	1.46	1.25	0.19
5	0.28	6.08	0	0	0	0	0
6	4.04	0	5.11	3.36	2.75	2.27	0.15
7	0.19	0.05	0.20	0.20	0.19	0.19	0.16
8	2.41	3.17	5.82	4.06	2.97	2.43	0.50
9	3.44	2.87	5.30	2.72	2.81	2.35	1.01
10	0.04	0.64	0	0	0	0	0
11	0	0	0	0	0	0	0
12	2.85	2.49	2.88	2.32	1.97	1.68	0.76
13	2.66	3.24	3.29	2.99	2.80	2.62	1.67
14	0.25	0.03	0.30	0.26	0.24	0.22	0.11
15	1.83	4.59	2.46	1.83	1.43	1.06	0.00
16	0	0	0	0	0	0	0
17	0.19	0.19	0.17	0.16	0.17	0.17	0.13
18	0	0	0	0	0	0	0
19	1.05	1.38	1.32	1.16	1.05	0.95	0.44
20	6.85	1.72	8.58	7.93	7.51	7.12	5.10
21	1.39	6.60	0	0	0	0	0
22	11.26	4.10	9.31	8.82	8.62	8.43	7.43
23	13.80	16.01	11.94	10.77	10.01	9.32	6.15
24	3.31	2.31	4.19	3.43	2.97	2.49	0.75
25	0	0	0	0	0	0	0
26	0	0	0	0	0	0	0
27	12.69	8.65	10.19	9.03	8.28	7.59	5.53

Figure 7. The Case Region Zonation for Acceleration of 0.35g, based on Iwasaki Relationship

Ahmadi and Norouzi work  on seismic constants of Iran regions suggest a=1.894 and b=0.4944 for Alborz.

For evaluating the non-occurrence probability in time t of an earthquake with magnitude of M, set n=0 in equation (8)  so:

(10)

Substituting equation (9) in (10) gives:

(11)

The maximum acceleration in different regions is a function of the earthquake magnitude (M) and its distance to the earthquake center, suggested by Donovan and identified for Iran by Ahmadi et al. (1989):

(12)

Eliminating M in equations (11) and (12) result in:

(13)

Seismic risk probability is evaluated as the occurrence probability of at least one earthquake with an acceleration of a_g (or larger) in return cycle of T and epicenter distance of R:

(14)

Liquefaction Occurrence Risk Analysis

As shown in the Zonation map, the probability of liquefaction occurrence on the surface is high in the boreholes 3, 20, 22, 23, 27 and the risk analysis is required for these regions. For this purpose, the cyclic shear stresses are evaluated for different values of acceleration (0.1g to 0.5g, with intervals of 0.05g) and for 3 seismographs of Loma Prieta, Tabas and Qazvin using EERA software. CRR values are obtained using Seed’s equation (R. B. Seed et al., 2003).

Occurrence on the surface values is evaluated using Iwasaki method. The seismic risk probability is evaluated as the occurrence probability of at least one earthquake with an acceleration of a_g  (or larger) in return cycle of T and epicentral distance of R, using equations (13) and (14).

It is important to evaluate the susceptibility of occurrence on the surface value to different seismic parameters such as return cycle and epicentral distance, and for finding the seismic risk curves. So, in this study the seismic risk analysis is performed for 3 seismographs of Loma Prieta, Tabas and Qazvin for different epicentral distances of 10, 20, 30, 40, and 50 km and return cycles of 10, 50, 100, 200 and 500 years.

Finally, eliminating the acceleration between the curves of the seismic risk and of the liquefaction occurrence on the surface, gives the probability of increase for each value of the liquefaction occurrence.

The calculation results for the borehole No.20 is shown in Figs. (8) to (11) for example.

Figure 8. Occurrence on the surface for different accelerations

Figure 9. Occurrence on the surface of different seismographs,
for epicentral distance of 30 km, and return cycle of 50 years

Figure 10. Occurrence on the surface of different return cycles for epicentral distance of 30 km.

Figure 11. Occurrence on the surface of different epicentral distance for return cycle of 50 years.

Conclusions

• The analysis indicated that the seismic response of a site and its behavior type (linear or nonlinear) is greatly dependent on the subterranean layers and the earthquakes characteristics. At certain period ranges, the spectra of 2800 code differ significantly from the obtained response spectra. This necessitates a perfect geotechnical study for evaluating the site response spectra in important buildings.
• In some boreholes an increased nonlinear behavior is occurred, and the acceleration response spectra is decreased in short periods and increased in long periods, so there is more difference from code 2800 spectra points to a destruction risk of higher buildings. This is resulted from a weak layer (with a penetration number less than 10) in depths of 11 m. t0 15 m. in the boreholes. In addition, peak ground acceleration is less than the bedrock acceleration in these boreholes. There is an attenuation of the acceleration instead of amplification in these regions.
• Equal linear analysis is useful to evaluate the stresses resulted from earthquake for prediction of liquefaction occurrence in a place with simple site conditions. (A simple method with a few input parameters and a good approximation, for the mentioned conditions)
• Probabilistic methods including various factors of uncertainty, both in loading and liquefaction resistance can be used to evaluate the soil resistance.
• In the case region Zonation, there are 5 boreholes of P_L>5 that are not certain about liquefaction occurrence on the surface and require more investigations. These regions are identified as high-risk liquefaction, on Zonation map.
• Increasing the earthquake acceleration results in an increase of the liquefaction occurrence probability.
• Increasing the return cycle results in an increase of the liquefaction occurrence on the surface probability.
• Increasing the epicentral distance results in a decreasing of the liquefaction occurrence on the surface probability.
• In this study, the liquefaction occurrence on the surface is evaluated to be less than 15 for different boreholes, seismographs, return cycles and epicentral distances. Here, there is no certain case of liquefaction occurrence on the surface.

References

1. Seed, R. B., K. O. Cetin, et al. (2003) “Recent Advances in SoilLiquefaction Engineering: A Unified and Consistent Framework,”26th Annual ASCE Los Angeles Geotechnical Spring Seminar.
2. Iwasaki, T. (1982) “Microzonation for Soil Liquefaction Potential Using Simplified Methods,” Proc. 3rd Int. Conf. On Microzonation, Seattle, WA, Vol.3, pp.1319-1330.
3. Bardet, J. P., K. Ichii, C. H. Lin (2000) EERA, A Computer Program for Equivalent-linear Earthquake Site Response Analysis of Layered Soil Deposits, University of Southern California, Department of Civil Engineering.
4. Idriss, I. M., H.B. Seed (1968) “Seismic Response of Horizontal Soil Layers,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol.94, No.  SM4, July, pp.1033-1031.
5. Youd, T. L., I. M. Idriss, Eds. (2001) “Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998NCEER/NSF workshop on evaluation of liquefaction resistance of Soils," J. Geotech. and Geoenvir. Engr. , NSCE, Vol.111, No.10, pp.817-833.
6. Mirhosseini, S. Majdoddin, (2002)  Final Report of Liquefaction Zonation for Tehran South East, International Institute of Earthquake Engineering and Seismology, Tehran.

7. Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard No.2800-05)  3rd Edition, (2005)  Building and Housing Research Center.
8. Ahmadi, G., N.Mostaghel, A. Nowroozi (1989) “Earthquake Risk Analysis of Iran – Probabilistic Seismic Risks for Various Peak Ground Accelerations,” Iranian Journal of Science & Technology, Vol.13, No.2-3.
9. Bajelan, Akram (2006) Risk Analysis of Tehran South East Considering Site Effect, M.Sc. Thesis in Geotechnical Engineering, Mazandaran University, Supervised by Janalizadeh Choob-basti, Asskar, Ph.D.

[1] International Institute of Earthquake Engineering and Seismology

[2] Equivalent-linear Earthquake Response Analysis

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