Evaluation of liquefaction potential of soil deposits using artificial neural networks
The Authors
Adel M. Hanna, Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Canada
Derin Ural, Civil Engineering Department, Istanbul Technical University, Istanbul, Turkey
Gokhan Saygili, Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, Texas, USA
Acknowledgements
The financial support from the National Science and Engineering Research Council of Canada (NSERC) and Concordia University are acknowledged.
Abstract
Purpose – In the literature, several empirical methods can be found to predict the occurrence of nonlinear soil liquefaction in soil layers. These methods are limited to the seismic conditions and the parameters used in developing the model. This paper seeks to present General Regression Neural Network (GRNN) model that addresses the collective knowledge built in simplified procedure.
Design/methodology/approach – The GRNN model incorporates the soil and seismic parameters of the region. It was developed in four phases; identification, collection, implementation, and verification. The data used consisted of 3,895 case records, mostly from the cone penetration test (CPT) results produced from the two major earthquakes that took place in Turkey and Taiwan in 1999. The case records were divided randomly into training, testing and validation datasets. Soil liquefaction decision in terms of seismic demand and seismic capacity is determined by the stress-based method and strain-based method, and further tested with the well-known Chinese criteria.
Findings – The results produced by the proposed GRNN model explore effectively the complex relationship between the soil and seismic input parameters and further forecast the liquefaction potential with an overall success ratio of 94 percent. Liquefaction decisions were further validated by the SPT, confirming the viability of the SPT-to-CPT data conversion, which is the main limitation of most of the simplified methods.
Originality/value – The proposed GRNN model provides a viable tool to geotechnical engineers to predict seismic condition in sites susceptible to liquefaction. The model can be constantly updated when new data are available, which will improve its predictability.
Article Type:
Research paper
Keyword(s):
Phase transformations; Regression analysis; Neural networks; Earthquakes; Soil testing.
Journal:
Engineering Computations: International Journal for Computer-Aided Engineering and Software
Volume:
24
Number:
1
Year:
2007
pp:
5-16
Copyright ©
Emerald Group Publishing Limited
ISSN:
0264-4401
AI artificial intelligence
ANOVA analysis of variance
ANN artificial neural network
a max peak horizontal acceleration at ground surface
a t threshold acceleration
BPNN back propagation neural network
CSR cyclic stress ratio
d w depth of ground water table
f s CPT sleeve friction resistance
GRNN General Regression Neural Network
IBL instance based learning models
Max maximum value
Min minimum value
M v earthquake magnitude
R f CPT friction ratio
S standard deviation
q c CPT cone tip resistance
V s shear wave velocity
z depth of soil specimen
α significance level
(G/G max)t Modulus reduction factor at the threshold strain, γ t
γ τ threshold strain
μ Mean value
σ Smoothing factor, or bandwidth
σ vo Total vertical stress
σ′vo Effective vertical stress
τ av /σ′ vo Cyclic stress ratio
Introduction
When the pore water pressure in a soil layer is significantly increased, the effective shear strength is significantly reduced and further the soil may reach the liquid state or rather liquefied. Soils under the undrained condition and subjected to dynamic loading are more susceptible to liquefaction. In the literature, several empirical methods, based on laboratory or in situ field tests results, can be found to predict the liquefaction potential in soils. Laboratory testing is often affected by the method of sampling and testing, especially for cohesionless soils. Furthermore, due the complexity of the problem, researchers were unable to develop analytical solutions for soil liquefaction. Accordingly, geotechnical engineers relied heavily on field test results and validated empirical correlations.
During the last two decades, artificial intelligence (AI) has been successfully used in several applications in civil engineering because of its heuristic problem-solving capabilities. The artificial neural network (ANN) is one of the AI approaches that can be classified as “machine learning.” It has the ability to simulate the learning capabilities of the human brain by automating the process of knowledge acquisition and data mining. The ANN is a collection of interconnected computational elements called “neurons” that have performance characteristics similar to the biological neurons (Fausett, 1994). This brain-like structure makes ANN models superior to knowledge-based models and mathematical formulae in making predictions that involve intuitive judgment and possess high degrees of nonlinearity.
In the literature, simplified methods based on cone penetration test (CPT) results can be found (Robertson and Wride, 1998; Stark and Olson, 1995; Suzuki et al., 1995; Gilstrap and Youd, 1998; Youd et al., 2001). In addition, CPT test results were used to develop soil liquefaction assessment methods using neural network methodology (Goh, 1996, 2002; Juang et al., 1999, 2000; Barai and Agarwal, 2002). Goh (1996) developed a back propagation neural network (BPNN) to assess liquefaction potential from CPT data. He reported that neural networks were proven to be feasible tools for soil liquefaction assessments, simpler to apply, and yield more reliable results when compared to conventional methods. In this model, Goh had used a relatively small data set, which is considered the main limitation of ANN approaches. Goh (2002) developed probabilistic neural network (PNN) models to analyze the databases based on CPT and shear wave velocity data. In this model, soil particle-size information was introduced as an input data and the liquefaction potential was considered a classification problem.
Juang et al. (1999) developed two BPNN models using model-based data and field results to compare the Olsen and Robertson methods for liquefaction potential evaluations. They reported that the Robertson method was accurate but conservative; furthermore, both methods are fairly accurate in predicting liquefaction resistance of sandy soils. Lai et al. (2004) proposed a discriminate model for soil liquefaction potential evaluation using CPT data collected from Taiwan earthquake region. They compared the results produced with the statistical method and the empirical charts of Robertson and Wride (1998); Olsen (1997). They reported good agreement with Robertson and Wride, and less than satisfactory agreement with Olsen (1997) charts. Juang et al. (2000) trained a neural network model to develop a CPT-based empirical equation. They reported good agreements with most of the existing methods. They described the method as easy to apply and applicable to a wider range of soils. Barai and Agarwal (2002) developed an instance based learning (IBL) model to predict soil liquefaction potential. The IBL model was tested with CPT data sets and was reported to yield better results when compared to existing regression models. These versatile applications make ANN models valuable problem-solving tools in the field of geotechnical engineering, which outperforms the conventional techniques in terms of accuracy and efficiency.
Artificial neural networks (ANN)
ANNs are advanced tools stimulated by the physical and computational characteristics of the human brain. Like biological neurons, they consist of interconnected information processing neural elements (neurons) working in union to make decisions, classifications, and predictions. Neural networks are capable of learning linear and nonlinear functions that make them influential tools in the analysis of complex relations. Interconnections among neurons are established by weights, which are applied to all values passing through one neuron to another. Changing weights improves adaptabilities and prediction capabilities of neural networks.
Neural networks are arranged mainly in three layers namely: input layer; output layer, and the hidden layers. Through the learning process, input and output data of a specific engineering problem are given, and the aforementioned weights among neurons are updated without requiring human development of algorithms. In the validation phase, the trained network makes predictions for a new set of data that has never been introduced during the previous phases. The neural network will provide accurate prediction, as long as large volumes of data covering all possible governing parameters and field conditions are used during the learning process. Extensive information regarding the characteristics of neural network methodology is outlined in detail in the literature (Ghaboussi, 1992; Hammerstrom, 1993; Flood and Kartam, 1994).
The General Regression Neural Networks (GRNNs) were first introduced by Specht (1990, 1991, 1996) as an alternative to feed-forward neural networks. Unlike feed-forward neural networks, GRNN requires neither time-consuming trials nor over-training conditions. Furthermore, GRNN does not require initial setting of learning parameters; instead, a smoothing factor or bandwidth of all the parameters is calculated and accordingly, the training time is relatively short (Wasserman, 1993). The success of the network depends on the smoothing factor that indicates how closely the predictions match the actual values in the training patterns. To the contrary to PNN to categorize data, the GRNN is a universal tool used to produce continuous outputs with only one pass through the training set.
Field data
In 1999, two major earthquakes, namely Chi-Chi, Taiwan earthquake (magnitude M w=7.6) and Kocaeli, Turkey earthquake (magnitude M w=7.4). The ground failure throughout the city of Adapazari (Turkey) and the cities of Wufeng, Nantou and Yuanlin (Taiwan) was attributed to the induced soil liquefaction.
Following the 1999 Kocaeli, Turkey earthquake, a collaborative research program was carried by group of well respected research institutes around the world; namely: University of California at Berkeley, Brigham Young University, University of California at Los Angeles, ZETAS Corporation, Sakarya University, Bogazici University and Middle East Technical University with the support of the US National Science Foundation, California Department of Transportation, California Energy Commission, and Pacific Gas and Electric Company in the region. A total of 135 CPT profiles out of which 19 were seismic CPT and 46 soil borings with multiple SPT (at 0.8 m spacing) were completed in the city of Adapazari. Details of these investigations were made available by the “Pacific Earthquake Engineering Research Center” (PEER, 2002) in the web site: http://peer.berkeley.edu/turkey/adapazari/
For Taiwan earthquake, a series of site investigation programs were undertaken in 2000 by the National Center for Research in Earthquake Engineering (NCREE) in Taiwan and by the authors of this paper (in 2001-2002) with funding from “PEER.” The “PEER” and “NCREE” investigation programs resulted in a total of 92 CPT, out of which 63 were seismic CPT and 98 soil borings with SPT (at 1.0 m spacing). The majority of the tests performed by “NCREE” were in the city of Yuanlin, whereas the tests performed by “PEER” and some of the “NCREE” were in the cities of Nantou and Wufeng. Results of these investigations were made available by Stewart et al. (2001) and “PEER” (2003).
GRNN model
The proposed GRNN model was developed in four phases: identification, collection, implementation, and verification. An iterative procedure was followed to maximize the accuracy of the proposed model.
Identification phase
In this phase, soil and seismic parameters governing soil liquefaction potential were identified, considering the engineering and statistical significance of each parameter.
In the proposed model, 12 soil and seismic parameters are incorporated representing the engineering behavior of the soil layer. These parameters are:
- It is well known that soil responses to stresses increasing with depth; thus the location of the soil layers in question (z) is considered valuable parameter in assessing liquefaction potential.
- In order to establish the pore water pressure on the soil layer in question, the location of the ground water table (d w) is also considered as a viable parameter.
- CPT penetration resistance has been commonly used for characterization of liquefaction resistance. Thus, the CPT test parameters, namely CPT tip resistance (q c), CPT sleeve friction resistance (f s), and CPT friction ratio (R f) are used as an index parameters for liquefaction assessment.
- It is reported that an increase in the overburden pressure increases the susceptibility of soils to cyclic liquefaction (Boulanger, 2003; Seed et al., 2003). Accordingly, total and effective overburden stresses (σ vo and σ′vo) are included in the proposed model as governing parameters.
- Shear wave velocity (V s) represent the capacity of soil against liquefaction; thus it is into the network as an index of liquefaction resistance. The shear wave velocities, were measured from the related seismic cone penetration test and spectral analysis of surface wave test. Laboratory shear wave measurements can be used to supplement the CPT profile where in situ shear wave velocity measurements are not available.
- Earthquake magnitude (M v) and maximum horizontal acceleration at ground surface (a max) characterize the nature of loading, intensity of seismic ground shaking induced by the earthquakes. These values were reported in the soil data of the respective site.
- Conventional liquefaction potential assessment procedures profoundly rely on empirical correlations such as cyclic stress ratio (τ av/σ′vo) for stress-based methodology and threshold acceleration (a t) for strain-based methodology, which are derived from field test results and earthquake characteristics.
Cyclic stress ratio is the normalized measurement of the cyclic load severity and it represents the seismic demand on soil to liquefy (Seed and Idriss, 1971).
Dobry et al. (1982) reported that liquefaction resistance of saturated undrained soil layer can be quantified by threshold shear strain, which is independent from the method of sample preparation, and it is approximately 0.01 percent. By utilizing this value, the acceleration corresponding to the threshold shear strain is evaluated by the strain-based assessment procedure for liquefaction occurrence. The threshold acceleration value together with the strain-based factor of safety states the threshold strain, which is required for liquefaction to occur.
With respect to the statistical significance, the analysis of variance (ANOVA) tests were carried out to determine the association between soil liquefaction potential and the soil and seismic variables. It should be noted herein that the maximum horizontal acceleration at ground surface was already proven to be an influential parameter, and accordingly it was not included into the ANOVA test. Table I presents ANOVA analysis. In this table, the first column lists the parameters that were introduced in GRNN architecture. The subsequent columns present the following statistical characteristics: the minimum value (Min), the maximum value (Max), the mean value (μ), and the standard deviation (S), respectively. The last column presents the P-values of the ANOVA analysis. Small P-values indicate that populations have different means. By using a significance level α=0.05, the probability of committing a “Type-1” error is assumed to be 5 percent. Based on the statistical results given in Table I, it can be concluded that the listed parameters have significant effects on soil liquefaction potential as they all produced values P<0.05.
Collection phase
The data set consisted of 3,895 case records: 1,812 for the Kocaeli earthquake and 2,083 for the Taiwan earthquakes. The data set represents 1,665 cases that liquefied and 2,230 cases that did not liquefy. Table II summarizes the data base used in this analysis. In this table, columns 1-11 list the values measured/collected for the governing parameters described above. Furthermore, the distributions of the peak accelerations recorded by strong motion stations are given in Table III. In this analysis, the closest measurements of all available strong ground motion recorded are taken into account to characterize the region realistically. Column 13 presents the output of the GRNN in terms of the liquefaction resistance of the soil deposits.
It should be reported herein that the continuous soil profile obtained by CPT does not provide the detailed definition of the soil. Furthermore, Seed et al. (2003) concluded that SPT-based correlations are well defined and have provided lesser levels of uncertainty than CPT-based simplified procedure. Accordingly, SPT test results supported by the shear wave velocity measurements will be capable of identifying and predicting liquefaction potential of soils. In this analysis, the liquefaction decision was evaluated by using the three following criteria:
- The stress-based liquefaction triggering analyses for SPT tests by Youd et al. (2001). They developed a relationship between cyclic stress ratio and the corrected standard penetration resistance for sands and silty sands for variable peak ground acceleration and earthquake magnitudes. Cyclic resistance ratios for 7.5 magnitude earthquakes are determined from the results of the corrected SPT corrected N values produced by the SPT. With respect to the magnitude-scaling factor, the equation given by Andrus and Stokoe (1997) was utilized.
- Soils with significant plasticity are evaluated for liquefaction susceptibility by the Chinese criteria proposed by Finn et al. (1994). This criteria stipulate that soils with plastic fines can liquefy if all the four following conditions are met:
- percent finer than 0.005 mm ≤20 percent;
- (liquid limit + 1 percent)≤35 percent;
- (water content + 2 percent) ≥0.9; and
- liquidity index (based on liquid limit + 1 percent and water content + 2 percent)≤0.75 (Rauch, 1997).
- The strain-based procedure (Dobry et al., 1981, 1982), as given in equation (1), the threshold acceleration can be calculated, as follows:
Equation 1 where: V s is the shear wave velocity; γ t is the threshold strain; (G/G max) is the modulus reduction factor at the threshold; and r d is the stress reduction coefficient.
The modulus reduction factor at the threshold, (G/G max)t was assumed to be 0.8 with a strain level of an order of 0.01 percent (Hardin and Drnevich, 1972). Factor of safety in threshold acceleration criteria is given by equation (2) as follows: Equation 2 For values of F a≤1 not necessarily means that liquefaction will occur. However, it implies that there will be massive sliding of the grain-to-grain contact surfaces which is essential for generating the pore water pressure and therefore crucial for liquefaction (Rauch, 1997).
Implementation phase
The neural network software (NeuroShell 2) developed by the Ward Systems Group (1996) in the USA was used for training, testing, and validating the GRNN model. This software is capable of implementing different neural network architectures including BPNN, GRNN, and PNN.
In this phase, the collected data was randomly categorized into three subsets: training, testing and validation. The training set generates the algorithm with the best smoothing parameter. The testing set is used for observing the capabilities of the generated algorithm to assess the intricate relationships amid input and output values. The validation set is used to examine the trained algorithm on a separate data set that was not previously introduced to the network. Therefore, the validation set can be regarded as the true/genuine test for the performance of the model.
In this investigation, 3,895 case records were randomly divided as follows: 2,922 for the development phase, 521 for the testing phase, and the remaining 452 were for validation. The input layer includes 12 neurons; one for each governing parameter. The output layer includes one neuron to predict liquefaction. In this paper, the “City Block Distance Norm” was implemented for the nonlinear regression of the soil liquefaction (Specht, 1990). The liquefaction potential is characterized by the binary number “1” represents the occurrence of liquefaction and “0” represents the non-occurrence of liquefaction.
An iterative procedure was followed to maximize the accuracy of the results produced. This was implemented by allowing the outcome of the training phase to be applied to the testing data in order to obtain the smoothing factor having the smallest error for the network. Furthermore, the statistical and engineering significance analyses revealed the irrelevant parameters and accordingly they were not incorporated in the model.
After several trials, a GRNN model was developed for soil liquefaction potential estimations, having a smoothing factor of σ=0.0332. The error was limited to 0.3 (i.e. 30 percent), which imply that network prediction greater than 0.30 is considered incorrect. In the parameter sensitivity study, most influential parameters impacting liquefaction assessment are outlined and shown in Figure 1.
Validation phase
In this phase, the architecture prediction capabilities of the GRNN model was compared to a set of data that were not used during model training and testing. The validation data was randomly selected from both Kocaeli and Chi-Chi earthquakes, and corresponds to approximately 12 percent of the data set collected. The results of this phase are also given in Table III and summarized in Table IV and presented in graphical form in Figure 2. As shown in Figure 2, the results produced by the proposed GRNN model compare well with the field data.
Conclusion
An AI computational approach “General Regression Neural Network” (GRNN) was developed to predict liquefaction potential in soil deposits. The model utilizes 12 soil and seismic parameters that characterize soil types, material properties, seismic characteristics, magnitude and nature of loads, and stresses and strains, strengths, saturation and seismological aspects of the soil. These parameters are real world parameters that can easily be obtained using widely accepted testing techniques and empirical formulas. The sensitivity of each of these parameters to liquefaction potential in soil was examined. In this investigation, 3,895 case records were used and randomly divided for the development, testing, and validation. These data is considered reliable that were obtained following the two critical earthquakes in Turkey and Taiwan.
In this model, the SPT-based liquefaction potential, is incorporated into CPT-based soil and seismic data. Therefore, the model verifies the feasibility of an SPT-to-CPT data conversion throughout the liquefaction potential analysis, which believed to be the primary limitation of the simplified techniques available in the literature.
Contrary to conventional methods for analysis of liquefaction, this study has integrated input parameters that account for all possible variations in the field. It is believed that this study, which integrates and transfers knowledge collected from the two severe earthquakes will contribute to the ongoing development of soil liquefaction analysis. Furthermore, the proposed model could be constantly upgraded when more field data and case history become available.
Equation 1
Equation 2
Figure 1Parameter sensitivity study
Figure 2Network's performance on soil liquefaction potential
Table IANOVA and parameter statistics
Table IISummary of CPT data-set for GRNN model
Table IIIMaximum horizontal accelerations recorded by strong motion stations
Table IVResults of GRNN Model
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Corresponding author
Adel M. Hanna can be contacted at: hanna@civil.concordia.ca