Liquefaction maps in Babol City, Iran through probabilistic and deterministic approaches
- Mehran Naghizadehrokni^{1, 3}Email authorView ORCID ID profile,
- Asskar Janalizadeh Choobbasti^{2} and
- Mohsen Naghizadehrokni^{3}
Received: 15 October 2017
Accepted: 11 December 2017
Published: 4 January 2018
Abstract
Background
During an earthquake, significant damage can result due to instability of the soil in the area affected by internal seismic waves. Liquefaction is known as one of the major causes of ground failure due to the earthquake. Various procedures have been classified for assessing liquefaction phenomenon into two main groups, including the deterministic and probabilistic approaches.
Results
Four deterministic methods and one probabilistic approach, which is a reliability procedure are considered for assessing the liquefaction potential in Babol City. The main purpose of this comprehensive research is to evaluate the liquefaction potential and to determine the validation and accuracy of the reliability approach. For this purpose, 60 boreholes including almost 600 field records in different parts of Babol City are analyzed and liquefaction and non-liquefaction areas are identified. Microzonation maps are provided by result analysis of the deterministic and probabilistic procedures. Finally, a 2D borderline, including (CSR) and (N_{ spt }) is obtained by analyzing all data.
Conclusions
The present study illustrates that the evaluation of liquefaction potential by using reliability approach is accurate and this procedure can be recognized as one of the best methods for assessing liquefaction. The map obtained utilizing a reliability approach and the borderline provided in this study, can be utilized for recognizing liquefaction and non-liquefaction areas based on different safety factor and probabilistic procedures.
Keywords
Background
Loose sand and silt that is saturated with water can behave like a liquid when shaken by an earthquake. (Seed and Idriss 1971). Soil liquefaction describes a phenomenon whereby a saturated or partially saturated soil substantially loses strength and stiffness in response to an applied stress, usually earthquake shaking or other sudden change in stress condition, causing it to behave like a liquid. (Kutanaei and Choobbasti 2015). On the basis of both the field and laboratory types of soil behavior observations, attempts are made to identifying the best methods for evaluating the liquefaction potential of a particular soil. In the literature, several simplified methods can be found, which are useful in assessing the nonlinear liquefaction potential of soil (Zhang and Goh 2016). Various procedures, known as conventional methods, have been developed by utilizing case studies and undisturbed soil samples (Rokni et al. 2017; Youd et al. 2001).
An important aspect of geotechnical engineering is the estimation of liquefaction. There are several approaches for determining of soil liquefaction. The cost of collecting high quality undisturbed samples is considerably high and the laboratory conditions cannot simulate the actual conditions of the field; therefore, methods based on in-situ tests, such as the Standard Penetration Test (SPT), the Cone Penetration Test (CPT) and the Shear-wave Velocity Test (Vs), are applied by geotechnical engineers to estimate the soil liquefaction. Civil engineers usually make use of a factor of safety (FS) to evaluate the safety of a structure (Bolton Seed et al. 1985; Youd et al. 2001).
The safety factor is defined as the strength of a member divided by the load applied to it. It is the requirement of most designed codes that the calculated safety factor of a member should be greater than a specified safety factor, a value at least larger than one, in order to ensure the safety of the designed structure. Since the specified safety factor is largely determined by experience; hence, there is no rational way of determining such a factor. Since the safety factor-based design method does not account for the variability of the member strength or the applied loading, the probability of failing structures cannot be known. Simplified procedures, originally proposed by Seed (Seed and Idriss 1971), which involved the standard penetration test (SPT) (Toshio Iwasaki 1986), are frequently used in evaluating the liquefaction potential of soils. There are several revisions and updates of the procedures because of its original development. The liquefaction of soil is predicted to occur by using a deterministic method if the factor of safety (FS), which is the ratio of the cyclic resistance ratio (CRR) over cyclic stress ratio (CSR), is less than or equal to one. No soil liquefaction is predicted if (FS) >1. In the proposed method, a compilation of methods based on outdoor and laboratory tests are used for liquefaction potential (Rokni et al. 2017; Choobbasti (2015)).
Reliability calculations provide a means of evaluation by combining the effects of uncertainties and provide a logical framework for choosing appropriate factors of safety for the degree of uncertainty and the consequences of failure (Ishihara 1993; Choobbasti (2015)). Thus, a reliability assessment of liquefaction potential seems to be useful in making better engineering decisions. Recently, Hwang (Hwang and Yang 2001) has been conducted an analysis which quantified uncertainties in the (CSR) and (CRR). In this analysis, the uncertainties in the (CSR) and (CRR) are represented in terms of corresponding probability density functions. The probability density function (PDF) of (CSR) is obtained based on a first order second moment (FOSM) (Chameau and Clough 1983) method while the (PDF) of (CRR) is obtained from the first derivative of the (CRR) function, based on a logistic regression analysis of data regarding earthquakes which occurred in the past. However, the (PDF) of (CRR) did not account for the uncertainty in (SPT) resistance. Thus, it is necessary to use a (PDF) of (CRR) which accounts for uncertainties in (SPT) resistance, in order to quantify its effects on liquefaction reliability. Since a variety of approaches provide diverse results geotechnical data in this study are analyzed using 4 deterministic and one probabilistic methods, in order to assess the liquefaction potential in Babol and the results are presented by liquefaction microzonation map and compared. The main purpose of this study is to assess liquefaction potential and provide some guidelines for liquefaction and no-liquefaction areas of Babol City by different methods and finding the best procedure for assessing liquefaction potential. The final aim is providing a 2-D board line based on (CSR) and (N_{ spt }) parameters for recognizing the liquefaction and mon-liquefaction areas.
Study area and geotechnical investigation
The structural of earth, especially the tectonic style, of Iran was highly influenced by the development and history of the Tethyan region. The tectonic events, which occurred around the Iranian Plate margins were related to the rifting processes of Gondwana and the subsequent collision with the Arabian plate from the west-southwest. Fault areas were adjacent the Alborz and Kopeh-Dagh regions to the north, the Makran and Zagros ranges to the west and south, and the east Iran ranges, which border this terrain to the east (Farrokhzad et al. 2012).
Liquefaction is developed in loose sandy soils in saturated condition. Almost all area of Babol city have loose sandy soils and in saturated condition, because of Babolroud River. Hence to confront the effects of liquefaction in Babol, recognition of liquefiable regions is very requisite (Farrokhzad et al. 2012).
Methodology of deterministic approaches
In this study, (σ_{ v }) and (\( {\sigma}_v^{\hbox{'}} \))σv are the totalσv’ and effective vertical stress, respectively, and are calculated at different depths. (A_{max})amax is the peak horizontal ground surface acceleration, which is 0.3 g for Babol, this amount is achieved based on Iranian seismic design code (2800 standard) for Babol City (No 2005), (g) is gravity which is equal to 9.81 and (r_{ d }) is the stress reduction factor obtained for each depth (Idriss and Boulanger 2006; Yaghmaei-Sabegh and Mohammad-Alizadeh 2012).
The values of CSR calculated using Eq. (1) pertain to the equivalent uniform shear stress induced by the earthquake ground motions generated by an earthquake having a moment magnitude M. It has been customary to adjust the values of CSR calculated by Eq. (1) so that the adjusted values of CSR would pertain to the equivalent uniform shear stress induced by the earthquake ground motions generated by an earthquake having a moment magnitude M = 7.5, i.e., CSR_{7.5} (Idriss and Boulanger 2006).
The factor of safety versus liquefaction is obtained for each record. The liquefaction and non-liquefaction regions are divided into an area where liquefaction is predicted to occur (FS < 1) and no liquefaction is predicted to occur (FS > 1) (Cetin et al. 2004).
All SPT records are analyzed using the method based on the Technical Specifications of the Highway Japan to recognize liquefiable and non-liquefiable segments, as well. There are some similarities between this method and the Seed Approach, in terms of assessing liquefaction potential. The safety of a factor must be calculated for both procedures. A combination of outdoor test methods is used to estimate the potential of liquefaction. The first step is to survey the following vital criteria for evaluating liquefaction potential in Babol: water table ≤10 m, depth of layer susceptible to liquefaction ≤20 m, and diameter of gravel soil at (D_{50}) > 2 mm, (D_{50}) < 10 mm, and (D_{10}) < 1 mm (Adalier and Elgamal 2004).
The safety of factor is calculated at different depths and the soil is analyzed to identify the liquefiable and non-liquefiable areas.
In this equation, (N_{65}) is the equivalent N-value, (N) is the N-value of the subsoil, and (\( {\sigma}_v^{\hbox{'}} \)) is the effective overburden pressure of the subsoil (kN/m^{2}) calculated in the approach at different depths. In the following step, the equivalent acceleration is calculated by using Eq. (6).
Correction N-values and predictions should be done when the fraction of fines content is relatively large. When the fines content (grain size is 75 mm or less) is 5% or greater, the equivalent N-value should be corrected before applying in Fig. 2 Corrections of the equivalent N-value are divided into the following three cases.
Case 1: when the plasticity index is less than 10 or cannot be determined, or when the fines content is less than 15%.
- 1)
When N + ∆N falls within the range I, use range I.
- 2)
When N + ∆N fall within the range II, uses range II.
- 3)
When N + ∆N falls within the range III or IV and (N_{65})/0.5is within range I, II or III, use range III.
- 4)
When N + ∆N falls within range III or IV and (N_{65})/0.5 is within range IV, use range IV.
Here, the range III is used for the case 3, even when the equivalent N-value (after correction) with (N_{65})/0.5 is in the range I or II, because the results from the fines content correction are too conservative. The reason that the range IV is not used for the case 3, even when range IV is given by a correction N + ∆N, is that the reliability of the plasticity index in the equation is low when the value is 10 ~ 20. Therefore, judging the subsoil as the range IV “possibility of liquefaction is very low” is considered as risky.
Case 3: when the plasticity index is 20 or greater and the fines content is 15% or higher.
The equivalent N-value (after correction) should be set as N + ∆N. The range should be determined according to the equivalent N-value (after correction) and the equivalent acceleration.
The soil layer is categorized according to a diagram that is divided into four segments (Zhang et al. 2015). Possibility of liquefaction is very high, high, low and very low in sections I, II, III, IV and V, respectively. A total of 50 diagrams are drawn for all bore logs and the liquefaction potential is evaluated based on (A_{ eq }) and (N_{65}) for different records.
All records are then analyzed using the Iwasaki method (Iwasaki et al. 1984). (LPI) has already been suggested in order to evaluate liquefaction potential. It can be said that the severity of liquefaction is proportional to:
The weighting factor, (w (z)), as suggested by Iwasaki et al. 1984 (Toshio Iwasaki et al. 1984), ranges from one at the surface to zero at 20 m (Toshio Iwasaki 1986). (FS) which is safety factor as defined by Iwasaki (Iwasaki et al. 1981) is straight forward from blow counts from the standard penetration tests (SPT) and median grain size when calculating the liquefaction resistance. (FS) is utilized as defined in the Seed-Idriss simplified procedure. The (LPI) index is calculated at different depths between 0 to 20 m and the liquefaction and non-liquefaction areas are identified using the index. Iwasaki (T Iwasaki et al. 1981) concluded that severe liquefaction is likely at sites with (LPI)>15 and that severe liquefaction is unlikely at sites with (LPI)<5. After analyzing all records by this method, it is clear that most areas in Babol can be classified as liquefied sections.
Methodology of reliability probabilistic model
In the aforementioned equation, (P_{L}) represents failure probability, (σ_{ z }) represents the standard deviation, (μ_{ z }) represents the mean value, (β) represents the reliability index and (Φ (β)) represents the cumulative probability (Duncan 2000; Juang et al. 2000).
A computer program is written in MATLAB environment to assess the liquefaction potential based on reliability method for approximately 600 SPT field records in the study area. The seismic information, mean, and coefficient of variation associated with effective parameters are introduced to the program as fixed input parameters to assess liquefaction and parameters relevant to the genetic algorithm (Janalizadechoobbasti et al. 2016).
Operation description and related parameter in GA cycle
Operation | Description | Related Parameters | Parameter description |
---|---|---|---|
Population | GA starts with choice of some individuals (potential answers for the problem) generated using a random generator. The set of chosen values are called population and the first set is referred to as ‘initial population’. Members of the population are chosen to act as parents to produce children for next generation (next set of potential answers). | Npop | The size of the population is the number of the members that constitute the population. It is shown usually by parameter ‘Npop’. The number of initial population is a matter of concern and is usually adopted based on the sensitivity analysis. In this study, it is selected as Npop =50 after sensitivity analysis. |
Generation | In each cycle in GA, when the number of the produced children (new potential answers) is equal to the size of population(Np), then one generation is formed. | MaxGen | Maximum number of generation ‘MaxGen’ is a predefined number which is a criterion that checks the termination process. When MaxGen is reached, the GA process is terminated even if the convergence criterion is not satisfied. |
Crossover | Operates on two chromosomes and swaps some of their genes which creates two new chromosomes representing two new individuals. In GA context, these new individuals may be considered as new potential answers. | Pc | Crossover operation is carried in a probabilistic manner and hence a probability number is assigned to it which is referred to as ‘crossover probability’ or ‘Pc’. Similar to Npop, sensitivity analysis may be carried to select the best value for Pc or it may be adopted based on some other inference. |
Mutation | This operator occasionally changes the produced children (new potential answers) based on probabilistic principles by exchanging some of their genes and preserves the diversity of the population (set of potential answers) by introducing new members and also prevents the local optimums. | Pm | Mutation occurs probabilistically according to a chosen rate which, again, may be adopted based on sensitivity analysis. It implies on the probability for the mutation of a gene usually indexed by binary numbers ‘0’ and ‘1’ in the chromosomes’ string. If the total number of handled genes is assumed to be n, then Pm × n genes are mutated. |
Result and discussion
The typical bore log data in Babol
Row | Depth (m) | γ (Kg/m^{3}) | N _{ spt } | F_{ c }(%) | σ_{ v }(kN/m^{2}) | \( {\upsigma}_v^{\hbox{'}} \)(kN/m^{2}) | F _{s1} | F _{s2} | F _{ sa } | β | P_{ L }(%) |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 19.3 | 6 | 78.3 | 38.6 | 19 | 0.46 | 0.026 | 3 | 0.68 | 26.5 |
2 | 4 | 18.1 | 4 | 78.3 | 72.4 | 33.2 | 0.24 | 0.49 | 3 | −1.4 | 93 |
3 | 6 | 19.4 | 7 | 100 | 116.4 | 57.6 | 0.33 | 0.017 | 1 | −9.4 | 100 |
4 | 8 | 19.8 | 10 | 52.5 | 158.4 | 80 | 0.41 | 0.47 | 3 | −1.02 | 84.6 |
5 | 10 | 18.6 | 12 | 3.1 | 186 | 88 | 0.37 | 0.27 | 4 | −1.34 | 91 |
6 | 12 | 19.3 | 20 | 4.2 | 231.6 | 114 | 0.59 | 0.34 | 3 | −1.2 | 88.5 |
7 | 14 | 19.3 | 20 | 4.2 | 270.2 | 133 | 0.58 | 0.34 | 2 | −0.05 | 52.2 |
8 | 16 | 19.9 | 21 | 100 | 318.4 | 161.6 | 0.79 | 0.92 | 4 | −1.19 | 88.4 |
9 | 18 | 20.3 | 20 | 100 | 365.4 | 189 | 0.76 | 0.97 | 4 | −0.2 | 60.7 |
10 | 20 | 20.6 | 22 | 81.9 | 412 | 216 | 0.86 | 1.03 | 4 | 0.89 | 18 |
11 | 22 | 20.5 | 21 | 100 | 451 | 235.4 | 0.83 | 1.06 | 4 | – | – |
A comparison of the (F_{S1}), (F_{S2}) profiles, similar to those shown in Fig. 5b, are quite useful as they show which layers are likely to liquefy. However, this assessment of the liquefaction potential is essentially deterministic. As a result of the uncertainties involved in the calculation of (CSR) and (CRR), such a deterministic approach is rather inappropriate. The drawing of the (P_{ L }) profile as shown in Fig. 5d, offers an alternative on which engineering decisions may be based.
Liquefaction hazard maps
Liquefaction hazard maps are useful tools for identifying areas with a high likelihood of liquefaction-induced ground deformation. Since the creation of improved gadgets, with the advances in computer technologies, geographic information systems (GIS) are now being used to generate hazard maps. Here, a zone map from Babol city is provided which illustrates the liquefaction and non-liquefaction areas through GIS program. After the collection of all information associated with boreholes, followed by their analysis and determination of the non-liquefaction and liquefaction areas, data are entered in (GIS) and liquefaction and non-liquefaction regions are specified with the help of Kriging Approach which is one of the best methods of interpolation (Journel 1986). In this paper, liquefaction maps are drawn through four deterministic procedures which include: Seed et al., OCDI, Highway Bridge of Japan and Iwasaki procedures, respectively and one probabilistic approach, which is the reliability method.
As it can be seen in the map derived from Highway Method, all sections in the map are recognized as liquefaction and non-liquefaction areas. Almost all southern segments of Babol are identified as non-liquefaction areas by this method. While, center of the city is recognized as liquefaction area and it mean that this section has potential of liquefaction. Concerning the north area, as it can be seen, there are some liquefiable and non-liquefiable areas in the north.
Seed approach gives the same results to Highway method especially in central and northern area in terms of identifying the liquefaction and non-liquefaction segments. It can be concluded that we can achive the same results for assessing liquefaction potential by utilizing both approaches. Whereas, there are some little differences in southern area as there are some liquefiable segments in southern area whereas in previous procedure all southern area of Babol were recognized as liquefaction areas.
In this map which is based on OCDI method it can be argued that some western sections in the center of Babol just has very high potential for liquefaction and the severity of liquefaction has been reduced in other sections. As it can be seen center of the city has high potential for liquefaction and the severity of liquefaction has been reduced during approaching to southern area. Some segments of northern area do not have any potential for liquefaction whereas the above section of northern area, the severity of liquefaction has been increased to low liquefaction potential.
From what is earlier discussed, by comparing maps derived from deterministic and probabilistic approaches, it can be concluded that the map obtained by reliability method has an acceptable accuracy. The reason for this trust in the reliability procedure is that in the analysis of reliability, the potential of indicators, which is one of the best ways to assess the safety against liquefaction is utilized. Furthermore, this index provides more certain in comparison with deterministic methods and includes details of statistical variables and parameters loading resistance, as well while deterministic approaches are based on measurements in location.
Liquefaction limit state
Conclusion
In this study, liquefaction potential is evaluated in Babol city through four deterministic procedures, including Seed, OCDI, Iwasaki and Highway Bridge of Japan methods, respectively and one probabilistic approach, which is the reliability method. Almost 60 boreholes are analyzed in the area of study and liquefied and non-liquefied regions are determined. To better understand the results, analyzed data are presented for microzonation maps. There are almost similar answers in the central and northern areas in all maps derived from deterministic procedures, which can be concluded that central areas of Babol are recognized as liquefaction with high severety; however, considerable discrepancies resulted in the answers in the southern part of Babol and this issue demonstrated the weakness of the deterministic approaches, since similar data are obtained with different results.
After assessing and analyzing all data by reliability method in terms of determining liquefaction and non-liquefaction areas, a borderline in a 2D environment, including (CSR) and (N_{ spt }) is obtained. Liquefaction assessment can be made through this borderline. The initial impression from the microzonation map which is obtained by probabilistic approach is that almost all areas in Babol, except for the northern part of the city are considered as being liquefied with different intensity. Finally, by comparing the maps obtained for the deterministic and probabilistic methods it is concluded that the map obtained from a reliability method had the highest accuracy. From all that have been discussed so far, by comparing the maps obtained by deterministic and probabilistic procedures, it is concluded that the map which is obtained from a reliability approach possessed the highest accuracy.
Probabilistic reliability method is considered as the most logical and practical approach for accounting the different uncertainties, including both the model and measurement uncertainties. Therefore, it is recommended that this new approach can be used in discussions of sub-zones since the evaluation of liquefaction by only using deterministic methods are insufficient and inaccurate. Overall, it can be stated that the map presented in this study can have numerous applications for the expansion and development of the city of Babol and in comparison with similar researches in this area; it is more accurate due to the leveraging reliability procedure.
Declarations
Acknowledgements
We thank Dr. Mobing Afzalirad for some data inputs and comments on the manuscript.
Funding
This work does not have any funding.
Authors’ contributions
All authors contributed to the database construction and analysis; all read and approved the submitted manuscript.
Competing interests
The authors declare that they have no competing interests.
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