Fuzzy logic based assessment of seismic soil liquefaction potential and its application to foundations of bridge piers

Abstract

Liquefaction is an important damage potential event after earthquakes. Therefore, liquefaction potential of soil should be estimated correctly to decrease these damages. It has been developed a lot of methods for liquefaction estimation based on semi-empirical simplified procedure. In this study, fuzzy logic soil liquefaction potential determination method was first described and then compared with both field observations and other semi-empirical simplified soil liquefaction determination methods. 250 site observations given in the literature were used in both methods. Soil liquefaction potential was predicted successfully using this both methods for the 220 cases out of 250. It was made comparison using these methods for remaining 30 cases. The fuzzy soil liquefaction assessment with certain probabilities provided the authors involved in the design and construction stages to make a flexible decision. Then fuzzy logic liquefaction determination method is applied on the Sirt bridge case in Afyonkarahisar /Turkey. It was decided to construct a sufficient amount of piles under the Sirt bridge foundation for the purpose of decreasing the effects of a possible soil liquefaction occurrence.

Keywords

Earthquake soil liquefaction fuzzy logic bridge foundation

1 Introduction

Estimation of liquefaction potential of soil deposits beneath engineering structures as well as determination of the treatment methods of loose cohesionless soils requires good engineering judgment in seismic regions. There have been many developed soil liquefaction prediction methods since the original semi-empirical simplified procedure developed by Researchers [1 –21]. Some of them are based on field tests; mainly these are preferred in engineering analyses because of their simplicity. However, developed correlations do not always give the same results due to the variety of soil and earthquake characteristics [22, 23] because the impact of parameters having an effect on soil liquefaction is quite variable. Another way for determining soil liquefaction potential is to use either probability or more complex dynamic modeling. Beside those methods, soft computing methods such as artificial intelligence, fuzzy logic, genetic algorithm or a combination have recently been applied to estimate soil liquefaction risk [22 –28].

However, fuzzy logic soil liquefaction risk prediction studies are new to geotechnical engineering and not well known. There are only a few published studies in the literature: Kumar et al. [22] compared computational soil liquefaction using the neuro-fuzzy approach with other conventional methods. Chen et al. [23] combined fuzzy theory with genetic algorithms to evaluate earthquake-induced liquefaction potential. Another attempt to estimate soil liquefaction risk based on fuzzy logic was made using a fuzzy-neural network by Chern et al. [24]. However, this study was not depending on a pure fuzzy prediction method. Instead, it depended on artificial intelligence.

A neuro-fuzzy system to analyze liquefaction-induced lateral spread was also introduced by García and Romo [27]. In their study, García and Romo did not directly evaluate soil liquefaction potential. Instead, they focused on liquefaction-induced lateral spread by the application of both neuro and fuzzy methods.

Rahman and Wang [28] also combined both artificial intelligence and fuzzy method to estimate liquefaction potential of soil deposits. In their study, they considered magnitude and acceleration of earthquakes, total and effective vertical soil stresses, SPT-N, fine percent, mean grain size-(D₅₀) and ground water depth as the parameters affecting soil liquefaction. However, the degree of the effects of soil age, ground slope and mean grain size on soil liquefaction is not actually sentential and not easy to treat in liquefaction studies. It is also very difficult to determine soil types numerically in a fuzzy set. Therefore, instead of dealing soil types numerically, linguistic classifications such as “alluvium, talus, etc.” seem more convenient if considered in fuzzy sets. Furthermore, because undisturbed laboratory tests for cohesionless soils is not easy, it is better to take into account in-situ test results directly instead of dealing with relative density conversion for soil liquefaction risk studies.

Elton and et al. [26] in their fuzzy type soil liquefaction study considered soil type, soil age and soil depth, ground water depth, soil gradation, mean grain size, SPT-(N₁)₆₀ blow count, relative density, and width and thickness of liquefiable soil stratum following parameters as the main factors affecting the soil liquefaction. In their study, they also decided that the liquefaction risk is low if the SPT-N value is between 8 and 11 and very low if it is higher than 11. However, it is well known that soil liquefaction risk can still be high even for SPT values between 11 and 30. In addition, after the result of 3-D distribution plots of the soil and earthquake parameters reported from different soil liquefaction studies [3 , 29–35] for the earthquakes given Table 1. Cavus [30] evaluated that the only way to consider the soil liquefaction risk as low is only possible if SPT-N counts are greater than 25.

Table 1
Earthquakes where soil liquefaction parameters were reported

Country Location Date Magnitude a_max/g

Japan Mino-Owari 1891 7.9 0.20–0.32

Japan Kanto 1923 7.9 0.13–0.23

Japan Tohnankai 1944 8.0 0.16–0.20

Japan Fukui 1948 7.3 0.35–0.40

Japan Niigata 1964 7.5 0.16

Japan Tokachi-Oki 1968 7.9 0.20–0.23

Japan Miyagiken-Oki 1978 6.7 0.10–0.14

Japan Miyagiken-Oki 1974 7.4 0.20–0.28

Japan Chibakenchubu 1980 6.1 0.10

USA San Francisco 1957 5.5 0.19

USA Alasca 1964 8.3 0.16

USA San Fernando 1971 6.6 0.45

USA Loma Priet 1989 7.1

USA Imperial Valley 1979 6.6 0.2–0.60

Pan America Guatemala 1976 7.5 0.14

USA Chaleston site 1886 0.20–0.50

USA Borah peak 1983 7.5 0.30–0.50

USA Luzon site 1990 7.8 0.13–0.15

Country	Location	Date	Magnitude	a_max/g
Japan	Mino-Owari	1891	7.9	0.20–0.32
Japan	Kanto	1923	7.9	0.13–0.23
Japan	Tohnankai	1944	8.0	0.16–0.20
Japan	Fukui	1948	7.3	0.35–0.40
Japan	Niigata	1964	7.5	0.16
Japan	Tokachi-Oki	1968	7.9	0.20–0.23
Japan	Miyagiken-Oki	1978	6.7	0.10–0.14
Japan	Miyagiken-Oki	1974	7.4	0.20–0.28
Japan	Chibakenchubu	1980	6.1	0.10
USA	San Francisco	1957	5.5	0.19
USA	Alasca	1964	8.3	0.16
USA	San Fernando	1971	6.6	0.45
USA	Loma Priet	1989	7.1
USA	Imperial Valley	1979	6.6	0.2–0.60
Pan America	Guatemala	1976	7.5	0.14
USA	Chaleston site	1886		0.20–0.50
USA	Borah peak	1983	7.5	0.30–0.50
USA	Luzon site	1990	7.8	0.13–0.15

The aim of this study, to compare semi-empirical simplified soil liquefaction determination method and fuzzy logic soil liquefaction potential determination method. For this purpose, 250 site observations given in the literature were used in both methods. Soil liquefaction potential was predicted successful in this both methods for the 220 cases out of 250. It was made comparison using these methods for remaining 30 cases. The fuzzy soil liquefaction assessment with certain probabilities provided the authors involved in the design and construction stages to make a flexible decision. Then fuzzy logic liquefaction determination method is applied on the Sirt bridge case in Afyonkarahisar/Turkey.

2 Methodoloji

2.1 Seismic liquefaction assessment methods

2.1.1 The conventional simplified soil liquefaction estimation methods

Simplified soil liquefaction method was first developed by Seed and Idriss [36]. This method is based on the evaluation of standard penetration test blow counts (SPT) with respect to cyclic stress of the soil. Correlation curves were developed as related to cyclic stress ratio (CSR) or cyclic resistance ratio (CRR) and corrected SPT blow counts (SPT, N1, 60). This method had been revised later by Seed and Idriss [37], Seed et al. [11, 12], Youd et al. [17], Idriss and Boulanger [4, 5], Cetin et al. [21]. In addition, soil liquefaction risk evaluation based upon cone penetration test CPT) and small-strain shear wave velocity (Vs) were also developed by Stark and Olson [15], Robertson and Wride [10], Andrus and Stokoe [2, 3].

2.1.2 Fuzzy logic

The notion fuzzy logic, a superset of Boolean logic that was extended to handle uncertainty in data, was conceived by Zadeh in 1965 [38]. Fuzzy logic comprises a simple, rule-based IF X AND Y THEN Z approach to solve a control problem rather than model a system mathematically. The fuzzy logic model is empirically-based, relying on an operator’s experience rather than their technical comprehending of the system. Fuzzy logic usually comprises fuzzification, an application of the rule base to fuzzy data, the inference of fuzzy results and the defuzzification of fuzzy results stages. Fuzzification is a procedure that transforms the observed (real) data to a fuzzy form using the membership function that described the problem characteristics. The rule base describes the relationships among the membership functions, and it forms the resulting membership function. Defuzzification makes the real (model estimation) value from the resulting membership function [38].

2.2 Simplified soil liquefaction methods used in the study

Along with fuzzy logic assessment method, two basic simplified liquefaction assessment procedures were used in this study. One is depending upon the SPT based evaluation of Idriss and Boulanger [4, 5] (Fig. 1). The other is depending on the correlation of CRR and shear waves developed by Andrus and Stokoe [2, 3] (Fig. 2).

Fig.1

SPT Based Liquafection triggering curves [4, 5].

Fig.2

Recomended Liquefaction Assessment Chart Based on V_S1 and CSR for magnitude Earthquakes [2].

2.3 Development of a fuzzy rule-based model for seismic liquefaction

Determination of soil liquefaction potential by the fuzzy logic method was developed using 250 cases for the earthquakes given in Table 1 [30]. Five parameters (maximum earthquake surface acceleration, soil standard penetration blow count, shear wave velocity, groundwater, and soil depth) were taken into consideration for the fuzzy soil liquefaction assessment modeling. The reasons for the consideration of these parameters for the fuzzy sets are summarizedbelow:

the parameters significantly affect soil liquefaction

the parameters are also used in traditional semi-empirical soil liquefaction assessment procedures

the parameters are the most available and reported parameters given in the literature (in excess of at least 250 cases)

the parameters can easily be obtained either theoretically or experimentally from either in-situ or laboratory tests,

the parameters generally give meaningful and clear fuzzy set intervals for fuzzification.

A summary flowchart for evaluating soil liquefaction based on the fuzzy method [30] is given in Fig. 3.

Fig.3

Flowchart for evaluating soil liquefaction based on the fuzzy method [30].

In this fuzzy soil liquefaction modeling, application of the knowledge base form to soil liquefaction prediction was undertaken by considering various combinations of five antecedents (maximum earthquake surface acceleration, soil standard penetration blow count, shear wave velocity, groundwater, and soil depth) along with one consequent rule (see Fig. 3).

In the modeling, each antecedent divided into 2, 3 or 4 subsets such as low, medium, high, etc. (see Fig. 3). Later, considering field outcomes and the results of observations of reported site liquefaction occurrences, three different combinations among the liquefaction parameters (SPT-N blow count, shear wave velocity, soil and groundwater depths and maximum ground surface acceleration) were generated to decide interval boundaries of each subset of each antecedent parameter for fuzzy modeling. So, the fuzzy interval boundaries of the subsets for all five antecedents were constituted such as are given in Fig. 3.

Then, fuzzy inference mechanism, 216 fuzzy rules were also constituted [30]. In all of those rules, various levels of the five fuzzy antecedent parameters for the liquefaction study were combined. Because much space would have to be given over to present all those developed 216 rules in this paper and because not all the rules also were involved in the calculations, only several sample rules of almost 30 that were found applicable or he calculation case are listed inTable 2.

Table 2

Examples of fuzzy if/then rules with subsets of 5 antecedents and 1 consequence used for calculation of soil liquefaction potential

Rule No	SPT (N₁)₆₀ subsets	Shear wave velocity (Vs) subsets	Groundwater depth subsets	Soil depth subsets	Bedrock acceleration subsets	Liquefaction risk
1	Low	Low	Shallow	Low	High	Very High
2	Low	Low	Shallow	Low	Medium	Very High
3	Low	Low	Medium	High	High	Low
4	Low	Low	Deep	Low	High	High
5	Low	Low	Very Deep	Low	High	Low
6	Medium	Low	Shallow	Medium	High	High
7	Medium	Low	Medium	Medium	High	High
8	Medium	High	Shallow	High	Medium	Medium
9	Medium	High	Deep	Low	Low	Very Low
10	High	High	Shallow	Low	Low	Very Low
11	High	High	Very Deep	High	High	Very Low

In Table 2, for instance, rule 7 corresponds to the following combination of antecedents:

“If [SPT-(N₁)₆₀ is Medium or Shear wave velocity is Low] and (Groundwater depth is Medium) and (Soil depth is Medium) and (Bedrock acceleration is High), then (Soil Liquefaction Risk) is High”.

The use of the five antecedents and their levels leading to consequent liquefaction potential is clearly described (see Fig. 3). The Mamdani inference process is used to handle the rules in the fuzzy logic soil liquefaction modeling.

2.3.1 Evaluation the developed fuzzy method

The developed method [30] was tested for 250 reported site observations given in the literature and also by comparing semi-empirical simplified soil liquefaction procedures. Both this fuzzy model and the semi-empirical simplified soil liquefaction procedures successfully predicted soil liquefaction potential as observed in the field for the 220 cases out of 250.

However, the remaining 30 cases (out of 250) were in some sense deviant when compared with outcomes of site observations wherein both conventional past simplified soil liquefaction studies and this fuzzy method could not completely adequately estimate the field liquefaction occurrences after earthquakes (Tables 3 and 4). This is because there are also many other parameters such as soil gradation, fine content, deposit age, and so forth that have some impact on soil liquefaction. However, even for those 30 field cases, the fuzzy logic modeling estimates soil liquefaction potential more number adequate than the conventional simplified methods (see Tables 3 and 4). One of the superiorities of the fuzzy logic soil liquefaction assessment method over the semi-empirical procedures is the quality of giving probabilistic results. Because the conventional simplified semi-empirical soil liquefaction assessment procedures only gives binary results such as either “yes” or “no.” However, contrary to the crisp results of the deterministic simplified assessment methods, the liquefaction risk outcome in this fuzzy soil liquefaction prediction procedure can be expressed with both linguistic and numerical fuzzy subsets of liquefaction outcomes as well as risk percentages of the possibility of liquefaction/non-liquefaction situations.

Table 3
Comparison of outcomes of the fuzzy liquefaction method, andrus and stokoe, idriss and boulanger and field observations for extreme 30 cases out of 250 [30]

Case No SPT (N₁)₆₀ V_s (m/s) Groundwater Depth (m) Soil Depth (m) a_max/g Field Observation (Liquefaction occurred or not occurred) Andrus and Stokoe Idriss and Boulanger This Study (Fuzzy Approach) (Fuzzy Approach)

Probability % Risk

1 15,70 188 1,10 5,20 0,16 Yes Yes Yes 85 Very high

2 14,74 185 2,00 11,10 0,16 Yes Yes Yes 55 Likely

3 19,61 197 0,50 4,50 0,16 No Yes Yes 69 High

4 34,20 218 0,50 5,00 0,16 No No No 36 Low

5 16,58 191 8,40 8,50 0,50 Yes Yes Yes 68 High

6 12,90 180 8,40 13,30 0,50 No Yes Yes 39 Low

7 4,78 150 5,80 9,90 0,50 No No Yes 56 Likely

8 31,06 212 5,80 10,70 0,50 No No No 29 Very low

9 22,42 200 5,80 11,60 0,50 No Yes Yes 40 Low

10 13,38 184 5,80 12,80 0,50 No Yes Yes 39 Low

11 20,64 200 4,30 9,10 0,50 No Yes Yes 51 Likely

12 1,91 125 4,70 10,20 0,50 No Yes Yes 54 Likely

13 5,27 140 4,70 11,10 0,50 No Yes Yes 49 Likely

14 2,87 130 1,50 10,30 0,15 No Yes Yes 58 Likely

15 7,75 160 1,50 3,50 0,15 Yes Yes Yes 84 Very High

16 23,66 200 1,30 3,00 0,40 Yes Yes Yes 52 Likely

17 29,51 210 3,50 4,00 0,40 No Yes Yes 28 Very low

18 18,03 195 1,60 9,50 0,40 Yes Yes Yes 70 High

19 30,35 212 2,80 3,10 0,20 No Yes No 32 Very low

20 15,78 198 1,10 5,50 0,20 Yes Yes Yes 92 Very High

21 21,96 200 3,10 3,30 0,20 No Yes Yes 46 Low

22 30,23 210 0,70 8,20 0,20 Yes Yes Yes 33 Low

23 6,40 150 0,80 5,20 0,10 Yes Yes Yes 24 Very low

24 18,19 195 2,30 6,00 0,20 No Yes Yes 70 High

25 14,23 184 0,40 12,00 0,20 No Yes Yes 57 likely

26 17,37 193 0,40 13,10 0,20 No Yes Yes 46 Low

27 24,35 203 0,80 11,10 0,20 No Yes Yes 33 Low

28 17,19 192 1,80 2,50 0,25 No Yes Yes 85 Very high

29 9,84 170 5,50 7,00 0,24 No Yes Yes 76 High

30 8,74 167 2,10 3,00 0,14 No Yes Yes 85 Very high

Case No	SPT (N₁)₆₀	V_s (m/s)	Groundwater Depth (m)	Soil Depth (m)	a_max/g	Field Observation (Liquefaction occurred or not occurred)	Andrus and Stokoe	Idriss and Boulanger	This Study (Fuzzy Approach) (Fuzzy Approach)
1	15,70	188	1,10	5,20	0,16	Yes	Yes	Yes	85	Very high
2	14,74	185	2,00	11,10	0,16	Yes	Yes	Yes	55	Likely
3	19,61	197	0,50	4,50	0,16	No	Yes	Yes	69	High
4	34,20	218	0,50	5,00	0,16	No	No	No	36	Low
5	16,58	191	8,40	8,50	0,50	Yes	Yes	Yes	68	High
6	12,90	180	8,40	13,30	0,50	No	Yes	Yes	39	Low
7	4,78	150	5,80	9,90	0,50	No	No	Yes	56	Likely
8	31,06	212	5,80	10,70	0,50	No	No	No	29	Very low
9	22,42	200	5,80	11,60	0,50	No	Yes	Yes	40	Low
10	13,38	184	5,80	12,80	0,50	No	Yes	Yes	39	Low
11	20,64	200	4,30	9,10	0,50	No	Yes	Yes	51	Likely
12	1,91	125	4,70	10,20	0,50	No	Yes	Yes	54	Likely
13	5,27	140	4,70	11,10	0,50	No	Yes	Yes	49	Likely
14	2,87	130	1,50	10,30	0,15	No	Yes	Yes	58	Likely
15	7,75	160	1,50	3,50	0,15	Yes	Yes	Yes	84	Very High
16	23,66	200	1,30	3,00	0,40	Yes	Yes	Yes	52	Likely
17	29,51	210	3,50	4,00	0,40	No	Yes	Yes	28	Very low
18	18,03	195	1,60	9,50	0,40	Yes	Yes	Yes	70	High
19	30,35	212	2,80	3,10	0,20	No	Yes	No	32	Very low
20	15,78	198	1,10	5,50	0,20	Yes	Yes	Yes	92	Very High
21	21,96	200	3,10	3,30	0,20	No	Yes	Yes	46	Low
22	30,23	210	0,70	8,20	0,20	Yes	Yes	Yes	33	Low
23	6,40	150	0,80	5,20	0,10	Yes	Yes	Yes	24	Very low
24	18,19	195	2,30	6,00	0,20	No	Yes	Yes	70	High
25	14,23	184	0,40	12,00	0,20	No	Yes	Yes	57	likely
26	17,37	193	0,40	13,10	0,20	No	Yes	Yes	46	Low
27	24,35	203	0,80	11,10	0,20	No	Yes	Yes	33	Low
28	17,19	192	1,80	2,50	0,25	No	Yes	Yes	85	Very high
29	9,84	170	5,50	7,00	0,24	No	Yes	Yes	76	High
30	8,74	167	2,10	3,00	0,14	No	Yes	Yes	85	Very high

Table 4

Comparison of fuzzy logic method with field observations and results of calculations performed using conventional semi-empirical simplified methods

Liquefaction potential of 4 method

Yes

Cases

O: Observation, F: Fuzzy, I: Idriss and Boulanger, A: Andrus and Stokoe.

When Tables 3 and 4 are studied it is seen that almost 60% of the 30 field soil liquefaction observations were predicted successfully by the fuzzy modeling, whereas only 40% cases were estimated successfully by using conventional liquefaction studies.

In this evaluation in Table 4, if the probability of liquefaction is greater than 50%, the risk of liquefaction was considered “yes” or if less than 50% “no". The cases as seen in Table 3 wherein liquefaction was not observed correspond usually with the soils containing over 35% fines. So taking this factor into account would further enhance the prediction capability of the developed fuzzy model. Overall, it could be said that the fuzzy method discriminates liquefaction and non-liquefaction cases better than the rigid binary evaluations of the semi-empirical simplified approaches because it does not involve crisp decisions.

3 Application of fuzzy logic soil liquefaction for the sirt bridge site

Estimation of liquefaction potential of soil deposits beneath bridge foundations and determination of foundation post bearing capacities and proper treatments are very important and require good engineering judgment in seismic zones. In this sense, a flowchart summarizing identification of soil liquefaction potential and foundation capacity evaluation for bridge structures is provided for the engineers who work on the design of bridge structures.

The Sirt Bridge is a 32-m long highway bridge located on Akarcay River in Afyonkarahisar Province, Turkey. Soil liquefaction potential prediction of the Sirt bridge piers is studied by the fuzzy logic method as explained in Section 2. Because the method covers uncertain, complex relationships among earthquake characteristics, soil parameters, and site liquefaction potential. Then the bridge was designed and constructed based on the suggestions and results of this fuzzy soil liquefaction modeling.

Seismic mechanisms and geology of the bridge site are critical owing to earthquake potential (Fig. 4). Two active faults are located near the bridge site. The first, the Mount Sultan fault, is almost 100 km long. It is an active and normal fault pulsed reversely. Afyonkarahisar graben is considered a continuation of this fault. The graben extends 130 km from northwest to southwest.

Fig.4

Seismotectonic map of the Afyon-Aksehir graben and adjacent areas [41].

The second, called Buyuk karabag, is a 40-km long gravity type normal fault of the Neocene age and extends from northeast to southwest. Both faults are almost 25 km from the bridge site. In 2000, an earthquake of moment magnitude 6 struck the region. Two years later, in 2002, a 15-km deep earthquake of magnitude of 6.5 and a maximum bed rock acceleration of 0.113 g struck the region resulting in 43 deaths and 250 injured [39 –41].

At the time of this earthquake, some indications of liquefaction, such as sand boils, were observed in the vicinity of the Sirt bridge site. In addition, the soil conditions under the Sirt bridge foundation are also susceptible to soil liquefaction because of shallow groundwater and deposition of loose silt, sand and organic clay soils.

Bedrock under the bridge is located at more than 100-m depth and is composed mainly from three rock structures: Paleozoic metamorphic, Mesozoic sea, and Volcanic. Beneath the bridge foundation there is Neocene and Quaternary Periods soil stratum more than 100 m thick. This thick alluvium consisting of silty clay, organic clay, sand and gravel is mostly saturated and extends in the plane (approximately 30–40 km) stretching from Mount Sultan to Mount Emirdag.

For each soil depth beneath the bridge foundation, the shear wave velocity and the universal SPT-(N₁)₆₀ value of the alluvium soil were determined after field tests. The soil depth to 30 m is mostly silty sand or clayey sand. All soil and earthquake properties used as inputs of the fuzzy soil liquefaction modeling for each soil stratum are summarized in Table 5.

Table 5

Comparison of outcomes of the fuzzy liquefaction method, andrus and stokoe, idriss and boulanger for the sirt bridge foundation soil

Soil Depth (m)	(N₁,₆₀)	a_max/g	V_s (m/s)	Groundwater Depth, m	Fuzy		Andrus and Stokoe	Idriss and Boulanger
					Probability %	Risk
3.45	9	0.28	215	3.5	72	High	No	Yes
4.95	5	0.28	150	3.5	77	High	Yes	Yes
6.45	11	0.28	230	3.5	62	High	No	Yes
9.45	10	0.28	225	3.5	58	High	No	Yes
10.95	8	0.28	195	3.5	60	High	Yes	Yes
12.45	7	0.28	210	3.5	51	Likely	Yes	Yes
13.95	8	0.28	225	3.5	37	Low	No	Yes
15.45	9	0.28	245	3.5	38	Low	No	Yes
16.95	7	0.28	210	3.5	35	Low	Yes	Yes
18.45	7	0.28	220	3.5	29	Low	No	Yes
19.95	7	0.28	230	3.5	27	Low	No	Yes
21.45	7	0.28	220	3.5	25	Low	No	Yes
22.95	6	0.28	210	3.5	26	Low	No	Yes
24.45	6	0.28	205	3.5	27	Low	Yes	Yes
25.95	7	0.28	235	3.5	25	Low	No	Yes

At the bridge, site peak bedrock acceleration was estimated as 0.15 g for an earthquake magnitude of 6.5 using acceleration attenuation correlations with respect to the fault distance to the site developed from earthquake records in Turkey [42]. Due to the acceleration amplification from the bedrock to the surface of the thick alluvium beneath the bridge foundation, the ground surface acceleration was determined as 0.28 g for a bedrock acceleration of 0.15 g by using the bedrock/soft-soil acceleration relationship developed by Idriss [33].

A soil liquefaction risk prediction of the site was started first by transforming soil and earthquake input parameters into fuzzy subsets (see Fig. 3). Later, Mamdani’s minimum inference algorithm was applied to the constituted rules [28] for each depth, and then the α_cut membership values for linguistic fuzzy outputs of liquefaction potential were obtained. Subsequently, Mamdani’s maximum inference process was applied to combine α_cut of linguistic fuzzy sets for each soil depth. Finally, the center of gravity defuzzification method was applied to estimate the liquefaction risks numerically for each soil depth beneath the bridge foundation. The calculated results of the fuzzy soil liquefaction modeling of the Sirt bridge foundation for different depths are presentedin Table 6 along with outcomes of the calculations based on Seed’s simplified SPT [12] and Andrus & Stokoe’s shear wave velocity liquefaction assessments [2].

Table 6

Soil liquefaction risks of the Sirt Bridge foundation based on this fuzzy logic assessment procedure and also other semi-empirical simplified methods

Results of soil liquefaction analyses of Sirt Bridge Foundation	No	A		A	A			A	A		A	A	A	A		A
								F	F	F	F	F	F	F	F	F
	Likely						F
	Yes	I	I	I	I	I	I	I	I	I	I	I	I	I	I	I
			A			A	A			A					A
		F	F	F	F	F
Depths (m)		3,45	4,95	6,45	9,45	10,95	12,45	13,95	15,45	16,95	18,45	19,95	21,45	22,95	24,45	25,95

F: Fuzzy method, A: Andrus and Stokoe, I: Idriss and Boulanger.

3.1 Discussion and practical implications of the method for the design

The probabilistic expression of the fuzzy logic liquefaction potential determination method given in this study provided for us an advantageous design over the binary liquefaction potential expressions of the conventional semi-empirical simplified procedures. This owed to the fact that we could assign different weights to percent potential in the case of the Sirt Bridge depending on the criticality of the project. For instance, in our case, the traffic load of the bridge was not so heavy and the risk of soil liquefaction was found to be less for depths deeper than 10 meters. Therefore, as opposed to the binary (yes/no type) outcomes of conventional simplified analyses, we could drive the piles deeper than 10 meters, where soil liquefaction is less risky. Notably, the soil liquefaction potential becomes lower for depths deeper than 16.95 m (see Table 6). By contrast, outcomes of the calculations performed using conventional simplified methods gave us results suggesting soil liquefaction would certainly occur even for these deeper zones (between 12.45 and 25.95 m depths) (SeeTable 6).

In conclusion, by taking the fuzzy logic method outcomes into consideration seismic soil liquefaction potential for the Sirt bridge piers was divided into two regions with respect to risks. One region was quite risky until the 10-m depth. The other zone is deeper than 10 m and is much less risky. Thus, frictional piles beneath pier foundations might safely be extended through the 12.45–25.95 m depth. So it was decided to construct a sufficient amount of piles under the Sirt bridge foundation for the purpose of decreasing the effects of a possible soil liquefaction occurrence in the upper 10-m zone on the bridge piers.

The lengths of the cast in-place piles were chosen such that they will provide sufficient pile-side friction strength to carry and transform the bridge loads to the less risky region (10 m– 25 m). Thus, ten cast-in place reinforced concrete piles of 1.00 m diameters were driven into the foundation soil beneath each bridge pier.

4 Conclusion

In this study, it was compared a semi-empirical simplified soil liquefaction method and fuzzy logic type soil liquefaction potential determination method. Then fuzzy logic liquefaction determination method is applied on the Sirt bridge case. Soil liquefaction potential estimation could be treated as a fuzzy process, because soil and earthquake characteristics of each site are variable and have different impacts on soil liquefaction. In addition, as seen in the Sirt bridge case, a fuzzy soil liquefaction potential assessment procedure can aid in better discrimination of liquefaction potential of the soil stratums as opposed to conventional simplified methods, which give only binary (yes/no) results. Moreover, a fuzzy liquefaction method presented results with some probability that allowed us to make more flexible decisions.

In conclusion, the fuzzy soil liquefaction assessment method applied successfully on a real case, the Sirt bridge pier foundations. According to the outcomes of this study, the foundation soils of the bridge piers were strengthened by piles with 25-m lengths driven down to the less liquefiable soil stratum. The construction of the bridge was completed in 2010 and has been giving service successfully for traffic since that time although there has not been a strong earthquake in the region since the time of construction to judge the performance of the pile structures against any liquefaction that might occur.

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